Free ebooks ==> www.ebook777.com While chemical products are useful in their own right—they address the demands and needs of the masses—they also drain our natural resources and generate unwanted pollution. Green Chemical Engineering: An Introduction to Catalysis, Kinetics, and Chemical Processes encourages minimized use of non-renewable natural resources and fosters maximized pollution prevention. This text stresses the importance of developing processes that are environmentally friendly and incorporate the role of green chemistry and reaction engineering in designing these processes.
Consisting of six chapters organized into two sections, this text:
• Covers the basic principles of chemical kinetics and catalysis
• Gives a brief introduction to classification and the various types of chemical reactors
• Discusses in detail the differential and integral methods of analysis of rate equations for different types of reactions • Presents the development of rate equations for solid catalyzed reactions and enzyme catalyzed biochemical reactions
• Explains methods for estimation of kinetic parameters from batch reactor data
• Details topics on homogeneous reactors
• Includes graphical procedures for the design of multiple reactors
• Contains topics on heterogeneous reactors including catalytic and non-catalytic reactors
• Reviews various models for non-catalytic gas–solid and gas–liquid reactions
• Introduces global rate equations and explicit design equations for a variety of non-catalytic reactors
• Gives an overview of novel green reactors and the application of CFD technique in the modeling of green reactors
• Offers detailed discussions of a number of novel reactors
• Provides a brief introduction to CFD and the application of CFD
• Highlights the development of a green catalytic process and the application of a green catalyst in the treatment of industrial effluent Comprehensive and thorough in its coverage, Green Chemical Engineering: An Introduction to Catalysis, Kinetics, and Chemical Processes explains the basic concepts of green engineering and reactor design fundamentals, and provides key knowledge for students at technical universities and professionals already working in the industry.
• Access online or download to your smartphone, tablet or PC/Mac • Search the full text of this and other titles you own • Make and share notes and highlights • Copy and paste text and figures for use in your own documents • Customize your view by changing font size and layout
WITH VITALSOURCE ® EBOOK
K15526
an informa business
www.crcpress.com
6000 Broken Sound Parkway, NW Suite 300, Boca Raton, FL 33487 711 Third Avenue New York, NY 10017 2 Park Square, Milton Park Abingdon, Oxon OX14 4RN, UK
Green Chemical Engineering
Focused on practical application rather than theory, the book integrates chemical reaction engineering and green chemical engineering, and is divided into two sections. The first half of the book covers the basic principles of chemical reaction engineering and reactor design, while the second half of the book explores topics on green reactors, green catalysis, and green processes. The authors mix in elaborate illustrations along with important developments, practical applications, and recent case studies. They also include numerous exercises, examples, and problems covering the various concepts of reaction engineering addressed in this book, and provide MATLAB® software used for developing computer codes and solving a number of reaction engineering problems.
Suresh Sundaramoorthy
CHEMICAL ENGINEERING
Green Chemical Engineering An Introduction to Catalysis, Kinetics, and Chemical Processes
S. Suresh and S. Sundaramoorthy
ISBN: 978-1-4665-5883-0
90000 9 781466 558830
www.Ebook777.com
Free ebooks ==> www.ebook777.com
Green Chemical Engineering An Introduction to Catalysis, Kinetics, and Chemical Processes
www.Ebook777.com
Free ebooks ==> www.ebook777.com
www.Ebook777.com
Free ebooks ==> www.ebook777.com
Green Chemical Engineering An Introduction to Catalysis, Kinetics, and Chemical Processes
S. Suresh and S. Sundaramoorthy
www.Ebook777.com
Free ebooks ==> www.ebook777.com MATLAB® is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks does not warrant the accuracy of the text or exercises in this book. This book’s use or discussion of MATLAB® software or related products does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular use of the MATLAB® software.
CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2015 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Version Date: 20141029 International Standard Book Number-13: 978-1-4665-5885-4 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com (http:// www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com
www.Ebook777.com
Free ebooks ==> www.ebook777.com
To my beloved parents and my wife S. Arisutha. S. Suresh
To all my teachers and inquisitive students. S. Sundaramoorthy
www.Ebook777.com
Free ebooks ==> www.ebook777.com
www.Ebook777.com
Free ebooks ==> www.ebook777.com
Contents Foreword....................................................................................................................................... xiii Preface..............................................................................................................................................xv Acknowledgements..................................................................................................................... xix Authors.......................................................................................................................................... xxi Nomenclature............................................................................................................................. xxiii 1 Introduction..............................................................................................................................1 1.1 Principles of Green Chemistry and Green Chemical Engineering........................2 1.2 Chemical Reaction Engineering: The Heart of Green Chemical Engineering...................................................................................................4
Section I Kinetics, Catalysis and Chemical Reactors 2 Introduction to Kinetics and Chemical Reactors..............................................................9 2.1 Kinetics of Chemical Reactions....................................................................................9 2.1.1 Reaction Rate.....................................................................................................9 2.1.2 Extent of Conversion...................................................................................... 10 2.1.3 Rate Equation.................................................................................................. 11 2.1.3.1 Activation Energy and Heat of Reaction..................................... 11 2.1.3.2 Limiting Reactant............................................................................ 14 2.1.4 Elementary and Non-Elementary Reactions.............................................. 15 2.1.5 Reversible Reactions....................................................................................... 16 2.1.6 Determination of Rate Equations for Single Reactions from Batch Reactor Data.......................................................................................... 17 2.1.6.1 A Graphical Method for the Estimation of k and n.................... 21 2.1.6.2 Estimation of Kinetic Parameters for the Reaction between Reactants A and B........................................... 23 2.1.7 Integrated Forms of Kinetic Rate Equations for Some Simple Reactions............................................................................................. 24 2.1.7.1 First-Order Reaction....................................................................... 24 2.1.7.2 Second-Order Reaction................................................................... 25 2.1.7.3 Third-Order Reaction..................................................................... 27 2.1.7.4 Second-Order Irreversible Reaction between A and B.............. 28 2.1.7.5 Reversible First-Order Reaction.................................................... 29 2.1.7.6 Zero-Order Reaction.......................................................................30 2.1.8 Multiple Reactions.......................................................................................... 39 2.1.8.1 Series Reaction................................................................................. 39 2.1.8.2 Parallel Reaction..............................................................................43 2.1.9 Autocatalytic Reactions.................................................................................. 45 2.1.10 Non-Elementary Reactions and Stationary State Approximations......... 47 2.1.10.1 Estimation of Kinetic Parameters for Non-Elementary Reactions by Linear Regression.................................................... 48 vii
www.Ebook777.com
Free ebooks ==> www.ebook777.com viii
Contents
2.1.11 Catalysis: Mechanism of Catalytic Reactions—A Brief Introduction..... 52 2.1.11.1 Kinetics of Solid Catalysed Chemical Reactions: Langmuir–Hinshelwood Model................................................... 53 2.1.12 Kinetics of Enzyme-Catalysed Biochemical Reactions............................. 62 2.2 Chemical Reactors: An Introduction......................................................................... 67 2.2.1 Homogeneous Reactors: Holding Vessels................................................... 67 2.2.1.1 Ideal Continuous Stirred Tank Reactor (CSTR).......................... 69 2.2.1.2 Ideal Tubular Reactor...................................................................... 70 2.2.2 Heterogeneous Reactors—Mass Transfer Equipment............................... 73 2.2.2.1 Heterogeneous Catalytic Reactors................................................ 76 Appendix 2A: Catalysis and Chemisorption...................................................................... 79 2A.1 Catalysis: An Introduction............................................................................ 79 2A.1.1 Types of Catalysis............................................................................ 79 2A.1.2 An Overview of the Basic Concepts of Catalysis....................... 82 2A.2 Heterogeneous Catalysis and Chemisorption............................................ 82 2A.2.1 Adsorption Isotherms....................................................................83 2A.3 Catalyst Deactivation and Regeneration..................................................... 86 2A.4 Case Studies: Removal of Pollutants by Adsorption................................. 88 2A.4.1 Adsorptive Removal of Phenol by Activated Palash Leaves................................................................................... 88 2A.4.2 Adsorptive Removal of Various Dyes by Synthesised Zeolite...................................................................... 98 2A.5 Conclusions.................................................................................................... 106 Appendix 2B: Fitting Experimental Data to Linear Equations by Regression............. 106 2B.1 Fitting Experimental Data to Linear Equations by Regression............. 106 2B.2 Fitting Data to a Linear Equation of the Type y = a1x1 + a2x2 + x0........... 108 Excercise Problems............................................................................................................... 111 MATLAB® Programs............................................................................................................ 114 3 Homogeneous Reactors...................................................................................................... 135 3.1 Homogeneous Ideal Reactors................................................................................... 135 3.1.1 Design Equations for Ideal Reactors.......................................................... 135 3.1.1.1 Design Equation for First-Order Irreversible Reaction............ 137 3.1.1.2 Design Equation for Second-Order Irreversible Reaction..................................................................... 137 3.1.1.3 Design Equation for First-Order Reversible Reaction.............. 138 3.1.2 Graphical Procedure for Design of Homogeneous Reactors.................. 143 3.1.3 Multiple Reactors: Reactors Connected in Series..................................... 147 3.1.3.1 System of N Numbers of Ideal CSTRs in Series........................ 147 3.1.3.2 Optimal Sizing of Two CSTRs Connected in Series................. 154 3.1.3.3 CSTR and PFR in Series................................................................ 157 3.1.4 Design of Reactors for Multiple Reactions................................................ 163 3.1.4.1 Design of CSTR for Chain Polymerisation Reaction................ 169 3.1.5 Non-Isothermal Reactors............................................................................. 174 3.1.5.1 Design Equations for Non-Isothermal Reactors....................... 175 3.1.5.2 Optimal Progression of Temperature for Reversible Exothermic Reactions................................................................... 177 3.1.5.3 Design of Non-Isothermal Reactors with and without Heat Exchange Q........................................................................... 183
www.Ebook777.com
Free ebooks ==> www.ebook777.com ix
Contents
3.1.5.4 Non-Isothermal CSTR Operation: Multiple Steady States and Stability........................................................................ 193 3.2 Homogeneous Non-Ideal Reactors.......................................................................... 197 3.2.1 Non-Ideal Reactors versus Ideal Reactors................................................. 197 3.2.2 Non-Ideal Mixing Patterns.......................................................................... 198 3.2.3 Residence Time Distribution: A Tool for Analysis of Fluid Mixing Pattern.................................................................................... 200 3.2.3.1 Tracer Experiment......................................................................... 202 3.2.3.2 Mean θ and Variance σ2 of Residence Time Distribution.......................................................................... 206 3.2.3.3 Residence Time Distribution for Ideal Reactors....................... 206 3.2.3.4 RTD as a Diagnostic Tool............................................................. 210 3.2.4 Tanks in Series Model.................................................................................. 210 3.2.4.1 Estimation of Parameter N........................................................... 215 3.2.4.2 Conversion according to Tanks in Series Model...................... 216 3.2.5 Axial Dispersion Model............................................................................... 219 3.2.5.1 Conversion according to Axial Dispersion Model...................223 3.2.6 Laminar Flow Reactor.................................................................................. 231 3.2.6.1 Conversion in Laminar Flow Reactor........................................ 233 3.2.7 Non-Ideal CSTR with Dead Zone and Bypass......................................... 237 3.2.7.1 Conversion according to Non-Ideal CSTR with Dead Zone and Bypass........................................................................... 239 3.2.8 Micro-Mixing and Segregated Flow.......................................................... 244 3.2.8.1 Micro-Mixing and the Order of Reaction.................................. 248 3.2.8.2 Conversion of a First-Order Reaction in Ideal Reactors with Completely Segregated Flow.............................. 250 3.2.8.3 Micro-Mixing and Ideal PFR....................................................... 252 Appendix 3A: Estimation of Peclet Number—Derivation of Equation Using Method of Moments..................................................................................................254 Exercise Problems................................................................................................................. 258 MATLAB® Programs............................................................................................................ 262 4 Heterogeneous Reactors..................................................................................................... 289 4.1 Heterogeneous Non-Catalytic Reactors...................................................................... 289 4.1.1 Heterogeneous Gas–Solid Reactions......................................................... 289 4.1.1.1 Shrinking Core Model.................................................................. 291 4.1.1.2 Reactors for Gas–Solid Reactions................................................ 299 4.1.2 Heterogeneous Gas–Liquid Reactions....................................................... 317 4.1.2.1 Derivation of Global Rate Equations.......................................... 320 4.1.2.2 Design of Packed Bed Reactors for Gas–Liquid Reactions..... 327 4.2 Heterogeneous Catalytic Reactions and Reactors.................................................334 4.2.1 Reaction in a Single Catalyst Pellet............................................................334 4.2.1.1 Internal Pore Diffusion and Reaction in a Slab-Shaped Catalyst Pellet................................................................................. 337 4.2.1.2 Internal Pore Diffusion and Reaction in a Spherical Catalyst Pellet................................................................................. 341 4.2.1.3 Modified Thiele Modulus Φ′.......................................................346 4.2.1.4 Modification of the Thiele Modulus for a Reversible Reaction..........................................................................................348
www.Ebook777.com
Free ebooks ==> www.ebook777.com x
Contents
4.2.1.5 Diffusion and Reaction in a Single Cylindrical Pore within the Catalyst Pellet............................................................. 350 4.2.1.6 Global Rate Equation.................................................................... 353 4.2.2 Catalytic Reactors.........................................................................................354 4.2.2.1 Two-Phase Catalytic Reactors...................................................... 355 4.2.2.2 Three-Phase Catalytic Reactors................................................... 365 Exercise Problems................................................................................................................. 370 MATLAB® Programs............................................................................................................ 372
Section II Green Chemical Processes and Applications 5 Green Reactor Modelling................................................................................................... 395 5.1 Novel Reactor Technology........................................................................................ 395 5.1.1 Micro-Reactor................................................................................................ 395 5.1.1.1 Characteristics of Micro-Reactors............................................... 396 5.1.2 Microwave Reactor....................................................................................... 399 5.1.3 High-Pressure Reactor.................................................................................400 5.1.4 Spinning Disk Reactor.................................................................................400 5.2 Some Reactor Design Software and Their Applications...................................... 402 5.2.1 gPROMS: For Simulation and Modelling of Reactors............................. 402 5.2.2 ANSYS—Reactor Design............................................................................. 403 5.2.2.1 Computational Fluid Dynamics................................................. 403 5.2.2.2 CFD Modelling of Multiphase Systems..................................... 407 5.3 ASPEN Plus Simulation of RCSTR Model.............................................................. 418 5.3.1 Simulation of CSTR Model.......................................................................... 419 5.3.2 Conclusions.................................................................................................... 427 6 Application of Green Catalysis and Processes.............................................................. 429 6.1 Introduction to Application of Green Catalysis and Processes...........................430 6.2 Case Study 1: Treatment of Industrial Effluents Using Various Green Catalyses...................................................................................................................... 431 6.2.1 Introduction................................................................................................... 432 6.2.1.1 Properties of Zeolites....................................................................434 6.2.1.2 Zeolite Na-Y.................................................................................... 436 6.2.1.3 Applications of Zeolites................................................................440 6.2.2 Adsorption of Dyes onto Zeolite................................................................442 6.2.2.1 Acid Orange 7 Dye........................................................................443 6.2.2.2 Methyl Orange Dye.......................................................................443 6.2.2.3 Methylene Blue..............................................................................443 6.2.2.4 Safranine Dyes...............................................................................444 6.2.3 Catalytic WPO...............................................................................................445 6.2.3.1 Experimental Design....................................................................445 6.2.3.2 Results and Discussions............................................................... 451 6.2.3.3 Conclusions and Recommendations.......................................... 459 6.3 Case Study 2: Thermolysis of Petrochemical Industrial Effluent....................... 466 6.3.1 Source of Wastewater................................................................................... 467 6.3.2 Experimental Procedure.............................................................................. 467 6.3.3 Kinetic Studies.............................................................................................. 468
www.Ebook777.com
Free ebooks ==> www.ebook777.com xi
Contents
6.4
6.3.4 Results and Discussion................................................................................ 470 6.3.5 Conclusions.................................................................................................... 472 Case Study 3: Catalytic Wet-Air Oxidation Processes.......................................... 474 6.4.1 Introduction .................................................................................................. 475 6.4.1.1 Alcohol Production in India........................................................ 476 6.4.1.2 Wastewater Generation and Characteristics............................. 479 6.4.1.3 Wastewater Treatment Methods................................................. 481 6.4.1.4 Drawbacks of Different Technologies........................................ 481 6.4.1.5 Wet Air Oxidation......................................................................... 482 6.4.2 Literature Survey..........................................................................................483 6.4.3 Experimental Setup and Design................................................................. 486 6.4.4 Results and Discussions.............................................................................. 486 6.4.5 Conclusions.................................................................................................... 491
References.................................................................................................................................... 493 Further Reading.......................................................................................................................... 499 Index.............................................................................................................................................. 501
www.Ebook777.com
Free ebooks ==> www.ebook777.com
www.Ebook777.com
Free ebooks ==> www.ebook777.com
Foreword I am delighted to write this foreword for a timely and well-organised book that integrates chemical reaction engineering and green chemical engineering. Recently, clear signs have emerged informing us that we may have hit the carrying capacity of our planet as a result of our incessant endeavour towards economic growth. In this regard, there is an urgent need to educate everyone, particularly young chemical engineers, about environmentally benign processing and sustainability. Having known the authors for a long time, I am not surprised that the book is comprehensive and thorough in its coverage. With precise writing and elaborate illustrations, the book should be very accessible to both graduate and undergraduate students. The authors have also struck a neat balance between analytical and numerical approaches— students will be enriched by the elegance of the analytical derivations and the numerical/ CFD approaches that help them to solve problems not amenable to analytical approaches. Faculty teaching courses on numerical methods and students who are in the process of mastering computational methods for problem solving will also find this book a useful resource. Case studies discussed in Chapter 6 can form the basis for capstone design projects or to introduce mini-projects within courses such as reaction engineering, sustainability and so forth. I wish to congratulate the authors for putting together this informative and educational textbook. This book reflects the long-term student-centric approaches that the authors have adopted during their many years of university teaching as well as the concern they have for our planet. With this pedagogical base and care for the environment, the book is sure to resonate with readers for a long time to come. Lakshminarayanan Samavedham Department of Chemical and Biomolecular Engineering National University of Singapore Singapore
xiii
www.Ebook777.com
Free ebooks ==> www.ebook777.com
www.Ebook777.com
Free ebooks ==> www.ebook777.com
Preface The chemical industry, an important prime mover of economic growth and development of any nation, focuses on producing useful chemical products that are essential for meeting the high quality and standard of living demanded by humankind. Although the contribution of the chemical industry to wealth generation is well recognised, it is generally perceived as a major source of pollution and environmental degradation. Chemical industries transform renewable and non-renewable chemical resources available in nature into useful chemical products and in the process generate unwanted side products that pollute the environment. Waste generated by these activities has slowly but surely impacted the environment and, if left unchecked, has the potential to threaten the very existence of humankind. Economic growth and development will become unsustainable unless the impact of these activities on the environment is reduced or minimised. There is a growing need to devise new technologies and methods of chemical processing that generate little or no pollution and are benign to the environment. Green Chemical Engineering is a novel approach that accounts for environmental impact in the design, development and operation of various chemical engineering processes and helps in making those processes less environmentally impactive. The main goal of green chemical engineering is to achieve sustainability through pollution prevention and minimum utilisation of non-renewable natural resources. Sustainability is essentially about meeting the needs of the present generation without compromising the ability of future generations to meet their own needs. A chemical reactor is the most important component of any chemical processing industry in which key chemical transformations take place. It is the efficiency with which these transformations occur in a chemical reactor that determines the amount of waste generated in the chemical process. Hence, designing a chemical reactor to achieve maximum performance is the key for waste minimisation. Chemical reaction engineering (CRE) provides a scientific basis and methodology for quantifying the performance of a reactor as a function of design and operational variables. Thus, CRE plays a central role in green chemical engineering. Understanding various factors that influence the performance of a chemical reactor would provide a sound basis for designing the reactor to achieve maximum performance. Some key factors which influence reactor performance are feed rate and reactor size, operating temperature and pressure, kinetic rate, transport rate, fluid flow and mixing pattern, adsorption characteristics, pore structure and surface topology of the catalyst. Reactor performance is a result of a complex interplay of all these factors. Incorporating the influence of these factors in the reactor design requires highly sophisticated computational tools such as CFD (computational fluid dynamics), advanced experimental measurement techniques and computer-based molecular simulation tools.
Organisation of the Book In this book, we have made an attempt to integrate the concepts of ‘chemical reaction engineering’ with ‘green chemical engineering’, highlighting the role of ‘chemical reaction engineering’ in the design and development of ‘green processes and green technologies’ xv
www.Ebook777.com
Free ebooks ==> www.ebook777.com xvi
Preface
that are benign to the environment. The book is organised into two main sections. Section I, which includes Chapters 2 through 4, covers the basic principles of chemical reaction engineering and reactor design. Section II, which includes Chapters 5 and 6, covers topics on green reactors, green catalysis and green processes. Chapter 1 presents a brief introduction on green chemical engineering, highlighting the need for developing processes that are environment friendly and the role of green chemistry and reaction engineering in designing such processes. Chapter 2 covers the basic principles of chemical kinetics and catalysis and gives a brief introduction on classification and types of chemical reactors. Differential and integral methods of analysis of rate equations for different types of reactions—irreversible and reversible reactions, autocatalytic reactions, elementary and non-elementary reactions, and series and parallel reactions are discussed in detail. Development of rate equations for solid catalysed reactions and enzyme catalysed biochemical reactions are presented. Methods for estimation of kinetic parameters from batch reactor data are explained with a number of illustrative examples and solved problems. Chapter 3 covers topics on homogeneous reactors including ideal, non-ideal and nonisothermal reactors. Explicit design equations are derived for ideal homogeneous reactors. Graphical procedures for design of multiple reactors are presented. Design of homogeneous reactors for series parallel reactions and polymerisation reactions are discussed. Procedures are developed for optimal design of non-isothermal reactors and adiabatic reactors. Topics on non-ideal reactors highlighting various models for non-ideal mixing patterns are covered in detail. Concepts are explained through a number of illustrative examples and solved problems. Chapter 4 covers topics on heterogeneous reactors including catalytic and non-catalytic reactors. Various models for non-catalytic gas–solid and gas–liquid reactions are presented and global rate equations are derived. Explicit design equations are derived for a variety of non-catalytic reactors—fluidised-bed, moving-bed and packed-bed reactors. Global rate equations are derived for reactions occurring in a catalyst pellet accounting for external and internal mass transfer and surface reaction. Design equations are derived for a number of catalytic reactors—packed-bed, fluidised-bed and slurry reactors. The designs of catalytic and non-catalytic reactors are illustrated through solved examples. Chapter 5 gives an overview of novel green reactors and the application of the CFD technique in modelling of green reactors. This chapter presents detailed discussions on a number of novel reactors, namely, the microreactor, microwave reactor and spinning disc reactor. A brief introduction on CFD and the application of CFD in modelling laminar mixing in a stirred tank reactor is presented. Chapter 6 covers applications and case studies on the development of green catalysts and green processes. Three case studies are presented in this chapter highlighting the development of a green catalytic process and the application of a green catalyst in the treatment of industrial effluent. A number of solved and exercise problems are included in Chapters 2 through 4 for better understanding of various concepts of reaction engineering covered in this book. An important feature of this book is the use of MATLAB® software to develop computer codes for solving a number of reaction engineering problems. The listing of the codes are included at the end of Chapters 2 through 4. The MATLAB codes are also made available in the CD accompanying the book. The reader can make use of these codes for solving a variety of problems illustrated in the book and also for solving more advanced level problems. In our opinion, the concepts of reaction engineering presented in this book will be useful reference material for teaching chemical reaction engineering at the undergraduate
www.Ebook777.com
Free ebooks ==> www.ebook777.com xvii
Preface
and graduate level. Graduate and research students will find the material on green chemical engineering presented in this book useful for understanding the basic concepts of green engineering and for pursuing further research in this area. Thus, this book intends to address both pedagogical and research interests of the readers in the area of green process engineering. Any comments or suggestions on this book may kindly be mailed to sureshpecchem@ gmail.com or
[email protected]. S. Suresh Department of Chemical Engineering Maulana Azad National Institute of Technology Bhopal, Madhya Pradesh, India S. Sundaramoorthy Department of Chemical Engineering Pondicherry Engineering College Puducherry, India MATLAB® and Simulink® are registered trademarks of The MathWorks, Inc. For product information, please contact: The MathWorks, Inc. 3 Apple Hill Drive Natick, MA 01760-2098 USA Tel: 508 647 7000 Fax: 508-647-7001 E-mail:
[email protected] Web: www.mathworks.com
www.Ebook777.com
Free ebooks ==> www.ebook777.com
www.Ebook777.com
Free ebooks ==> www.ebook777.com
Acknowledgements A number of people have contributed directly or indirectly in our endeavour to write this book. Each of us would first wish to acknowledge separately those individuals who helped us achieve this goal. S. Suresh It is a pleasant privilege to acknowledge Professor C.N.R. Rao, director, International Centre for Material Science (India), Professor P.K. Bhattacharya of the Department of Chemical Engineering, Indian Institute of Technology Kanpur (India), Professor I.M. Mishra of the Department of Chemical Engineering, Indian Institute of Technology Roorkee (India), Professor K.K. Appukuttan, director, MANIT Bhopal (India) and Dr. V.C. Srivastava of the Department of Chemical Engineering, Indian Institute of Technology Roorkee (India), for their constant advice and encouragement. A special thanks to Dr. Sachin Kumar Sharma, director of research, Viresco Energy LLC, USA and Dr. Amit Keshav, Department of Chemical Engineering, NIT Raipur (India) for helping me at different times during the preparation of chapters, problems and case studies. Last but not the least, I wish to appreciate the role of my family members, my parents and my wife, S. Arisutha and my daughter Krithi for constant support and endurance during the period of writing this book S. Sundaramoorthy A special thanks to my teachers Professor M.G. Subba Rau and Professor P.N. Singh at Karnataka Regional Engineering College, Surathkal, India (now known as NIT Surathkal), who inspired me through their love and passion for teaching. I am very grateful to my beloved teacher and research supervisor Professor Ch. Durgaprasad Rao at IIT Madras, India for being a great source of inspiration and encouragement all through my research and academic career. My respectful thanks to Professor K. Ethirajulu, former principal of Pondicherry Engineering College (PEC) whose valuable thoughts, words and deeds have profoundly influenced my academic career. My special thanks to Professor D. Govindarajulu, principal, PEC for his support and encouragement in writing this book. Last but not the least, I wish to place on record my gratitude to my wife Hemalatha, and my son Arunsenthil for their constant encouragement, support, love and affection. Both of us would jointly acknowledge the support extended by the following people in writing this book: We profoundly thank Dr. Lakshminarayanan Samavedham, associate professor, National University of Singapore for going through the manuscript and for penning his valuable thoughts in the Foreword. A number of faculty and staff members of MANIT Bhopal (India) and PEC Puducherry (India) have encouraged us in various ways, personal as well as professional and we are grateful to all of them. xix
www.Ebook777.com
Free ebooks ==> www.ebook777.com xx
Acknowledgements
We thank Mr Ravi Kusma Teja, Mr Shakti Nath Das, Mr Shashank Tiwari and all other students of MANIT who have cheerfully typeset pages and pages of handwritten manuscript of this book. It has been a great pleasure working with CRC Press (Taylor & Francis Group) and we look forward to yet another opportunity of working with them again in future.
www.Ebook777.com
Free ebooks ==> www.ebook777.com
Authors S. Suresh is an assistant professor of chemical engineering at Maulana Azad National Institute of Technology, Bhopal, India. He earned a PhD from the Indian Institute of Technology, Roorkee, India, in the area of environmental pollution control. He has held various research positions at a number of universities in India including Pondicherry University, Indian Institute of Technology Kanpur and the International Centre for Materials Science, JNCASR, Bangalore. His research interests are in the areas of separation processes, reactor design, adsorption, catalysis, waste utilisation and nanomaterials. He has written a number of research articles and books in his area of research. In recognition of his research contributions, he has received a number of awards and honours including the Young Scientist Award instituted by the Government of Uttarakhand, India and the Best Environmental Engineer award conferred by the Institution of Engineers (India). S. Sundaramoorthy is a professor of chemical engineering at Pondicherry Engineering College, Puducherry, India. He earned his PhD from the Indian Institute of Technology Madras, India, in the area of process control. He has over 28 years of teaching and research experience. Dr. Sundaramoorthy has held teaching and visiting research positions, respectively, at the National Institute of Technology Karnataka, Surathkal and the National University of Singapore. His research interests are in the areas of model-based predictive control, membrane separations, process integration and optimisation. He has published many research articles and has delivered a number of keynote and invited lectures at international and national conferences.
xxi
www.Ebook777.com
Free ebooks ==> www.ebook777.com
www.Ebook777.com
Free ebooks ==> www.ebook777.com
Nomenclature
Notations a activity of a catalyst a,b,…,r,s stoichiometric coefficients for reacting substances A, B…R, S… a interfacial area per unit volume of tower (m2/m3) A cross-sectional area of a reactor (m2) A,B reactants C concentration (mg/L) CM Monod constant (mol/m3); or Michaelis constant (mol/m3) Cp heat capacity (J/mol K) ’ ’’ mean specific heat of feed, and of completely converted product stream, per mole of key CpA , CpA entering reactant (J/mol A+ all else with it) d diameter (m) d order of deactivation D molecular diffusion coefficient (m2/s) De effective diffusion coefficient in porous structures (m3/m solid.s) ei(x) an exponential integral °C degree Celsius C0 initial concentration of adsorbate in solution Ce equilibrium liquid-phase concentration CL heat capacity of a liquid Cp heat capacity of a gas at constant pressure CS adsorbent concentration in the solution C t equilibrium liquid phase concentration after time t C0 initial concentration of adsorbate in solution C0,i initial concentration of each component in solution Ce unadsorbed concentration of the single-component at equilibrium D dipole moment; diffusivity; distillate flow rate; amount of distillate; desorbent De , Deff effective diffusivity (m2/s) D i impeller diameter Dp effective packing diameter; particle diameter Ds surface diffusivity E(θ) E-curve w. r. t. time F feed rate (mol/s or kg/s) F(θ) F-curve w. r. t. time Ea activation energy [ES] concentration of complex ES [S] concentration of substrate S [E] concentration of free enzyme E H phase distribution coefficient or Henry’s law constant; for gas-phase systems H = p/C (Pa.m3/mol) H A’ , H A’’ Enthalpy of unreacted feed stream, and of completely converted product stream, per mole of A (J/mol A + all else) ΔHr, ΔHf, ΔHc heat or enthalpy change of reaction, of formation, and of combustion (J or J/mol) k reaction rate constant (mol/m3)1−n s−1 kd rate constant for the deactivation of catalyst keff effective thermal conductivity (W/m K) k g mass transfer coefficient of the gas film (mol/m2 Pa s)
xxiii
www.Ebook777.com
Free ebooks ==> www.ebook777.com xxiv
Nomenclature
kl mass transfer coefficient of the liquid film (m3 liquid/m2 surface s) K equilibrium constant of a reaction for the stoichiometry mass flow rate (kg/s) m M mass (kg) n order of reaction N number of equal-size mixed flow reactors in series NA moles of component A PA partial pressure of component A (Pa) pA* partial pressure of A in gas which would be in equilibrium with CA in the liquid; hence, pA* = H ACA (Pa) Q heat duty (J/s = W) qt adsorbed quantity of dye (mg/g) rc radius of unreacted core (m) R radius of particle (m) R ideal gas law constant, = 8.314 J/mol K = 1.987 cal/mol K = 0.08206 lit atm/mol K R recycle ratio s space velocity (s−1) S surface (m2) t time (s) T temperature (K or °C) u* dimensionless velocity v volumetric flow rate (m3/s) V volume (m3) W mass of solids in the reactor (kg) XA fraction of A converted, the conversion X A moles A/moles inert in the liquid XA fractional conversion of A YA moles A/mole inert in the gas F(t) fractional uptake of adsorbate on adsorbent, 0 www.ebook777.com xxvi
Nomenclature
overall mean of response T t time; residence time; average residence time tb time to breakthrough in adsorption tE elution time in chromatography T absolute temperature Tc critical temperature U superficial velocity; overall heat-transfer coefficient; liquid stream molar flow rate Ua superficial vapour velocity u velocity; interstitial velocity; bulk average velocity; flow average velocity uc superficial liquid velocity Ur usage rate us superficial velocity uv gas velocity V vapour; volume; vapour flow rate; overflow rate; volume of the solution Vp pore volume per unit mass of particle w mass fraction; mass of the adsorbent Wi initial weight of the sample Wτ actual weight of the sample Wf final weight of the sample x mole fraction in liquid-phase; mole fraction in any phase; distance; mass fraction in raffinate; mass fraction in underflow; mass fraction of particles X equilibrium moisture XB bound moisture content Xc critical free moisture content XT total moisture content XAe fraction of the adsorbate adsorbed on the adsorbent under equilibrium X i mass of solute per volume of solid y mole fraction in vapour phase; distance; mass fraction in extract; mass fraction in overflow Y mole or mass ratio; mass ratio of soluble material to solvent in overflow; concentration of solute in solvent z mole fraction in any phase; overall mole fraction in combined phases
Greek Letters δ dirac delta function, an ideal pulse occurring at time t = 0 (s−1) µ viscosity of fluid (kg/m s) ρ density or molar density (kg/m3 or mol/m3) σ2 variance of a tracer curve or distribution function (s2) τ time for complete conversion of a reactant particle to product (s); time Φ Thiele modulus γ HATTA number β constant of Redlich–Peterson isotherm λ wavelength η effectiveness factor θ mean residence time θB batch reaction time ρs density of solid particles ρB molal density of reactant εs fractional solids hold up of the bed εd volume fraction of the dense phase ε bed porosity Σ summation symbol Å Angstrom
www.Ebook777.com
Free ebooks ==> www.ebook777.com xxvii
Nomenclature
Abbreviations AAS atomic absorption spectrometry AC activated carbon AFS atomic fluorescence spectrometry ASTM American Society of Testing Material Avg average bar 0.9869 atmosphere or 100 kPa bbl barrel BET Brunauer–Emmett–Teller BFA bagasse fly ash BFB bubbling fluidised bed BJH Barrett–Joyner–Halenda BOD Bio-chemical oxygen demand BR batch reactor Btu British thermal unit C degrees Celsius, K-273.3 CAD computer aided design CAE computer aided engineering cal calorie CEC cation exchange capacity CFB circulating fluidised bed CFD computational fluid dynamics cfs cubic feet per second CI color index cm centimeter cmHg pressure in centimetres head of mercury COD chemical oxygen demand cP centipoise CSTR continuous stirred tank reactor CT computed tomography CWPO catalytic wet peroxide oxidation D-R Dubinin–Radushkevich DOE design of experiments DOF degree of freedom DTA differential thermal analysis DWW distillery wastewater e exponential function E-factor environmental factor ECCP European Climate Change Programme ECD electron capture detector EDAX energy-dispersive atomic x-ray EOF electro osmotic flow eq equivalent exp exponential function F degree Fahrenheit, R 459.7 FA fly ash FF fast fluidised bed FID flame ionisation detector ft feet FTIR fourier transform infra red spectroscopy g gram g-mol gram-mole GAC granular activated carbon GC gas chromatography GC–MS gas chromatography–mass spectrometry GDP gross domestic product
www.Ebook777.com
Free ebooks ==> www.ebook777.com xxviii
Nomenclature
gpd gallons per day GUI graphical user interface h hour HPLC high-performance liquid chromatography HYBRID hybrid fractional error function JCPDS Joint Committee on Powder Diffraction Standards J joule K degrees Kelvin kg kilogram kmol kilogram-mole L litre lb pound lbf pound-force LFR laminar flow reactor LHHW Langmuir–Hinshelwood–Hougan–Watson LHS left-hand side of an equation ln logarithm to the base e log logarithm to the base 10 M-M Michaelis–Menten max maximum meq milliequivalents MFR mixed flow reactor mg milligram min minute; minimum m meter mm milimeter mmHg pressure in mm head of mercury M molar mmol millimole (0.001 mole) mol gram-mole MPSD Marquardt’s percent standard deviation MTBE methyl tert-butyl ether MW molecular weight mw molecular weight (kg/mol) N Newton; normal Nm nanometer P phenol PCM progressive conversion model PC pneumatic conveying Pe Peclet number PFR plug flow reactor PLA poly lactic acid ppm parts per million psi pounds force per square inch psia pounds force per square inch absolute PTFE polytetrafluroethylene R-P Redlich–Peterson RHA rice husk ash RHS right-hand side of an equation Rpm rotation per min RTD residence time distribution SBU secondary building unit SCM shrinking-core model SDR spinning disk reactor SEM scanning electron microscope s second SSE sum of square of error
www.Ebook777.com
Free ebooks ==> www.ebook777.com xxix
Nomenclature
SSE sum of squares of error stm steam STP standard conditions of temperature and pressure (usually 1 atm and either 0°C or 60°F) SZ synthesised zirconia TB turbulent fluidised bed TCD thermal conductivity detector TGA thermogravimetric analysis TG thermal gravimetry USEPA United States Environmental Agency Protection VOC volatile organic compound vs versus WAO wet air oxidation wt Weight XRD x-ray diffraction yr year y year Zr zirconia ZX zeolite µm micrometer
Dimensions and Units Conversion Factors for American Engineering and CGS Units to SI Units
To Convert from
To
Multiply by
Area ft2 in.2
m2 m2
0.0929 6.452 × 10−4
Acceleration ft/h2
m/s2
2.325 × 10−8
Density Lbm/ft2 Lbm/gal (US) g/cm3
kg/m3 kg/m3 kg/m3 = g/L
16.02 119.8 1000
Diffusivity, kinematic viscosity ft2/h m2/s cm2/s m2/s Energy, work, heat ft. lbf Btu (IT) cal (IT) erg kW h
J = N m J = N m J = N m J = N m J = N m
2.581 × 10−5 1 × 10−4 1.356 1055 4.187 1 × 10−7 3.6 × 106 continued
www.Ebook777.com
Free ebooks ==> www.ebook777.com xxx
Nomenclature
To Convert from
To
Multiply by
Enthalpy Btu (IT)/lbm Cal (IT)/g
J/kg = N m/kg J/kg = N m/kg
2326 4187
Force lbf dyne
N N
4.448 1 × 10−5
Heat-transfer coefficient Btu (IT)/h ft2 °F W/m2 K cal (IT)/s cm2 °C W/m2 K
5.679 4.187 × 10−4
Interfacial tension lbf/ft dyne/cm
N/m = kg/s2 N/m = kg/s2
14.59 1 × 10−4
Length ft in.
m m
0.3048 0.0254
Mass lbm ton tonne (metric ton)
kg kg kg
0.4536 907.2 1000
Mass flow rate lbm/h lbm/s
kg/s kg/s
1.26 × 10−4 0.4536
Mass flux, mass velocity lbm/h ft2 Kg/s m2
1.356 × 10−3
Power ft lbf/h ft lbf/s hp btu(IT)/h
W = J/s =N m/s W = J/s =N m/s W = J/s =N m/s W = J/s =N m/s
3.766 × 10−4 1.356 745.7 0.2931
Pressure lbf/ft2 lbf/in2 atm Bar torr = mmHg In. Hg In. H2O
Pa = N/m2 Pa = N/m2 Pa = N/m2 Pa = N/m2 Pa = N/m2 Pa = N/m2 Pa = N/m2
47.88 6895 1.013 × 105 1 × 105 133.3 3386 249.1
Specific heat Btu(IT)/lbm °F cal/g °C
J/kg K = N m/kg K J/kg K = N m/kg K
4187 4187
Surface tension lbf/ft dyne/cm erg/cm2
N/m N/m N/m
14.59 0.001 0.001 continued
www.Ebook777.com
Free ebooks ==> www.ebook777.com xxxi
Nomenclature
To Convert from
To
Multiply by
Thermal Conductivity Btu (IT) Ft/h ft2 °F W/m K = J/s m K cal (IT) cm/s cm2 °C W/m K = J/s m K
1.731 418.7
Velocity ft/h ft/s
m/s m/s
8.467 × 10−4 0.3048
Viscosity lbm/ft s lbm/ft h cP
kg/m s kg/m s kg/m s
1.488 4.134 × 10−4 0.001
Volume ft3 l gal (US)
m3 m3 m3
0.02832 1 × 10−3 3.785 × 10−3
Physical Constants Universal (Ideal) Gas Law Constant, R 1987 cal/mol K or Btu/lbmol °F 8315 J/kmol K or Pa m3/kmol K 8.315 kPa m3/kmol K 0.08325 bar L/mol K 82.06 atm cm3/mol K 0.7302 atm ft3/lbmol °R 10.73 psia ft3/lbmol °R 1544 ft lbf/lbmol R 62.36 mmHg L/mol K 21.9 in. Hg ft3/lbmol °R Atmospheric Pressure (Sea Level) 101.3 kPa = 101300 Pa = 1.013 bar 760 torr = 29.92 in. Hg 1 atm = 14.696 psia Avogadro’s Number 6.022 × 1023 molecules/mol Boltzmann Constant 1.381 × 10−23 J/K molecules
www.Ebook777.com
Free ebooks ==> www.ebook777.com xxxii
Nomenclature
Faraday’s Constant 96,490 charge/g-equivalent Gravitational Acceleration (Sea Level) 9.807 m/s2 = 32.174 ft/s2 Joule’s Constant (Mechanical Equivalent of Heat) 4.184 J/cal 778.2 ft lbf/Btu Planck’s Constant 6.626 × 10−34 J s/molecule Speed of Light in Vacuum 2.998 × 108 m/s Stefan–Boltzmann Constant 5.671 × 10−8 W/m2 K4 0.1712 × 10−8 Btu/h ft2 °R4
www.Ebook777.com
Free ebooks ==> www.ebook777.com
1 Introduction Chemical engineering deals with the transformation of chemicals from one form (raw materials which are renewable and non-renewable resources) to another form (products), which is useful to man for meeting the requirements of comfortable living. This process of accomplishing the transformation from raw material form to product form invariably leads to the generation of some unwanted side products (pollutants) and depletion of renewable and non-renewable resources. The demand for useful chemical products (such as cement, sugar, pulp and paper, pharmaceuticals, petroleum and petrochemicals, etc.) is ever growing with a rising population and affluent living standards driven by economic growth. By 2025, the production capacity of chemicals in Asia alone, which is the most populous region on the earth, is expected to increase by five to six times its capacity in 2000. This will result in faster consumption of natural resources such as fossil fuel and fresh water and steeper rise in the levels of pollution in the environment. The long-term and short-term impact of this on the environment, if left unchecked, has the potential to threaten the very existence of life on earth. Environment factor or E-factor is defined as the mass of waste generated per unit mass of a product created and, hence, is a measure of impact on the environment caused by a chemical industry. The E-factor values for different categories of chemical industries are listed in Table 1.1. Contrary to common belief, chemical industries producing high valueadded chemical products such as pharmaceuticals and fine chemicals contribute more to environmental degradation than refining and bulk chemical industries. Economic growth and development at the expense of environmental degradation is unsustainable in the long run. The need and the necessity for striking a suitable balance between economic development and environmental degradation have given birth to the concept of sustainable development. In 1987, the United Nations World Commission on Environment and Development defined sustainable development as meeting the needs of the present without compromising the ability of future generations to meet their own needs. Bakshi and Fiksel have defined a sustainable process or product as one in which resource consumption and waste generation are kept at acceptable levels while making a positive contribution to societal needs, and generating long-term profit to the business enterprise. Thus, sustainable development involves complex interaction between industry, society and the ecosystem. Although chemical industries contribute to 12–15% of the gross domestic product (GDP) of any developing nation, they are generally perceived by society as a major source of pollution and a major cause for environmental degradation. So, there is a greater expectation on the chemical engineering community to play a responsible role in protecting the environment by way of developing and adapting newer technologies and newer methods of production that are friendlier to the environment. Any technology that is environment friendly is known as ‘Green Technology’. Green technologies are sustainable technologies of higher material and energy efficiencies that use renewable resources and prevent or minimise pollution at the source rather than treating it at the end of the pipe. One may consider the total pollution generated in producing a chemical as a 1
www.Ebook777.com
Free ebooks ==> www.ebook777.com 2
Green Chemical Engineering
Table 1.1 E-Factor Values for Different Categories of Chemical Industries Categories of Chemical Industries Oil refinery Bulk chemicals Fine chemicals Pharmaceuticals
Production Capacity (Tonnes/Year)
E-Factor (Waste/Product Ratio by Weight)
106–108 104–106 102–104 101–103
0.1 1–5 5–50 25–100
product of total global population, consumption per capita and the inefficiency of the process. It is not possible to regulate or reduce the population growth or consumption per capita as any attempt to curb these factors through governmental regulations would lead to social and political unrest and economic instability. So, the only viable option for reduction or minimisation of pollution is to develop newer technologies and processes that are more efficient in terms of material and energy utilisation and minimisation of waste generated.
1.1 Principles of Green Chemistry and Green Chemical Engineering Paul Anastas and John Warner in their book published in 1998 introduced the concept of green chemistry as a philosophy for the design of chemical products and processes that reduce or eliminate the use and generation of hazardous substances. The founders of green chemistry formulated 12 basic principles, the application of which in the practice of chemical engineering is expected to lead to the development of ecofriendly products and processes. The 12 basic principles of green chemistry are discussed below: 1. Prevent waste: Design the process such that waste is prevented at the outset rather than treating or cleaning up waste after it has been generated. 2. Maximise atom economy: Synthesise or design methods that maximise incorporation of all material used in the process into the final product so that the generation of waste is minimised. Select an alternative synthesis route or raw material such that the amount of side reactions generating undesired by-products is minimal. Atom economy, which is defined as Atom economy =
Molecular weight of desired product Sum of molecular weight of all the products produced
is taken as a measure of how efficiently the raw material is used. Raw material yielding maximum atom efficiency is selected. For example, maleic anhydride can be produced using either benzene or n-butane as raw material and the corresponding reactions are
2C6H6 + 9 O2 → 2C 4H 2O 3 + H 2O + 4CO 2 (from benzene)
www.Ebook777.com
Free ebooks ==> www.ebook777.com 3
Introduction
C 4H10 + 3.5O 2 → C 4H 2O 2 + 4H 2O (from n-butane)
Atom economy for the n-butane route is 57.6% and 44.4% for the benzene route. Thus, n-butane is preferred over benzene as a raw material for production of maleic anhydride. Choosing an atom efficient raw material is the first step in designing an environment-friendly chemical process. 3. Design less hazardous chemical synthesis: Synthesise or design methods that use and generate substances that minimise toxicity to the environment. 4. Design safer chemicals and products: Design chemical products with least toxic contamination to the environment. 5. Use safer solvents and auxiliaries: Reduce the use of solvents that cause pollution. If necessary, use solvents that are benign to the environment. In this context, supercritical CO2 (scCO2) and ionic liquids show remarkable potential as ecofriendly substitutes for solvents that are toxic to the environment. 6. Design for energy efficiency: Design processes for higher energy efficiency so that net consumption of energy (fuel) is minimised and the impact of energy usage on the environment is reduced. The processes that operate at ambient temperature and pressure consume less energy and are preferred over high-temperature and high-pressure systems. The possibility of reducing energy and material consumption through appropriate processes and heat integration should be explored. Novel combo systems that integrate reactors with mass exchangers offer plenty of opportunities for the design of energy-efficient chemical processes. 7. Use renewable feed stocks: Choose a raw material or a feed stock that is renewable rather than depleting, wherever possible. The alternate route for synthesis of chemicals using biomass as feed stock is an option to be explored. For example, biochemical synthesis of adipic acid using d-glucose as a feed stock is an ecofriendly alternative to the traditional chemical synthesis of adipic acid using benzene as feed stock. 8. Reduce or avoid the use of chemical derivatives: The use of chemical derivatives should be avoided or minimised as this can lead to the need for additional reagents and further generation of waste. 9. Use catalysis in place of stoichiometric reagents: Catalyst-based synthesis of chemicals results in lower pollution generation compared to synthesis routes that make use of stoichiometric reagents. Thus, a catalyst plays a crucial role in the design of environmentally benign chemical processes. A significant improvement in waste reduction can be achieved through proper selection and design of solid catalysts. 10. Design chemicals to degrade after use: Chemical products should be so designed that at the end of their function, they break down into innocuous products and do not persist in the environment. For example, biopolymers such as poly lactic acid (PLA) and polyhydroxyalkanoates (PHA), used as substitutes for chemical plastics, exhibit excellent biodegradability, unlike plastics. 11. Analyse in real time for pollution prevention: Develop analytical methods that allow for real-time monitoring and control prior to the formation of hazardous substance. 12. Minimise potential for accident through safer chemistry: Substances used in chemical processes should be chosen to minimise the potential for chemical accidents including releases, explosions and fire.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 4
Green Chemical Engineering
1.2 Chemical Reaction Engineering: The Heart of Green Chemical Engineering Any chemical plant can be perceived as a system of units arranged in a particular sequence of material processing steps required to transform raw material to a final product. All processing units in a chemical industry can be broadly grouped into three sections: raw material pretreatment section, reactor section and separation or purification section. Of these three sections, the reactor section in which key chemical transformations take place is the heart of chemical processing and any improvement in the performance of the reactor section is likely to have a major impact on pollution prevention. Thus, chemical reaction engineering plays a central role in green chemical processing. Although the principles of green chemistry provide a road map to the development of green processes, it is the selection, design and operation of the reactor that determines whether a process would be successful or not. In most chemical processes, the choice of the reactor and its operation has a very strong influence on the number and type of separation units required on the upstream and downstream sides and hence has a profound impact on the environment. Chemical reaction engineering provides the methodology for quantifying the reactor performance as a function of design and operational variables. Reactor performance, which is measured in terms of fractional conversion of reactants and product selectivity, is influenced by a number of factors such as feed rate, reactor size, temperature, kinetic rate, transport rate, mixing and flow patterns. Appropriate quantification (or modelling) of reactor performance requires a multi-scale approach involving system characterisation in a wide range of scales, from molecular to macro (reactor length in metres). So, pollution prevention through proper choice and operation of the reactor requires the related issues to be addressed in all these scales. At the molecular level, understanding process chemistry helps to achieve maximum atom efficiency, understanding complex reaction mechanisms leads to the development of appropriate kinetic rate expressions used in reactor design and understanding the mechanism of catalytic reactions leads to the design of a catalyst for achieving maximum selectivity. At a meso scale, understanding fluid mixing and transport in eddies, transport in multiphase systems, transport within pores of a catalyst pellet and the effect of local transport on reaction rate is crucial for the design of reactors that achieve optimum performance. At a macro scale, understanding the effect of hydrodynamics on reactor performance is crucial for scale up and operation of reactors. Thus, a multiscale reactor modelling approach, which integrates the system description at all these three scales (molecular, meso and macro), is needed for the design of reactors to achieve optimum performance. Multiscale reactor modelling and design approach requires highly sophisticated and advanced computational tools and experimental techniques. A proper quantification of reactor performance requires an appropriate description of how the reacting species are brought into contact by fluid mixing. In a multiphase reactor, one should be able to describe the flow and mixing patterns in each one of the phases. In the traditional approach to reactor design, either plug flow or completely mixed flow is usually assumed in each one of the phases. If this assumption does not match with the experimental observation, an axial dispersion model is assumed and the model parameter (Peclet number) tuned to match the experimental measurements. However, this traditional approach lacks the predictability required for design, scale-up and operation of novel and non-traditional reactors having complex fluid mixing patterns. A better description of the flow, mixing and phase
www.Ebook777.com
Free ebooks ==> www.ebook777.com 5
Introduction
contacting pattern is required to develop more realistic reactor models. In this context, sophisticated computational fluid dynamics (CFD)-based models can capture and describe the complexities of fluid mixing more realistically. Thus, CFD is an important computational tool useful for the design of novel reactors. However, sophisticated experimental measurement techniques are necessary to get information on fluid velocity and turbulence to validate the CFD-based models. The selection and design of a catalyst play a crucial role in achieving high reactor performance and making the process environmentally benign. On selecting a catalyst that is appropriate for a particular application, the catalyst can be tailor made for optimum yield and selectivity. Advanced experimental and computer simulation techniques are used to study the surface topology, adsorption characteristics, pore structure and transport properties that are useful for the design of a catalyst having requisite characteristics. A novel catalyst design combined with advanced reactor design technology can make any process economically viable and environmentally beneficial. This book is written with a view of highlighting the importance and significance of chemical reaction engineering in green chemical processing. The book is organized into two sections. Section I includes Chapters 2 through 4 covering the concepts of reaction engineering, chemical kinetics, catalysis and chemical reactors. Section II, which includes Chapters 5 and 6, highlights the modelling of green reactors and the applications of green catalysis and processes.
www.Ebook777.com
Free ebooks ==> www.ebook777.com
www.Ebook777.com
Free ebooks ==> www.ebook777.com
Section I
Kinetics, Catalysis and Chemical Reactors
www.Ebook777.com
Free ebooks ==> www.ebook777.com
www.Ebook777.com
Free ebooks ==> www.ebook777.com
2 Introduction to Kinetics and Chemical Reactors Design and operation of chemical reactors in a chemical industry profoundly influence the impact that the industry may have on the surrounding environment. Understanding different types of reactions and characterising their kinetic behaviour are important for optimal design and operation of chemical reactors. This chapter outlines the basic principles of chemical kinetics, methods of obtaining rate equations for different types of reactions, principles of catalysis and kinetics of catalytic reactions. A brief introduction on the types and classification of reactors is presented in this chapter.
2.1 Kinetics of Chemical Reactions A chemical reaction is a process in which chemical compounds in one form (reactants) are transformed into another form (products). This transformation occurs at a speed that is influenced by a number of factors such as temperature, pressure and so on. Chemical kinetics deals with developing mathematical expressions for the speed or rate of chemical reactions. Studies on chemical kinetics provide data and information about the speed of reactions that are required for the engineering design of reactors. A review of some essential principles of chemical kinetics is presented in this chapter. 2.1.1 Reaction Rate Reaction rate is a measure of the speed of a chemical reaction. Consider an irreversible homogeneous reaction
aA + bB → cC + dD
taking place in a vessel (batch reactor) of fixed volume V. Assume that a uniform condition is maintained in the reaction vessel by proper stirring of the fluid. Let nA, nB, nC and nD be the number of moles of A, B, C and D, respectively, in the reaction vessel at some particular time t. Let dnA, dnB, dnC and dnD be the change due to reaction in the number of moles of A, B, C and D, respectively, after a time lapse dt. The rate of reaction or specific reaction rate is defined as a change in the number of moles of a reactant or product per unit time per unit volume. Thus, 1 dnA ⋅ V dt 1 dnB rB = rate of conversion of B per unit volume = ⋅ V dt
rA = rate of conversion of A per unit volume =
9
www.Ebook777.com
Free ebooks ==> www.ebook777.com 10
Green Chemical Engineering
1 dnC ⋅ V dt 1 dnD rD = rate of conversion of D per unit volume = ⋅ V dt rC = rate of conversion of C per unit volume =
Rates of reactions of chemical species participating in the reaction are related to each other through the stoichiometric coefficients of the reaction as r=
(−rA ) (−rB ) (rC ) (rD ) = = = a b c d
(2.1)
where r is called the specific reaction rate of the reaction in general (and not any particular chemical species) and its dimension is (kmol/m3) (s). For a constant-volume liquid-phase reaction, the rate can be expressed in terms of concentration of A, CA = nA/V as dC rA = A dt
(2.2)
Note that rA is negative for reactants and (−rA) is positive. 2.1.2 Extent of Conversion The extent of conversion is a measure of fractional conversion of reactants achieved in a specified time. Let nA0 and nB0 be the initial number of moles of A and B, respectively, present in the reaction vessel of volume V. Let nA and nB be the number of moles of A and B, respectively, present in the vessel after some time t. The extent of conversion or fractional conversion of A is defined as the number moles of A converted in a specified time per moles of A present at the time of start-up. Thus, x A = Fractional conversion of A =
nA 0 − nA n = 1− A nA 0 nA 0
xB = Fractional conversion of B =
nB0 − nB n = 1− B nB0 nB0
Similarly,
In terms of concentrations of A and B, we can write
xA = 1 −
CA CA0
and xB = 1 −
CB CB 0
(2.3)
where CA0 and CB0 are initial concentrations of A and B. Substituting CA = CA0(1 − X A) in Equation 2.2, we can write the rate equation rA in terms of conversion X A as
dX A (− rA ) = C A 0 dt
www.Ebook777.com
(2.4)
Free ebooks ==> www.ebook777.com Introduction to Kinetics and Chemical Reactors
11
2.1.3 Rate Equation According to the law of mass action, which is based on experimental observations, it is found that the reaction rate, rA, can be expressed as −rA = kCAnCBm
(2.5)
where k: specific reaction rate constant (kmol)/(m3) (s) (kmol/m3)m+n n: order of reaction with respect to A m: order of reaction with respect to B Equation 2.5 is called the rate equation. n and m are called partial orders of the reaction with respect to A and B, and (n+m) is called the global order of the reaction. Studies on chemical kinetics of the reaction are aimed at developing an appropriate rate equation for the reaction. This is done by conducting the given reaction in a controlled manner in a batch or flow reactor, and observing the progress of the reaction over time through appropriate measurements of concentrations of chemical compounds participating in the reaction. The validity of law of mass action has been explained using collision theory. According to collision theory, reaction between compounds A and B is caused primarily by a collision between molecules of A and B. The higher the concentrations of A and B, the higher the chances of collision between molecules of A and B. Thus, the rate of reaction increases with increase in concentrations of A and B (CA and CB). The higher the temperature of the reaction medium, the higher the internal energy of the molecules and the greater the intensity of collisions between the molecules. Thus, the rate of reaction increases with an increase in temperature. The influence of temperature on the rate of reaction is explained by the Arrhenius law, which defines the relationship between the reaction rate constant k and the temperature as k = k0 e − ∆E/RT
(2.6)
where k0: frequency factor ΔE: activation energy of the reaction R: gas law constant T: temperature in K Thus, the rate equation is a product of a temperature-dependent term and a concentration-dependent term. 2.1.3.1 Activation Energy and Heat of Reaction Every reaction is associated with some change in the energy levels of chemical species participating in the reaction. This energy transformation is shown in the energy level diagram (Figure 2.1). Reactants at some energy state ER kJ/kmol (Point R in the diagram) pass through a highenergy activated state E* kJ/kmol (Point A) before finally getting transformed into products that are at an energy state Ep kJ/kmol (Point P). The energy required to raise the reactants to an activated state is called activation energy ΔE:
∆E = (E* − ER ) kJ/kmol (2.7)
www.Ebook777.com
Free ebooks ==> www.ebook777.com 12
Green Chemical Engineering
A
Activation energy
E* (activated state)
∆E P
Energy
EP (product)
∆HR R
Heat of reaction
ER (reactant)
Reaction coordinates Figure 2.1 Energy diagram for endothermic reaction.
Activation energy ΔE is also referred to as an energy barrier, as reactants have to necessarily cross this barrier before getting converted into products. The larger the value of ΔE (energy barrier), the slower the rate of reaction. It is the intrinsic mechanism of a chemical reaction that determines the magnitude of activation energy. For some reactions, the activation energy may be so high that the reaction may be rendered infeasible. The net change in energy (or enthalpy) associated with the chemical reaction is called the heat of reaction ∆H R , defined as (2.8)
∆H R = (EP − ER ) kJ/kmol
Endothermic reactions are reactions in which the specific enthalpy of the products Ep is greater than the specific enthalpy of the reactants ER (Ep > ER), and the heat of reaction ΔHR is positive. Endothermic reactions take away heat from the reaction medium and hence require a continuous supply of heat. On the contrary, exothermic reactions are reactions in which Ep www.ebook777.com 13
Introduction to Kinetics and Chemical Reactors
E* (activated state)
A
Activation energy
∆E
R Energy
∆HR
ER (reactant) P EP (product)
Heat of reaction
Reaction coordinates Figure 2.2 Energy diagram for exothermic reaction.
According to the Arrhenius law, k = k0 e − ∆E/RT
which can also be written in the linear equation form as
ln k = ln k0 −
∆E RT
Thus, a plot of ln k versus 1/T is a straight line with slope m = −ΔE/RT and intercept I = ln k0. 1 −1 (K ) T
3.3 × 10−3
3.1 × 10−3
2.92 × 10−3
2.75 × 10−3
ln k
−2.65
−1.67
−0.673
−0.009
From the plot of ln k versus 1/T shown in Figure P2.1: Slope m = −4904.7 and intercept I = 13.55.
The activation energy = −R ⋅ m = 8.314 × 4904.7 = 40,778 kJ/kmol K
and k0 = eI = 7,64,756 kJ/kmol. Note: Refer MATLAB program: cal_active_energy.m
www.Ebook777.com
Free ebooks ==> www.ebook777.com 14
Green Chemical Engineering
0.5 0
ln k
–0.5 –1 –1.5 –2 –2.5 –3 2.60
Slope = –4904.7 Intercept = 13.55
2.80
3.00
3.20
3.40
(1/T × 10–3), K–1 Figure P2.1 Plot of ln k versus 1/T for estimation of activation energy.
2.1.3.2 Limiting Reactant Consider the chemical reaction between compounds A and B, aA + bB → cC, and let the rate equation be
(− rA ) = kCAnCBm
(2.9)
Both reactants A and B will get completely converted into products if the reactants A and B are present in the exact stoichiometric mole ratio. ∗ CB0 is the minimum initial concentration of B required for the complete conversion of A.
CB∗ 0 =
b CA0 a
(2.10)
where CA0 is the initial concentration of A. Assume that reactant B is made available very much in excess of the minimum quantity required, that is, CB0 CB∗ 0 . Then reactant A, but not reactant B, will get completely converted into product. Even after complete conversion of A, a large amount of B will remain unconverted in the reaction vessel. As reactant B is present in excess, change in concentration of B is negligible compared to the initial concentration of B, CB0 and hence CB can be treated as a constant for all practical purposes, that is, CB = CB0. The rate Equation 2.9 gets reduced to
− rA = k ′C An
(2.11)
where k ′ = kCBm . Reactant A is called the limiting reactant and it is the concentration of A, CA, that controls the rate of reaction. Consider a second-order reaction between A and B with the rate equation expressed as
− rA = kCACB
www.Ebook777.com
(2.12)
Free ebooks ==> www.ebook777.com 15
Introduction to Kinetics and Chemical Reactors
If reactant B is used in excess quantity and A is the limiting reactant, then the rate Equation 2.12 gets reduced to
− rA = k ′C A
which is a first-order rate equation. This reaction is called a pseudo-first-order reaction. 2.1.4 Elementary and Non-Elementary Reactions Elementary reactions are single-step reactions in which a reaction leading to the formation of product occurs on direct collision between reactant molecules and no intermediate compounds are formed. Consider the reaction between reactants A and B leading to the formation of product C, and let aA + bB → cC be the stoichiometric equation for this reaction. Let the observed reaction rate of A be
−rA = kCAnCBm
(2.13)
For an elementary reaction, there is one-to-one correspondence between the order of the reaction observed and the stoichiometric coefficients. If this reaction is an elementary reaction, then n = a and m = b, and the rate equation is
−rA = kCAaCBb
(2.14)
The reaction is non-elementary if it occurs not in a single step but in multiple steps with the formation of intermediate transition compounds in each of these steps. Nonelementary reactions are split into a number of elementary reaction steps and this defines the mechanism of the non-elementary reaction. For non-elementary reactions, there is no one-to-one correspondence between the observed rate equation and the stoichiometric equation. For example, the rate equation for the reaction
H 2 + Br2 → 2HBr
obtained from the experimental measurements (data) is reported as r( HBr ) =
1/2 k1CH2 CBr 2 C HBr k2 + CBr2
(
)
(2.15)
which has no correspondence to the stoichiometric equation. Thus, the reaction between H2 and Br2 is a non-elementary reaction. The derivation of a rate equation for a nonelementary reaction is a trial-and-error procedure involving the following steps:
i. Propose a mechanism for the non-elementary reaction by splitting the nonelementary reaction into a number of elementary reaction steps. ii. Write down the rate equations for each of the elementary steps using the law of mass action. Derive an overall rate equation by combining the rate expressions written for each of the elementary steps.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 16
Green Chemical Engineering
iii. Compare the rate equation derived for the proposed mechanism with the observed rate equation obtained from the experimental data. If it compares well, the proposed mechanism holds good. Otherwise, propose a new mechanism and repeat the above steps. The deviation of rate equation for non-elementary reactions is discussed later (Section 2.1.10). 2.1.5 Reversible Reactions Reversible reactions are reactions that proceed in both forward and reverse directions. Consider a reversible reaction between the reactants A and B leading to the formation of products C and D:
k1 aA + bB cC + dD k∗ 2
The reaction is split into a forward step 1 and a reverse step 2, both of which are assumed to be elementary reaction steps. In the forward step 1, A reacts with B resulting in the formation of product C and D and the rate of forward reaction is
(−rA ) = k1CAaCBb
(2.16)
where k1 is the kinetic rate constant of the forward reaction. In the reverse step 2, C reacts with D leading to the formation of A and B and the rate of reverse reaction is
rA = k 2CCcCDd
(2.17)
where k2 is the kinetic rate constant of the reverse reaction. The net rate of reaction of A is
(−rA ) = k1CAaCBb − k 2CCcCDd
(2.18)
An example of a reversible reaction is the reaction between H2 and N2 leading to the production of NH3.
N 2 + 3NH 3 3NH 3
However, this reaction is not an elementary reaction. A reversible reaction is said to be at an equilibrium state when the forward reaction rate is equal to the reverse reaction rate. Thus, at equilibrium, the net rate of reaction (−rA) is zero. If CAe, CBe, CCe and CDe are the a b c d equilibrium concentrations of A, B, C and D, respectively, then k1CAe CBe = k 2CCe CDe . The equilibrium constant K is defined as
d k C c CDe K = 1 = Ce a b k 2 CAeCBe
(2.19)
Equilibrium constant K is the ratio of the forward reaction rate constant k1 to the reverse reaction rate constant k2. The effect of temperature T on the equilibrium constant K is described by the Van’t Hoff relation
www.Ebook777.com
Free ebooks ==> www.ebook777.com 17
Introduction to Kinetics and Chemical Reactors
d ∆H R ln K = 2 dT RT
(2.20)
where ΔHR is the heat of the reaction. The value of equilibrium constant K at the reaction temperature can be obtained using the Van’t Hoff equation and for this value of K, the equilibrium conversion of A, xAe can be calculated by solving Equation 2.19. Substituting K = (k1/k2) in the Van’t Hoff equation and integrating it with respect to T, we get
ln
∆H R k1 =− + ln(C ) k2 RT
(2.21)
where ln(C) is the integration constant. Equation 2.21 can be written as
− k1 = Ce k2
∆H R RT
(2.21a)
If ΔE1 and ΔE2 are the activation energies of the forward and reverse reactions, respectively, we can write the Arrhenius equation for k1 and k2 as ∆E − 2 k1 = k 2 0 e RT k1 = k1 0 e
−
∆E1 RT
(2.22)
where k1 0 and k 2 0 are the frequency factors for the forward and reverse reactions, respectively. Substituting Equation 2.22 for k1 and k2 in Equation 2.21a, we get
∆H R = ∆E1 − ∆E2
(2.23)
The energy level diagrams for the endothermic and exothermic reversible reactions are shown in Figure 2.3. For an endothermic reaction, ΔE1 > ΔE2, and for an exothermic reaction, ΔE1 www.ebook777.com 18
Green Chemical Engineering
(a)
E* (activated state)
Activation energy of forward reaction
Activation energy of reverse reaction
∆E2
∆E1
P
Energy
EP
∆HR Heat of reaction
R ER (reactant)
Reaction coordinates (b)
Activation energy of forward reaction
E* ∆E1 ∆E2
Energy
R ∆HR
Heat of reaction
Activation energy of reverse reaction
ER P E P
Reaction coordinates Figure 2.3 Energy level diagrams for reversible reactions. (a) Endothermic reaction. (b) Exothermic reaction.
V CA
Figure 2.4 Constant-volume batch reactor.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 19
Introduction to Kinetics and Chemical Reactors
where k: reaction rate constant n: order of reaction Taking unsteady-state molal balance of A around the batch reactor, we have Rate of flow of A into the reactor
Rate of flow = of A out of the reactor
+
Rate of conversion of A in the reactor +
Rate of accumulation (2.25) of A in the reactor (2.26)
Rateof conversion = (− rA )V of A in thereactor
(2.27)
Rateof accumulation d(C AV ) dC =V A = dt dt of A in thereactor
Substituting Equations 2.26 and 2.27 in the general molal balance Equation 2.25, we have
dC − A = (−rA ) dt
(2.28)
Solving Equation 2.28 for a specified rate expression, we can obtain CA as a function of time. The determination of the rate equation for a given reaction is a reverse step in which the rate equation is determined from the values of CA observed or measured at different time instances. A typical plot of CA versus t drawn using the data collected in a batch reactor experiment is shown in Figure 2.5. The plot of CA versus t is a smooth curve passing through the points corresponding to experimental data. Some N numbers of discrete points 1,2,3,…,N are marked on this curve, tangents are drawn at these discrete points, and the slopes of these tangents are determined. The slopes of the tangents give the values of derivative −dCA/dt at concentrations CA1, CA2, CA3,…,CAN corresponding to the discrete points 1, 2, 3,…,N. The values of these derivatives give the rate (−rA) of reaction at concentrations CA1, CA2, CA3,…,CAN. Taking logarithm on both sides of the rate Equation 2.24, we get
ln[(−rA )] = ln[k ] + n ln[C A ]
(2.29)
This represents the equation of a straight line y = a0x + a1 with y = ln[(−rA)], x = ln[CA], a0 = n, and a1 = ln[k]. Thus, a plot of ln[(−rA)] versus ln[CA], shown in Figure 2.6 drawn for the observed data, is a straight line with slope n and intercept ln[k]. The values of ‘k’ and ‘n’ are determined by measuring the slope and intercept of the straight line plot (Figure 2.6). Alternatively, the values of kinetic parameter k and n can be determined by fitting the observed experimental data to a straight line equation y = a 0x + a1 by the method of linear regression (see Appendix A). This method of rate expression determination, known as the differential method, is based on the calculation of derivative (dCA/dt). This method will not give accurate results if the experimental data are prone to measurement errors. However, the integral method, which normally
www.Ebook777.com
Free ebooks ==> www.ebook777.com 20
Green Chemical Engineering
CA0 1 CA
2 CA3
3
CA5 t3
–(dCA/dt)CA3 = slope of tangent 4
t
5
6
7
t5
Figure 2.5 Plot of CA versus t for a batch reactor.
evens out the measurement noise, gives more accurate results. In the integral method, rate equations are expressed in integrated form by integrating Equation 2.28 for reactions of different order. By assuming an order n for the reaction, the value of reaction rate constant k is estimated by fitting the experimental data with the integrated form of the rate equation corresponding to the reaction order n. This is repeated by changing the reaction order (n = 1,2,…) until the best fit of the experimental data with the integrated form of the rate equation is obtained. The value of reaction order and the rate constant corresponding to the best fit are taken as the estimated values of k and n. The integral method is a trial-and-error method in which a value of reaction order n has to be guessed in each iteration. An appropriate guess value for n would reduce the number of trials required for the calculation of kinetic parameters. A simple graphical method is presented in the following section for estimating an appropriate initial guess value for reaction order n and k.
ln(–rA)
Slope = n
Intercept = ln k ln(CA) Figure 2.6 Plot of ln (−rA) versus ln(CA) for the estimation of kinetic parameters.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 21
Introduction to Kinetics and Chemical Reactors
2.1.6.1 A Graphical Method for the Estimation of k and n Substituting the rate equation (−rA ) = kC An in Equation 2.28, we get dC A n dt = −kC A
(2.30)
Integrating Equation 2.30, we get CA
∫
CA 0
t
dC A = − k dt C An
∫ 0
(2.31)
1 1 1 − n − 1 = kt n −1 n − 1 CA CA0
(2.32)
The terms in Equation 2.32 are rearranged and written as 1
y =
(2.33)
1
[1 + (n − 1)k ’t] n −1
where
C y = A CA0
and k ’ = kC An−01
(2.34)
A plot of y versus t is drawn (Figure 2.7) using the CA versus t data collected from the batch reactor experiment. Draw a tangent to the y versus t curve at t = 0 (point P on the curve). Let this tangent intersect the t-axis at t = t1. Let the value of y at t = t1 be y1. At point Q corresponding to (t1, y1) on the y versus t curve, draw a tangent; this tangent intersects
y
P
Q
y1
t1
t2 t
Figure 2.7 Plot of y versus t for the batch reactor.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 22
Green Chemical Engineering
the t-axis at t = t2. The slope of the tangent at t = 0 is (dy/dt) t =0 . Taking the derivative of y with respect to t, we get n
− dy n − 1 dt = − k ′[1 + (n − 1)k ’t]
(2.35)
At t = 0, (dy/dt) = − k ′. The slope of the tangent at t = 0 (from the Figure 2.7) is −(1/t1). t=0 This implies that t1 =
1 k’
(2.36)
Substituting Equation 2.33 for y in Equation 2.35, we get dy n dt = −k ’ y
(2.37)
At t = t1, y = y1. Substituting y = y1 at t = t1 in Equation 2.37, we get dy dt
= − k ’ y1n t = t1
(2.38)
The slope of the tangent at t = t2 (from Figure 2.7) is −y1/(t2 − t1). Thus y1n y1 = (t2 − t1 ) t1
and
y1n −1 =
t1 (t2 − t1 )
(2.39)
Taking logarithm on both sides of Equation 2.39, we get an equation for n as
t1 ln (t2 − t1 ) n = 1+ ln[ y1 ]
(2.40)
As k ′ = kCAn−01 and k’ = (1/t1), the value of k can be estimated using the equation
k =
1 t1 (C An−01 )
(2.41)
Note that this method of parameter estimation does not hold good for first-order reaction (n = 1). The values of k and n estimated using the procedure presented in this section are to be taken only as approximate initial guess values. The integral method will give more accurate estimates of k and n.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 23
Introduction to Kinetics and Chemical Reactors
2.1.6.2 Estimation of Kinetic Parameters for the Reaction between Reactants A and B Consider the reaction between reactants A and B
aA + bB → cC
whose rate equation is (− rA ) = kCAnCBm
(2.42)
Assume that this reaction is carried out in a batch reactor with excess quantity of B, CB = CB0. Then, Equation 2.42 reduces to a rate equation of order n with respect to reactant A, which is the limiting reactant. (−rA ) = k ’CAn
(2.43)
where k ’ = kCBm0
(2.44)
Carry out the reaction in a batch reactor with different initial excess concentrations of B, CB0 = CB1 0 , CB2 0 ,…, CBN0 . For each one of these values of CB0, record the variation of CA with respect to time. The plots of CA versus t for different values of CB0 are shown in Figure 2.8. Calculate the values of k’ and n (Section 2.6.1) using the data corresponding to CA versus t plots recorded for different initial excess concentrations of B, CB0 = CB1 0 , CB2 0 , … , CBN0 . Let the estimated values of k′ be k ’ = k1′ , k′2 , k′3 , … , k′N . Taking logarithm on both sides of Equation 2.44, we get ln k ’ = ln k + m ln CB0
CA0
C
CA
C
B
B
=C
B0 N
=C
B0 3
C
B
C
B
=C
=C
B0 1
B0 2
t Figure 2.8 CA versus t plot for different values of CB0 for the estimation of kinetic parameters.
www.Ebook777.com
(2.45)
Free ebooks ==> www.ebook777.com 24
Green Chemical Engineering
ln(k′)
Slope = m
Intercept = ln k ln(CB0) Figure 2.9 ln k′ versus ln CB0 plot for the estimation of kinetic parameters.
The plot of ln k′ versus ln CB0 is a straight line with slope m and intercept ln k. The values of m and k are obtained by making a plot of ln k′ versus ln CB0 (Figure 2.9) and measuring the slope and intercept of the straight line. 2.1.7 Integrated Forms of Kinetic Rate Equations for Some Simple Reactions The rate equations in integrated form obtained by integrating Equation 2.28 are required for the estimation of kinetic parameters using the integral method of rate equation determination. In this section, integrated forms of rate equation are derived for some of the simple reactions. 2.1.7.1 First-Order Reaction Consider a first-order reaction A k →B
carried out in a batch reactor of volume V. CA0 is the initial concentration of A. The rate equation is (−rA ) = kC A . Substituting (−rA ) in Equation 2.28, we get dCA = −kC A dt
(2.46)
Integrating Equation 2.46, we have CA
∫
CAO
t
dCA = −k dt CA
∫ 0
(2.47)
www.Ebook777.com
Free ebooks ==> www.ebook777.com 25
Introduction to Kinetics and Chemical Reactors
and C ln A = − kt CA0
(2.48)
Writing CA in terms of fractional conversion xA, CA = CA0(1 − xA), we obtain the integrated form of the rate equation for first-order reaction as 1 kt = ln 1 − xA
(2.49)
1 A plot of ln versus t is a straight line passing through the origin having slope 1 − xA k (Figure 2.10). The value of k is estimated from this plot by measuring the slope of the straight line. The half-life period t1/2 of a reaction is defined as the time required for the concentration of the limiting reactant CA to get reduced to half of the initial concentration CA0. Substituting CA = CA0/2 and t = t1/2 in Equation 2.48, we get t1/2 =
1 ln 2 k
(2.50)
Thus, the value of k can be estimated from the half-life period t1/2 of the first-order reaction using Equation 2.50. 2.1.7.2 Second-Order Reaction Consider a second-order reaction 2A k →B
kt =
1 1 – xA Slope = k
t Figure 2.10 Plot of integrated form of the rate equation for first-order reaction.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 26
Green Chemical Engineering
with rate equation (−rA ) = kC A2 . Substituting this rate equation in Equation 2.28, we have dCA = −kC A2 dt
(2.51)
Integrating Equation 2.51, we have CA
t
∫
CAO
dCA = −k dt C A2
∫
(2.52)
0
and 1 1 C − C = kt AO A
(2.53)
Writing CA in terms of fractional conversion xA, CA = CA0(1 − xA), we obtain the integrated form of the rate equation for second-order reaction as kt =
1 xA CA 0 1 − x A
(2.54)
1 xA versus t (Figure 2.11) and calCA 0 1 − x A culating the slope of the straight line passing through the origin. Half-life period Thus, the value of k is estimated by plotting
t1/2 =
kt =
1 CA0
1 kC A 0
(2.55)
xA
1 – xA Slope = k
t Figure 2.11 Plot of integrated form of the rate equation for second-order reaction.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 27
Introduction to Kinetics and Chemical Reactors
2.1.7.3 Third-Order Reaction For a third-order reaction 3A k →B
with rate equation (−rA ) = kC A3
dCA = −kC A3 dt
(2.56)
Integrating Equation 2.56, we get CA
∫
CAO
t
dCA = −k dt C A3
∫ 0
and 1 1 C 2 − C 2 = 2kt A A0
(2.57)
Substituting CA = CA0(1 − xA), we get kt =
1 1 2C A2 0 1 − x A
(
)
2
− 1
(2.58)
1 1 versus t (Figure 2.12) is a straight line passing 1 − 2CA2 0 1 − x A 2 through the origin with a slope equal to k. Thus, the plot of
(
kt =
)
1 1 –1 2CA02 (1 – xA)2 Slope = k
t Figure 2.12 Plot of integrated form of rate equation for third-order reaction.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 28
Green Chemical Engineering
Half-life period t1/2 =
3 2kCA2 0
(2.59)
2.1.7.4 Second-Order Irreversible Reaction between A and B Consider an irreversible reaction between reactants A and B A + B k →C + D
with rate equation
(−rA ) = kC ACB
(2.60)
Let CA0 and CB0 be the initial concentration of A and B in the batch reactor. Define M=
CB 0 CA0
(2.61)
As (CA0 − CA) = (CB0 − CB), we can write
CB = CB0 − CA 0 + CA = CA 0 ( M − 1) + CA
(2.62)
Substituting Equation 2.62 for CB in Equation 2.28, we get
(
)
(2.63)
dCA = − k dt CA 0 ( M − 1) + CA
(2.64)
dCA = − kC A CA 0 ( M − 1) + CA dt
which on integration gives
CA
∫(
CA 0
t
)
∫ 0
Integrating Equation 2.64, by the method of partial fraction, we get kt =
C ( M − 1) + C A 1 ln A 0 CA 0 ( M − 1) MC A
(2.65)
Substituting CA = CA0(1 − xA), we get kt =
M − xA 1 ln CA 0 ( M − 1) M(1 − x A )
(2.66)
www.Ebook777.com
Free ebooks ==> www.ebook777.com 29
Introduction to Kinetics and Chemical Reactors
kt =
M – xA 1 CA0 (M – 1) M(1 – xA) Slope = k
t Figure 2.13 → C + D. Plot of integrated form of the rate equation for the reaction A + B k
Thus, a plot of
M − xA 1 versus t (Figure 2.13) is a straight line with a ln CA 0 ( M − 1) M(1 − x A )
slope equal to k. The half-life period t1/2 is
t1/2 =
1 2M − 1 ln kC A 0 ( M − 1) M
(2.67)
Note that for M = 1, Equations 2.66 and 2.67 get reduced to the form of integrated Equations 2.54 and 2.55 derived for second-order reaction in Section 2.1.7.2. 2.1.7.5 Reversible First-Order Reaction Consider a reversible first-order reaction k
1 A B k
2
The rate equation is
−rA = k1CA − k 2CB
(2.68)
Let CAe and CBe be the concentrations of A and B at equilibrium. Then, the equilibrium constant K is
K =
k1 C = Be k2 C Ae
(2.69)
Let CA0 be the initial concentration of A. As (CA0 − CA) = CB
CA 0 = C A + CB = CAc + CBe
www.Ebook777.com
(2.70)
Free ebooks ==> www.ebook777.com 30
Green Chemical Engineering
Combining Equations 2.69 and 2.70, we get CAe =
CA0 1+ K
(2.71)
and CB = ( 1 + K ) C Ae − CA
(2.72)
Substituting Equation 2.69 in Equation 2.68, we get
C − rA = k1 C A − B K
1 − rA = k1 C A − ((1 + K )CAe − CA ) K −rA =
k1(1 + K ) ( CA − CAe ) K
(2.73)
Substituting Equation 2.73 for (−rA) in Equation 2.28 and integrating it, we get CA
∫
CA 0
t
dCA k (1 + K ) dt =− 1 K (CA − CAe )
∫ 0
(2.74)
which reduces to
k1(1 + K ) KC A 0 C − C Ae = ln t = ln A 0 K C A − CAe (1 + K )C A − CA 0
(2.75)
KCA 0 Thus, a plot of ln versus t (Figure 2.14) is a straight line with slope ( 1 + K ) C − C A A0 k1(1 + K ) . K Rate constant k1 can be estimated by measuring the slope of this straight line plot. The half-life period t1/2 is t1/2 =
k 2k ln k1(1 + K ) K − 1
2.1.7.6 Zero-Order Reaction Consider a reaction
A k →B
www.Ebook777.com
(2.76)
Free ebooks ==> www.ebook777.com 31
Introduction to Kinetics and Chemical Reactors
ln
kCA0 Slope =
(1 + k)CA – CA0
k(1 + k) k
t Figure 2.14 Plot of integrated form of the rate equation for reversible reaction.
in which reactant A is present so much in abundance that the change in concentration of A can be treated as negligible during the period of reaction. In this case, the rate of reaction is independent of the concentration of A, CA and the reaction is a zero-order reaction. Then −dC A =k dt
(2.77)
where k is the reaction rate constant. Integrating Equation 2.77, we get CA 0 − C A = kt
(2.78)
Substituting CA = CA0(1 − xA), we get
kt = CA0xA The plot of (CA0xA) versus t is a straight line with slope k (Figure 2.15).
kt = CA0xA
Slope = k
t Figure 2.15 Plot of integral form of rate equation for zero-order reaction.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 32
Green Chemical Engineering
Table 2.1 Integrated Form of Rate Equations Reaction
Integrated Form of Rate Equation
Rate Equation
A k →B
(− rA ) = k
kt = CA 0 x A
(− rA ) = kCA
1 kt = ln 1 − x A
Zero order A k →B First order 2A k →B
(− rA ) = kCA2
Second order 3A k →B
(− rA ) = kCA3
Third order A + B k →C + D Second order
(− rA ) = − kCACB C M = B0 CA0
kt =
1 xA CA 0 1 − x A
kt =
1 2CA2 0
kt =
M − xA 1 ln CA 0 ( M − 1) M(1 − x A )
1 − 1 (1 − x A )2
For M ≠ 1
xA 1 ln CA 0 1 − x A For M = 1 kt =
Reversible first-order reaction
− rA =
k
1 A B k 2
k1 (1 + K ) K (CA − CAe )
k1 (1 + K ) t K KCA 0 = ln (1 + K )CA − CA 0
Note: For a mth order irreversible reaction with rate equation (−rA) = KCAm, kt = t1/2 =
(2m −1 − 1) . (m − 1)kCA( m0−1)
Half-Life Period t1/2 t1/2 =
CA0 2k
t1/2 =
1 ln 2 k
t1/2 =
1 kCA 0
t1/2 =
3 2kCA2 0
1 2M − 1 ln kCA 0 ( M − 1) M For M ≠ 1
t1/2 =
1 kCA 0 For M = 1
t1/2 =
t1/2 =
k 2k ln k1 (1 + K ) K − 1
1 (m − 1)c(Am0 −1)
1 − 1 and m −1 ( ) − x 1 A
The half-life period t1/2 for zero-order reaction is
t1/2 =
CA0 2k
(2.79)
The integrated forms of the rate equations derived for various reactions are summarised and listed in Table 2.1. Problem 2.2 A single irreversible reaction A k → B of unknown order n is carried out in a batch reactor. Taking a solution containing 5 kmol/m3 of reactant A in the batch vessel, the reactor is maintained at a constant temperature of 315 K. The solution in the reaction vessel is sampled at different time instants and the concentration of A is measured. The measured values of the concentration of A are tabulated below:
www.Ebook777.com
Free ebooks ==> www.ebook777.com 33
Introduction to Kinetics and Chemical Reactors
Time, t (min) 0 1.1 4.7 7.7 11.3 15.6 20.8 35.6 46.1 60.0 78.8 105 143 202 300 480
CA (kmol/m3) 5 4.75 4.5 4.25 4.0 3.75 3.5 3.0 2.75 2.5 2.25 2.0 1.75 1.5 1.25 1.00
Using the differential method of rate equation analysis, estimate the reaction order n and rate constant k. Using the data given in the problem, a graph of CA versus t is drawn (Figure P2.2a). Tangents are drawn at nine points on the plot corresponding to different values of CA and the slopes of these tangents are measured. These values are listed in the table below.
CA
( − rA ) =
4.25 4.0 3.5 3.0 2.75 2.50 2.25 2.0 1.75
−dC A dt
0.125 0.0645 0.0461 0.0333 0.0218 0.0179 0.0122 0.0085 0.0055
ln (−rA)
ln(CA)
−2.08 −2.74 −3.08 −3.40 −3.84 −4.02 −4.41 −4.77 −5.20
1.45 1.39 1.25 1.10 1.01 0.92 0.81 0.69 0.56
Let the rate equation be written as (− rA ) = kCAn
which in the linear form is
ln(− rA ) = ln k + n ln C A
www.Ebook777.com
Free ebooks ==> www.ebook777.com 34
Green Chemical Engineering
5
Reactant conc. CA (kmol/m3)
(a)
4
3
2
1
0
0
100
200
300
400
500
Time (t, min) (b)
–2 –2.5
ln (–rA)
–3
Slope = 2.7102 Intercept = –6.6016
–3.5 –4 –4.5 –5 –5.5 0.4
0.6
0.8
1
1.2 1.4 ln (CA)
1.6
1.8
2
Figure P2.2 (a) Plot of CA versus t using the data given in the problem. (b) Plot of ln(−rA) versus ln(CA) for estimation of kinetic parameters.
A plot of ln(−rA) versus ln(CA) (Figure P2.2b) gives a straight line with slope m = n and intercept I = ln k. From this plot m = 3.3, that is, reaction order n = 3.3 I = −6.9, that is, rate constant k = e−6.9 = 1.01 × 10−3 The reaction is actually a third-order reaction with value of k = 1 × 10−3. Note: Refer MATLAB program: diff_anal_kinet.m
www.Ebook777.com
Free ebooks ==> www.ebook777.com 35
Introduction to Kinetics and Chemical Reactors
Problem 2.3 Solve Problem 2.2 using the integral form of the rate equation. The differential method of analysis (Problem 2.2) indicates that the reaction is third order. For a third-order reaction, the integral form of the rate equation is 1 1 − 1 2CA2 0 (1 − x A )2 1 1 − 1 versus t will be a straight line passing through the Thus, a plot of 2CA2 0 (1 − x A )2 origin with a slope equal to k. This plot is shown in Figure P2.3.
kt =
Time, t (min) 0 1.1 4.7 7.7 11.3 15.6 20.8 35.6 46.1
CA (kmol/m3)
kt =
1 1 − 1 2C A2 0 (1 − x A )2
5 4.75 4.5 4.25 4.0 3.75 3.5 3.0 2.75
0 2.16 × 10−3 4.69 × 10−3 7.68 × 10−3 0.0113 0.0156 0.0208 0.0356 0.0461
Time, t (min)
CA (kmol/m3)
60.0 78.8 105 143 202 300 480
2.5 2.25 2.0 1.75 1.5 1.25 1.00
y=
0.060 0.0788 0.1050 0.1433 0.2022 0.300 0.480
Slope of the straight line = m = 10−3. So, rate constant k = 10−3 and reaction order n = 3. Note: Refer MATLAB program: integral_anal_kinet.m 0.5
kt =
1 1 –1 2C2A0 (1 – xA)2
0.45
Slope = 10–3
0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0
0
100
200
300
400
1 1 − 1 2C A2 0 (1 − x A )2
500
Time (t, min) Figure P2.3 Plot of integral form of rate equation for III order reaction.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 36
Green Chemical Engineering
Problem 2.4 Calculate the kinetic parameters k and n for the batch reactor data given in Problem 2.2 using the half-life period method. For the irreversible nth-order reaction, the half-life period (t1/2) is given by the equation t1/2 =
2n −1 − 1 (n − 1)kCAOn−1
Using the batch reactor data (Problem 2.2) and the corresponding plot of CA versus t, halflife period (t1/2) values are calculated for different values of (CA0). These values are given in the table below.
CA0
5 4.5
t1/2 = t CA 0 − tCA = CA 0 CA = 2 t(CA = 2.5) = 60 t1/2 = 60 t(CA = 5) = 0 t( 2.25) = 78.8 t1/2 = 74.1 t( 4.5) = 4.7
ln CA0
ln t1/2
1.609
4.09
1.504
4.31
4
t( 2.0 ) = 105 t1/2 = 93.7 t( 4.0 ) = 11.3
1.386
4.54
3.5
t(1.75) = 143 t1/2 = 122.2 t( 3.5) = 20.8
1.253
4.81
3
t(1.5) = 202 t1/2 = 166.4 t( 3.0 ) = 35.6
1.099
5.11
2.5
t(1.25) = 300 t1/2 = 240 t( 2.5) = 60
0.916
5.48
2
t(1.0 ) = 480 t1/2 = 375 t( 2.0 ) = 105
0.693
5.93
Writing the half-life period equation in linear form, we get 2n −1 − 1 ln [t1/2 ] = ln − (n − 1)ln [CA 0 ] (n − 1)k
A plot of ln [t1/2] versus ln [CAO] is a straight line with slope m = −(n − 1) and intercept I = ln[2n−1 − 1/(n − 1)k]. This plot is shown in Figure P2.4. From this plot, we find the values of slope and intercept as m = −2 I = 7.32 Slope = −2 = −(n − 1)
www.Ebook777.com
Free ebooks ==> www.ebook777.com 37
Introduction to Kinetics and Chemical Reactors
7 6
ln (t1/2)
5
Slope = –2 Intercept = 7.32
4 3 2 1 0
0.6
0.8
1.0
1.2
1.4
1.6
1.8
ln (CA) Figure P2.4
Plot of ln[t1/2] versus ln[CAO] for estimation of kinetic rate parameters. So, the reaction order n = 3
2n −1 − 1 ln = I = 7.32 (n − 1)k
2n −1 − 1 ⇒ = 1510 (n − 1)k So 2n −1 − 1 22 − 1 −4 k = = (2)1510 = 9.93 × 10 ≈ 0.001 1 1510 n − ( )
Problem 2.5 k A first-order reversible reaction A B is carried out in a batch reaction vessel at a constant temperature. The initial concentration of A is CA0 = 4 kmol/m3. The reaction is monitored for 10 min by sampling the reactor fluid every 1 min and measuring the concentration of A. The concentration of A measured at intervals of 1 min is reported below:
Time, t (min) CA (kmol/m3)
0 4
1 3.6
2 3.4
3 3.0
4 2.8
5 2.6
6 2.4
7 2.3
8 2.2
9 2.1
10 2.0
The concentration of A in the vessel, when measured after 1 h was found to be 1.5 kmol/m3. Estimate the equilibrium constant K and rate constant k.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 38
Green Chemical Engineering
The integrated form of the rate equation is k1(1 + K ) C − C Ae t = ln A 0 K CA − CAe
CA0 = 4 kmol/m3 and CAe = 1.5 kmol/m3 CA0 1+ K
CAe =
K =
4 K = −1 1.5
K = 1.667
CA0 −1 CAe
Using the data given in the problem, a plot of ln[CA0 − CAe /CA − CAe ] versus t is drawn (Figure P2.5). This plot is a straight line passing through the origin having slope m = k1(1 + K)/K. Time, t (min)
CA (kmol/ m3)
C − C Ae ln A 0 C A − C Ae
4 3.6 3.4 3.0 2.8 2.6 2.4 2.3 2.2 2.1 2.0
0 0.174 0.275 0.511 0.654 0.821 1.022 1.139 1.273 1.427 1.609
0 1 2 3 4 5 6 7 8 9 10
From the straight line plot, slope m is calculated:
m=
k1 =
k1 (1 + K ) = 0.159 K
0.159K 0.159 × 1.667 = = 0.099 (1 + K ) 2.667 k1 = 0.1 min−1
Note: Refer MATLAB program: integral_anal_kinet2.m
www.Ebook777.com
Free ebooks ==> www.ebook777.com 39
Introduction to Kinetics and Chemical Reactors
1.8 1.6
Slope = 0.159
kt = ln
CA0 – CAe CA – CAe
1.4 1.2 1 0.8 0.6 0.4 0.2 0
0
2
4
6
8
10
Time (t, min) Figure P2.5 C − CAe A plot of ln A 0 versus t for I order reversible reaction. CA − CAe
2.1.8 Multiple Reactions Multiple reactions are broadly classified as ‘series reactions’ and ‘parallel reactions’. A series reaction is a reaction in which a reactant A gets converted into a product C in two steps with the formation of an intermediate product B. 1 2 A k → B k →C
In the case of a parallel reaction, the reactant A gets converted simultaneously into a number of products, say B, C and D B
k1 k2
A
C
k3
D
Series–parallel reactions are reactions that are combinations of both series and parallel reactions. For example A
k1
B
k2 k3
C D
2.1.8.1 Series Reaction Consider a series reaction
1 2 A k → B k →C
www.Ebook777.com
Free ebooks ==> www.ebook777.com 40
Green Chemical Engineering
carried out in a batch reactor. Let CA0 be the initial concentration of A, with no B or C present, initially. This reaction proceeds in two sequential steps and assume that both the reaction steps follow first-order kinetics. Then, r1, rate of conversion of A to B is
r1 = k1C A
(2.80)
r2 = k 2CB
(2.81)
And r2, rate of conversion of B to C is
The rates of change of concentrations of A, B and C are written as
dCA = −k1CA dt
(2.82)
dCB = k1CA − k 2CB dt
(2.83)
dCc = k 2CB dt
(2.84)
CA = CA 0 e − k1t
(2.85)
Integrating Equation 2.82, we get
Substituting Equation 2.85 for CA in Equation 2.83 and solving the first-order differential equation for CB, we get CB =
C A 0 k1 e − k2t − e − k1t ( k1 − k 2 )
(2.86)
As, CA0 = CA + CB + Cc, we can write Cc = CA0 − CA − CB and thus we get
1 Cc = CA 0 1 − k1e − k2t − k 2e − k1t ( k1 − k 2 )
(
)
(2.87)
Figure 2.16 shows the variations of CA, CB and CC with respect to time It is seen in Figure 2.17 that CA keeps on decreasing with time, CD keeps increasing with time and CB increases initially, reaches a maximum value of CB,max at time tmax and then decreases with time. If B is the desired product to be produced in the batch reactor, then the reactor should be operated for a batch time equal to tmax at which the production of B is maximum. tmax is calculated by taking derivative of CB with respect to t and equating it to 0
dCB dt
= t = tmax
C A 0 k1 − k 2e − k2tmax + k1e − k1tmax = 0 ( k1 − k 2 )
www.Ebook777.com
(2.88)
Free ebooks ==> www.ebook777.com 41
Introduction to Kinetics and Chemical Reactors
(Concentration of A, B and C)
CAO
CA
CB,max
CB
CC
CA* CC*
tmax
t
Figure 2.16 k1 2 Variation of CA, CB and CC with time for series reaction A → B k → C.
Solving Equation 2.88 for tmax, we get
tmax =
1 k ln 1 ( k1 − k 2 ) k 2
(2.89)
Substituting t = tmax in Equation 2.86, we get k2
CB ,max
k ( k1 − k2 ) = CA0 1 k2
(2.90)
In the case of a single reaction carried out in a reactor, fractional conversion of the limiting reactant (xA) achieved in the reactor is usually taken as the index of reactor performance. In the case of multiple reactions, as conversion of limiting reactant leads to the formation of multiple products, conversion alone cannot be taken as an indication of good performance. Performance is considered to be good if conversion of a certain quantity of reactant leads to the formation of a larger proportion of desired product and a relatively lower proportion of undesired product. Thus, for multiple reactions, performance is characterised by two more factors apart from conversion, namely, yield and selectivity. Overall yield γ is defined as the fraction of the overall limiting reactant that is converted into the desired product. Overall selectivity Φ is defined as the ratio of the amount of desired product to the amount of undesired product produced. If B is the 1 2 desired product and C is the undesired product of the series reaction A k → B k → C, then for any batch time t Overall yield = γ =
CB (C A 0 − C A )
www.Ebook777.com
(2.91)
Free ebooks ==> www.ebook777.com 42
Green Chemical Engineering
and Overall selectivity = Φ =
CB CC
(2.92)
We also define point yield γ and point selectivity Φ, respectively, as the yield and selectivity at a particular time instant of reaction. Thus, at any time instant, if (−dCA) is the number of moles of A converted in one unit volume of the reactor, dCB and dCC are the moles of B and C produced, then Point yield = γ =
( dCB ) ( −dCA )
(2.93)
and Point selectivity = Φ =
( dCB ) ( dCC )
(2.94)
γ and Φ can be expressed in terms of reaction rates as
γ =
(dCB )
(− dCA )
=
dCB dt dCA − dt
= 1−
k 2 CB k C 1
(2.95)
A
and
Φ=
(dCB ) (dCC )
=
dCB dt dCC dt
=
k2 CA −1 k1 CB
(2.96)
For series reactions, yield and selectivity vary with time and conversion. Problem 2.6 1 2 The measured data recorded on a series reaction A k → B k → C carried out in a batch reactor shows that the maximum concentration of B, CBmax, which is 50% of the initial concentration of A, CA0, is achieved in a reaction time of 13.8 min. Only A is present in the batch reactor at the time of start-up. Estimate the values of rate constants k1 and k2
k2
CB max k1 ( k2 − k1 ) C = k A0 2
www.Ebook777.com
Free ebooks ==> www.ebook777.com 43
Introduction to Kinetics and Chemical Reactors
and 1 k ln 1 ( k1 − k 2 ) k 2
tmax =
It is given in the problem that
CB max = 0.5 and tmax = 13.8 min CA0
k2 C k ln B max = ln 1 C A0 (k 2 − k1 ) k 2 C ln B max = − k 2 CA0
1
tmax
k2 = −
k2 = −
1 C ln B max tmax C A 0
1 ln (0.5) = 0.05 min −1 13.8 1
k2
1
( k2 − k1 ) k k k1 Let x = 1 , then k1 = 1 1− k2 = x (1− x ) k2 k2 k2 1
x ( 1− x ) =
CB max = 0.5 CA0
By trial and error, we find x = 2. Thus, k1 = 0.1 min−1 2.1.8.2 Parallel Reaction Consider a parallel reaction B (Desired product)
k1 A
k2
C
in which the reactant A gets simultaneously converted into products C and D and assumes that the reaction follows first-order kinetics. The rate of conversion of A to B, r1, is
r1 = k1C A
(2.97)
And the rate of conversion of A to C, r2, is
r2 = k 2CA
www.Ebook777.com
(2.98)
Free ebooks ==> www.ebook777.com 44
Green Chemical Engineering
The rates of change of concentrations of A, B and C in batch reactor are
dCA = − ( k1 + k 2 ) C A dt
(2.99)
dCB = k1C A dt
(2.100)
dCc = k 2C A dt
(2.101)
CA = CA 0 e −(k1 + k2 )t
(2.102)
Integrating Equation 2.99, we get
where CA0 is the initial concentration of A. Substituting Equation 2.102 for CA in Equations 2.100 and 2.101 and integrating, we get
(
)
(2.103)
(
)
(2.104)
CB =
C A 0 k1 1 − e −( k1 + k2 )t ( k1 + k 2 )
CC =
CA0k2 1 − e −( k1 + k2 )t ( k1 + k 2 )
Variations of CA, CB and CC are shown in Figure 2.17.
CAO
CC CA
(Concentration of A, B and C)
CB
t Figure 2.17 Variations of CA, CB and CC with time for parallel reaction A
k1
B .
k2
C
www.Ebook777.com
Free ebooks ==> www.ebook777.com 45
Introduction to Kinetics and Chemical Reactors
Taking B as the desired product and C as the undesired product of reaction, overall yield and overall selectivity for the parallel reaction are Overall yield = γ =
CB k1 = (C A 0 − C A ) k 1 + k 2
(2.105)
and Overall selectivity = Φ =
CB k = 1 CC k2
(2.106)
k1 k1 + k 2
(2.107)
Point yield and point selectivities are
γ =
(dCB )
(− dCA )
=
dCB dt dCA − dt
=
and
Φ=
(dCB ) (dCC )
=
dCB dt dCC dt
=
k1 k2
(2.108)
For parallel reactions, yield and selectivity are independent of concentration. Thus, overall yield is the same as the point yield and overall selectivity is the same as the point selectivity. 2.1.9 Autocatalytic Reactions Autocatalytic reactions are a type of self-catalytic reaction in which the product produced by the reaction acts as a catalyst for the very same reaction. An irreversible reaction A k →B in which the product B acts as a catalyst is an autocatalytic reaction represented as A + B k →B + B
The rate equation for the autocatalytic reaction is (−rA ) = kC ACB
where k: reaction rate constant CA: concentration of A CB: concentration of B
www.Ebook777.com
(2.109)
Free ebooks ==> www.ebook777.com 46
Green Chemical Engineering
Let CA0 and CB0 be the initial concentration of A and B present in the batch reaction vessel. Note that the autocatalytic reaction requires some amount of B to be present initially for the reaction to get initiated. As the total number of moles of A and B put together does not change with time C A 0 + CB 0 = C A + C B = C0
(2.110)
Substituting CB = C0 − CA in the rate Equation 2.109, we get (− rA ) = kCA (C0 − C A )
(2.111)
The plot of (−rA) versus CA is shown in Figure 2.18. Initially, when CA = CA0, the product B is rate controlling as CB ≪CA. So as the reaction progresses with time, CA will keep decreasing and CB will keep increasing resulting in a progressive increase in the rate of reaction (−rA). As the value of CA keeps diminishing with time, after a certain concentration CA = C∗A is reached, CA will attain a value much lower than CB(CA ≪CB) and reactant A will start controlling the rate. So for CA < C ∗A reaction rate, (−rA) will decrease as CA decreases with time. Thus, the rate of reaction attains a maximum value at CA = C∗A . C∗A is calculated by equating d(− rA )/dCA to zero C∗A =
C0 2
(2.112)
Substituting the rate Equation 2.111 in Equation 2.28, we get dCA = − kC A (C0 − CA ) dt
(2.113)
Maximum rate
(–rA)
t=0
CA* =
C0 2
CAO CA
Figure 2.18 Plot of (−rA) versus CA for autocatalytic reaction.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 47
Introduction to Kinetics and Chemical Reactors
Integrating Equation 2.113 using the method of partial fraction, we get kt =
1 CA 0 (C0 − CA ) ln ⋅ C0 CB0 CA
(2.114)
An important example of autocatalytic reaction is the fermentation reaction in which a microorganism (B) multiplies on the consumption of organic feed (A). 2.1.10 Non-Elementary Reactions and Stationary State Approximations Non-elementary reactions are reactions for which there are no one-to-one correspondences between the observed rate expression and the stoichiometric equation (Section 2.1.4). Rate equations for such non-elementary reactions are derived by proposing a reaction mechanism that defines the way in which the non-elementary reaction is split into a number of elementary reaction steps. For example, Lindemann (1922) proposed a mechanism to explain the spontaneous decomposition of azomethane
( CH3 )2 N 2
→ C 2H6 +N 2
This reaction is of the type A → B + C and is split into three elementary steps: Step 1: One molecule of A collides with another molecule of A producing an extra-energetic molecule A*, which is unstable. 1 A + A k → A∗ + A
The rate of this reaction step is
r1 = k1C A2
(2.115)
Step 2: Energised molecule A* returns to a stable state by collision with a molecule of A 2 A∗ + A k →A + A
The rate of this step is
r2 = k 2C∗AC A
(2.116)
Step 3: The energised molecule A* decomposes to products B and C 3 A∗ k →B + C
at a rate r3
r3 = k 3C∗A CA and C∗A are the concentrations of A and A*, respectively.
www.Ebook777.com
(2.117)
Free ebooks ==> www.ebook777.com 48
Green Chemical Engineering
It is assumed that the slowest of the three steps is step 3, which is the formation of products B and C by decomposition of A*. In any multistep reaction, the slowest step is the rate-controlling step and the rate of the slowest step is taken as the overall rate of reaction. Thus, the rate of reaction r is
r=
dCB dCC = = k 3 C∗A dt dt
(2.118)
Rate of change of C∗A with respect to time t is
dC∗A = k1CA2 −k 2C∗ACA − k 3C∗A dt
(2.119)
Extra-energetic molecule A* is an intermediate compound, which is highly unstable. We assume that it disappears at the rate at which it is created. A* is assumed to be in a pseudoequilibrium state, at which the rate of formation of A* is equal to the rate of disappearance of A*. So, net change in the concentration of A* is zero
dC∗A =0 dt
(2.120)
This approximation is known as ‘stationary state approximation’ and holds good for all the intermediate compounds that are formed in multistep reactions. Applying this stationary state assumption, we get
CA∗ =
k1CA2 k 3 + k 2CA
(2.121)
Substituting Equation 2.121 for C∗A in the rate Equation 2.118, we get the rate equation for the non-elementary reaction in the final form as
(−rA ) =
k1k 2CA2 k 3 + k 2CA
(2.122)
This rate equation is reported to explain well the experimentally observed time variations of reactant and product concentrations and hence it is taken as the most appropriate rate equation for the given reaction. It may be noted that the rate equation reduces to a second-order rate equation (− rA ) = (k1k 2 /k 3 )CA2 for low concentrations of A and a first-order rate equation (− rA ) = k1C A for high concentrations of A. Stationary state approximation is widely used for the derivation of rate equations for non-elementary reactions. We will see a few more applications of stationary state approximations in the forthcoming sections. 2.1.10.1 Estimation of Kinetic Parameters for Non-Elementary Reactions by Linear Regression The rate equation for the non-elementary reaction derived in Section 2.1.10 can be written in terms of two independent parameters k1 and K 2 as
www.Ebook777.com
Free ebooks ==> www.ebook777.com 49
Introduction to Kinetics and Chemical Reactors
(−rA ) =
k1C A2 1 + K 2C A
(2.123)
In this section, we present a method for the estimation of parameters k1 and K 2 using the experimental readings on variation of CA with time recorded in a batch reactor experiment. The differential equation for variation of CA with time is written as dCA k1CA2 = dt 1 + K 2CA
(2.124)
Integrating this equation, we get CA
( 1 + K 2CA ) dCA = k1CA2 CA 0
∫
t
∫ dt 0
(2.125)
On integration, Equation 1.125 gets reduced to t=
K2 1 xA 1 ln + k1 CA 0 (1 − x A ) k1 1 − x A
(2.126)
This equation can be written in linear form as
y = a1x1 + a2 x2
(2.127)
where
xA x1 = CA 0 (1 − x A )
1 x2 = ln 1 − xA a1 =
a2 =
K2 k1
1 k1
and y = t
Using the CA versus time t data recorded in the batch reactor experiment, values of x1, x2 and y are calculated and this is illustrated in Table 2.2. Using the values of x1, x2 and y listed in Table 2.2, the values of coefficients a1 and a2 are estimated by the method of linear regression (Appendix B). Parameters k1 and k2 are calculated using the estimated values of a1 and a2, k1 = 1/a1, k2 = a2/a1.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 50
Green Chemical Engineering
Table 2.2 Illustration of Calculation of x1, x2 and y from the Batch Reactor Data for Estimation of Kinetic Parameters xA = 1 −
t
CA
0 t1 t2 t3 . . . ti . . tN
CA0 CA1 CA2 CA3 . . . CAi . . CAN
CA C A0
xA x1 = C A 0 (1 − x A )
0 xA1 xA2 xA3 . . . xAi . . xAN
1 x2 = ln 1 − x A
y=t
0 x21 x22 x23 . . . x2i . . x2N
0 y1 y2 y3 . . . yi . . yN
0 x11 x12 x13 . . . x1i . . x1N
Problem 2.7 A liquid-phase reaction A → B + C is carried out in a batch reaction vessel at a temperature of 150°C. Dissociation of reactant A to products B and C follows non-elementary rate steps and the rate equation is given by
(− rA ) =
k1CA2 kmol 1 + k 2C A m 3 min
The concentration of CA in the reaction vessel is monitored at different time intervals and these values are reported below: Time, t (min) 0 7.5 16 35 60 85 120 170 240 360
CA (kmol/m3) 2 1.9 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4
Estimate the rate constants k1 and k2. is
The initial concentration of A, CA0 = 2 kmol/m3. The integrated form of the rate equation
t=
k2 1 1 xA + ln k1 CA 0 (1 − x A ) k1 1 − x A
www.Ebook777.com
Free ebooks ==> www.ebook777.com 51
Introduction to Kinetics and Chemical Reactors
This equation written in linear form is
y = a1x1 + a2x2
xA 1 where y = t; x1 = ; x2 = ln CA 0 (1 − x A ) 1 − x A and coefficients a1 and a2 are
a1 =
1 k ; a2 = 2 k1 k1
The conversion x A = 1 − (CA /CA0 ) . The values of x1 and x2 are calculated using CA versus t data and listed in the table below.
Time, t (min) 0 7.5 16 35 60 85 120 170 240 360
CA (kmol/m3) 2 1.9 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4
xA x1 = C A 0 (1 − x A )
xA 0 0.05 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
1 x2 = ln 1 − xA
0 0.0263 0.0555 0.1250 0.2143 0.3333 0.5000 0.7500 1.1667 2.00
0 0.507 0.1054 0.2231 0.3566 0.5108 0.6931 0.9163 1.2040 1.6094
By fitting the data to the linear equation, the values of the coefficients a1 and a2 are estimated as
a1 = 93.42
a2 = 107.9
And the values of parameters k1 and k2 are
k1 =
1 = 0.0107 a1
k1 =
a2 = 1.1553 a1
Note: Refer MATLAB program: kinet_non_elem.m
www.Ebook777.com
Free ebooks ==> www.ebook777.com 52
Green Chemical Engineering
2.1.11 Catalysis: Mechanism of Catalytic Reactions—A Brief Introduction Reactants, in the process of getting converted into products, pass through a high-energy activated state. The energy required to transform the reactants to an activated state is the activation energy, ΔE. The activation energy determines the speed or rate of a chemical reaction at a particular temperature. The larger the value of activation energy ΔE, the slower the speed of reaction. At times, for certain reactions, the activation energy is so high and the rate so low that the reaction may be considered as infeasible for all practical purposes. For example, the activation energy involving reaction between N2 and O2 in the atmospheric air is so high that the reaction is infeasible at ambient temperature (otherwise, no O2 would have been left in the atmosphere for sustenance of life on Earth). However, if the atmospheric air gets exposed to a very high temperature of around 800–1000°C, N2 will react with O2 to produce oxides of N2 (NO/NO2/N2O), as the rise in temperature would substantially increase the rate of reaction. However, temperature cannot be raised beyond a certain limit as a very high temperature may lead to decomposition of chemical products. If a chemical reaction required is infeasible due to high activation energy and if the reaction temperature cannot exceed some permissible limit, it is necessary to look for an alternate reaction mechanism with lower activation energy so as to make the reaction practically feasible at a reasonably high temperature. This is indeed achieved by the addition of a catalyst. A catalyst is a foreign substance that, when added to a reaction, splits the single-step reaction into a multistep reaction having much lower activation energy than the original reaction. Reduction in activation energy results in a multifold increase in reaction rate. Consider a single-step reaction between compounds A and B having a high activation energy ΔE, which renders the reaction practically infeasible:
A + B → C : ΔE Let a catalyst denoted as X be added to the reaction. Represent the catalysed reaction as
A + B X →C
Normally, a catalyst is a solid substance on the surface of which the chemical compound A or B or both A and B get chemically adsorbed (i.e. chemisorbed). Let us assume for the time being that only A and not B gets chemisorbed on to the surface of X. This would result in the split up of the single-step reaction into multistep cyclic reactions listed below: Step 1: Adsorption of A on to X, with activation energy ΔE1
A + X ⇔ A ⋅ X : ΔE1
This is a reversible step in which the chemisorbed compound A ⋅ X attains equilibrium with free molecules of A and vacant catalyst surface X. Step 2: Reaction of B with A ⋅ X, with activation energy ΔE2
B + A ⋅ X → C ⋅ X : ΔE2 Step 3: Desorption of C from X, with activation energy ΔE3
C ⋅ X ⇔ C + X : ΔE3
www.Ebook777.com
Free ebooks ==> www.ebook777.com 53
Introduction to Kinetics and Chemical Reactors
Uncatalysed reaction
Energy ∆E2
∆E ∆E1
Catalysed reaction
∆E3 A·X+B C·X
C (product)
A+B Reactants Reaction coordinate
Figure 2.19 Energy diagram for uncatalysed and catalysed reactions.
This is also a reversible step in which chemisorbed compound C ⋅ X attains equilibrium with free molecules of C and vacant catalyst surface. The three reaction steps listed above constitute the mechanism of a solid catalysed reaction, proposed by Langmuir and Hinshelwood. The energy diagram for uncatalysed and catalysed reactions is shown in Figure 2.19. It is seen that the activation energies ΔE1, ΔE2 and ΔE3 associated with steps 1, 2 and 3 of the catalysed reaction are much lower than the activation energy of the uncatalysed reaction. Thus, the catalyst provides an alternative reaction path with reduced activation energy resulting in substantial increase in the reaction rate. Further, reaction steps 1, 2 and 3 are cyclic, as the catalyst material that takes part in the reaction cycle gets regenerated in each cycle. Thus, a catalyst is a material that takes part in the reaction without actually getting consumed by the reaction. By repeatedly taking part in the reaction cycle, one molecule of catalyst material can convert infinitely many molecules of reactants into products. Derivation of kinetic rate equations for solid catalysed chemical reactions is presented in the following section. Phenomena of catalysis and its applications are more elaborately discussed in Appendix A. 2.1.11.1 Kinetics of Solid Catalysed Chemical Reactions: Langmuir–Hinshelwood Model Langmuir–Hinshelwood proposed a model to explain the kinetics of solid catalysed chemical reactions. Later, Hougan and Watson applied the Langmuir–Hinshelwood model to a number of complex reactions. Hence, the kinetic model for solid catalysed reactions is generally referred to in the literature as the Langmuir–Hinshelwood–Hougan–Watson (LHHW) model. According to this model, the catalytic reaction involves three steps, namely, adsorption, surface reaction and desorption. In the adsorption step, the reactant molecule gets chemisorbed on to the free vacant site (active site) in the solid catalyst particle resulting in the formation of an intermediate compound. In the reaction step, this chemisorbed intermediate compound undergoes reaction on the catalyst surface resulting in the formation of the product. Finally, in the desorption step, the chemisorbed product molecule gets desorbed from the catalyst surface. In this section, rate equations are developed for some of the standard reactions.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 54
Green Chemical Engineering
I. Rate equation for A ⇔ B Consider a reversible catalytic reaction X
A⇔B
We will write the rate equations for the three steps: Step 1 (Adsorption): Chemisorption of reactant A on to vacant site l resulting in the formation of intermediate compound A ⋅ l is a reversible step kA A + l A⋅l k A′
The equation for the rate of adsorption of A, rA, is written assuming simple mass action law to be applicable: C rA = k A CACl − Al KA
(2.128)
where CA: concentration of A on the catalyst surface (not attached to the surface) Cl: concentration of vacant site CAl: concentration of chemisorbed A k A: chemisorption rate constant of A k K A: adsorption equilibrium constant of A = A k A′ k A′ : Desorption rate constant of A Step 2 (Surface Reaction): The reaction of chemisorbed A leading to the formation of product B at the chemisorbed active site k
r Al Bl k′
r
The rate of surface reaction, rs, is
C rs = k r CAl − Bl Kr
(2.129)
where CB1: concentration of chemisorbed product B kr: reaction rate constant of forward reaction kr Kr: reaction equilibrium constant = ’ kr k r′ : reaction rate constant of reverse reaction Step 3 (Desorption): The desorption of chemisorbed B resulting in the release of product molecule B from the active site l is a reversible step.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 55
Introduction to Kinetics and Chemical Reactors
k′
B Bl B + l k
B
The rate of desorption of B, rB, is C rB = kB Bl − CACl KB
(2.130)
where CB: concentration of product B on the catalyst surface (not attached to the surface) kB: rate constant of adsorption of B k KB: adsorption equilibrium constant of B = B’ kB kB′ rate constant of desorption of B Of the three steps, the surface reaction step is the slowest and is the rate-controlling step. So the rate of the surface reaction, rr, is taken as the overall rate of catalytic reaction C r = k r C Al − Bl Kr
(2.131)
Further, it is assumed that the intermediate compounds formed, namely, CAl and CBl, are in a state of pseudo-equilibrium. The rate at which an intermediate compound is formed (by absorption) is the same as the rate at which it is dissociated (by desorption). So the intermediate compounds Al and Bl are in a stationary state. Thus, taking rA = 0 and rB = 0, we get
CAl = K A CA Cl (2.132)
CBl = KB CB Cl (2.133)
Substituting Equations 2.132 and 2.133 for CAl and CBl, respectively, in Equation 2.131, we get C r = k r K A Cl C A − B K
(2.134)
where K = net equilibrium constant =
Kr K A KB
Any active site on the catalyst particle is either vacant or adsorbed to A or adsorbed to B. So the total fixed number of active sites Ct in a catalyst particle is the sum of vacant sites (Cl), sites chemisorbed to A (CAl) and sites chemisorbed to B (CBl). Thus
Ct = Cl + CAl + CBl (2.135) Substituting CAl = k ACACl and CBl = KBCBCl in Equation 2.135, we get
Cl =
Ct 1 + k AC A + kBCB
www.Ebook777.com
(2.136)
Free ebooks ==> www.ebook777.com 56
Green Chemical Engineering
Substituting Equation 2.136 for Cl in rate Equation 2.134, we get the overall rate equation as
C CA − B K r = k r K ACt 1 + K ACA + K BCB
(2.137)
We can write the rate equation in the final form as
C CA − B K r = k 1 + K ACA + K BCB
(2.138)
where k: overall rate constant = krK ACt II. Rate equation for A + B C Consider the reversible catalytic reaction A + B C
There are two possible mechanisms for this reaction depending on whether both A and B are chemisorbed or only A and not B is chemisorbed to the active site. In this section, rate equations are derived for both the mechanisms. a. Mechanism 1 (A but not B is chemisorbed) In this reaction mechanism, reactant A is chemisorbed to the vacant site and B reacts directly with the chemisorbed A. Step 1 (Adsorption): Chemisorption of reactant A on to the vacant site l resulting in the formation of intermediate compound Al. k
A A + l Al k′
A
The rate of adsorption of A, rA, is
C rA = k A CACl − Al KA
(2.139)
where k A: adsorption rate constant of A K A: adsorption equilibrium constant of A Step 2 (Reaction): B reacts directly with chemisorbed A, leading to the formation of product C (adsorbed to the active site) k
r B + Al Cl k′ r
www.Ebook777.com
Free ebooks ==> www.ebook777.com 57
Introduction to Kinetics and Chemical Reactors
The rate of reaction, rr, is C rr = k r CBCAl − Cl Kr
(2.140)
where CCl: concentration of chemisorbed C Kr: reaction equilibrium constant = kr: reaction rate constant
kr k r′
Step 3 (Desorption): Desorption of chemisorbed C leading to the release of product C from the active site. kc′ Cl C+l kc
The rate of desorption of C, rC, is
C rC = kC Cl − CCCl KC
(2.141)
where kC: adsorption rate constant of C KC: adsorption equilibrium constant of C Surface reaction is the slowest step and is rate controlling. So the rate of surface reaction, rr, is taken as the overall rate of the catalytic reaction, r C r = k r CBCAl − Bl Kr
(2.142)
Further assuming that the intermediate products formed Al and Cl are in a stationary state, we get
CAl = K ACACl (2.143)
CCl = KCCCCl (2.144)
Substituting Equations 2.143 and 2.144 for CAl and Ccl, respectively, in the rate Equation 2.142, we get C r = k r K A Cl C A CB − C K
where
K: overall equilibrium constant =
Kr K A KC
www.Ebook777.com
(2.145)
Free ebooks ==> www.ebook777.com 58
Green Chemical Engineering
The total fixed number of active sites Ct in the catalyst particle is the sum of vacant sites (Cl), sites chemisorbed to reactant A (CAl) and sites chemisorbed to product (CCl).
Ct = Cl + CAl + CCl (2.146) Substituting CAl = K ACACl and CCl = KCCCCl in Equation 2.146, we get Cl =
Ct 1 + K AC A + KCCC
(2.147)
Substituting Equation 2.147 for Cl in Equation 2.145, we get the rate equation as
CC C ACB − K r = ( k r K ACt ) 1 + K AC A + KCCC
(2.148)
Finally, the rate equation is written as C k C A CB − C K r= 1 + K A C A + KCCC
(2.149)
where k: overall rate constant = krK ACt b. Mechanism 2 (Both A and B are chemisorbed) In this reaction mechanism, both the reactants A and B are chemisorbed to the vacant active sites and the reaction takes place between molecules of A and B chemisorbed to adjacent sites. Step 1 (Adsorption): Chemisorptions of A to the vacant active site l resulting in the formation of intermediate product Al: kA A + l Al k ′
A
Rate of adsorption of A, rA, is
C rA = k A CA Cl − Al KA
(2.150)
Chemisorptions of B to the vacant site l leading to the formation of intermediate product Bl: k
B B + l Bl k′ B
www.Ebook777.com
Free ebooks ==> www.ebook777.com 59
Introduction to Kinetics and Chemical Reactors
Rate of adsorption of B, rB, is C rB = kB CBCl − Bl KB
(2.151)
Step 2 (Surface Reaction): Reaction between A and B chemisorbed to the adjacent sites leading to the formation of product C that is adsorbed to one of the two adjusted sites leaving the other site vacant kr Al + Bl Cl + l kr′
A chemisorbed molecule of A cannot react with any chemisorbed molecule of B other than the one chemisorbed to a site adjacent to it. So the forward rate is taken as proportional to the concentration of adsorbed A (CAl) multiplied by the fraction of the adjacent sites (θB) occupied by B molecules. This fraction θB = (CBl/Ct), where Ct is the concentration of total number of active sites. Similarly, the reserve rate is proportional to the concentration of adsorped C(CCl) multiplied by the fraction of the adjacent vacant sites (θl), where θl = (Cl/Ct). So the rate of surface reaction, rr, is C C rr = k rCAl Bl − k r′ Ccl l Ct Ct
(2.152)
that is rR =
kr C C C AlCBl − Cl l Ct KR
(2.153)
Step 3 (Desorption): Desorption of chemisorbed C leading to the release of product C from the active site l k′
c Cl C + l k
c
Rate of desorption of C, rC, is
C rC = kc Cl − CCCl KC
(2.154)
Surface reaction is the slowest step and is rate controlling. So overall rate r of the catalytic reaction is
r=
kr C C C AlCBl − Cl l Ct KR
(2.155)
Assuming that all the intermediate compounds Al, Bl and Cl are in stationary state, we get
CAl = K A CA Cl (2.156)
www.Ebook777.com
Free ebooks ==> www.ebook777.com 60
Green Chemical Engineering
CBl = KB CB Cl (2.157)
CCl = KC CC Cl (2.158) Substituting CAl = K ACACl, CBl = KBCBCl and CCl = KCCCCl in Equation 2.155, we get k rCl2 k C K A K BCACB − C C Ct KR
r=
(2.159)
Total number of active sites (Ct) in a catalyst particle is the sum of all vacant sites (Cl), sites chemisorbed to A (CAl), sites chemisorbed to B (CBl) and sites chemisorbed to C (CCl).
Ct = Cl + CAl + CBl + CCl (2.160)
Substituting Equations 2.156, 2.157 and 2.158 for CAl, CBl and CCl respectively, in Equation 2.160, we get
Cl =
Ct K AC A + K BCB + KCCC + 1
(2.161)
Substituting Equation 2.161 for Cl in the rate Equation 2.159, we get
CC C ACB − K r = ( k rCt K A K B ) [1 + K ACA + KBCB + KCCC ]2
(2.162)
which can be finally written as
CC CACB − K r=k [1 + K ACA + KBCB + KCCC ]2
where k = overall rate constant = krK AKBCt and
K K K K = overall equilibrium constant = R A B KC
Problem 2.8 The experimental data on a gas-phase reaction
A + B → C
over a solid catalyst has been reported.
www.Ebook777.com
(2.163)
Free ebooks ==> www.ebook777.com 61
Introduction to Kinetics and Chemical Reactors
Rate ( −rA )
mol g.cat.h
PA(atm)
PB(atm)
PC(atm)
0.04338
0.112
1.276
0.102
0.02037
0.212
0.555
0.205
0.01393
0.325
0.328
0.226
0.0809
0.450
0.193
0.352
0.00643
0.487
0.158
0.423
0.00487
0.546
0.122
0.510
0.00384
0.632
0.093
0.532
0.00305
0.738
0.073
0.629
0.00245
0.772
0.060
0.702
0.00213
0.823
0.052
0.754
0.00175
0.921
0.043
0.857
By fitting the experimental data to the rate equation
(− rA ) =
kPA PB 1 + K A PA + KC PC
estimate the values of rate constant k and the adsorption equilibrium constants K A and KC. The rate equation can be written in linear form by inverting the rate expression 1 1 1 K A 1 KC PC = + + (− rA ) k PA PB k PB k PA PB
define,
y=
1 1 P 1 ; x1 = ; x2 = ; x3 = C PA PB PB PA PB (− rA )
The rate equation can be written in linear form as
y = a1x1 + a2 x2 + a3 x3
where the coefficients a1, a2 and a3 are
a1 =
1 K K ; a2 = A ; a3 = C k k k
www.Ebook777.com
Free ebooks ==> www.ebook777.com 62
Green Chemical Engineering
The values of x1, x2, x3 and y are calculated and listed in the table below. 1 PB
1 x1 = PA PB
x2 =
6.9973 8.499 9.381 11.514 13.02 15.02 17.01 18.56 21.59 23.37 25.25
0.7837 1.802 3.049 5.183 6.329 8.197 10.753 13.70 16.67 19.23 23.26
x3 =
PC PA PB
0.7137 1.742 2.120 4.053 5.509 7.656 9.051 11.68 15.15 17.62 21.64
y=
1 ( − rA )
23.05 49.09 71.79 123.61 155.52 205.34 258.40 327.87 408.16 469.48 571.43
By fitting the data to the linear equation, the values of the coefficients a1 and a2 are estimated as (linear regression) a1 = 0.6450
a2 = 14.79
a3 = 9.73 And the values of kinetic parameters k, K A and KC are 1 = 1.5505 a1
k =
KA =
a2 = 22.93 a1
KC =
a3 = 15.08 a1
Note: Refer MATLAB program: kinet_lang_hins.m 2.1.12 Kinetics of Enzyme-Catalysed Biochemical Reactions Enzymes are biological catalysts present in the cells of microorganisms. They act upon organic reactants called substrates and convert them into products (Suresh et al., 2009a,b,c). In biological treatment processes, substrates are organic pollutants that act as nutrients necessary to sustain the growth of microorganisms. Enzymes present in microorganisms act upon organic pollutants and break them down into non-hazardous products. Enzymecatalysed reactions are biological reactions in which the conversion of substrates into products is catalysed by enzymes. Michaelis–Menton proposed a mechanism for enzymecatalysed reactions, which is represented as
k1 k3 E + S ES → P k 2
www.Ebook777.com
Free ebooks ==> www.ebook777.com 63
Introduction to Kinetics and Chemical Reactors
where E is the enzyme, S is the substrate and P is the product. In this reaction mechanism, the substrate binds on the enzyme E to form energised complex ES. The energised complex ES is in dynamic equilibrium with free substrate S and free enzyme E. The energised complex gets converted into product P. The reaction step involving the formation of product is the slowest step that is rate controlling. Thus, the rate of formation of product, r p, is written as
rp = k3 ⋅ [ES] (2.164)
where [ES]: concentration of complex ES Complex ES is assumed to be in a stationary state as the rate of formation of ES is equal to the rate of dissociation of ES. Thus
k1[E][s] = k2[ES] (2.165)
or [ES] =
[E][S] kM
(2.166)
[E]: Concentration of free enzyme E [S]: Concentration of substrate S k kM: Equilibrium constant = 1 k2 The total amount of enzyme E0 is fixed as there is no net consumption of enzyme. Thus, total concentration of enzyme, E0, is the sum of concentrations of free enzyme [E] and bound enzyme [ES].
E0 = [E] + [ES] (2.167) Substituting [E] = E0 − [ES] in Equation 2.166 and solving for [ES], we get
[ES] =
E0 [S] k M + [S]
(2.168)
On insertion of Equation 2.168 in Equation 2.164, we get the rate equation for the enzymecatalysed reaction as
rP =
k[S] k M + [S]
(2.169)
where k = k3E0. This equation is known as the Michaelis–Menton equation. A plot of rate rp versus substrate concentration [S] (Figure 2.20) shows that the rate equation follows first-order kinetics rp = (k/k M )[S] at low substrate concentrations and zero-order kinetics rp = k at high substrate concentrations. The tangent to rp versus [S] plot drawn at [S] = 0 intersects rp = k at a point corresponding to [S] = kM. This method of tangent can be used to determine the kinetic parameters k and kM. Alternatively, we can write the rate equation in linear form as (1/rp ) = (k M /k )(1/[S]) + (1/k ) by inverting Equation 2.169. Thus, by making a linear plot of
www.Ebook777.com
Free ebooks ==> www.ebook777.com 64
Green Chemical Engineering
k
A
rP (rate)
Tangent at [S] = 0 B Substrate concentration [S]
kM
Figure 2.20 Rate rp versus substrate concentration [S] for enzyme-catalysed reaction.
(1/rp) versus (1/[S]) and calculating the slope (kM/k) and intercept (1/k) of the straight line, the kinetic parameters k and kM can be estimated. There are some enzyme-catalysed reactions in which the substrate [S] inhibits the formation of product P by binding to the energised complex ES to form a complex ES2. The mechanism of this reaction is represented as k3
E + S ES → P ES + S ES2
The formation of product P is the rate-controlling step, and the overall rate equation is
rP = k3[ES] (2.170)
Assuming the intermediate complexes ES and ES2 to be in a pseudo-equilibrium state (stationary state), we can write the equations for [ES] and [ES2] as
[ES] =
[E][S] KM
(2.171)
[ES2 ] =
[ES][S] KS
(2.172)
where K M and KS are the equilibrium constants. As there is no net consumption of enzyme, total enzyme concentration E0 is fixed and it is equal to the sum of free enzymes and bound enzymes. Thus
E0 = [E] + [ES] + [ES2] (2.173)
www.Ebook777.com
Free ebooks ==> www.ebook777.com 65
Introduction to Kinetics and Chemical Reactors
Solving Equations 2.171, 2.172 and 2.173 for [ES], we get
[ES] =
E0 [S] K M + [S ] +
[S]2
(2.174)
KS
Inserting Equation 2.174 in Equation 2.170, we obtain the rate equation for the substrateinhibited enzyme-catalysed reaction as k [S ]
rP = kM
[S]2 + [S ] +
(2.175)
KS
where k = k3E0 . Problem 2.9 A 2 kmol/m3 of a substrate S kept in a batch reaction vessel undergoes reaction in the presence of an enzyme. Concentration of substrate recorded as a function of time is reported in the table below. Time, t (h)
CS (kmol/m3)
0 0.5 1.0 1.5 2.0 2.5 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0
2 1.78 1.56 1.34 1.12 0.926 0.748 0.422 0.238 0.104 0.044 0.018 0.008 0.003
Verify if the given data confirm to the Michaelis–Menton kinetic rate equation
rP =
kCS k M + CS
A plot of Cs versus t is made using the experimental data given in the problem. A fifth power polynomial fits the given data with minimum error as shown in Figure P2.9a. The rate rP = −dCS/dt is evaluated by taking the derivative of the polynomial equation and
www.Ebook777.com
Free ebooks ==> www.ebook777.com 66
Green Chemical Engineering
calculating values of the derivative for different values of Cs. By inverting the kinetic rate equation, we obtain the rate expression in linear form as
y = a0 + a1x
where x = 1/CS; y = 1/rP; a0 = 1/k; a1 = K M/k. Thus, a plot of 1/rP versus 1/CS is a straight line with slope = a1 and intercept = a0 (Figure P2.9b). The data used for this plot are listed in the table below.
CS 2.0 1.78 1.56 1.34 1.12 0.926 0.748 0.422 0.238 0.104 0.044 0.018 0.008 0.003
(a)
rP
1 CS
0.4058 0.4391 0.4494 0.4412 0.4186 0.3854 0.3449 0.2536 0.1643 0.0904 0.0395 0.0129 0.0062 0.0089
0.500 0.5618 0.6410 0.7463 0.8929 1.080 1.337 2.3697 4.202 9.615 22.73 55.55 125 —
1.8
Slope = 1.0384 Intercept = 1.5604
25
1.6 1.4
20
1.2
1/(–rA)
Substrate conc. CS (kmol/m3)
2.4645 2.277 2.225 2.266 2.389 2.595 2.899 3.943 6.087 11.061 25.344 77.50 160.6 —
(b) 30
2
1 0.8
15 10
0.6 0.4
5
0.2 0
1 rP
0
5 Time (t, h)
10
0
0
5
10
15
20
25
1/Cs
Figure P2.9 (a) Fitting the CS versus t data to a polynomial equation (of power 5). (b) (1/rA) versus (1/CA) plot for estimation of kinetic parameters of the Michaelis–Menton equation.
www.Ebook777.com
Free ebooks ==> www.ebook777.com Introduction to Kinetics and Chemical Reactors
67
The values of coefficients a0 and a1 are
a0 = 0.8993
a1 = 1.2874
k =
KM =
1 = 1.112 a0 a1 = 1.4316 a0
Note: Refer MATLAB program: kinet_enzyme_cat.m
2.2 Chemical Reactors: An Introduction Chemical reactors are process vessels that are used in chemical industries for carrying out chemical reactions. Based on the mode of operation, reactors are broadly classified as batch reactors and continuous-flow reactors. In batch reactors, reactants are fed into the reaction vessel at the time of start-up and the products drawn out of the vessel after a specified period of time called reaction time (or batch time). Continuous-flow reactors are encountered more often in practice than batch reactors, as more than 80% of process industries are continuous processing industries. In the case of continuous-flow reactors, reactants are fed into, and products drawn out of, the reaction vessel continuously. Based on the nature of the reaction carried out in a reactor, it is classified as a homogeneous or heterogeneous reactor. Homogeneous reactors are single-phase reactors in which all the reacting species are in one single phase (either gas or liquid). Heterogeneous reactors are multiphase reactors in which reactions occur between chemical species spread across different phases (gas, liquid and solid). Heterogeneous reactors are further classified as non-catalytic and catalytic reactors. In catalytic reactors, solid catalysts are used to speed up the chemical reaction. A broad classification of reactors is depicted in Figure 2.21. 2.2.1 Homogeneous Reactors: Holding Vessels Homogeneous reactors are simple holding vessels that are designed to accommodate a specified volume of the reaction medium containing reactants and products. They are gasphase reactors if all the reactants and products are in a gaseous state; and liquid-phase reactors if all the reacting species and products formed are in a liquid state. As homogeneous reactors are single-phase reactors, the reacting species are free to move from one location to another within the reactor volume; thus, with increased mobility, the frequency of collision between the reacting molecules and chances of occurrence of reaction increases. Mobility of molecules at a specified temperature is higher in gas-phase reactors than in liquid-phase reactors. In liquid-phase reactors, mobility of the molecules can be
www.Ebook777.com
Free ebooks ==> www.ebook777.com 68
Green Chemical Engineering
Chemical reactors
Homogeneous reactors (single phase)
Gas-phase reactor A(g) + bB(g) → P
Liquid-phase reactor A(l) + bB(l) → P
Gas–solid reactors A(g) + bB(s) → P
Heterogeneous reactors (multiphase)
Non-catalytic reactors (two phase)
Catalytic reactors
Gas–liquid reactors A(g) + bB(ℓ) → P
Two phase reactors A(g/l) X(CAT) P
Three phase reactors X(CAT) A(g) + bB(l) P
Figure 2.21 Classification of reactors.
increased by keeping the reacting phase in a turbulent state. This is done either by mixing the reaction medium with the help of an agitator or by maintaining turbulent flow conditions in the reactor. Homogeneous reactors, being simple holding vessels, take the shape of either a ‘tank’ or a ‘tube’. If the L/D (length by diameter) ratio of the vessel is between 1 and 3, the reactor is called a tank reactor and if the L/D ratio is greater than 50, the reactor is called a tubular reactor. The reacting phase in the tank reactor is maintained in a turbulent state by mixing the fluid with the help of a stirrer (or agitator) and hence the tank reactor is known as a continuous stirred tank reactor (CSTR). A schematic diagram of a CSTR with a constant volumetric hold up V and a steady volumetric fluid flow rate q is shown in Figure 2.22. In tubular reactors, fluid mixing or turbulence is achieved in the reaction phase by maintaining turbulent flow conditions in the tubular vessel. A schematic diagram of a tubular reactor is shown in Figure 2.23. The process design of a homogeneous reactor involves the calculation of the reactor volume required to achieve a specified fractional conversion of the reacting species to the final product. For a given feed flow rate q, it is the reactor volume v that determines the
q
q V
Figure 2.22 Continuous stirred tank reactor.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 69
Introduction to Kinetics and Chemical Reactors
q
q
V
Figure 2.23 Tubular reactor.
space time (τ = v/q), which is the mean reaction time available for the reacting species to undergo reaction in the vessel volume. The extent of conversion achieved within the available reaction time depends on the rate of reaction and the level of fluid mixing (turbulence) that is prevalent in the reactor volume. Fluid mixing is achieved with the help of an agitator in the CSTR and by maintaining turbulant flow conditions in the tubular reactor. Appropriate design of a homogeneous reactor requires a deeper understanding of the fluid mixing pattern and its effect on the reaction and will necessarily involve the formulation and solution of complex flow equations that are practically intractable. As a first step towards addressing this complexity and providing a tractable solution to the reactor design problem, certain simplified assumptions about fluid mixing patterns are made and the reactors having these simple fluid mixing patterns are termed as ideal reactors. Thus, we have ideal CSTRs and ideal tubular reactors in which fluid mixing is assumed to take place in a predefined manner or pattern. 2.2.1.1 Ideal Continuous Stirred Tank Reactor (CSTR) Ideal CSTR is a CSTR in which the mixing of fluid in the agitated vessel is assumed to be thorough or perfect. Perfect mixing is that which results in uniformity of solute concentration in the vessel volume. Consider a feed stream (Figure 2.24) flowing at volumetric rate q, having a reactant A at concentration CAO, being fed into an ideal CSTR with constant fluid hold up V. Let CAf be the concentration of reactant A in the outlet stream. The reactor is assumed to be at steady state. As the mixing is assumed to be perfect in the reaction vessel, uniformity in the concentration of A is achieved throughout the reactor volume and this concentration will be equal to the concentration of A in the outlet stream, that is, CAf. This assumption simplifies the design of an ideal CSTR, as discussed below. Assume that a reaction of the type A → B is carried out in the reactor and the kinetic rate equation is (−rA ) = kC A n
(2.176)
q CA0
q CAf V
CAf
Figure 2.24 Ideal CSTR.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 70
Green Chemical Engineering
where (−rA) is the specific reaction rate of disappearance of A in kmol/(s) (m3), k is the reaction rate constant and n is the order of reaction. k is related to the reaction temperature T by the Arrhenius law k = k0 e − ∆E/RT
(2.177)
where k0 is called the frequency factor, ΔE is the activation energy and R is the gas law constant. k can be treated as a constant if constant temperature is assumed (i.e. heat of reaction is neglected). Taking a steady-state balance of A around the reactor, we get Rate of flow of A Rate of flow of A = + into the reactor out of the reactor
Rate of disappearance of A due to reaction in the reactor
(2.178)
that is qCA 0 = qCA f + (− rA (C Af ))V
(2.179)
Re-arranging Equation 2.179, we get τ=
(CA 0 − CAf ) V = q (− rA (C A f ))
(2.180)
where τ is the space time. Equation 2.180 is called the design equation or performance equation for ideal CSTR. The fractional conversion of A, xAf and the final concentration of A, CAf in the outlet stream are related by Equation 2.181. CAf = CA 0 (1 − X A f )
(2.181)
The design of an ideal CSTR amounts to calculating the reactor volume V (using Equation 2.180) required to achieve a specified conversion xAf of reactant A present in the feed stream at concentration CA0. 2.2.1.2 Ideal Tubular Reactor Fluid mixing in tubular reactors is achieved by maintaining very high velocity of the fluid through the tubular vessel so that the flow is turbulent with Reynolds number value exceeding 50,000. For such high turbulent flow conditions, the velocity gradient in the radial direction is negligible except in the viscous sub-layer region closer to the wall, as shown in Figure 2.25. If the velocity gradient in the radial direction is completely neglected from the central axis to the tube wall, the velocity profile assumes a flat shape (see Figure 2.25) and the fluid flow with flat velocity profile is known as plug flow. Plug flow is a theoretical approximation to the turbulent flow. Plug flow cannot exist in reality as it contradicts the no-slip (zero-velocity) condition at the tube wall. The plug flow condition also implies that the fluid elements move at the same velocity in the axial (flow) direction.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 71
Introduction to Kinetics and Chemical Reactors
Viscous sublayer
Plug flow (flat velocity profile) Laminar flow (parabolic velocity profile)
Turbulent flow (nearly flat velocity profile)
Figure 2.25 Velocity profile in tubular vessel.
According to the principle of analogy between momentum and mass transfer, velocity profile and concentration profile are identical to each other in a given flow situation. Thus, flat velocity profile assumed in the plug flow condition implies that the concentration profile will also be flat. It means that the reactant concentration at a particular axial position in the tubular vessel does not vary in the radial direction, that is, the reactant concentration is uniform in the radial direction. As uniformity in concentration is achievable only through complete mixing, one may state that the plug flow condition ensures complete mixing in the radial direction. Thus, the plug flow reactor (PFR) is an idealisation of a tubular reactor in which the flow is highly turbulent and a complete mixing of fluid takes place in the radial direction. 2.2.1.2.1 Ideal Plug Flow Reactor The plug flow reactor, by itself, is an ideal tubular reactor in which the fluid mixing in the radial direction is assumed to be thorough/complete. Having defined the mixing pattern in the radial direction, the question about the pattern of mixing in the axial direction arises. How do the fluid elements mix in the axial (flow) direction? A simple thing to assume is that the fluid elements do not mix at all in the axial direction. Thus, a plug flow reactor in which there is no mixing of fluid elements in the axial direction is termed as an ideal plug flow reactor. The ideal plug flow reactor is a tubular reactor in which there is complete mixing in the radial direction and no mixing in the axial direction. Consider a reacting fluid containing the reactant A at concentration CA0, being fed into an ideal PFR (Figure 2.26) of volume V at a volumetric flow rate ‘q’. Let A → B be the reaction carried out in the reactor and the kinetic rate equation is (− rA ) = kCA n . As the fluid moves through the reactor from inlet to outlet, the concentration of the reactant A, CA in the fluid decreases gradually due to the reaction and it attains a final value of CAf when it leaves the reactor. Change in reactant concentration CA through the reactor volume is depicted in Figure 2.27.
q CAO
CA + dCA
CA q
q dV
Figure 2.26 Ideal PFR.
www.Ebook777.com
q CAf
Free ebooks ==> www.ebook777.com 72
Green Chemical Engineering
CAO
Ideal PFR
CA Ideal CSTR CAf Inlet
Outlet
Reactor volume
Figure 2.27 Variation of reactant concentration CA through reactor volume.
Compared to PFR in which the concentration of A changes gradually from inlet to outlet through the reactor volume, in the CSTR, the concentration of A drops abruptly from CA0 to CAf at the reactor inlet and remains constant at CAf throughout the reactor volume. In an ideal PFR, although CA decreases in the axial direction, its value remains constant in the radial direction. Consider a section of elemental volume dV at an arbitrary position in the reactor (Figure 2.26). Let dCA be a change in concentration of A through volume dV. Taking a steady-state balance of A across the elemental volume dV, we get Rate of flow of A Rate of flow of A = + into the section dV out of the section dV
Rate of disappearance of A in the section dV due to reaction
that is qCA 0 = qCA f + (− rA (C Af ))dV
(2.182)
Rearranging the above equation, we get V
CAf
dCA
∫ dV = − q ∫ ( −r (C 0
CA 0
A
Af
))
(2.183)
that is
V τ= = q
CAo
dCA
∫ ( −r (C
CAf
A
Af
))
(2.184)
where τ is the space time. This equation is the design equation or the performance equation for ideal PFR. This equation is used for calculating the volume of ideal PFR required for achieving specified fractional conversion.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 73
Introduction to Kinetics and Chemical Reactors
2.2.2 Heterogeneous Reactors—Mass Transfer Equipment Unlike homogeneous reactors in which all the reacting chemical compounds are present in one single phase, in the heterogeneous reactors, the reactants are distributed in different phases. Heterogeneous reactors are multiphase reaction vessels that are designed to handle reactions occurring between chemical compounds present in two or more different phases. Consider a chemical reaction between compound A in phase P1 and compound B in the phase P2.
A( P1) + B( P 2) → Products
(2.185)
Reaction between compounds A and B can take place only if the two phases P1 and P2 are brought into contact with each other so that compound A in phase P1 will move to phase P2 crossing the phase boundary separating the two phases (Figure 2.28). Phase boundary (or interphase) is the common area of contact between the two phases. For example, the outer surface of a gas bubble rising through a column of liquid represents the phase boundary between the gas and the liquid phases. This phenomenon of transfer of a chemical compound from one phase to another across the phase boundary is known as mass transfer. The number of moles of A transferred across the phase boundary per unit time is the mass transfer rate, which increases with the interfacial area. The larger the interfacial area, the better the contact between the two phases and the higher the mass transfer rate. Process equipments that are used for mass transfer operations (e.g. absorption, distillation and adsorption) are essentially the process vessels that are specially designed to bring about better contact between two different phases by providing maximum interfacial area per unit volume of the vessel. So mass transfer equipment can also be called phase-contacting equipment or simply contacting equipment. In multiphase reactions, the mass transfer rate plays a crucial role in determining the overall rate of conversion of reactant to product. In the multiphase reaction between compound A and B discussed above, A moves from phase P1 to phase P2 and the reaction between A and B occurs in phase P2. Compound A is the limiting reactant as the overall conversion of A to final product is limited by the availability of A in phase P2, in which the reaction occurs. The larger the rate of mass transfer of A from phase Pl to phase P2, the higher the concentration of A in phase P2 and the greater the rate of reaction in phase P2. Thus, the mass transfer rate has a stronger influence on the overall conversion.
P1 Phase
A
B P2 Phase
Phase boundary Figure 2.28 Multiphase reaction.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 74
Green Chemical Engineering
Gas (CO2)
Liquid (NaOH solution)
CAf Bed of inert packing materials such as Raschig ring CAO Gas (CO2)
Liquid (Na2CO3 + H2O + NaOH)
Figure 2.29 Gas–liquid packed bed reactor.
Any mass transfer equipment that is used for contacting two different phases P1 and P2 can also be used as a heterogeneous reactor for carrying out reactions involving these phases. For example, consider a chemical reaction between CO2 (compound A) in gas phase (P1) and NaOH solution (compound B) in liquid phase (P2)
CO 2 ( g ) + 2NaOH(l) → Na 2CO 3 + H 2O
(2.186)
This reaction can be carried out in a packed tower, which is usually used for mass transfer operations involving gas and liquid phases such as absorption. Here, the reactor is the packed bed reactor (Figure 2.29). Consider the chemical reaction between FeS2 in the powder form (solid phase) and O2 in the gas phase:
2FeS 2 (s) + 5O 2 ( g ) → 2FeO + 4SO 2
As gas and solid phases are involved in this reaction, any gas–solid-containing equipment such as a fluidised bed can be used to carry out this reaction. Here, the heterogeneous reactor is the fluidised bed reactor (Figure 2.30). All heterogeneous reactors are essentially (some) types of mass transfer equipment, and hence their design involves the application of mass transfer principles. Consider the reaction between compound A (in phase P1) and compound B (in phase P2) being carried out in a heterogeneous reactor operating at steady state. At a particular location in the reactor, let CA1 and CA2 be the steady-state concentrations of compound A in phase P1 and phase P2, respectively (see Figure 2.31). Compound A is transferred from phase P1 to phase P2 across the phase boundary and it happens at a rate r1, which is proportional to the concentration difference driving force (CA1 – CA2), that is
r1 = k m ai (CA1 − CA 2 )
(2.187)
where r1 is the rate of transfer of A in kmol of A per m3 volume of reactor, ai is the specific interfacial area in m2 per m3 volume of reactor and km is the overall mass transfer coefficient. Assuming phase P2 to be a homogeneous phase (well-mixed phase) and compound
www.Ebook777.com
Free ebooks ==> www.ebook777.com 75
Introduction to Kinetics and Chemical Reactors
Solid feed S (FeS2)
Gas (O2 + SO2)
Solid (product)
Gas (O2) Figure 2.30 Gas–solid fluidised bed reactor.
A to be the limiting reactant, conversion of A into the final product takes place at a rate r2 in phase P2, which is proportional to the concentration CA2 (first-order kinetics), that is
r2 = krf2CA2 (2.188)
where r2 is the rate of conversion of A in kmol of A per m3 of the volume of phase P2, f2 is the fractional volume of phase P2 in the reactor and kr is the reaction rate constant. At steady state, rates r1 and r2 are equal. Equating r1 to r2 and solving the equation for CA2, we get CA 2 =
k m ai C A1 ( km ai + kr f2 )
k2
P1 Phase
A CA1
CA2 k1
B P2
Phase
Phase boundary Figure 2.31 Reactant concentrations in a multiphase reactant.
www.Ebook777.com
(2.189)
Free ebooks ==> www.ebook777.com 76
Green Chemical Engineering
Substituting Equation 2.189 for CA2 in Equation 2.188, we get an expression for rate ‘r’ that accounts for both mass transfer rate and kinetic reaction rate. This rate equation r=
C A1 1 1 + k a k r f2 m i
(2.190)
is called the global rate equation, and is used in the design of heterogeneous reactors. Both mass transfer coefficient km and reaction rate constant kr appear in the global rate equation (Equation 2.190), emphasising the fact that this rate equation accounts for the combined effect of mass transfer rate and kinetic reaction rate on the overall rate of conversion. Heterogeneous reactors discussed in this section so far are reactors that handle multiphase reactions, which take place without the aid of catalysts. Hence, these reactors are called non-catalytic reactors. Non-catalytic heterogeneous reactors are essentially twophase reactors broadly classified as ‘gas–solid reactors’ and ‘gas–liquid reactors’ based on the phases that are handled in them. We have already seen examples of these reactors in this section. 2.2.2.1 Heterogeneous Catalytic Reactors Chemical reactions that proceed at very slow rates can be speeded up by the addition of a foreign substance called a catalyst. Catalytic reactions are those reactions that take place with the aid of a catalyst substance and the reactors used for catalytic reactions are called catalytic reactors. Catalysts used in many reactions are solid substances and hence most of the catalytic reactors are heterogeneous reactors. Usually, very expensive metals such as platinum, silver or gold are used as catalyst material. However, the catalyst material is required only in very small quantity as the catalyst gets regenerated in each reaction cycle and is repeatedly reused. Unlike other chemical reagents, the catalyst is not fed continuously into the reaction vessel. A fixed quantity of catalyst material is kept in the reaction vessel and other chemical reactants (reacting fluids) are made to pass continuously over them through the reaction vessel. As the catalyst material is present in the reaction vessel only in very small quantity, it is necessary to provide sufficient contact between the catalyst material and the reacting fluid, so that a large number of reacting fluid molecules come into contact with each one of the catalyst molecules in the reaction vessel. This is achieved by taking porous support material such as alumina (Al2O3) and impregnating the catalyst molecules into its pores. Catalyst materials along with the supporting material constitute a catalyst pellet. Catalyst pellets are prepared in regular shapes such as sphere, cylinder and cubes and in sizes varying from 1″ to 5″. By virtue of their high porosity, support materials have a large surface area per unit volume of pellet. As the catalyst material is spread over the surface of the pores in the support material, a large interfacial area is made available for contact between the catalyst material and the reacting fluid per unit volume of the catalyst pellet although the quantity of catalyst material is very low. Schematic diagram of a spherical catalyst pellet is shown in the Figure 2.32. The diagram shows the pores in the catalyst pellet; the dots represent the catalyst material. The dots are the active site on to which the reacting molecules get adsorbed and converted into products. Catalytic reactors are heterogeneous reactors with a fixed quantity of catalyst pellets (or catalyst material in the form of powder) in a vessel, through which the fluid containing the reactants is passed continuously. The
www.Ebook777.com
Free ebooks ==> www.ebook777.com 77
Introduction to Kinetics and Chemical Reactors
Crystal material (Pt)
Pore Support material (Al2O3) Figure 2.32 Schematic diagram of a spherical catalyst pellet.
fluid stream containing the reactants is fed into the vessel at one end (inlet) and the stream containing the product and the unreacted reactants is drawn out from the other end (outlet). Catalyst pellets immersed in a fluid stream containing the reactants and products are found throughout the reaction vessel. In this case, the global rate equation should account for
i. Rate of transfer of reactant from the bulk fluid stream to the surface of the catalyst pellet (known as external mass transport) ii. Rate of transfer of reactant from the surface of the catalyst pellet to the active site by the diffusion through the pores (known as internal mass transport) iii. Rate of reaction at the active site Catalytic reactors are broadly classified as two-phase reactors and three-phase reactors depending upon the number of phases involved in the catalytic reaction. Consider a reaction between C2H4 (ethylene) and H2-producing C2H6 (ethane) in the presence of a solid catalyst CuO–Mgo (X):
CuO − MgO ( X )
C 2H 4 ( g ) + H 2 ( g ) → C 2H6 ( g )
(2.191)
The reactants and the products are in the gas phase and the catalyst is solid. The catalytic reactor used for carrying out this reaction is a two-phase reactor as the gas and solid phases are involved in the reaction. This reaction is usually carried out in a packed bed reactor, which is filled with catalyst pellets (see Figure 2.33). Consider the reaction between H2 (gas phase) and vegetable oil (liquid phase) taking place in the presence of a nickel powder catalyst (solid phase).
Vegetable oil(l) + H 2 ( g ) Ni(CAT) → Hydrogenated oil (Vanaspathi)
(2.192)
This reaction involves three phases. A reactor called a slurry reactor is used to carry out the reaction (see Figure 2.34). A slurry of nickel (catalyst) powder in oil is fed into the slurry reactor and the gas containing H2 is bubbled through the slurry. Slurry containing the nickel and hydrogenated
www.Ebook777.com
Free ebooks ==> www.ebook777.com 78
Green Chemical Engineering
Gas (C2H6 + C2H4 + H2)
Bed of catalyst pellets
Gas (C2H4 + H2) Figure 2.33 Packed bed catalytic reactor (two phase reactor).
oil product is drawn out, and the nickel is separated and recycled back to the feed. In this case, the global rate equation should account for i. Rate of transfer of H2 from gas bubble to liquid oil across the gas–liquid phase boundary ii. Rate of transfer of dissolved H2 from liquid oil to nickel catalyst powder across the liquid–solid phase boundary iii. Rate of reaction of H2 with oil on the nickel surface
H2
Slurry (Ni + hydrogenated oil) Nickel powder Gas bubble containing H2 Oil Slurry (Ni + oil)
Gas (H2) Figure 2.34 Slurry reactor (three phase reactor).
www.Ebook777.com
Free ebooks ==> www.ebook777.com Introduction to Kinetics and Chemical Reactors
79
Appendix 2A: Catalysis and Chemisorption 2A.1 Catalysis: An Introduction Catalysis is a kinetic phenomenon in which the rate of a chemical reaction is increased by the addition of a substance (catalyst), which does not appear in the overall stoichiometric equation of the chemical reaction. Catalysts have been in use for over 2000 years. The first observed uses of catalysts were in the making of wine, cheese and bread. In making these products, it was necessary to add small amounts of the previous batch to make the current batch. Conversion of starch into sugars in the presence of acids, combustion of hydrogen over platinum, decomposition of hydrogen peroxide in alkaline and water solutions in the presence of metals and so on were critically summarised by J.J. Berzelius in 1836, who proposed the existence of a certain body, which ‘effects the chemical changes, does not take part in the reaction and remains unaltered through the reaction’. Later, it was J. Liebig and W. Ostwald who noted that the catalyst increases the rate of a chemical reaction without getting consumed by the reaction. A catalyst is a substance that alters the rate of a reaction but remains unchanged after the reaction. Many chemical reactions that are not feasible under normal conditions can be carried out in the presence of a catalyst. It is difficult to exaggerate the importance of catalysis since many life processes and industrial processes would not be possible without it. Several industrially important reactions that drive the large-scale production of chemical products such as sulphuric acid, agricultural fertilisers, plastics and fuels are catalytic reactions. Catalytic cracking, catalytic reforming, aromatisation, isomerisation and so on in petrochemical industries, hydrogenation of vegetable oil, enzymatic reactions in food processing, conversion of sulphur dioxide into sulphur trioxide, ammonia synthesis, etc., are some of the common examples of industrially important catalytic chemical processes. Catalysts change reaction rates by promoting different mechanisms for the reactions. It is to be noted that even though a catalyst is not consumed in the reaction, it does take part in the chemical reaction but is not observed in the overall reaction. Catalysts activate molecules and reduce the activation energy necessary for reactions to occur. Catalysts do not change the state of equilibrium; they only act to increase the rates at which the equilibrium state is attained. Catalysts can affect yield and selectivity of a chemical reaction because of their ability to change the reaction mechanism. Catalysis is an active area of research. Figure A.1 shows the yearly progress in the number of research publications appearing in the area of catalysis. These figures clearly indicate the increasing interest in the application of catalysis in chemical engineering and a number of allied areas, including environmental engineering, biochemical engineering, energy engineering, material science and nanotechnology.
2A.1.1 Types of Catalysis Catalysis is of crucial importance for the chemical industry and thus chemical engineering. Catalysts applied in industry come in many different forms, from heterogeneous catalysts in the form of porous solids to homogeneous catalysts dissolved in the liquid reaction mixture to biological catalysts in the form of enzymes.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 80
Green Chemical Engineering
Catalysis + chemical engineering Catalysis + environmental engineering Catalysis + energy engineering Catalysis + biochemical engineering Catalysis + chemistry Catalysis + materials science Catalysis + nanotechnology Catalysis + reactor design Catalysis + homogeneous reactor design Catalysis + heterogeneous reactor design
Figure A.1 Number of research papers that appeared on the topics of ‘Catalysis + (Chemical Engineering, Environmental Engineering, Energy Engineering, Biochemical Engineering, Chemistry, Materials Science, Nanotechnology, Reactor Design, Homogeneous Reactor Design and Heterogeneous Reactor Design)’ as listed in the Elsevier Publications (Science Direct) during the years 1823–2014 (a total of 95,111, 35,389, 67,816, 15,479, 2,08,450, 1,74,198, 12,070, 25,278, 9375 and 11,310 articles appeared as on January 14, 2014).
I. We may classify catalysis primarily on the basis of nature of species responsible for the catalytic activity: 1. Molecular catalysis. The term ‘molecular catalysis’ is used for catalytic systems in which the catalyst entity is a molecular species similar to that of the reacting chemical compound. Chemical compounds such as molybdenum complexes and large molecules such as enzymes are used as catalyst substances in molecular catalysis. Molecular catalysts are mostly seen in homogeneous catalytic systems in which the catalyst and the reacting compound are both in the same phase (liquid phase). However, molecular catalysts are also found in multiphase (heterogeneous) systems, such as those involving attachment of molecular entities to polymers. 2. Surface catalysis. As the name implies, surface catalysis occurs on the surface atoms of an extended solid. This often involves surface atoms of dissimilar nature and property and hence different types of catalytic sites (unlike molecular catalysis, in which all the sites are equivalent). Because the catalyst is a solid, surface catalysis is by nature heterogeneous. 3. Enzyme catalysis. Enzymes are proteins, polymers of amino acids, which catalyse reactions in living organisms—biochemical and biological reactions. The systems involved may be colloidal, that is, between homogeneous and heterogeneous. Some enzymes are very specific in catalysing a particular reaction (e.g. the enzyme sucrose catalyses the inversion of sucrose). 4. Autocatalysis. Autocatalysis is a type of reaction in which one of the products acts as a catalyst. The rate of reaction is experimentally observed to increase and go
www.Ebook777.com
Free ebooks ==> www.ebook777.com Introduction to Kinetics and Chemical Reactors
81
through a maximum as the reactant is used up. Some biochemical reactions are autocatalytic. II. Another classification of catalysis is based on the number of phases present in the catalytic system: homogeneous (single phase) and heterogeneous (multiphase) catalysis. 1. Homogeneous catalysis. In homogeneous catalysis, the reactants and the catalyst are in the same phase. Examples include the gas-phase decomposition of many substances, including diethyl ether and acetaldehyde, catalysed by iodine, and liquid-phase esterification reactions, catalysed by mineral acids (an example of the general phenomenon of acid–base catalysis). The molybdenum catalyst and other molecular catalysts are soluble in various liquids and are used in homogeneous catalysis. Gas-phase species can also serve as catalysts. Homogeneous catalysts are molecular catalysts, but the converse is not necessarily true. Homogeneous catalysis is responsible for about 20% of the commercial catalytic reactions in the chemical industry. 2. Heterogeneous catalysis. In heterogeneous catalysis, the catalyst and the reactants are in different phases. Examples include many gas-phase reactions catalysed by solids (e.g. oxidation of SO2 in the presence of V2O5). Others involve two liquid phases (e.g. emulsion copolymerisation of styrene and butadiene, with the hydrocarbons forming one phase and an aqueous solution of organic peroxides as catalysts forming the other phase). Heterogeneous catalysts are either molecular catalysts or surface catalysts. Heterogeneous molecular catalysts have molecular catalytic centres such as the molybdenum species attached to solids or polymers. In heterogeneous catalysis, the observed rate of reaction may include effects of the rates of transport processes in addition to intrinsic reaction rates. Approximately 80% of commercial catalytic reactions involve heterogeneous catalysis. Greater flexibility and added cost of separation of catalysts from the homogeneous system make heterogeneous catalysts more attractive and widely used compared to homogeneous catalyst. Heterogeneous catalysts are further classified as porous, non-porous and supported catalysts. A catalyst that has a large surface area resulting from pores is called a porous catalyst (Gota and Suresh 2014). This large surface area available for solid–fluid interaction is highly useful in attaining a significant reaction rate. An example of a high surface area catalyst is the alumina–silica cracking catalyst. It has a pore volume of 0.6 cm3/g. The average pore radius is 4 nm. The corresponding surface area is around 300 m2/g. The Raney nickel catalyst used in the hydrogenation of vegetable and animal oil and platinum-onalumina catalyst in reforming of petroleum naphtha to produce high octane ratings are other good examples of porous and high surface area catalysts. Non-porous catalysts are monolithic catalysts. These are used in processes where heat removal is a major consideration because extra catalyst surface can enhance the reaction rate and heat removal can become severe. An example of a non-porous catalyst is platinum gauze used in ammonia oxidation in the nitric acid process. When minute particles of an active material are dispersed on a less active substance to produce a catalytic effect, such catalysts are called supported catalysts. The active material is usually a pure metal or a metal alloy. Examples of supported catalysts are the platinum on-alumina catalyst used in petroleum reforming and vanadium pentoxide on silica catalyst used in oxidation of sulphur dioxide.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 82
Green Chemical Engineering
2A.1.2 An Overview of the Basic Concepts of Catalysis The following points summarise the nature and concept of catalysis: 1. A catalyst increases the rate of a reaction by lowering the energy requirement for the reaction. This results from the ability of the catalyst to form bonds with the reaction intermediates, which offsets the energy required to break the reactant bonds. In increasing the rate of a reaction, a catalyst acts by providing an easier path, which can generally be represented by the formation of an intermediate between catalyst and reactant, followed by the appearance of product(s) and regeneration of the catalyst. The easier path is usually associated with a lower energy barrier, that is, lower activation energy. 2. A catalyst does not appear in the stoichiometric description of the reaction, although it appears directly or indirectly in the rate law and in the mechanism. It is not a reactant or a product in the stoichiometric sense. 3. The amount of catalyst does not change due to reaction. 4. In addition to accelerating the rate of reactions, a catalyst controls reaction selectivity by accelerating the rate of one (desired) reaction much more than others. 5. A catalyst increases only the rate of a reaction and not the thermodynamic affinity. Since the presence of the catalyst does not affect the Gibbs energy of reactants or products, it does not alter the equilibrium constant. Since the rates of the forward and the reverse reactions must be equal once equilibrium is reached, a catalyst must accelerate the rates of both the forward and reverse reactions. If a catalyst lowers the energy requirement for the reaction in one direction, it must also lower the energy requirement in the other direction. 2A.2 Heterogeneous Catalysis and Chemisorption When catalysed by a solid, a liquid or gas phase chemical reaction actually occurs on the surface of the catalyst and involves the reaction of molecules or atoms, which are adsorbed on the active centres (sites) of the surface. The catalyst increases the rate of reaction through its ability to adsorb the reactants in such a form that the activation energy necessary for reaction is reduced far below its value in the uncatalysed reaction. In order to convert the reactant in bulk fluid phase into the product, it is necessary for the reactant to be transferred from its position in the fluid to the catalytic interface and adsorbed on the surface, and to undergo reaction to form the adsorbed product. The product is then desorbed and transferred from the interface to a position in the bulk fluid phase. The rate at which each of these steps occurs influences the distribution of concentrations in the system and plays a part in determining the overall reaction rate. The activated adsorption of reactants and the activated desorption of the products as well as the surface reaction of adsorbed reactants to form products is a chemical phenomenon and involves relatively large activation energy, and is therefore highly sensitive to temperature. The actual chemical transformations frequently proceed by several successive stages, each with its own characteristic state. Therefore, in many cases, it is permissible to consider only the slowest single step and assume that the equilibrium is maintained in all other steps. The slowest activated step can be termed as a rate-controlling step. If the surface reaction is rate controlling, it is assumed that the other steps (adsorption and desorption steps) are in equilibrium.
www.Ebook777.com
Free ebooks ==> www.ebook777.com Introduction to Kinetics and Chemical Reactors
83
Activated adsorption is a highly specific reaction between the adsorbate and the activated surface (active site) and possesses the characteristics of a reversible chemical reaction. When adsorption equilibrium is reached, the rates of adsorption and desorption become equal. The reaction on the surface of a catalyst can be considered to be between an adsorbed reactant molecule and a molecule in the bulk fluid phase or between adsorbed molecules on adjacently situated active centres. The reaction proceeds at a rate proportional to the concentrations of adjacently adsorbed reactants. It is assumed that the active centres of the catalyst surface are distributed in a regular geometrical pattern determined by the lattice structure. It can be assumed that the area of catalyst surface has uniform active centres and all these centres behave similarly. If active surfaces are not uniform and if, during adsorption and reaction, some active centres become inactive, the result is an increase in the energy of activation and a decrease in the heat of adsorption (Suresh and Keshav, 2012). In any catalytic reaction, four important steps are involved:
i. Mass transfer of reactants to and from the exterior surface of particles and main body of fluid ii. Diffusion of reactants and products into and out of the pore structure of the catalyst particles iii. Activated adsorption of reactants and desorption of products iv. Surface reaction of adsorbed reactants For reactions in which (i) and (ii) are controlling, the effect of temperature is generally very small and is present only insofar as the kinetic motion of the reactant molecules is influenced by temperature. Similarly, when (i) and (ii) are the controlling steps, particle size exerts a strong effect on reaction rate. Generally, the mass transfer and diffusion are factors of a secondary nature and steps (iii) and (iv) involving activated adsorption and/or the surface reaction are considered as key rate-controlling factors. 2A.2.1 Adsorption Isotherms Surface adsorption to a solid falls into two broad categories: physisorption (physical adsorption) and chemisorption (chemical adsorption). Physisorption is a non-specific loose binding of the adsorbate to the solid via a Van der Waals-type interaction. Multilayered adsorption is possible and it is easily disrupted by increasing temperature. Chemisorption involves a more specific binding of the absorbate to the solid. It is a process that is more akin to a chemical reaction and, hence, only monolayer adsorption is possible. The difference between physisorption and chemisorption is typified by the behaviour of nitrogen on iron. At the temperature of −190°C, liquid nitrogen is adsorbed physically on iron as nitrogen molecules. The amount of N2 adsorbed decreases rapidly as the temperature rises. At room temperature, iron does not adsorb nitrogen at all. At high temperatures, ~500°C, nitrogen is chemisorbed on the iron surface as nitrogen atoms. The type of adsorption associated with heterogeneous catalysis is chemisorption. If the adsorbent and adsorbate are contacted long enough, equilibrium will be established between the amount of adsorbate adsorbed and the amount of adsorbate in solution. The equilibrium relationship is described by adsorption isotherms. Liquid-phase adsorption, in general, is a more complex phenomenon than gas-phase adsorption. For example, although one may envision monolayer coverage in liquid adsorption, the
www.Ebook777.com
Free ebooks ==> www.ebook777.com 84
Green Chemical Engineering
adsorbed molecules are not necessarily tightly packed with identical orientation. Other complications include the presence of solvent molecules and the formation of micelles from adsorbed molecules. Various isotherm equations such as those of Freundlich, Langmuir, Temkin, Dubinin–Radushkevich (D–R) and Redlich–Peterson (R–P) have been reported in the literature to describe the equilibrium characteristics of adsorption. Adsorption isotherms are mostly empirical expressions for representing experimental data within limited concentration ranges. 2A.2.1.1 Langmuir Isotherm The Langmuir isotherm best describes the chemisorption process. Irving Langmuir was awarded the Nobel Prize in 1932 for his investigations concerning surface chemistry. Langmuir’s isotherm describing the adsorption of adsorbate (A) onto the surface of the adsorbent (S) is based on three assumptions: • The adsorbate present in the solution in contact with the surface of the adsorbant is strongly attracted to the surface. • The surface has a specific number of sites where the solute molecules can be adsorbed. • The adsorption involves the attachment of only one layer of molecules to the surface, that is, monolayer adsorption. Chemisorption is a monolayer adsorption. The rate of adsorption of solute A present in the fluid phase in contact with the surface of the adsorbent is proportional to the number of molecules of A (partial pressure of A in gas phase or concentration of A in liquid phase) in the fluid phase and the number of free active sites on the surface. Define ra as rate of adsorption of A on to the surface S. raα PA and raα 1 − θ, where θ is the fraction of occupied sites and PA is the partial pressure of A in the gas phase, 1 − θ is the fraction of free sites available for adsorption of A. We can write
raα PA (1 − θ)
ra = k1 PA (1 − θ)
(A.1)
The rate of desorption of A from the adsorbed active site is proportional to the number of occupied sites. Define rd as the rate of desorption of A.
rdα θ
rd = k 2 θ
(A.2)
At equilibrium, ra = rd, that is
k1 PA (1 − θ) = k 2 θ Solving the above equation for θ, we have
θ=
k1PA k 2 + k1PA
www.Ebook777.com
(A.3)
Free ebooks ==> www.ebook777.com Introduction to Kinetics and Chemical Reactors
85
Define q as q=
mole of solute adsorbed gram of solid
At equilibrium, qαθ q = k 3θ (A.4)
Substituting Equation A.3 in Equation A.4, we get q=
k 3 k1PA k 2 + k1PA
(A.5)
which can be written as q= q=
k 3 PA k2 + PA k1 K1 PA K 2 + PA
(A.6)
where K1 = k3 and K 2 = k2/k1. An adsorption isotherm establishes the relationship between the amount of adsorbate adsorbed to the solid surface and the concentration of adsorbate remaining in the solution. Thus, Equation A.6 is the Langmuir adsorption isotherm equation. Equation A.6 can also be expressed in terms of concentration of A for liquid-phase systems. q=
K1 C A K 2 + CA
(A.7)
2A.2.1.2 Freundlich Isotherm In 1909, Freundlich gave an empirical expression representing the isothermal variation of quantity of gas adsorbed by unit mass of solid adsorbent with pressure. This equation is known as the Freundlich adsorption isotherm. The Freundlich adsorption isotherm is mathematically expressed for gas-phase adsorption as
q αPA n
or q = kPA n
(A.8)
or q = kC A n
(A.9)
And for liquid-phase adsorption as
q αCA n
where k and n are constants for a given adsorbate and adsorbent at a particular temperature. It is used in cases where the actual identity of the solute is not known, such as adsorption of coloured material from sugar, vegetable oil and so on.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 86
Green Chemical Engineering
2A.2.1.3 Other Well-Known Isotherm Models A number of adsorption isotherm models, other than the two models presented in the previous section, are reported in the literature. Some well-known isotherm models are presented in Table A.1. A large number of researchers in the field of environmental engineering have used Freundlich (1906) and Langmuir (1918) isotherm equations to represent equilibrium adsorption data using activated carbon–organic contaminant systems, despite the fact that these equations have serious limitations in their usage. The most popular Freundlich isotherm, for example, is suitable for highly heterogeneous surfaces (Halsey and Taylor, 1947); however, it is only valid for adsorption data over a restricted range of concentrations. For highly heterogeneous surfaces, extremely low concentrations are required to follow Henry’s law. However, Freundlich’s equation does not approach Henry’s law at vanishing concentrations. The Langmuir equation, although it follows Henry’s law at vanishing concentrations, is valid for homogeneous surfaces. The Redlich–Peterson equation (1959) incorporates three parameters into an empirical isotherm and, therefore, can be applied either in homogeneous or heterogeneous systems. 2A.3 Catalyst Deactivation and Regeneration During the course of operation, the activity of the catalyst gets reduced and it will not be able to provide the desired performance. The activities of a catalyst normally decrease with time. In the development of a new catalytic process, the life of the catalyst is usually a major economic consideration. Shutting down a process for regenerating or replacing the catalyst at frequent intervals is economically prohibitive. The rate at which the catalyst is deactivated may be very fast, such as for hydrocarbon-cracking catalysts, or may be very slow, such as for the promoted iron catalysts used for ammonia synthesis, which may remain on-stream for several years without appreciable loss of activity. An understanding of how catalysts lose activity is important. In some systems, catalyst activity decreases so slowly that exchange for new material or regeneration is required Table A.1 Some of the Well-Known Adsorption Isotherm Models S. No.
Isotherm Model
Equation
Assumption (i) The heat of adsorption of all the molecules in the layer decreases linearly with coverage due to adsorbate–adsorbate interactions, and (ii) that the adsorption is characterised by a uniform distribution of binding energies up to some maximum binding energy It approaches the Freundlich model at high concentrations and is in accord with the low concentration limit of the Langmuir equation. Furthermore, the R–P equation incorporates three parameters into an empirical isotherm and, therefore, can be applied in either homogeneous or heterogeneous systems due to its high versatility.
1.
Temkin (1940)
qe = BT ln KT + BT ln Ce
2.
Redlich–Peterson (1959)
qe =
3.
Dubinin– Radushkevich (1947)
qe = qm exp(− K ε 2 )
K R Ce 1 + aRCeβ
www.Ebook777.com
Free ebooks ==> www.ebook777.com 87
Introduction to Kinetics and Chemical Reactors
only at long intervals running from a few months to years. Catalysts for cracking and hydrocarbon reactions promoted catalysts for synthetic ammonia and catalysts containing metals such as platinum and silver are examples of catalysts which get deactivated slowly. The decrease in activity is due to poisons, fouling, sintering, ageing and coking, which can be caused by substances present either in the reactant stream or produced by the reaction. Rapid deactivation is caused by physical deposition of a substance, which blocks the active sites of the catalyst. Carbon deposition on catalysts used in the petroleum industry falls into this category. The carbon covers the active sites of the catalyst and may also partially plug the pore entrances. In this type of poisoning, the catalyst is regenerated by passing air and/or steam. The regeneration process itself is a heterogeneous reaction. Compounds of sulphur and other materials are frequently chemisorbed on nickel, copper and platinum catalysts. These are called chemisorbed poisons. For example, in sulphur dioxide oxidation arsenic, present in very small quantity in the reactant stream, poisons the catalyst. The toxicity of a poison (P) depends upon the enthalpy of adsorption of the poison, and the free energy of the adsorption process, which controls the equilibrium constant for chemisorption of the poison (Kp). The fraction of sites blocked by a reversibly adsorbed poison (θP) can be calculated using a Langmuir isotherm model θP =
K p Pp 1 + K A PA + K P Pp
(A.10)
where K A and Kp are the adsorption constants for the reactant (A) and the poison, respectively, and pA and pP are the partial pressures of the reactant and poison. The catalyst activity is proportional to the fraction of unblocked sites, 1 − θP. The compound responsible for poisoning is usually an impurity in the feed stream. However, occasionally, the products of the desired reaction may also act as poisons. There are three main types of poisons:
1. Molecules with reactive heteroatoms (e.g. sulphur) 2. Molecules with multiple bonds between atoms (e.g. unsaturated hydrocarbons) 3. Metallic compounds or metal ions (e.g. Hg, Pd, Bi, Sn, Cu, Fe)
Some metallic compounds present in trace level (ppm) in petroleum feed, adsorbed to the active site of the catalyst, act and change the selectivity of the reaction by producing more and more unwanted products. When water vapour is present in the sulphur dioxide–air mixture supplied to a platinum–alumina catalyst, a decrease in oxidation activity occurs. This type of poisoning is due to the effect of water on the structure of the alumina carrier and is known as stability poisoning. The resulting increase in diffusional resistance may dramatically increase the Thiele modulus, and reduce the effectiveness factor for the reaction. In extreme cases, the pressure drop through a catalyst bed may also increase dramatically. There are some substances that do not act as catalysts but enhance the efficiency of catalysts and prolong their lives. Such substances are called catalyst promoters. The promoter may react with the catalyst and form several active sites to enhance catalyst activity. For example, the catalytic activity of V2O5 in the oxidation of sulphur dioxide is enhanced appreciably when sulphates of alkali metals are added in small amounts. It prevents reduction in surface area during catalyst use and increases activity over a period of time.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 88
Green Chemical Engineering
Deactivation caused by a change in the surface structure of a catalyst due to prolonged exposure to elevated temperature in the reacting atmosphere is called sintering. Gradual change in crystal surface by the deposit of a foreign material on the active portion of the catalyst surface is called the ageing phenomenon. There are some substances, called inhibitors, which decrease the rate of reaction. If an undesirable side reaction occurs, inhibitors can be useful in reducing the activity of the catalyst. For example, in an ethylene oxidation reaction, ethylene oxide is the desired product. Under the same conditions, CO2 and H2O are also formed by complete oxidation, which is undesirable and needs to be suppressed. In this process, silver supported on alumina is a good catalyst. If a halogen compound is added to the catalyst, CO2 and water formation is reduced. This is also useful in reducing the activity of a catalyst, thus avoiding an undesirable side reaction. 2A.4 Case Studies: Removal of Pollutants by Adsorption In the following section, two case studies are presented to illustrate the application of adsorption in the removal of industrial pollutants. 2A.4.1 Adsorptive Removal of Phenol by Activated Palash Leaves Phenol (P) and its derivatives are organic compounds that are regarded as environmentally relevant contaminants. They are widely found in pesticides, dyestuffs, pharmaceuticals, oil refineries, coke plants, plastics industry, petrochemicals and other industries effluents (Suresh et al., 2012a). Ps and its substituted compounds are important environmental pollutants because of their toxic effects towards life in the aquatic environment. It gets rapidly absorbed through the skin. Most phenolic compounds are toxic and many are known or suspected human carcinogens. This has led to the classification of P and other substituted Ps by the United States Environmental Protection Agency (USEPA) as priority pollutants. USEPA recommends a maximum concentration level of 1 µg/mL of total phenolic compounds in water supplies. Adsorption processes using granular activated carbon (GAC) are widely employed for the removal of trace organic contaminants such as P, aniline (AN) and its derivatives from drinking water and industrial effluents. Over the last decade it has been established that the adsorption technique, being efficient (Suresh and Keshav, 2012) and economical, has proved more advantageous over other physico-chemical methods such as the photochemical method, electrochemical treatment, biodegradation and so on, for the removal of phenol from wastewater. Commercially available activated carbons are very expensive, therefore, in recent years, many studies have examined the preparation of activated carbon from low-cost and readily available materials, mainly industrial and agricultural by-product waste such as carboxylated diaminoethane sporopollenin, orange peel (Suresh and Keshav, 2012), bagasse fly ash (Suresh et al., 2012; Soni et al., 2012), banana pith, sunflower seed hull, cashew net shell (Suresh et al., 2012b), maize cob waste, rice husk (Suresh et al., 2012c), bean waste, chitin and chitosin. Critical review of low-cost adsorbents for waste and wastewater treatment has been presented by Bailey et al. (1986). Another category of biomass that acts as adsorbent is plant leaves. The few that researchers investigated included palm tree leaves (Suresh et al., 2012d) and waste tea leaves (Suresh et al., 2011a,b). Some of the advantages of using low-cost adsorbents include simple technique requiring little processing, good adsorption capacity, low cost, free availability and easy regeneration. Thus, in the present study, palash leaves have been used as adsorbent as they are
www.Ebook777.com
Free ebooks ==> www.ebook777.com 89
Introduction to Kinetics and Chemical Reactors
freely available and low cost. The present study shows the feasibility of using activated palash leaves as a sorbent for the removal of phenol through its physico-chemical characteristics. To understand the behaviour/mechanism of sorption, a kinetic study has been carried out. 2A.4.1.1 Materials and Methods All the reagents were analytical reagent (AR) grade. Phenol was purchased from Ranbaxy Fine Chemicals, New Delhi, India. The initial pH was adjusted with 0.1 N NaOH or 0.1 N HCl solutions. A stock solution of 1000 mg/L was prepared by dissolving accurately weighed amounts of phenol in double distilled water (DWW). The desirable experimental concentration of solutions was prepared by diluting the stock solution with distilled water when and if necessary. Palash leaves collected from a MANIT Campus, Bhopal, India were first washed with DWW and then dried. The dried adsorbent was crushed in a laboratory mill and sieved to obtain particles ranging from 1 to 2 mm. The mass was then placed in a furnace and heated slowly to reach the desired temperature of 600°C. It was left for 1 h and then cooled to ambient temperature. The material was activated by treating with phosphoric acid in a heating plate with constant for 3 days. The activated adsorbent was washed repeatedly with DWW until neutral pH was obtained and dried overnight in a vacuum oven at 100°C. The dried sample was sieved to 200 mesh particle size and stored in desiccators. The batch experiment was conducted in a 100 mL stopper Erlenmeyer flask which consisted of 20 mL of phenol solution of known concentration, pH and a known amount of the activated palash leaves. This mixture was agitated with a temperature controlled at constant speed of 150 rpm (Metrex Scientific Instruments, New Delhi) maintained at 303 K. Samples were withdrawn at appropriate intervals and were filtered using 0.45 µm filter paper to determine the residual concentrations using UV-visible spectrophotometer. Experiments were carried out at initial pH ranging from 2 to 9, which was adjusted by the addition of dilute 0.1 N HCl or 0.1 N NaOH solutions. The phenol removal from the solution was calculated as
% Phenol removal = 100(C0 − C t )/C0
(A.11)
and the adsorptive uptake of phenol by activated palash leaves (mg/g) was calculated as
qt = (C0 − C t )V/m
where C0 is the initial phenol concentration (mg/L), Ct is the phenol concentration (mg/L) at any time t, V is the volume of the solution (l) and w is the mass of the adsorbent (g). 2A.4.1.2 Kinetic Studies The kinetic behaviour of the adsorption of phenol onto adsorbent was studied in 100 mL stopper conical flasks at 303 K. These solutions were filtered after a particular time interval and analysed through a spectrophotometer for phenol concentration. The modelling kinetic equation of adsorption has been well known and reported by many researchers (Suresh et al., 2011c,d,e). The different contact times help in determining the uptake capacities of the dye at varying time intervals, keeping the amount of adsorbent fixed. The effect of contact time was
www.Ebook777.com
Free ebooks ==> www.ebook777.com 90
Green Chemical Engineering
140 120
C0 (mg/L) 50 100 250 500 1000
qt (mg/g)
100 80 60 40 20 0
0
500
1000
1500
Time (min) Figure A.2 Effect of contact time and initial concentration on the adsorption of phenol by activated palash leaves. Experimental data points given by the symbols and the lines predicted by the pseudo-second-order model. m = 10 g/L, T = 303 K, pH = 6.2.
performed at T = 30°C, pH = 2 and C0 = 1000 mg/L, m = 10 g/L (Figure A.2). The maximum percentage removal of phenol onto the activated palash leaves was ~80% within 60 min of the experiments. The kinetics of adsorption control the efficiency of the process and equilibrium time. It also describes the rate of adsorbate uptake onto activated palash leaves. In order to identify the potential rate-controlling steps involved in the process of adsorption, two kinetic models were studied and used to fit the experimental data from the adsorption of phenol onto activated palash leaves. These models are the pseudo-first-order and pseudo-secondorder models. Pseudo-first-order kinetic model: The sorption of organic molecules from a liquid phase to a solid phase can be considered as a reversible process with equilibrium being established between the solution and the solid phase. Assuming a non-dissociating molecular adsorption of adsorbates onto adsorbent particles, the sorption phenomenon can be described as the diffusion-controlled process (Fogler, 1998).
kA A+S A⋅S k D
(A.12)
where A is the adsorbate and S is the active site on the adsorbent and A ⋅ S is the activated complex. k A and kD are the adsorption and desorption rate constants, respectively. It can be shown using first-order kinetics that, with no adsorbate initially present on the adsorbent (i.e. CAS0 = 0 at t = 0), the fractional uptake of the adsorbate by the adsorbent can be expressed as
XA k = 1 − exp k ACS + A t X Ae KS
(A.13)
www.Ebook777.com
Free ebooks ==> www.ebook777.com 91
Introduction to Kinetics and Chemical Reactors
where X Ae = fraction of the adsorbate adsorbed on the adsorbent under equilibrium condition (i.e. CASe/CA0) KS = k A kD
(
CS = adsorbent concentration in the solution
Thus, the plot of ln 1 − X A X
Ae
) versus t for various values of C
A0
at a constant CS will
give a straight line, which will be coincident on the ordinate at t = 0. Constants kA and kD can be obtained using relevant relations and the slope of each curve for a given value of CS. Equation 3.2.2 can be transformed as
log(qe − qt ) = log qe −
kf t 2.303
(A.14)
where
k k f = k ACS + A kS q = XA
(A.15)
and qe = X Ae
This equation is the so-called Lagergren equation (Lagergren, 1898). This equation is, however, valid only for the initial period of adsorption. Various investigators have erroneously fitted this equation to the adsorbate uptake data for later periods, ignoring the data of the initial period. A plot of log(qe − qt) versus t enables the determination of kinetic constants. Experimental results do not follow the pseudo-first-order model for the whole period because they differ in two important aspects: (i) kf (qe − qt) does not represent the number of available sites, and (ii) logqe was not equal to the intercept of the plot of log (qe − qt) against t (Ho and McKay, 1999). This equation is, however, valid only for the initial period of adsorption. Various investigators have erroneously fitted this equation to the adsorbate uptake data for later periods, ignoring the data of the initial period for the model fitting. The values of the pseudo-first-order adsorption rate constant (kf) (Table A.2) were determined from Equation A.13 by plotting log(qe − qt) against t for phenol adsorption onto activated palash leaves with CA0 = 50–1000 mg/L at 30°C for the first 24 h. Experimental results did not follow first-order kinetics given by Equation A.13 as there were differences in two important aspects: (i) kf (qe − qt) does not represent the number of available sites and (ii) log qe was not equal to the intercept of the plot of log(qe − qt) against t. Pseudo-second-order kinetic model: For cellulose-based sorbents having fibres, which may have polar functional groups, chemical bonding of polar functional groups may occur with solute ions and these groups may impart cation exchange capacity to the adsorbents (Ho and McKay, 1998, 1999, 2000). For such sorption systems, the rate of sorption to the surface should be proportional to a driving force times an area, and the sorption rate equation may be given as
dqt = kS (qe − qt )2 dt
www.Ebook777.com
(A.16)
Free ebooks ==> www.ebook777.com 92
Green Chemical Engineering
Table A.2 Kinetic Parameters for the Removal of Phenol by Activated Palash Leaves Co(mg/L)
qe,calc(mg/g)
Pseudo-First-Order Model 50 6.47 100 12.59 250 32.27 500 62.61 1000 32.27 Pseudo-Second-Order Model 50 6.47 100 12.75 250 32.27 500 62.61 1000 131.29 Co(mg/L)
Kid1 (mol/g min1/2)
Weber-Morris 50 100 250 500 1000
0.003 0.748 0.011 0.014 7.102
KS (g/mg min)
h(mg/g min)
R2
MPSD
6.47 11.99 32.27 62.60 114.47
1.12 2.12 12.79 8.77 2.02
0.999 0.799 0.999 0.999 0.972
0.13 93.15 0.47 0.26 58.40
8.17 3.19 2.05 4.05 7.2
34.82 1.48 10.83 41.52 3.68
0.999 0.992 0.999 0.999 0.991
4.05 15.99 5.12 2.79 34.59
Kid2 (mol/g min1/2)
I2
I1
R2
6.45 4.534 32.13 62.14 20.19
0.875 0.889 0.793 0.964 0.994
0.00004 0.013 0.0001 0.0002 0.705
6.56 12.17 32.16 62.69 104.02
R2
0.893 0.678 0.957 0.984 0.787
Note: t = 24 h, C0 = 50–1000 mg/L, m = 10 g/L, T = 303 K.
where kS is the pseudo-second-order rate constant (g/mg min). Integrating Equation 3.2.5 and noting that qt = 0 at t = 0, the following equation is obtained:
t 1 1 = + t qt kS qe2 qe
(A.17)
The initial sorption rate, h (mg/g min), as t → 0 can be defined as
h = kS qe2
(A.18)
The equilibrium adsorption capacity (qe) and the initial sorption rate (h) along with the pseudo-second-order constant kS can be determined from the slope and the intercept of the plot of t/qt versus t. The adsorption capacity depends upon the initial sorbate concentration, C0, system temperature, T, solution, pH, sorbate particle size, sorbate dose, w, sorbate characteristics and so on. The kinetic model is concerned only with the effect of observable parameters on the overall rate (Ho, 2006). The linearised plot of t/qt versus t is the so-called ratio correlation. Here, t is present in both the ordinate and the abscissa of the plot and it would, of course, yield a perfect correlation coefficient (R2 = 1.0) in all cases. Therefore, this kinetic expression would become
www.Ebook777.com
Free ebooks ==> www.ebook777.com Introduction to Kinetics and Chemical Reactors
93
best fit if compared with first-order or other kinetic expressions used in the sorption studies (Lyberatos, 2006). Therefore, it is not appropriate to use the coefficient of determination of linear regression method for comparing the best-fitting of kinetic models. Non-linear fitting could be adopted to obtain the kinetic parameters (Ho, 2006). Equation A.17 seems to be valid at low and high times of sorption. At t → ∞, qt → qe and at t → 0, qt → 0. In a very fast adsorption situation, it is too difficult to measure the adsorption rate in the timescale of kinetic experiments. In such situations, it is better to provide a qualitative discussion of the kinetic results. The qe and the h along with the kS can be determined from the non-linear fitting of the data using a solver add-in function of MS Excel for Windows. The linear correlation coefficients values for the pseudo-second-order kinetic model were greater than those of the pseudo-first-order kinetic model. This indicates the applicability of the pseudo-second-order kinetic model to describe the adsorption process of phenol onto activated palash leaves. It suggests that this adsorption depends on the adsorbate as well as the adsorbent and involves chemisorptions in addition to physisorption. The chemisorptions might be the rate-limiting step where valency forces are involved via electrons sharing or exchange between the adsorbent and the adsorbate. The effect of contact time on the qt values for Co = 50–1000 mg/L for P at m = 10 g/L and T = 303 K is shown in Figure A.2. The adsorption was followed over a period of 24 h. These durations are considered to be, approximately, the equilibration times for the adsorption process. It may be seen that in the first 1 h, brisk adsorption of P occurred at all Co and, thereafter, the adsorption rate decreased gradually and the adsorption reached equilibrium. Residual concentrations at 5 h contact time were found to be higher by a maximum of ~2% than those obtained after 24 h contact time for P. Therefore, after 5 h contact time, a steady-state approximation was assumed and a quasi-equilibrium situation was accepted for Co ≤ 250 mg/L. For P adsorption onto activated palash leaves, equilibrium adsorption times were found to be 5 h (97.2%), 5 h (97.3%), 8 h (97.2%), 5 h (98.6%) and 5 h (99.2%), respectively, at Co values of 50–1000 mg/L. The rate of P removal by activated palash leaves is fast for the first 1 h. This is obvious from the fact that a large number of vacant surface sites are available for adsorption during the initial stage, but with the passage of time the remaining vacant surface sites are difficult to occupy due to repulsive forces between the solute molecules in the solid and bulk liquid phases. Also, the adsorbates get adsorbed into the meso-pores of carbon that get almost saturated during the initial stage of adsorption. Thereafter, the adsorbates have to traverse farther and deeper into the pores, encountering much greater resistance. This results in the slowing down of adsorption during the latter period. Various researchers reported that Co provides an important driving helping to overcome all mass transfer resistances of adsorbates between the aqueous and solid phases. The increase in Co also enhances the interaction between adsorbate molecules and the vacant sorption sites on the carbon and surface functional groups. Therefore, an increase in Co enhances the adsorption uptake of P onto granular-activated carbon (Suresh et al., 2011e). The results of the fit of these models are given in Table A.2. The fit of experimental data to the pseudo-first-order and the pseudo-second-order equations seemed to be quite good when correlation coefficients (R2) obtained from non-linear regression analyses were examined. However, it was very difficult to decide which model represented the experimental data better, just on the basis of R2. A better criterion to find the best model for the experimental data would be Marquardt’s percent standard deviation (MPSD) parameter. It is known that the lower the MPSD value, the better the fit. When the MPSD values
www.Ebook777.com
Free ebooks ==> www.ebook777.com 94
Green Chemical Engineering
given in Table A.2 are examined, it can be seen that they are much smaller for the pseudosecond-order model as compared with those for the pseudo-first-order model, leading to the conclusion that the kinetic data of adsorption of P onto activated palash leaves fit to the pseudo-second-order model better than the pseudo-first-order model. Similar conclusions were made by various researchers (Suresh et al., 2011e) for removal of Aniline and 4-chlorophenol onto various types of ACs. 2A.4.1.3 Adsorption Diffusion Study The mathematical treatment of Boyd et al. (1947) and Reichenberg (1953) to distinguish between particle diffusion and film diffusion, and the mass action-controlled mechanism of exchange have laid the foundations of sorption/ion-exchange kinetics. In adsorption systems, the mass transfer of solute or adsorbate onto and within the adsorbent particle directly affects the adsorption rate. It is not only important to study the rate at which the solute is removed from an aqueous solution in order to apply adsorption by solid particles to industrial uses, but it is also necessary to identify the step that governs the overall removal rate in the adsorption process in order to interpret the experimental data. There are essentially four stages in the adsorption of an organic/ inorganic species by a porous adsorbent (McKay et al., 2001).
1. Transport of adsorbate from the bulk of the solution to the exterior film surrounding the adsorbent particle 2. Movement of adsorbate across the external liquid film to the external surface sites on the adsorbent particle (film diffusion) 3. Migration of adsorbate within the pores of the adsorbent by intra-particle diffusion (pore diffusion) 4. Adsorption of adsorbate at internal surface sites All these processes play a role in the overall sorption within the pores of the adsorbent. In a rapidly stirred, well-mixed batch adsorption, mass transport from the bulk solution to the external surface of the adsorbent is usually fast. Therefore, the resistance to the transport of the adsorbate from the bulk of the solution to the exterior film surrounding the adsorbent may be small and can be neglected. In addition, the adsorption of adsorbate at surface sites (step 4) is usually very rapid, thus offering negligible resistance in comparison to other steps, that is, steps 2 and 3. Thus, these processes are usually not considered to be rate-limiting steps in the sorption process. In most cases, steps 2 and 3 may control the sorption phenomena. For the remaining two steps in the overall adsorbate transport, three distinct cases may occur: Case I: external transport > internal transport Case II: external transport < internal transport Case III: external transport ≈ internal transport In cases I and II, the rate is governed by film and pore diffusion, respectively. In case III, the transport of ions to the boundary may not be possible at a significant rate, thereby leading to the formation of a liquid film with a concentration gradient surrounding the adsorbent particles. Usually, external transport is the rate-limiting step in systems that have (a) poor phase mixing, (b) dilute concentration of adsorbate, (c) small particle size and (d) high affinity
www.Ebook777.com
Free ebooks ==> www.ebook777.com 95
Introduction to Kinetics and Chemical Reactors
of the adsorbate for the adsorbent. In contrast, the intra-particle step limits the overall transfer for those systems that have (a) a high concentration of adsorbate, (b) a good phase mixing, (c) large particle size of the adsorbents and (d) low affinity of the adsorbate for adsorbent. Kinetic data can further be used to know about the step offering larger resistance in the overall sorption phenomena using Bangham’s equation.
C0 k0 B m log log = log + α log ( t ) 2.303V C0 − qt m
(A.19)
where C0 is the initial concentration of the adsorbate in the solution (mg/L), V is the volume of solution (L), m is the adsorbent concentration (g/L), qt(mg/g) is the amount of adsorbate retained by the adsorbent at time t, and α(< 1) and k0B are constants. If the loglog(CO/ (CO − qtm)) versus log(t) plot yields very good perfect linear curves, then the diffusion of the adsorbate into the pores of the adsorbent is considered as the only rate-controlling step in the kinetic process (Tutem et al., 1998). 2A.4.1.4 Intra-Particle Diffusion Study The possibility of intra-particle diffusion can be explored by using the intra-particle diffusion model (Weber et al., 1963).
qt = kidt1/2 + I
(A.20)
where kid is the intra-particle diffusion rate constant, and values of I give an idea about the thickness of the boundary layer. Many investigators have represented the data points of q versus t0.5 by straight lines— the lower straight portion depicting macro-pore diffusion and the upper one representing micro-pore diffusion. Extrapolation of the linear portions of the plots back to the ordinate gives the intercept, which provides the measure of the boundary layer thickness. The deviation of straight lines from the origin is attributed to the difference in the rate of mass transfer between the initial and final stages of adsorption. Further, such deviation of the straight line from the origin indicates that the pore diffusion is not the sole rate-controlling step. The slope of the Weber and Morris plot is defined as a rate parameter (kid), characteristic of the rate of adsorption in the region where intra-particle diffusion is rate controlling. The higher the value of kid, the higher the intra-particle diffusion rate. In the present study, experiments were conducted at a well-mixed condition of 150 rpm with P concentration ranging from 50 to 1000 mg/L to properly understand the controlling mechanism. In general, external mass transfer is characterised by the initial solute uptake (Suresh et al., 2011e) and can be calculated with the assumption that the uptake is linear for the first initial rapid phase (in the present study, the first 30 min). For P adsorption onto activated palash leaves, the calculated K S values were found and shown in Table A.2. Figure A.3 shows the Weber and Morris (1963) plot of qt versus t0.5 for all the adsorbates and the parametric values are given in Table A.2. If the plot of qt versus t0.5 satisfies the linear relationship with the experimental data, then the sorption process is supposed to be controlled by intra-particle diffusion only. However, if the data exhibit multi-linear plots, then two or more steps influence the sorption process. The slope of the linear portions are defined as rate parameters (kid,1 and kid,2) and are characteristics of the rate of adsorption in
www.Ebook777.com
Free ebooks ==> www.ebook777.com 96
Green Chemical Engineering
140
C0 (mg/L) 50 100 250 500 1000
120
qt (mg/g)
100 80 60 40 20 0
0
10
20
t0.5 (min0.5)
30
40
Figure A.3 Weber and Morris intra-particle diffusion plot for the removal of phenol by activated palash leaves. T = 303 K, m = 10 g/L.
the region where intra-particle diffusion is rate controlling. In Figure A.3, the data points are related by two straight lines. The curvature from the origin to the start of the first straight portion (not shown in figure) represents the boundary layer diffusion and/or external mass transfer effects (Suresh et al., 2011c). The first straight portion depicts macropore diffusion and is attributed to the gradual equilibrium stage with intra-particle diffusion dominating. The second represents meso-pore diffusion and is the final equilibrium stage for which the intra-particle diffusion starts to slow down due to the extremely low adsorbate concentration left in the solution. Extrapolation of the linear portions of the plots back to the y-axis gives the intercepts, which provide the measure of the boundary or film layer thickness. The deviation of straight lines from the origin indicates that the pore diffusion is not the sole rate-controlling step. Therefore, the adsorption proceeds via a complex mechanism consisting of both surface adsorption and intra-particle transport within the pores of carbon. The portion of the plots are nearly parallel (kid,2 ≈ 0.00004–0.72 mg/g min0.5), suggesting that the rate of adsorption P into the meso-pores of activated palash leaves is comparable at all Co. The slopes of the first portions (kid,1) are higher for higher Co for P, which corresponds to an enhanced diffusion of P through macro-pores. This is due to the greater driving force at higher Co. 2A.4.1.5 Determination of Diffusivity Kinetic data could be treated by the models given by Boyd et al. (1947), which is valid under the experimental conditions used. With diffusion rate controlling in the adsorption particles of spherical shape, the solution of the simultaneous set of differential and algebraic equations leads to (Reichenberg, 1953; Helfferich, 1962) F(t) = 1 −
6 π2
∞
∑z z =1
1 2
− z 2π2Det exp 2 Ra
www.Ebook777.com
(A.21)
Free ebooks ==> www.ebook777.com 97
Introduction to Kinetics and Chemical Reactors
or F(t) = 1 −
6 π2
∞
∑z
1 2
z =1
exp − z 2Bt
(A.22)
where F(t) = qt/qe is the fractional attainment of equilibrium at time t, De is the effective diffusion coefficient of the adsorbate in the adsorbent phase (m2/s), Ra is the radius of the adsorbent particle assumed to be spherical (m), z is an integer and B=
π2De Ra2
(A.23)
Bt values could be obtained for each observed value of F(t) from Reichenberg’s table (Reichenberg, 1953). The linearity test of Bt versus time plots is employed to distinguish between the film diffusion- and particle diffusion-controlled adsorption. If the plot of Bt versus time (having slope B) is a straight line passing through the origin, then the adsorption rate is considered to be governed by the particle diffusion mechanism; otherwise, it is governed by film diffusion. For cylindrical particles, if one assumes that the diffusion takes place radially and the diffusion in the angular and axial directions is negligible, one gets the solution given by Skelland (1974), which after rearrangement leads to F(t) = 1 −
4 π2
∞
∑b z =1
1 2 n
exp −De bn2t
(A.24)
where bn’s are roots of J0(bnpR) = 0. Vermeulen’s approximation (Vermeulen, 1953) of Equation 3.3.2 fits the whole range 0 < F(t) < 1 for adsorption on to spherical particles. This approximation is given as
−π2Det F(t) = 1 − exp 2 Ra
1/2
(A.25)
This equation could further be simplified to cover most of the data points for calculating effective particle diffusivity, that is,
π2Det 1 ln = R2 2 a (1 − F (t))
(A.26)
The De can be calculated from the slope of the plot of ln 1 (1 − F 2 (t)) versus t. The multiphasic nature of the intra-particle diffusion plot confirms the presence of both surface and pore diffusion. In order to predict the actual slow step involved, the kinetic data were further analysed using Boyd kinetic expression. Equation A.22 was used to calculate Bt values at different time t. The linearity of the plot of Bt versus time was used to distinguish whether surface and intra-particle transport controls the adsorption rate. It
www.Ebook777.com
Free ebooks ==> www.ebook777.com 98
Green Chemical Engineering
was observed that the relation between Bt and t was non-linear (R2 = 0.900 – 0.892) at all concentrations, confirming that surface diffusion is not the sole rate-limiting step. Thus, both surface and pore diffusion seem to be the rate-limiting step in the adsorption process and the adsorption proceeds via a complex mechanism. The values of effective diffusion coefficient (De) as calculated from Equation A.26. Average values of De were found to be 2.12 × 10−10 for the adsorption of P onto activated palash leaves. Similar average values of De(0.388 × 10−10) were reported by Suresh et al. (2011) for adsorption of phenol derivatives onto AC. 2A.4.1.6 Solvent and Thermal Desorption Study Solvent desorption studies help in finding the mechanism of an adsorption process. If the adsorbates adsorbed onto the adsorbent can be desorbed by water, it can be said that the attachment of the adsorbate onto the adsorbent is by weak bonds. If strong acid, such as HNO3 and HCl, or strong bases, such as NaOH, can substantially desorb the adsorbent, it can be said that the attachment of the adsorbate onto the adsorbent is by ion exchange. If organic acids, such as CH3COOH, can desorb the adsorbent, it can be said that the adsorption of the adsorbate onto the adsorbent is by chemisorption. Various solvents, namely, ethanol, HNO3, HCl, NaOH, CH3COOH, acetone and water, were used for the elution of AN or P or CP or NP from the GAC (Suresh et al., 2011f). Spent-GAC was thermal desorbed by a process described in the material and method section. Thermally desorbed GAC was again used for adsorption. It is necessary to properly dispose of the spent-GAC and/or utilise it for some beneficial purpose, if possible. The dried spent-GAC can be used directly or by making fire-briquettes in furnace combustors/incinerators to recover its energy value. The spent adsorbents pose problems to their disposal and management. The recent trend emphasises on utilising them for some beneficial purpose and rendering them innocuous and benign to the environment. The use of low-cost adsorbents for the treatment of various wastewaters generates large volumes of solid waste. These solid wastes have a great potential for energy recovery. However, the separation of the adsorbents from the solvents by sedimentation, filtration, centrifugation, dewatering and drying is very important. These aspects are being studied separately in the laboratory by other researchers and, therefore, have not been dealt with in this study. The dried metal-loaded spent bagasse fly ash, rice husk ash and activated carbon can be used directly or by making fire-briquettes in furnace combustors/incinerators to recover energy value. The blank and metal-loaded adsorbents were studied for their thermal degradation characteristics by a thermogravimetric (TG) instrument. The oxidation kinetics of these adsorbents were studied using different kinetic models (Suresh et al., 2011f). 2A.4.2 Adsorptive Removal of Various Dyes by Synthesised Zeolite Materials: Sodium hydroxide and hydrochloric acid and different dyes such as methyl orange, methylene blue and safranine T were procured from Ranbaxy Fine Chemicals, New Delhi, India. Physico-chemical properties of the synthesised zeolite used in the present investigations are given in detail in Chapter 6. 2A.4.2.1 Regeneration of Zeolite Regeneration of zeolite was done by placing the used zeolite in the furnace at around 550°C for 5 h. The catalyst is regenerated by calcination at high temperatures. By calcination, the
www.Ebook777.com
Free ebooks ==> www.ebook777.com 99
Introduction to Kinetics and Chemical Reactors
adsorbent structure becomes stable. At higher temperatures, moisture with other volatile matters goes out and also the adsorbed compounds are desorbed so that the entire surface of the catalyst becomes available for re-adsorption. 2A.4.2.2 Adsorption of Different Dyes over Zeolite The adsorbent used in the experiment was zeolite synthesised from fly ash. Dyes solution with a concentration of 1000 mg/L was prepared from analytical-grade reagent and DDW. Adsorption kinetics and isotherm experiments for all samples were undertaken using a batch equilibrium technique. The adsorption of dye was performed by shaking 0.1 g of adsorbent in 100 mL of dye solution with an initial concentration of 50–1000 mg/L at 150 rpm at different temperatures. The determination of dye concentration was done on a spectrophotometer by measuring absorbance at λmax of 464, 630 and 560 nm for methyl orange, methylene blue and safranine T, respectively. In accordance with the Lambert–Beer law, the absorbance was found to vary linearly with concentration, and dilutions were undertaken when the absorbance exceeded 0.6. The data obtained from the adsorption tests were then used to calculate the adsorption capacity, qt (mol/g), of the adsorbent by a mass–balance relationship, which represents the amount of adsorbed dye per amount of dry adsorbent. All experimental runs were conducted at 28 ± 2°C. 2A.4.2.3 Application of Synthesised Zeolites Adsorbent for the Removal of Dyes The present investigation describes the adsorption of methylene blue (MB), methyl orange (MO) and safranine T (S), the organic dyestuffs commonly used for tracer studies over zeolite synthesised from fly ash (SZ). In the present case, adsorption of dyes were found to fit the Freundlich isotherms better than the Langmuir isotherm onto surface of SZ (figures not shown here). The time-dependent amount of dye adsorbed (qt) was calculated from the concentration changes during the adsorption process using the following equation. The removal of dye from the solution and the adsorptive uptake in solid phase (qt) were calculated as follows:
Percentage removal = 100(C0 − Ct )/C0
Adsorption uptake of dye by zeolite, qt = (C0 − Ct )V/w
(A.27)
(A.28)
where C0 is the initial dye concentration (g/L), Ct is the dye concentration (mg/L) at any time t, V is the volume of the solution (L), w is the mass of the adsorbent (g) and qt is the adsorbed quantity of dye (mg/g). 2A.4.2.4 Adsorption Kinetic Study Kinetics studies and dynamic continuous-flow investigations offering information on the rate of adsorption, together with hydrodynamic parameters, are very important for adsorption process design. The study of the adsorption equilibrium and kinetics is essential to supply the basic information required for the design and operation of adsorption equipment. Adsorption techniques have gained favour in recent years because they are considered efficient for the removal of trace organic pollutants from water that cannot be removed using other treatment processes. In addition, adsorption and desorption kinetics are technologically
www.Ebook777.com
Free ebooks ==> www.ebook777.com 100
Green Chemical Engineering
important, because the diffusion within solid particles is a phenomenon of great importance in catalysis, metallurgy, microelectronics, materials science and numerous other scientific and technological applications. A mass transfer occurs during the adsorption process; the first step is the solute transfer through the adsorbent external surface film, and the others are the solute fluid diffusion into the pore holes and the adsorbed molecules’ migration along the pore surfaces, if it takes place. The former is characterised by the external mass-transfer coefficient and the latter ones by the internal pore and surface diffusivities. Available bulk adsorbate concentration in the liquid phase and adsorbed solute concentration on the solid phase are considered time-dependent. So it is possible to see how the rate of adsorption changes with time by plotting the concentration decay curve in the liquid phase or the adsorbate concentration growth curve on the solid phase. Determining the best model: Error analysis: Some of the different error functions were employed in adsorption study to find the most suitable isotherm model to represent the experimental data. These error functions are given in Table A.3. The most commonly used one, the sum of the squares of the errors function, has a major drawback, in that it provides isotherm parameters showing a better fit at the higher end of the adsorbate concentration. This is because the magnitude of the errors and hence the square of the errors increases as the adsorbate concentration increases. Isotherm parameters determined using the sum of the absolute errors method provide a better fit as the magnitude of the errors increases,
Table A.3 Kinetic Parameters for the Removal of Various Dyes (C0 = 1000 mg/L) by Synthesised and Commercial Zeolite Synthesised Zeolite (mg/L) Equations Pseudo-First-Order kf (1/min) qe,cal (mg/g) qe, exp (mg/g) R2 (non-linear) MPSD Pseudo-Second-Order ks (g/mg min) h (mg/g min) qe,cal (mg/g) R2 (non-linear) MPSD Weber Morris Kid1 (mg/g min1/2) I1 R2 Kid2 (mg/g min1/2) I2 R2
Commercial Zeolite (mg/L)
MO
MB
S
MO
MB
0.4472 94.68 92.81 0.9957 18.46
0.3398 98.14 97.26 0.9879 19.58
0.4988 98.79 98.99 0.9966 8.93
0.4472 94.68 92.51 0.9972 17.35
0.3398 98.14 96.26 0.9873 24.83
0.4988 98.79 97.99 0.9963 14.27
0.0168 151.29 94.82 0.9971 15.86
0.0599 579.54 98.35 0.9973 17.78
0.0263 255.35 98.55 0.9984 6.31
0.0158 151.29 94.81 0.9980 14.77
0.0459 579.54 98.35 0.9976 23.44
0.0123 255.35 98.55 0.9980 10.81
0.385 86.82 0.779 0.049 90.56 0.671
0.388 89.40 0.930 0.041 95.69 0.908
0.416 91.67 0.960 0.029 97.92 0.937
0.488 83.53 0.824 0.040 90.78 0.710
0.347 88.75 0.921 0.041 94.69 0.908
0.416 90.67 0.960 0.029 96.92 0.937
www.Ebook777.com
S
Free ebooks ==> www.ebook777.com 101
Introduction to Kinetics and Chemical Reactors
biasing the fit towards the high concentration data. The average relative error function attempts to minimise the fractional error distribution across the entire concentration range. The hybrid fractional error function was developed in order to improve the fit of the SSE method at low concentration values by dividing the measured value. In addition, a divisor was included as a term for the number of degrees of freedom for the system—the number of data points (n) minus the number of parameters (p) within the isotherm equation. MPSD error function (Marquardt, 1963) has been used previously by a number of researchers in the field. It is similar in some respects to a geometric mean error distribution modified according to the number of degrees of freedom of the system. A number of investigators use a correlation coefficient to determine the best-fit kinetic model from the experimental data. The model of which the correlation coefficient is closer to unity is considered better than the other to represent the kinetic data. However, comparison of error between the experimental and predicted values for different models may be a better way to approximate the best-fit kinetic model. As different forms of the equation affected R2 values more significantly during the linear analysis, the non-linear analysis might be a method of avoiding such errors. In our adsorption kinetics study, MPSD error function was used to calculate deviations:
1 MPSD = 100 n−p
n
∑ i =1
2
(qe ,exp − qe , calc ) qe ,exp i
(A.29)
The MPSD is similar in some respects to a geometric mean error distribution modified according to the number of degrees of freedom of the system. 2A.4.2.5 Kinetic Experiments over Zeolite with Different Dyes In the sorption experiments, dye solutions were added to different quantities of sorbents into glass-stoppered bottles and subsequently placed on a shaker for 24 h at 28 ± 2°C. From the initial concentrations of sorbents (g/L) and dyes (mg/L), the amounts adsorbed in the sorbent were measured. Percent removal of dyes over synthesised zeolite as a function of contact time, shown in Figure A.4. The amounts sorbed were determined by the difference between initial and final concentrations and expressed as mg of dye/g of sorbent. Under the conditions of the experiments, all systems approached equilibrium within 15 h of contact time. The adsorption capacity of synthesised zeolite was higher due to larger pore size and surface area compared to commercial zeolite. The molecular size of methyl orange facilitates adsorption, resulting in higher adsorption capacity than methylene blue and safranine T. Reduced adsorption in synthesised zeolite (SZ) is due to the inability of the molecule to penetrate all the internal pore structures and less available surface. The effect of contact time (0–24 h) on the qt values for C0 = 1000 mg/L at m = 1 g/L and T = 303 K is shown in Figure A.5. The contact time of 24 h was considered to be approximately the equilibration time for the adsorption process. It may be seen that in the first 1 h, brisk adsorption of C and R occurred at all C0 and, thereafter, the adsorption rate decreased gradually and the adsorption reached equilibrium. For C0 ≤ 250 mg/L for both the adsorbates, the residual concentrations at 5 h contact time were found to be higher by a maximum of ~2% than those obtained after 24 h contact time. Therefore, after 5 h contact time, a steady-state approximation was assumed and a quasi-equilibrium situation was accepted for C0 ≤ 250 mg/L.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 102
Green Chemical Engineering
80 70
Percent removal
60 50 40 Methyl orange Methylene blue Safranine T
30 20 10 0
0
4
8
12
16
20
24
Contact time (h) Figure A.4 Adsorption of dyes over synthesised zeolite.
Figure A.4 shows that qe increases with an increase of C0. C0 provides the necessary driving force to overcome the resistance for mass transfer of methyl orange, methyl blue and safranine T between the aqueous phase and the solid phase. The increase in C0 also enhances the interaction between adsorbate molecules and the vacant sorption sites on the SZ and the surface functional groups. Therefore, an increase in C0 enhances the adsorption uptake of methyl orange, methyl blue and safranine T by synthesised and commercial zeolite.
95
95
qt (mg/g)
(b) 100
qt (mg/g)
(a) 100
90
85
90
Methyl orange
0
500
Methyl orange
Methyl blue
Methyl blue
Safranine T
Safranine T
1000
Time (min)
1500
85
0
500
1000
1500
Time (min)
Figure A.5 Effect of contact time on the adsorption of dyes by SZ and commercial zeolite (CZ). Experimental data points given by the symbols and the lines predicted by the pseudo-second-order model (not shown here). T = 303 K, m = 1 g/L. (a) SZ, (b) CZ.
www.Ebook777.com
Free ebooks ==> www.ebook777.com Introduction to Kinetics and Chemical Reactors
103
Controlling mechanism: It is well established that the adsorption of an adsorbate from the aqueous phase onto an adsorbent involves broadly the following basic steps: (1) transport of the adsorbate from the bulk of the solution to the exterior surface of the liquid film surrounding the adsorbent particle (external transport), (2) transport across the film to the exterior surface of the adsorbent (film diffusion), (3) the transport of the adsorbate within the adsorbent either by bulk and/or pore diffusion and/or by surface diffusion and (4) the adsorption onto the surface of the adsorbent. The overall adsorption process may be controlled either by one or a combination of steps. In a rapidly stirred batch adsorption process, the first and fourth of the above steps are considered to be fast enough (Weber, 1972), thereby rendering the other two responsible for determining the overall rate of adsorption. Either one or both of these two steps can be rate controlling. The rate of uptake is limited by several characteristics of the adsorbate, adsorbent and the solution phase. Particle size and the functional groups of the adsorbent, concentration of the adsorbate, diffusion coefficient of the adsorbate in the bulk phase and the pores of the adsorbent, affinity of the adsorbate towards the adsorbent and degree of mixing are some of the important factors (Suresh et al., 2011c,d,e). For the adsorption process, the external mass transfer controls the sorption process for systems that have poor mixing, dilute concentration of adsorbate, small particle sizes of adsorbent and higher affinity of adsorbate for adsorbent. Although the intra-particle diffusion controls the adsorption process for a system with good mixing, large particle size of the adsorbent, high concentration of the adsorbate and lower affinity of adsorbate for adsorbent. In the present study, experiments were conducted at a well-agitated (150 rpm) condition, with dye concentration 1000 mg/L, to properly understand the controlling mechanism. In general, external mass transfer is characterised by the initial solute uptake (Suresh et al., 2011c, d) and can be calculated from the slope of plot between C/C0 versus time. The slope of these plots can be calculated either by assuming the polynomial relation between C/C0 and time or on the assumption that the relationship was linear for the first initial rapid phase (the first 30 min in the present study). Using the second technique, the initial adsorption rates (kS) (1/min) were obtained as (C30 min/C0)/30. For methyl orange, methyl blue and safranine T adsorption onto SZ and CZ, the calculated kS values were found to be 0.0168, 0.0599 and 0.02631/min for C0 values of 1000 mg/L, respectively. The respective values for methyl orange, methyl blue and safranine T adsorption were 0.0158, 0.0459 and 0.01231/min. Because of the well-mixed condition, it is expected that the rate of uptake would be governed by the intra-particle or surface diffusion transport. Kumar et al. (2003) found intra-particle diffusion to be the rate-controlling step for the uptake of methyl orange, methyl blue and safranine T onto synthesised and commercial zeolite for C0 = 1000 mg/L. If the Weber and Morris (1963) plot of qt versus t0.5 satisfies the linear relationship with the experimental data, then the sorption process is supposed to be controlled by intra-particle diffusion only. However, if the data exhibit multi-linear plots, then two or more steps influence the sorption process. Figure A.6 presents the plots of qt versus t0.5 for all the adsorbates and the parametric values are given in Table A.3. In this figure, the data points are related by two straight lines. The curvature from the origin to the start of the first straight portion (not shown in figure) represents the boundary layer diffusion and/or external mass transfer effects (Crank, 1965). The first straight portion depicts macro-pore diffusion and the second represents meso-pore diffusion. These show only the pore diffusion data. Extrapolation of the linear portions of the plots back to the ordinate gives the intercepts, which provide the measure of the boundary or film layer thickness. The first linear portion is attributed to the gradual equilibrium stage with intra-particle diffusion dominating. The second portion is
www.Ebook777.com
Free ebooks ==> www.ebook777.com 104
Green Chemical Engineering
95
95
qt (mg/g)
(b) 100
qt (mg/g)
(a) 100
90
85
90
Methyl orange Methyl blue Safraine T 0
10
20
t0.5 (min0.5)
30
Methyl orange Methyl blue Safranine T
40
85
0
10
20
t0.5 (min0.5)
30
40
Figure A.6 Weber and Morris intra-particle diffusion plot for the removal of dyes by SZ and CZ. T = 303 K, m = 10 g/L. (a) Synthesized zeolite, (b) commercial zeolite.
the final equilibrium stage for which the intra-particle diffusion starts to slow down due to the extremely low residual adsorbate concentration in the solution (Suresh et al., 2011e). The deviation of straight lines from the origin indicates that the pore diffusion is not the sole rate-controlling step. Therefore, the adsorption proceeds via a complex mechanism consisting of both surface adsorption and intra-particle transport within the pores of synthesised and commercial zeolite. It can be inferred from Figure A.6 that the diffusion of methyl orange, methyl blue and safranine T from the bulk phase to the external surface of synthesised and commercial zeolite, which begins at the start of the adsorption process, is the fastest. The slope of the linear portions are defined as rate parameters (kid,1 and kid,2) and are characteristics of the rate of adsorption in the region where intra-particle diffusion is rate controlling. It seems that the intra-particle diffusion of methyl orange, methyl blue and safranine T into mesopores (second linear portion) is the rate-controlling step in the adsorption process. The portion of the plots are nearly parallel (kid,2 ≈ 0.029–0.049 mg/g min0.5), suggesting that the rate of adsorption of methyl orange, methyl blue and safranine T into the meso-pores of synthesised and commercial zeolite is comparable at all C0. Slopes of first portions (kid,1) are higher for higher C0 for SZ. This corresponds to an enhanced diffusion of SZ through macro-pores, and is attributed to the greater driving force at higher C0. The multi-phasic nature of the intra-particle diffusion plot confirms the presence of both surface and pore diffusion. In order to predict the actual slow step involved, the kinetic data were further analysed using the Boyd kinetic expression. Equation A.22 was used to calculate Bt values at different time t. The linearity of the plot of Bt versus time was used to distinguish whether surface and intra-particle transport controls the adsorption rate. It was observed that the relation between Bt and t (not shown here) was non-linear (R2 = 0.671–0.937 for synthesised zeolite and R2 = 0.710–0.937 for commercial zeolite) at all concentrations, confirming that surface diffusion is a rate-limiting step. Thus, both surface and pore diffusion seem to be the rate-limiting step in the adsorption process and the adsorption proceeds via a complex mechanism. Average values of De as calculated from Equation A.26 were found to be 2.92 × 10−13 and 2.44 × 10−13 m2/s, respectively, for the adsorption of methyl orange, methyl blue and
www.Ebook777.com
Free ebooks ==> www.ebook777.com 105
Introduction to Kinetics and Chemical Reactors
safranine T onto SZ and CZ. This shows that synthesised zeolite has a little higher overall pore diffusion rate. 2A.4.2.6 Adsorption Kinetics Two kinetic models, namely, pseudo-first-order and pseudo-second-order, were used to investigate the adsorption process of methyl orange, methyl blue and safranine T onto synthesised and commercial zeolite. Kinetic parameters along with correlation coefficient for the pseudo-second-order kinetic model are listed in Table A.3. The calculated correlation coefficient is closer to unity for the pseudo-second-order kinetic model than the pseudo-first-order kinetic model. Therefore, the sorption reaction can be approximated more favourably by the pseudo-second-order kinetic model for methyl orange, methyl blue and safranine T onto synthesised and commercial zeolite. MPSD error function values as shown in Table A.3 are also considerably lower for the pseudo-second-order kinetic model, reinforcing the applicability of the pseudo-second-order kinetic model. It may be seen that the initial sorption rate (h) continuously increased with increase in C0. This is due to the increase in driving force due to the increase in C0. 2A.4.2.7 Adsorption Behaviour of Regenerated Adsorbents The high-temperature regeneration was conducted at 540°C for 5 h. The regenerated synthesised zeolite was tested again for methyl orange adsorption. Figure A.7 represents the comparison of the performance of fresh and regenerated synthesised zeolite for the adsorption of S. It shows lower adsorption compared with the fresh sample. Adsorption of dyes on adsorbents will usually be deposited on the surface and pores of solids. Hightemperature calcination results in the decomposition of adsorbed dyes to gases, thus releasing the surface and pores for re-adsorption. Thermal stability of zeolites: Crystalline zeolites are more resistive to heat than amorphous materials; the main reason being the geometrical structure of the crystalline framework. However, the effects of silica/alumina ratio and level of cation exchange on thermal stability also cannot be denied. Commercial zeolites having a high (SiO2/Al2O3) ratio can resist
Percent removal (safranine T)
70 60
50 40 30
Synthesised zeolite Regenerated zeolite
20 10 0
0
4
8
12 16 Contact time (h)
20
Figure A.7 Adsorption over fresh and regenerated zeolite (synthesised) on safranine T.
www.Ebook777.com
24
Free ebooks ==> www.ebook777.com 106
Green Chemical Engineering
much higher temperatures. The zeolite presently prepared was observed to lose its crystallinity beyond 973 K and the crystalline structure was mostly collapsed above 1073 K (Figure A.7).
2A.5 Conclusions Zeolites of X-type were synthesised from fly ash by alkali fusion followed by hydrothermal treatment. The main crystalline phase of fly ash could be converted into different types of pure zeolites at suitable treatment conditions. The properties of zeolite material formed strongly depended upon the treatment conditions and composition of the raw materials. Zeolites of varying surface area, silica/alumina ratio and crystallinity were obtained by changing the reaction parameters such as ageing time, fusion temperature and fly ash/ NaOH ratio. The cost of synthesised zeolites was very low as compared with commercial zeolite available in the market, as it has been prepared from waste fly ash. The synthesised zeolites were used successfully for the removal of dyes from aqueous solutions. They can also be applied to wastewater treatment and ion exchange applications. This work, therefore, shall be very useful to synthesise zeolites at low cost and apply them in commercially important fields. The kinetics of adsorption were found to be described by pseudo-second-order equation. Results of the intra-particle diffusion model show that the pore diffusion is not the only rate-limiting step. The effective diffusion coefficient of methyl orange, methyl blue and safranine T was of the order of 2.94 × 10−13 and 2.44 × 10−13 m2/s. The percent removal with increase in the pH of the solution increases is almost constant within the range of solution pH 8–10. The high-temperature regeneration was conducted at 540°C for 5 h, which shows that the regenerated catalyst has adsorption capacity slightly less than the fresh catalyst.
Appendix 2B: Fitting Experimental Data to Linear Equations by Regression 2B.1 Fitting Experimental Data to Linear Equations by Regression Assume that a data set of N experimental readings (shown in Table B.1) has to be fitted to a linear equation of the type y = a1x + a0. Best linear fit of the data represents a straight line (in Figure B.1, y versus x graph) around which the data points are evenly scattered. Finding the best fit involves calculation of appropriate values for the coefficients a0 and a1 in such a way that the net error between observed values of y and value of yˆ predicted by straight line equation is the least. The least square parameter estimation method estimates Table B.1 Data Set of N Experimental Readings x y
x1 y1
x2 y2
x3 y3
x4 y4
. .
. .
xi yi
. .
www.Ebook777.com
xN yN
Free ebooks ==> www.ebook777.com 107
Introduction to Kinetics and Chemical Reactors
(xN, yN)
y = a1x + a0 y (x2, y2)
(x3, y3)
(x4, y4) Slope = a1
(x1, y1) Intercept (a0) x Figure B.1 Linear plot of y versus x data.
the value of coefficients a0 and a1 such that the sum of squares of errors between observed y and predicted yˆ is minimum. Thus, values of a0 and a1 are calculated by minimising sum of square of errors J N
J =
∑
2
( y i − yi ) =
i =1
N
∑ (a x + a 1 i
0
− yi )
2
i =1
(B.1)
Applying necessary conditions for minimum of J, we have ∂J = 2 a1 ∂a0
∂J = 2 a1 ∂a1
N
∑ i =1
∑x i =1
∑ y = 0
+ a0
N
N
(B.2)
i
i =1
N
2 i
N
xi + Na0 −
∑ x − ∑ x y = 0 i =1
(B.3)
i i
i
i =1
Equations B.2 and B.3 are linear simultaneous equations written in the matrix form as AX = b
(B.4)
where
N A= N xi i =1
∑
N
∑ i =1 N
∑ i =1
xi a0 ; X = a ; b = 1 xi2
i =1 N xi y i i =1 N
∑y
i
∑
www.Ebook777.com
(B.5)
Free ebooks ==> www.ebook777.com 108
Green Chemical Engineering
Solving Equation B.4, we get estimated values for coefficients a0 and a1. The matrix equation AX = b is called a normal equation. If the problem is to obtain a linear fit to data passing through the origin, then the straight line equation is yˆ i = a1x . Coefficient a1 is calculated by minimising N
∑
J =
N
2
( y i − yi ) =
i =1
∑
( a1xi − yi )
i =1
2
(B.6)
and the necessary condition for minimum is ∂J = 2 a1 ∂a1
N
∑
N
2 i
x −
i =1
∑ i =1
xi y i = 0
So a1 =
N
∑x y i
i =1 N
∑x
2 i
i =1
i
(B.7)
2B.2 Fitting Data to a Linear Equation of the Type y = a1x1 + a 2 x2 + a 0 A data set of N experimental readings (in Table B.2) has to be fitted to a linear equation of the type y = a1x1 + a2x2 + a0. Using the method of least squares discussed in the previous section, the values of coefficient a0, a1 and a2 are estimated by minimising sum of square of errors J: N
J =
∑
2
( y i − yi ) =
i =1
N
∑ (a x
1 1i
+ a2 x2i + a0 − yi )
2
i =1
(B.8)
Applying necessary conditions for minimum of J, we have ∂J = 2 a1 ∂a0
N
∑
N
x1i + a2
i =1
∑
N
x2i + Na0 −
i =1
∑ y = 0
(B.9)
i
i =1
Table B.2 Data Set of N Experimental Readings x1 x2 y
x11 x21 y1
x12 x22 y2
x13 x23 y3
. . .
. . .
x1i x2i yi
. . .
x1N x2N yN
www.Ebook777.com
Free ebooks ==> www.ebook777.com 109
Introduction to Kinetics and Chemical Reactors
∂J = 2 a1 ∂a1
∑ N
∂J = 2 a1 ∂a2
N
N
x12i + a2
i =1
∑
∑
N
x1i x2i + a0
i =1
i =1
N
x1i x2i + a2
i =1
∑
N
x1i −
∑ i =1
∑
i 1i
i =1
N
x22i + a0
∑y x N
x2i −
i =1
∑y x
i 2i
i =1
=0
(B.10)
=0
(B.11)
Equations B.9, B.10 and B.11 are linear simultaneous equations written in the matrix form as AX = b
(B.12)
where
N N A = x1i = i 1 N x2i i =1
x2i i =1 a0 N x1i x2i ; X = a1 ; b = i =1 a2 N xi22 i =1
N
∑
N
∑
x1i
i =1 N
∑
∑x
∑
N
2 i1
i =1
i =1 N x1i yi i =1 N x2i y i i =1 N
∑y
∑
∑
∑
∑
∑x x
1i 2 i
i =1
i
(B.13)
Coefficients a0, a1 and a2 are estimated by solving Equation B.13. If the problem is to fit the data to a linear equation of the type y = a1x1 + a2x2, then the coefficients are calculated by minimising J: N
J =
∑
N
2
( y i − yi ) =
i =1
∑ (a x
1 1i
+ a2 x2i − yi )
i =1
2
(B.14)
Applying the necessary conditions for minimum of J
∂J = 2 a1 ∂a1
∑ N
∂J = 2 a1 ∂a2
N
i =1
∑ i =1
N
x12i + a2
∑ i =1
∑ x y = 0
∑
N
x22i −
i =1
(B.15)
1i i
i =1
N
x1i x2i + a2
N
x1i x2i −
∑x i =1
y = 0 (B.16)
2i i
Equations B.15 and B.16 are written in the matrix form as
AX = b
www.Ebook777.com
(B.17)
Free ebooks ==> www.ebook777.com 110
Green Chemical Engineering
A=
x1i x2i a1 i =1 ; X = a ; b = N 2 x22i i =1
N
∑
N
∑
x12i
i =1
N
∑x x
∑
1i 2 i
i =1
N
yi x2i
∑y x i
i =1 N
∑ i =1
1i
(B.18)
a1 and a2 are estimated by solving Equation B.18. The derivation of normal equation AX = b for fitting a data set of N experimental readings to a linear equation in m variables can be generalised as follows: For linear equation y = a0 + a1x1 + a2 x2 + + am xm
Data matrix D is generated using the experimental readings as 1 x11 x21 x31 . . xm1 y1 1 x x x . . x y 12 22 32 m 2 2 1 x13 x23 x33 . . xm 3 y3 D= and y = . . . . . . . . . . . . . . . . 1 x1N x2 N x3 N . . xmn y N
Now, terms A and b in the normal equation AX = b are calculated as A = DT D
and b = DT y
and x = [a0
a1
a2
...am ]T
For the linear equation passing through the origin
y = a1x1 + a2x2 + …+ amxm The data matrix D is x11 x21 x31 . . xm1 x x x .. x 12 22 32 m 2 x13 x23 x33 . . xm 3 D= . . . . . . . . . . . . x1N x2 N x3 N . . xmn
and x = a1
a2
a3
...am
T
Refer MATLAB program lin_regres.m for the linear regression discussed in this section.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 111
Introduction to Kinetics and Chemical Reactors
Exercise Problems
1. Data on the effect of temperature T on kinetic rate constant k for a first-order irreversible reaction are reported below: T (K) k (1/min)
330 0.0362
370 0.616
410 6.04
450 39.67
Assuming that the Arrhenius law is applicable, estimate the values of activation energy E and frequency factor k0. (Answer: ΔE = 72,000 kJ/kmol; k0 = 9 × 109 kJ/kmol) 2. Experimental data on the variation of equilibrium conversion xAe with temperature T for a first-order reversible exothermic reaction are reported below: T (K) Equilibrium conversion xAe
500 0.959
550 0.907
600 0.819
650 0.703
Estimate the heat of reaction. (Answer: ΔHR = −42,000 kJ/kmol) 3. An irreversible liquid-phase reaction A → B is carried out in a batch reactor at constant temperature taking 1 kmol/m3 of A in the vessel initially. The reacting fluid is sampled at different time instances and the concentration of A, CA is measured. The measured values of CA are reported in the table below. Time, t (min) 0 1 2 3 4 5 10 15 20 30 40 50 70 90 100
CA (kmol/m3) 1.000 0.909 0.833 0.769 0.714 0.666 0.500 0.400 0.333 0.250 0.200 0.166 0.125 0.100 0.091
Estimate the order n of the reaction and the rate constant k using differential method of rate analysis. (Answer: n = 2; k = 0.1)
www.Ebook777.com
Free ebooks ==> www.ebook777.com 112
Green Chemical Engineering
4. Calculate the kinetic parameters k and n for the batch reactor data given in Problem 3 using the half-life period method. 5. An irreversible second-order reaction A + B → C + D with rate equation (−rA) = kCACB is carried out in a constant-volume batch reactor at constant temperature. The reactor contains 1 kmol/m3 of A and 2 kmol/m3 of B at the time of start-up. Variation of concentration of A with time is measured and reported in the table below. Time, t (h) 0 0.54 1.20 1.90 2.90 4.10 5.60 7.70 11.00 17.00
CA (kmol/m3) 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1
Estimate the value of rate constant k using the integral method of analysis. (Answer: k = 0.1) 6. Verify if a non-elementary liquid-phase reaction A → B + C follows the rate equation
(− rA ) =
k1 CA2 kmol/m 3s 1 + k 2C A
and estimate the values of the rate constants k1 and k2. The concentration of A, CA, measured at different time intervals in a batch reactor experiment is reported below: Time, t (min) 0 16 35 57 84 119 166 237 361 680
CA (kmol/m3) 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1
(Answer: k1 = 0.02; k2 = 2)
www.Ebook777.com
Free ebooks ==> www.ebook777.com 113
Introduction to Kinetics and Chemical Reactors
B 7. A first-order parallel reaction A carried out in a batch reactor at constant temC 3 perature taking 10 kmol/m of A at the time of start-up. The reaction is arrested after 20 min and the concentration of compounds A, B and C are measured. The concentrations of A and B are 5 and 4.1667 kmol/m3, respectively. Estimate the values of the rate constants k1 and k2. (Answer: k1 = 2.89 × 10−2; k2 = 5.78 × 10−3) 8. The experimental data on a gas-phase reaction A + B → C carried out on the solid catalyst particles at a pressure of 5 atm are reported below:
PA (atm)
PB (atm)
PC (atm)
0.2 0.1 0.2 0.3 0.3 0.5 0.7 0.6 0.9 0.35 0.2
0.1 0.2 0.3 0.3 0.4 0.5 0.6 0.6 0.9 0.7 0.8
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.95 0.25 0.45
(−rA) kmol A/min kg ⋅ catalyst 3.56 × 10−4 3.13 × 10−4 3.84 × 10−4 5.00 × 10−4 4.63 × 10−4 4.61 × 10−4 5.10 × 10−4 5.33 × 10−4 4.85 × 10−4 1.98 × 10−4 1.95 × 10−4
Verify if the experimental data fit the Langmuir–Hinshelwood model equation for the rate
(− rA ) =
kPA PB (1 + K A PA + K BPB + KC PC )2
and estimate the parameters k, K A, KB and KC. (Answer: k = 120; K A = 10; KB = 20; KC = 15) 9. The experimental data on a gas-phase reaction A + B → C carried out on the solid catalyst particles at a pressure of 5 atm are reported below: PA (atm) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.95 0.25 0.45
PB (atm) 0.2 0.1 0.2 0.3 0.3 0.5 0.7 0.6 0.9 0.35 0.2
PC (atm)
(− rA) kmol A/min kg ⋅ catalyst
0.1 0.2 0.3 0.3 0.4 0.5 0.6 0.6 0.9 0.7 0.8
0.4000 0.2286 0.7200 0.8000 0.8000 1.3333 1.8667 1.6696 2.3586 0.5385 0.4000
www.Ebook777.com
Free ebooks ==> www.ebook777.com 114
Green Chemical Engineering
Verify if the experimental data fit the Langmuir–Hinshelwood model equation for the rate (− rA ) =
kPA PB (1 + K A PA + KC PC )
and estimate the parameters k, K A and KC. (Answer: k = 80; K A = 20; KC = 10) 10. 1 kmol/m3 of a substrate S placed in a batch reactor undergoes reaction in the presence of an enzyme. The concentration of substrate S recorded as a function of time is reported in the table below.
Time, t (h) 0 1.53 3.12 4.78 6.55 8.47 10.58 13.02 16.05 20.51
CS (kmol/m3) 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1
Verify if the given data confirm to the Michaelis–Menton kinetic rate equation (rP ) =
kCS K M + CS
and estimate the values of kinetic parameters k and K M. (Answer: k = 0.1; K M = 0.5)
MATLAB ® Programs List of MATLAB Programs Program Name
Description
Kinetics of Chemical Reactions cal_active_energy. diff_anal_kinet.m half_life_kinet.m integral_anal_kinet.m
Program to calculate activation energy from the kinetic data Program for differential analysis of kinetic data Program for estimation of kinetic parameters using a half-life period method of kinetic data analysis Program for integral analysis of kinetic data
www.Ebook777.com
Free ebooks ==> www.ebook777.com 115
Introduction to Kinetics and Chemical Reactors
Program Name
Description
integral_form_rate.m
Function subroutine to define an integral form of rate equation
integral_anal_kinet2.m
Program for integral analysis of kinetic data
multiple_reactions.m
Program to plot concentration versus time plots for series reaction A → B → C and parallel reaction A → B ↓ C
kinet_non_elem.m
Program for estimation of kinetic parameters of non-elementary reaction A → B + C Reaction rate is (−ra) = (k1*Ca^2)/(1 + K2*Ca)
kinet_lang_hins.m
Program for estimation of kinetic parameters of solid catalysed reaction— Langmuir–Hinshelwood model for A + B → C Reaction rate is (−ra) = (k* Pa* Pb)/(1 + Ka* Pa + Kc* Pc)
kinet_enzyme_cat.m
Program for estimation of kinetic parameters of enzyme-catalysed reaction S → P Michaelis–Menton rate equation Reaction rate is (−ra) = (k1* Cs)/(Km + Cs)
General-Purpose Programs lin_regres.m
Function subroutine for multi-variable linear regression to fit the data to a linear equation of the form y = a0 + a1*x1 + a2*x2…am*xm and estimate the values of coefficients
lin_plot.m
Function subroutine to make a linear plot of the given x–y data and estimate the coefficients
polyn_regres.m
Function subroutine to fit the experimental data to a polynomial equation y = a0 + a1x + a2x^2 +… and estimate the coefficients
polynom_plot
Function subroutine to make a polynomial plot of the given x–y data and calculate the coefficient values
MATLAB PROGRAMS PROGRAM: cal_active_energy.m % program to calculate activation energy from the kinetic data % INPUT DATA %_________________________________________________________________ k_data = [303 323 343 363 ; 0.071 0.189 0.510 0.991] ;
% Temperature in K % k 1/Sec
% CALCULATIONS %_________________________________________________________________ vec_size = size(k_data) ; n = vec_size(1,2) ;% number of readings for i = 1:n T_val = k_data(1,i) ; k_val = k_data(2,i) ; xy_data(i,1) = 1/T_val ;
www.Ebook777.com
Free ebooks ==> www.ebook777.com 116
Green Chemical Engineering
xy_data(i,2) = log(k_val) ; end ; x_label = ′1/T′ ; y_label = ′ln k′ ; coef_vec = lin_plot(xy_data,1,x_label,y_label) ; a0 = coef_vec(1) ; a1 = coef_vec(2) ; k0 = exp(a0) ; % frequency factor 1/Sec delE = −1*(a1)*(8.314) ; % activation energy KJ/Kgmoles % DISPLAY RESULTS %_________________________________________________________________ fprintf(′— — — — — — — — — — — — —— — — — — — — fprintf(′ACTIVATION ENERGY CALCULATION \n′) ; fprintf(′ \n′) ; fprintf(′Frequency factor 1/Sec : fprintf(′Activation Energy KJ/Kgmole : fprintf(′ \n′) ; fprintf(′— — — — — — — — — — — — — — — — — — —
— — — — — — — — — — \n′) ; %10.4f \n′,k0) ; %10.4f \n′,delE) ; — — — — — — — — — — \n′) ;
PROGRAM: diff_anal_kinet.m % program for differential analysis of kinetic data clear all ; % INPUT DATA %_________________________________________________________________ % Ca Vs t Batch data % time ca_t_data = [0 1.1 4.7 7.7 11.3 15.6 20.8 35.6 46.1 60.0 78.8 105 143 202 300 480
Ca 5 ; 4.75 ; 4.5 ; 4.25 ; 4.0 ; 3.75 ; 3.50 ; 3.0 ; 2.75 ; 2.5 ; 2.25 ; 2.0 ; 1.75 ; 1.5 ; 1.25 ; 1.00] ;
% fitting the data to a polynomial of power n_p
www.Ebook777.com
Free ebooks ==> www.ebook777.com Introduction to Kinetics and Chemical Reactors
117
n_p = 6 ; % choose power of polynomial fit_well = 1 ; % 0 - enter initial value 0 % 1 - change to 1 after the choice of polynomial fits the data well n_trim = 3 ;
% number of last data points to be trimmed % for estimation of kinetic parameters
% CALCULATIONS %_________________________________________________________________ vec_size = size(ca_t_data) ; n = vec_size(1,1) ;% number of readings for i = 1:n t_val = ca_t_data(i,1) ; Ca_val = ca_t_data(i,2) ; Ca(i) = Ca_val ; t(i) = t_val ; end ; % fitting the data to a polynomial of power n_p xlabel_s = ′t - time′ ; ylabel_s = ′Ca - Kgmoles/m3′ ; coef_vec = polynom_plot(ca_t_data,n_p,xlabel_s,ylabel_s) ; if fit_well == 1 % Taking the polynomial fit, rate is calculated as derivative of the % polynomial for i = 1:n t_val = t(i) ; yt_val = coef_vec(2) ; for j = 2:n_p yt_val = yt_val + (j)*coef_vec(j+1)*t_val∧(j-1) ; end ; ra(i) = yt_val ; end ; % estimation of kinetic parameters count = 0 ; for i = 1:(n-n_trim) Ca_val = Ca(i) ; ra_val = ra(i) ; if ra_val < 0 count = count + 1; xy_data(count,1) = log(Ca_val) ; xy_data(count,2) = log(-1*ra_val) ; end ; end ;
www.Ebook777.com
Free ebooks ==> www.ebook777.com 118
Green Chemical Engineering
x_label = ′ln Ca′ ; y_label = ′ln (−ra)′ ; coef_vec = lin_plot(xy_data,1,x_label,y_label) ; intercept = coef_vec(1) ; slope = coef_vec(2) ; n_order = slope ; k = exp(intercept) ; % DISPLAY RESULTS %_________________________________________________________________ fprintf(′— — —— — — — — — — — — — — — — — — — — — — — — — — — — — — \n′); fprintf(′DIFFERENTIAL METHOD OF ANALYSIS - KINETIC PARAMETERS k AND n \n′); fprintf(′ \n′) ; fprintf(′Reaction Order n : %10.4f \n′,n_order) ; fprintf(′Reaction Rate Constant k : %10.4f \n′,k) ; fprintf(′ \n′) ; fprintf(′ Conc. Ca Rate ra \n′) ; fprintf(′ \n′) ; for i = 1:n fprintf(′ %10.4f %10.4f \n′,Ca(i),ra(i)) ; end ; fprintf(′ \n′) ; fprintf(′— — — — — — — — — — — — — — — — — — — — — — — — — — — — — \n′) ; end ; % of fit_well PROGRAM: half_life_kinet.m % program for estimation of kinetic parameters using % half life period method of kinetic data analysis clear all ; % INPUT DATA %_________________________________________________________________ % Ca Vs t Batch data % time ca_t_data = [0 1.1 4.7 7.7 11.3 15.6 20.8 35.6 46.1 60.0 78.8 105 143 202 300 480
Ca 5 ; 4.75 ; 4.5 ; 4.25 ; 4.0 ; 3.75 ; 3.50 ; 3.0 ; 2.75 ; 2.5 ; 2.25 ; 2.0 ; 1.75 ; 1.5 ; 1.25 ; 1.00] ;
www.Ebook777.com
Free ebooks ==> www.ebook777.com Introduction to Kinetics and Chemical Reactors
119
% fitting the data to a polynomial of power n_p n_p = 6 ; % choose power of polynomial fit_well = 1 ; % 0 - enter initial value 0 % 1 - change to 1 after the choice of polynomial fits the data well % CALCULATIONS %_________________________________________________________________ vec_size = size(ca_t_data) ; n = vec_size(1,1) ;% number of readings for i = 1:n t_val = ca_t_data(i,1) ; Ca_val = ca_t_data(i,2) ; Ca(i) = Ca_val ; t(i) = t_val ; end ; % fitting the data to a polynomial of power n_p xlabel_s = ′t - time′ ; ylabel_s = ′Ca - Kgmoles/m3′ ; coef_vec = polynom_plot(ca_t_data,n_p,xlabel_s,ylabel_s) ; if fit_well == 1 % Calculation of half life periods for different values of Ca nh = 10 ; % number of concentrations for half life calculation Ca0 = Ca(1); Caf = 0.5*(Ca0 - Ca(n)); t0 = t(1) ; tf = t(n) ; for ii = 1:nh Ca_val = Ca0 + ((ii-1)/(nh-1))*(Caf - Ca0) ; Ca_vec(ii) = Ca_val ; end ; nj = 5000 ; eps = 0.001 ; for ii = 1:nh Ca0_val = Ca_vec(ii) ; Ca0_half = Ca0_val/2 ; count1 = 0 ; count2 = 0 ; t_Ca0 = 0 ; t_Ca0_h = 0 ; for jj = 1:nj t_val = t0 + ((jj-1)/(nj-1))*(tf - t0) ; Ca_val = coef_vec(1) ; for j = 1:n_p Ca_val = Ca_val + coef_vec(j+1)*t_val∧j ; end ;
www.Ebook777.com
Free ebooks ==> www.ebook777.com 120
Green Chemical Engineering
if abs(Ca0_val - Ca_val) < eps*Ca0_val count1 = count1 + 1 ; t_Ca0 = t_Ca0 + t_val ; end ; if abs(Ca0_half - Ca_val) < eps*Ca0_half count2 = count2 + 1 ; t_Ca0_h = t_Ca0_h + t_val ; end ; end ; if ii == 1 t_Ca0 = t0 ; else t_Ca0 = t_Ca0/count1 ; end ; t_Ca0_h = t_Ca0_h/count2 ; t_half = t_Ca0_h - t_Ca0 ; t_h_vec(ii) = t_half ; end ; % estimation of kinetic parameters for ii = 1:nh Ca0_val = Ca_vec(ii) ; t_half = t_h_vec(ii) ; xy_data(ii,1) = log(Ca0_val) ; xy_data(ii,2) = log(t_half) ; end ; x_label = ′ln Ca0′ ; y_label = ′ln (t_half)′ ; coef_vec = lin_plot(xy_data,1,x_label,y_label) ; intercept = coef_vec(1) ; slope = coef_vec(2) ; n_order = −1*slope + 1 ; k = ((2)∧(n_order-1) - 1)/((exp(intercept))*(n_order-1)) ; % DISPLAY RESULTS %_________________________________________________________________ fprintf(′— — — — — — — — — — — — — — — — — — — — — — — — — — — — \n′) ; fprintf(′HALF LIFE PERIOD METHOD OF ANALYSIS - KINETIC PARAMETERS k AND n \n′) ; fprintf(′ \n′) ; fprintf(′Reaction Order n : %10.4f \n′,n_order) ; fprintf(′Reaction Rate Constant k : %10.4f \n′,k) ; fprintf(′ \n′) ; fprintf(′ Ca0 t_half \n′) ; fprintf(′ \n′) ; for i = 1:nh fprintf(′ %10.4f %10.4f \n′,Ca_vec(i),t_h_vec(i)) ; end ;
www.Ebook777.com
Free ebooks ==> www.ebook777.com 121
Introduction to Kinetics and Chemical Reactors
fprintf(′ \n′) ; fprintf(′— — — — — — — — — — — — — — —
— — — — — — — — — — — — — — \n′) ;
PROGRAM: integral_anal_kinet.m % program for integral analysis of kinetic data clear all ; % INPUT DATA %_________________________________________________________________ % Ca Vs t Batch data % time ca_t_data = [0 1.1 4.7 7.7 11.3 15.6 20.8 35.6 46.1 60.0 78.8 105 143 202 300 480
Ca 5 ; 4.75 ; 4.5 ; 4.25 ; 4.0 ; 3.75 ; 3.50 ; 3.0 ; 2.75 ; 2.5 ; 2.25 ; 2.0 ; 1.75 ; 1.5 ; 1.25 ; 1.00] ;
% define the integral form of the rate equation in integral_form_rate reaction_type = 3 ; % % % % % %
0 1 2 3 4 5
-
zero order irreversible first order irreversible second order irreversible third order irreversible second order irreversible first order reversible
-
(-ra) (-ra) (-ra) (-ra) (-ra) (-ra)
= = = = = =
k k*Ca k*Ca∧2 k*Ca∧3 k*Ca*Cb k′*(Ca-Cae)
% fitting the data to the reaction type fit_well = 1 ;% 0 - enter 0 if the reaction type does not fit the data well % 1 - enter 1 if the reaction type fits the data well % CALCULATIONS %_________________________________________________________________ vec_size = size(ca_t_data) ; n = vec_size(1,1) ; % number of readings for i = 1:n t_val = ca_t_data(i,1) ;
www.Ebook777.com
Free ebooks ==> www.ebook777.com 122
Green Chemical Engineering
Ca_val = ca_t_data(i,2) ; Ca(i) = Ca_val ; t(i) = t_val ; end ; Ca0 = Ca(1) ; for i = 1:n t_val = t(i) ; Ca_val = Ca(i) ; xa = 1 - (Ca_val/Ca0) ; kt = integral_form_rate(Ca0,xa,reaction_type); xy_data(i,1) = t_val ; xy_data(i,2) = kt ; end ; x_label = ′t - Time′ ; y_label = ′kt - Integral Form of Rate Equation′ ; coef_vec = lin_plot(xy_data,0,x_label,y_label) ; if fit_well == 1 k = coef_vec(1) ; % DISPLAY RESULTS % _________________________________________________________________ fprintf(′— — — — — — — — — — — — — — — — — — — — — — — — — — — — — \n′) ; fprintf(′INTEGRAL METHOD OF ANALYSIS - KINETIC PARAMETERS k \n′) ; fprintf(′ \n′) ; if reaction_type == 0 fprintf(′Reaction is zero order irreversible - (-ra) = k*\n′) ; end ; if reaction_type == 1 fprintf(′Reaction is first order irreversible - (-ra) = k*Ca \n′) ; end ; if reaction_type == 2 fprintf(′Reaction is second order irreversible - (-ra) = k*Ca∧2 \n′) ; end ; if reaction_type == 3 fprintf(′Reaction is third order irreversible - (-ra) = k*Ca∧3 \n′) ; end ; if reaction_type == 4 fprintf(′Reaction is second order irreversible - (-ra) = k*Ca*Cb \n′) ; end ; if reaction_type == 5 fprintf(′Reaction is first order reversible - (-ra) = (k(1+K)/K)*(CaCae)′ \n′) ; end fprintf(′ \n′) ; fprintf(′Reaction Rate Constant k : %10.4f \n′,k) ; fprintf(′ \n′) ;
www.Ebook777.com
Free ebooks ==> www.ebook777.com Introduction to Kinetics and Chemical Reactors
123
fprintf(′— — — — — — — — — — — — — — — — — — — — — — — — — — — — — \n′) ; end ;% of fit_well FUNCTION SUBROUTINE: integral_form_rate.m % program subroutine to define integral form of rate equation function kt = integral_form_rate(Ca0,xa,eqn_no) if eqn_no == 0 kt = Ca0*xa ; end ;
% zero order irreversible reaction A ---> B
if eqn_no == 1 % first order irreversible reaction A ---> B kt = log(1/(1-xa)) ; end ; if eqn_no == 2 % second order irreversible reaction A ---> B kt = (1/Ca0)*(xa/(1-xa)) ; end ; if eqn_no == 3 % third order irreversible reaction A ---> B kt = (1/(2*Ca0∧2))*(1/(1-xa)∧2 - 1) ; end ; if eqn_no == 4 % second order irreversible reaction A + B ---> C M = 2 ; % M = Cb0/Ca0 if M == 1 kt = (1/Ca0)*(xa/(1-xa)) ; else kt = (1/(Ca0*(M-1)))*log((M-xa)/(M*(1-xa))) ; end ; end ; if eqn_no == 5 % first order reversible reaction A ⇔ B K = 1.667 ; % K = Cae/Cae - equilibrium constant Ca = Ca0*(1-xa) ; kt = (K/(K+1))*log((K*Ca0)/((1+K)*Ca - Ca0)) ; end ; PROGRAM: integral_anal_kinet2.m % program for integral analysis of kinetic data clear all ; % INPUT DATA %_________________________________________________________________ % Ca Vs t Batch data % time Ca ca_t_data = [0 4 ; 1 3.6 ; 2 3.4 ;
www.Ebook777.com
Free ebooks ==> www.ebook777.com 124
Green Chemical Engineering
3 4 5 6 7 8 9 10
3.0 2.8 2.6 2.4 2.3 2.2 2.1 2.0
reaction_type = 5 ; % % % % % %
0 1 2 3 4 5
; ; ; ; ; ; ; ] ; -
zero order irreversible first order irreversible second order irreversible third order irreversible second order irreversible first order reversible
-
(-ra) (-ra) (-ra) (-ra) (-ra) (-ra)
= = = = = =
k k*Ca k*Ca∧2 k*Ca∧3 k*Ca*Cb k′*(Ca-Cae)
% fitting the data to the reaction type fit_well = 1 ; % 0 - enter 0 if the reaction type does not fit the data well % 1 - enter 1 if the reaction type fits the data well % CALCULATIONS %_________________________________________________________________ vec_size = size(ca_t_data) ; n = vec_size(1,1) ;% number of readings for i = 1:n t_val = ca_t_data(i,1) ; Ca_val = ca_t_data(i,2) ; Ca(i) = Ca_val ; t(i) = t_val ; end ; Ca0 = Ca(1) ; for i = 1:n t_val = t(i) ; Ca_val = Ca(i) ; xa = 1 - (Ca_val/Ca0) ; kt = integral_form_rate(Ca0,xa,reaction_type); xy_data(i,1) = t_val ; xy_data(i,2) = kt ; end ; x_label = ′t - Time′ ; y_label = ′kt - Integral Form of Rate Equation′ ; coef_vec = lin_plot(xy_data,0,x_label,y_label) ; if fit_well = = 1 k = coef_vec(1) ; % DISPLAY RESULTS % _________________________________________________________________
www.Ebook777.com
Free ebooks ==> www.ebook777.com Introduction to Kinetics and Chemical Reactors
125
fprintf(′— — — — — — — — — — — — — — — — — — — — — — — — — — — — — \n′) ; fprintf(′INTEGRAL METHOD OF ANALYSIS - KINETIC PARAMETERS k \n′) ; fprintf(′ \n′) ; if reaction_type == 0 fprintf(′Reaction is zero order irreversible - (-ra) = k*\n′) ; end ; if reaction_type == 1 fprintf(′Reaction is first order irreversible - (-ra) = k*Ca \n′) ; end ; if reaction_type == 2 fprintf(′Reaction is second order irreversible - (-ra) = k*Ca∧2 \n′) ; end ; if reaction_type == 3 fprintf(′Reaction is third order irreversible - (-ra) = k*Ca∧3 \n′) ; end ; if reaction_type == 4 fprintf(′Reaction is second order irreversible - (-ra) = k*Ca*Cb \n′) ; end ; if reaction_type == 5 fprintf(′Reaction is first order reversible - (-ra) = (k(1+K)/K)*(CaCae) \n′) ; end fprintf(′ \n′) ; fprintf(′Reaction Rate Constant k : %10.4f \n′,k) ; fprintf(′ \n′) ; fprintf(′— — — — — — — — — — — — — — — — — — — — — — — — — — — — — \n′) ; end ;% of fit_well PROGRAM: multiple_reactions.m % programdspf to plot concentration vs time plots for % series reaction A--> B--> C and % parallel reaction A--> B % | % C % INPUT DATA %_________________________________________________________________ reaction_type = 2 ; % 1 - Series Reaction % 2 - Parallel Reaction k1 = 0.1 ; k2 = 0.05 ; % CALCULATIONS %_________________________________________________________________ tmax = 10*(1/k1) ; n_p = 200 ; if reaction_type == 1 for i = 1:n_p t = ((i-1)/(n_p - 1))*tmax ; Ca = exp(-1*k1*t) ;
www.Ebook777.com
Free ebooks ==> www.ebook777.com 126
Green Chemical Engineering
Cb = (k1/(k1-k2))*(exp(-1*k2*t) - exp(-1*k1*t)) ; Cc = 1 - Ca - Cb ; t_vec(i) = t ; Ca_vec(i) = Ca ; Cb_vec(i) = Cb ; Cc_vec(i) = Cc ; end ; title(′Series Reaction′) ; plot(t_vec,Ca_vec,′-b′,t_vec,Cb_vec,′-r′,t_vec,Cc_vec,′-g′) ; xlabel(′t - time′) ; ylabel(′Concentration′) ; legend(′Ca′,′Cb′,′Cc′) ; end ; if reaction_type == 2 for i = 1:n_p t = ((i-1)/(n_p - 1))*tmax ; Ca = exp(-1*(k1+k2)*t) ; Cb = (k1/(k1+k2))*(1 - Ca) ; Cc = (k2/(k1+k2))*(1 - Ca) ; t_vec(i) = t ; Ca_vec(i) = Ca ; Cb_vec(i) = Cb ; Cc_vec(i) = Cc ; end ; title(′Parallel Reaction′) ; plot(t_vec,Ca_vec,′-b′,t_vec,Cb_vec,′-r′,t_vec,Cc_vec,′-g′) ; xlabel(′t - time′) ; ylabel(′Concentration′) ; legend(′Ca′,′Cb′,′Cc′) ; end ; PROGRAM: kinet_non_elem.m % Estimation of Kinetic parameters of non elementary reaction A--> B + C % Reaction rate - (-ra) = (k1*Ca∧2)/(1+K2*Ca) clear all ; % INPUT DATA %_________________________________________________________________ % Ca Vs t Batch data % time Ca ca_t_data = [0 2 ; 7.5 1.9 ; 16 1.8 ; 35 1.6 ; 60 1.4 ; 85 1.2 ; 120 1.0 ; 170 0.8 ; 240 0.6 ; 360 0.4] ;
www.Ebook777.com
Free ebooks ==> www.ebook777.com Introduction to Kinetics and Chemical Reactors
127
% CALCULATION %_________________________________________________________________ vec_size = size(ca_t_data) ; n = vec_size(1,1) ; % number of readings for i = 1:n t_val = ca_t_data(i,1) ; Ca_val = ca_t_data(i,2) ; Ca(i) = Ca_val ; t(i) = t_val ; end ; Ca0 = Ca(1) ; for i = 1:n t_val = t(i) ; Ca_val = Ca(i) ; xa = 1 - Ca_val/Ca0 ; x1 = xa/(Ca0*(1-xa)) ; x2 = log(1/(1-xa)) ; y = t_val ; xy_data(i,1) = x1 ; xy_data(i,2) = x2 ; xy_data(i,3) = y ; end ; coef_vec = lin_regres(xy_data,0) ; a1 = coef_vec(1) ; a2 = coef_vec(2) ; k1 = 1/a1 ; K2 = a2/a1 ; % DISPLAY RESULT %_________________________________________________________________ fprintf(′— — — — — — — — — — — — — — — — — — — — — — — — — — — — — \n′) ; fprintf(′ESTIMATION OF KINETIC PARAMETERS k1 AND K2 FOR NON ELEMENTARY REACTION \n′) ; fprintf(′RATE EQUATION - (-ra) = (k1*Ca∧2)/(1+K2*Ca) \n′) ; fprintf(′ \n′) ; fprintf(′Reaction Rate Constant k1 : %10.4f \n′,k1) ; fprintf(′Equilibrium Constant K2 : %10.4f \n′,K2) ; fprintf(′ \n′) ; fprintf(′ \n′) ; fprintf(′— — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — \n′) ; PROGRAM: kinet_lang_hins.m % Estimation of Kinetic parameters of solid catalysed reaction % Langmuir Hinselwood Model for A + B ----> C
www.Ebook777.com
Free ebooks ==> www.ebook777.com 128
Green Chemical Engineering
% Reaction rate - (-ra) = (k*Pa*Pb)/(1+Ka*Pa+Kc*Pc) clear all ; % INPUT DATA %_________________________________________________________________ % rate data % rate_data =
(-ra) [0.04338 0.02037 0.01393 0.00809 0.00643 0.00487 0.00387 0.00305 0.00245 0.00213 0.00175
Pa(atm) 0.112 0.212 0.325 0.450 0.486 0.546 0.632 0.738 0.772 0.823 0.921
Pb(atm) 1.276 0.555 0.328 0.193 0.158 0.122 0.093 0.073 0.060 0.052 0.043
Pc(atm) 0.102 ; 0.205 ; 0.226 ; 0.352 ; 0.423 ; 0.510 ; 0.532 ; 0.629 ; 0.702 ; 0.754 ; 0.857 ] ;
% CALCULATION %_________________________________________________________________ vec_size = size(rate_data) ; n = vec_size(1,1) ;% number of readings for i = 1:n ra_val = rate_data(i,1) ; Pa_val = rate_data(i,2) ; Pb_val = rate_data(i,3) ; Pc_val = rate_data(i,4) ; x1 = 1/(Pa_val*Pb_val) ; x2 = 1/Pb_val ; x3 = Pc_val/(Pa_val*Pb_val) ; y = (1/ra_val) ; xy_data(i,1) = x1 ; xy_data(i,2) = x2 ; xy_data(i,3) = x3 ; xy_data(i,4) = y ; end ; coef_vec = lin_regres(xy_data,0) ; a1 = coef_vec(1) ; a2 = coef_vec(2) ; a3 = coef_vec(3) ; k = 1/a1 ; Ka = (a2/a1) ; Kc = (a3/a1) ; % DISPLAY RESULT %_________________________________________________________________
www.Ebook777.com
Free ebooks ==> www.ebook777.com Introduction to Kinetics and Chemical Reactors
129
fprintf(′— — — —— — — — — — — — — — — — — — — — — — — — — — — — \n′) ; fprintf(′ESTIMATION OF KINETIC PARAMETERS OF SOLID CATALYSED REACTION \n′) ; fprintf(′LANGMUIR - HINELWOOD MODEL for A + B ----> \n′) ; fprintf(′RATE EQUATION - (-ra) = (k*Pa*Pb)/(1+Ka*Pa+Kc*Pc) \n′) ; fprintf(′ \n′) ; fprintf(′Reaction Rate Constant k : %10.4f \n′,k) ; fprintf(′Adsorption Equilibrium Constant of A Ka : %10.4f \n′,Ka) ; fprintf(′Adsorption Equilibrium Constant of C Kc : %10.4f \n′,Kc) ; fprintf(′ \n′) ; fprintf(′ \n′) ; fprintf(′— — — — — — — — — — — — — — — — — — — — — — — — — — — — \n′) ; PROGRAM: kinet_enzyme_cat.m % Estimation of Kinetic parameters of Enzyme Catalysed Reaction S ---> P % Michaelis - Menton rate equation % Reaction rate - (-ra) = (k1*Cs)/(Km+Cs) clear all ; % INPUT DATA %_________________________________________________________________ % Cs Vs t Batch data % time ca_t_data = [0 0.5 1.0 1.5 2.0 2.5 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0
Cs 2 ; 1.78 ; 1.56 ; 1.34 ; 1.12 ; 0.926 ; 0.748 ; 0.422 ; 0.238 ; 0.104 ; 0.044 ; 0.018 ; 0.008 ; 0.003] ;
% fitting the data to a polynomial of power n_p n_p = 5 ; % choose power of polynomial fit_well = 1 ; % 0 - enter initial value 0 % 1 - change to 1 after the choice of polynomial fits the data well n_trim = 3 ;
% number of last data points to be trimmed % for estimation of kinetic parameters
% CALCULATION %_________________________________________________________________
www.Ebook777.com
Free ebooks ==> www.ebook777.com 130
Green Chemical Engineering
vec_size = size(ca_t_data) ; n = vec_size(1,1) ; % number of readings for i = 1:n t_val = ca_t_data(i,1) ; Cs_val = ca_t_data(i,2) ; Cs(i) = Cs_val ; t(i) = t_val ; end ; % fitting the data to a polynomial of power n_p xlabel_s = ′t - time′ ; ylabel_s = ′Cs - Kgmoles/m3′ ; coef_vec = polynom_plot(ca_t_data,n_p,xlabel_s,ylabel_s) ; if fit_well == 1 % Taking the polynomial fit, rate is calculated as derivative of the % polynomial for i = 1:n t_val = t(i) ; yt_val = coef_vec(2) ; for j = 2:n_p yt_val = yt_val + (j)*coef_vec(j+1)*t_val∧(j-1) ; end ; ra(i) = yt_val ; end ; % estimation of kinetic parameters count = 0 ; for i = 1:(n-n_trim) Cs_val = Cs(i) ; ra_val = ra(i) ; if ra_val \lt 0 count = count + 1; xy_data(count,1) = 1/Cs_val ; xy_data(count,2) = 1/(-1*ra_val) ; end ; end ; x_label = ′1/Cs′ ; y_label = ′1/(-ra)′ ; coef_vec = lin_plot(xy_data,1,x_label,y_label) ; intercept = coef_vec(1) ; slope = coef_vec(2) ; k = 1/intercept ; Km = slope/intercept ;
www.Ebook777.com
Free ebooks ==> www.ebook777.com Introduction to Kinetics and Chemical Reactors
131
% DISPLAY RESULT %_________________________________________________________________ fprintf(′— — — —— — — — — — — — — — — — — — — — — — — — — — — — — — \n′) ; fprintf(′ESTIMATION OF KINETIC PARAMETERS k AND KmFOR ENZYME CATALYSED REACTION \n′) ; fprintf(′MICHAELIS-MENTON RATE EQUATION \n′) ; fprintf(′RATE EQUATION - (-ra) = (k*CS)/(Km+Cs) \n′) ; fprintf(′ \n′) ; fprintf(′Reaction Rate Constant k : %10.4f \n′,k) ; fprintf(′Equilibrium Constant Km : %10.4f \n′,Km) ; fprintf(′ \n′) ; fprintf(′ \n′) ; fprintf(′— — — — — — — — — — — — — — — — — — — — — — — — — — — — — \n′) ; end ;% of fit_well FUNCTION SUBROUTINE: lin_regres.m function coef_vec = lin_regres(xy_data,type) % multi variable linear regression programm y = a0 + a1*x1 + a2*x2… am*xm % % m = number of variables ; n = number of data points % type = 1 if not passing through origin % type = 0 if passing through origin vec_size = size(xy_data) ; n = vec_size(1,1) ; % number of readings m = vec_size(1,2) - 1 ; % number of input variables if type == 1 for i = 1:n D_mat(i,1) = 1 ; for j = 1:m x_val = xy_data(i,j) ; D_mat(i,j+1) = x_val ; end ; y_val = xy_data(i,m+1) ; y_vec(i,1) = y_val ; end ; a_mat = D_mat′*D_mat ; b_vec = D_mat′*y_vec ; coef_vec = inv(a_mat)*b_vec ; end ; if type == 0 for i = 1:n for j = 1:m x_val = xy_data(i,j) ; D0_mat(i,j) = x_val ; end ; y_val = xy_data(i,m+1) ; y0_vec(i,1) = y_val ;
www.Ebook777.com
Free ebooks ==> www.ebook777.com 132
Green Chemical Engineering
end ; a0_mat = D0_mat′*D0_mat ; b0_vec = D0_mat′*y0_vec ; coef_vec = inv(a0_mat)*b0_vec ; end ; FUNCTION SUBROUTINE: lin_plot.m % subroutine to make a linear plot of the given x-y data function coef_vec = lin_plot(xy_data,plot_type,xlabel_s,ylabel_s) vec_size = size(xy_data) ; n = vec_size(1,1) ; % number of readings coef_vec = lin_regres(xy_data,plot_type) ; if plot_type == 1 a0 = coef_vec(1) ; a1 = coef_vec(2) ; end ; if plot_type == 0 a0 = 0 ; a1 = coef_vec(1) ; end ; for i = 1:n x_val = xy_data(i,1) ; y_val = xy_data(i,2) ; yt_val = a0 + a1*x_val ; x(i) = x_val ; y(i) = y_val ; yt(i) = yt_val ; end; % graph plot(x,y,′*′,x,yt,′-r′) ; ylabel(ylabel_s) ; xlabel(xlabel_s) ; legend(′Data Points′,′Straight Line Fit′); a0_s = num2str(a0) ; a1_s = num2str(a1) ; va = axis ; xs = va(2) - va(1) ; ys = va(4) - va(3) ; text(va(1)+0.1*xs,va(3)+0.95*ys,strcat(′Slope text(va(1)+0.1*xs,va(3)+0.88*ys,strcat(′Intercept
= ′,a1_s)); = ′,a0_s));
FUNCTION SUBROUTINE: polyn_regres.m % program to fit the experimental data to polynomial equation % y = a0 + a1x + a2x∧2 +… function coef_vec = polyn_regres(xy_data,n_p) % n_p - polynomial power
www.Ebook777.com
Free ebooks ==> www.ebook777.com Introduction to Kinetics and Chemical Reactors
vec_size = size(xy_data) ; n = vec_size(1,1) ; % number of readings for i = 1:n x_val = xy_data(i,1) ; for j = 1:n_p xyp_data(i,j) = x_val∧j ; end ; y_val = xy_data(i,2) ; xyp_data(i,n_p+1) = y_val ; end ; coef_vec = lin_regres(xyp_data,1) ; FUNCTION SUBROUTINE: polynom_plot.m % subroutine to make a polynomial plot of the given x-y data and calculate % the coefficient values function coef_vec = polynom_plot(xy_data,n_p,xlabel_s,ylabel_s) % n_p - polynomial power vec_size = size(xy_data) ; n = vec_size(1,1) ; % number of readings coef_vec = polyn_regres(xy_data,n_p) ; a0 = coef_vec(1) ; for i = 1:n x_val = xy_data(i,1) ; y_val = xy_data(i,2) ; yt_val = a0 ; for j = 1:n_p coef_val = coef_vec(j+1) ; yt_val = yt_val + coef_val*x_val∧j ; end ; x(i) = x_val ; y(i) = y_val ; yt(i) = yt_val ; end; % graph plot(x,y,′*′,x,yt,′-r′) ; ylabel(ylabel_s) ; xlabel(xlabel_s) ; legend(′Data Points′,′Polynomial Fit′);
www.Ebook777.com
133
Free ebooks ==> www.ebook777.com
www.Ebook777.com
Free ebooks ==> www.ebook777.com
3 Homogeneous Reactors As mentioned in the previous chapter, chemical reactors are broadly classified as homogeneous (single phase) reactors and heterogeneous (multiphase) reactors. This chapter outlines various methods for design of homogeneous reactors. Design of ideal, non-ideal and non-isothermal reactors are discussed in detail.
3.1 Homogeneous Ideal Reactors Homogeneous reactors are simple holding vessels that are used for carrying out homogeneous gas-phase or liquid-phase reactions (Section 2.2.1). Based on the shape of the reaction vessel, these reactors are broadly classified as continuous stirred tank reactors (CSTR) and tubular reactors. Fluid mixing pattern in the reaction vessel is one of the factors that influences the extent of conversion achieved in the reactor. Reactors in which mixing of fluid is assumed to follow a predefined pattern are known as ideal reactors. Thus, an ideal CSTR is a CSTR in which mixing of fluid is perfect or complete, leading to uniformity in concentration of chemical compounds in the vessel. The ideal plug flow reactor (PFR) is a tubular reactor in which there is perfect mixing of fluid in the radial direction and no mixing of fluid in the axial direction. In reality, the mixing pattern of fluid will be different from the mixing patterns assumed in ideal reactors and these reactors are called non-ideal reactors. However, in practice, a homogeneous reactor is designed assuming it to be an ‘ideal reactor’ and the effect of deviations from ideality on the reactor performance is accounted for at the post-design stage. Design and performance of ideal reactors are discussed in this section. Characterisation and performance analysis of non-ideal reactors will be discussed later in Section 3.2. 3.1.1 Design Equations for Ideal Reactors The design of a continuous-flow reactor involves the calculation of reactor volume (V) required to achieve a specified conversion (xAf) of the reactant given the amount of fluid (flow rate q) processed in the reactor and the concentrations of reactants (CA0) in the feed. The design equations are derived (Section 2.2.1) by writing the steady-state molal balance equation for the limiting reactant. The design equations for an ideal CSTR and an ideal PFR (represented in Figures 3.1 and 3.2) are as follows: For an ideal CSTR,
τ=
CA 0 − CAf V = q (− rA (C Af ))
(3.1)
135
www.Ebook777.com
Free ebooks ==> www.ebook777.com 136
Green Chemical Engineering
q CA0 CAf q
V
Figure 3.1 Schematic diagram of an ideal CSTR.
For an ideal PFR, τ=
V = q
CAO
dCA
∫ (−r (C ))
CAf
A
A
(3.2)
where V: reactor volume (m3) q: volumetric flow rate (m3/s) CA0: concentration of reactant A in the feed (kmol/m3) CAf : concentration of reactant A in the fluid outlet (kmol/m3) −rA(CA): specific rate of conversion of A (kmol/m3 s) defined by the kinetic rate equation τ is defined as space time, which is the mean time of residence of fluid in the reaction vessel. This is the quantum of time that is made available for the fluid to undergo reaction in the vessel. The larger the value of τ, the larger the extent of conversion (X Af = 1 − (CAf/CAO)) achieved in the reactor. For a specified amount of fluid (flow rate q) processed in the reaction vessel, it is the volume V of the reactor that determines the space, time τ(τ = V/q) and the extent of conversion (X Af) achieved. For any reaction, given the rate equation −rA(CA), an ideal CSTR or an ideal PFR can be designed using Equation 3.1 or 3.2, respectively. According to the Arrhenius law, reaction rate constant k is a function of temperature and it increases with an increase in temperature: k = k o e −∆E/RT
q
V
CA0
Figure 3.2 Schematic diagram of an ideal PFR.
www.Ebook777.com
(3.3)
q CAf
Free ebooks ==> www.ebook777.com 137
Homogeneous Reactors
For a reactor operating in an isothermal condition, the value of k is taken as a constant. Assumption of an isothermal condition is justified if the heat of reaction (ΔHR) is neglected. The design of reactors operating in an isothermal condition is presented in the following sections. The design of non-isothermal reactors will be discussed later in Section 3.1.5. 3.1.1.1 Design Equation for First-Order Irreversible Reaction Consider a first-order irreversible reaction A k → B, −rA = kCA carried out in a constantvolume isothermal homogeneous reactor. Substituting the first-order rate equation into the design equations, For an ideal CSTR, we get τ=
CA 0 − CAf 1 X Af V = = q kC Af k 1 − X Af
(3.4)
For an ideal PFR, we get V τ= = q
CA0
dCA
∫ kC
CAf
A
=
1 CA0 1 1 ln = ln k C Af k 1 − X Af
(3.5)
The space times τ required to achieve a specified conversion for an ideal CSTR and for an ideal PFR are calculated using Equations 3.4 and 3.5, respectively. Equations 3.4 and 3.5 can be rearranged to obtain expressions for the calculation of fractional conversion X Af achieved in a specified space time τ. For an ideal CSTR, X Af =
kτ 1 + kτ
(3.6)
For an ideal PFR, X Af = 1 − e − kτ
(3.7)
3.1.1.2 Design Equation for Second-Order Irreversible Reaction Consider a second-order irreversible reaction A k → B, − rA = kCA2 carried out in a constantvolume isothermal homogeneous reactor. The design equations are as follows: For an ideal CSTR, τ=
CA 0 − C Af 1 V = = 2 q kC Af kC A 0
X Af 2 (1 − X Af )
(3.8)
For an ideal PFR,
V τ= = q
CA0
dCA
∫ kC
CAf
2 A
=
1 1 1 1 − = k CAf CA 0 kCA 0
X Af 1 − X Af
www.Ebook777.com
(3.9)
Free ebooks ==> www.ebook777.com 138
Green Chemical Engineering
Equations 3.8 and 3.9 are used for calculating τ for a specified conversion X Af. Rearranging Equation 3.8 for an ideal CSTR, we get a quadratic equation in X Af 2 (k τCA 0 )X Af − (1 + 2k τC A 0 )X Af + (k τC A 0 ) = 0
(3.10)
which on solving gives X Af =
1 + 2k τCA 0 − 1 + 4k τCA 0 2k τCA 0
(3.11)
Similarly, rearranging Equation 3.9 for an ideal PFR, we get X Af =
k τCA 0 1 + k τC A 0
(3.12)
Equations 3.11 and 3.12 are used for calculating conversion X Af achieved for a specified value of space time τ in an ideal CSTR and an ideal PFR, respectively. 3.1.1.3 Design Equation for First-Order Reversible Reaction k1
Consider a reversible first-order reaction A B, carried out in a constant-volume isotherk2
mal homogeneous reactor. The rate equation is (Section 2.1.7.5) − rA =
k1(1 + K ) (C A − CAe ) K
(3.13)
where
Equilibrium constant K =
Equilibrium conversion CAe =
k1 k2
(3.14)
CA0 1+ K
(3.15)
The design equations are as follows: For an ideal CSTR, τ=
C A 0 − C Af V = k1(1 + K )/K (C Af − C Ae ) q
(3.16)
Defining xAe as the equilibrium conversion, we can write
CAe = CA 0 (1 − x Ae )
www.Ebook777.com
(3.17)
Free ebooks ==> www.ebook777.com 139
Homogeneous Reactors
and x Ae = 1 −
CAe K = CA0 1+ K
(3.18)
Substituting Equations 3.17 and 3.18 into Equation 3.16, we get τ=
X Af V K = q k1(1 + K ) x Ae − X Af
(3.19)
For an ideal PFR, V τ= = q
CA 0
CAf
=
dCA
∫ (k (1 + K ))/(K )(C 1
Af
− CAe )
(3.20)
C − C Ae K ln A 0 k1(1 + K ) C Af − C Ae
(3.21)
and finally τ=
K x Ae ln k1(1 + K ) x Ae − X Af
(3.22)
Rearranging Equations 3.19 and 3.22, we obtain expressions for calculating conversion X Af for a specified value of space time τ: For an ideal CSTR, k τ X Af = x Ae 1 + kτ
(3.23)
For an ideal PFR,
X Af = x Ae (1 − e − kτ )
(3.24)
where
k (1 + K ) k = 1 K
Design equations derived for an ideal CSTR and an ideal PFR for some typical reactions are summarised in Table 3.1.
www.Ebook777.com
− rA = k1CA − k 2CB
k2
AB
k1
1 kCAn−01
X Af n (1 − X Af )
1 X Af 2 kCAO (1 − X Af )
1 X Af k 1 − X Af
K x Ae ln k1 (1 + K ) x Ae − X Af k (1 + K ) k = 1 K k K = 1 k2
τ=
τ=
τ=
τ=
Equation for τ
X Af =
Ideal CSTR
kτ 1 + kτ
k τ X Af = x Ae 1 + k τ K x Ae = 1+ K
—
1 + 2k τCA 0 − 1 + 4k τCA 0 2k τCA 0
X Af =
Equation for XAf
τ=
1 X Af kCA 0 1 − X Af
1 1 ln k 1 − X Af
τ=
k1 (1 + K ) CA 0 − CAe ln K CAf − CAe
1 1 ln − 1 (n − 1)kCAn−01 (1 − X Af )n − 1
τ=
τ=
Equation for τ
Ideal PFR
—
k τCA 0 1 + k τCA 0
X Af = x Ae (1 − e − kτ )
X Af =
X Af = 1 − e − kτ
Equation for XAf
140
Reversible first-order reaction
− rA = kCAn
A k →B
nth-order irreversible reaction
− rA = kCA2
A k → B,
Second-order irreversible reaction
A → B, − rA = kCA
k
First-order irreversible reaction
Reaction Type
Design Equations for Ideal CSTR and Ideal PFR
Table 3.1
Free ebooks ==> www.ebook777.com Green Chemical Engineering
www.Ebook777.com
Free ebooks ==> www.ebook777.com 141
Homogeneous Reactors
Problem 3.1 If the space time required to achieve 80% conversion in an ideal PFR is 10 min, what is the space time required to achieve the same conversion in an ideal CSTR? The reaction is second-order irreversible. The feed concentration of the reactant is 4 kmol/m3. What are the conversions in the PFR and the CSTR if space time is doubled? For a second-order irreversible reaction, τ PFR =
⇒k =
1 kC A 0
X Af 1 − X Af
1 τ PFRC A 0
X Af 1 − X Af
Substituting τPFR = 10, CA0 = 4 and X Af = 0.8 into this equation, we get k =
m3 1 1 0.8 = 0 . 1 kmoles min (10)( 4) 1 − 0.8
Space time for an ideal CSTR τ CSTR =
τ CSTR =
X Af kC A 0 (1 − X Af )2 0.8 (0.1)( 4)(1 − 0.8)2
τ CSTR = 50 min If the space time is doubled, then τ PFR = 20 and τ CSTR = 100
Conversion in PFR
X Af =
k τCA 0 (0.1)(20)( 4) = = 88.9% 1 + k τC A 0 1 + (0.1)(20)( 4)
Conversion in the CSTR
X Af =
X Af =
(1 + 2k τCA 0 ) − 1 + 4k τCA 0 2k τCA 0
[1 + 2(0.1)(100)(4)] −
1 + 4(0.1)(100)( 4) (2)(0.1)(100)( 4)
X Af = 85.4%
www.Ebook777.com
Free ebooks ==> www.ebook777.com 142
Green Chemical Engineering
Problem 3.2 k1 A first-order reversible reaction A B is carried out in an ideal CSTR. For a space time of 10 min, 40% conversion of A is achieved in the reactor. Conversion dropped to 30% level when the feed flow rate is doubled. Calculate the rate constant k and the equilibrium constant K. For a reversible first-order reaction, X Af k τ = x Ae 1 + k τ
where
k (1 + K ) k = 1 K
x Ae =
K 1+ K
For τ1 = 10 min, x1Af = 0.4. 2 = 0.3. When the flow rate is doubled, the space time τ2 is τ2 = 5 min. So, for τ2 = 5 min, x Af
x1Af τ 1 + k τ 2 = 1 2 τ 2 1 + k τ1 x Af
1 + k τ 2 x1Af τ 2 0.4 5 2 = = 0.667 = = 2 1 + k τ 3 x Af τ1 0.3 10 1
3(1 + k τ 2 ) = 2(1 + k τ1 )
1 3−2 = 0.2 = k = 2τ1 − 3τ 2 (2 × 10 − 3 × 5)
x Ae =
=
X Af (1 + k τ) k τ (0.4)(1 + (0.2)10) = 0.60 (0.2)(10)
Equilibrium conversion is 60%
x Ae =
K ⇒ K = 1.5 1+ K
www.Ebook777.com
Free ebooks ==> www.ebook777.com 143
Homogeneous Reactors
k (1 + K ) kK (0.2)(1.5) k = 1 ⇒ k1 = = = 0.12 K 1+ K (1 + 1.5)
So, rate constant k1 = 0.12 min−1 and K = 1.5. 3.1.2 Graphical Procedure for Design of Homogeneous Reactors It may not be always possible to derive analytical expressions for the design of homogeneous reactors for all types of reactions. In such cases, the graphical procedure presented in this section is useful. i. Ideal CSTR: The design equation for an ideal CSTR can be written in terms of the final concentration of limiting reactant A, that is, CAf, or the final conversion of A, X Af, achieved. τ=
CA 0 − C Af CA 0 X Af V = = q (− rA (C Af )) (− rA (X Af ))
(3.25)
Using the rate equation for the given reaction [−rA(CA)], a plot of 1/[(−rA(CA))] versus CA (Figure 3.3) or a plot of 1/[(−rA(xA))] versus xA (Figure 3.3) is drawn and a rectangle ABCD is constructed on the plot. According to CSTR design Equation 3.25, the area of rectangle ABCD on 1/[(−rA(CA))] versus CA plot gives the value of space time τ and the area of rectangle ABCD on 1/[(−rA(xA))] versus xA plot gives the value of τ/CA0. Thus, space time τ can be calculated by measuring area ABCD. ii. Ideal PFR: Similarly, the design equation for an ideal PFR is written in terms of the final concentration of the limiting reactant A, CAf, or the final conversion of A, X Af, CA0
τ=
∫
CAf
dCA = CA0 (− rA (C A ))
X Af
dx A
∫ (−r (x )) 0
A
A
(3.26) AB = xAf
AB = CA0 – CAf 1 CD = [–rA(CAf)] 1 [–rA(CAf)]
Area of rectangle ABCD = cτ A0
Area of rectangle ABCD = τ
D
C
D
1 [–rA(CA)]
CD =
1 [–rA(xAf)]
C 1 [–rA(xAf)]
1 [–rA(xA)]
A C Af
CA
CA0
B
B A
XA
Figure 3.3 Graphical procedure for design of CSTR.
www.Ebook777.com
XAf
Free ebooks ==> www.ebook777.com 144
Green Chemical Engineering
1 [–rA(CAf)]
1 [–rA(CA)]
F
Area of section ABEF = τ
CAf
CA
CA0
E
1 [–rA(xAf)]
1 [–rA(xA)]
E
A
τ Area ABEF = cA0
D
F B
A
B
xA
xAf
Figure 3.4 Graphical procedure for design of PFR.
By making a plot of 1/(−rA(CA)) versus CA (Figure 3.4) or a plot of 1/(−rA(xA)) versus xA (Figure 3.4), using the rate equation (−rA(CA)) applicable for the given reaction, the area of the section ABEF under the curve is calculated. According to PFR design Equation 3.26, the area of the section ABEF on 1/[(−rA(CA))] versus CA plot gives the value of space time τ and the area of the section ABEF on 1/[(−rA(xA))] versus xA plot gives the value of τ/CA0. Thus, for any reaction (of order greater than or equal to 1), a CSTR compared to PFR requires a larger volume (or space time) to achieve a specified conversion (see Figure 3.5). Spatial variation of reactant concentration CA through the reactor volume in a CSTR (Figure 3.6) shows a sudden drop in the value of CA from CA0 to CAf at the reactor inlet, whereas in a PFR, CA drops gradually from CA0 at the inlet to CAf at τ Area ABCD = c A0
CSTR
C
D
Area ABCE = cτ A0
1 [–rA(xA)]
τ cA0 E
A
xA
CSTR
PFR
τ > c A0
B x Af
Figure 3.5 Comparison of space times of CSTR and PFR required for a specified conversion xAf.
www.Ebook777.com
PFR
Free ebooks ==> www.ebook777.com 145
Homogeneous Reactors
CA0
Ideal PFR CA = mean concentration of A in a PFR
CA CA Reactor inlet
Reactor outlet
CAf Ideal CSTR 0
Normalised reactor volume
1
Figure 3.6 Spatial variations of CA in CSTR and PFR.
the outlet. Thus, the concentration level of A, CA, is always higher in a PFR than in a CSTR. So, the net rate of reaction is always higher in a PFR than in a CSTR. Hence, a PFR compared to a CSTR requires smaller space time to achieve a specified level of conversion X Af. Problem 3.3 A continuous-flow reactor is to be designed to carry out a second-order reversible reaction k1 A B and achieve 90% equilibrium conversion. The rate equation is k2 (− rA ) = k1C A2 − k 2CB2
The feed contains 5 kmol/m3 of A. The reaction rate constant k1 = 0.1 (m3/kmol) (1/min) and the equilibrium constant K = 9. What is the space time required to achieve the specified conversion in (i) an ideal CSTR and (ii) an ideal PFR? Use the graphical method. The equation for the calculation of space time τ in an ideal CSTR is
τ=
(C A 0 − C Af ) (C A 0 X Af ) = (− rA (C Af )) (− rA (X Af ))
and in an ideal PFR is CA 0
τ=
∫
C Af
dC A =C − r ( A (CA )) A0
X Af
dx A
∫ (−r (x )) 0
A
A
The rate equation can be written in terms of both reactant concentration CA and fractional conversion xA as follows:
− rA (C A ) = k1C A2 − k 2CB2
www.Ebook777.com
Free ebooks ==> www.ebook777.com 146
Green Chemical Engineering
and
CB = C AO − C A , K =
k1 k2
So (C − C A )2 − rA (C A ) = k1 C A2 − A 0 K
In terms of fractional conversion xA x2 − rA ( x A ) = k1C A2 0 (1 − x A )2 − A K
The equilibrium constant K is
K =
2 x Ae CBe (C A 0 x Ae )2 = = 2 C Ae (C A 0 (1 − x Ae ))2 1 − x Ae
2
From the given data, K = 9, ⇒ ( x Ae /1 − x Ae ) = 3 and xAe = 0.75 (equilibrium conversion is 75%). The final conversion X Af = 0.9xAe = 0.675 and CAf = CA0(1 − X Af) = 5(1 − 0.675) = 1.625 kmol/m3. The rate for different values of xA (or CA) is calculated and listed in the table given below: xA 0 0.0675 0.135 0.2025 0.270 0.3375 0.405 0.4725 0.540 0.6075 0.6750 0.7425
CA = CA0(1 − XAf)
−rA
1 −rA
5 4.663 4.325 3.988 3.650 3.313 2.975 2.638 2.30 1.963 1.625 1.2875
2.5 2.173 1.866 1.579 1.257 1.066 0.8395 0.6336 0.4480 0.2826 0.1375 0.0051
0.40 0.462 0.536 0.633 0.796 0.938 1.191 1.578 2.232 3.539 7.273 198.00
1/−rA versus CA and 1/−rA versus xA plots are drawn and these graphs are shown in Figures P3.3a and P3.3b, respectively. For an ideal CSTR,
τ=
(C A 0 − CAf ) = (7.273)(5 − 1.625) = 24.5 min − rA (CAf )
(
)
www.Ebook777.com
Free ebooks ==> www.ebook777.com 147
Homogeneous Reactors
8
(b) 8
7
7
6
6
5
5
1/(–rA)
1/(–rA)
(a)
4
4
3
3
2
2
1
1
0
0
2
3 CA
5
6
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
XA
Figure P3.3 (a) Plot of 1/ −rA versus CA. (b) Plot of 1/ −rA versus xA.
For an ideal PFR, X Af
τ = CA0
dx A
∫ (−r (x )) 0
A
A
Using the trapezoidal rule of numerical integration, X Af
τ = CA0
dx A
∫ (−r (x )) = 0
A
A
0.0675 [(0.4 + 7.273) + 2(0.462 + 0.536 + + 3.539)] 2
= 0.03375 [(7.273) + 2(11.905)] = 1.0626
τ PFR = 5 × 1.0626 = 5.31 min
Note: Refer the MATLAB program: react_dsn_cstr_pfr.m 3.1.3 Multiple Reactors: Reactors Connected in Series The design and performance analysis of a system of reactors connected in series are presented in this section. 3.1.3.1 System of N Numbers of Ideal CSTRs in Series Consider a system of N numbers of ideal CSTRs connected in series (Figure 3.7). Let q be the volumetric flow rate of fluid flowing through the battery of reactors. Let V1, V2, Vi,…,VN
www.Ebook777.com
Free ebooks ==> www.ebook777.com 148
Green Chemical Engineering
q
q CA0 V1
CAN–1 q
q
CA1
CA3
CA2
V2
V3
CA2
CA1
q VN
CA3
CAN = CAf
CAN
Figure 3.7 N numbers of ideal CSTRs connected in series.
be the volumes of the reactors. The space times are τ1, τ2, τi,…, τN where τ i = Vi/q is the space time of any ith reactor. Let CA0 be the concentration of reactant A in the feed. CA1, CA2, CAi,…, CAN are the concentrations of reactant A in the reactors. CAf = CAN is the final concentration of A in the Nth reactor and X Af = 1 − (CAf/CA0) is the net fractional conversion of A achieved. We wish to calculate the conversion of AxAf in this system of reactors. a. First-order reaction: Consider a first-order reaction A k → B carried out in this system of N reactors. The rate equation is (−rA) = kCA. Applying the design equation derived for the first-order reaction in an ideal CSTR (Section 3.1.1.1) for the sequence of reactors 1,2,3,…,N, we have C A 0 − C A1 kCA1 C − CA 2 τ 2 = A1 kC A 2
C AN −1 = 1 + kτ N
(3.27)
1 (1 + k τ1 )(1 + k τ 2 )(1 + k τ N )
(3.28)
τ1 =
⇒ CA 2 . . .
τN =
CA0 1 + k τ1 C A1 = 1 + kτ2
⇒ C A1 =
CAN −1 − C AN ⇒ C AN kC AN
Thus, the conversion xAf = 1 − (CAf/CA0) is
X Af = 1 −
As a special case, assume that all the reactors are of uniform size having equal space time τ = V/q, then
X Af = 1 −
1 (1 + k τ)N
(3.29)
Problem 3.4 A first-order reaction with rate constant k = 0.1 min−1 is carried out in a series of three unequal-volume CSTRs with space time τ1 = 1 min, τ2 = 2 min and τ3 = 4 min. What is the
www.Ebook777.com
Free ebooks ==> www.ebook777.com 149
Homogeneous Reactors
net conversion? Compare this with the conversion in one single large CSTR whose volume is equal to the volume of all the three CSTRs put together. Conversion in a series of three CSTRs is
X Af = 1 −
X Af = 1 −
1 (1 + k τ1 )(1 + k τ 2 )(1 + k τ 3 )
1 (1 + 0.1 × 1)(1 + 0.1 × 2)(1 + 0.1 × 4)
X Af = 0.4589 (45.89% conversion) Space time τ of a single large CSTR is
τ = τ1 + τ 2 + τ 3 = 1 + 2 + 4 = 7 min Conversion in one CSTR is X Af = 1 −
X Af = 1 −
1 (1 + k τ)
1 = 0.4117 (41.17% conversion) (1 + 0.1 × 7 )
b. Second-order reaction: Consider a second-order reaction A k → B carried out in 2 the system of N reactors connected in series. The rate equation is (− rA ) = k1CA . The design equation for an ith reactor in this sequence of N reactors is
τi =
CAi −1 − CAi (3.30) kC Ai 2
Rearranging Equation 3.30, we get a quadratic equation in CAi:
2 (k τ i )CAi + C Ai − CAi −1 = 0 (3.31)
Solving this quadratic equation, we get
CAi =
1 + 4k τ iCAi −1 − 1 (3.32) 2k τ i
www.Ebook777.com
Free ebooks ==> www.ebook777.com 150
Green Chemical Engineering
Solving this equation sequentially for i = 1,2,3,…,N, we get
C A1 =
1 + 4k τ1C A 0 − 1 2k τ 1
CA 2 =
1 + 4k τ 2C A1 − 1 2k τ 2
CA 3 =
1 + 4 k τ 3C A 2 − 1 2k τ 3 . . .
C Af = CAN =
1 + 4k τ N CAN −1 2k τ N
(3.33) − 1
The final conversion X Af = 1 − (CAf/CA0) is calculated from the value of CAf. Problem 3.5 A second-order reaction with rate constant k = 0.05 m3/kmol (min) is carried out in a series of three unequal-volume CSTRs with space time τ1 = 1 min, τ2 = 2 min and τ3 = 4 min, respectively. The feed concentration of reactant A is CA0 = 2 kmol/m3. What is the net conversion? What is the conversion if the feed direction is reversed? (i.e. τ1 = 4, τ2 = 2 and τ3 = 1). For the forward feed direction,
τ1 = 1 min, τ2 = 2 min and τ3 = 4 min k = 0.05 m3/kmol (min); CA0 = 2 kmol/m3
C A1 =
1 + 4k τ1C A 0 − 1 = 2k τ 1
1 + 4(0.05)(1)(2) − 1 2(0.05)(1)
CA1 = 1.832 kmol/m3 CA 2 =
1 + 4 k τ 2C A 1 − 1 = 2k τ 2
1 + 4(0.05)(1.832)(2) − 1 2(0.05)(2)
CA2 = 1.582 kmol/m3 CA 3 =
1 + 4 k τ 3C A 2 − 1 = 2k τ 3
1 + 4(0.05)( 4)(1.582) − 1 2(0.05)( 4)
www.Ebook777.com
Free ebooks ==> www.ebook777.com 151
Homogeneous Reactors
CA3 = 1.263 kmol/m3 Net conversion is X Af = 1 − (CA3/CA0) = 1 − (1.263/2) = 0.3685 (36.85% conversion). For the reverse feed direction, τ1 = 4 min, τ2 = 2 min and τ3 = 1 min
C A1 =
1 + 4k τ1C A 0 − 1 = 2k τ 1
1 + 4(0.05)( 4)(2) − 1 2(0.05)( 4)
CA1 = 1.531 kgmol/m3 CA 2 =
1 + 4 k τ 2C A 1 − 1 = 2k τ 2
1 + 4(0.05)(1.531)(2) − 1 2(0.05)(2)
CA2 = 1.349 kgmol/m3
CA 3 =
1 + 4 k τ 3C A 2 − 1 = 2k τ 3
1 + 4(0.05)(1)(1.349) − 1 2(0.05)(1)
CA3 = 1.269 kgmol/m3 Net conversion is X Af = 1 −
CA 3 1.263 = 1− = 0.3657 (36.57% conversion) CA0 2
c. Graphical procedure for higher-order reactions: For reactions of order higher than 2, it is not possible to obtain analytical expressions for the calculation of conversion X Af. A graphical construction method presented in this section is used for such calculations. The design equation for the ith reactor in the sequence of N CSTRs is τi =
CAi −1 − CAi (3.34) (− rA (CAi ))
which is rewritten as
1 (− rA (CAi )) (3.35) − = τ i CAi −1 − CAi
Construct a plot of (−rA(CA)) versus CA using the rate equation for the given reaction (Figure 3.8). According to Equation 3.35, a line with slope (−1/τi) passing through the point corresponding to CA = CAi−1 on the CA axis will intersect the curve (Figure 3.8) at a point corresponding to (CAi,(−rA(CAi))). So, starting at a point A0 corresponding to CA = CA0 on the CA axis, draw a straight line with slope = (−1/τ1) passing through A0. This line will intersect the curve at B0 corresponding to (CA1,(−rA(CA1))). The point B0 is projected on to the CA axis at point A1. Now, A1 corresponds to CA = CA1. This procedure is repeated N times to obtain the value of CAN = CAf. The extent of conversion xAf = 1 − (CAf/CA0).
www.Ebook777.com
Free ebooks ==> www.ebook777.com 152
Green Chemical Engineering
(–rA(CA1))
B0
Slope: –1 τ2
B1
Slope: –1 τ1
(–rA(CA)) B2
Slope: –1 τ3
A3 CA3
A2 CA2
A1 CA1
A0 CA0
CA Figure 3.8 Graphical construction method for calculation of conversion in a system of N CSTRs in series.
Problem 3.6 Calculate the conversion of the second-order reversible reaction (Problem 3.3) carried out in a series of three equal-volume CSTRs with space time of 1 min in each one of the reactors. Use the graphical construction method. A graph of −rA(CA) versus CA is plotted (Figure P3.6). Starting from the point (CA0,0), draw a straight line with slope m = −(1/τ1) = −1. This line intersects the −rA(CA) versus CA plot at a point corresponding to the concentration of A in the first reactor CA1 = 3.7 kmol/m3. Starting from the point CA1,0), repeat the procedure to obtain CA2 = 2.9 kmol/m3. Repeat this once more and we get the final concentration CA3 = 2.4 kmol/m3. Thus, the net conversion achieved in the three CSTRs connected in series is xAf = 1 − (CA3/CA0) = 1 − (2.4/5) = 52%. Note: Refer the MATLAB program: n_cstr_series2.m 2.5
(–rA(CA))
2 1.5 1 0.5 0 –0.5
CA3 0
0.5
1
1.5
2
2.5 CA
CA2 3
CA1 3.5
CA0 4
4.5
Figure P3.6 Plot of −rA versus CA.
www.Ebook777.com
5
Free ebooks ==> www.ebook777.com 153
Homogeneous Reactors
d. Graphical construction method to calculate the number of equal-volume CSTRs for a specified conversion X Af. A graphical construction method proposed by Eldridge and Piret is presented here for calculating the number of ideal CSTRs required to achieve a specified conversion X Af in a system of N equal-volume ideal CSTRs connected in series. Let τ = V/q be the space time of one reactor. The design equation for the ith CSTR in the sequence of N CSTRs connected in series is τ ( X Ai − X Ai −1 ) C = (− rA (xAi )) A0
(3.36)
where X Ai and X Ai−1 are the conversions of A in the ith reactor and the (i − 1)th reactor, respectively. This design equation is rearranged and written as τ x Ai −1 = x Ai − (− rA (x Ai )) CA 0
(3.37)
Using the rate equation for the given reaction, construct a plot of y versus X A (Figure 3.9)
x A3 ,
(x
y=
x
A
(3.38)
A3 )
τ y = x Ai − (− rA (x Ai )) C A 0
A
3
xA3
y = xA– 3
P (xAi, xAi–1)
(x
A2 ,
x
A2 )
y = xAi–1
A2
xA2
xA1
(xA1, xA1) A1 1
A0 τ (–rA(0)) CA0
XA0
B0 xA1
τ (–rA(xA)) CA0
B2 (xA3, xA2)
2 B1 (xA2, xA1) (xA1, xA0) xA2
xA
xA3
Figure 3.9 Graphical construction method for calculation of number of CSTRs required for specified conversion.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 154
Green Chemical Engineering
According to Equation 3.37 representing the y versus X A plot, this plot is a locus of points (X A1,X A0), (X A2,X A1), (X A3,X A2),…,(XAi,X Ai−1) and so on. Draw the line y = X A, which is a locus of points (X A0,X A0), (X A1,X A1), (X A2,X A2), (X A3,X A3),…,(XAi,X Ai). Project the point A0(X A0,X A0), that is, (0,0) on the y = X A line onto point B0(X A1,X A0) on the y versus X A plot. Project the point B0(X A1,X A0) on the y versus X A plot onto the point A1(X A1,X A1) on the y = xA line. Next, project the point A1(X A1,X A1) on the y = xA line onto point B1(X A2,X A1) on the y versus X A plot. This procedure is repeated N number of times until X AN ≥ X Af (specified conversion). Now, N gives the value of the number of CSTRs required to achieve the specified conversion in a system of N equal-volume ideal CSTRs connected in series. Problem 3.7 It is proposed to carry out the second-order reversible reaction (Problem 3.3) in a battery of equal-volume CSTRs connected in series. The space time of each one of the CSTRs is 1 min. Calculate the number of CSTRs required to achieve 62% net conversion of reactant A. Use the graphical construction method. A graph of the equation y = xA − (τ/CAO)(−rA(xA)) versus xA is plotted (Figure P3.7) on xAi − xAi−1 axes. As τ = 1 min, CAO = 5 kmol/m3, k1 = 0.1 m3/kmol · min and K = 9. x A2 2 2 − rA ( x A ) = k1C AO (1 − x A ) − K
x2 = 2.5 (1 − x A )2 − A 9
x2 y = x A − 0.5 (1 − x A )2 − A 9
xA y xA y
0 −0.5 0.35 0.158
0.05 −0.40 0.40 0.242
0.10 −0.30 0.45 0.324
0.15 −0.20 0.50 0.402
0.20 −0.11 0.55 0.479
0.25 −0.017 0.60 0.553
0.30 0.072 0.65 0.625
From the plot, it is clear that the specified conversion of 62% is achieved in six CSTRs. Note: Refer the MATLAB program: n_cstr_series1.m 3.1.3.2 Optimal Sizing of Two CSTRs Connected in Series Consider a reaction carried out in a system of CSTRs connected in series (see Figure 3.10). We would like to optimally size the two CSTRs for a specified value of final conversion (X Af = X A2). Let τ1 and τ2 be the space times of the two CSTRs, and X A1 be the conversion in the first reactor. The design equations for the two CSTRs are τ1 =
C A 0 x A1 (− rA (x A1 ))
www.Ebook777.com
(3.39)
Free ebooks ==> www.ebook777.com 155
Homogeneous Reactors
0.8 0.6
XA2
XAi–1
0.4
XA5
XA4
XA3
XA1
0.2 0
–0.2 –0.4 –0.6
0
0.1
0.2
0.3
XAi
0.4
0.5
0.6
0.7
Figure P3.7 Plot of X Ai − 1 versus X Ai.
τ2 =
C A 0 ( x A 2 − x A1 ) (− rA (x A 2 ))
(3.40)
For a fixed value of X A2 = X Af (final conversion specified), X A1 is calculated such that the total space time τ = τ1 + τ2 is minimum. Applying the necessary condition for minimum, we have C AO ( x Af − x A1 ) d CAO x A1 dτ =0 dx = dx − r ( x ) + − rA ( x Af ) A1 A1 ( A A1 )
(
)
1 1 1 d + − ⇒ C A 0 x A1 dx A1 ( − rA ( x A1 )) ( − rA ( x A1 )) − rA ( x Af )
(
(3.41)
)
= 0
q
q
CA2
CA0 V τ1 = q1
CA1
V1
q CA1 XA1
V τ2 = q2
XAf = XA2
CA2 V2
Figure 3.10 A system of two CSTRs connected in series.
www.Ebook777.com
(3.42)
Free ebooks ==> www.ebook777.com 156
Green Chemical Engineering
⇒
( (
)
)
1/ − rA ( x Af ) − 1/ ( − rA ( x A1 )) d 1 = dx A1 ( − rA ( x A1 )) x A1
(3.43)
Define 1 1 = ; rA1 (− rA (xA1 ))
1 1 = rAf − rA ( x Af )
(
)
(3.44)
then
(
)
1/(rAf ) − 1/(rA1 ) d 1 = dx A1 rA1 x A1
(3.45)
Calculate the value of x A1 = x*A1 at which Equation 3.45 is satisfied. Optimal reactor sizes are calculated by substituting the value of x A1 = x*A1 into Equations 3.39 and 3.40. On a plot of 1/(−rA(xA)) versus xA (Figure 3.11), x A = x*A1 represents a point R at which the tangent to the curve is parallel to the chord PQ. This gives a graphical procedure for calculating x*A1 (Figure 3.11). * However, the analytical equation for x A1 can be derived for a first-order reaction by applying the condition for optimality (Equation 3.45). The rate equation for a first-order equation is (− rA ) = kCA 0 (1 − x A )
(3.46)
At xA = xA1, (−rA(xA1)) = kCA0(1 − xA1) and at xA = xAf, (−rA(xAf)) = kCA0(1 − xAf). Substituting these equations into the condition for optimality, we have
1 1 – rAf rA1
1 –rA(xA)
Slope of PQ =
xA1
1 –rA(xAf)
Q
Tangent to the curve
1 at rA = xA1 having a slope = d dxA1 rA1
R
P
1 rA1
τ1 CAO 0
xA1
x*A1
τ2 CAO
xA
xAf
Figure 3.11 Graphical procedure for optimal sizing of two CSTRs in series.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 157
Homogeneous Reactors
( (
)
)
1/ kC A 0 (1 − x Af ) − 1/ ( kC A 0 (1 − x A1 )) d 1 = dx A1 ( kCA 0 (1 − x A1 )) x A1
( x Af − x A1 ) 1 = 2 (1 − x A1 ) x A1(1 − x Af )(1 − x A1 )
x A1(1 − x Af ) = (1 − x A1 )( x Af − x A1 )
(3.47) (3.48)
(3.49)
the equation reduces to a quadratic equation in xA1 x A2 1 − 2x A1 + x Af = 0
(3.50)
whose feasible root is x A* 1 = 1 − 1 − x Af
(3.51)
Optimal space time values for the two reactors are 1 x A* 1 k 1 − x A* 1
(3.52)
1 x Af − x A* 1 * k 1 − x Af
(3.53)
τ1 =
τ2 =
Note that
(
x Af − 1 − 1 − x Af x Af − x A* 1 = 1 − x Af 1 − x Af
=
1 − 1 − x Af
1 − x Af
=
)=
(
1 − x Af − 1 − x Af 1 − x Af
)
x A* 1 1 − x A* 1
This implies that τ1 = τ2. Thus, for a first-order reaction, equal volumes of CSTRs correspond to the total minimum volume required for any specified conversion. 3.1.3.3 CSTR and PFR in Series Consider a system of one CSTR and one PFR connected in series (Figures 3.12 and 3.13). Assume that both the reactors are of equal size and have equal space time τ. We wish to calculate the space time τ of the PFR or the CSTR required to achieve the specified final conversion xAf for the following cases:
www.Ebook777.com
Free ebooks ==> www.ebook777.com 158
Green Chemical Engineering
xA0 = 0 CA0 q
xA1 CA1 q
τ
V
τ
V
xAf CAf q
Figure 3.12 PFR followed by CSTR.
i. PFR followed by CSTR: The design equation for PFR is xA1
dx A
∫ ( − r ( x ))
(3.54)
C A 0 ( x A f − x A1 ) − rA ( x Af )
(3.55)
τ = CA0
0
A
A
The design equation for CSTR is τ=
(
)
For the specified final conversion xAf, the conversion xA1 achieved in the PFR is calculated such that the space times for both the reactors are equal, that is, xA1
CA0
dx A
∫ ( − r ( x )) = A
0
A
CA 0 ( x Af − x A1 ) − rA ( x Af )
(
)
(3.56)
Substituting the calculated value of xA1 into the CSTR design Equation 3.55, we get the value of space time τ. The graphical method for calculation of τ is illustrated in Figure 3.14. A graph of 1/[(−rA(xA))] versus xA is plotted using the rate equation for xA0 = 0 CA0 q
V
τ
xA1 CA1 q
V
τ
Figure 3.13 CSTR followed by PFR.
www.Ebook777.com
xAf CAf q
Free ebooks ==> www.ebook777.com 159
Homogeneous Reactors
D
1 [–rA(xA)] τ CA0
PFR
= area OAEF
C
E
τ CA0
F
CSTR
= area ABCD
Fixed (given) O
A x A1 xA
B xA1
Figure 3.14 Graphical method for calculation of τ for PFR followed by CSTR.
the given reaction. On this graph, fix the point A corresponding to xA = xA1 on the xA axis by trial and error such that area OAEF = area ABCD. Space time τ = CAO.area ABCD. ii. CSTR followed by PFR: Design equation for CSTR is τ=
C A 0 ( x A1 ) (− rA (x A1 ))
(3.57)
Design equation for PFR is x Af
τ = CA0
dx A
∫ ( − r ( x ))
xA1
A
(3.58)
A
For the specified final conversion xAf, the conversion xA1 achieved in the CSTR is calculated such that the space times for both the reactors are equal. CAO x A1 =C (− rA (x A1 )) AO
x Af
dx A
∫ ( − r ( x ))
xA1
A
(3.59)
A
Substituting the calculated value of xA1 into the CSTR design Equation 3.57, we get the value of space time τ. The graphical method for calculation of τ is illustrated in Figure 3.15. Point A on the xA axis corresponding to xA = xA1 is fixed by trial and error such that area OADE = area ABCD. Space time τ = CAO.area OADE. Problem 3.8 k
→ B carried out in a system of one CSTR and one For a first-order irreversible reaction A PFR connected in series, show that the overall conversion is independent of which reactor precedes when the reactor volumes are equal.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 160
Green Chemical Engineering
xA1 is calculated such that area OADE = area ABCD
1 –r A(xA)
Area OADE =
τ CA0
C
τ = Area ABCD CA0
D
E
PFR
CSTR
0
B XAf
A XA1 XA
Figure 3.15 Graphical method for calculation of xAf for CSTR followed by PFR.
Consider the PFR followed by the CSTR, the rate equation for the first-order reaction is CA0
xA1
V
xA = 0
xAf
V
A k →B
(− rA ) = kCAO (1 − x A ) Space time τ for the PFR is xA1
τ = CAO
1
dx A
∫ (−r (x )) = − k ln(1 − x 0
A
A1
)
A
x A1 = 1 − e − k τ
Space time τ for the CSTR is τ=
CAO ( x Af − x A1 ) ( x Af − x A1 ) = k(1 − x Af ) − rA ( x Af )
(
)
www.Ebook777.com
Free ebooks ==> www.ebook777.com 161
Homogeneous Reactors
k τ(1 − x Af ) = x Af − x A1
Rearranging the terms in the above equation, we get x Af =
k τ + x A1 k τ + (1 − e − kτ ) = (1 + k τ) (1 + k τ) x Af = 1 −
e − kτ (1 + k τ)
Consider the CSTR followed by the PFR. CA0 xA = 0
xA1
V
V
xAf
Space time τ for the CSTR is τ=
CAO x A1
(− rA (x A1 )) x A1 =
=
x A1 k(1 − x A1 )
kτ 1 + kτ
Space time τ for the PFR is x Af
τ = CAO
1
dx A
1 − x Af A1
∫ (−r (x )) = − k ln 1 − x
xA1
A
A
1 − x Af − kτ 1 − x = −e A1
x Af = 1 − (1 − x A1 ) e − k τ
k τ − kτ x Af = 1 − 1 − e 1 + kτ
x Af = 1 −
e − kτ 1 + kτ
www.Ebook777.com
Free ebooks ==> www.ebook777.com 162
Green Chemical Engineering
Thus, the conversion xAf is the same for both the cases. Thus, the conversion is independent of whether CSTR precedes PFR or PFR precedes CSTR. For an irreversible autocatalytic reaction (Section 2.1.9) A + B → B + B
with rate equation
(−rA) = kCA(C0 − CA) (3.60) where C0 = CA0 + CB0. The plot of 1/(−rA(CA)) versus CA (Figure 3.16) shows that a CSTR followed by a PFR requires the least space time to achieve a specified conversion xAf. The feed containing reactant A at concentration CA0 is first fed to a CSTR in which the reactant concentration is reduced from CA0 to CA* in space time τ1. This is followed by a PFR in which the concentration of A is reduced from CA* to CAf in space time τ2. The values of τ1 and τ2 are calculated using the design equations for CSTR and PFR, respectively. τ1 =
CAO − C∗A − rA (C ∗A )
(
C∗A
τ1 =
dCA
∫ (−r (C )) A
CAf
(3.61)
)
(3.62)
A
Substituting the rate Equation 3.60 into Equations 3.61 and 3.62, we get
1 (–rACA) τ2 CA0
F PFR
= area BEFC C D
τ1 CA0
CSTR
E CAf
B CA*
=
CA
C0 2
A
CA0
Figure 3.16 CSTR followed by PFR for autocatalytic reaction.
www.Ebook777.com
= area ABCD
Free ebooks ==> www.ebook777.com 163
Homogeneous Reactors
τ1 = τ2 =
1 CAO − C∗A k CA∗ (CO − CA∗ )
(
(3.63)
)
CO − C Af C A∗ 1 ln kCO (CO − C A∗ )CAf
(3.64)
Taking the initial concentration of B, CBO to be negligible, we have CO ≈ CAO and C ≈ CAO /2. Then, the equations for τ1 and τ2 are reduced to the final form as * A
τ1 =
τ2 =
2 kC AO
x Af 1 ln kCO 1 − x Af
(3.65)
(3.66)
Problem 3.9 For an irreversible autocatalytic reaction A + B k → B + B, minimum space time is required for a specified conversion of A in a system of CSTR followed by a PFR compared to that in a single CSTR or in a single PFR. Calculate the space time of the CSTR and the PFR connected in series given the feed concentration CAO = 5 kmol/m3, rate constant k = 0.02 m3/kmol · min and the final conversion xAf = 0.8. As k = 0.02, CAO = 5 and xAf = 0.8 τ CSTR =
τ PFR =
2 2 = = 20 min kC AO (0.02)(5)
x Af 1 1 0.8 = 13.9 min ln ln = kC AO 1 − x Af (0.02)(5) 1 − 0.8
3.1.4 Design of Reactors for Multiple Reactions Reactors for multiple reactions (series or parallel reactions) are designed to achieve maximum yield or selectivity of desired products (Section 2.1.8). Consider a series reaction
1 2 A k → B k →C
carried out in a CSTR (Figure 3.17). Let CAO be the concentration of A in the feed (CBO = CCO = 0) and τ be the space time. The rate equations for A, B and C are
(− rA ) = −
dC A = k1CA dt
www.Ebook777.com
(3.67)
Free ebooks ==> www.ebook777.com 164
Green Chemical Engineering
q CA0 = 0 CB0 = 0 CC0 = 0
CAf CBf CCf
q CAf CBf CCf
Figure 3.17 Series reaction in a CSTR.
(rB ) =
dCB = k1CA − k 2CB dt
(3.68)
dCc = k 2CB dt
(3.69)
(rC ) =
CAf, CBf and CCf are the final concentrations of A, B and C in the effluent stream. Taking steady-state molal balance of A, B and C around the CSTR, we get the following equations: For reactant A, qCAO = qCAf + V (− rA )
that is, qCAO = qCAf + V (k1CAf )
CAf =
CAO 1 + k1τ
(3.70)
For product B, qCBO = qCBf − V (rB )
that is, 0 = qCBf − V (k1C Af − k 2CBf ) CBf =
k1τC Af 1 + k2τ
For product C,
qCCO = qCCf − V (rC )
www.Ebook777.com
(3.71)
Free ebooks ==> www.ebook777.com 165
Homogeneous Reactors
that is, 0 = qCCf − Vk 2CBf CCf = k 2τCBf
(3.72)
Overall selectivity of B (desired product) ΦB is CBf 1 ΦB = = CCf k 2τ
(3.73)
As space time τ increases, selectivity Φ B decreases and conversion of A x Af = 1 − (C Af /C AO ) increases x Af =
k1τ 1 + k1τ
(3.74)
Combining Equations 3.73 and 3.74, we can write overall selectivity Φ B in terms of total conversion xAf as k 1 − x Af ΦB = 1 k 2 x Af
(3.75)
Thus, selectivity Φ decreases with an increase in conversion xAf. 1 2 For the series reaction A k → B k → C carried out in a PFR, the equation for overall selectivity derived for the batch reactor (Section 2.1.8) can be used for PFR after replacing the term t (for batch time) in the batch reactor equation by space time τ. Thus, for the series reaction in a PFR − k1 τ
CBf
CAf = CAO e CAO k1 e − k2 τ − e − k1τ = ( k1 − k 2 )
1 Ccf = CAO 1 − k1e − k2 τ − k 2e − k1τ ( k1 − k 2 )
(
)
(3.76)
Thus, the overall selectivity Φ in a PFR is
ΦB =
k1 (e − k2 τ − e − k1τ ) (CBf ) = (CCf ) k1(1 − e − k2 τ ) − k 2 (1 − e − k1τ )
(3.77)
and conversion x Af = 1 − e − k1τ . Combining equations for Φ B and xAf and eliminating the space time τ, we get an expression for Φ B in terms of xAf as ΦB =
(1 − x Af ) − (1 − x Af )( k2 /k1 ) (1 − x Af )( k2 /k1 ) − 1 − (k 2 /k1 )x Af
(
)
www.Ebook777.com
(3.78)
Free ebooks ==> www.ebook777.com 166
Green Chemical Engineering
ΦB (overall) selectivity)
PFR
CSTR
xAf (Final conversion) Figure 3.18 k1 2 → B k → C. Selectivity versus conversion for series reaction A
The overall selectivity decreases with an increase in total conversion xAf for both CSTR and PFR. For any particular conversion xAf, overall selectivity Φ B is always higher in a PFR than in a CSTR as shown in Figure 3.18. Thus, the design of a reactor for a series reaction is a trade-off between conversion and selectivity. Now, consider a parallel reaction
A
k1 k2
B (Desired product)
carried out in a CSTR. CAO is
C
the concentration of A in the feed (CBO = CCO = 0). CAf, CBf and CCf are respectively the concentrations of A, B and C in the effluent stream. τ is the space time. The rate equations for A, B and C are (− rA ) = (k1 + k 2 )CA (rB ) = k1CA (rC ) = k2CA
(3.79)
Taking the steady-state molal balance of A, B and C around the CSTR, we obtain the following equations: For reactant A, qCAO = qCAf + V (− rA )
qCAO = qCAf + V (k1 + k 2 )CAf
CAf =
CAO 1 + (k1 + k 2 )τ
For product B,
qCBO = qCBf − V (rB )
www.Ebook777.com
(3.80)
Free ebooks ==> www.ebook777.com 167
Homogeneous Reactors
that is, 0 = qCBf − V (k1C Af ) (3.81)
CBf = k1τCAf
For product C,
qCCO = qCCf − V (rC )
that is, 0 = qCCf − Vk 2CAf
(3.82)
CCf = k 2τC Af
Thus, the overall selectivity of B (desired product) ΦB is CBf k1 ΦB = = CCf k 2
(3.83)
The overall selectivity of the desired product for parallel reaction is independent of conversion xAf and space time τ. We derived the same result for the parallel reaction carried out in a batch reactor (Section 2.1.8.2). Thus, the overall selectivity is independent of the type of reactor used. Problem 3.10 1 2 Consider the first-order irreversible series reaction A k → B k → C carried out in an ideal CSTR to maximise the production of product B. Show that the space time τ for maximum production of B is τ max = 1/ k1k 2 and the maximum product concentration CBmax is
CB max = ( k1 C AO / k1 + k 2 ).
q CAO CBO = 0, CCO = 0
q V
CA CB
CC
The rate equations are
(− rA ) = k1C A
(rB ) = k1CA − k 2CB
(rC ) = k 2CB
Taking the steady-state molal balance of A, B and C, we get
CAO = k1C A + τ ( k1CA )
www.Ebook777.com
Free ebooks ==> www.ebook777.com 168
Green Chemical Engineering
CBO = CB − τ ( k1CA − k 2CB )
CCO = CC − τ ( k 2CB ) Rearranging the above equations, we get CA =
CAO (1 + k1τ)
CB =
k1CAO τ (1 + k1τ)(1 + k 2τ)
CC =
k1k 2CAO τ 2 (1 + k1τ)(1 + k 2τ)
For maximum CB , (dCB /dτ) = 0
(1 + k1τ ) (1 + k2τ ) k1CAO − (k1CAO τ ) (1 + k1τ ) k2 + (1 + k2τ ) k1 dCB = 2 dτ (1 + k1τ ) (1 + k 2τ )
dCB = 0 implies dτ
(1 + k1τ ) (1 + k2τ ) = τ (1 + k1τ ) k2 + (1 + k2τ ) k1 Cancelling the terms on both sides of the equation, we get τ max =
1 k1k 2
Substituting τ = (1/ k1k 2 ) into the equation for CB, we get CB ,max =
(
1 + k1 1/ k1k2
CB ,max = CB ,max =
(
k1CAO 1/ k1k 2
(
)) (1 + k (1/ 2
C AO k1/k 2
)(
))
k1k2
)
1 + k1 /k 2 1 + k 2 /k1
(
C AO k1 k1 + k 2
)
2
=
CAO k1 k1 + k 2
www.Ebook777.com
Free ebooks ==> www.ebook777.com 169
Homogeneous Reactors
3.1.4.1 Design of CSTR for Chain Polymerisation Reaction A chain polymerisation reaction is a special type of multiple reaction in which polymeric compounds of different chain lengths are produced by a sequence of simultaneous reactions. Reaction is initiated by a monomer molecule M reacting with another monomer molecule to produce a polymer chain P2 having two monomers
M + M k → P2
This is followed by a chain of reactions in which one monomer molecule M reacts with a polymer chain Pr having r monomers to produce a polymer chain Pr+1 having r + 1 monomers.
M + P2 k→ P3
M + P3 k → P4
............
. . . . . . . . .. . . .
M + Pr k → Pr +1
Each one of the reaction steps is assumed to be a simple elementary reaction of order 2. All the reaction steps have the same rate constant k. Thus, the rate equations for the reaction steps are as follows: = kCMCpr
2 rP2 = kCM rP3 = kCMCp 2 rP4 = kCMCp 2 . . .
rPr + 1
(3.84)
where CM: concentration of monomer M CPr : concentration of the polymer chain of chain length r (having r monomers) rPr : rate of formation of polymer Pr In this section, we will develop design equations for the CSTR (Figure 3.19) used for carrying out this polymerisation reaction. Define space time τ = V/q and fractional conversion of monomer M, xM = 1 − (CM/CMO). CM is the final concentration of unconverted monomer in the reactor effluent. CP 2 , CP 3 , … , CPr
www.Ebook777.com
Free ebooks ==> www.ebook777.com 170
Green Chemical Engineering
q CMO q CM CP2 CP3
V CM
· · ·
CPr Figure 3.19 CSTR for a chain polymerisation reaction.
are the concentration of polymers P2,…,Pr in the reactor effluent. Thus, the product is a mixture of polymer compounds of different chain lengths. Taking a steady-state monomer balance around the CSTR, we have
Rate of flow of Rate of flow of = + monomer in monomer out
Rate of conversion of monomer
2 qCMO = qCM + V 2kCM + kCMCP 2 + kC MCP 3 +
(3.85)
(3.86)
This equation reduces to
CMO = CM + k τC M 2CM +
∞
∑C
Pr
r=2
(3.87)
Taking a steady-state molal balance of polymer chains P2,…,Pr around the CSTR, we get
Rate of flow of Rate of flow of = − polymer Pr in polymer Pr out
Net rate of production of polymer Pr in the reactor
(3.88)
This equation for polymer chain P2 is
2 0 = qCP 2 − V kCM − kCMCP 2
(3.89)
and for polymer chain Pr+1 is
0 = qCPr +1 − V [ kCMCPr − kCMCPr + 1 ] for all r = 2, 3, …
www.Ebook777.com
(3.90)
Free ebooks ==> www.ebook777.com 171
Homogeneous Reactors
Writing Equations 3.89 and 3.90 for r = 2, 3,…, ∞, we get CP 2 = k τC M [C M − CP 2 ] CP 3 = k τC M [CP 2 − CP 3 ] CP 4 = k τC M [CP 3 − CP 4 ] . . . CPr + 1 = k τC M [CPr
− CPr + 1 ]
(3.91)
Summing up the left-hand side and the right-hand side of Equations 3.91, we get ∞
∑C
Pr
2 = k τCM
(3.92)
r=2
Inserting Equation 3.92 into Equation 3.87, we get a cubic equation in CM
(k τ ) C 2 2
3 M
2 + (2k τ)CM + CM − CMO = 0
(3.93)
Solving this cubic Equation 3.93, we get the value of CM for the specified values of rate constant k and the space time τ. Using this value of CM, we can calculate the conversion xM = 1 − (CM/CMO). Conversely, for a specified conversion xM, calculate CM = CMO(1 − xM) and inserting this value of CM in Equation 3.93, we calculate the space time τ by solving this quadratic equation in variable τ. The resulting equation for space time is C CM MO − τ= 3/ 2 kC M
(
)
(3.94)
As the product of the reaction is a mixture of polymer compounds of different chain lengths, the product quality is a strong function of weight distribution of these polymer compounds. Define Wr as the weight fraction of the polymer compound Pr (of chain length r) in the product. If Mw is the molecular weight of monomer M, we can write Wr as
(
)
VCpr ( rMw ) weight of Pr in the product Wr = = V C C M − h t of all polymer compounds in the product weigh M) w ( MO rCPr Wr = (CMO − CM )
(3.95)
www.Ebook777.com
Free ebooks ==> www.ebook777.com 172
Green Chemical Engineering
Solving Equations 3.89 and 3.90 for CP2, CP3, CP4…, we get 2 k τC M k τCMC p 2 = = CM 1 + k τm 1 + k τC M 3 k τC M k τC MCp 3 = CM = 1 + k τC M 1 + k τC M . . . r −1 k τCM CPr = CM 1 + k τCM Cp 2 =
Cp 3 CP 4
2 k τC M 1 + k τC M
(3.96)
Inserting Equation 3.96 into Equation 3.95, we get the equation for weight distribution Wr as Wr =
rCM k τCM (CMO − CM ) 1 + k τCM
r −1
(3.97)
Rearranging Equation 3.94, we get
CMO k τC M = − 1 CM
(3.98)
Inserting Equation 3.98 into Equation 3.97, we get
(
r(1 − x M ) 1 − 1 − xM Wr = ( x M )
)
r −1
(3.99)
Equation 3.99 can be used to obtain the product distribution curve Wr versus r (Figure 3.20) for any specified conversion xM. The distribution of polymer chains in the product is an important property that defines the quality of polymer produced. Polymerisation reactors are usually designed to produce products having a specified distribution of polymer chains. Problem 3.11 A chain polymerisation reaction of the type discussed in Section 3.1.4.1 is carried out in a CSTR. The monomer concentration in the feed is CMO = 10 kmol/m3. Rate constant k = 0.05 m3/kmol.(min). Calculate the space time required for 80% conversion of monomer. Sketch the product distribution of polymer chains produced in the reactor.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 173
Homogeneous Reactors
wr (weight fraction)
r (chain length) Figure 3.20 Product distribution curve for chain polymerisation reaction in a CSTR.
Feed concentration CMO = 10 kmol/m3 Fractional conversion xAf = 0.8 Final product concentration CM = CMO(1 −xAf) = 2 kmol/m3 Rate constant k = 0.05 m3/kmol (min) The space time τ τ=
10 − 2 C MO − C M = = 12.36 min 3/ 2 (kC M ) (0.05)(2)3/2
The product distribution is
)
(
)
r(1 − x Af ) 1 − 1 − 0.8 x Af
Wr =
r(1 − 0.8) 1 − 1 − 0.8 0.8
(
Wr =
r −1
r −1
Wr = 0.25r(0.5528)r −1
r Wr r Wr
0 0 6 0.077
1 0.25 7 0.05
2 0.2764 8 0.032
3 0.229 9 0.02
4 0.169 10 0.012
5 0.117 20 0.00006
A plot of product distribution is shown in Figure P3.11.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 174
Green Chemical Engineering
0.3
Weight fraction (Wr)
0.25 0.2
0.15 0.1
0.05 0
0
5
10 15 20 Polymer chain length (r)
25
30
Figure P3.11 Product distribution of polymer chains.
3.1.5 Non-Isothermal Reactors Non-isothermal reactors are the reactors in which the temperature of the fluid in the reaction vessel changes significantly due to the heat of reaction (ΔHR). The temperature of a reacting fluid kept in a batch reactor would gradually increase with time for an exothermic reaction (ΔHR is negative) or decrease with time for an endothermic reaction (ΔHR is positive) as shown in Figure 3.21. The temperature remains constant (isothermal reactor) if the heat of reaction is negligible (ΔHR ≈ 0). An isothermal condition can be maintained by removing the heat generated by an exothermic reaction or by adding the heat that is consumed by an endothermic reaction. The rate of any reaction is a strong function of temperature. Consider an nth-order Exothermic reaction (∆HR is – ve)
Isothermal reactor (∆HR is 0)
T (temperature) T0
Endothermic reaction (∆HR is + ve)
t (time) Figure 3.21 Progression of temperature with time in a batch reactor.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 175
Homogeneous Reactors
Exothermic reaction (∆HR is – ve) B (–rA) rate r0
A Endothermic reaction (∆HR is +ve) t (time)
Figure 3.22 Progression of rate with time in a batch reactor. n k → B with rate equation (− rA ) = kCA carried out in a batch reactor. Inserting reaction A the Arrhenius law into the rate equation, the rate as a function of conversion X A and temperature T is expressed as
(−rA (xA , T )) = ( k0e − ∆E/RT ) (CAO (1 − xA ))n
(3.100)
The rate increases with an increase in temperature. However, with an increase in the conversion of AxA, the concentration of A would decrease and hence the rate would decrease. The progression of rate with time in the batch reactor is shown in Figure 3.22 for exothermic and endothermic reactions. For an endothermic reaction, with the progression of time, the conversion xA increases and the temperature decreases. So the rate decreases with time. For an exothermic reaction, both conversion xA and temperature T increase with time. A rise in the temperature causes an increase in rate initially. However, as the conversion continues to increase with time, a significant decrease in the availability of the reactant would start limiting the rate even though the temperature is on the rise. So, the rate that was rising initially would start falling eventually after touching a peak value (at point B). 3.1.5.1 Design Equations for Non-Isothermal Reactors Design calculations for non-isothermal reactors should account for the effect of temperature on rate. Thus, the rate equation used in the design calculations is treated as a function of both conversion xA and temperature T, −rA = (−rA(xA, T)). i. Design equation for the batch reactor (Figures 3.23): x Af
θB = CAO
dx A
∫ (−r (x 0
A
A
, T ))
(3.101)
www.Ebook777.com
Free ebooks ==> www.ebook777.com 176
Green Chemical Engineering
T
CA xA
Figure 3.23 Non-isothermal batch reactor.
where θB: batch reaction time xAf : the final fractional conversion of A T: temperature of the fluid in the reactor ii. Design equation for CSTR (Figure 3.24): τ=
CAO x Af V = − rA (x Af , Tf ) q
(3.102)
where τ: space time xAf : the final fractional conversion of A Tf: temperature of the fluid in the reactor vessel CA0: feed concentration of A T0: feed temperature q CA0 T0 q CAf V
Tf
XAf Tf
Figure 3.24 Non-isothermal CSTR.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 177
Homogeneous Reactors
q
q
V
CA0 T0
CAf Tf
Figure 3.25 Non-isothermal PFR.
iii. Design equation for PFR (Figure 3.25): V τ= = CA0 q
x Af
dx A
∫ −r (x 0
A
A
, T)
(3.103)
An equation relating temperature T and conversion xA is required to design the non- isothermal reactors. This relationship between temperature T and conversion xA is obtained by setting up a heat balance equation around the reactor (Section 3.1.5.3). In certain cases, reactor temperature T is deliberately varied with conversion xA by regulating the heat supply to the reactor or heat removal from the reactor. One such case is the non-isothermal reactor in which a reversible exothermic reaction is carried out. In the case of a reversible exothermic reaction, there is an optimum temperature T* for every value of conversion xA at which the rate is maximum. A specified conversion xAf will be achieved in a CSTR or a PFR with the smallest volume or in a batch reactor in the shortest reaction time if the temperature in the reaction vessel is maintained at the optimum level. This optimal temperature policy in which temperature is varied as a function of conversion xA is known as the optimal progression of temperature presented in the following section. 3.1.5.2 Optimal Progression of Temperature for Reversible Exothermic Reactions k1 Consider a reversible first-order reaction A B. The rate equation for this reaction is k 2
(− rA ) = k1C AO (1 − x A ) − k 2C AO x A
(3.104)
xA: fractional conversion of A CAO: initial concentration of A k1 and k2 are respectively the rate constants for the forward and reverse reactions. Using the Arrhenius law, k1 and k2 are expressed as
k1 = k10 e −∆E1 /RT
(3.105)
k 2 = k 20 e −∆E2 /RT
(3.106)
where k10 and k20 are frequency factors, ΔE1 and ΔE2 are the activation energies for the forward and reverse reaction, respectively.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 178
Green Chemical Engineering
At equilibrium, the net rate is zero, that is, (−rA) = 0 and the conversion xA = xAe. Substituting xA = xAe and (−rA) = 0 into Equation 3.104 and solving the equation for equilibrium conversion, xAe, we get x Ae =
1 1 + ( k 2 /k1 )
(3.107)
From Equations 3.105 and 3.106, we have k2 k = 20 e(∆E1 − ∆E2 )/RT k1 k10
(3.108)
We can write k2/k1 in terms of the heat of reaction ΔHR = (ΔE1 − ΔE2) k2 k = 20 e ∆HR /RT k1 k10
(3.109)
For an endothermic reaction, ΔHR is positive and hence (k2/k1) decreases with an increase in temperature (Equation 3.109) and equilibrium conversion xAe increases with a decrease in (k2/k1) (Equation 3.107). Thus, the equilibrium conversion xAe increases with an increase in temperature for an endothermic reaction, whereas for an exothermic reaction, ΔHR is negative and hence (k2/k1) increases with an increase in temperature and the equilibrium conversion xAe decreases with (k2/k1). Thus, the equilibrium conversion xAe decreases with an increase in temperature for an exothermic reaction. The effect of temperature T on equilibrium conversion xAe is shown in Figure 3.26. Thus, equilibrium conversion xAe is favoured by higher temperature for an endothermic reaction and lower temperature for an exothermic reaction. However, the net rate of reaction is always favoured by high temperature for both the exothermic and endothermic
Exothermic reaction
1+ Endothermic reaction
T0
1
* = xAe
Equilibrium conversion (xAe)
Temperature (T)
Figure 3.26 Effect of temperature T on equilibrium conversion xAe.
www.Ebook777.com
k20 k10
Free ebooks ==> www.ebook777.com 179
Homogeneous Reactors
5 4
xA5 3
xA4 (–rA(xA, T))
2
xA3 xA2
1
xA1 To
pt1
To To To
pt2 pt3 pt4
To
pt5
Temperature (T) Figure 3.27 Optimal progression of temperature for exothermic reversible reaction.
reactions. Hence, operating a reactor at the highest feasible temperature favours both the equilibrium conversion and the rate for an endothermic reaction. However, for an exothermic reaction, high equilibrium conversion is attained at a slower rate at low temperatures, whereas low equilibrium conversion is attained at a faster rate at high temperatures. Thus, for an exothermic reaction, an appropriate trade-off between equilibrium conversion and rate is achieved by maintaining the reactor temperature at an optimal value, which is neither too high nor too low. A plot of the rate −rA(xA, T) versus temperature T (Figure 3.27) for fixed values of conversion xA for an exothermic reversible reaction shows that the rate attains a maximum value at a particular temperature for each value of conversion xA. The optimal temperature T = Topt for a specified conversion xA is the temperature at which the net rate (−rA) of reaction is maximum. An expression for calculations of optimal temperature is obtained by taking the derivative of (−rA) with respect to T and equating it to zero, that is,
d (− rA (x A , T )) xA = 0 dT
(3.110)
Inserting the rate Equation 3.104 into Equation 3.110, we have
d (k1CA0 (1 − xA ) − k1CA0 xA ) xA = 0 dT
(3.111)
Rearranging Equation 3.111, we get
(1 − x A )
dk1 dk = xA 2 dT dT
www.Ebook777.com
(3.112)
Free ebooks ==> www.ebook777.com 180
Green Chemical Engineering
Substituting the Arrhenius equation for k1 and k2 into Equation 3.112 and taking derivatives of k1 and k2 with respect to T, we get
∆E1 ∆E2 (1 − x A )k10 e − ∆E1 /RT = x A k20 e − ∆E2 /RT 2 RT RT 2
(3.113)
Solving the above equation for temperature T, we obtain the expression for optimal temperature Topt as Topt =
(− ∆H R ) R ln [ k 20 /k10 ⋅ ∆E2 /∆E1 ⋅ x A /1 − x A ]
(3.114)
This equation defines the optimal progression of temperature for an exothermic reversible reaction. 3.1.5.2.1 Design of Reactors for Exothermic Reversible Reaction with Optimal Temperature Progression In this section, we present the procedures for the design of reactors used for an exothermic reversible reaction k
1 A B k
2
with rate expression defined by the following equations:
(− rA ( x A , T )) = k1CAO (1 − x A ) − k 2CAO x A where k1 = k10 e − ∆E1 /RT − ∆E2 /RT k1 = k 20 e
(3.115)
and the reactor temperature following the optimal path of temperature progression defined by the following equation: Topt =
−∆H R R ln [(k 20 /k10 )(∆E2 /∆E1 )( x A /1 − x A )]
(3.116)
i. Design of the batch reactor Batch time θB required for a specified conversion xAf is calculated using the batch reactor design Equation 3.101 x Af
θB = C A 0
dx A
∫ (−r (x 0
A
A
, T ))
(3.117)
A numerical method (such as the trapezoidal rule) is used for evaluating the integral term in the design Equation 3.117. Choose n values of xA = xA1, xA2, xA3,…,xAN at
www.Ebook777.com
Free ebooks ==> www.ebook777.com 181
Homogeneous Reactors
Table 3.2 Illustration of Batch Reactor Design XA
XA1
Topt (−rA(xA, T)) 1 (−rA ( x A , T ))
XA2
T1 r1
XA3
T2 r2
y1 =
1 r1
T3 r3
y2 =
1 r2
y3 =
1 r3
.
.
. . .
. . .
XAf TN rN yN =
1 rN
equal intervals (Δx) between the limits of integration, 0 ≤ xA ≤ xAf. For each value of xA, calculate the optimal temperature Topt using Equation 3.116, and calculate the rate (−rA(xA,T)) using Equation 3.115. These calculations are illustrated in Table 3.2. Using the trapezoidal rule for integration x Af
dx A
∫ (−r (x 0
A
A , T ))
(y + yN ) = ∆x 1 + ( y 2 + y 3 + y 4 + + y N − 1 ) 2
(3.118)
By inserting this value of integral in the design Equation 3.117, batch time èB is calculated. ii. Design of CSTR Space time τ required for the specified conversion xAf is calculated using the CSTR design Equation 3.102.
τ=
(
CA 0 x Af − rA (T f , x Af )
(3.119)
)
For the specified value of final conversion xAf, the value of optimal temperature Topt is calculated using Equation 3.116. Substituting the values of xA = xAf and T = Topt into the rate Equation 3.115, the rate of reaction is calculated and the space time τ is evaluated using Equation 3.119. iii. Design of PFR The space time required for the specified conversion xAf is calculated using PFR design Equation 3.103 x Af
τ = CA0
dx A
∫ [−r (T , x )] 0
A
A
(3.220)
The procedure for the calculation of space time for a PFR is similar to the procedure for the calculation of batch time for a batch reactor as the design equations are similar.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 182
Green Chemical Engineering
Problem 3.12 k1 An exothermic reversible reaction A B with rate equation has the following kinetic k2 parameters:
(− rA ) = k1C AO (1 − x A ) − k 2C AO x A
k1 = k10 e − ∆E1 /RT ; k10 = 21s−1 and ∆E1 = 32, 200 kJ/kmol
k 2 = k 20 e − ∆E2 /RT ; k 20 = 4200s−1 and ∆E2 = 64, 400 kJ/kmol
The reaction is to be carried out in a continuous-flow reactor in which optimum temperature policy is maintained. Calculate the space time required for 80% conversion of A. The feed concentration of A is CAO = 0.8 kmol/m3 and the reactor temperature is to be restricted to remain below 900 K. Show the calculations for (a) an ideal PFR and (b) an ideal CSTR. Optimal temperature policy is given by Topt =
(− ∆H R ) R ln [ k 20 /k10 ⋅ ∆E2 /∆E1 ⋅ x A /1 − x A ]
∆H R = ∆E1 − ∆E2 = 32, 200 − 64, 400 = −32, 200 kJ/kmol
− ∆H R = 32, 200 kJ/kmol and R = 8, 314 kJ/kmol.K
k 20 4200 = = 200 k10 21
∆E2 64, 400 = =2 ∆E1 32, 200
32, 200 8.314.ln [ 400 ⋅ ( x A /1 − x A )]
(− rA ) = k1C AO (1 − x A ) − k 2C AO x A
k1 = k10 e −∆E1 /RT
k 2 = k 20 e −∆E2 /RT
Topt =
a. Plug flow reactor The equation for space time τ is x Af
τ = CAO
dx A
∫ (−r (x 0
A
A
, T ))
www.Ebook777.com
Free ebooks ==> www.ebook777.com 183
Homogeneous Reactors
The integral term in the equation is calculated using the trapezoidal rule. xA
Topt (K)
k1
k2
(−rA)
1 (−rA )
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
900 900 841 753 693 646 605 566 525
0.284 0.284 0.210 0.123 0.0785 0.0521 0.0348 0.0224 0.0131
0.768 0.768 0.420 0.143 0.0586 0.0261 0.0116 0.0048 0.0017
0.2272 0.1430 0.0672 0.0342 0.0189 0.0105 0.0056 0.0027 1.05 × 10−3
4.4 7.0 14.9 29.2 52.9 95.2 178.6 370 952.4
Using the trapezoidal rule x Af
dx A
∫ (−r (x
0
A
A
, T ))
=
x Af
0.1 [(4.4 + 952.4) + 2(7.0 + 14.9 + 28.9 + + 370)] 2
dx A
∫ (−r ) (x
0
A
A
, T)
= 0.05 [ 956.8 + 2(747.8)] = 122.62
τ = 0.8 × 122.62 = 98.1 s
b. Ideal CSTR The equation for space time τ is τ=
(
C AO x Af
)
− rA (T f , x Af )
For xAf = 0.8, Topt = 525 K and (−rA) = 1.05 × 10−3 So
τ=
(0.8)(0.8) = 609.5 s (1.05 × 10 −3 )
Thus, the space time τ for CSTR is 6.4 times larger compared to that of PFR. Note: Refer the MATLAB program: react_dsm_opt_temp.m 3.1.5.3 Design of Non-Isothermal Reactors with and without Heat Exchange Q In this section, equations relating reaction temperature T and conversion xA are derived by accounting for the heat of reaction ΔHR and the heat Q, which is either added to or removed from the reactor. This is done by writing the overall heat balance equation for the reactor.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 184
Green Chemical Engineering
Heat content in the fluid flowing in
(Reactor volume) (Heat generated due to reaction) + (Heat accumulated)
Heat content in the fluid flowing out
Heat supply (Q) Figure 3.28 Schematic diagram showing various heat components associated with a reactor section.
The general heat balance equation for a reactor (or a section of the reactor) represented in Figure 3.28 is
Rateof heat Flowing into + The reactor
Rateof heat Q supplied to + thereactor
Rate of heat generated Rateof heat = accumulated in + e actor ( )in the r Q G the reactor due to reaction
Rateof Heat flowing out of the Reactor
(3.221) Q is positive for heat supply and negative for heat removal. Application of heat balance equation in the design of non-isothermal batch and flow reactors is demonstrated in the following sections: i. Design of non-isothermal batch reactor: Consider an nth-order reaction A k → B carried out in a batch reactor of volume V (Figure 3.29). CA0 is the initial concentration of A, T0 is the initial temperature, ΔHR is the heat of reaction and xA is the conversion of A at time t lapsed after start-up of the reactor.
V T CA
Q
Figure 3.29 Non-isothermal batch reactor.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 185
Homogeneous Reactors
The rate equation is (− rA ( x A , T )) = kCAn where k = k0 e−ΔE/RT and CA = CA0(1 − xA) Substituting appropriate terms into the heat balance Equation 3.221, we have
{0} + {Q} + {(− ∆H R )(V )(− rA (xA , T ))} =
d [ MCPT ] + {0} dt
(3.222)
where M: mass hold of the reactor (kg) CP mean specific heat (kJ/kg°C) Rearranging Equation 3.222, we get dT (−∆H R ) Q = (− rA (x A , T )) + dt MCP ρCP
(3.223)
The molal balance equation (or the design equation) for the batch reactor is −
dCA = ( − rA ( x A , T )) dt
which is written in terms of conversion xA as dx A (− rA (xA , T )) = dt CA0
(3.224)
Solving the first-order differential Equations 3.223 and 3.224 simultaneously, we obtain the time variations of conversion xA and temperature T in the batch reactor (Figure 3.30).
T versus t
Tf (final temperature)
T XAf (final conversion)
XA T0 XA versus t 0
t ( time)
θB (Batch time)
Figure 3.30 Variation X A and T with time in a batch reactor.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 186
Green Chemical Engineering
For adiabatic operation, Q = 0. Substituting Q = 0 into Equation 3.223 and dividing it by Equation 3.224, we get (− ∆H R )CA 0 dT = dx A ρCp
(3.225)
Define (∆T )AD =
(− ∆H R )CA 0 ρCp
(3.226)
Integrating Equation 3.225 with the initial condition (T = TO for xA = 0), we get temperature T as a function of conversion xA. T = T0 + (∆TAD )x A
(3.227)
It may be noted that temperature T increases linearly with conversion xA for exothermic reaction (ΔHR is negative) and decreases with conversion for the endothermic reaction (ΔHR is positive). For complete conversion (xA = 1), net change (increase or decrease) in temperature is the maximum, which is equal to ΔTAD. Thus, ΔTAD is defined as the maximum change in temperature attained in an adiabatic reactor. The batch time θB for adiabatic operation is calculated using the design equation x Af
θB = C A 0
dx A
∫ (−r (x 0
A
A
, T ))
(3.228)
For a value of xA, 0 ≤ xA ≤ xAf, the corresponding value of temperature T is calculated using Equation 3.227 and the rate −rA(xA,T) is evaluated by inserting the value of temperature into the rate equation. The batch time θB is calculated by numerical integration of Equation 3.228 as discussed in Section 3.2.5.1. Problem 3.13 An endothermic irreversible second-order reaction 2A k → B is carried out in a batch reactor. The reaction mixture is heated to an initial temperature of 450°C. The reaction then proceeds adiabatically. Calculate the time required to reach a conversion of 80%. The initial concentration of A is CAO = 5 kmol/m3. The fluid density is ρ = 995 kg/m3. The mean specific heat is CP = 2.5 kJ/kg K. The heat of reaction ΔHR is 98470 kJ/kgmol. The rate constant k is given by the Arrhenius equation.
k = 1.2e −14000/RT (m 3/kmol) (min) The equation for the batch reaction time is x Af
θB = CAO
dx A
∫ (−r (x 0
A
A
, T ))
www.Ebook777.com
Free ebooks ==> www.ebook777.com 187
Homogeneous Reactors
where for a second-order irreversible reaction, 2 − rA ( x A , T ) = k CAO (1 − x A )2 ; k = 1.2e −14000/RT
The temperature for the adiabatic reaction is T = TO + (∆T )AD x A
(∆T )AD =
(∆T )AD =
(− ∆H R )CAO ρCP
(−98, 470)(5) = −197.9K (995)(2.5)
T = 450 + 273 = 723K
T = 723 − 197.9x A The integral term in the equation is evaluated using the trapezoidal rule:
0.8
dx A
∫ (− r ) = 0
A
xA
T(K)
k
(−rA)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
723.0 703.2 683.4 663.6 643.8 624.1 604.3 584.7 564.7
0.1168 0.1100 0.1025 0.0946 0.0874 0.0806 0.0737 0.0674 0.0610
2.92 2.23 1.64 1.16 0.787 0.504 0.295 0.152 0.061
1/(−rA) 0.3425 0.4484 0.6098 0.8621 1.271 1.984 3.390 6.580 16.393
0.1 [(0.3425 + 16.393) + 2(0.4484 + 0.6098 + + 6.580)] = 2.351 2 θB = 5 × 2.351 = 11.76 min
Note: Refer the MATLAB program: react_dsn_adiab1.m ii. Design of non-isothermal PFR: A schematic diagram of non-isothermal PFR is shown in Figure 3.31. Heat is added to the reactor at a rate Q by passing a hot fluid through the jacket. Writing the heat balance equation for a section of the reactor volume dV, we have
{ρqC T } + {dQ} + {(−∆H p
R
{
}
)(− rA ( x A , T )dV )} = {0} + ρqCp (T + dT )
www.Ebook777.com
(3.229)
Free ebooks ==> www.ebook777.com 188
Green Chemical Engineering
dQ q
q CA0, T0
q xA + dxA
xA CA T
q
CA + dCA T + dT
CAf , xAf ’ Tf Q
Q Figure 3.31 Non-isothermal PFR.
Rearranging Equation 3.229, we get
1 dQ dT − ∆H R = (− rA ( x A , T )) + dV ρqCp ρqCp dV
(3.230)
dQ is the rate of heat transferred to the reactor section of volume dV across the jacket wall of area dAJ
dQ = U (TJ − T )dAJ
(3.231)
U: overall heat transfer coefficient (kw/m2°C) TJ: temperature of the heating fluid in the jacket If dL is the length of the reactor section and D is the reactor tube diameter, then
dAJ = πDdL π 2 dV = D dL 4
(3.232)
Inserting Equations 3.232 and 3.231 into Equation 3.230, we get
4U dT − ∆H R = (− rA ( x A , T )) + (TJ − T ) dV ρqCp DρqCp
(3.233)
Taking the molal balance of reactant A in the reactor section of volume dV, we get
dx A 1 = (− rA ( x A , T )) dV qCAo
(3.234)
By solving the first-order differential Equations 3.233 and 3.234 simultaneously, we obtain the variations of conversion xA and temperature T through the reactor volume V. This is shown in Figure 3.32.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 189
Homogeneous Reactors
T vs V
Tf (final temperature)
T XAf (final conversion)
XA T0 XA vs V 0
Vf
Reactor volume (V )
Figure 3.32 Spatial variation of T and xA in a PFR.
For a PFR operating in an adiabatic condition, dQ = 0. Substituting dQ = 0 into Equation 3.230 and dividing it by Equation 3.234, we get
(− ∆H R )CAO dT = dx A ρCP
(3.235)
Equation 3.235 is the same as Equation 3.225 derived for the adiabatic batch reactor. Thus, the variation of temperature T with conversion X A in a PFR operating under adiabatic conditions is written as
T = TO + (∆T )ad X A
(3.236)
where
(− ∆H R )C A 0 (∆T )ad = ρCP
(3.237)
(ΔT)ad is the maximum change (increase or decrease) in temperature attained in an adiabatic PFR. The space time required τ to achieve a specified conversion xAf in an adiabatic PFR is calculated using the design equation derived for PFR in Equation 3.220 xA f
τ = CAO
dx A
∫ (− r ( x , T ) 0
A
A
(3.238)
For any value of xA, 0 ≤ xA ≤ xAf, temperature T is calculated using Equation 3.236 and the rate of reaction (−rA(xA,T)) for this value of X A and T is calculated using the rate equation. Space time τ is calculated using Equation 3.238 by numerical integration.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 190
Green Chemical Engineering
q CA0 T0
xAf, CAf, Tf q
Q
V Tf CA
Tj′
Figure 3.33 Non-isothermal CSTR.
iii. Design of non-isothermal CSTR: The schematic diagram of a non-isothermal CSTR is shown in Figure 3.33. Heat is added to the reactor at a rate Q by passing the hot fluid through the jacket. Tj is the temperature of the hot fluid in the jacket. Aj is the jacket area across which heat is transferred. The net heat balance equation for the CSTR is
{ρqC T } + {Q} + {(−∆H ) (qC p O
R
{
}
x ) = {0} + ρqCpTf
AO Af
}
(3.239)
Rearranging this equation, we get
− ∆H RC AO Q Tf = TO + x Af + ρCp ρqCp
(3.240)
The net rate of heat transferred to the reactor Q is
Q = UA j (Tj − Tf )
(3.241)
where U is the overall heat transfer coefficient. Equations 3.240 and 3.241 are solved to obtain the reactor temperature Tf corresponding to the specified value of final conversion xAf. The rate of reaction is calculated by inserting the values of xAf and Tf into the rate equation. Substituting this value of rate (−rA(xAF, Tf) in the CSTR design equation τ=
(C AO x Af ) v = q (− rA ( x Af , Tf ))
www.Ebook777.com
(3.242)
Free ebooks ==> www.ebook777.com 191
Homogeneous Reactors
the space time τ required to achieve the specified conversion is calculated. For the CSTR operating in an adiabatic condition, Q = 0. Substituting Q = 0 into Equation 3.240, we obtain the equation for Tf as Tf = TO + (∆T )ad x Af
(3.243)
where (− ∆H R )C AO (∆T )ad = ρCP
(3.244)
Equation 3.244 is similar to Equations 3.225 and 3.235 derived for the batch reactor and PFR operating in an adiabatic condition. Problem 3.14 An exothermic first-order reaction A k → B with rate equation (−rA) = kCA and rate constant k defined by the Arrhenius equation k = 35e −9000/RT Hr −1
is to be carried out in a continuous-flow reactor. The concentration of A in the feed is CAO = 1 kmol/m3. The density and mean specific heat of the fluid are ρ = 998 kg/m3 and CP = 4.2kJ/kg K , respectively. The heat of reaction is ΔHR = −210,000 kJ/kmol. Feed temperature is TO = 400 K. For a final conversion of 80%, calculate a. Space time τ in a PFR operated adiabatically b. Space time τ in a CSTR operated adiabatically c. Space time τ in a CSTR operated isothermally at temperature Tf = 400 K, calculate the heat to be exchanged for isothermal operation. Assume a feed rate of 100 L/min. The rate equation for the first-order reaction is (− rA ) = kC AO (1 − x A )
where k = 35e−9000/RT HR−1. The reactor temperature T for adiabatic operation is T = TO + (∆T )AD x A
(∆T )AD =
(− ∆H R )C AO (2, 10, 000)(1) K = 50.1 K = ρCP (998)( 4.2) T = 400 + 50.1x A
www.Ebook777.com
Free ebooks ==> www.ebook777.com 192
Green Chemical Engineering
a. Adiabatic PFR: The integral term in the design equation is calculated using the trapezoidal rule: xA
T(K)
k
(−rA)
1 ( −rA )
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
400 405 410 415 420 425 430 435.1 440.1
2.33 2.42 2.50 2.57 2.65 2.73 2.81 2.90 2.99
2.33 2.178 2.00 1.80 1.59 1.365 1.124 0.870 0.598
0.429 0.459 0.500 0.556 0.629 0.723 0.890 1.149 1.672
The PFR design equation for the calculation of space time τ is x Af
τ = CAO dx A
∫ (−r (x 0
A
0
x Af
A
A
, T ))
=
dx A
∫ (− r ( x
A
, T ))
0.1 [(0.429 + 1.672) + 2(0.459 + 0.500 + + 1.149)] 2
= 0.05 [(2.101) + 2( 4.906)] = 0.596 h
b. Adiabatic CSTR: The design equation for space time τ for CSTR is τ=
(
C AO x Af
)
− rA (T f , x Af )
where Tf = TO + (ΔT)ADxAf
xAf = 0.8
Tf = 400 + 50.1 × (0.8) = 440.1 The corresponding value of −rA is 0.598
τ=
(1)(0.8) = 1.34 h (0.598)
c. Isothermal CSTR: The reactor is operated in an isothermal state by maintaining a constant temperature of Tf = 400 K.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 193
Homogeneous Reactors
At Tf = 400 K, k = 2.33 HR−1 (−rA(Tf, xAf)) = kCAO(1 − xAf)
= (2.33)(1)(1 − 0.8) = 0.466 kmol/m3h τ=
CAO x Af (1)(0.8) = = 1.72 h − rA (Tf , x Af ) 0.466
(
)
To keep the reactor in an isothermal state, the heat liberated due to exothermic reaction has to be continuously exchanged. This heat exchange rate Q is
Q = (ΔHR)(qCAOxAf)
Q = (−2,10,000)(1)(0.8)q = −1,68,000 kJ(q) Say, for a feed rate of 100 L/min,
q=
(100)(10 −3 ) = 1.667 × 10 −3 m 3/s (60)
The heat removal rate Q is
Q = 280 kW Note: Refer the MATLAB program: react_dsn_adiab2.m
3.1.5.4 Non-Isothermal CSTR Operation: Multiple Steady States and Stability Consider an exothermic first-order irreversible reaction A k → B carried out in a CSTR (Figure 3.34). The rate equation is
(− rA ( x A , T )) = k o e − ∆E/RT CAO (1 − x A )
(3.245)
CAO and TO are the feed concentration of A and the feed temperature, respectively. xAf is the final conversion and Tf is the final temperature attained when CSTR is operating at steady state. ΔHR is the heat of reaction. The heat generated due to exothermic reaction is removed by passing a coolant fluid through the jacket. TC is the steady temperature attained by the coolant fluid in the jacket. The net conversion of xAf in the CSTR is a function of temperature Tf attained at steady state.
x Af =
− ∆E/RT
f τ koe − ∆E/RT f 1 + koe τ
(3.246)
where τ is the space time. For a given space time τ, conversion xAf increases with an increase in temperature Tf. The temperature Tf in the CSTR attains a steady value when the net rate
www.Ebook777.com
Free ebooks ==> www.ebook777.com 194
Green Chemical Engineering
q CA0
xAf, CAf, Tf
T0
q
mc
V Tf CAf
mc
Tc
Figure 3.34 Non-isothermal CSTR operation.
of heat generation QG is equal to the net rate of heat removal QR. The net rate of heat generation QG is the heat of reaction −ΔHR multiplied by kmol of A converted per second.
QG = −ΔHR(qCA0xAf)
Inserting Equation 3.246 for xAf in the above equation, we get the equation for the heat generation rate QG as a function of the reactor temperature Tf attained at steady state. QG (Tf ) =
− ∆E/RT f
(− ∆H R )qCAO ko τe − ∆E/RT f 1 + k o τe
(3.247)
A plot of QG versus Tf is a sigmoidal curve (S-shaped curve) shown in Figure 3.35. The net rate of heat removal QR is QR = ρqCP (Tf − T0 ) + UAC (T f − TC )
(3.248)
where U: overall heat transfer coefficient AC: cooling jacket area (m2) For a given coolant flow rate (fixed value of U) and coolant temperature TC, the heat removal rate QR is a linear function of reactor temperature Tf.
(
)
(
QR (Tf ) = ρqCP + UAC Tf − ρqCPT0 + UACTC
)
(3.249)
Thus, the plot of QR versus Tf is a straight line with positive slope = (ρqCP + UAC ) and negative intercept = ρqCPT0 + UACTC . As QG = QR at steady state, the point of intersection of the QR versus Tf line with the QG versus Tf sigmoidal curve would correspond to the steady-state reactor temperature attained for a given coolant flow rate. Depending upon the value of the slope and intercept of the QR versus Tf line, one of the three conditions listed below would apply:
(
)
www.Ebook777.com
Free ebooks ==> www.ebook777.com 195
Homogeneous Reactors
QR Vs T
3 T4
2 1
QG QR
T3 QR Vs Tf
QG Vs Tf
T5
Ignition point
dQ Slope of QG Vs Tf curve at T4 = G dTf T4 dQ R Slope of QR Vs Tf line = dTf
dQG Slope of QG Vs Tf curve at T3 = dTf T
3
T1 Quenching point
dQ G Slope of QG Vs Tf curve at T2 = dTf T
T2
T3–δ T3 T3+δ QR Vs Tf
2
Tf
Figure 3.35 Multiple steady states in a non-isothermal CSTR.
1. The QR versus Tf line would intersect the QG versus Tf curve at a point corresponding to a high value of steady-state temperature T5 and a high conversion xAf. This would happen at low coolant flow rates. The reactor is said to be operating at an ignition point as the temperature is too high. 2. The QR versus Tf line would intersect the QG versus Tf curve at A point corresponding to a low value of steady-state temperature T1 and a low conversion xAf. This would be the case if the coolant flow rate is too high. The reactor is said to be in a quenched state as the temperature is too low. 3. The QR versus Tf line would intersect the QG versus Tf at three points corresponding to three steady-state temperature values T2, T3 and T4. This would happen for a coolant flow rate that is neither too high nor too low. In this case, CSTR would attain one of the three steady states: an ignition state of high temperature T4 and high conversion, a quenching state of low temperature T2 and low conversion, an intermediate state of medium temperature T3 and medium conversion. Consider a CSTR at steady state corresponding to the temperature T3. Assume that the steady state is perturbed by a momentary disturbance that causes the temperature to rise from T3 to T3 + δ (Figure 3.35). At T3 + δ, the heat generation rate QG is greater than the heat removal rate QR. As a result, temperature would increase further and this rise of temperature would continue until the temperature attains the new steady-state value of T4. On the other hand, if the perturbation causes the temperature to fall from T3 to T3 − δ, the temperature would drop further as QG www.ebook777.com 196
Green Chemical Engineering
temperatures T2 and T4 would force the CSTR to move away from this state only temporarily but finally return to the original state. Thus, the steady states corresponding to temperatures T2 and T4 are stable steady states. The ignition state (corresponding to T4) is not preferred even though the conversion is high if the product of the reaction is highly heat sensitive and is likely to decompose at high temperatures. The quenching state (corresponding to T2) is also not a preferred state as the conversion is too low. Thus, the unstable middle state corresponding to the medium temperature is the most preferred state of operation. However, a feedback controller has to be put in place to maintain the CSTR in this unstable state. It is seen that (Figure 3.35) the slope of the QG versus Tf plot (dQG/dTf) is greater than the slope of the QR versus Tf line (dQR/dTf) at unstable state and is less than (dQR/dTf) at stable states. Thus, the condition for stability of a non-isothermal CSTR is dQG dQR dT < dT f f
(3.250)
This stability condition is known as Van Heedran’s stability criteria. The condition of multiple steady states does not arise for a non-isothermal CSTR in which an endothermic reaction is carried out with heat addition as, in this case, the QR versus Tf plot is a straight line with negative slope = −(ρqCP + UAC ) and positive intercept = (ρqCPTC + UACTC ).
(
(
)
QR (Tf ) = − ρqCP + UAC Tf + ρqCPTC + UACTC
)
(3.251)
This line will intersect the QG versus Tf curve at only one point as shown in Figure 3.36. (Refer MATLAB program cstr_multiplicity.m for illustration of multiple steady states in non-isothermal CSTR.)
QR
Q
R
vs
QG vs Tf
T f
QG
Steady state T1
T1= steady-state temperature T1
Tf
Figure 3.36 Single steady state in a CSTR in which an endothermic reaction is taking place.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 197
Homogeneous Reactors
3.2 Homogeneous Non-Ideal Reactors 3.2.1 Non-Ideal Reactors versus Ideal Reactors Homogeneous reactors, which are simple holding vessels, are classified as tank reactors and tubular reactors based on the shape of the vessel. Hold-up volume V of a fluid in the reaction vessel determines the space time τ, for a given volumetric feed rate q (τ = V/q) of the fluid. Space time is the average time of residence of a fluid in the reaction vessel, which is also the average time available for the fluid to undergo reaction in the vessel. Hence, space time ‘τ’ is one of the key factors that will decide the extent of conversion (fractional version xAf) of a reaction achievable in the reaction vessel. The design of a homogeneous reactor involves the calculation of space time or the vessel volume for a given fluid rate required to achieve the specified conversion xAf of the given reaction. The design calculation requires the kinetic rate equation for the given reaction. In addition to this rate expression, the design calculation also requires details about the pattern of fluid mixing in the reaction vessel and its effect on the fractional conversion. As a first step towards simplifying the design calculations, some simple fluid mixing patterns are assumed and the reactors having such simple patterns of fluid mixing are termed as ideal reactors. Thus, an ideal CSTR is an ideal tank reactor and an ideal PFR is an ideal tubular reactor. In an ideal CSTR, the mixing of fluid in the tank is achieved with the help of a stirrer and the mixing is assumed to be perfect. Perfect mixing leads to uniformity in concentration of chemical compounds within the tank volume. Thus, the concentration of the reactant in the tank holdup will be the same as the final reactant concentration in the outlet stream. In an ideal PFR, it is assumed that the mixing of a fluid is perfect (complete) in the radial direction and no mixing of the fluid takes place in the axial direction. Owing to perfect mixing in the radial direction, a uniform concentration of reactant is achieved in the radial direction. As there is no mixing of fluid in the axial direction, all the fluid elements stay in the vessel for the same duration of time. These simplified assumptions about fluid mixing pattern lead to derivation of elegant design equations (Section 2.2.1) for an ideal CSTR and an ideal PFR. These design equations are as follows: For an ideal CSTR, τ=
(CAO − CAf ) V = q (− rA (C Af ))
(3.252)
For an ideal PFR,
V τ= = q
CAf
dCA
∫ (−r (C ))
CAO
A
A
(3.253)
Using these design equations, one can calculate the volume V of the reactor required to achieve a specified fractional conversion x A f ( x A f = 1 − (CAf /C A 0 )) of reactant A in the reactor. Here, q is the volumetric feed flow rate and (−rA(CA)) is the kinetic rate expression for the rate of disappearance of reactant A. In reality, will a reactor designed using the above equations achieve the specified conversion xAf? Definitely not, because the design equations used here are applicable to ideal
www.Ebook777.com
Free ebooks ==> www.ebook777.com 198
Green Chemical Engineering
reactors and the actual reactors are not ideal reactors. In an actual reactor, the fluid mixing pattern will not be the same as the one assumed in an ideal reactor. A real reactor that is not an ideal reactor is called a non-ideal reactor. A non-ideal reactor is defined as a reactor in which the fluid mixing pattern is different from the one assumed in an ideal reactor. In reality, all reactors are non-ideal. Ideal reactors are essentially theoretical reactors that are not real. Instead of designing an ideal reactor that is not real, can we not design a reactor whose performance (fractional conversion xAf can be taken as a performance metric) is as close as the one achievable in a real reactor? Such a design approach would require prior knowledge about the fluid mixing pattern in the reaction vessel. As mixing of fluid in a vessel is influenced by a number of design factors (e.g. beeding on the inner wall of the vessel provided for mechanical strength), it is not possible to predict the fluid mixing pattern prior to design. Thus, it is not possible to design a reactor accounting for the actual fluid mixing pattern in the vessel as the exact fluid mixing pattern is not known a priori. So, a practical approach to this problem is to design the reactor assuming it as an ‘ideal reactor’ and provide a factor of safety in the design calculations to account for unknown discrepancies between the real and ideal reactors. For example, say we find the volume of CSTR required to achieve 80% conversion to be 1 m3 using the ideal CSTR design equation, but we take the actual volume to be 15% more than the calculated volume, that is, 1.15 m3. Even after providing the factor of safety in the design, we are not sure if, in reality, the reactor would actually achieve the specified performance of 80% conversion. To ascertain this, certain studies have to be conducted on the actual reactor after it is designed, fabricated and installed. The main purpose of these studies is to evaluate the performance of the actual reactor which is a non-ideal reactor. This section of the chapter deals with studies on non-ideal reactors. It may be noted that studies on non-ideal reactors are aimed at the performance evaluation of reactors and not at the design of reactors. 3.2.2 Non-Ideal Mixing Patterns Fluid mixing patterns, seen in real reactors, which are different from the mixing patterns defined for ideal reactors, are called non-ideal mixing patterns or are simply known as non-idealities. Any deviation from the ideal is considered as non-ideal. Some of the commonly observed non-ideal mixing patterns are discussed here. i. Dead zone in a CSTR: In a CSTR, if the mixing is improper, fluid in certain portions of the reactor volume near sharp corners and edges will not get mixed well with the fluid in the complete mixing zone. This portion of the fluid volume that gets excluded from the well-mixed volume is called the dead zone or dead volume (see Figure 3.37). Reaction occurs only in the well-mixed zone and not in the dead zone as there is no mixing of fluid in the dead zone. The volume of the well-mixed zone is called active volume denoted as Va and Vd is the volume of the dead zone. Dead volume Vd is the hidden volume that does not contribute to the reaction. A schematic representation of the dead zone is shown in Figure 3.38. ii. Bypass or short-circuiting in a CSTR: In a CSTR, if the gap between the fluid inlet and outlet ports is not sufficiently wide, certain fraction of the feed stream will bypass or short-circuit the well-mixed zone of the reactor volume and exit through the outlet port (Figure 3.39). No reaction will occur in the bypass stream as there is no mixing of fluid in this stream. A schematic representation of CSTR with bypass
www.Ebook777.com
Free ebooks ==> www.ebook777.com 199
Homogeneous Reactors
q q
Dead zone near A sharp edge Well-mixed zone
V
Dead zone near A sharp corner Figure 3.37 CSTR with ‘dead volume’.
q
q
Va
Vd Figure 3.38 Schematic representation of ‘dead volume’.
is shown in Figure 3.40. Here, qb is the volumetric flow rate of fluid in the bypass stream, qa is the volumetric flow rate of fluid through the active well mixed zone. iii. Axial mixing in a tubular flow reactor: In a tubular flow reactor (which is treated as an ideal PFR), presence of vortices near inlet and outlet ports will cause fluid mixing in the axial direction, which is a deviation from the mixing pattern (no axial mixing) assumed in an ideal PFR (see Figure 3.41).
q q V V
Figure 3.39 CSTR with bypass.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 200
Green Chemical Engineering
qb q
qb
V qa
qa
q
Figure 3.40 Schematic representation of CSTR with bypass.
Figure 3.41 Axial mixing in a tubular reactor.
Figure 3.42 Laminar flow reactor.
iv. Laminar flow reactor: A tubular flow reactor, in which the fluid flow is laminar, represents gross deviation from the plug flow assumed in an ideal PFR. Laminar flow is a streamlined flow of fluid (see Figure 3.42) in which the fluid elements mix neither in the radial direction nor in the axial direction. Whereas in an ideal PFR, there is complete mixing of fluid in the radial direction and no mixing of fluid in the axial direction. 3.2.3 Residence Time Distribution: A Tool for Analysis of Fluid Mixing Pattern Non-ideality in a homogeneous reactor refers to any kind of deviation from the fluid mixing pattern defined for ideal reactors (ideal CSTR and ideal PFR). In reality, all the reactors are non-ideal. In order to evaluate the performance of any reactor (i.e. extent of conversion achieved in a reactor), it is necessary to diagnose the non-ideality in the reactor. Diagnosis of non-ideality involves identification of type of non-ideality pattern of fluid mixing and assessment of the degree of non-ideality (a quantitative measure of extent of
www.Ebook777.com
Free ebooks ==> www.ebook777.com 201
Homogeneous Reactors
q
V
q
Figure 3.43 A reaction vessel.
deviation from ideality). In order to diagnose the non-ideality in the given reactor, a diagnostic test called tracer test is performed on the reactor and a report called residence time distribution (RTD) report is generated from this diagnostic test. Consider a fluid flowing through a reaction vessel of volume V at volumetric flow rate q (see Figure 3.43). Residence time θ of a fluid element is the time duration of residence of the fluid element in the vessel from the time it enters the vessel to the time it leaves the vessel. Assume that the fluid is composed of discrete fluid elements and a fixed number of fluid elements enter the vessel at any given time. The fluid elements on entering the vessel will disperse through the vessel tracking different flow paths and residing for different time durations in the vessel. The flow paths tracked by the fluid elements and the corresponding residence times of fluid elements in the vessel depend on the fluid mixing pattern prevalent in the vessel. Thus, of the fixed number of fluid elements leaving the vessel at any given time, different fluid elements would have resided for different time durations in the vessel, leading to a distribution of residence times in the vessel. As the RTD of fluid elements in a vessel depends on the fluid mixing pattern prevalent in the vessel, the information on RTD can be used effectively for the diagnosis of non-ideality in the reactor. The distribution of residence times of fluid elements in a vessel is expressed in terms of a function called RTD function denoted as F(θ). F(θ) is defined as the fraction of the fluid elements (leaving the vessel at any time) whose residence time is less than or equal to θ. F(θ) = 0 at θ = 0 as no fluid element can have zero residence time and F(θ) = 1 as θ → ∞ as all the fluid elements reside in the vessel only for finite time duration. Further, F(θ) is monotonically increasing function of ‘θ’ as F(θ + Δθ) ≥ F(θ) for all θ + Δθ > θ. A sketch of a typical RTD function F(θ) is shown in Figure 3.44.
1
F(θ + ∆θ) F(θ) F(θ)
0
θ (θ + ∆θ)
Figure 3.44 RTD function.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 202
Green Chemical Engineering
E(θ)
θ Figure 3.45 Exit age distribution.
ΔF(θ) = F(θ + Δθ) − F(θ) is the fraction of the fluid elements leaving the reaction vessel at any time whose residence time is between θ and θ + Δθ. Taking limit as Δθ → 0, we define another distribution function of θ denoted as E(θ) E(θ) = Lt
∆θ → 0
∆F(θ) dF(θ) = ∆θ dθ
(3.254)
E(θ) is called ‘exit age distribution function’. The age of a fluid element in the reaction vessel at any time instant is defined as the time spent by the fluid element in the vessel at that time instant. Exit age is the total time spent by the fluid element in the vessel from the time of entry to the time of exit. Thus, exit age of the fluid element is also the residence time. E(θ)dθ = dF(θ) is the fraction of fluid elements (leaving the reactor at any time) whose residence time is between θ and θ + Δθ, which is equal to θ as dθ → 0. E(θ) = 0 at θ = 0 as well as at θ → ∞ as fluid elements have finite residence time value greater than zero. Figure 3.45 represents a typical exit age distribution function. It may be noted that
∞
1
0
0
∫ E(θ)dθ = ∫ dF(θ) = 1.
3.2.3.1 Tracer Experiment RTD function is obtained by performing a tracer experiment on the reaction vessel (Figure 3.46). (Tracer)
(Injection valve)
q
Detector
V C0
(Reaction vessel)
q C(θ)
Figure 3.46 Schematic diagram of tracer experiment.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 203
Homogeneous Reactors
An inert fluid (not the reactant) is pumped through the reaction vessel of volume V at steady volumetric flow rate q. A tracer material is injected with the fluid stream in a small quantity at the reactor inlet at some reference time θ = 0 to mark the fluid that entered the vessel at θ = 0 and distinguish them from the fluid that have entered prior to θ = 0. Let C0 be the concentration of tracer molecules at the inlet. A detector is used to measure the concentration of tracer molecules C at the reactor outlet. As some of the marked fluid elements spend longer time in the vessel than the others, the concentration of tracer molecules C(θ) in the vessel outlet varies with time θ. By recording the variation of outlet tracer concentration C(θ) with time θ, the RTD function is obtained for the reaction vessel. The tracer test is classified as step test and impulse test depending upon the mode of injection of the tracer at the inlet. In the step test, the tracer input is a step function. Here the tracer is injected continuously into the feed stream starting from a reference time θ = 0. The tracer concentration at the outlet is recorded as a function of time. Input and output concentrations of the tracer are shown in Figure 3.47. The output response curve for the tracer test is called C-curve. Tracer concentration at the inlet Ci(θ) = C0 for all θ ≥ 0, as the tracer is added continuously starting from time θ = 0. All the fluid elements entering the vessel at and after time θ = 0 are marked uniformly with the tracer. At any time θ > 0, qC0 is the amount of fluid elements entering the vessel, which is the same as the amount of fluid elements leaving the vessel. Of this total amount of fluid elements qC0 leaving the vessel at any time θ > 0, only qC(θ) fluid element is marked by the tracer. This qC(θ) represents the fluid elements that have resided, in the vessel for a time span lesser than or equal to θ. As the RTD F(θ) is defined as the fraction of the fluid elements whose residence time is less than or equal to θ, we have qC(θ) C(θ) F(θ) = = qC0 C0 step
(3.255)
Using this equation, the RTD function F(θ (called F-curve) is obtained from the C-curve of the step test and is shown in Figure 3.48. In the impulse tracer test, the tracer input is an impulse function. Here, a fixed amount of tracer is injected in one shot into the fluid stream at some reference time θ = 0. Theoretically, (a)
(b)
C0
C0
CL(θ)
C(θ) C(θ1)
θ
θ1
θ
Figure 3.47 Tracer concentration for step test. (a) Tracer input concentration. (b) Tracer output concentration (C-curve).
www.Ebook777.com
Free ebooks ==> www.ebook777.com 204
Green Chemical Engineering
1 F(θ) =
C(θ) C0
step
θ Figure 3.48 F-curve from the C-curve.
the tracer injection time is infinitesimally small and the tracer concentration is infinitely large at the time of injection. However, in practice, tracer concentration in the feed stream is a finite value of C0 during the time Δθ0 of tracer injection. Figure 3.49 depicts the input and output concentration of tracer. Total amount of tracer injected at the inlet is M = qC0Δθ. As the tracer is added in the inlet stream in one shot, all the tracer material will gradually set washed out of the vessel over some finite period of time and hence C(θ) → 0 as θ → ∞. The total amount of tracer coming out of the vessel in the effluent stream between time θ and θ + dθ is qC(θ) dθ; this is the amount of fluid elements in the effluent stream that has resided in the vessel between time θ and θ + dθ. By definition, E(θ)dθ is the fraction of the fluid elements coming out in the effluent stream at any time θ that has resided in the vessel between time θ and θ + dθ. Thus E(θ)dθ =
(a)
Theoretical
Ci(θ)
qC(θ)dθ M
(3.256)
(b)
C(θ) Practical
C0
C(θ)
∆θ
θ
θ
θ
Figure 3.49 Tracer concentration for impulse test. (a) Tracer input concentration. (b) Tracer output concentration (C-curve).
www.Ebook777.com
Free ebooks ==> www.ebook777.com 205
Homogeneous Reactors
The total amount of tracer M injected in the feed stream is equal to the amount of tracer washed out of the vessel into the effluent stream. Thus ∞
∫
M = q C(θ)dθ
(3.257)
0
Combining Equations 3.256 and 3.257, we get C(θ) E(θ) = ∞ C(θ)dθ 0 impulse
∫
(3.258)
Using the above equation, the exit age distribution function E(θ) is obtained from the C-curve of the impulse tracer test and is shown in Figure 3.50. Thus, the RTD functions F(θ) and E(θ) are obtained from the step test and the impulse test, respectively. As F(θ) and E(θ) are related to each other by the following equations dF(θ) dθ
(3.259)
∫ E(θ) dθ
(3.260)
E(θ) =
θ
F(θ) =
0
by knowing either one of the two distribution functions, the other one can be obtained using these equations.
E(θ) =
∞
C(θ)
Area under E-curve=
∫0 C(θ)dθ
∞
∫0 E(θ)dθ = 1
θ Figure 3.50 E-curve from the C-curve.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 206
3.2.3.2 Mean
Green Chemical Engineering
θ and Variance σ2 of Residence Time Distribution
Mean and variance of any given distribution are the parameters that characterise the statistical nature of the distribution. Thus, for the RTD defined by the function F(θ) (or E(θ)), the mean residence time θ and the variance σ2 are given by the following equations: ∞
θ=
∫ θE(θ)dθ 0
(3.261)
∞
∫ (θ − θ) E(θ)dθ
σ2 =
2
0
(3.262)
Equation 3.262 for variance σ2 can be rewritten as ∞
σ2 =
∫ (θ
2
− 2θθ + θ 2 )E(θ)dθ
0
∞
2
σ =
(3.263)
∞
∞
∫ E(θ)dθ − 2θ∫ θE(θ)dθ + θ ∫ E(θ)dθ 2
0
0
0
(3.264)
∞
2
σ =
∫ θ E(θ)dθ − (θ) 2
0
2
(3.265)
It may be noted that mean residence time can also be expressed in terms of V and q as
θ = V /q
(3.266)
It will be seen later that the parameters θ and σ2 play a crucial role in characterising the non-idealities in the reaction vessel. 3.2.3.3 Residence Time Distribution for Ideal Reactors The RTD function F(θ) or E(θ), obtained from the tracer experiment conducted on the reaction vessel, can be used to characterise the non-ideality as the fluid mixing pattern in the vessel has a strong influence on the distribution of residence time. Given the RTD for a reaction vessel, we would first like to know if the mixing patterns in the reaction vessel match well with the mixing patterns assumed for ideal reactors (ideal CSTR or ideal PFR). This can be done by comparing the RTD function (F-curve or E-curve) for the given reactors with the RTD functions for the ideal CSTR or ideal PFR. For this, we should know the RTD functions for ideal reactors. As the ideal CSTR and ideal PFR are theoretical reactors, the RTD function equations for these reactors are derived theoretically.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 207
Homogeneous Reactors
q q
Ci(θ)
C(θ)
V C(θ)
Figure 3.51 Schematic of an ideal CSTR.
i. RTD for an ideal CSTR: Consider an ideal CSTR of volume ‘V’ through which an inert fluid is pumped at volumetric flow rate ‘q’ (Figure 3.51). Assume that the CSTR is subjected to a step test by continuous injection of tracer at the inlet, starting from a reference time θ = 0. Inlet tracer concentration is Ci(θ) = C0. For all θ ≥ 0. At any time θ > 0, the outlet concentration of the tracer is C(θ). As the CSTR is ideal, mixing in the vessel is uniform and the concentration of the tracer in the vessel is the same everywhere and is equal to the outlet concentration C(θ). Taking an unsteady-state tracer balance around the reactor,
Rate of flow tracer Rate of flow tracer = + into the vessel out of the vessel
Rate of accumulation of tracer in the vessel
that is
qC0 = qC(θ) + V
dC(θ) dθ
(3.267)
Dividing all the terms in the above equation by q and defining the mean residence time θ = V/q, we get
C0 = C(θ) + θ
dC(θ) dθ
(3.268)
Rearranging the terms in the above equation and integrating on both sides, θ
∫ 0
dθ = θ
C(θ )
∫C 0
dC(θ) 0 − C(θ)
θ C − C(θ) = − ln 0 C0 θ
(3.269) (3.270)
www.Ebook777.com
Free ebooks ==> www.ebook777.com 208
Green Chemical Engineering
We get C(θ) F(θ) = = 1 − e − θ/ θ CO step
(3.271)
and E(θ) =
dF(θ) 1 − θ/θ = e dθ θ
(3.272)
Equations 3.271 and 3.272 define the theoretical expression for F(θ) and E(θ) for the ideal CSTR. Sketches of F(θ) and E(θ) for the ideal CSTR are shown in Figures 3.52 and 3.53, respectively. ii. RTD for an ideal PFR: Consider an ideal PFR of volume V through which an inert fluid is flowing at volumetric flow rate ‘q’ (Figure 3.54). The tracer is injected at the inlet at the reference time θ = 0. Ci(θ) and C(θ) are the tracer concentrations, at the inlet and the outlet, respectively. In an ideal PFR, there is complete mixing in the radial direction and no mixing in the axial direction. So, the tracer material injected at the inlet, at time θ = 0, spreads uniformly in the radial direction (due to complete mixing) and all the tracer elements move at the same velocity in the axial direction (no axial mixing and flat velocity profile). Thus, all the fluid elements have the same residence time, which is equal to the mean residence time θ = V/q. Thus, C(θ) is the same as Ci(θ) shifted along the time axis by θ. C(θ) = Ci (θ − θ )
(3.273)
1 Ideal CSTR
Ideal PFR
F(θ)
Non-ideal reactor 0
θ
θ
Figure 3.52 F-curves for ideal and non-ideal reactors.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 209
Homogeneous Reactors
Ideal CSTR Ideal PFR
E(θ) 1 θ
Non-ideal reactor
0
θ
θ
Figure 3.53 E-curve for ideal and non-ideal reactors.
Thus, F(θ) is a unit step function shifted along the time axis by θ and E(θ) is a unit impulse function shifted along time axis by θ. Sketches of F(θ) and E(θ) for ideal PFR are shown in Figures 3.52 and 3.53, respectively. Thus, for ideal PFR
0, θ < θ F(θ) = 1, θ ≥ θ
(3.274)
0, θ < θ E(θ) = ∞ , θ = θ 0, θ > θ
(3.275)
and
Although E(θ) at θ = 0 is infinite, the area under the E-curve is a finite value equal to 1, that is ∞
θ+
0
−
∫ E(θ) dθ = ∫ E(θ) dθ = 1
q Ci(θ)
θ
(3.276)
V
q C(θ)
Figure 3.54 Schematic of an ideal PFR.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 210
Green Chemical Engineering
3.2.3.4 RTD as a Diagnostic Tool RTD functions (F-curve or E-curve) for ideal CSTR and ideal PFR serve as signatures with which the RTD obtained for any reaction vessel can be compared to get an idea about the extent by which the actual reactor deviates from the ideal reactor. For example, the sketches of the F-curve and the E-curve obtained for some reaction vessel shown (by dotted lines) in the Figures 3.52 and 3.53 indicate significant deviation from the RTD plots of both ideal CSTR and ideal PFR. This clearly shows that the reaction vessel is highly non-ideal. Thus, RTD serves as a simple diagnostic tool to find out if a reaction vessel is ideal or non-ideal. Diagnosing the non-ideality does not stop with finding out if the reaction vessel is ideal or non-ideal. On knowing that the reactor is non-ideal, it is necessary to predict the impact of non-ideality on the reactor performance, which is the conversion achievable in the reactor. For this, the non-ideality has to be quantified first. Quantification of non-ideality involves assigning some kind of metric or measure for the extent of deviation from ideality. By comparing the RTD of the reaction vessel with the RTD of ideal reactors, one can get a qualitative idea about the gap or deviation between the real and the ideal reactors. However, one has to come up with an appropriate quantification of this gap in such a manner that this quantification will be useful for predicting the conversion achievable in the reactor. A general approach for quantification of non-ideality is to propose a mathematical model for characterising the non-ideality and make an estimate of model parameters using the RTD obtained from the tracer experiment. The estimated values of the model parameters are taken as a quantification of non-ideality. Some of the non-ideal reactor models are presented in the following sections. 3.2.4 Tanks in Series Model In an ideal CSTR, complete mixing of fluid results in uniform concentration of chemical species in the reaction vessel. In an ideal PFR, there is complete mixing of fluid in the radial direction and no mixing of fluid in the axial direction, resulting in the concentration of chemical species varying only in the axial direction and not in the radial direction. Imagine that an ideal PFR is being sliced into an infinite number of thin strips along the axial direction. The concentration of chemical species in each one of these thin strips is uniform as there is complete mixing of fluid in the radial direction. So, each one of these strips can be treated as an ideal CSTR of infinitesimally small volume. Thus, an ideal PFR is equivalent to infinite numbers of infinitesimally small ideal CSTRs connected in series. This result leads to an interesting concept that a non-ideal reaction vessel of given volume may be considered as equivalent to N numbers of ideal CSTRs each one of volume V/N connected in series. Such a representation of a non-ideal reactor is known as tanks in series model in which the word tank denotes an ideal CSTR. In this model, N takes the value of 1 for an ideal CSTR and ∞ for an ideal PFR. Thus, N is the parameter of tanks in series model, which takes a value between 1 and infinity for any real reactor. A schematic representation of tanks in series model is shown in Figure 3.55. Consider a non-ideal reaction vessel of volume V through which inert fluid flows at a volumetric flow rate q. The mean residence time θ is θ=
V q
www.Ebook777.com
(3.277)
Free ebooks ==> www.ebook777.com 211
Homogeneous Reactors
q
q
V
C0
Non-ideal reactor
C(θ)
Equivalent to
C1
q C0
v1
C1
1
C2
Ci–1
Ci
v2
C2
vi′
Ci
2
CN–1
i
vN
CN
q CN
N
Figure 3.55 Schematic representation of N tanks in series model.
Assume that a step tracer test is conducted on the reaction vessel. C0 is the inlet concentration of tracer at time θ = 0 and C(θ) is the outlet tracer concentration at time θ. According to tanks in series model, this non-ideal reaction vessel is treated as N equal-volume ideal CSTRs connected in series (Figure 3.55). The residence time of fluid in each one of the CSTRs is
(V/N ) = θ θ = q N
(3.278)
C1,C2,…,CN are the tracer concentrations in N ideal CSTRs. The outlet tracer concentration of the Nth ideal CSTR is the effluent tracer concentration of the non-ideal reactor.
C(θ) = CN (θ)
(3.279)
Taking the unsteady-state tracer balance in the ith CSTR, we get
V dCi (θ) qCi −1(θ) = qCi (θ) + N dθ
(3.280)
Dividing all the terms in the above equation by q, we get
dC (θ) Ci −1(θ) = Ci + θ i dθ
www.Ebook777.com
(3.281)
Free ebooks ==> www.ebook777.com 212
Green Chemical Engineering
Writing the equation in the form of standard first-order differential equation [(dy/dx) + P(x)y = Q(x)], we have
1 dCi (θ) 1 dθ + θ Ci (θ) = θ Ci −1(θ)
(3.282)
The solution to the above equation is
d 1 [Ci (θ)I ⋅ F] = Ci −1(θ)I ⋅ F dθ θ
(3.283)
where the integration factor I ⋅ F is 1
I⋅F = e
∫ θ dθ
θ
(3.284)
= e θ
Substituting Equation 3.284 in Equation 3.283 and integrating Equation 3.283, we get θ
θ
1 Ci (θ)e θ = Ci −1(θ) ⋅ e θ dθ + I θ
∫
(3.285)
where I is the integration constant. CN(θ) is calculated by solving Equation 3.285 recursively taking i = 1, 2, 3,…, N. Taking i = 1 and solving Equation 3.285, we get
θ θ C C1(θ)e θ = 0 θ e θ + I θ
C1(θ) = C0 + Ie
−
θ θ
(3.286) (3.287)
Substituting C1(θ) = 0 at θ = 0 in the above equation, we set the integration constant I = −C0 and the equation for C1(θ) is
θ − C1(θ) = C0 1 − e θ
(3.288)
Taking i = 2 and substituting Equation 3.288 in Equation 3.285, we get θ
θ
θ
1 C2 (θ)e θ = C1(θ) e θ dθ − C0 θ C C2 (θ)e θ = 0 θ
∫
∫
θ θ θ e θ dθ − C − 1 e 0
(3.289)
(3.290)
www.Ebook777.com
Free ebooks ==> www.ebook777.com 213
Homogeneous Reactors
θ θ e θ − θ − C0
(3.291)
θ θ − C2 (θ) = C0 1 − 1 + e θ θ
(3.292)
θ
C C2 (θ)e θ = 0 θ
Rearranging the above equation, we get
Similarly, taking i = 3 and substituting Equation 3.292 in Equation 3.285, we get the equation for C3(θ) as 2 θ θ 1 θ − C3 (θ) = C0 1 − 1 + + e θ θ 2! θ
(3.293)
Continuing these calculations by taking i = 4, 5,… up to N, we get the equation for CN(θ) as 2 N −1 θ θ 1 θ 1 θ − θ CN (θ) = C0 1 − 1 + + + + e θ 2! θ ( N − 1) ! θ
(3.294)
By definition, the RTD function F(θ) is C(θ) CN (θ) F(θ) = = C0 step C0
(3.295)
And so
2 N −1 θ θ 1 θ 1 θ − θ F(θ) = 1 − 1 + + + + e θ 2! θ ( N − 1) ! θ
(3.296)
The exit age distribution E(θ) is calculated from F(θ) by taking the derivative of F(θ) with respect to θ as E(θ) = (dF(θ)/dθ). Thus, we get the equation for E(θ) as
E(θ) =
1 θ ( N − 1)! θ
N −1
.
e −(θ/θ ) θ
(3.297)
Substituting θ = θ/N in Equation 3.297, we get the final equation for E(θ) as
E(θ) =
N Nθ ( N − 1)! θ
N −1
.
e − ( N θ/ θ ) θ
(3.298)
It may be verified that Equation 3.298 for N = 1 reduces to E(θ) = e −(θ/θ )/θ , which is the exit age distribution equation for an ideal CSTR. The E(θ) versus θ plots for different
www.Ebook777.com
Free ebooks ==> www.ebook777.com 214
Green Chemical Engineering
3 2.5
n=1 n=5 n = 10 n = 20 n = 50
n = 50
2 n = 20
E 1.5 1 n=
n = 10 1
n=5
0.5 0
0
1
2
θ
3
4
5
Figure 3.56 E(θ) versus θ plots for different values of N tanks in series model.
values of N greater than 1 are shown in Figure 3.56. (This plot is generated by running the MATLAB program e_curve_tismodel.m.) It may be seen that the E(θ) versus θ plots shifts away from the ideal CSTR plot and moves towards the ideal PFR plot as the value of N increases. Given a plot of E(θ) versus θ obtained from the tracer experiment (see Figure 3.56) performed on a reaction vessel, this experimental plot can be matched with the theoretical plot of E(θ) versus θ obtained using Equation 3.298 for some value of N. This value of model parameter ‘N’ may be taken as a measure of non-ideality in the real reactor. Ideal PFR and ideal CSTR represent two extreme limits of interage fluid mixing. Interage fluid mixing is defined as the mixing between fluid elements of different ages in a vessel. In an ideal PFR, there is complete mixing (radial direction) of fluid elements of the same age but no two fluid elements of different ages mix with each other (no axial mixing). Thus, there is no interage fluid mixing in an ideal PFR, whereas, in an ideal CSTR, there is thorough mixing of fluid elements of all ages. Thus, in an interage fluid mixing scale (Figure 3.57), ideal PFR and ideal CSTR correspond to zero mixing and infinite mixing, respectively. In a non-ideal reactor, the extent of interage fluid mixing varies between 0 and ∞. Thus, the value of model parameter N can also be taken as a measure of interage fluid mixing in the non-ideal reactor.
N=α zero mixing
Ideal PFR
1 www.ebook777.com 216
Green Chemical Engineering
Repeating the integration step, we get ∞
∫θ e N
−
Nθ θ
0
∞
∫θ
N −1
e
−
Nθ θ
0
∞
Nθ − θ dθ = N θ N −1e θ dθ N
∫ 0
∞
Nθ − θ dθ = ( N − 1) θ N − 2e θ dθ and so on N
∫ 0
(3.304)
Combining Equations 3.303 and 3.304, we get ∞
∫
θ
N +1
e
−
Nθ θ
0
θ dθ = ( N + 1) ! N
N +1 ∞
∫
e
−
Nθ θ
dθ
(3.305)
0
and finally, ∞
∫θ
N +1
0
e
−
Nθ θ
θ dθ = ( N + 1)! N
N+2
(3.306)
Substituting Equation 3.306 in Equation 3.302, we get 2
( N + 1)! θ − ( θ )2 σ = ( N − 1)! N
(3.307)
2
and finally Equation 3.307 is reduced to the form
σ2 1 = 2 θ N
(3.308)
Using this Equation 3.308 and the values of mean and variance calculated from the E-curve data, the value of model parameter N is estimated for the given reaction vessel. It may be seen from Equation 3.308 that the variance (σ2 = 0) is minimum for an ideal PFR (N = ∞) and is maximum (σ 2 = θ 2 ) for an ideal CSTR (N = 1). Although N is defined as a whole number, that is, integer, it can also take a fractional value. 3.2.4.2 Conversion according to Tanks in Series Model The main purpose of understanding the fluid mixing pattern in a reaction vessel is to use this knowledge for evaluating the performance of the reactor in terms of the conversion achieved in the reactor. Assume that an irreversible reaction A → B is carried out in a reaction vessel of volume V. Let q be the volumetric fluid rate, CA0 the feed concentration of A, (− rA ) = kCAn is the kinetic rate equation and CAf the effluent concentration of A. According to the tanks in series model, the reactor is represented by N equal volume ideal CSTRs connected in series (Figure 3.59).
www.Ebook777.com
Free ebooks ==> www.ebook777.com 217
Homogeneous Reactors
q
q
V Non-ideal reactor
CA0
CAf
Equivalent to q CA0
CA1 v N
CA1
1
CA2
CAi–1
v N
CA2
CAi v N
CAi
2
CAN–1
i
q
CAN
v N
CN
N
Figure 3.59 Reaction in a non-ideal reactor represented by tank in series model.
Taking the steady-state balance of reactant A for the ith CSTR, we get
qCAi −1 = qCAi + (− rA (C Ai ))V/N
(3.309)
Writing Equation 3.309 in terms of space time τ = V/q,
n kτ CAi −1 = CAi + CAi N
(3.310)
Equation 3.310 for i = 1,2,3,… up to N is written as
kτ CA 0 = C A1 + C An1 N
kτ CA1 = C A 2 + C An 2 N
kτ n CAN −1 = CAN + CAN N
(3.311)
Starting with the value of CA0, Equations 3.311 can be solved recursively to calculate CA1, CA2,…, CAN. The fractional conversion of A in the reactors xAf is
x Af = 1 −
C Af C = 1 − AN CA0 CA0
www.Ebook777.com
(3.312)
Free ebooks ==> www.ebook777.com 218
Green Chemical Engineering
In this equation, the numbers of ideal CSTRs, N is the parameter of the tanks in series model. This parameter N is estimated using the E-curve, obtained from the tracer experiment conducted on the reaction vessel. As a special case, consider a first-order reaction (n = 1). Substituting n = 1 in Equation 3.311 and solving the equation recursively for i = 1, 2, 3,…, n, we get CAN =
CA0 (1 + (k τ/N ))N
(3.313)
And the fractional conversion xAf is x Af = 1 −
1 (1 + (k τ/N ))N
(3.314)
For an ideal CSTR, Equation 3.314 for N = 1 reduces to x Af =
kτ 1 + kτ
(3.315)
And for an ideal PFR, Equation 3.314 for N = ∞ is x Af = 1 − e − k τ
(3.316)
As
kτ lim 1 + N →∞ N
N
= ek τ
Equations 3.315 and 3.316 define the lower and upper limits, respectively, on the fractional conversion xAf achievable in a non-ideal reactor represented by tanks in series model, that is, the fractional conversion for a first-order reaction in a non-ideal reactor represented by tanks in series model is always higher than the conversion in an ideal CSTR, and lower than the conversion in an ideal PFR with space time τ being the same in all the reactors. Consider a second-order reaction (n = 2). Substituting n = 2 in Equation 3.310, we get a quadratic equation
kτ 2 C Ai + C Ai − C Ai −1 = 0 N
Solving this quadratic equation recursively for i = 1, 2, 3,…, n, we get
C A1 =
−1 + 1 + ( 4k τC A 0 /N ) (2k τ/N )
CA 2 =
−1 + 1 + ( 4k τCA1/N ) (2k τ/N )
www.Ebook777.com
(3.317)
Free ebooks ==> www.ebook777.com 219
Homogeneous Reactors
CAN =
−1 + 1 + ( 4k τC AN −1/N ) (2k τ/N )
(3.318)
And the final conversion xAf is x Af = 1 −
CAN CA0
(3.319)
3.2.5 Axial Dispersion Model In an ideal PFR, fluid elements do not mix in the axial direction (i.e. flow direction). However, in an actual tubular reactor, some amount of axial mixing of fluid elements may occur due to a number of reasons (such as vortex formation at tube inlet). A mathematical model called axial dispersion model was proposed by P. V. Danckwarts to account for axial mixing of fluid elements in the tubular (plug flow) reactor. Dispersion of tracer material through a PFR with axial mixing as compared to the tracer dispersion through an ideal PFR is shown in Figure 3.60. In a PFR with axial mixing of fluid elements, the tracer material injected (as an impulse input) at the reactor inlet spreads in the axial direction while it is being drifted in the flow direction by the bulk flow of the (a) C (θ)
C (θ) θ1
– θ
θ3
θ2 θ
q
θ
q
(b) C (θ)
C (θ) θ1
q
θ2
θ
θ3
θ q
Figure 3.60 (a) Dispersion of tracer in ideal PFR, (b) dispersion of tracer in PFR with axial mixing.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 220
Green Chemical Engineering
fluid. Whereas in an ideal PFR, the tracer material, while it is being carried along by the bulk fluid moving at velocity ū, does not spread in the axial direction. In a PFR with axial mixing characteristics, the gradual spreading (dispersion) of the tracer material in the axial direction after a time lapse of θ1, θ2 and θ3 (θ3 > θ2 > θ1) from the time of injection of tracer is depicted in Figure 3.60. The dispersion flux of the tracer material J (kmol/m2s) is written as J = −D
dC dz
(3.320)
where dC/dz is the tracer concentration gradient and D is the dispersion coefficient expressed in the unit m2/s. D = 0 for an ideal PFR as there is no mixing (dispersion) of fluid in the axial direction and D = ∞ for an ideal CSTR as there is complete mixing of the fluid in all the directions (i.e. both in the axial and radial directions). For a non-ideal PFR with axial mixing, D assumes a finite value greater than zero. Consider a tubular reaction vessel (Figure 3.61) of length L and cross-sectional area A. q is the volumetric flow rate of the fluid flowing through the vessel. u = q/A is the mean velocity of the fluid. θ = L/u is the mean residence time of the fluid. Tracer test is conducted on the vessel by injecting the tracer material into the fluid at inlet. C(Z, θ) is the concentration of the tracer in the fluid at a distance Z from the inlet and at the time θ after the time of injection of tracer. Taking an unsteady-state tracer balance around the vessel section of thickness ΔZ at a distance Z from the inlet, we get Rate of flow of tracer by bulk flow Rate of flow of tracer by bulk flow = + + rate of dispersion of tracer At Z rate of dispersion of tracer At Z + ∆Z + {rate of accumulation of tracer in section ∆Z} (3.321)
{AuC(Z, θ) + AJ(Z, θ)}Z = {AuC(Z + ∆Z , θ) + AJ (Z + ∆Z , θ)}Z + ∆Z +
∂ ( A∆ZC(Z , θ)) ∂θ
Substituting Equation 3.320 for J in Equation 3.322,
q
q
q
A c(z + ∆z)
c(z)
z
∆z L
Figure 3.61 Non-ideal PFR with axial mixing.
www.Ebook777.com
q
(3.322)
Free ebooks ==> www.ebook777.com 221
Homogeneous Reactors
∂C ∂C ∂C AuC(Z , θ) − AD = AuC(Z + ∆Z , θ) − AD + A∆Z ∂Z Z ∂Z Z + ∆Z ∂θ
(3.323)
Cancelling the term ‘A’ in Equation 3.323
∂C ∂C ∂C uC(Z , θ) − D = uC(Z + ∆Z , θ) − D + ∆Z Z ∂ Z ∂θ ∂ Z Z + ∆Z
(3.324)
dividing all the terms in Equation 3.324 by ΔZ and taking limits as ΔZ → 0, we get
D
∂ 2C ∂C ∂C −u − =0 ∂z 2 ∂z ∂θ
(3.325)
by defining dimensionless distance from the inlet ʓ = Z/L and dimensionless time θ = θu/L = (θ/ θ ), Equation 3.325 is rewritten in terms of ʓ and θ as
2 D ∂ C u ∂C u ∂C − 2 2 − =0 L dB L ∂B L ∂θ
(3.326)
Dividing the above equation by (u/L), we get
2 D ∂ C ∂C ∂C − =0 2 − uL ∂B ∂B ∂θ
(3.327)
defining a dimensionless number called ‘Peclet number’ Pe Pe =
uL D
(3.328)
We rewrite the Equation 3.327 as
1 ∂ 2C ∂C ∂C − − =0 Pe ∂B 2 ∂B ∂θ
(3.329)
Equation 3.329 is the axial dispersion model equation and the Peclet number Pe is the model parameter. Pe = ∞ for an ideal PFR and Pe = 0 for an ideal CSTR. Pe is a finite value greater than 0 for any non-ideal PFR with axial mixing. The solution to the model Equation 3.329 depends on the boundary conditions defined at ʓ = 0 (vessel inlet) and ʓ = 1 (vessel outlet). The boundary (inlet or outlet) of a vessel is defined as closed if the dispersion (axial mixing) begins (at the inlet) or terminates (at the outlet) at the boundary and no dispersion occurs outside the boundary. On the contrary, a boundary is defined as open if the dispersion begins or terminates at a location outside the boundary. Thus, there are four possible boundary conditions, namely, open (inlet)–open (outlet), open (inlet)–closed (outlet), closed (inlet)–open (outlet) and closed (inlet)–closed (outlet). Of these four boundary conditions, the closed–closed boundary condition (called the Danckwarts’ boundary condition) is regarded as the most appropriate representation of the realistic condition. The Danckwarts’ closed–closed boundary condition is discussed here.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 222
Green Chemical Engineering
The boundary condition at the inlet (ʓ = 0) is derived by setting the values of Z = 0− (just outside the vessel inlet), Z + ΔZ = 0+ (just inside the vessel inlet) and ΔZ = 0 (thickness of the inlet boundary) in the balance Equation 3.324: dC dC = uC (0 + ) − D dZ 0− dZ 0+
uC(0 − ) − D
(3.330)
dC = 0 as there is no dispersion outside the dz 0− vessel inlet. The tracer concentration is C0 at the point of tracer injection, which is just outside the vessel inlet. So, C(0− ) = C0. Thus, Equation 3.330 reduces to The vessel inlet is a closed boundary. D
C0 = C( 0 + ) −
1 ∂C Pe ∂B B = 0+
(3.331)
Similarly, boundary conditions at the outlet (ʓ = 1) is derived by setting the values of Z = L− (just inside the vessel outlet), Z + ΔZ = L + (just outside the vessel outlet) and ΔZ = 0 (thickness of the outlet boundary) in the balance Equation 3.324. uC(L− ) − D
dC dC = uC(L+ ) − D dZ L− dZ L+
(3.332)
D(dC/dZ) L+ = 0 as the vessel outlet is a closed boundary and there is no dispersion outside the vessel outlet. Thus, Equation 3.332 reduces to uC(L− ) − D
dC = uC(L+ ) dZ L−
(3.333)
The concentration of tracer C(Z) has to be a continuous (or smooth) function of Z at the vessel outlet (Z = L) as there is nothing unusual at the vessel outlet (such as tracer addition and tracer removal) that could cause an abrupt change in tracer concentration. Thus, C(L−) = C(L +). This condition of continuity of C(Z) at Z = L reduces Equation 3.333 to
dC =0 dB B=1
(3.334)
Equations 3.331 and 3.334 define the Danckwarts’ closed–closed boundary conditions. If C(B , θ ) represents the solution to the Danckwarts’ model Equation 3.329 with the boundary conditions (3.331) and (3.334), then the RTD function for the axial dispersion model is
C (1, θ ) F(θ ) = C0
and
www.Ebook777.com
(3.335)
Free ebooks ==> www.ebook777.com 223
Homogeneous Reactors
E(θ)
Pe = 0 (ideal CSTR)
Pe = ∞ (ideal PFR)
Pe = 5 1 θ
Pe = 10 Pe = 30
θ
θ
Figure 3.62 E(θ) versus θ is a function of pellet number.
dF(θ ) E(θ ) = dθ
(3.336)
The plot of E(θ) versus θ as a function of the Peclet number Pe is shown in Figure 3.62. It can be seen that the plot of E(θ) versus θ shifts away from the ideal CSTR plot and moves towards the ideal PFR plot as Pe increases. Given a plot of E(θ) versus θ obtained from the tracer experiment, the value of the parameter Pe is estimated as the value for which the experimental plot fits well with the theoretical plot of E(θ) versus θ shown in Figure 3.62. But one cannot derive a theoretical expression for E(θ) as it is not possible to obtain an analytical solution to the model Equation 3.329 with Danckwarts’ boundary conditions (3.331) and (3.334). However, an explicit equation relating the variance σ2 and mean θ of the RTD to the Peclet number Pe has been derived using the method of moments without actually solving the model equation. This equation
σ2 2 2 = − (1 − e − Pe ) θ2 Pe Pe 2
(3.337)
is used for the estimation of Pe given the mean θ and variance σ2 of the RTD function E(θ) (E-curve obtained from tracer experiment). The derivation of Equation 3.337 is presented in Appendix B. 3.2.5.1 Conversion according to Axial Dispersion Model Consider a first-order irreversible reaction A k → B carried out in a non-ideal PFR with axial mixing (Figure 3.63). L is the length and A is the cross-sectional area of the tubular vessel. q is the volumetric fluid flow rate and u = q/A is the mean velocity of the fluid. CAO and CAf are the feed and the exit concentrations of A CA(Z) is the concentration of A in the fluid, at a distance Z from the inlet. (−rA) = kCA is the specific reaction rate, where k is the specific reaction rate constant.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 224
Green Chemical Engineering
CA0
q
q A
q
CA(z)
CA(z + ∆z)
CAf q
∆z
z L
Figure 3.63 Non-ideal PFR with axial mixing.
Taking a steady-state balance of A around the vessel section of thickness ΔZ positioned at a distance Z from inlet
Rate of bulk flow of A Rate of bulk flow of A = + Rate of dispersion of A At Z + Rate of dispersion of A At Z + ∆Z Rate of disappearance of A + due to reaction in section ∆Z
(3.338)
dCA (Z) dC A (Z) = AuCA (Z + ∆Z) − AD + A∆Z(kC A (Z)) (3.339) AuC A (Z) − AD dZ Z dZ Z + ∆Z Dividing Equation 3.338 by ΔZ and taking limit at ΔZ → 0, we get D
d 2CA dC − u A − kC A = 0 dZ 2 dZ
(3.340)
where D is the dispersion coefficient. Defining the dimensionless distance from the inlet ʓ as ʓ = (Z/L), space time τ = (L/u ) , we can rewrite Equation 3.340 as 1 d 2C A dC A − − (k τ)C A = 0 Pe dB 2 dB
(3.341)
where Pe = (D/uL) is the Peclet number and (C A = (CA /CA 0 )) is the dimensionless concentration of A. The Danckwarts’ boundary conditions are At ʓ = 0 (reactor inlet) 1 dC A (0+ ) C A (0 + ) − =1 Pe dB
(3.342)
and at ʓ = 1 (reactor outlet)
dC A dB
=0 B= 1
(3.343)
www.Ebook777.com
Free ebooks ==> www.ebook777.com 225
Homogeneous Reactors
The solution to the second-order differential Equation 3.340 is
C A (B) = A1e m1B + A2e m2 B
(3.344)
Pe(1 + α ) 2 Pe(1 − α ) m2 = 2
(3.345)
where m1 =
are the roots of the characteristic equation (1/Pe)m2 − m − kτ = 0 and α=
1+
4k τ Pe
(3.346)
The integration constant A1 and A2 are calculated using the boundary conditions (3.342) A dC and (3.343). Evaluating the derivative at ʓ = 0 and ʓ = 1, we have dζ dC A A Pe(1 + α ) A2Pe(1 − α ) = 1 + (3.347) dB B= 0 2 2 dC A dζ
= B= 1
Pe
Pe
A1Pe(1 + α ) 2 (1+ α) A2Pe(1 − α ) 2 (1− α) e e + 2 2
(3.348)
Substituting Equations 3.347 and 3.348 in the boundary conditions (3.342) and (3.343) and solving A1 and A2, we set
A1 =
2(1 − α )e −( Pe/2)α (1 − α )2 e −( Pe/2)α − (1 + α )2 e + ( Pe/2)α
(3.349)
A2 =
2(1 + α )e + ( Pe/2)α (1 − α ) e − (1 + α )2 e + ( Pe/2)α
(3.350)
2 − ( Pe /2 )α
The fractional conversion of A x Af is
x Af = 1 − C A (1)
(3.351)
and Pe
Pe
( 1+ α ) ( 1− α ) + A2e 2 C A (1) = A1e 2 Pe Pe Pe α α C A (1) = A1e 2 + A2e − 2 e 2
(3.352)
www.Ebook777.com
(3.353)
Free ebooks ==> www.ebook777.com 226
Green Chemical Engineering
Combining Equations 3.349, 3.350, 3.351 and 3.353, we get 4αe Pe/2
x Af = 1 − (1 + α )2 e
+
Pe α 2
− (1 − α )2 e
−
Pe α 2
(3.354)
The value of Pe estimated for the non-ideal PFR is used in the above equation to predict the conversion for a first-order reaction. Problem 3.15 Tracer tests are performed on two different reaction vessels. Responses of the impulse tests conducted on the two reactors are reported below: Time (θ) Reactor I Tracer concentration C(θ) g/l Reactor II Tracer concentration C(θ) g/l
0
1
2
3
4
5
6
7
0
1.3
4.0
5.0
4.5
3.5
2.5
0
0.4
1.3
2.4
3.8
5.1
5.5
8
9
10
11
12
13
14
1.7 1.1 0.5
0.2
0
0
0
0
4.5 3.1 1.9
1.1
0.5
0.2
0
0
a. Calculate the mean (θ ) and the variance (σ2).
b. Calculate the conversion of a first-order reaction with rate constant k = 0.421 min−1 achieved in the reaction vessels assuming that the tanks in series model hold good. c. What are the conversions in the reactors if the axial dispersion model is applicable?
a. Using the impulse response data reported in the problem, C-curve (C(θ) versus θ) is plotted for the two reactors (Figure P3.15).
Tracer concentration C(θ) (g/L)
6 5 4
Reactor I Reactor II
3 2 1 0
0
2
4
6 8 Time (min)
10
12
Figure P3.15 Response of impulse test.
www.Ebook777.com
14
Free ebooks ==> www.ebook777.com 227
Homogeneous Reactors
E(θ) is calculated using the equation E(θ) =
C(θ) ∞
∫ C(θ)dθ
0
and the mean θ and variance σ 2 are calculated using the equations ∞
θ=
∫ θE(θ)dθ 0
∞
2
σ =
∫ θ E(θ)dθ − θ 2
2
0
The integral terms appearing in these equations are calculated using the trapezoidal rule, given by the equation yN
∫ ydx =
y1
∆x ( y1 + y N ) + 2( y 2 + y 3 + y 4 + + y N −1 ) 2
where y1 , y 2 , … , y N are the values of y at x equal to x1 , x2 , … , x N and so on, and ∆x = x2 − x1 = x3 − x2 … . The calculation of integrals by numerical integration is illustrated in the table shown below: For Reactor I θ 0 1 2 3 4 5 6 7 8 9 10 11 Integral values
C(θ)
E(θ)
θ E(θ)
θ2E(θ)
0 1.3 4.0 5.0 4.5 3.5 2.5 1.7 1.1 0.5 0.2 0
0 0.0535 0.1646 0.2058 0.1852 0.1440 0.1029 0.0700 0.0453 0.0206 0.0082 0
0 0.0535 0.3292 0.6174 0.7408 0.7200 0.6174 0.4900 0.3624 0.1854 0.082 0
0 0.0535 0.6584 1.8522 2.9632 3.6000 3.7044 3.4300 2.8992 1.6686 0.8200 0
∞
∫ 0
∞
C(θ)dθ = 24.3
∫
∞
E(θ)dθ = 1.0
0
∫
∞
θE(θ)dθ = 4.198
0
∞
θ=
∫ θE(θ)dθ = 4.198 min 0
www.Ebook777.com
∫ θ E(θ)dθ = 21.65 2
0
Free ebooks ==> www.ebook777.com 228
Green Chemical Engineering
∞
2
σ =
∫ θ E(θ)dθ − θ 2
2
= 2.165 − ( 4.198)2 = 4.03
0
For Reactor II θ
C(θ)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 Integral values
0 0.4 1.3 2.4 3.8 5.1 5.5 4.5 3.1 1.9 1.1 0.5 0.2 0
0 0.0134 0.0436 0.0805 0.1275 0.1711 0.1846 0.1510 0.1040 0.0638 0.0369 0.0168 0.0067 0
∞
∫
θ E(θ)
θ2E(θ)
0 0.0134 0.0872 0.02415 0.5100 0.8555 1.1076 1.057 0.8320 0.5742 0.3690 0.1848 0.0804 0
0 0.0134 0.1744 0.7245 2.0400 4.2775 6.6456 7.3990 6.6560 5.1678 3.6900 2.0328 0.9648 0
E(θ)
∞
∫
C(θ)dθ = 29.8
0
∞
E(θ)dθ = 1.0
0
∫
∞
θE(θ)dθ = 5.913
0
∞
θ=
∫ θE(θ)dθ = 5.913 min 0
∞
σ2 =
∫ θ E(θ)dθ − θ 2
2
= 39.79 − (5.913)2 = 4.83
0
b. Tanks in series model holds good, so 1 σ2 = 2 θ N
For Reactor I,
N =
θ2 ( 4.198)2 = = 4.37 σ2 4.03
N =
θ2 (5.913)2 = = 7.24 2 σ 4.83
For Reactor II,
www.Ebook777.com
∫ θ E(θ)dθ = 39.79 2
0
Free ebooks ==> www.ebook777.com 229
Homogeneous Reactors
For the first-order reaction with reaction rate constant k, conversion x Af is x Af = 1 −
1 (1 − k τ/N )N
and space time τ = θ. For Reactor I, x Af = 1 −
1 = 0.773 (1 − (0.421 × 4.198)/4.37 )4.37 x Af = 77.3%
Note that for ideal CSTR, x Af =
kτ 0.421 × 4.198 = = 63.8% 1 + k τ 1 + (0.421 × 4.198)
For ideal PFR, x Af = 1 − e − k τ = 82.92%
So, conversion in the non-ideal reactor lies between the conversion in an ideal CSTR and the conversion in an ideal PFR. For Reactor II, x Af = 1 −
1 = 88.23% (1 − (0.421 × 5.913)/7.24)7.24
Compare this with the conversion for ideal CSTR, x Af =
kτ 0.421 × 5.913 = = 71.3% 1 + k τ 1 + (0.421 × 5.913)
and in an ideal PFR, x Af = 1 − e − k τ = 91.7%
c. Axial dispersion model holds good, So σ2 2 2 = − 2 1 − e − Pe 2 θ Pe Pe
(
)
For Reactor I,
σ2 4.03 = = 0.2287 θ2 ( 4.198)2
www.Ebook777.com
Free ebooks ==> www.ebook777.com 230
Green Chemical Engineering
By a trial-and-error method, we calculate the Peclet number value as Pe = 7.6
For Reactor II,
σ2 4.83 = = 0.1381 θ2 (5.913)2
By a trial-and-error method, we calculate the Peclet number value as Pe = 13.40
For the first-order reaction with reaction rate constant k, the conversion is x Af = 1 −
((1 + α) e
4αe( Pe/2)
2 ( Pe/2 )α
− (1 − α )2 e( − Pe/2)α
)
where α=
1+
4k τ Pe
and τ = θ
For Reactor I,
kτ = (0.421)( 4.198) = 1.767
α=
1+
4 × 1.767 = 1.389 7.6
and x Af = 77.8%. For Reactor II,
kτ = (0.421)(5.913) = 2.489
α=
1+
4 × 2.489 = 1.320 13.4
and x Af = 88.5%. It may be noted that both tanks in series model and axial dispersion model predict the same conversion values. Note: Refer MATLAB program: non_id_conversion.m
www.Ebook777.com
Free ebooks ==> www.ebook777.com 231
Homogeneous Reactors
3.2.6 Laminar Flow Reactor A tubular reactor in which the fluid flow is laminar is regarded as a non-ideal reactor, as discussed in Section 3.2.2. Laminar flow is the flow pattern in which the fluid elements move in streamlines in an orderly manner and no two fluid elements moving in two different streamlines mix with each other. Thus, the fluid elements mix neither in the axial direction nor in the radial direction. This pattern of fluid flow is called ‘fully segregated flow’. Laminar flow of fluid in a tubular vessel is depicted in Figure 3.64. All fluid elements flowing in a streamline at a radial distance r move at an axial velocity u(r) 2 r u(r ) = u* 1 − R
(3.355)
where u* is the maximum stream velocity, which is the velocity of the fluid moving at the central axis (r = 0) and R is the tube radius. θ(r) is the residence time of the fluid element moving in a streamline at radial distance r θ(r ) =
L L = u(r ) u* (1 − (r/R)2 )
(3.356)
As the maximum stream velocity u* is twice the average velocity u for laminar flow, u = 2u , we have ∗
θ(r ) =
θ 2(1 − (r/R)2 )
(3.357)
Equation 3.37 shows that the residence time of fluid elements is spatially distributed (in the radial direction) with the fluid elements moving in the central axis (r = 0) having the minimum residence time of θ/2. Fluid flowing through a radial section bound between r Parabolic velocity profile u(r) = u* 1 –
r R
Fluid stream lines q
q
L Figure 3.64 Fluid stream lines in a laminar flow reactor.
www.Ebook777.com
2
Free ebooks ==> www.ebook777.com 232
Green Chemical Engineering
and r + dr has a residence time in the vessel varying between θ and θ + dθ. The volumetric flow rate of the fluid dq flowing through this radial section is dq = u(r )(2πr )dr
(3.358)
Dividing dq by the total volumetric flow rate q = (π R 2 )u, we get the fraction of the fluid elements whose residence time is between θ and θ + dθ, which is by definition E(θ)dθ. dq u(r )(2πr )dr = E(θ)dθ = q u(πR2 )
(3.359)
that is, E(θ)dθ =
2u(r )rdr uR2
(3.360)
Combining Equations 3.355 and 3.357, we get 2
u(r ) r θ = 1 − = 2u R 2θ
(
Taking derivatives on both sides of the equation 1 − ( r/R)
(3.361)
2
) = θ/2θ , we get
2 θ r d 1 − = d R 2θ
(3.362)
2rdr θdθ = R2 2θ 2
(3.363)
that is
Substituting Equations 3.363 and 3.361 in Equation 3.360, we get an expression for E(θ) as
E(θ) =
( θ )2 2θ 3
(3.364)
This equation holds good only for θ ≥ (θ/2) as no fluid element entering the vessel comes out before a time θ = (θ/2) . Thus,
0 E(θ) = 2 θ 2θ 3
θ 2 θ θ≥ 2
θ<
www.Ebook777.com
(3.365)
Free ebooks ==> www.ebook777.com 233
Homogeneous Reactors
Laminar flow reactor 4 θ
Ideal PFR
E(θ) Ideal CSTR 1 θ
θ 2
θ
θ
Figure 3.65 RTD plot for laminar flow reactor.
At θ =
4 θ , E(θ) = 2 θ
A plot of E(θ) versus θ for the laminar flow reactor is shown in Figure 3.65. 3.2.6.1 Conversion in Laminar Flow Reactor The flow pattern in the laminar flow reactor is called ‘fully segregated flow’ as the fluid elements do not mix either in the axial direction or in the radial direction. We can think of a fluid element as a cluster or a group of fluid molecules moving together from the inlet to the exit of the reaction vessel. There is thorough mixing of fluid molecules within each cluster, leading to the conversion of reactants to products. However, a molecule in one cluster does not mix with a molecule in another cluster in a mixing pattern, which is completely segregated. Segregated flow of fluid elements along a streamline in a laminar flow reactor is depicted in Figure 3.66.
CA0
CAf
L Figure 3.66 Segregated flow in a laminar flow model.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 234
Green Chemical Engineering
Each one of the fluid elements, which is a completely segregated cluster of fluid molecules, can be treated as a micro-batch reactor. The residence time θ of a fluid element is taken as the batch reaction time to determine the conversion achieved in the fluid element. Consider a first-order reaction A k → B carried out in the laminar flow reactor. (− rA ) = kCA is the kinetic rate equation. The rate of change of reactant concentration CA in a single fluid element (treated as a batch reactor) is given by dCA = − kC A dt
(3.366)
Integrating this equation from time t = 0 to t = θ (θ is the residence time of the fluid element), as the concentration CA of A in the fluid element changes from inlet feed concentration CA0 to exit concentration CAb θ
CAb
dCA = − kdt CA
∫
∫ 0
CA0
(3.367)
We get CAb = e − kθ CAO
(3.368)
The fractional conversion xAb(θ) achieved in the fluid element having a residence time of θ in the reaction vessel is
x Ab (θ) = 1 −
CAb = 1 − e − kθ CAO
(3.369)
Thus, the fractional conversion achieved in a fluid element is a function of residence time θ of the fluid element in the reaction vessel. Given the RTD E(θ), the average value of conversion achieved in all the fluid elements leaving the reaction vessel at any time is calculated and it is taken as the final conversion xAf. Thus ∞
∫
x Af = x Ab (θ)E(θ)dθ
0
(3.370)
This equation is a general equation for the calculation of conversion in any segregated flow reactor. For a laminar flow reactor, that is modelled as a segregated flow reactor, we get an equation for xAf by substituting Equations 3.369 and 3.365 in 3.370: ∞
x Af =
∫
θ /2
( θ )2 (1 − e − kθ ) 3 dθ 2θ
(3.371)
www.Ebook777.com
Free ebooks ==> www.ebook777.com 235
Homogeneous Reactors
that is, x Af
( θ )2 = 1− 2
∞
∫
θ /2
e − kθ dθ θ3
(3.372)
Similarly, for a second-order reaction, the fractional conversion xAb(θ) achieved in the single fluid element is obtained by integrating dC A /dt = − kC A between t = 0 and t = θ. x Ab (θ) =
kC A 0θ 1 + kC A 0θ
(3.373)
Substituting Equations 3.365 and 3.373 in Equation 3.370, we get an expression for conversion xAf in a laminar flow reactor for a second-order reaction: ∞
x Af =
∫
θ/2
kC A 0θ (θ )2 1 + kC θ 2θ 3 dθ A0
(3.374)
which reduces to x Af
kC A 0 θ 2 = 2
∞
dθ
∫ θ (1 + kC 2
θ /2
A0
θ)
(3.375)
Problem 3.16 A first-order reaction with rate constant k = 0.15 min−1 is to be carried out in a tubular flow reactor. A conversion of 80% of reactant was predicted, assuming ideal plug flow condition in the reactor. However, on calculating the Reynolds number, it was found that the flow was laminar. What is the conversion expected in the reactor? For a first-order reaction with rate constant k, the conversion in the ideal PFR is x Af = 1 − e − k τ
and τ =
1 1 ln k 1 − x Af
For k = 0.15 and x Af = 0.8
Space time = τ =
1 1 ln = 10.73 min 0.15 1 − 0.8
For the tubular reactor mean residence time θ = τ = 10.73 . The conversion of a first-order reaction in a laminar flow reactor is x Af
θ2 = 1− 2
∞
∫
θ/2
e − kθ θ 3 dθ
www.Ebook777.com
Free ebooks ==> www.ebook777.com 236
Green Chemical Engineering
The integral term in this equation is calculated numerically, using trapezoidal rule. This calculation is shown in the below table:
θ θ = 5.365 2 5.765 6.165 6.565 6.965 7.365 7.765 8.165 8.565 8.965 9.365 9.765 10.165 10.565 10.965 11.365 11.765 12.165 12.565 12.965 13.365 13.765 14.165 14.565 14.965 15.365 15.765 16.165
Using trapezoidal calculate ∞
∫
θ /2
rule,
0.4472
2.898
0.4212 0.3966 0.3735 0.3518 0.3313 0.3120 0.2938 0.2767 0.2606 0.2454 0.2311 0.2176 0.2050 0.1931 0.1818 0.1712 0.1613 0.1519 0.1430 0.1347 0.1268 0.1195 0.1125 0.1059 0.0998 0.0940 0.0885
2.198 1.693 1.320 1.041 0.829 0.666 0.539 0.440 0.322 0.299 0.248 0.207 0.174 0.146 0.124 0.105 0.0896 0.0766 0.0656 0.0564 0.0486 0.0420 0.0364 0.0316 0.0275 0.0240 0.0210
∆x ( y1 + y N ) + 2( y 2 + y 3 + y 4 + + y N −1 ) , 2
e − kθ 0.4 −3 θ 3 dθ = 2 [(2.898 + 0.0210) + 2(2.198 + 1.693 + 1.320 + + 0.0240)] × 10 ∞
∫ yy1N ydx =
e − kθ
e − kθ −3 θ 3 × 10
∫
θ /2
e − kθ −3 θ 3 dθ = (0.2)(10 ) [(2.919) + 2(10.849)]
www.Ebook777.com
we
Free ebooks ==> www.ebook777.com 237
Homogeneous Reactors
∞
∫
θ /2
e − kθ −3 θ 3 dθ = 4.924 × 10
Substituting the value of the integral term in the equation for the calculation of conversion x Af , we get x Af = 1 −
(10.73)2
( 4.924 × 10 ) −3
2
x Af = 71.65%
Thus, the conversion in the laminar flow reactor is lower than the conversion (80%) in the ideal PFR of the same size. Note: Refer MATLAB program: non_id_conversion.m 3.2.7 Non-Ideal CSTR with Dead Zone and Bypass Non-ideal features such as dead zone and bypass seen in a CSTR occur as a result of improper fluid mixing in the reaction vessel. A typical E-curve for a non-ideal CSTR with dead zone and bypass is shown in Figure 3.67. The tracer material trapped in the dead zone of a CSTR is released slowly into the effluent stream and this is seen as a long tail in the E-curve. The tracer material, drawn into the bypass stream, short-circuits the active volume and appears in the effluent stream within a short span of time. This is seen as an extended peak near t = 0 in the E-curve. A mathematical model that accounts for both dead zone and bypass in a CSTR is presented in this section. Consider a CSTR of volume V through which a fluid flows at volumetric rate q. Out of Extended peak due to bypass E(θ)
1 θ
Ideal CSTR
Non-ideal CSTR Long tail due to dead zone
θ Figure 3.67 E-curve for a non-ideal CSTR with dead zone and bypass.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 238
Green Chemical Engineering
qb
C0
C0
C0 q
qa
Ca Va qa
Ca(θ)
C(θ) q
Vd
Figure 3.68 Schematic diagram of non-ideal CSTR with bypass and dead zone.
the total volume V, dead zone occupies a volume Vd and the remaining volume Va = V − Vd is the actual active volume in which a complete mixing of fluid occurs. Of the total fluid q flowing through the CSTR per unit time, only qa passes through the active volume and qb = q − qa bypasses/short-circuits the active volume. A schematic representation of a CSTR with dead zone and bypass is shown in Figure 3.68. Define β as the fraction of the total volume V occupied by the active zone
Va = βV (3.376) And γ as the fraction of the total fluid rate q that flows through the active zone
qa = γq (3.377)
β and γ are the model parameters. For an ideal CSTR, β = 1 and γ = 1. For any non-ideal CSTR with dead zone and bypass, β and γ assume values less than 1. Thus, (1 − β) and (1 − γ) are measures of dead zone and bypass in the non-ideal CSTR. The reaction vessel is subjected to a tracer test to obtain the RTD F(θ) or E(θ), which is further used for the estimation of model parameters. Assume that a step test is conducted and C0 is the feed tracer concentration, C(θ) is the effluent tracer concentration and Ca(θ) is the tracer concentration in the active volume. Tracer concentration in the bypass stream is the same as the feed concentration C0. Taking an unsteady-state tracer balance around the active volume, we get dC (θ) qaC0 = qaCa (θ) + Va a dθ
(3.378)
Dividing by qa, we get C0 = Ca (θ) +
Va qa
dCa (θ) dθ
www.Ebook777.com
(3.379)
Free ebooks ==> www.ebook777.com 239
Homogeneous Reactors
By definition
Va βV β = = θ qa γq γ
(3.380)
where θ is the mean residence time. Solving the first-order differential Equation 3.378, we get
− γθ Ca (θ) = C0 1 − e βθ
(3.381)
Taking a steady-state solute balance at the outlet junction point, we have
q C(θ) = qaCa (θ) + qbCo
(3.382)
Substituting Equation 3.380 in Equation 3.381 and dividing by qCo, we get
− γθ C(θ) = γ 1 − e βθ + (1 − γ ) C0
(3.383)
We obtain an expression for F(θ) by rearranging Equation 3.383
F(θ) = 1 − γe
− γθ βθ
(3.384)
We get E(θ) by differentiating F(θ) with respect to θ: − γθ
γ2 E(θ) = e βθ βθ
(3.385)
Taking logarithm on both sides of the equation, we get
γ2 γ ln(E(θ)) = ln − θ βθ βθ
(3.386)
Thus, a plot of ln(E(θ)) versus θ is a straight line with slope, s = −γ /βθ and intercept, I = ln( γ 2 /βθ ) (Figure 3.69). Values of the model parameters β and γ are estimated by making a plot of ln(E(θ)) versus θ, and measuring the slope s = (− γ /βθ) and intercept I = ln( γ 2 /βθ) of the straight line plot. 3.2.7.1 Conversion according to Non-Ideal CSTR with Dead Zone and Bypass Consider a first-order reaction A k → B carried out in non-ideal CSTR with dead zone and bypass (Figure 3.70). (−rA) = kCA is the kinetic rate equation. CA0 and CAf are the concentrations of A in the feed and the effluent streams. CAa is the concentration of A in the active
www.Ebook777.com
Free ebooks ==> www.ebook777.com 240
Green Chemical Engineering
Intercept = γ2 ln βθ
Slope = –
γ βθ
ln[E(θ)]
θ Figure 3.69 Plot of ln(E(θ)) versus θ for a non-ideal CSTR with dead zone and bypass.
volume. The concentration of A in the bypass stream is the same as the feed concentration CAo. The active volume is treated as an ideal CSTR. Taking a steady-state balance of reactant A around the active volume, we get
qaCA 0 = qaC Aa = Va (kCAa )
(3.387)
V CA 0 = C Aa + a kC Aa qa
(3.388)
Dividing by qa,
and Va βV β = = τ qa γq γ
(3.389)
CA0
CA0 q
qb qa
qa Va CAa
CAa
Vd
Figure 3.70 Reaction in a non-ideal CSTR with dead zone and bypass.
www.Ebook777.com
CAf q
Free ebooks ==> www.ebook777.com 241
Homogeneous Reactors
where τ =
V is the space time. Rearranging Equation 3.388, we get q CAa =
CA0 1 + (β/γ )k τ
(3.390)
Taking a steady-state balance of A at the outlet junction point, qCAf = qaCAa + qbCA 0
(3.391)
Substituting Equation 3.390 in Equation 3.391 and dividing by qCA0, we get
CAf γ = + (1 − γ ) CA0 1 + (β/γ )k τ
(3.392)
CAf βk τ = 1− CA0 1 + (β/γ )k τ
(3.393)
that is,
C The fractional conversion X Af = 1 − Af achieved in the non-ideal CSTR is CAO x Af =
βk τ 1 + (β/γ )k τ
(3.394)
The values of β and γ estimated using the RTD data (E-curve) are substituted in Equation 3.394 to calculate the fractional conversion X Af. Problem 3.17 An impulse tracer test is conducted on a CSTR. The response to impulse input is reported in the below table: Time θ (min)
0
0.05 0.1
Tracer Conc. C(θ) g/l
0
3.38 3.34 3.30
Time (θ) (min)
6
7.0
Tracer Conc. C(θ) g/l
0.91 0.71 0.54 0.42
8.0
0.2
9.0
0.3
0.4
0.5
3.20
3.13
10.0 0.32
12.0 0.25
0.8
1.0
2.0
3.0
4.0
5.0
3.05 3.0
2.74
2.61
2.0
1.54
1.20
14.0
18.0
20.0
22.0
24.0
26.0
16.0
0.15 0.09 0.052 0.031 0.02 0.01 0
Detect if CSTR has any ‘dead zone’ or ‘bypass’. If so, quantify them. If a first-order reaction with rate constant k = 0.64 min−1 is carried out in this reaction vessel, what is the expected conversion? What is the drop in the value of conversion compared to the conversion in an ideal CSTR?
www.Ebook777.com
Free ebooks ==> www.ebook777.com 242
Green Chemical Engineering
Using the tracer test data, reported in the problem, construct the below table: θ
C(θ)
0 0.05 0.1 0.2 0.3 0.4 0.5 0.8 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0 24.0 26.0 Integral values
0 3.38 3.34 3.30 3.20 3.13 3.05 3.0 2.74 2.61 2.0 1.54 1.20 0.91 0.71 0.54 0.42 0.32 0.25 0.15 0.09 0.052 0.031 0.02 0.01 0
θE(θ)
ln [E(θ)]
0 0.2112 0.2087 0.2062 0.20 0.1956 0.1906 0.1875 0.1712 0.1631 0.1250 0.0962 0.0750 0.0569 0.0444 0.0337 0.0262 0.020 0.0156 0.0094 0.0056 0.0032 0.0019 0.0012 0.0006 0
0 0.0106 0.0209 0.0412 0.060 0.0782 0.0953 0.1500 0.1712 0.3262 0.375 0.3848 0.375 0.3414 0.3108 0.2696 0.2358 0.200 0.1872 0.1316 0.0896 0.0576 0.0380 0.0264 0.0144 0
— −1.5549 −1.5668 −1.5788 −1.6096 −1.6317 −1.6576 −1.6741 −1.7648 −1.8134 −2.0796 −2.341 −2.5904 −2.8671 −3.1152 −3.3889 −3.6402 −3.9122 −4.159 −4.6699 −5.1807 −5.7293 −6.2465 −6.6848 −7.3779 — —
∞
∞
∫
E(θ)
C(θ)dθ = 16.0
∫
∞
E(θ)dθ = 1.0
0
0
∫ θE(θ)dθ = 4.20 0
Make a straight line plot of ln [ E(θ)] versus θ (Figure P3.17). From this plot, calculate slope
γ S = − = −0.2372 and intercept βθ γ2 I = ln = −1.4725 βθ
∞
Mean residence time θ =
∫ θE(θ)dθ = 4.2 min 0
www.Ebook777.com
Free ebooks ==> www.ebook777.com 243
Homogeneous Reactors
–1 –2
Slope = –0.23722 Intercept = –1.4725
ln(E)
–3 –4 –5 –6 –7 –8
0
5
10 15 Time (min)
20
25
Figure P3.17 Plot of ln [E(θ)] versus θ.
γ = 0.2372 βθ
γ2 βθ = 0.2294 Solving the above equation, we get
γ = 0.9668
β = 0.9715
Thus, dead zone accounts for (1 − β) = 0.0285 or 2.85% and bypass (1 – γ) = 0.0332 or 3.32%. The reaction rate constant k = 0.64 min−1. So, fractional conversion x Af is x Af =
βk τ = 1 + (β/γ ) k τ
(0.9715)(0.64)( 4.2) = 0.7054 or 70.54% 0.9715 (0.64)( 4.2) 1+ 0.9668
The conversion in ideal CSTR is
x Af =
kτ (0.64)( 4.2) = = 72.86% 1 + k τ 1 + (0.64)( 4.2)
Thus, there is a 2.32% drop in conversion compared to that of an ideal CSTR. Note: Refer MATLAB program: non_id_dead_bypass.m
www.Ebook777.com
Free ebooks ==> www.ebook777.com 244
Green Chemical Engineering
3.2.8 Micro-Mixing and Segregated Flow A question that arises while discussing about fluid mixing in a reactor vessel is ‘How intimate is the mixing of fluid elements?’ Does the mixing of fluid take place down to the molecular level? A situation in which fluid mixing takes place at the molecular level is called ‘complete micro-mixing’. Here the fluid element is a fluid molecule. On the other hand, if the fluid is assumed to be composed of discrete fluid elements, each one of which is a cluster of molecules moving together as an individual group from reactor inlet to the outlet, then the flow pattern is called ‘completely segregated flow’. In the completely segregated flow situation, a molecule in one fluid element does not mix with a molecule in another fluid element although there is an intimate mixing of fluid molecules within each one of the fluid elements. In a micro-mixing scale (see Figure 3.71), ‘complete micromixing’ and ‘completely segregated flow’ represent two extreme points. Between these two extremes, there are various levels of micro-mixing in which mixing of fluid takes place within a mixture of segregated fluid elements and individual fluid molecules present in different proportions. A parameter λ, which denotes the extent of micro-mixing, is assumed to vary between 0 (for completely segregated flow) and 1 (for complete micro-mixing). The level of micro-mixing in a reaction vessel will determine the conversion achievable in the reactor as it is the mixing of fluid elements at the molecular level that is responsible for the reaction between the molecules. The RTD, which is used for the analysis of fluid mixing pattern, does not provide any information about micro-mixing as the RTD analysis does not distinguish between a segregated fluid element and an individual fluid molecule. However, RTD information is useful in calculating the conversion in a segregated flow reactor with no micro-mixing. In the segregated flow model, the conversion in a fluid element is determined by the residence time θ of the fluid element in the reaction vessel. Here, the fluid element, which is completely segregated, is treated as a micro-batch reactor. X Ab(θ), the conversion in a batch reactor achieved in a batch reaction time of θ, is taken as the conversion in the fluid element having a residence time of θ in the reactor. For example,
Individual fluid molecule
Segregated fluid element
No micro-mixing
λ
Completely segregated flow λ=0
Complete micro-mixing λ=1
Extent of micro-mixing
Figure 3.71 Micro-mixing scale.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 245
Homogeneous Reactors
For a first-order reaction A k → B , with rate equation (−rA) = kCA,
x Ab (θ) = 1 − e − k (θ)
(3.395)
And for a second-order reaction A k → B , with rate equation (−rA) = kCA2,
kC A 0θ 1 + kC A 0θ
x Ab (θ) =
(3.396)
Given the RTD E(θ) for the reaction vessel obtained from the tracer test, the conversion in the segregated flow reactor X As is calculated as the average of conversions achieved in all the fluid elements leaving the reaction vessel at any particular time, that is ∞
x As =
∫x
Ab
(θ)E(θ)d(θ)
(3.397)
0
This equation is used for calculating conversion X As in a segregated flow reactor with no micro-mixing. If X Am is the conversion in a reactor assuming complete micro-mixing, X As is the conversion assuming completely segregated flow in the reactor and λ is the extent of micro-mixing in the reaction vessel, then the actual conversion X Af in the reactor can be written as
xAf = λxAm + (1 − λ )xAs
(3.398)
Problem 3.18 Calculate the conversion of a first-order reaction with rate constant k = 0.421 min−1 carried out in Reactor I of Problem 3.15 assuming that the reactor is a completely segregated flow reactor. The conversion of a reactant in a completely segregated flow reactor is calculated using the equation ∞
x
As
=
∫x
Ab
E(θ)dθ
0
For a first-order reaction, the equation for conversion in a batch reactor is
(
x Ab = 1 − e − kθ
)
Using E(θ) versus θ data for Reactor I (Problem 3.15), conversion is calculated by numerical integration illustrated in the below table:
www.Ebook777.com
Free ebooks ==> www.ebook777.com 246
Green Chemical Engineering
θ
E(θ)
1
0.0535
0.3436
0.0184
2
0.1646
0.5691
0.0937
3
0.2058
0.7172
0.1476
4
0.1852
0.8144
0.1508
5
0.1440
0.8782
0.1265
6
0.1029
0.9200
0.0947
7
0.0700
0.9475
0.0663
8
0.0453
0.9655
0.0437
9
0.0206
0.9774
0.0201
10
0.0082
0.9852
0.0081
11
0
0.9903
—
xAb = (1 – e–kθ)
—
xAbE(θ)
0
—
∞
x As =
∫x
Ab
E(θ)dθ = 0.7699
0
Thus, the conversion is 77%. Problem 3.19 A total of 80% conversion is reported in an ideal CSTR with complete micro-mixing for → B whose rate equation is (− rA ) = kCA2 . What would be the a second-order reaction A k conversion if completely segregated flow condition is assumed? For a second-order reaction in an ideal CSTR with complete micro-mixing, the design equation for the calculation of space time is τ=
x Af kC AO (1 − x Af )2 x Af = 0.8
k τC AO =
x Af 0.8 = = 20 (1 − x Af )2 (1 − 0.8)2
As mean residence time, θ = τ
k θC AO = 20 The conversion x As in a completely segregated flow reactor is ∞
x As =
∫x
Ab
E(θ)dθ
0
www.Ebook777.com
Free ebooks ==> www.ebook777.com 247
Homogeneous Reactors
For a second-order reaction, the conversion in a batch reactor x Ab (θ) is x Ab (θ) =
(
)
20 θ/ θ kC AOθ = 1 + kC AOθ 1 + 20 θ/ θ
(
)
and for an ideal CSTR E(θ) =
e − θ/ θ θ
Substituting equations x Ab (θ) and E(θ) in equation x As, we obtain ∞
x As =
(
20 θ/ θ
)
∫ 1 + 20 (θ/θ ) e
− θ/ θ
(
d θ/ θ
)
0
Define θ = θ/ θ and we can write the above equation as ∞
x As =
∫ 0
20θ e − θ dθ 1 + 20θ
Conversion x As is calculated by the numerical integration of the equation using trapezoidal rule as illustrated in the below table:
θ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 4.0 5.0 10.0
20θ − θ e 1 + 20θ 0 0.6032 0.6550 0.6350 0.5958 0.5514 0.5066 0.4635 0.4229 0.3852 0.3504 0.2891 0.2381 0.1958 0.1608 0.1320 0.1083 0.0889 0.0729 0.0597 0.0490 0.0181 0.0067 0.00005
www.Ebook777.com
Free ebooks ==> www.ebook777.com 248
Green Chemical Engineering
1.0
∫
0
10
∫
0
20θ − θ 0.1 e dθ = 2 [(0 + 0.3504) + 2(0.6032 + + 0.3852)] 1 + 20θ
20θ − θ e dθ = 0.05 [(0.3504) + 2( 4.8186)] = 0.5 1 + 20θ
3.0
20θ − θ 0.2 [(0.3504 + 0.0490) + 2(0.2891 + + 0.0597 )] e dθ = 2 1 + 20θ 1.0
∫
= 0.1[(0.3994) + 2(1.3456)] = 0.309
5.0
20θ − θ 1.0 [(0.0490 + 0.0067 ) + 2(0.0181)] e dθ = 2 1 + 20θ 3.0
∫
= 0.5 [(0.0557 ) + 0.0362] = 0.0460
5.0
20θ − θ 5 e dθ = [(0.0067 + 0.00005)] = 0.0169 2 1 + 20θ 3.0
x As = [ 0.5 + 0.309 + 0.0460 + 0.0169] = 0.8719
∫
The conversion is 87.19% Thus, for a second-order reaction (n > 1), conversion in a segregated flow reactor is higher than the conversion in a completely micro-mixed reactor of the same volume. Note: Refer MATLAB program: seg_flow_II_order.m 3.2.8.1 Micro-Mixing and the Order of Reaction Consider an nth-order reaction A k → B , with kinetic rate expression (−rA) = kCAn, carried out in a reaction vessel. Consider an incremental volume ΔV of the reaction vessel and two fluid elements of equal volume (ΔV/2) moving through the incremental volume ΔV. Let CA1 and CA2 be the concentration of A in the two fluid elements (see Figure 3.72). Let us analyse two extreme cases of micro-mixing, namely, complete micro-mixing and completely segregated flow. In the complete micro-mixing case, two fluid elements mix at the inlet and move through the incremental volume as one single unit of volume ΔV within which complete mixing of molecules (micro-mixing) occurs. The concentration of A in the mixed fluid unit of volume ΔV is the average of CA1 and CA2, that is, CA = CA1 + C A 2 /2 (neglecting the net change in concentration through the incremental volume ΔV). If Δθ is the residence time of the mixed fluid unit through the incremental volume, then change in fractional conversion of A, ΔX Am, through the incremental volume is given by
www.Ebook777.com
Free ebooks ==> www.ebook777.com 249
Homogeneous Reactors
CA1
∆V 2
Fluid element 1
∆V Incremental reactor volume CA2
∆V 2 Fluid element 2
Figure 3.72 Two fluid elements moving through an incremental volume ΔV of the reactor.
k ∆θ [(C A1 + CA 2 )/2] ∆θ ⋅ rA (C A ) = (CA1 + CA 2 /2) (C A1 + CA 2 /2) n
∆x Am =
(3.399)
In the completely segregated flow case, both the fluid elements move through the incremental volume as two separate units without mixing with each other. Changes in frac2 in the two fluid elements are given by tional conversion of A ∆X 1As and ∆X As
1 ∆xAs =
∆θ ⋅ rA (C A1 ) ∆θk(CA1 )n = C A1 C A1
(3.400)
2 ∆xAs =
∆θ ⋅ rA (C A 2 ) ∆θk(CA 2 )n = CA 2 CA 2
(3.401)
and
The net change in the fractional conversion of A, ΔX As, through the incremental volume ΔV is ∆xAs =
2 CA1∆x1As + CA 2∆x As C A1 + C A 2
(3.402)
that is
∆xAs =
∆θ ⋅ k CAn1 + CAn 2 (CA1 + CA 2 )
www.Ebook777.com
(3.403)
Free ebooks ==> www.ebook777.com 250
Green Chemical Engineering
Thus ∆xAm = ∆x As
[(CA1 + CA 2 )/2]n
(3.404)
(CAn1 + CAn 2 /2)
The equation for different values of n shows that 1 for n = 1 ∆xAm = >1 for n < 1 ∆x As 1
(3.405)
Thus, for a first-order reaction, the conversion is the same regardless of the extent of micro-mixing. Segregated flow favours higher-order reactions and micro-mixing favours fractional order reactions. Thus, higher conversion is achieved for a second-order reaction in a reactor with segregated flow than in a reactor with complete micro-mixing. 3.2.8.2 Conversion of a First-Order Reaction in Ideal Reactors with Completely Segregated Flow A. Ideal CSTR with completely segregated flow: Consider a first-order reaction A k → B with kinetic rate expression (−rA) = kCA carried out in an ideal CSTR with completely segregated flow (see Figure 3.73). τ = v/q is the space time. The exit age distribution E(θ) for an ideal CSTR is E(θ) =
θ
1 −θ e θ
where θ = v/q is the mean residence time, which is the same as the space time τ. For completely segregated flow, the conversion X AS in the reactor is given by q CA0
q CAf
V
Figure 3.73 An ideal CSTR with complete segregated flow.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 251
Homogeneous Reactors
∞
x As =
∫x
Ab
(θ)E(θ)dθ
(3.406)
0
where X Ab(θ) for a first-order reaction is X Ab (θ) = 1 − e − kθ
(3.407)
Thus ∞
X As =
− θ/ θ
e ∫ (1 − e ) θ − kθ
0
dθ
∞ 1 −θ − k − θ 1 θ θ = e − e dθ θ 0
∫
∞
1 θ θ − k + θ θ 1 = − θe θ + e θ 1 + k θ 0
=
(3.408)
kθ 1 + kθ
As θ = τ x As =
kτ 1 + kτ
(3.409)
This is same as the conversion of a first-order reaction in an ideal CSTR with complete micro-mixing. This proves the point that the conversion of a first-order reaction in an ideal CSTR is the same regardless of the extent of micro-mixing. B. Ideal PFR with completely segregated flow: Consider an ideal PFR with completely segregated flow (Figure 3.74). τ = v/q is the space time, which is same as the mean residence time θ.
q
q
CA0
CAf
Figure 3.74 Ideal PFR with complete segregated flow.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 252
Green Chemical Engineering
The exit age distribution E(θ) for an ideal PFR is 0 , θ < θ E(θ) = ∞ , θ = θ 0, θ > θ
(3.410)
For completely segregated flow, conversion X As is ∞
x As =
∫x
Ab
(θ) E (θ) dθ
0
∞
=
∫ (1 − e )E (θ) dθ − kθ
0
θ−
=
θ+
− kθ
− kθ
θ−
0
(
= 0 + 1 − e − kθ
∞
∫ (1 − e ) E (θ) dθ + ∫ (1 − e )E (θ) dθ + ∫ (1 − e ) E (θ) dθ − kθ
θ+
θ+
) ∫ E (θ) dθ + 0 θ−
Thus
x As = (1 − e − k θ )
x As = (1 − e − k τ )
(3.411)
As θ = τ , we get
(3.412)
This is same as the conversion X Am is an ideal PFR with complete micro-mixing and once again it is shown that the extent of micro-mixing has no effect on the conversion for a first-order reaction. This analysis proves that the information on RTD E(θ) available for a reaction vessel is completely sufficient to calculate the conversion of a first-order reaction in the reaction vessel. However, for any higher-order reactions, additional information about the extent of micro-mixing is required. A number of models are proposed in the literature to account for micro-mixing. 3.2.8.3 Micro-Mixing and Ideal PFR Define X Am(τ) as the conversion of reactant A achieved in a space time τ in an ideal PFR with complete micro-mixing. X Am(τ) is calculated by solving the performance equation for the ideal PFR, for any reaction whose specific reaction rate is (−rA(X A)). Here, the reaction may be of any order n.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 253
Homogeneous Reactors
x Am ( τ )
∫
τ = CA0
0
dx A [ −rA (xA )]
(3.413)
Define X Ab(θ) as the conversion of A achieved in a batch reaction time θ in the batch reactor. X Ab(θ) is calculated by solving x Ab ( τ )
∫
θ = CA0
0
dx A − r [ A ( x A )]
(3.414)
Note that x Am (τ) = x Ab (τ)
(3.415)
that is, the conversion achieved in a space time τ in an ideal PFR with complete micromixing is the same as the conversion achieved in a batch reaction time τ in the batch reactor. Define X As(τ) as the conversion achieved in a space time τ in an ideal PFR with completely segregated flow. ∞
x As (τ) =
∫x
Ab
(θ)E(θ)dθ
0
(3.416)
The exit age distribution E(θ) for an ideal PFR is 0 , θ < θ E(θ) = ∞ , θ = θ 0, θ > θ
(3.417)
where θ is the mean residence time, which is also equal to the space time τ. Thus x As ( τ ) =
θ−
∫x 0
Ab
θ−
∞
θ+
θ+
(θ)E (θ) dθ + ∫ xAb (θ) E (θ) dθ + ∫ x Ab (θ) E (θ) dθ θ+
∫
= 0 + xAb (θ ) E (θ )dθ + 0 θ−
∞
∫
= xAb (θ ) E (θ )dθ
0
= xAb (θ )
www.Ebook777.com
(3.418)
Free ebooks ==> www.ebook777.com 254
Green Chemical Engineering
As θ = τ x As (τ) = x Ab (τ)
(3.419)
Comparing Equations 3.415 and 3.419, we have x Am (τ) = x As (τ)
(3.420)
This implies that the conversion in an ideal PFR with complete micro-mixing is the same as the conversion in an ideal PFR with completely segregated flow for reactions of any order. Thus, the extent of micro-mixing has no effect on the conversion in an ideal PFR for reactions of any order.
Appendix 3A: Estimation of Peclet Number—Derivation of Equation Using Method of Moments Danckwarts’ model equation for tubular vessel with axial dispersion is
( )
( )
( )
2 ∂C B , θ ∂C B , θ 1 ∂ C B, θ = 0 (C.1) − − Pe ∂B 2 ∂B ∂θ
where Pe: Peclet number = UL/D ʓ: Dimensionless distance from inlet = z/L Dimensionless time = θ/ θ θ: θ: Mean residence time = L/U C(B , θ ): Tracer concentration at a distance ʓ and time θ Danckwarts’ closed–closed boundary conditions are At B = 0 (vessel inlet) At B = 1 (vessel outlet)
1 dC(B , θ ) C0 (θ ) = C(0 + , θ ) − (C.2) Pe dB B = 0 1 dC(B , θ ) = 0 (C.3) Pe dB B = 0
Assume that the vessel is subjected to an impulse tracer test. For a unit impulse input, the tracer concentration at the vessel inlet C0 (θ ) is
C0 (θ ) = δ(θ ) (C.4)
www.Ebook777.com
Free ebooks ==> www.ebook777.com 255
Homogeneous Reactors
where δ(θ ) is the unit impulse function (Dirac delta function). The tracer concentration at the vessel output C(1, θ ) is the normalised E-curve E(θ ) (Figure 3.75), that is E(θ ) = C(1, θ ) (C.5)
Dimensionless mean residence time (θ ) and variance (σ 2 ) are ∞
θ
∫ θ E(θ )dθ = θ = 1
( θ ) =
(C.6)
0
and ∞
2
σ =
∫ θ E(θ )dθ − 1 2
(C.7)
0
Define the Laplace transformation of C(B , θ ) as ∞
{
} ∫ C(B, θ )e
C(B , s) = L C(B , θ ) =
− sθ
dθ (C.8)
0
Then
{ }
E(s) = L E(θ ) = C(1, s) (C.9)
Taking Laplace transformation of Danckwarts’ model Equation C.1, we get a secondorder ordinary differential equation in ʓ 1 d 2C(B , s) dC(B , s) − − sC(B , s) = 0 (C.10) Pe dB 2 dB
~ E(θ)
~ θ Figure 3.75 Normalised E-curve.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 256
Green Chemical Engineering
Taking Laplace transformation of Danckwarts’ boundary conditions (C.2) and (C.3), we get
C(0, s) −
1 dC(B , s) = 1 (C.11) Pe dB B = 0
dC(B , s) = 0 dB B=1
(C.12)
The characteristic equation for the second-order differential Equation C.10 is 1/Pe m2 − m − s = 0 and the corresponding roots are
m1 =
Pe (1 + α) (C.13) 2
m2 =
Pe (1 − α) (C.14) 2
α=
4s 1+ Pe
where
(C.15)
The solution to the differential Equation C.10 in terms of the roots of the characteristic equation is C(B , s) = A1e m1B + A2e m2 B (C.16)
Substituting Equation C.16 in the boundary conditions (C.11) and (C.12) and solving for A1 and A2, we get
A1 =
2(1 − α )e − αPe/2 (C.17) (1 − α )2 e − αPe/2 − (1 + α )2 e αPe/2
A2 =
−2(1 + α )e αPe/2 (C.18) (1 − α ) e − (1 + α )2 e αPe/2 2 − αPe/2
Substituting Equations C.17 and C.18 for A1 and A2, respectively, in Equation C.16, we get the final equation for C(B , s)
C(B , s) = A1
2e BPe/2 (1 + α )e αPe/2(1− B ) − (1 − α )e − αPe/2(1− B ) (1 + α )2 e αPe/2 − (1 − α )2 e − αPe/2
www.Ebook777.com
(C.19)
Free ebooks ==> www.ebook777.com 257
Homogeneous Reactors
At ʓ = 1, Equation C.19 reduces to
E(s) = C(1, s) =
4αe Pe/2 (C.20) − (1 − α )2 e − αPe/2
2 αPe/2
(1 + α ) e
Using Maclurin series expansion of e − sθ s2θ 2 e − sθ = 1 − sθ + − ⋅⋅⋅⋅ 2!
∞ in E ( s) = ∫ 0 E(θ )e − sθ dθ , we get
∞
E(s) = ∞
E(s) =
∫ 0
s2θ 2 E(θ ) 1 − sθ + − ⋅ ⋅ ⋅ ⋅ dθ 2! 0
∫
∞
∞
s2 2 θ E(θ)dθ − ⋅ ⋅ ⋅ ⋅ (C.21) E(θ )dθ − s θ E(θ )dθ + 2!
∫ 0
∫ 0
which finally reduces to ∞
∞
s2 2 s3 3 θ E(θ)dθ − θ E(θ)dθ + ⋅ ⋅ ⋅ ⋅ (C.22) E(s) = 1 − s + 2! 3!
∫ 0
∫ 0
From Equation C.22, we deduce ∞
d 2E(s) θ 2E(θ )dθ = 2 ds s = 0 0
∫
(C.23)
∞ Substituting Equation C.23 for ∫ 0 θ 2E(θ )dθ in Equation C.7, we get an expression for the 2 calculation of variance σ as
d 2E(s) − 1 (C.24) σ 2 = 2 ds s = 0
After tedious steps involving the evaluation of first and second derivatives of E(s), we can show that
σ 2 =
2 2 − (1 − e − Pe ) (C.25) Pe Pe 2
www.Ebook777.com
Free ebooks ==> www.ebook777.com 258
Green Chemical Engineering
The variance σ 2 of the normal E-curve E(θ) is defined as ∞
2
σ =
∫ θ E(θ) dθ − θ (C.26) 2
2
0
and
E(θ ) = θE(θ) (C.27)
Combining Equations C.26 and C.27, we get σ2 θ 2 =
∞
∫ θ E(θ ) dθ − 1 = σ (C.28) 2
2
0
From Equations C.25 and C.28, we finally have σ2 2 2 = − 2 (1 − e − Pe ) (C.29) 2 θ Pe Pe
Exercise Problems
1. A continuous-flow reactor A is to be designed to carry out a liquid-phase secondorder irreversible reaction A + B → C + D. The rate equation is (− rA ) = k C A CB . The concentrations of A and B in the feed solution are 5 kmol/m3 and 10 kmol/ m3, respectively. The rate constant k = 0.1 m3/kmol min. Calculate the space time required to achieve 80% conversion of A in (i) an ideal CSTR and (ii) an ideal PFR. (Answer: (i) 6.67 min; (ii) 2.20 min) 2. A total of 80% conversion of A is achieved when an irreversible reaction A → B with rate equation (− rA ) = kC An is carried out in an ideal CSTR having space time of 200 s. The conversion drops to a value of 73%, when the feed flow rate is doubled. Estimate the reaction order n and the rate constant k. (Answer: n = 2; k = 0.1) 3. A continuous-flow reactor is to be designed to carry out a non-elementary liquidphase reaction A → B + C whose rate equation is given by (− rA ) =
k1CA2 kmol/m3 s 1 + k 2CA
where the kinetic rate constants are k1 = 0.02 and k2 = 2. The feed concentration of A is 1 kmol/m3. Calculate the space time required to achieve 80% conversion in (i) an ideal CSTR and (ii) an ideal PFR. (Answer: (i) 1400 s; (ii) 361.3 s) 4. Calculate the space time required to achieve 95% of the equilibrium conversion of a first-order reversible reaction A B carried out in an ideal PFR. The feed concentration of A is 1 kmol/m3. The rate constant of the forward reaction is k1 = 0.1 s−1 and the equilibrium constant is K = 5. (Answer: 32.65 s)
www.Ebook777.com
Free ebooks ==> www.ebook777.com 259
Homogeneous Reactors
5. A third-order irreversible reaction A → B with rate equation (rA ) = kCA2 is carried out in a battery of six numbers ideal CSTRs of equal volumes connected in series. The rate constant is k = 0.1 (m3/kmol)2/min. The feed concentration of A is 2 kmol/m3. The space time of each one of the CSTRs is 2 min. (i) What is the net conversion of A achieved in the battery of CSTRs? (ii) What is the conversion in one single CSTR having space time equal to the sum of space times of all the six CSTRs? (Answer: (i) 65.58%; (ii) 52.25%) 6. An irreversible second-order reaction A + B → C + D with rate equation (− rA ) = kCACB is to be carried out in a battery of CSTRs of equal volumes connected in series. The rate constant is k = 0.1 m3/kmol/min. The concentrations of A and B in the feed solution are 1 and 2 kmol/m3, respectively. The space time of each one of the CSTRs is 2 min. Calculate the number of CSTRs required to achieve 80% conversion of A. (Answer: 7 CSTRs and final conversion Xaf = 82.1%)
7. A third-order irreversible reaction A → B with rate equation (− rA ) = kCA2 and rate constant k = 0.1 (m3/kmol)2/min is carried out in a battery of three numbers ideal CSTRs of unequal volumes connected in series. The space times of the three CSTRs are 2, 4 and 6 min, respectively. The concentration of A in the feed to the first CSTR is 2 kmol/m3. What is the net conversion of A achieved? What is the conversion if the feed direction is reversed? (Answer: (i) 62.3%; (ii) 61.2%)
8. A third-order irreversible reaction A → B with rate equation (− rA ) = kCA2 and rate constant k = 0.1 (m3/kmol)2/min is carried out in a system of one CSTR and one PFR connected in series. Both CSTR and PFR are of equal size having a space time of 6 min each. The concentration of A in the feed solution is 2 kmol/m3. (i) What is the conversion if the feed solution enters the CSTR first? (ii) What is the conversion if the feed solution enters the PFR first? (Answer: (i) 64.5%; (ii) 67.1%) 9. An irreversible second-order reaction A + B → C + D with rate equation (− rA ) = kCACB and rate constant k = 0.1 m3/kmol/min is carried out in a sequence of five reactors connected in series. The configurations of the reactors are as follows:
Reactor Number 1 2 3 4 5
Reactor Type PFR CSTR CSTR PFR CSTR
Space Time (Min) 4 3 3 4 3
The feed solution contains 1 kmol/m3 of A and 2 kmol/m3 of B. Calculate the final conversion of A. (Answer: Final conversion is 88%) 10. Calculate the optimal space times of two CSTRs connected in series in which a second-order irreversible reaction A → B with rate equation (− rA ) = kCA2 and rate
www.Ebook777.com
Free ebooks ==> www.ebook777.com 260
Green Chemical Engineering
constant k = 0.1 m3/kmol/min is carried out. Concentration of A in the feed solution is 1 kmol/m3. A total of 80% conversion of A is to be achieved in the two CSTRs. What is the conversion of A in the first CSTR corresponding to the optimal space time? (Answer: Optimal space times are 37.5 and 50; conversion in the first CSTR is 60%) 11. Calculate the conversion of A (X Af) and the overall selectivity of B (Ø) achieved in a space time of 5 min in the CSTR and in the PFR for a first-order series reaction A → B → C . The values of kinetic rate constants are k1 = 0.5 min−1 and k2 = 0.1 min−1. (Answer: For CSTR, X Af = 71.4% and Ø = 2; for PFR, X Af = 91.8% and Ø = 2.5) 12. Calculate the space time required to achieve 90% conversion of monomer in a CSTR in which a chain polymerisation reaction is carried out at constant temperature. The concentration of the monomer in the feed solution is Cmo = 5 kmol/m3 and the rate constant is k = 0.1 m3/kmol/min. Sketch the product distribution of polymer chains produced in the reactor. (Answer: Space time is 43.2 min) 13. An exothermic reversible reaction A B with rate equation (− rA ) = k1C A 0 (1 − x A ) − k 2CA 0 x A and kinetic rate constants k1 = k10 e −
∆E1 RT
, k10 = 50 s−1 & ∆E1 = 64, 000 kJ kmol
∆E1 /RT
k 2 = k 20 e − , k 20 = 500 s − c & ∆E2 = 90, 000 kJ kmol Is carried out in an ideal PFR in which optimal temperature policy is maintained with the maximum value of the reactor temperature restricted to 900 K. Calculate the space time required to achieve 70% conversion of A. The concentration of A in the feed solution is 0.5 kmol/m3. (Answer: Space time is 207.7 s) 14. An exothermic first-order irreversible reaction A → B with rate constant −10 , 000
RT h−1 is to be carried out in an adiabatic continuous-flow reack = 400 e tor. The concentration of A in the feed solution is 1 kmol/m3 and the feed temperature is 300 K. The density and mean specific heat of feed solution are respectively 1000 kg/m3 and C p = 4.17 kJ/kgK . The heat of reaction is ∆H R = −1, 00, 000 kJ kmol . Calculate the space time required in (i) PFR and in (ii) CSTR for 80% conversion of A. (Answer: (i) 0.265 h (ii) 0.947 h) 15. An endothermic third-order irreversible reaction A → B with rate constant −72 , 000
RT (m3/kmol)2/min is to be carried out in an adiabatic contink = 106 e uous-flow reactor. Concentration of A in the feed solution is 2 kmol/m3 and the feed temperature is 973 K. Density and mean specific heat of feed solution is, respectively, P = 1000 kg/m 3 and Cp = 4.17 kJ/kg K . Heat of reaction is ∆H R = 1, 200, 000 kJ kmol. Calculate the space time required in (i) CSTR and (ii) PFR for 70% conversion of A. (Answer: (i) 25.62 min; (ii) 1.624 min)
www.Ebook777.com
Free ebooks ==> www.ebook777.com 261
Homogeneous Reactors
16. An exothermic first-order irreversible reaction A → B with rate constant −12 , 000
T s−1 is carried out in a CSTR provided with cooling coil for k = 2 × 1013 e removal of heat generated by exothermic reaction. Concentration of A in the feed solution is 7 kmol/m3. The temperature of the coolant is maintained at 295 K. The heat of reaction is ∆H R = −2.5 × 107 J kmol. Density and mean specific heat of feed solution is respectively P = 900 kg/m 3 and C p = 2400 J /kg K . UA = 10,000 W/K, where U is the overall heat transfer coefficient and A is the area of heat transfer. The space time is 500 s. Calculate the steady-state reactor temperature and the conversion for feed temperature of (i) 275, (ii) 290 and (iii) 310 K. (Answer: (i) T = 277.8 K X Af = 0.17%, (ii) T = 291.6 K, 325.7 K, 358.5 K X Af = 1.32%, 49.9%, 96.7%, (iii) T = 377.7 K X Af = 99.4%) 17. The following tracer data are available for a reactor system:
Time (Min) 0 1 2 3 4 5 6 7
Tracer Concentration (g/L) 0 0.2 0.6 1.2 2.6 4.5 5.5 6.5
Time (Min) 8 9 10 11 12 13 14 15
Tracer Concentration (g/L) 5.5 4.5 3.0 2.1 1.2 0.5 0.2 0
i. Calculate the mean and the variance. ii. Assuming that the tanks in series model is applicable, estimate the value of parameter N and calculate the conversion of a first-order reaction having rate constant k = 0.25 min−1. iii. Assuming that the axial dispersion model is applicable, estimate the value of the Peclet number and calculate the conversion of a first-order reaction having rate constant k = 0.25 min−1. iv. Assuming that the segregated flow model is applicable, calculate the conversion of a first-order reaction having rate constant k = 0.25 min−1. (Answer: (i) Mean = 7.3 min, variance = 5.96; (ii) N = 8.92, Xaf = 80.95%; (iii) Pe = 16.8, Xaf = 81.11%; (iv) Xaf = 80.65%) 18. Calculate the conversion of a first-order reaction in a tubular flow reactor in which flow condition is laminar. Rate constant is k = 0.25 min−1. The mean residence time of the fluid in the reactor is 7.3 min. (Answer: 74.3%)
19. A second-order irreversible reaction A → B with rate equation (− rA ) = kCA2 and rate constant k = 0.1 m3/kmol/min is carried out in a laminar flow reactor. The concentration of A in the feed solution is 5 kmol/m3. The mean residence time of fluid in the reactor is 5.9 min. Calculate the conversion of A. (Answer: 70.5%)
www.Ebook777.com
Free ebooks ==> www.ebook777.com 262
Green Chemical Engineering
MATLAB Programs List of MATLAB Programs Program Name
Description
Homogeneous Ideal Reactors react_dsn_cstr_pfr.m Program for the design of ideal CSTR/PFR cal_rate.m Program subroutine to define the rate equation n_cstrs_series1.m Program to calculate number of CSTRs in series required to achieve specified conversion n_cstrs_series2.m Program to calculate conversion achieved in a specified number of CSTRs connected in series reactor_sequence.m Program to calculate conversion in a sequence of reactors (both CSTR and PFR) react_polymer.m Program to design polymerisation reactor used for chain polymerisation reaction react_dsn_opt_ Program to design batch reactor/CSTR/PFR for first-order exothermic reversible tmp.m reaction following optimal temperature progression policy react_dsn_adiab1.m Program to design batch reactor/CSTR/PFR for second-order endothermic irreversible reaction operating at adiabatic condition react_dsn_adiab2.m Program to design batch reactor/CSTR/PFR for first-order exothermic irreversible reaction operating at adiabatic condition cstr_multiplicity2.m Program for calculation of multiple steady states of non-isothermal CSTR in which the I orderexothermic reaction is carried out
MATLAB Programs PROGRAM: react_dsn_cstr_pfr.m % program for the design of ideal CSTR / PFR clear all % INPUT DATA %_________________________________________________________________ eqn_no = 6 ; % define the rate equation and rate constant in cal_rate Ca0 = 5 ; % feed concentration of A Kgmoles/m3 xaf = 0.675 ; % final conversion % CALCULATIONS %_________________________________________________________________ np = 50 ; for i = 1:np xa = ((i-1)/(np-1))*xaf ; ra = cal_rate(Ca0,xa,eqn_no) ; xy_data(1,i) = xa ; xy_data(2,i) = (1/ra) ; end ; int_val = trapez_integral(xy_data) ; tau_pfr = Ca0*int_val ;
www.Ebook777.com
Free ebooks ==> www.ebook777.com 263
Homogeneous Reactors
raf = cal_rate(Ca0,xaf,eqn_no) ; tau_cstr = (Ca0*xaf)/raf ; % DISPLAY RESULTS %_________________________________________________________________ fprintf(′---------------------------------------------------------- \n'); fprintf(′DESIGN OF IDEAL REACTORS \n′) ; fprintf(′ \n′) ; fprintf(′ \n′) ; fprintf(′IDEAL CSTR - Space time : %10.4f \n′,tau_cstr) ; fprintf(′IDEAL PFR - Space time : %10.4f \n′,tau_pfr) ; fprintf(′ \n′) ; fprintf(′---------------------------------------------------------- \n’); FUNCTION SUBROUTINE: cal_rate.m % program subroutine to define the rate equation function ra = cal_rate(Ca0,xa,eqn_no) Ca = Ca0*(1-xa) ; if eqn_no == 0 k = 0.1 ; ra = k ; end ;
% zero order irreversible reaction A ---> B
if eqn_no == 1 k = 0.1 ; ra = k*Ca ; end ;
% first order irreversible reaction A ---> B
if eqn_no == 2 k = 0.05 ; ra = k*Ca∧2 ; end ;
% second order irreversible reaction A ---> B
if eqn_no == 3 k = 0.1 ; ra = k*Ca∧3 ; end ;
% third order irreversible reaction A ---> B
if eqn_no == 4 % second order irreversible reaction A + B ---> C k = 0.1 ; M = 2 ; % M = Cb0/Ca0 ra = k*Ca*(Ca0*(M-1) + Ca) ; end ; if eqn_no == 5 % first order reversible reaction A B k = 0.1 ; K = 2 ; % K = Cae/Cae - equilibrium constant Cb = Ca0 - Ca ; ra = k*(Ca - Cb/K) ; end ;
www.Ebook777.com
Free ebooks ==> www.ebook777.com 264
Green Chemical Engineering
if eqn_no == 6 % second order reversible reaction A B k = 0.1 ; K = 9 ; % K = Cae/Cae - equilibrium constant Cb = Ca0 - Ca ; ra = k*(Ca∧2 - (Cb∧2)/K) ; end ; PROGRAM: n_cstrs_series1.m % program to calculate number of CSTRs in series required to achieve % specified conversion clear all % INPUT DATA %_________________________________________________________________ eqn_no = 6 ; Ca0 = 5 ; xaf = 0.62 ; tau = 0.5 ;
% % % %
define the rate equation and rate constant in cal_rate feed concentration of A Kgmoles/m3 final conversion space time
% CALCULATIONS %_________________________________________________________________ n_p = 20 ; xf = 1.1*xaf ; for i = 1:n_p xa = ((i-1)/(n_p-1))*xf ; ra = cal_rate(Ca0,xa,eqn_no); y_val = xa - (tau/Ca0)*ra ; x1(i) = xa ; y1(i) = y_val ; x2(i) = xa ; y2(i) = xa ; end ; ys = 0 ; n = 1 ; ys_vec(1) = ys ; while ys www.ebook777.com 266
Green Chemical Engineering
% INPUT DATA %_________________________________________________________________ eqn_no = 6 ; Ca0 = 5 ; n = 9 ; tau = 0.5 ;
% % % %
define the rate equation and rate constant in cal_rate feed concentration of A Kgmoles/m3 number of CSTRs connected in series space time
% CALCULATIONS %_________________________________________________________________ n_p = 40 ; for i = 1:n_p Ca = ((i-1)/(n_p-1))*Ca0 ; xa = 1 - (Ca/Ca0) ; ra = cal_rate(Ca0,xa,eqn_no); x1(i) = Ca ; y1(i) = ra ; end ; x2 = [0 Ca0] ; y2 = [0 0] ; Cas = Ca0 ; Cas_vec(1) = Cas ; for ii = 1:n % calculation for each one of n CSTRs xs = 0 ; n_t = 5000 ; eps = 0.01 ; count = 0 ; for j = 1:n_t Ca = Cas - ((j-1)/(n_t-1))*Cas ; x = 1 - (Ca/Ca0) ; rax = cal_rate(Ca0,x,eqn_no); y_x = (Cas - Ca)/tau ; if abs(y_x - rax) www.ebook777.com 267
Homogeneous Reactors
Cas_val = Cas_vec((jn+1)/2) x3(jn) = Cas_val ; y3(jn) = 0 ; else % jn is even x_val = Cas_vec((jn/2) + 1) y_val = ras_vec(jn/2) ; x3(jn) = x_val ; y3(jn) = y_val ; end ; end ;
;
;
xaf = 1 - Cas_vec(n+1)/Ca0 ; % DISPLAY RESULTS %_________________________________________________________________ % graph plot(x1,y1,′-r′,x2,y2,′-b′,x3,y3,′-c′) ; xlabel(′Ca - Concentration of A′) ; ylabel(′ra - Rate ′) ; % display fprintf(′——————————————————————————————————- \n′) ; fprintf(′NUMBER OF CSTRS IN SERIES \n′) ; fprintf(′ \n′) ; fprintf(′Space time of one CSTR min fprintf(′Number of CSTRs fprintf(′Fractional Conversion fprintf(′ \n′) ; fprintf(′ \n′) ; fprintf(′ Reactor No. Conversion \n′) ; fprintf(′ \n′) ; for ii = 1:n fprintf(′ %5i %10.4f \n′,ii,xas(ii)) ; end ; fprintf(′ \n′) ; fprintf(′——————————————————————————————————- \n′) ;
: : :
%10.4f \n′,tau) ; %5i \n′,n) ; %10.4f \n′,xaf) ;
PROGRAM: reactor_sequence.m % Program to calculate conversion in a sequence of reactors clear all % INPUT DATA %_________________________________________________________________ eqn_no = 2 ; Ca0 = 2 ;
% define the rate equation and rate constant in cal_rate % feed concentration of A Kgmoles/m3
% enter the type and space time of reactors connected in series % reactor no
1
2
3
4
www.Ebook777.com
Free ebooks ==> www.ebook777.com 268
r_seq_mat = [ 2 4
Green Chemical Engineering
1 4
2 2
1 ; 1 ] ;
% reactor type 1 - CSTR, 2 - PFR % space time
% CALCULATIONS %_________________________________________________________________ vec_size = size(r_seq_mat) ; n_data = vec_size(1,2) ; for i = 1:n_data r_type_val = r_seq_mat(1,i) ; tau_val = r_seq_mat(2,i) ; r_type(i) = r_type_val ; tau(i) = tau_val ; end ; x0 = 0 ; delx = 0.0001 ; nx = 50 ; for i = 1:n_data r_type_val = r_type(i) ; tau_val = tau(i) ; if r_type_val == 1 % CSTR x = x0 + delx ; ra = cal_rate(Ca0,x,eqn_no) ; f_val = ((x - x0) - (tau_val/Ca0)*ra) ; if f_val 0 flag = 1 ; xf = x -0.5*delx ; end ; end ; else flag = 1 ; while flag == 1 x = x + delx ; ra = cal_rate(Ca0,x,eqn_no) ; f_val = ((x - x0) - (tau_val/Ca0)*ra) ; if f_val < 0 flag = 0 ; xf = x -0.5*delx ; end ; end ; end ; xaf_vec(i) = xf ; x0 = xf ; end ;
www.Ebook777.com
Free ebooks ==> www.ebook777.com Homogeneous Reactors
if r_type_val == 2 % PFR x = x0 + delx ; for j = 1:nx xj = x0 + ((j-1)/(nx-1))*(x-x0) ; raj = cal_rate(Ca0,xj,eqn_no) ; xy_data(1,j) = xj ; xy_data(2,j) = (1/raj) ; end ; integ_val = trapez_integral(xy_data) ; f_val = (1-(Ca0/tau_val)*integ_val) ; if f_val 0 flag = 1 ; xf = x -0.5*delx ; end ; end ; else flag = 1 ; while flag == 1 x = x + delx ; for j = 1:nx xj = x0 + ((j-1)/(nx-1))*(x-x0) ; raj = cal_rate(Ca0,xj,eqn_no) ; xy_data(1,j) = xj ; xy_data(2,j) = (1/raj) ; end ; integ_val = trapez_integral(xy_data) ; f_val = (1-(Ca0/tau_val)*integ_val) ; if f_val www.ebook777.com 270
Green Chemical Engineering
fprintf(′---------------------------------------------------------- \n’); fprintf(′CONVERSION IN A REACTOR SEQUENCE \n′) ; fprintf(′ \n′) ; fprintf(′Initial Concentration Ca0 : %10.4f \n′,Ca0) ; fprintf(′Final Conversion xaf : %10.4f \n′,xaf) ; fprintf(′Number of Reactors n : %5i \n′,n_data) ; fprintf(′ \n′) ; fprintf(′ Reactor No. Type Conversion \n′) ; fprintf(′ \n′) ; for i = 1:n_data fprintf(′ %5i %5i %10.4f \n′,i,r_type(i),xaf_vec(i)) ; end ; fprintf(′ \n′) ; fprintf(′ Reactor Type 1 - CSTR Reactor Type 2 - PFR \n′) ; fprintf(′ \n′) ; fprintf(′---------------------------------------------------------- \n’); PROGRAM: react_polymer.m % Program to design Polymerization Reactor used for chain polymerization % reaction clear all ; % INPUT DATA %_________________________________________________________________ m0 = 10 ; % monomer concentration in Kgmoles/m3 xaf = 0.8 ; % fractional conversion k = 0.05 ; % Second order rate constant m3/Kgmoles Min % CALCULATIONS %_________________________________________________________________ m = m0*(1-xaf) ; % final monomer concentration tau = (sqrt(m0) - sqrt(m))/(k*m∧(3/2)) ; % space time % polymer product distribution wr_vec(1) = 0 ; r_vec(1) = 0 ; r_length = 30 ; % chain length for r = 1:r_length r_vec(r+1) = r ; wr = (r*(1-xaf)/xaf)*(1-sqrt(1-xaf))∧(r-1) ; % weight fraction wr_vec(r+1) = wr ; end ; % plot of product distribution plot(r_vec,wr_vec,′-r′) ; xlabel(′r - chain length′) ; ylabel(′wr - weight fraction′) ; % DISPLAY RESULTS %_________________________________________________________________ fprintf(′---------------------------------------------------------- \n’);
www.Ebook777.com
Free ebooks ==> www.ebook777.com Homogeneous Reactors
271
fprintf(′DESIGN OF CHAIN POLYMERIZATION REACTOR \n′) ; fprintf(′ \n′) ; fprintf(′Initial monomer concentration m0 : %10.4f \n′,m0) ; fprintf(′Final Conversion xaf : %10.4f \n′,xaf) ; fprintf(′Space time tau : %10.4f \n′,tau) ; fprintf(′ \n′) ; fprintf(′---------------------------------------------------------- \n’); PROGRAM: react_dsn_opt_tmp.m % Program to design Batch Reactor / CSTR / PFR for first order % exothermic reversible reaction following optimal % temperature progression policy clear all % INPUT DATA %_________________________________________________________________ k10 = 21 ; % frequency factor for forward reaction 1/Sec k20 = 4200 ; % frequency factor for forward reaction 1/Sec del_E1 = 32200 ; % activation energy of forward reaction Kj/Kgmoles del_E2 = 64400 ; % activation energy of forward reaction Kj/Kgmoles Ca0 = 0.8 ; % feed concentration/intial concentration of A Kgmoles/m3 xaf = 0.88 ; % final fractional conversion Tmax = 900 ; % maximum permissable temperature K % CALCULATIONS %_________________________________________________________________ % Batch Reactor / PFR calculations del_Hr = del_E1 - del_E2 ; % heat of reaction in Kj/Kgmoles R = 8.314 ; % gas law constant in Kj/Kgmoles K n_int_p = 9 ; % number of intehration points for i = 1:n_int_p xa = ((i-1)/(n_int_p - 1))*xaf ; if xa == 0 Topt = Tmax ; else Topt = (-1*del_Hr)/(R*log((k20/k10)*(del_E2/del_E1)*(xa/(1-xa)))) ; if Topt > Tmax Topt = Tmax ; end ; end ; k1 = k10*exp(-1*del_E1/(R*Topt)) ; k2 = k20*exp(-1*del_E2/(R*Topt)) ; ra = k1*Ca0*(1-xa) - k2*Ca0*xa ; int_mat(1,i) = xa ; int_mat(2,i) = (1/ra) ; end ; integral_val = trapez_integral(int_mat) ;
www.Ebook777.com
Free ebooks ==> www.ebook777.com 272
Green Chemical Engineering
t_batch = Ca0*integral_val ; % batch time / space time of PFR % CSTR calculations Topt = (-1*del_Hr)/(R*log((k20/k10)*(del_E2/del_E1)*(xaf/(1-xaf)))) ; k1 = k10*exp(-1*del_E1/(R*Topt)) ; k2 = k20*exp(-1*del_E2/(R*Topt)) ; raf = k1*Ca0*(1-xaf) - k2*Ca0*xaf ; tau_cstr = (Ca0*xaf)/raf ; fprintf(′---------------------------------------------------------- \n’); fprintf(′DESIGN OF BATCH REACTOR/CSTR/PFR - OPTIMAL TEMPERATURE POLICY \n′) ; fprintf(′ \n′) ; fprintf(′Feed Concentration Ca0 Kgmoles/m3 : %10.4f \n′,Ca0) ; fprintf(′Fractional Conversion : %10.4f \n′,xaf) ; fprintf(′Maximum Temperature K : %10.4f \n′,Tmax) ; fprintf(′ \n′) ; fprintf(′IDEAL CSTR - Space Time : %10.4f \n′,tau_cstr) ; fprintf(′PFR / BATCH REACTOR - Batch Time : %10.4f \n′,t_batch) ; fprintf(′Exit / Final Temperature - K : %10.4f \n′,Topt) ; fprintf(′ \n′) ; fprintf(′---------------------------------------------------------- \n’); PROGRAM: react_dsn_adiab1.m % Program to design Batch Reactor / CSTR / PFR for second order % endothermic irreversible reaction operating at adiabatic condition clear all % INPUT DATA %_________________________________________________________________ k0 = 1.2 ; del_E = 14000; Ca0 = 5 ; T0 = (450+273); xaf = 0.8 ; del_Hr = 98470; ro = 995 ; cp = 2.5 ;
% % % % % % % %
frequency factor m3/kgmole min activation energy of forward reaction Kj/Kgmoles feed concentration/intial concentration of A Kgmoles/m3 feed temperature/initial temperature K final fractional conversion heat of reaction Kj/Kgmole density Kg/m3 specific capacity Kj/Kg K
% CALCULATIONS %_________________________________________________________________ % Batch Reactor / PFR calculations R = 8.314 ; % gas law constant in Kj/Kgmoles K delt_ad = (-1*del_Hr*Ca0)/(ro*cp) ; n_int_p = 50 ; % number of intehration points for i = 1:n_int_p xa = ((i-1)/(n_int_p - 1))*xaf ; T = T0 + delt_ad*xa ;
www.Ebook777.com
Free ebooks ==> www.ebook777.com 273
Homogeneous Reactors
k = k0*exp(-1*del_E/(R*T)) ; ra = k*(Ca0*(1-xa))∧2 ; int_mat(1,i) = xa ; int_mat(2,i) = (1/ra) ; end ; integral_val = trapez_integral(int_mat) ; t_batch = Ca0*integral_val ; % batch time / space time of PFR % CSTR calculations T = T0 + delt_ad*xaf ; k = k0*exp(-1*del_E/(R*T)) ; raf = k*(Ca0*(1-xaf))∧2 ; tau_cstr = (Ca0*xaf)/(raf) ; tau_cstr = (Ca0*xaf)/(raf) ; % DISPLAY RESULTS %_________________________________________________________________ fprintf(′---------------------------------------------------------- \n’); fprintf(′DESIGN OF BATCH REACTOR / CSTR / PFR - ADIABATIC OPERATION \n′) ; fprintf(′ \n′) ; fprintf(′Feed Concentration Ca0 Kgmoles/m3 : %10.4f \n′,Ca0) ; fprintf(′Fractional Conversion : %10.4f \n′,xaf) ; fprintf(′Feed Temperature K : %10.4f \n′,T0) ; fprintf(′ \n′) ; fprintf(′IDEAL CSTR - Space Time : %10.4f \n′,tau_cstr) ; fprintf(′PFR / BATCH REACTOR - Batch Time : %10.4f \n′,t_batch) ; fprintf(′Exit / Final Temperature - K : %10.4f \n′,T) ; fprintf(′ \n′) ; fprintf(′---------------------------------------------------------- \n’); PROGRAM: react_dsn_adiab2.m % Program to design Batch Reactor / CSTR / PFR for first order exothermic % irreversible reaction operating at adiabatic condition clear all % INPUT DATA %_________________________________________________________________ k0 = 35 ; del_E = 9000 ; Ca0 = 1 ; T0 = 400 ; xaf = 0.8 ; del_Hr = -210000; ro = 998 ; cp = 4.2 ;
% % % % % % % %
frequency factor 1/Hr activation energy of forward reaction Kj/Kgmoles feed concentration/intial concentration of A Kgmoles/m3 feed temperature / initial temperature K final fractional conversion heat of reaction Kj/Kgmole density Kg/m3 specific capacity Kj/Kg K
% CALCULATIONS %_________________________________________________________________
www.Ebook777.com
Free ebooks ==> www.ebook777.com 274
Green Chemical Engineering
% Batch Reactor / PFR calculations R = 8.314 ; % gas law constant in Kj/Kgmoles K delt_ad = (-1*del_Hr*Ca0)/(ro*cp) ; n_int_p = 50 ; % number of intehration points for i = 1:n_int_p xa = ((i-1)/(n_int_p - 1))*xaf ; T = T0 + delt_ad*xa ; k = k0*exp(-1*del_E/(R*T)) ; ra = k*Ca0*(1-xa) ; int_mat(1,i) = xa ; int_mat(2,i) = (1/ra) ; end ; integral_val = trapez_integral(int_mat) ; t_batch = Ca0*integral_val ; % batch time / space time of PFR % CSTR calculations T = T0 + delt_ad*xaf ; k = k0*exp(-1*del_E/(R*T)) ; raf = k*Ca0*(1-xaf) ; tau_cstr = (Ca0*xaf)/(raf) ; tau_cstr = (Ca0*xaf)/(raf) ; % DISPLAY RESULTS %_________________________________________________________________ fprintf(′---------------------------------------------------------- \n’); fprintf(′DESIGN OF BATCH REACTOR/CSTR/PFR - ADIABATIC OPERATION \n′) ; fprintf(′ \n′) ; fprintf(′Feed Concentration Ca0 Kgmoles/m3 : %10.4f \n′,Ca0) ; fprintf(′Fractional Conversion : %10.4f \n′,xaf) ; fprintf(′Feed Temperature K : %10.4f \n′,T0) ; fprintf(′ \n′) ; fprintf(′IDEAL CSTR - Space Time : %10.4f \n′,tau_cstr) ; fprintf(′PFR / BATCH REACTOR - Batch Time : %10.4f \n′,t_batch) ; fprintf(′Exit / Final Temperature - K : %10.4f \n′,T) ; fprintf(′ \n′) ; fprintf(′---------------------------------------------------------- \n’); PROGRAM: cstr_multiplicity.m % Multiplicity and Stability of Non Isothermal CSTR % I Order Exothermic Reaction clear all % INPUT DATA %_________________________________________________________________
www.Ebook777.com
Free ebooks ==> www.ebook777.com 275
Homogeneous Reactors
Ca0 = 7 ; k0 = 2*10∧13 ; E0_by_R = 12000 ; delHr = -2.5*10∧7 ; cp = 2400 ; ro = 900 ;
% % % % % %
feed concentration Kgmoles/m3 frequency factor 1/Sec activation energy / R K heat of reaction J/Kgmole mean specific heat J/Kg K density Kg/m3
V = 15 ; q = 0.03 ; Tc = 295 ; T0 = [275 290 310] ;
% % % %
reactor volume m3 volumetric flow rate m3/s coolant temperature K define 3 feed temperatures K
UA = 10000
% value of UA in W/K
T_min T_max
;
= 270 ; = 390 ;
% Minimum Temperature % Maximum Temperature
% CALCULATIONS %_________________________________________________________________ T01 = T0(1) ; T02 = T0(2) ; T03 = T0(3) ; tau = V/q ; nt = 10000 ; delt = (T_max - T_min)/(nt -1) ; for i = 1:nt T = T_min + ((i-1)/(nt-1))*(T_max - T_min) k = k0*exp(-E0_by_R/T) ; Qg = ((-1*delHr)*q*Ca0*k*tau)/(1+k*tau) ; Qr1 = (ro*q*cp+UA)*T - (ro*q*cp*T01+UA*Tc) Qr2 = (ro*q*cp+UA)*T - (ro*q*cp*T02+UA*Tc) Qr3 = (ro*q*cp+UA)*T - (ro*q*cp*T03+UA*Tc) T_vec(i) = T ; Qg_vec(i) = Qg ; Qr1_vec(i) = Qr1 ; Qr2_vec(i) = Qr2 ; Qr3_vec(i) = Qr3 ; end ;
; % ; ; ;
heat generation % heat removal at T01 % heat removal at T02 % heat removal at T03
% calculate the steady state temperature and conversion count1 = 0 ; count2 = 0 ; count3 = 0 ; Qg = Qg_vec(1) ; Qr1 = Qr1_vec(1) ; Qr2 = Qr2_vec(1) ; Qr3 = Qr3_vec(1) ; f1 = Qg - Qr1 ; f2 = Qg - Qr2 ; f3 = Qg - Qr3 ;
www.Ebook777.com
Free ebooks ==> www.ebook777.com 276
Green Chemical Engineering
if f1 1 n_factorial = 1 ; for nf = n:-1:1 n_factorial = n_factorial*nf ; end ; end ; PROGRAM: E_curve_lfr.m % Program to Plot dimensionless E-curve for Laminar Flow Reactor clear all ; thetahat_max = 4 ; % define range of thetahat theta_hat(1) = 0 ; E_thetahat_cstr(1) = 1 ; E_thetahat_lfr(1) = 0 ; for j = 1:10000 thetahat = j*(thetahat_max/10000) ; theta_hat(j+1) = thetahat ; if thetahat www.ebook777.com 282
Green Chemical Engineering
vec_size = size(imp_tracer_data) ; n_data = vec_size(1,2) ; [theta_bar sigma_sqr] = cal_mean_var(imp_tracer_data) ; tau = theta_bar ; % space time % Ideal PFR xaf_pfr = 1 - exp(-1*k*tau) ; %Ideal CSTR xaf_cstr = (k*tau)/(1+k*tau) ; % Tanks in series model n_t = cal_n_tank(theta_bar,sigma_sqr)
;
xaf_tis = 1 - 1/((1+(k*tau/n_t))∧n_t) ; % Axial dispersion model pe = cal_pe(theta_bar,sigma_sqr)
;
beta = sqrt(1+(4*k*tau/pe)) ; xaf_adm = 1 - ((4*beta*exp(pe/2)))/((1+beta)∧2*exp(pe*beta/2) (1-beta)∧2*exp(-1*pe*beta/2)) ; % completely segregated flow model E = cal_E_theta(imp_tracer_data) ; for i = 1:n_data t = E(1,i) ; x_batch = 1 - exp(-k*t) ; x_E(1,i) = t ; x_E(2,i) = x_batch*E(2,i) ; end; xaf_sfm = trapez_integral(x_E) ; % Laminar flow reactor of same size t_min = theta_bar / 2 ; t_max = 10*theta_bar ; for j = 1:100 t = t_min xl_E(1,j) xl_E(2,j) end ;
; + (j-1)*(t_max - t_min)/99 ; = t ; = (exp(-1*k*t))/(t∧3) ;
integral_xl_E = trapez_integral(xl_E) ;
www.Ebook777.com
Free ebooks ==> www.ebook777.com Homogeneous Reactors
283
xaf_lfr = 1 - ((theta_bar∧2)/2)*integral_xl_E ; % display of results fprintf(′---------------------------------------------------------- \n’); fprintf(′CONVERSION OF I ORDER REACTION IN NON IDEAL REACTOR \n′) ; fprintf(′ \n′) ; fprintf(′Rate Constant 1/MIN : %12.8f \n′,k) ; fprintf(′Space Time MIN : %12.8f \n′,tau) ; fprintf(′ \n′) ; fprintf(′ \n′) ; fprintf(′IDEAL CSTR - Fracational conersion : %10.4f \n′,xaf_ cstr) ; fprintf(′IDEAL PFR - Fractional conversion : %10.4f \n′,xaf_ pfr) ; fprintf(′TANKS IN SERIES MODEL - Parameter N : %10.4f \n′,n_t) ; fprintf(′ - Fractional conversion : %10.4f \n′,xaf_ tis) ; fprintf(′AXIAL DISPERSION MODEL - Parameter Pe : %10.4f \n′,pe) ; fprintf(′ - Fractional conversion : %10.4f \n′,xaf_ adm) ; fprintf(′SEGREGATED FLOW MODEL - Fractional conversion : %10.4f \n′,xaf_ sfm) ; fprintf(′LAMINAR FLOW MODEL - Fractional conversion : %10.4f \n′,xaf_ lfr) ; fprintf(′ \n′) ; fprintf(′---------------------------------------------------------- \n’); FUNCTION SUBROUTINE: cal_E_theta.m % Subroutine to calculate E versus theta from the impulse tracer test data function E = cal_E_theta(imp_tracer_data) vec_size = size(imp_tracer_data) ; n_data = vec_size(1,2) ; integ_c
= trapez_integral(imp_tracer_data) ;
for i = 1:n_data time = imp_tracer_data(1,i) ; conc = imp_tracer_data(2,i) ; E(1,i) = time ; E(2,i) = conc/integ_c ; % E vs t data end ; FUNCTION SUBROUTINE: trapez_integral.m % Subroutine to evaluate the integral value by Trapezoidal Method function int_val = trapez_integral(xy_data)
www.Ebook777.com
Free ebooks ==> www.ebook777.com 284
Green Chemical Engineering
vec_size = size(xy_data) ; n_data = vec_size(1,2) ; for i = 1:n_data x_val = xy_data(1,i) ; y_val = xy_data(2,i) ; x(i) = x_val ; y(i) = y_val ; end ; int_val = 0 ; for i = 2:n_data x1 = x(i-1) ; x2 = x(i) ; y1 = y(i-1) ; y2 = y(i) ; int_val = int_val + 0.5*(x2 -x1)*(y1+y2) ; end ; FUNCTION SUBROUTINE: cal_mean_var.m % Subroutine to calculate mean and variance from impulse tracer test data function [theta_bar sigma_sqr] = cal_mean_var(imp_tracer_data) vec_size = size(imp_tracer_data) ; n_data = vec_size(1,2) ; integ_c
= trapez_integral(imp_tracer_data) ;
for i = 1:n_data time = imp_tracer_data(1,i) ; conc = imp_tracer_data(2,i) ; thetaE(1,i) = time ; theta2E(1,i) = time ; E(1,i) = time ; E(2,i) = conc/integ_c ; % E vs t data thetaE(2,i) = time*E(2,i) ; % (t*E) vs t data theta2E(2,i) = (time∧2)*E(2,i) ; % (t∧2*E) vs t data end ; integral_E = trapez_integral(E) ; theta_bar = trapez_integral(thetaE) ; integral_tsqr_E = trapez_integral(theta2E) ; sigma_sqr = integral_tsqr_E - (theta_bar)∧2 ; FUNCTION SUBROUTINE: cal_n_tank.m % program to calculate Number of Tanks N of Tanks in Series Model function n_tanks = cal_n_tank(theta_bar,sigma_sqr) n_tanks = (theta_bar∧2)/sigma_sqr ; FUNCTION SUBROUTINE: cal_pe.m % program to calculate Peclet Number Pe
www.Ebook777.com
Free ebooks ==> www.ebook777.com Homogeneous Reactors
285
function pe = cal_pe(theta_bar,sigma_sqr) r = sigma_sqr/(theta_bar∧2) ; pe_o = 2/r ; pe_n = 2/(r + (2/pe_o∧2)*(1-exp(-pe_o))) ; while abs(pe_n - pe_o) > = 0.0001*pe_o pe_o = pe_n ; pe_n = 2/(r + (2/pe_o∧2)*(1-exp(-pe_o))) ; end pe = pe_n ; r_cal = (2/pe) - (2/pe∧2)*(1-exp(-pe)) ; PROGRAM: non_id_dead_bypass.m % Program to detect dead space and bypass in nonideal cstr and estimate % conversion of I order reaction clear all ; % impluse tracer test data imp_tr_data = [ 0 0.05 0.1 0.2 0.3 0.4 0.5 0.8 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0 24.0 26.0 ; 0 3.38 3.34 3.3 3.2 3.13 3.05 3.00 2.74 2.61 2.0 1.54 1.2 0.91 0.71 0.54 0.42 0.32 0.25 0.15 0.09 0.052 0.031 0.02 0.01 0.0] ; k = 0.64 ; % kinetic rate constant in 1/MIN vec_size = size(imp_tr_data) ; n = vec_size(1,2) ; % number of readings [t_b s_s] = cal_mean_var(imp_tr_data); tau = t_b ; E = cal_E_theta(imp_tr_data) ; count = 0 ; for i = 1:n t_val = E(1,i) ; c_val = E(2,i) ; if (t_val ~= 0) && (c_val ~= 0) count = count+1 ; xy_data(count,1) = t_val ; xy_data(count,2) = log(c_val) ; end ; end ; xlabel_s = ′Time - MINS′ ; ylabel_s = ′ln(E)′ ; plot_type = 1 ; coef_vec = lin_plot(xy_data,plot_type,xlabel_s,ylabel_s);
www.Ebook777.com
Free ebooks ==> www.ebook777.com 286
Green Chemical Engineering
s = coef_vec(2) ; I = coef_vec(1) ; gama = exp(I)/(-s) ; beta = gama/((-s)*(t_b)) ; xaf_nideal = (beta*k*tau)/(1+(beta/gama)*k*tau) ; xaf_cstr = (k*tau)/(1+k*tau) ; % display of results fprintf(′---------------------------------------------------------- \n’); fprintf(′CONVERSION OF I ORDER REACTION IN NON IDEAL REACTOR \n′) ; fprintf(′ \n′) ; fprintf(′Rate Constant 1/MIN : %10.4f \n′,k) ; fprintf(′Space Time MIN : %10.4f \n′,tau) ; fprintf(′ \n′) ; fprintf(′IDEAL CSTR - Fracational conersion : %10.4f \n′,xaf_cstr) ; fprintf(′ \n′) ; fprintf(′CSTR WITH DEAD SPACE AND BYPASS - Parameter gama : %10.4f \n′,gama) ; fprintf(′ - Parameter beta : %10.4f \n′,beta); fprintf(′ - Fract.conversion: %10.4f \n′,xaf_ nideal) ; fprintf(′ \n′) ; fprintf(′---------------------------------------------------------- \n’); PROGRAM: seg_flow_II_order.m % Program to calculate conversion of second order reaction in nonideal % reactor - Segregated Flow Reactor & Laminar Flow Reactor clear all % Tracer data imp_tracer_data = [ 0 1 2 3 4 5 6
7
8
9 10 11 12 13 14 ; % t - time in minutes
0 0.4 1.3 2.4 3.8 5.1 5.5 4.5 3.1 1.9 1.1 0.5 0.2 0 0 ] ; % C - Concentration k = 0.05 ; % kinetic rate constant of second order reaction in (M3/ kg.moles)/Min Ca0 = 20 ; % Feed concentration Kg.Moles / M3 ; vec_size = size(imp_tracer_data) ; n_data = vec_size(1,2) ; [theta_bar sigma_sqr] = cal_mean_var(imp_tracer_data) ; tau = theta_bar ; % space time % Ideal PFR
www.Ebook777.com
Free ebooks ==> www.ebook777.com Homogeneous Reactors
287
xaf_pfr = (k*tau*Ca0) /(1+k*tau*Ca0) ; %Ideal CSTR xaf_cstr = 1 - (sqrt(1+4*k*tau*Ca0)-1)/(2*k*tau*Ca0) ; % completely segregated flow model E = cal_E_theta(imp_tracer_data) ; for i = 1:n_data t = E(1,i) ; x_batch = (k*t*Ca0)/(1+k*t*Ca0); x_E(1,i) = t ; x_E(2,i) = x_batch*E(2,i) ; end; xaf_sfm = trapez_integral(x_E) ; % Laminar flow reactor of same size t_min = theta_bar / 2 ; t_max = 10*theta_bar ; for j = 1:100 t = t_min x_batch = xl_E(1,j) xl_E(2,j) end ;
; + (j-1)*(t_max - t_min)/99 ; (k*t*Ca0)/(1+k*t*Ca0); = t ; = x_batch/(t∧3) ;
integral_xl_E = trapez_integral(xl_E) ; xaf_lfr = ((theta_bar∧2)/2)*integral_xl_E ; % display of results fprintf(′---------------------------------------------------------- \n’); fprintf(′CONVERSION OF II ORDER REACTION IN NON IDEAL REACTOR \n′) ; fprintf(′ \n′) ; fprintf(′Rate Constant (Kg.Moles/M3)/MIN : %12.4f \n′,k) ; fprintf(′Space Time MIN : %12.4f \n′,tau) ; fprintf(′ \n′) ; fprintf(′ \n′) ; fprintf(′IDEAL CSTR - Fracational conersion : %10.4f \n′,xaf_cstr) ; fprintf(′IDEAL PFR - Fractional conversion : %10.4f \n′,xaf_pfr) ; fprintf(′SEGREGATED FLOW MODEL - Fractional conversion : %10.4f \n′,xaf_sfm) ; fprintf(′LAMINAR FLOW MODEL - Fractional conversion : %10.4f \n′,xaf_lfr) ; fprintf(′ \n′) ; fprintf(′---------------------------------------------------------- \n’);
www.Ebook777.com
Free ebooks ==> www.ebook777.com
www.Ebook777.com
Free ebooks ==> www.ebook777.com
4 Heterogeneous Reactors Heterogeneous reactors are multiphase reactors in which the reaction medium is a multiphase medium. Heterogeneous reactors are broadly classified as ‘reactors in which multiphase non-catalytic reactions take place’ and ‘reactors in which multiphase catalytic reactions take place’. Principles of multiphase reaction kinetics and design of multiphase reactors are discussed in this chapter.
4.1 Heterogeneous Non-Catalytic Reactors In heterogeneous non-catalytic reactors, the reaction medium is a two-phase medium. The two-phase reaction medium is composed of a gas phase and a solid phase for the reaction between a gaseous reactant and a solid reactant, whereas for the reaction between a gaseous reactant and a liquid reactant the reaction phase is a two-phase gas–liquid medium. The design of heterogeneous non-catalytic reactors for gas–solid reactions and gas–liquid reactions are discussed in this section. 4.1.1 Heterogeneous Gas–Solid Reactions Consider a non-catalytic heterogeneous reaction between a reactant A in the gas phase and a reactant B in the solid phase: A( g ) + bB( s) → Products
Well-known examples are
1. Combustion of carbon
C(s) + O2(g) → CO2
2. Oxidation of zinc sulphide in the production of zinc
2ZnS(s) + 3O2(g) → 2ZnO + 2SO2
3. Reduction of iron oxide in the blast furnace Fe2O 3 (s) + 3CO(g ) ⇔ 2Fe + 3CO 2
289
www.Ebook777.com
Free ebooks ==> www.ebook777.com 290
Green Chemical Engineering
Solid particle (reactant B)
Gaseous molecule A
A A
A
B
A
A
Figure 4.1 A section of gas–solid reactor.
Here, the solid B is a non-catalytic reactant consumed in the reaction and the products are converted solid or gas or both solid and gas. The reactors used for this type of reaction are gas–solid contacting equipment such as a fluidised bed. The solid reactant B is usually the limiting reactant and gaseous reactant A is used in excess quantity. The fractional conversion of B, XB achieved in the reactor determines the performance of the reactor. Any section of the reactor, shown in Figure 4.1, usually has solid particles suspended in a stream of gas containing reactant A. Each one of the solid particles is a segregated element and the conversion of BxB(θ) achieved in a solid particle in a reaction time θ depends on
1. Rate of transfer of A from the bulk of the gas to the surface of the solid (external mass transfer) 2. Rate of diffusion of A through the solid pores (internal mass transfer) 3. Rate of reaction of A in the solid particle (kinetic rate)
Global rate is the rate equation derived by accounting for both the mass transfer rate (external and internal mass transfer) and the kinetic rate. It is the global rate that determines the conversion of B, XB(θ) achieved in a single particle. According to the progressive conversion model (PCM) applicable to porous solid particles, the gaseous molecule of A would diffuse through the pores and react with B, present on the inner surface of the particles. Here the reaction occurs at every point within the solid particle at the same time. The rate of reaction at any point within the solid particle depends on the concentration of A available at that point. This progressive conversion of B in a single solid particle is shown in Figure 4.2. The reaction would occur only on the outer surface of the solid particle if the solid is non-porous and A cannot penetrate into the solid. A model called shrinking core model (SCM) proposed for non-porous solid particles is widely used for the design of gas–solid reactors. The SCM is discussed in detail in the following section.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 291
Heterogeneous Reactors
(a)
(b)
Figure 4.2 Conversion of B in a single solid particle at time θ1 and θ2 (θ2 > θ1) according to the PCM. (a) At time θ1. (b) At time θ2 (>θ1).
4.1.1.1 Shrinking Core Model Consider a spherical solid particle of radius R containing the reactant B; the particle is in contact with a gaseous stream containing the reactant A at concentration CAg. The stoichiometric equation for the reaction between A and B is
A( g ) + bB( s) → Products
The concentration of A, CAg, in the bulk of the gas reactant A is assumed to remain unchanged with time as reactant A is present in excess quantity. Thus, the conversion of solid to product occurs in a constant gas environment. The solid particle is non-porous. So the reaction would occur only on the outer surface of the solid particle. However, the converted solid particle is assumed to be porous. Thus, on complete conversion of B present on the outer layer of a solid particle, a porous product layer would be formed. Reactant A would diffuse through this porous product layer (called ash layer) and react with reactant B present on the surface of the unreacted spherical core lying beneath the product layer. Thus, at any point of time, the spherical particle will have an unreacted core of radius rc surrounded by a product layer as shown in Figure 4.3. With the progress of the reaction, the central unreacted core will shrink in size and hence this model is known as SCM. CAs is the concentration of A on the surface of the solid particle and CAc is the concentration of A on the surface of the unreacted core. The global rate expression is derived by taking into account three rate equations, namely, 1. Rate of transfer of A (r1) from the bulk of the gas to the surface of the particle through the gas film resistance Rg
r1 = k g (CAg − CAs )( 4πR2 ) (kmol/s) (4.1)
where kg is the gas film mass transfer coefficient. 2. Rate of transfer of A (r2) by diffusion through the ash layer resistance R A from the surface of the particle to the surface of the unreacted core
r2 = DA
dC A dr
( 4πrc 2 ) r = rc
(4.2)
where DA is the effective diffusivity of A through the porous ash layer.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 292
Green Chemical Engineering
Ash (product) layer R A
Gas film
B rc
Unreacted core
R CAg
CAg rc
CA
CAg
CAs
CAs
r CA CAc
CAc
R
r=0
R
Figure 4.3 Profile of CA within the single solid particle according to SCM.
3. Rate of disappearance of A (r3) due to reaction on the surface of the unreacted core
r3 = kCAC ( 4πrC2 )
(4.3)
where k is the kinetic rate constant of the first-order reaction. Rr is the resistance to the reaction. Each one of the three rate steps is associated with a resistance and a driving force (difference in concentration CA, across the resistance). The overall rate of transfer of A (global rate) rA may be considered as the rate of flow of A through three resistances connected in series. RG
CAg
1 r1
RA
CAs
2 r2
RR
CAc
3 r3
0
Assuming that the solid particle is in the steady state at any time instant (pseudo-steady state), all the three rates are treated as equal:
rA = r1 = r2 = r3 (4.4)
www.Ebook777.com
Free ebooks ==> www.ebook777.com 293
Heterogeneous Reactors
And the overall resistance R0 is the sum of three resistances:
R0 = RG + R A + Rr (4.5)
As a special case, we may consider that only one of the three resistances is dominating and the corresponding rate step is controlling the overall rate. Accordingly, we consider three cases, namely,
1. Gas film resistance is rate controlling rA = r1 Ro = RG and CAs = CAc = 0
2. Ash layer diffusion is rate controlling rA = r2 R0 = RA and CAg = CAs
(4.6)
(4.7) and CAc = 0
3. Reaction is rate controlling
rA = r3 R0 = Rr
and CAg = CAs = CAc
(4.8)
The rate of disappearance of A rA and the rate of disappearance of B rB are related to each other through the stoichiometric equation as rA =
rB b
(4.9)
Define ρb as the molal density of B (kmol of B/m3) in the solid particle and nB as the number of unreacted moles of B in the solid particle at any time. Then 4 ∗ 3 ρb πrC 3
(4.10)
dnB dr = −( 4πrC2 ) ρB C dθ dθ
(4.11)
nB =
and
rB = −
and
rA = −4πrC2
ρB drC b dθ
www.Ebook777.com
(4.12)
Free ebooks ==> www.ebook777.com 294
Green Chemical Engineering
The fractional conversion of B in the solid particle xB(θ) at any time θ is xB (θ) = 1 −
nB nB0
(4.13)
where nB0 is the initial number of moles of B in the solid particle at the time of start of the reaction 4 nBO = ρB πR3 3
(4.14)
From Equations 4.10, 4.13 and 4.14, we get
r xB = 1 − C R
3
or
rC = (1 − xB )1/3 R
(4.15)
Equation 4.15 relates the fractional conversion xB to the radius rc of the unreacted core. We will derive the equation for calculating fractional conversion xb(θ) for each one of the ratecontrolling steps. 1. Gas film resistance is rate controlling Combining Equations 4.12, 4.1 and 4.6, we get
rA = −
( 4πrC2 )ρB drc = k gCAg ( 4πR2 ) b dθ
Rearranging the above equation and integrating it, we get θ
∫ 0
−ρB dθ = 2 bR k gCAg
rC
∫ r dr 2 C
R
(4.16)
C
and θ=
3 ρB r R 1 − C R 3bk gC Ag
(4.17)
Substituting xb of Equation 4.15 for xB in Equation 4.17, we get θ=
ρB xB R 3bk gC Ag
www.Ebook777.com
(4.18)
Free ebooks ==> www.ebook777.com 295
Heterogeneous Reactors
Substituting xb = 1, we get time for complete conversion of solid particle τ as ρb R 3bk gC Ag
τ=
(4.19)
It may be noted that τ is proportional to R, when gas film resistance controls the overall rate. From Equations 4.18 and 4.19, we have θ = xB τ
(4.20)
2. Ash layer resistance is rate controlling: Combining Equations 4.2, 4.12 and 4.7, we get rA = 4πrC2DA
dCA dr
r = rc
4πrC2ρB drc = − b dθ
(4.21)
The assumption of pseudo-steady state implies that the rate of diffusion of A through the ash layer is a constant that is independent of r, that is, at all values of r.
rA = DA 4πr 2
dC A = constant dr
(4.22)
Rearranging this equation and integrating between r = R and r = rc, we get o
∫
CAg
r dCA = A 4πDA
DACAg
rC
dr
∫r
2
R
r 1 1 = A − 4π rC R
(4.23)
and rA =
4πDACAg 1 1 r − R C
(4.24)
From Equations 4.21 and 4.24, we have
4πrC2 drc 4πDACAg −ρB = b dθ [(1/rC ) − (1/R)]
www.Ebook777.com
(4.25)
Free ebooks ==> www.ebook777.com 296
Green Chemical Engineering
Rearranging the above equation and integrating, we get θ
∫
0
θ=
rC
1 −ρB 1 dθ = rC2 − drc rC R DAC Ag b
∫ R
ρBR2 6bDAC Ag
1 −
(4.26)
2 3 r r 3 C + 2 C R R
(4.27)
Writing the above equation in terms of xB, θ=
ρBR2 1 + 2(1 − XB ) − 3(1 − XB )2/3 6bDAC Ag
(4.28)
or θ=
ρBR2 3 1 − (1 − XB )2/3 − 2XB 6bDAC Ag
(
)
(4.29)
Substituting xB = 1, we get τ for complete conversion of B as τ=
ρBR2 6bDAC Ag
(4.30)
Note that the time for complete conversion τ is proportional to R2 when ash layer resistance controls the overall rate. Combining Equations 4.30 and 4.29, we have
θ = 3 1 − (1 − XB )2/3 − 2XB τ
(
)
(4.31)
3. Reaction is rate controlling
Combining Equations 4.3, 4.8 and 4.12, we get
4πrC2 drc rA = 4πrC2kC Ag = −ρB b dθ
(4.32)
Rearranging the above equation and integrating, we get
−ρB b
rc
∫ R
θ
∫
drc = kC Ag dθ 0
www.Ebook777.com
Free ebooks ==> www.ebook777.com 297
Heterogeneous Reactors
and θ=
ρB rc R 1 − R bkC Ag
(4.33)
Writing the above equation in terms of XB, we get θ=
ρBR (1 − (1 − xB )1/3 ) bkCAg
(4.34)
Substituting xb = 1, we get time τ for complete conversion of B, as τ=
ρB R bkC Ag
(4.35)
We find that the time for complete conversion τ is proportional to R and θ = 1 − (1 − XB )1/3 τ
(4.36)
The results obtained using the SCM for the three rate-controlling mechanisms are summarised and presented in Table 4.1. These equations are used extensively in the design of a gas–solid reaction. A plot of conversion versus fractional reaction time θ/τ is shown in Figure 4.4. It may be noted from this plot that the fractional conversion of solid XB is the least when the gas film resistance controls the overall rate. This is because the gas film resistance limits the amount of A that would be available at the reaction site in the solid particle for conversion of B. The plots of XB versus θ/τ for the ash layer diffusion controlling mechanism and the chemical reaction rate-controlling mechanism intersect with each other at (θ/τ = 0.5) and XB = (7/8). Conversion is higher when the ash layer diffusion controls the
Table 4.1 Summary of the Results of the Shrinking Core Model θ τ
Rate-Controlling Mechanism
Time for Complete Conversion (τ)
Gas film resistance
ρB R 3bK g CAg
XB
Ash layer diffusion
ρB R2 6bDACAg
3 1 − (1 − XB )2/3 − 2XB
Reaction
ρB R bkCAg
1 − (1 − XB )1/3
(
XB(θ) XB =
)
θ τ
No explicit equation for XB(θ) θ XB = 1 − 1 − τ
www.Ebook777.com
3
Free ebooks ==> www.ebook777.com 298
Green Chemical Engineering
Chemical reaction resistance controlling
1 7/8
Gas film resistance controlling
Ash layer diffusion controlling xB
0.5
θ τ
1
0.5
Figure 4.4 XB versus θ/τ plot for different rate-controlling mechanisms.
overall rate for θ/τ 0.5. Problem 4.1 A sample containing a mixture of solid particles of three different sizes 4, 2 and 1 mm is kept in a constant environment oven for 2 h. Under these conditions, 4 mm particles are 24.9% converted, 2 mm particles are 46.7% converted and 1 mm particles are 80% converted.
a. What mechanism is rate controlling? b. What is the time required for complete conversion of all the solid particles in the sample?
a. For the gas film resistance-controlling mechanism, time θ required for conversion xB can be expressed as
θ = k1RxB
as ταR
Similarly, for the ash layer diffusion controlling mechanism
θ = k 2 R2 [3(1 − (1 − xB )2/3 ) − 2xB ] as ταR2
And for the reaction rate-controlling mechanism
θ = k 3 R[(1 − (1 − xB )1/3 ] as ταR
www.Ebook777.com
Free ebooks ==> www.ebook777.com 299
Heterogeneous Reactors
Using the data given in the problem, the values of coefficients k1, k2 and k3 are calculated and checked for consistency. These values are given in the table below.
Data θ = 2 h R = 4 mm xB = 0.249 θ = 2 h R = 2 mm xB = 0.467 θ = 2 h R = 1 mm xB = 0.80
Gas Film Resistance k1
Ash Layer Diffusion k2
Reaction Rate k3
2
5.353
5.492
2.14
5.328
5.285
2.5
5.348
4.817
The values of k2 for all the three data points are consistent. It may be concluded that the ash layer diffusion is rate controlling. b. The sample is a mixture of particles of three different sizes: 4, 2 and 1 mm. If in a given time, 4 mm particles are completely converted, then the particles of size smaller than 4 mm will also be converted completely. As ash layer diffusion is rate controlling, the time for complete conversion of 4 mm particle is τ = k2 R 2
The average value of k2 = 5.343. So
τ = 5.343(4)2 = 85.5 h
So, the oven has to be kept in operation for 85.5 h for all the particles in the sample to be completely converted. 4.1.1.2 Reactors for Gas–Solid Reactions Gas–solid reactions are carried out either in a batch reactor or in a continuous-flow reactor. Batch reactors are used primarily for studying the kinetics of gas–solid reactions and are rarely used in large-scale industrial production. In batch reactors, the solid particles kept in a vessel are treated in a constant environment with a stream of gas passing through the vessel, for a period of time required to achieve the specified conversion of solid. The batch time θB required to achieve the specified conversion of solid XB for a particular rate-controlling mechanism is calculated using an appropriate equation listed in Table 4.1. If all the particles are of uniform size and the time τ for complete conversion of solid particles of a particular size is given (obtained from batch experiments), then the calculation of batch time θB required for a specified conversion XB is straightforward. If the solid feed is a mixture of particles of different sizes, then the conversion achieved in a given batch time will not be the same for all the particles but would be different for different sizes of particles. The average conversion XB of the particles (for a given batch
www.Ebook777.com
Free ebooks ==> www.ebook777.com 300
Green Chemical Engineering
Table 4.2 Average Conversion XB of Solid Feed Containing Particles of Different Sizes Time for Complete Conversion a Mechanism I c III
θ τ
X bd
θB τ1
XB1
θB τ2
XB2
Particle Size Ri
Weight Fraction ωi
R1
ω1
R τ1 = τ 0 1 R0
R τ1 = τ 0 1 R0
2
1
R2
ω2
R τ2 = τ0 2 R0
R τ2 = τ0 2 R0
2
2 3
R3
ω3
R τ3 = τ0 3 R0
R τ3 = τ0 3 R0
2
θB τ3
XB3
4
R4
ω4
R τ 4 = τ0 4 R0
R τ 4 = τ0 4 R0
2
θB τ4
XB4
5
R5
ω5
R τ5 = τ0 5 R0
R τ5 = τ0 5 R0
2
θB τ5
XB5
S. No.
Mechanism IIb
…
…
…
…
…
…
…
…
…
…
…
…
…
…
m
Rm
ωm
R τm = τ0 m R0
θB τ5
XBm
a b c d
R τm = τ0 m R0
2
Mechanism I: Gas film resistance controlling. Mechanism II: Ash layer diffusion controlling. Mechanism III: Chemical reaction controlling. XB is calculated for the value of (θB/τ) using the appropriate equation listed in Table 4.1.
time θB) can be calculated knowing the particle size distribution and the time τ0 for the complete conversion of particles of a particular size R0. A sample of this calculation is shown in Table 4.2. n
Average conversion xb =
∑w x
(4.37)
i Bi
i =1
Continuous-flow reactors used for gas–solid reactions are essentially gas–solid contacting equipment through which both solid particles and the gaseous stream are passed continuously in counter-flow or cross-flow directions. 4.1.1.2.1 Cross-Flow Conveyer-Type Reactor In the cross-flow conveyor-type reactors (Figure 4.5), the solid particles are fed continuously from a hopper on to a conveyor belt and a gas is passed in the cross-flow direction. This type of reactor is used for the oxidation of metallic ores in metallurgical industries.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 301
Heterogeneous Reactors
Solid feed
Gas stream out
D L
Gas stream in Solid product Figure 4.5 Cross-flow converter-type reactor.
All the solid particles are treated in a constant environment for the same duration of time θ, which is the residence time of the solid particles in the reactor. θ is also the time taken by the conveyor belt to move from the first drum to the second drum.
θ=
L πDN
(4.38)
where L is the distance between the two drums, D is the diameter of the drum and N is the speed of revolution of the drum in rpm. The calculation of conversion XB for a given θ is the same as the calculation of conversion in a batch reactor for a specified batch time θ. Conversely, for a specified conversion XB, θ required to achieve the conversion can be calculated. Problem 4.2 A moving grate conveyer-type reactor is used for roasting iron ore particles in the presence of air. The feed to the reactor consists of 20% (by weight) of 1 mm particle, 30% of 2 mm particle, 30% of 4 mm particle and 20% of 6 mm particle. Conveyer speed is adjusted so that the solid particles reside in the reactor for a time duration of 10 min. SCM holds good and the reaction is rate controlling. The time taken for complete conversion of 4 mm particles is 4 h. Calculate
a. Mean conversion of solids b. Mean conversion of solids if the conveyer speed is halved
Residence time of solid particles θ = 10 min = 0.1677 h As the reaction is rate controlling, the time τ for complete conversion is proportional to R, ταR and
θ = 1 − (1 − XB )1/3 τ
θ or XB = 1 − 1 − τ
3
www.Ebook777.com
Free ebooks ==> www.ebook777.com 302
Green Chemical Engineering
Construct the following table.
S. No. 1 2 3 4
Time for Complete Conversion
Particle Size Ri (mm)
Weight Fraction wi
R τ i = i τ 0 (h) R0
θ τ
R1 = 1 R2 = 2 R3 = 4 R4 = 6
w1 = 0.2 w2 = 0.3 w3 = 0.3 w4 = 0.2
τ1 = 1 τ2 = 2 τ3 = 4 τ4 = 6
0.1667 0.0834 0.0417 0.0278
Conversion xBi xB1 = 0.428 xB2 = 0.230 xB3 = 0.120 xB4 = 0.081
Mean conversion 4
xB =
∑x W Bi
i
i =1
= w1xB1 + w2 xB 2 + w3 xB 3 + w4 xB 4 = 0.2054 = 20.54%
b. If the conveyer speed is halved, the residence time of solid particles in the reactor is doubled, That is, θ = 20 min = 0.3333 h. Reconstruct the table for θ = 0.333 h.
S. No. 1 2 3 4
Time for Complete Conversion
Particle Size Ri (mm)
Weight Fraction wi
R τ i = i τ o (h) RO
θ τ
R1 = 1 R2 = 2 R3 = 4 R4 = 6
w1 = 0.2 w2 = 0.3 w3 = 0.3 w4 = 0.2
τ1 = 1 τ2 = 2 τ3 = 4 τ4 = 6
0.333 0.1667 0.0834 0.0556
Conversion xBi xB1 = 0.703 xB2 = 0.421 xB3 = 0.230 xB4 = 0.158
Mean conversion 4
xB =
∑x W Bi
i
i =1
= 0.3675
= 36.75%
Note: Refer to MATLAB program: cal_xb_mean.m 4.1.1.2.2 Rotary Tubular Reactor The rotary tubular reactor is similar to that of the rotary dryer used for drying of freeflowing granular solids (Figure 4.6). The reactor has a long tubular drum, which is rotated at a constant speed.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 303
Heterogeneous Reactors
Solid feed (m, kg/s)
Flights
Solid particles Gas stream out
Gas stream in
Solid product
Figure 4.6 Rotary tubular reactor.
The tubular drum is mounted in a slightly tilted position. The solid is fed from the top end (of the tube) and the gaseous stream is passed from the bottom end in the counter-flow direction. Owing to the rotation of the drum, the flights fixed on the inner surface of the tube carry the solid particulate upwards and sprinkle them into the gaseous stream, facilitating thorough contact between the gas and the solid. The reaction is assumed to take place in a constant gas environment. The time of reaction θ between a solid particle and the gas is the time of residence of the solid in the reactor. Conversion of B, XB(θ) achieved in a solid particle is a function of θ and the xb(θ) is calculated using the appropriate equation listed in Table 4.1. If all the particles are of uniform size and all of them reside in the reactor for the same duration of time θ, then the net conversion of solid is xb (θ ). This is the case if all the solid particles move through the reactor without mixing. However, the solid particles are likely to mix or even bypass the main stream, resulting in a non-uniform distribution of residence time of solid particles in the reactor. If E(θ) is the exit age distribution of solid particles obtained by conducting a tracer test on the reactor, then the average conversion of B, xB , in the solid is calculated using ∞
∫
xb = xb (θ) E(θ) dθ
0
(4.39)
Problem 4.3 The reaction between free-flowing granular solid particles of 2 mm diameter and a gas stream is carried out in a rotary tubular reactor (somewhat like a rotary drier) in constant gas environment. SCM holds good and the reaction is rate controlling. Under this condition, it takes 1 h for complete conversion of 2 mm particles. Residence time distribution
www.Ebook777.com
Free ebooks ==> www.ebook777.com 304
Green Chemical Engineering
of solid particles in the reactor is obtained by conducting a tracer test in which a fixed quantity of marked solid particles (tracer) is added at the reactor inlet and the number of marked solid particles coming out of the vessel at different time intervals are recorded. These recorded values are given in the below table. Time (θ) (min) Number of tracer particles n(θ)
0 0
4 1
8 8
12 20
16 50
20 100
24 50
28 24
32 10
Calculate the average conversion of solids in the reactor. Time for complete conversion of 2 mm particles τ = 1 h = 60 min. Mean conversion of solid particles x B is ∞
xB =
∫ X (θ)E(θ) dθ B
0
where for reaction rate-controlling mechanism θ XB (θ) = 1 − 1 − τ
3
and E(θ) =
n(θ) ∞
∫ n(θ) dθ 0
A plot of n(θ) versus θ is shown in Figure P4.3. 100
Count of tracer particles n(θ)
90 80 70 60 50
40 30 20
10 0
0
10
20 30 Time θ (min)
40
Figure P4.3 Response of impulse tracer test on solids flow in a rotary tubular reactor.
www.Ebook777.com
50
36 5
40 1
44 0
Free ebooks ==> www.ebook777.com 305
Heterogeneous Reactors
These calculations are shown in the table below.
θ
n(θ)
0 4 8 12 16 20 24 28 32 36 40 44 Integral values
0 1 8 20 50 100 50 24 10 5 1 0 ∞
∫
E(θ)
θE(θ)
0 0.930 × 10−3 7.43 × 10−3 18.59 × 10−3 46.47 × 10−3 93.19 × 10−3 46.47 × 10−3 22.30 × 10−3 9.29 × 10−3 4.65 × 10−3 0.930 × 10−3 0 —
0 0.00372 0.05944 0.2231 0.7435 1.864 1.115 0.6244 0.2973 0.1674 0.0372 0 ∞
θ =
n(θ)dθ
∫
θ τ
XB(θ)
0 0.0667 0.1333 0.20 0.2667 0.3333 0.40 0.4667 0.5333 0.60 0.6666 0.7333 —
0 0.187 0.349 0.488 0.606 0.704 0.784 0.848 0.898 0.936 0.963 0.981 —
θE(θ)dθ
XB(θ)E(θ)dθ 0 0.174 × 10−3 2.593 × 10−3 9.072 × 10−3 28.16 × 10−3 65.60 × 10−3 36.43 × 10−3 18.91 × 10−3 8.34 × 10−3 4.35 × 10−3 0.8956 × 10−3 0 ∞
xB =
0
0
= 20.54
= 1076
∫ x (θ)E(θ) B
0
= 3.28
Integral terms in the equations are calculated numerically using the trapezoidal rule: ∞
4
∫ n(θ)dθ = 2 [(0 + 0) + 2(1 + 8 + 20 + 50 + 100 + 50 + 24 + 10 + 5 + 1)] 0
= 1076 ∞
θ=
4
∫ θE(θ)dθ = 2 [(0 + 0) + 2(0.00372 + 0.05944 + + 0.0372)] 0
= 20.54 min ∞
xB =
4
∫ x (θ)E(θ)dθ = 2 (0 + 0) + 2(0.174 + 2.593 + + 0.8956) × 10 B
−3
0
= 0.698 = 69.8%
Note: Refer the MATLAB program: cal_xb_mean2.m 4.1.1.2.3 Fluidised Bed Reactor A fluidised bed reactor, shown in Figure 4.7, is used for carrying out gas–solid reactions involving solid particles of size less than 1000 µm. Solid particles are fed continuously at a rate of ms, kg/s, into the fluidised bed, in which the particles are fluidised by the gas stream passing through the bed at a superficial velocity greater than the minimum fluidisation
www.Ebook777.com
Free ebooks ==> www.ebook777.com 306
Green Chemical Engineering
Solid feed (m, kg/s) Gas stream outlet
Solid product (m, kg/s)
Gas stream inlet Figure 4.7 Fluidised bed reactor.
velocity. The reaction between the solid and the gas is assumed to take place in a constant environment. The mean residence time θ of the solid particles in the bed is θ=
Ms ms
(4.40)
where Ms is the mass hold-up (in kg) of the solid particles in the bed. Solid particles are assumed to be in a perfectly mixed state and the exit age distribution E(θ) of the solid particle is e −(θ/θ ) E(θ) = θ
(4.41)
This is the same as the E(θ) for an ideal CSTR, in which the fluid is assumed to be in a perfectly mixed state. The average conversion of B, xB , in the reactor is ∞
∫
xB = xb (θ) E(θ) dθ =
0
∞
e − ( θ/ θ ) X B (θ ) dθ θ 0
∫
(4.42)
The appropriate equation for XB(θ) listed in Table 4.1 is substituted into Equation 4.42 to calculate xb . As xb(θ) = 1 for θ ≥ τ (time for complete conversion), the Equation 4.42 can be rewritten as τ
e − ( θ/ θ ) xb = XB (θ) dθ + θ 0
∫
τ
1 XB (θ) e −(θ/θ )dθ + = θ
∫ 0
∞
e −(θ/θ ) XB (θ) dθ θ τ
∫ ∞
∫ τ
e − ( θ/ θ ) dθ θ
(4.43)
www.Ebook777.com
Free ebooks ==> www.ebook777.com 307
Heterogeneous Reactors
and finally τ
1 xb = XB (θ)e −(θ/θ )dθ + e −( τ/θ ) θ
∫
0
(4.44)
In the following section, analytical equations for xB are derived for the gas–solid reaction mechanism in which (a) gas film resistance is rate controlling and (b) the reaction is rate controlling. a. Gas film resistance is rate controlling In this case, xb (θ) = θ/τ and τ
τ
∫
XB (θ) e −(θ/θ )dθ =
0
θ
∫ τ e
− ( θ/ θ )
dθ
(4.45)
0
τ
1 = θ e −(θ/θ ) dθ τ
∫
0
=
(4.46)
θ θ − e −( τ/θ ) τ + θ τ
(
)
(4.47)
Substituting Equation 4.47 into Equation 4.44, we get xB =
(
)
θ 1 − e − ( τ /θ ) τ
(4.48)
b. Reaction is rate controlling
In this case, xb (θ) = 1 − 1 −
θ τ
3
2
and τ
∫ x (θ)e B
3
θ θ θ xb (θ) = 3 − 3 + τ τ τ
0
τ
− ( θ/ θ )
3 3 dθ = θe −(θ/θ )dθ − 2 τ τ
∫ 0
τ
∫θ e
2 − ( θ/ θ )
0
(4.49)
1 dθ + 3 τ
τ
∫θ e
3 − ( θ/ θ )
0
dθ
(4.50)
Evaluating the integral terms in Equations 4.50, we get τ
∫ θe 0
− ( θ/ θ )
(
)
dθ = θ θ − e −( τ/θ ) τ + θ
(4.51)
www.Ebook777.com
Free ebooks ==> www.ebook777.com 308
Green Chemical Engineering
Table 4.3 Fractional Conversion xB of Solids in Gas–Solid Fluidised Bed Reactor Fractional Conversion of Solid xb
Rate-Controlling Mechanism Gas film resistance
xb =
Ash layer diffusion
θ (1 − e −( τ/θ ) ) τ
xb is obtained by numerical integration xb = e −( τ /θ ) +
Reaction
2
3
θ θ θ x b = 3 − 6 + 6 1 − e − ( τ /θ ) τ τ τ
(
1 θ
∫ x (θ)e b
−(θ/ θ )
dθ
)
Note: θ = mean residence time of solid particles; τ = time for complete conversion. τ
∫θ e
2 − ( θ/ θ )
(
0
τ
∫θ e
3 − ( θ/ θ )
)
dθ = θ 2θ 2 − e −( τ/θ ) τ 2 + 2τθ + 2θ 2
(4.52)
(
)
dθ = θ 6θ 3 − e −( τ/θ ) τ 3 + 3τ 2θ + 6τθ 2 + 6θ 3
0
(4.53)
Combining Equations 4.51, 4.52, 4.53, 4.44 and 4.50, we get 2
3
(
θ θ θ x b = 3 − 6 + 6 1 − e − ( τ /θ ) τ τ τ
)
(4.54)
The analytical equations for xb derived in this section are summarised and listed in Table 4.3. The equations listed in Table 4.3 are valid for solid particles that are of uniform size. However, for a mixture of solid particles of different sizes, xb can be calculated using the method illustrated in Table 4.2. Problem 4.4 Oxidation of iron ore particles in the presence of air is carried out in a fluidised bed reactor. Solids are fed to the reactor at the rate of 10 kg/min. Mass hold-up of solid particles in the reactor is 300 kg. Feed consists of 20% (by weight) of 1 mm particles, 30% of 1.5 mm particles, 30% of 2 mm particles and 20% of 3 mm particles. SCM holds good and the reaction is rate controlling. The time for complete conversion of 3 mm particles is 3 h. Calculate the mean conversion of solids in the fluidised bed reactor. As the reaction is rate controlling, the time for complete conversion τ is proportional to size R. ταR. It is given that time τ0 for complete conversion of R0 = 3 mm particles is 3 h.
R R τ = i τO = 3 3 RO
www.Ebook777.com
Free ebooks ==> www.ebook777.com 309
Heterogeneous Reactors
The mean residence time θ is θ=
( Mass hold-up) 300 MS = = = 30 min = 0.5 h mS ( Mass flow rate) 10
The equation for conversion XB (θ ) is 2
3
(
θ θ θ XB (θ) = 3 − 6 + 6 1 − e − τ/θ τ τ τ
)
Construct the table shown below: Time for Complete Conversion
S. No.
Particle Size Ri (mm)
Weight Fraction wi
R τ i = i τO (h) RO
θ τ
1 2 3 4
R1 = 1 R2 = 1.5 R3 = 2 R4 = 3
w1 = 0.2 w2 = 0.3 w3 = 0.3 w4 = 0.2
τ1 = 1 τ2 = 1.5 τ3 = 2 τ4 = 3
0.5 0.3333 0.25 0.1667
Conversion xBi xB1 = 0.648 xB2 = 0.544 xB3 = 0.467 xB4 = 0.361
Mean conversion 4
xB =
∑x W Bi
i
i =1
= w1xB1 + w2 xB 2 + w3 xB 3 + w4 xB 4 = 0.5051 = 50.51%
Note: Refer MATLAB program: cal_xb_mean3.m 4.1.1.2.4 Moving Bed Reactor The counter-flow moving bed reactor is a type of gas–solid reactor in which the solid particles move downward from the top to the bottom of the bed and the gas stream flows upward from the bottom to the top. Vertical kilns and transport reactors are examples of a moving bed reactor. A schematic diagram of the moving bed reactor is shown in Figure 4.8. Both solid and gas phases are in plug flow. All the solid particles move at a uniform velocity. Let dθ be the time taken by solid particles to move a distance dz through the bed. Then dθ =
∈S ρSSdz Solids hold-upin dz = ms Solids flow rate
www.Ebook777.com
(4.55)
Free ebooks ==> www.ebook777.com 310
Green Chemical Engineering
CAg = CAf Gas out
Solids in XB = 0
Z
XB
CAg
L
S Solids out (XB = XB0)
Gas in CAg = CA0 Figure 4.8 Counter-flow moving bed reactor.
where s: area of cross section of the bed ∈s: fractional solids hold-up of the bed (fraction of the bed volume occupied by solids) ρs: density of solid particles ms: mass flow rate of solid in kg/s From Equation 4.55,
dθ ∈S ρSS = dz ms
(4.56)
Fresh unreacted solid particles enter the bed and xB0 is the final conversion of B in the solid particles leaving the bed. CA0 and CAf are the concentrations of A in the inlet and the exit gas stream. At any distance Z from the solids inlet, gas and solid are assumed to have attained steady state instantaneously and hence the concentration of A, CAg, in the gas stream and the conversion xb of B in the solid do not change with time. Taking a steady-state balance of moles of A and moles of B between the position Z and the solids outlet, we get (VgS)(CAO − CAg ) =
1 ms ρB ( xBO − xB ) b ρs
(4.57)
where vg = superficial velocity of the gas ρb = molal density of reactant B in the solid = (ρs/MB); MB= molecular weight of reactant B b = stoichiometric coefficient
www.Ebook777.com
Free ebooks ==> www.ebook777.com 311
Heterogeneous Reactors
Rearranging Equation 4.57, we get CAg = CAO −
ms ( xBO − xB ) bSVg MB
(4.58)
Let dxB be the incremental change in conversion of B as the solid moves through a distance dz in the reactor, then dxB dx dθ = B dz dθ dz
(4.59)
dxB/dz is calculated for the three rate-controlling mechanisms using the equation listed in Table 4.1 as follows:
a. Gas film resistance is rate controlling
dxB 1 3bk gC Ag = = dθ τ ρBR
(4.60)
3bMBε sSk gC Ag dxB = dz ms R
(4.61)
and
b. Ash layer diffusion is rate controlling
3bCAg DA dxb (1 − xb )(1/3) (1 − xb )(1/3) = = dθ ρb R2 1 − (1 − xb )(1/3) 2τ 1 − (1 − xb )(1/3 )
(4.62)
dxb 3bMb ∈S S (1 − xb )(1/3) = 2 (1/3) C Ag DA dz R mS 1 − (1 − xb )
(4.63)
and
c. Reaction is rate controlling
3bkCAg (1 − xb )2/3 dxb 3(1 − xb )(2/3) = = dz τ ρb R
(4.64)
dxb 3bMb ∈S S = (1 − xb )(2/3) kC Ag dz RmS
(4.65)
and
www.Ebook777.com
Free ebooks ==> www.ebook777.com 312
Green Chemical Engineering
Table 4.4 dz/dxb for the Moving Bed Reactor Rate-controlling mechanism
dz = f ( xB ) dxB
Gas film resistance
f ( xB ) =
KR k g CAg
f ( xb ) =
(1/ 3) kR2 1 − (1 − xb ) DACAg (1 − xb )(1/3)
f ( xb ) =
kR kCAg
Ash layer diffusion
Reaction
1 (2/ 3 ) 1 ( ) − x b
Note: k = ms/3bMb ∈SS.
The equation for dz/dxb, which is the inverse of dxb/dz derived for the three rate-controlling mechanisms, is listed in Table 4.4. The equations for dZ/dxb listed in Table 4.4 are used for calculating the length L of the bed required to achieve a specified conversion xb0. dZ = f (XB ) dxb
(4.66)
Integrating this equation L
∫
xB 0
dZ =
0
∫ f (X ) dx B
(4.67)
B
0
Finally, the design equation for calculating the length L of the moving bed reactor is XB 0
L=
∫ 0
f (XB )dxB
(4.68)
L is calculated by numerical integration of Equation 4.68. For any value of xB, 0 www.ebook777.com 314
Green Chemical Engineering
The height of the moving bed reactor z is XB 0
z=
∫
f (XB ) dxB
0
where
f (XB ) =
K =
mS ( xBO − XB ) bSυ g MB
Volumetric gas flowrate q Gas velocity υ g = = A Cross-sectional area
S=
π 2 π 2 D = (1) = 0.78532 m 2 4 4
q = 200 m 3/min = 3.33 m 3/s
υg =
3.33 = 4.245 m/s 0.7853
mS = 50 kg/ min = 0.8333 kg/s
K =
(0.8333) mS = = 4.913 × 10 −3 3bSε s MB (3)(1)(120)(0.6)(0.7853) f (XB ) =
f (XB ) =
KR 2 1 − (1 − XB )1/3 DAC Ag (1 − XB )1/3
( 4.913 × 10 −3 )(5.0 × 10 −3 )2 1 − (1 − XB )1/3 (0.4039) 1 − (1 − XB )1/3 (1 − X )1/3 = C (1 − X )1/3 (3.041 × 10 −7 )C Ag B Ag B
mS 3bSε s MB
C Ag = C AO −
KR 2 1 − (1 − XB )1/3 DAC Ag (1 − XB )1/3
C Ag = C AO −
C AO =
mS ( xBO − XB ) bSυ g MB
(0.2)(1.013 × 10 5 ) PAO = = 4.659 × 10 −3 kmol/m 3 (8314)(273 + 250) RT
mS (0.8333) = = 2.083 × 10 −3 bSυ g MB (1)(0.7853)( 4.245)(120)
C Ag = ( 4.659 × 10 −3 ) − (2.083 × 10 −3 )(0.6 − XB )
www.Ebook777.com
Free ebooks ==> www.ebook777.com 315
Heterogeneous Reactors
C Ag = (3.409 + 2.083XB ) × 10 −3
Substituting the equation for CAg in f(XB)
f (XB ) =
1 − (1 − XB )1/3 ( 403.9) (3.409 + 2.083XB ) (1 − XB )1/3
The height of the tower is calculated by numerical integration of z = is illustrated in the table given below. XB 0 0.05 0.1 0.15 0.20 0.25 0.30
f(XB)
XB
f(XB)
0 1.982 3.992 6.043 8.154 10.346 12.643
0.35 0.40 0.45 0.50 0.55 0.60 –
15.077 17.677 20.496 23.595 27.051 30.974 –
∫
xBO
0
f (XB ) dxB . This
Using the trapezoidal rule 0.6
z=
∫ f (X ) dx B
0
B
=
0.05 [(0 + 30.974) + 2(1.982 + 3.992 + + 27.051)] 2
= 0.025(30.974 + 2(147.06))
Tower height = 8.13 m Note: Refer the MATLAB program: mbr_dsgn.m Problem 4.6 Repeat the design of the moving bed reactor (Problem 4.5) assuming that the reaction is rate controlling. The reaction is rate controlling. So τ=
ρB R bkC Ag
Using the batch experiment data τ = 8 h = 28,800 s
R = 2.5 mm = 2.5 × 10−3 m
ρB = 39.17 kmol/m3
CAg = 4.659 × 10−3 kmol/m3
www.Ebook777.com
Free ebooks ==> www.ebook777.com 316
Green Chemical Engineering
b = 1 k =
ρB R (39.17 )(2.5 × 10 −3 ) = (1)( 4.659 × 10 −3 )(28, 800) bτC Ag
k = 7.30 × 10−4 s−1 The height of the moving bed reactor z is 0.6
∫ f (X ) dx
z=
B
B
0
f (XB ) =
KR 1 kC Ag (1 − XB )2/3
where
K =
C Ag = C AO −
mS ( xBO − XB ) bSυ g MB
C Ag = (3.409 + 2.083XB ) × 10 −3
mS = 4.913 × 10 −3 3bMB ε SS
f (XB ) =
1 ( 4.913 × 10 −3 )(5.0 × 10 −3 ) (7.30 × 10 −4 )(3.409 + 2.083XB ) (1 − XB )2/3
f (XB ) =
1 (33.65) (3.409 + 2.083XB ) (1 − XB )2/3
The height of the tower is calculated by numerical integration of z = shown in the table below.
XB 0 0.05 0.1 0.15 0.20 0.25 0.30
f(XB)
XB
f(XB)
9.871 9.912 9.980 10.077 10.207 10.372 10.580
0.35 0.40 0.45 0.50 0.55 0.60
10.836 11.150 11.534 12.00 12.580 13.304
www.Ebook777.com
∫
xBO
0
f (XB ) dxB . This is
Free ebooks ==> www.ebook777.com 317
Heterogeneous Reactors
Using the trapezoidal rule 0.6
z=
∫ f (X )dx B
0
B
=
0.05 [(9.871 + 13.304) + 2(9.912 + 9.980 + + 12.580)] 2
= 0.025(23.175 + 2(119.23))
Tower height = 6.54 m 4.1.2 Heterogeneous Gas–Liquid Reactions Consider a non-catalytic heterogeneous reaction between a reactant A in the gas phase and a reactant B in the liquid phase.
A(g) + bB(l) → Products Typical examples of gas–liquid reactions are
1. CO2(g) + 2NaOH(l) → Na2CO3(l) + H2O(l) 2. 2NH3(g) + H2SO4(l) → (NH4)2SO4(l) 3. NO2(g) + H2O(l) → HNO3 Gas–liquid contacting equipments (such as packed towers) are used for carrying out gas–liquid reactions. The schematic diagram of a packed bed reactor is shown in Figure 4.9. This reactor is similar to the packed bed used for gas–liquid absorption. Liquid containing reactant B is passed from the top to the bottom of the bed packed with packing material such as ceramic raschig rings or berl saddle. Gaseous stream containing reactant A is passed through the tower from the bottom to the top. At any location within the reactor, gas and liquid are in contact with each other and are assumed to have attained steady state instantaneously. It means that the partial pressure PA of A in the gas
Liquid in CA0 = 0 CB0
Gas in (PA0)
(PAf) Gas out
CAf, CBf Liquid out
Figure 4.9 Packed bed gas–liquid reactor.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 318
Green Chemical Engineering
Gas phase
Gas film
Liquid film
Liquid phase Gas–liquid interphase
PA
CBb PAi CAi CBi
yG
CAb
yL
Figure 4.10 Gas–liquid interfacial diagram.
stream and the concentration CBb of B in the liquid stream do not change with time at any location within the packed bed reactor. The interfacial diagram showing the concentration profiles of A and B across the gas–liquid interphase at some location in the reactor is shown in Figure 4.10. Reactant A in the bulk of the gas phase at a partial pressure PA would be moving to the gas–liquid interphase through a resistance that is confined to a gas film of thickness yG adjacent to the interphase. The flux of A in the gas phase is
N AG = kG (PA − PAi )
(4.69)
where kG is the gas side mass transfer coefficient and PAi is the partial pressure of A in the gas at the interface. According to the film theory kG =
DAG yG
(4.70)
where DAg is diffusivity of A in the gas. Reactant A on reaching the interphase would dissolve in the liquid phase and attain a concentration CAi at the interphase, which is equal to the equilibrium concentration corresponding to PAi. Assuming Henry’s law to hold good
PAi = HACAi (4.71)
where HA is Henry’s law constant. Similarly, reactant B that is present in the bulk liquid phase at a concentration CBb would be moving to the interphase through a liquid film of thickness yL and attain a concentration CBi at the interphase. The flux of B in the liquid phase is
NBL = kBL (CBb − CBi) (4.72)
www.Ebook777.com
Free ebooks ==> www.ebook777.com 319
Heterogeneous Reactors
where kBL is the liquid side mass transfer coefficient of B and kBL =
DBL yL
(4.73)
where DBL is the diffusivity of B in the liquid phase. Reactant A that is dissolved in the liquid at the interphase would be diffusing through the liquid film and the flux NAL of A in the liquid film is governed by Fick’s law N AL = −DAL
dCA dy
(4.74)
where DAL: diffusivity of A in the liquid phase CA: concentration of A in the liquid film at a distance y from the interphase According to film theory, the mass transfer coefficient k AL of A in the liquid phase is k AL =
DAL yL
(4.75)
Reactant A, while diffusing through the liquid film, will simultaneously react with B present in the liquid film. Taking the moles of B present in the liquid to be in excess compared to the moles of A dissolved in the liquid, the reaction may be treated as a pseudofirst order and the rate (−rA) of disappearance of A due to the reaction is (−rA) = kCA (kmol/s ⋅ m3) (4.76) where k = reaction rate constant. The net rate of flow of A through the liquid film is controlled by both the mass transfer rate (diffusion) and the reaction rate. As both mass transfer (diffusion) and reaction occur simultaneously (not sequentially), the resistance to mass transfer (R1) and the resistance to reaction (R2) are acting parallel to each other as shown in Figure 4.11. As the two resistances are parallel to each other, it is the lowest resistance that controls the overall rate. Thus, for slow reaction (k → 0), the mass transfer rate dominates the
R 1=
1 kAL
R1 = Resistance to diffusion R2 = Resistance to reaction
R1 CAi
R2
CAb
CAb = Concentration of ‘A’ in the bulk liquid
R2 = 1 k Figure 4.11 Parallel resistances in liquid phase.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 320
Green Chemical Engineering
overall reaction rate (global rate), and for fast reactions (kAL → 0), the reaction dominates. Depending on the relative dominance of the two resistances, we have three cases:
1. Reaction is slow (mass transfer rate dominates). 2. Reaction is fast (reaction rate dominates). 3. Reaction is instantaneous.
In the following sections, we derive global rate equations (or flux equations) for the three cases listed above. 4.1.2.1 Derivation of Global Rate Equations 4.1.2.1.1 Slow Reaction The reaction between A and B occurs in the liquid film. As the reaction is slow, complete conversion of A would not be achieved within the liquid film and unreacted A would be present in the bulk liquid at a concentration CAb (CAb ≠ 0). Taking a steady-state molal balance of reactant A in the liquid film across a section of fluid lying between a distance y and y + Δy from the interphase (Figure 4.12).
AiNAL|y = AiNAL|y+Δy + (kCA)AiΔy (4.77)
where Ai is the interfacial area. Substituting Equation 4.74 for NAL into Equation 4.77, we get
dC dC −DAL A = −DAL A + (kC A )∆y dy y dy y + ∆y
Gas phase
Gas film
(4.78)
Liquid phase
Liquid film
y PAi
CBb
y + ∆y
CAi
CBi
CAb Interphase
ys
yL
Figure 4.12 Gas–liquid interphase for slow reaction.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 321
Heterogeneous Reactors
Dividing by Δy and taking limits as Δy → 0, we get a second-order differential equation DAL
d 2C A − kC A = 0 dy 2
(4.79)
The solution to Equation 4.79 is CA = A1e γy/yL + A2e − γy/yL
(4.80)
where k DAL
γ = yL
(4.81)
γ is a dimensionless number called Hatta number. Hatta number is the ratio of resistance to mass transfer to the resistance to reaction. The Hatta number value is larger for a faster reaction compared to that of a slower reaction as the resistance to reaction is lower than the resistance to mass transfer for a faster reaction. Combining Equations 4.75 and 4.81, we rewrite the equation for Hatta number γ as kDAL k AL
γ =
(4.82)
In general, γ 3 for fast reaction and γ is very large for instantaneous reaction. Substituting the boundary conditions
CA = CAi at y = 0 and CA = CAb at y = yL (4.83) into Equation 4.80, we get A1 + A2 = C Ai
γ
−γ 2
A1e + A
= C Ab
(4.84)
(4.85)
Solving Equation 4.84 for A1 and A2, we get CAb − CAi e − γ eγ − e−γ C − CAi e γ A2 = Abγ e − e−γ A1 =
Substituting Equation 4.85 for A1 and A2 in Equation 4.80, we get
γy y C Ab sinh + CAi sinh 1 − γ y L yL CA = sinh γ
www.Ebook777.com
(4.86)
Free ebooks ==> www.ebook777.com 322
Green Chemical Engineering
Flux NAL of A in the liquid film is calculated by evaluating dCA/dy at y = 0 and substitutdC ing dyA in Equation 4.74. Thus, taking the derivative of CA with respect to y and substiy =0 tuting y = 0 in the derivative term, we get
dCA dy
= y =0
γ [CAb − CAi cosh γ ] y L sinh γ
(4.87)
Substituting Equation 4.87 for (dCA/dy)y=0 into Equation 4.74, we get γk AL [C Ai cosh γ − C Ab ] sinh γ
N AL =
(4.88)
Equation 4.88 is rearranged and written as γk AL tanh γ
N AL =
C Ab C Ai − cosh γ
(4.89)
Substituting Henry’s law Equation 4.71 for CAi into Equation 4.89, we get N AL =
γk AL H A tanh γ
H ACAb PAi − cosh γ
(4.90)
As the steady-state condition is assumed at every location in the reactor, the flux NAG of A in the gas phase is equal to the flux NAL of A in the liquid film and this flux value is equal to the overall flux (or rate) NA: N A = N AG = N AL
(4.91)
Equating NAG in Equation 4.69 and NAL in Equation 4.90, we get kG (PA − PAi ) =
γk AL H A tanh γ
H ACAb PAi − cosh γ
(4.92)
Solving Equation 4.92 for PAi, we get PAi =
(k g PA + ( γk AL /H A tanh γ )( H ACAb / cosh γ )) (k g + ( γk AL /H A tanh γ ))
(4.93)
Substituting Equation 4.93 for PAi in Equation 4.69, we get the final equation for overall flux NA as NA =
(PA − (H ACAb / cosh γ ))
(1/k
g
+ ( H A tanh γ /γk AL )
)
www.Ebook777.com
(4.94)
Free ebooks ==> www.ebook777.com 323
Heterogeneous Reactors
For Hatta number γ = 0, the case in which no chemical reaction takes place, Equation 4.94 reduces to NA =
(PA − H ACAb ) ((1/k g ) + ( H A /k AL ))
(4.95)
which is the flux equation for any gas–liquid mass transfer operation such as absorption. 4.1.2.1.2 Fast Reaction The reaction proceeds at such a fast rate that reactant A would get completely converted into the product within the liquid film and there will not be any unconverted A present in the bulk liquid phase, that is, CAb = 0. Substituting CAb = 0 into Equation 4.94, we get the equation for overall flux (NA) for the fast reaction as NA =
PA ((1/k g ) + ( H A tanh γ /γk AL ))
(4.96)
Substituting CAb = 0 into Equation 4.89, we get the equation for flux (NAL) of A through the liquid film with chemical reaction as N AL =
γk ALCAi tanh γ
(4.97)
The flux of A through the liquid film would have been 0 N AL = k ALC Ai
(4.98)
had there not been any chemical reaction taking place in the liquid film. The flux of A with a chemical reaction is always higher than the flux of A without a chemical reaction. The enhancement of flux achieved due to reaction is denoted by the term enhancement factor E, which is defined as the ratio of the flux with a chemical reaction to the flux without a chemical reaction.
E=
N AL γ = 0 N AL tanh γ
(4.99)
Equation 4.96 for flux NA for the fast reaction case can be written in terms of the enhancement factor E as NA =
PA ((1/k g ) + ( H A /Ek AL ))
www.Ebook777.com
(4.100)
Free ebooks ==> www.ebook777.com 324
Green Chemical Engineering
4.1.2.1.3 Instantaneous Reaction Instantaneous reactions are infinitely fast reactions. The reaction of A occurs at a much faster rate than the transfer of A through the liquid film. Molecules of A, on encountering the molecules of B in the liquid film, would get converted into products instantaneously. If we assume that the flux NAL of A from the interphase to the bulk of the liquid and the flux NBL of B from the bulk of the liquid to the interphase are in the stoichiometric ratio, that is, N AL =
N BL b
(4.101)
then the reaction between A and B would occur on a plane within the liquid film located at a distance y1 from the interface as shown in the gas–liquid interfacial diagram (Figure 4.13). Complete conversion of A and B would be achieved on the reaction plane as both A and B are present on the reaction plane in an exact stoichiometric mole ratio at the time of reaction. However, soon after completion of the reaction, which is instantaneous, no molecule of unreacted A or unreacted B will be left out on the reaction plane. At y = y1 CA = 0 and CB = 0
(4.102)
As the transfer of A and B through the liquid film is by the mechanism of diffusion, equations for fluxes NAL and NBL can be written using Fick’s law of diffusion. DALCAi y1
N AL = N BL =
DBLCBb ( y L − y1 )
(4.103)
(4.104)
Liquid phase
Gas phase
Reaction plane
PA PAi CAi
Interphase
CBb
CA = 0
CB = 0
y1 yG
yL
Figure 4.13 Gas–liquid interphase for instantaneous reaction.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 325
Heterogeneous Reactors
Substituting Equations 4.103 and 4.104 for NAL and NBL into Equation 4.101 DALCAi DBLCBb = y1 b( y L − y1 )
(4.105)
Solving the above equation for y1, we get yL 1 1 + (DBL /DAL ) (CBb /CAi ) b
y1 =
(4.106)
Substituting Equation 4.106 into Equation 4.103 for y1 and using k AL = DAL/yL, we get the equation for flux NAL as
1 D C N AL = k ALC Ai 1 + BL Bb b DAL C Ai
(4.107)
As the steady-state condition is assumed, flux NAG of A in the gas is the same as the flux NAL of A in the liquid film. Hence
NAG = NAL = NA (4.108)
where NA is the overall flux of A. Equating NAG in Equation 4.69 to NAL in Equation 4.107 and using Henry’s law equation CAi = PAi/HA, we get k g (PA − PAi ) =
k AL PAi k AL DBL + CBb HA b DAL
(4.109)
Solving the above equation for PAi, we get PAi =
k g PA − (k AL /b)(DBL /DAL )CBb k g + (k AL /H A )
(4.110)
Substituting Equation 4.110 into Equation 4.69 for PAi, we get the final equation for overall flux NA as NA =
PA + ( H A /b)(DBL /DAL )CBb (1/k g ) + ( H A /k AL )
(4.111)
4.1.2.1.3.1 Instantaneous Reaction at a Gas–Liquid Interface Location of the reaction plane y1 with respect to the interface depends on the values of DBL and DAL and the concentration CBb of B in the bulk liquid phase (Equation 4.106). The reaction plane will be nearer to the interphase if diffusion of B in the liquid phase is relatively faster than A, that is, DBL > DAL.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 326
Green Chemical Engineering
Interphase Gas phase
Gas film
Liquid film
Liquid phase
* CBb (limiting value of CBb)
PA
CAi = 0 CBi = 0
YG
YL
Figure 4.14 Gas–liquid interface for instantaneous reaction at interface.
The reaction plane can be moved closer to the interphase by increasing the bulk concentration of B, CBb, in the liquid phase. If CBb exceeds a limiting value C∗Bb , the reaction plane will merge with interphase and the reaction would occur at the interface itself. This would result in zero concentrations of A and B at the interface (Figure 4.14) as complete conversion of A and B happens at the interface, that is, At y = 0, CAi = 0 and CBi = 0
(4.112)
* Thus, for CBb > CBb , the equation for overall flux NA reduces to
NA = kgPA (4.113)
The overall rate is completely controlled by the gas-phase mass transfer of A. The limit* ing value of CBb is calculated as follows: * At CBb = CBb ,
N BL =
* DBLCBb yL
(4.114)
Writing yL in terms of k AL using Equation 4.75, we have
N BL =
DBL * ⋅ k ALCBb DAL
www.Ebook777.com
(4.115)
Free ebooks ==> www.ebook777.com 327
Heterogeneous Reactors
Table 4.5 Flux NA for Gas–Liquid Reactions Category of Reaction
Equation for Flux NA
Slow reaction (γ 3)
Instantaneous reaction (large γ)
Reaction at a plane away from * interface (CBb < CBb ) * Reaction at interface (CBb > CBb )
Note: γ =
kDAL γ ,E= tanh γ k AL
NA =
PA − ( H ACAb / cosh γ ) (1/k g ) − ( H A /Ek AL )
NA =
(PA ) (1/k g + H A /Ek AL )
NA =
PA + ( H A /b)(DBL /DAL )CBb (1/k g ) + ( H A /k AL )
NA = kgPA
D k * and CBb = b AL G PA . DBL k AL
As fluxes NA and NBL are in the stoichiometric ratio NA =
N BL b
(4.116)
Combining Equations 4.113, 4.115 and 4.116, we get D k * CBb = b AL G PA DBL k AL
(4.117)
* Thus, if CBb ≥ CBb , the reaction would occur at the interface and Equation 4.113 holds * good for flux NA. If CBb < CBb , the reaction would occur at a plane away from the interface and flux NA is calculated using Equation 4.111. The equations derived for flux NA for the three cases are listed in Table 4.5. These equations are made use of in the design of gas–liquid reactors discussed in the following section.
4.1.2.2 Design of Packed Bed Reactors for Gas–Liquid Reactions Consider the gas–liquid reaction
A(g) + bB(l) → Products
carried out in a packed bed reactor shown in Figure 4.15. Define v: volumetric flow rate of the gas, m3/s L: volumetric flow rate of the liquid, m3/s S: cross-sectional area of the packed bed, m2 PA0, PAf : partial pressures of A in the gas at the reactor inlet and outlet, N/m2 CA0, CAf : concentrations of A in the liquid at the reactor inlet and outlet, kmol/m3
www.Ebook777.com
Free ebooks ==> www.ebook777.com 328
Green Chemical Engineering
PAf , ν
L, CA0, CB0
L CAb CBb
v PA + dPA
Z
∆z
z
L CAb CBb
v PA s
PA0 , ν
L, CAf , CBf
Figure 4.15 Schematic diagram of packed bed reactor for gas–liquid reaction.
CB0, CBf : concentrations of B in the liquid at the reactor inlet and outlet, kmol/m3 sp: specific surface area of the packing material, m2/m3 ∈: bed porosity Z: height of the packed bed xAf : fractional conversion of A achieved in the reactor The design of the packed bed reactor is concerned with calculating the height Z of the bed required to achieve a specified conversion xAf of A.
pAf x Af = 1 − pA 0
(4.118)
Consider a section of thickness dz of the bed at a distance z from the gas inlet. Let PA: partial pressure of A in the gas phase at z CAb: concentration of A in the liquid phase at z CBb: concentration of B in the liquid phase at z dPA: change in partial pressure of A in the gas across the section dz dCAL: change in concentration of A in the liquid across the section dz dCAb: change in concentration of B in the liquid across the section dz Assume constant volumetric flow rates of the gas and the liquid and constant temperature T in the bed. Taking a steady-state balance of A in the gas phase, across the section of the bed, we get
www.Ebook777.com
Free ebooks ==> www.ebook777.com 329
Heterogeneous Reactors
Rateof loss of A in thegas phase Rateof transfer of A from thegas phase to (4.119) = L G→ L across thesection rA , kmol / s theliquid phasein the section rA , kmol / s Writing the equations for the terms on either side of the above equation, we have −
υ dPA = N A [sdz(1 − ε)]sp RT
(4.120)
where R is the gas law constant and NA is the flux of A, whose equations are listed in Table 4.5. Rearranging Equation 4.120 and integrating between z = 0 and z = Z, we get Z
∫ 0
dz =
υ RTS(1 − ε)sp
PAO
∫
PAf
dPA NA
(4.121)
Finally, the design equation for the packed bed gas–liquid reactor is υ Z= RTS(1 − ε)sp
PAO
∫
PAf
dPA NA
(4.122)
The appropriate equation for flux NA given in Table 4.5 should be substituted in the above equation for calculating the tower height Z. Designing a reactor for a slow reaction would be of no practical value and so we would not consider the slow reaction case here. We will develop the design equations for the other two cases, namely, a fast reaction and an instantaneous reaction. 4.1.2.2.1 Fast Reaction Substituting the equation for NA for the fast reaction in the design Equation 4.122, we get an analytical equation for Z
1 HA 1 υ Z= + ln RTS(1 − ε)Sp k g Ek AL 1 − x Af
(4.123)
Problem 4.7 Deleye and Froment (1986) have reported the data on absorption of CO2 in aqueous solution of monoethanol amine (MEA) in a packed bed absorber. Gas containing CO2 at a partial pressure of 2 atm is to be purified by absorption into an aqueous solution of MEA in a packed bed filled with 5 cm diameter steel pal rings. Assuming excess concentration of MEA in the solution, the reaction between CO2 and MEA is treated as pseudo-first order reaction with rate constant k = 7.194 × 104 s−1. A quantity of 6500 m3/h of gas is treated with 1000 m3/h of MEA solution. Partial pressure of CO2 is to be reduced to 0.02 bar. Column diameter is 2 m and it is operating at a pressure of 14.3 bar and a temperature of 315 K. Calculate the height of the bed. The following data are reported. kG = 2.639 × 10−9 kmol/m2sPa k AL = 3.889 × 10−4 m/s
www.Ebook777.com
Free ebooks ==> www.ebook777.com 330
Green Chemical Engineering
DAL = 2.39 × 10−9 m2/s ε = bed porosity = 0.45 sp = specific surface area = 105 m2/m3 HA = Henry’s law constan t = 4.89 × 106 m3 Pa/kmol
Hatta number = γ =
kD AL k AL
Hatta number = γ =
(7.194 × 10 4 )(2.39 × 10 −9 ) 3.889 × 10 −4
= 33.72
So, the reaction is a fast reaction. Enhancement factor E = (γ/tanh γ) = 33.72. The equation for the height of the tower z is 1 υ H 1 ln z= + (RT )S(1 − ε)sP k g Ek AL 1 − x Af
Volumetric flow rate υ = (6500/3600) = 1.806 m3/s Area of cross section S = (π/4)D2 = (π/4)22 = 3.14 m 2 Fractional conversion xAf = 0.99 Substituting these values into the equation, 1.806 1 4.89 × 10 6 1 ln z= + − 9 −4 ( 8314 )( 3 . 14 )( 0 . 55 )( 105 ) 2 . 639 10 ( 3 3 . 72 )( 3 . 889 × 10 ) 1 − 0.99 × z = (3.803 × 10 −9 )(3.789 × 10 8 + 3.729 × 10 8 )( 4.605)
The height of the tower z = 13.2 m. Note: Refer the MATLAB program: react_dsn_pckbed1.m 4.1.2.2.2 Instantaneous Reaction The choice of appropriate equation for flux NA used in the design Equation 4.122 for the calculation of Z depends upon whether the reaction occurs on the gas–liquid interphase * or on a plane away from the interphase. This has to be ascertained by c alculating CBb for * each value of PA, PAf ≤ PA ≤ PA0 and checking if CBb www.ebook777.com 331
Heterogeneous Reactors
Rearranging this equation, we get
CBb = CBO −
b υ (PA − PAf ) RT L
The height of the packed bed is calculated by numerical integration of
(4.126)
∫
PA 0
PAf
(dPA /N A ).
n values of PA (PA1, PA2,…, PAm) are selected between PAf and PA0 at equal intervals; for each one of the values of PA lying between PAf and PA0 (PAf ≤ PA ≤ PA0), calculate CBb using Equation * * * * 4.126 and CBb using Equation 4.117. Check if CBb < CBb or CBb ≥ CBb . If CBb ≥ CBb , calculate * flux NA using Equation 4.111 and if CBb ≥ CBb , calculate flux NA using Equation 4.113. Problem 4.8 The absorption of HCl vapour into NaOH solution is an instantaneous irreversible reaction involving H+ and OH− ions.
HCl( g ) + NaOH(l) → NaCl + H 2 O
In a packed bed tower similar to the one discussed in Problem 4.7, a gaseous stream containing HCl vapour at a partial pressure of 0.2 bar is reacted with a liquid stream containing NaOH at a concentration of 0.08 kmol/m3. The gas stream is passed at the rate of 6500 m3/h and liquid flows counter-currently at the rate of 1000 m3/h. The reactor is operated at 3 bar pressure and 300 K temperature. Molecular diffusivities of HCl and NaOH in the aqueous solution are nearly equal. Calculate the height of the tower for 80% conversion of HCl. The tower diameter is 2 m. The following data are reported: kG = 2.1 × 10−9 kmol/m2s Pa k AL = 4.2 × 10−4 m/s ε = bed porosity = 0.45 sp = specific surface area = 105 m2/m3 HA = Henry’s law constant = 2.2 × 105 m3Pa/kmol υ, PAf = 0.04 bar
υ, PAO = 0.2 bar
CBO = 0.08 kmol/m, L
L, CBf
www.Ebook777.com
Free ebooks ==> www.ebook777.com 332
Green Chemical Engineering
The design equation for tower height is υ z= (RT )S(1 − ε)sP
where, for CBb < C
PAO
∫
PAf
dPA NA
* Bb
P + ( H A /b)(DBL /DAL )CBb NA = A H A /k AL + 1/kG
* For CBb > CBb
NA = kGPA
k bD * CBb = G AL PA k ALDBL
As DAL = DBL, 2.1 × 10 −9 * CBb = PA = 0.5 × 10 −5 PA pascal = 0.5PA bar 4.2 × 10 −4
CBb = CBO −
b υ (PA − PAf ) RT L
As conversion is xAf = 0.8, PAf = PAO(1 − xAf) = 0.04 bar
CBb = 0.08 −
1 1.806 (PA − 0.04) × 10 5 (8314)(300) 0.278
CBb = 0.08 − 0.2605(PA − 0.04) 1.806 z= (8314)(300)(0.785)(0.55)(105)
0.2
z = (1.608 × 10 −8 )
∫
0.04
0.2
∫
0.04
dPA NA
dPA NA
At the tower top
* CBb = 0.5PA = 0.5 × 0.04 = 0.02
CBO = 0.08 * So, CBb > CBb At the tower bottom
CBb = 0.08 − 0.2605(0.2 − 0.04) = 0.0383
* CBb = 0.5PA = 0.5 × 0.2 = 0.1
www.Ebook777.com
Free ebooks ==> www.ebook777.com 333
Heterogeneous Reactors
* So, CBb < CBb * At some height Z*, transition occurs where CBb = CBb ; PA = PA*
0.08 − 0.2605 (PA∗ − 0.04) = 0.5PA∗
0.09042 = 0.7605PA∗
PA∗ =
0.09042 = 0.12 0.7605
So, 0.2
∫
0.04
dPA = NA
0.12
0.2
* CBb > CBb
* CBb < CBb
dPA dPA + NA NA 0 .04 .12 0
∫
∫
0.2
1 0.12 1 H dPA = ln + + A k g 0.04 k g k AL ( PA + ( H A /b)(DBL /DAL )CBb ) 0.12
∫
0.2
= (0.523 × 10 9 ) + (1 × 10 9 )
∫ (P
0.12
PA +
A
dPA + ( H A /b)(DBL /DAL )CBb )
H A DBL CBb = PA + 2.2CBb b DAL
and CBb = (0.0904 − 0.2605PA) PA +
H A DBL CBb = PA + 2.2(0.0904 − 0.2605PA ) b DAL = 0.20 + 0.427 PA
0.2
dPA
∫ 0.20 + 0.427P
A
0.12 0.2
dPA
∫ 0.20 + 0.427P
0.12
=
=
A
1 [ln(0.20 + 0.427 PA )]00..212 0.427
1 1 0.20 + 0.427 × 0.20 0.2854 ln ln = 0.427 0.20 + 0.427 × 0.20 0.427 0.2512
= 0.30 0.2
∫
0.04
dPA = (0.523 × 10 9 ) + (0.30 × 10 9 ) NA 0.2
∫
0.04
dPA = 0.823 × 10 9 NA
Total z = 1.60 × 10 −8 + 0.823 × 109 = 13.2 m Note: Refer the MATLAB program: react_dsn_pckbed2.m
www.Ebook777.com
Free ebooks ==> www.ebook777.com 334
Green Chemical Engineering
4.2 Heterogeneous Catalytic Reactions and Reactors Catalytic reactions are the reactions in which catalysts are used to enhance the rate of reaction. Enhancement of the rate is achieved through reduction of activation energy. The mechanism and the kinetics of the catalytic reactions are discussed in Section 2.1.11. Heterogeneous catalytic reactions are the reactions in which the catalyst is a solid substance, and the reactants and the products are fluid substances (gas/liquid). Catalytic reactions are broadly classified as two-phase and three-phase reactions. A two-phase catalytic reaction is a reaction taking place in the presence of a solid catalyst between reactants that are in one single fluid phase (either a gas phase or a liquid phase). An example of a twophase catalytic reaction is the conversion of ortho-hydrogen (o-H2) to para-hydrogen (p-H2) in the presence of Ni-Al2O3 catalyst:
Ni − Al 2 O 3 ( X ) → p − H2 o − H2 ←
Three-phase catalytic reactions are solid-catalysed reactions taking place between one reactant in the gas phase and another reactant in the liquid phase. An example of a threephase catalytic reaction is the hydrogenation of vegetable oil in the presence of a Ni catalyst:
(X ) Vegetable oil( l ) + H 2( g ) Ni → hydrogenated oil( l ) ( vanaspathi)
Catalyst material is required only in a small quantity as it takes part in the reaction without actually getting consumed by the reaction. According to the Langmuir–Hinshelwood mechanism of solid-catalysed reactions, in each reaction cycle, reactants that are chemisorbed on the catalyst surface get converted into a product that in turn is desorbed from the catalyst surface, releasing the catalyst substance. Thus, in each cycle of reaction involving the conversion of reactants into products, the catalyst material is used and reused repeatedly. Catalytic reactors are essentially fluid–solid contacting equipment in which the fluid phase (gas/liquid) containing the reactants is passed continuously over a fixed quantity of catalyst particles. In order to achieve effective contact between the fluid and the catalyst, the solid catalyst substance is ground into fine particles and used in the reactor. In the fluidised bed catalytic reactors, catalyst material is used in the form of fine solid particles. This is the case if catalyst is an inexpensive metal such as Ni or MnO. But there are many reactions in which expensive metals such as platinum (Pt), silver (Ag) and gold are used as catalyst and they cannot be used in large quantities. In this case, the catalyst material is impregnated at a number of points (called active sites) scattered inside the pores of a porous support material such as Al2O3 (which is inexpensive). Here, the catalyst is prepared in the form of pellets of different shapes (sphere, cylinder, rectangular slab) and different sizes. Each pellet is a porous support material (like Al2O3) containing the catalyst material (like Pt, Ag) present at a number of active sites scattered all over the inner surface of the pores, as shown in Figure 4.16. In a packed bed catalytic reactor, the fluid containing the reactants is passed through a bed (packed with) catalyst pellets. 4.2.1 Reaction in a Single Catalyst Pellet Consider a gas-phase reaction A X → B taking place in the presence of a catalyst X. Assume that this reaction is carried out in a packed bed reactor in which the gas stream
www.Ebook777.com
Free ebooks ==> www.ebook777.com 335
Heterogeneous Reactors
Crystal material (Pt)
Pore Support material (Al2O3) Figure 4.16 Single catalyst pellet.
containing reactant ‘A’ is passed through a bed of solid catalyst pellets. Consider one single solid pellet (at some location within the bed) over which a gas stream containing reactant A at a concentration CAg is passing. Assume that at any time the gas in contact with the solid catalyst pellet is in the steady state and concentration of A in the gas CAg at any location within the bed does not change with time. Consider a single pore in a catalyst pellet shown in Figure 4.17. Reaction of A in the gas stream in contact with the solid catalyst pellet involves the following steps:
1. Transfer of A from the bulk gas to the pore mouth at the catalyst surface across the gas film resistance. This transfer occurs at a rate r1 and the driving force is (CAg − CAS), where CAS is the concentration of A at the catalyst surface. C A Ag 1 External surface of pellet CAl
4
CAs
2 CAa
3 5
CBg
CBa
7C
Bs
Bulk gas stream
Gas
film
6 Catalyst pellet
Active site CBl (containing the catalyst materials) Pore in the pellet
Figure 4.17 Single pore in a catalyst pellet in contact with fluid stream.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 336
Green Chemical Engineering
2. Transfer of A from the pore mouth (catalyst surface) to the active sites located on the inner surface of the pore by diffusion. This transfer occurs at a rate r2 and the a driving force is (CAS − CAa ), where CAa is the concentration of A on the surface of the active site. 3. Adsorption of A on the active site ‘l’. Moles of A on the surface of the active site at a concentration CAa attain equilibrium with moles of A adsorbed on the active site and CAl is the concentration of A adsorbed on the active site. 4. Conversion of A adsorbed on the active site into product B at a rate r4. CBl is the concentration of product B formed and remains adsorbed on the active site. 5. Desorption of B from the active site ‘l’. The moles of B adsorbed on the active site are in equilibrium with the moles of B desorbed from the active site and available on the surface of the active site at a concentration CBa. 6. Transfer of B from the surface of the active site through the pore by diffusion to the pore mouth at a rate r6. The driving force is (CBa − CBS), where CBS is the concentration of B at the pore mouth on the catalyst surface. 7. Transfer of B from the catalyst surface to the bulk gas across the gas film resistance at a rate r7. The driving force is (CBS − CBg), where CBg is the concentration of B in the bulk gas. Out of the seven steps listed above, steps 3 (adsorption), 4 (surface reaction) and 5 (desorption) constitute the mechanism of solid-catalysed reaction described by the Langmuir– Hinshelwood model (Section 2.1.11.1). Combining these three steps, a single rate equation for the kinetics of solid-catalysed reaction can be derived by making suitable assumptions. This rate equation derived by combining these three steps for an irreversible reaction A → B takes the form (Section 2.1.11.1)
rr =
k ′CAa 1 + K AC Aa + K BCBa
(4.127)
where k′: kinetic rate constant K A: adsorption equilibrium constant for A KB: adsorption equilibrium constant for B The rate of conversion of A at the active site of the solid catalyst is a function of concentrations of A and B (CAa and CBa) at the active site. If we assume the concentrations of A and B at the active site to be very small (CAa → 0 and CBa → 0), then the kinetic rate equation for the solid-catalysed reaction takes the form of a first-order kinetic equation and can be written as
rr = kCAa
(4.128)
where k is the kinetic rate constant of the first-order kinetic equation. The overall rate (global rate) of transfer of A, rA, from the bulk gas to the catalyst pellet is obtained by combining three rate equations listed below:
www.Ebook777.com
Free ebooks ==> www.ebook777.com 337
Heterogeneous Reactors
1. External mass transfer rate r1, which is the rate of transfer of A from the bulk gas to the surface of the catalyst pellet, is r1 = k g (CAg − CAS )( 4πR2 )
(4.129)
where R is the radius of sperical catalyst pellet, kg is the gas film mass transfer coefficient. 2. Internal mass transfer rate r2, which is the rate of diffusion of A from the surface of the catalyst pellet into the pores, is r2 = DA
dC A dr
( 4πR2 )
(4.130)
r=R
where DA is the effective diffusivity of A through the porous solid. 3. Kinetic reaction rate rr, which is the rate of conversion of A at the reaction site, is rr = kCAa
(4.131)
As the solid pellet in contact with the gas stream is at steady state rΛ = rr = r1 = r2
(4.132)
By equating rate expressions r1, r2 and rr, the internal concentration terms CAa and CAS are eliminated from the rate equation and the global rate equation for rA is derived as a function of bulk gas concentration CAg. The global rate expression takes into account the transfer of A across three resistances connected in series: RΓ
Rg CAg
r1
CAs
r2
Rr CAa
rk
0
where Rg: external gas film mass transfer resistance RΓ: internal pore diffusion resistance Rr: reaction resistance As a first step towards obtaining the global rate equation rΛ, a rate equation is derived by taking into account the rate of diffusion through the internal pores of the catalyst and the rate of reaction at the active sites (r2 and rr). The derivation of this rate equation for a slabshaped catalyst pellet and a spherical catalyst pellet is presented in the following sections. 4.2.1.1 Internal Pore Diffusion and Reaction in a Slab-Shaped Catalyst Pellet Consider a porous catalyst pellet (Figure 4.18) in the shape of a slab in contact with a gas stream containing reactant A at concentration CAg. A is transferred from the bulk gas to the surface of the slab and CAS is the concentration of A on the slab surface. Assume that the four sides of the slab are sealed and the reactant A can diffuse into the slab only in the x-direction through the two unsealed sides. Let S be the cross-sectional area of the
www.Ebook777.com
Free ebooks ==> www.ebook777.com 338
Green Chemical Engineering
2L
Slab surface
X = –L
X = +L
X=0 X X + ∆X CA
CA + ∆ CA
CAs
X = –L
CAs
X=0
X = +L
Figure 4.18 Slab-shaped catalyst pellet.
unsealed side and 2 L the width of the slab. Assume that the catalyst material present at the active sites inside the pores is uniformly distributed in the pellet volume. Define catalyst density ρp as the mass of the catalyst present in one unit volume of the pellet (kg catalyst per m3). The rate of conversion of A at a location inside the catalyst pellet at a distance x from the central axis (x = 0) is
(− rA′ ) = kCA
(kmol of A converted)/(s)(kg ⋅ catalyst)
(4.133)
where k: reaction rate constant m3/(kg ⋅ catalyst) (s) CA: concentration of A at x (kmol/m3) Diffusional flux of A through the pellet at position x from the central axis (x = 0) is
N A = DA
dC A dx
www.Ebook777.com
(4.134)
Free ebooks ==> www.ebook777.com 339
Heterogeneous Reactors
where DA: effective diffusivity of A through the solid slab Consider a section of the catalyst pellet of thickness Δx at a distance x from the central axis (x = 0). Taking a steady-state balance of A across this section, we have Rate of transfer Rate of transfer Rate of conversion + = of A into the section of A out of the section x of A in the section x + ∆x
S ⋅ DA
dCA dx
= S ⋅ DA x + ∆x
dCA dx
+ kC AS∆xρp
(4.136)
x
(4.135)
Dividing the terms in the above equation by (Δx ⋅ DA) and taking limits as Δx → 0, we get the second-order differential equation d 2CA ρp kC A − =0 dx 2 DA
(4.137)
With boundary conditions defined at x = ± L and x = 0 as At x = ± L ; C A = C AS dCA At x = 0 ; = 0 dx
(4.138)
Boundary condition (4.138) arises due to the symmetry of the catalyst pellet. The general solution to the homogeneous second-order differential Equation 4.137 with the characteristics equation m2 −
ρp k =0 DA
(4.139)
is, CA = A1e
(ρp k /DA )L( x/L)
+ A2e −
(ρp k /DA )L( x/L)
(4.140)
Define Φ=L
ρp k DA
(4.141)
Φ is a dimensionless number called the Thiele modulus. The Thiele modulus is the ratio of resistance to internal pore diffusion of A to the resistance to reaction of A. Φ=
(Resistance to internal pore diffusion of A) (Resistance to reaction of A)
www.Ebook777.com
(4.142)
Free ebooks ==> www.ebook777.com 340
Green Chemical Engineering
The value of Φ increases with an increase in resistance to internal pore diffusion. Also, the larger the size of the catalyst pellet, the larger is the value of Φ. The value of the Thiele modulus Φ can be taken as negligible for smaller-sized catalyst particles. Writing Equation 4.140 in terms of the Thiele modulus Φ, CA = A1e Φ( x/L) + A2e − Φ( x/L)
and substituting the boundary condition (4.138) into this equation, we get CAS = A1e Φ + A2e − Φ at x = L CAS = A1e − Φ + A2e Φ at x = − L
(4.143)
Solving Equation 4.143 for A1 and A2, we have A1 = A2
(4.144)
and A1 =
CAS e + e−Φ
(4.145)
Φ
Substituting Equations 4.144 and 4.145 for A1 and A2 into Equation 4.140, we get the equation for CA as CA =
CAS cosh Φ( x/L) cosh Φ
(4.146)
Taking the derivative of CA with respect to x and evaluating dCA/dx at x = 0, we find that Equation 4.146 fulfills the boundary condition (4.138) at x = 0. At x = L, dCA dx
= x=L
Φ CAS tanh Φ L
(4.147)
and flux NA at x = L is N A = DA
dCA dx
x=L
which is
NA =
DAΦCAS (tanh Φ ) L
www.Ebook777.com
(4.148)
Free ebooks ==> www.ebook777.com 341
Heterogeneous Reactors
The net rate of transfer of A, rA, at the catalyst surface is (rA ) = N A x = L (2S)
that is,
(rA ) =
2SDAΦCAS (tanh Φ ) L
(4.149)
Let rAo be the rate of transfer of A into the catalyst pellet had the resistance to internal pore diffusion been negligible. If the resistance to internal pore diffusion is neglected, then the concentration of A at all the active sites within the pores inside the catalyst pellet will be the same as the concentration of A at the surface of the catalyst pellet, that is, CA = CAS for all values of x, −L www.ebook777.com 343
Heterogeneous Reactors
where DA: effective diffusivity of A through the spherical pellet. Consider a section of thickness Δr at the radial position r. Taking a steady-state balance of A across this section, we have Rate of transfer Rate of transfer Rate of conversion + = of A into the section of A out of the section r of A in the section r + ∆r
(4.154)
Substituting appropriate equations for each one of the terms into Equation 4.154, we get ( 4πr 2 )DA
dCA dr
= ( 4πr 2 ) DA r + ∆r
dCA + kC A ( 4πr 2 )∆rρp dx r
(4.155)
where ρp is the catalyst density in the particle (kg ⋅ catalyst/m3). Dividing each one of the terms in Equation 4.155 by DA 4πr2 Δr and taking limits as Δr → 0, we get
1 d 2 dCA ρp kC A =0 r − r 2 dr dr DA
(4.156)
Writing Equation 4.156 in the standard second-order differential equation form, we get
d 2CA 2 dCA + − αCA = 0 2 dr r dr ρp k where α = DA
(4.157)
The boundary conditions at r = ±R and r = 0 are
CA = C AS At r = ± R and dCA = 0 At r = 0 dr
(4.158)
The above boundary condition arises due to the symmetry of the spherical pellet. Let us assume the general solution to Equation 4.157 to be
CA =
e mr r
(4.159)
Taking the first and second derivatives of CA with respect to r, we have
1 dCA m = e mr − 2 r dr r
www.Ebook777.com
(4.160)
Free ebooks ==> www.ebook777.com 344
Green Chemical Engineering
2 d 2CA 2m 2 mr m = e − 2 + 3 2 dr r r r
(4.161)
Substituting Equations 4.159, 4.160 and 4.161 for CA, dCA/dr and d2CA/dr2, respectively, into Equation 4.157, we get m2 2 m 2 2 1 αe mr m e mr =0 − 2 + 3 + e mr − 2 − r r r r r r r
which on cancellation of terms reduces to e mr 2 (m − α ) = 0 r
Thus, Equation 4.159 is a solution to the second-order differential Equation 4.157 for m = ± α . Hence, the general solution to Equation 4.157 can be written as CA =
A1 e r
(ρp k /DA )R( r /R)
+
A2 − e r
(ρp k /DA )R( r /R)
(4.162)
Defining the Thiele modulus Φ = R ρp k/DA , Equation 4.162 can be written in terms of Φ as CA = A1
e Φ ( r /R ) e − Φ ( r /R ) + A2 r r
(4.163)
The definition of the Thiele modulus Φ for a spherical catalyst is similar to the definition of Φ for a slab-shaped catalyst (Equation 4.141) with L in Equation 4.141 replaced by R. Substituting the boundary condition (4.158) into Equation 4.163, we have CAS =
A1 Φ A2 − Φ e + e R R
and CAS = −
at r = − R
at r = R
A1 − Φ A2 Φ e − e R R
(4.164)
Solving Equation 4.164 for the integration constants A1 and A2, we get
A1 = − A2
(4.165)
and
A1 =
RC AS e − e−Φ Φ
www.Ebook777.com
(4.166)
Free ebooks ==> www.ebook777.com 345
Heterogeneous Reactors
Substituting Equations 4.165 and 4.166 for A1 and A2 in Equation 4.163, we get
R CA = CAS r
r sinh Φ R sinh Φ
(4.167)
Taking derivative of CA with respect to r and evaluating dCA/dr at r = R, we have
dCA C R Φ Φr 1 Φr 1 = AS cosh − sinh dr Rr R r 2 sinh Φ R dCA dr
= r=R
C AS [Φ coth Φ − 1] R
(4.168)
Flux of A, from the bulk gas to the outer surface of the catalyst pellet, is N A = DA N A = DA
dCA dr
r=R
CAS [Φ coth Φ − 1] R
(4.169)
The rate of transfer of A from the bulk gas into the catalyst pellet is
(rA ) = ( N A )( 4πR2 )
(rA ) = 4πR DACAS (Φ coth Φ − 1)
(4.170)
The rate of transfer of A into the catalyst pellet is denoted as rAo if the resistance to internal pore diffusion is neglected. In this case, the concentration of A, CA, is uniformly the same at all points (active sites) inside the catalyst pellet and is equal to the concentration of A (CAS) at the outer surface, that is, CA = CAS for all values of r, −R www.ebook777.com 347
Heterogeneous Reactors
1
Slab pellet
η=1
Cylindrical pellet Spherical pellet
Φ
/
Φ
/
=1
/
Φ
=3
=2
η
η
η
η
1
2 Φ
3
Figure 4.22 Plots of η versus Φ for slab, cylinder and spherical-shaped catalyst pellets.
by expressing the effectiveness factor η as a function of a modified Thiele modulus Φ′, which is defined as Φ ′ = Lo
ρp k DA
(4.176)
where Lo is the equivalent length of the catalyst pellet, defined as
(Lo ) =
Volume of the pellet Surface area
(4.177)
For a slab-shaped catalyst pellet
2LS Lo = = L 2S and Φ ′ = Φ
(4.178)
For a cylindrical-shaped catalyst pellet
πR2L R Lo = = 2 2πRL Φ and Φ ′ = 2
(4.179)
For a spherical-shaped catalyst pellet
( 4/3)πR3 R Lo = = 3 4πR2 Φ and Φ ′ = 3
www.Ebook777.com
(4.180)
Free ebooks ==> www.ebook777.com 348
Green Chemical Engineering
1
η=1
η = 1/Φ′
η
Φ′
1
Figure 4.23 Plot of η versus Φ′ (modified Thiele modulus).
Thus, the three asymptotes η = 1/Φ , η = 2/Φ , η = 3/Φ , respectively, for a slab-shaped pellet, a cylindrical pellet and a spherical pellet are merged into a single asymptote η = 1/Φ ′ on a plot of η versus Φ’ as shown in Figure 4.23. In terms of the modified Thiele modulus Φ’, the effectiveness factor η is expressed as
η=
tanh Φ ′ Φ′
(4.181)
This equation is applicable for catalyst pellets of any regular shape. Further, the equation for flux NA for a catalyst pellet of any regular shape with equivalent length L0 is
N A = ηkρp L0CAS
(4.182)
4.2.1.4 Modification of the Thiele Modulus for a Reversible Reaction Consider a first-order reversible reaction k1
→B A← k2
taking place within a spherical catalyst pellet of radius R. The specific reaction rate of A is given by
(− rA ) = k1C A − k 2CB
(4.183)
where k1 and k2 are reaction rate constants for the forward and the reverse reactions, respectively. Define equilibrium constant K as
K =
k1 C = Be k2 CAe
www.Ebook777.com
(4.184)
Free ebooks ==> www.ebook777.com 349
Heterogeneous Reactors
where CAe and CBe are the equilibrium concentrations of A and B, respectively. Writing Equation 4.183 in terms of equilibrium constant K, we have C (− rA ) = k1 CA − B K
(4.185)
The total molal concentration of A and B is constant, as for every 1 mole of A reacted 1 mole of B is formed. Thus
CB = C Ae + CBe − CA
(4.186)
CB = (1 + K )CAe − CA
(4.187)
Substituting Equation 4.187 for CB into Equation 4.185, we get (− rA ) =
k1(1 + K ) (C A − C Ae ) K
(4.188)
Substituting this specific reaction rate Equation 4.188 into the molal balance Equation 4.155 derived for a spherical catalyst pellet, we get d 2CA 2 dCA ρp k1 1 + K + − (CA − CAe ) = 0 dr 2 r dr DA K
(4.189)
Substituting the equilibrium concentration CA = CAe into Equation 4.189, we have d 2CAe 2 dCAe + =0 dr 2 r dr
(4.190)
Subtracting Equation 4.190 from Equation 4.189, we get
ρ p k1 1 + K d 2CA′ 2 dCA′ + − C A′ = 0 dr 2 r dr DA K
(4.191)
CA′ = CA − C Ae
(4.192)
where And the boundary conditions are
CA′ = CAS ′ = CAS − CAe
at r = ± R
(4.193)
and
dCA′ = 0 at r = 0 dr
www.Ebook777.com
(4.194)
Free ebooks ==> www.ebook777.com 350
Green Chemical Engineering
Thus, we find that Equations 4.191 and 4.193 are analogous to the corresponding Equations 4.157 and 4.158 derived for an irreversible reaction in the spherical catalyst pellet except that CA is replaced by CA′ and the rate constant k is replaced by k1(1 + K/K). So, the equation for Thiele modulus Φ defined for an irreversible reaction will hold good for a reversible reaction with the rate constant k in Φ replaced by k1(1 + K/K). Thus, the Thiele modulus Φ for a reversible reaction in a spherical catalyst pellet is Φ=R
ρp k1(1 + K ) KDA
(4.195)
In general, the modified Thiele modulus Φ’ for the reversible reaction in a pellet of any regular shape is Φ ′ = LO
ρp k1(1 + K ) KDA
(4.196)
where Lo is the equivalent length of the pellet. The effectiveness factor η for a reversible reaction in a catalyst pellet is, η=
tanh Φ ′ Φ′
(4.197)
4.2.1.5 Diffusion and Reaction in a Single Cylindrical Pore within the Catalyst Pellet If a catalyst pellet (of any shape) has well-structured pores that are of uniform diameter d and length L and the pores are uniformly distributed throughout the volume of the pellet, then the overall rate equation can be derived by accounting for the rate of diffusion and rate of reaction in one single pore within the catalyst pellet. Consider a cylindrical pore of diameter d and length L (Figure 4.24) in a catalyst pellet in contact with a gas stream containing reactant A at concentration CAg. CAS is the concentration of A in the gas at the pore mouth on the outer surface of the catalyst pellet. Consider a section of the pore volume of thickness Δx at a distance x from the pore mouth. A diffuses into the pore and as it moves through the pore, it undergoes reaction by coming into contact with the catalyst material available at the active sites on the inner surface of the pore. The flux of A through the pore is ( N A ) = −DA
dCA dx
(4.198)
where DA: diffusivity of A through the pore CA: concentration of A in the gas at position x within the pore Specific reaction rate of A is
(− rA′ ) = kCA
(kmol of A converted)/(s) (kg of catalyst)
www.Ebook777.com
(4.199)
Free ebooks ==> www.ebook777.com 351
Heterogeneous Reactors
Active site
X+Δx X
d
CAs
X=0
L
X=L
Figure 4.24 Diffusion and reaction in a single pore in the catalyst pellet.
Define ρp: catalyst density kg of catalyst/m3 of pellet a: specific pore surface area m2 pore area/m3 of pellet Taking a steady-state balance of A across this section of the pore volume Rate of transfer Rate of transfer Rate of conversion + of A into the section = of A out of the section of A in the section x x + ∆x
dCA dC A ρp π 2 π 2 + (kC A ) (πd∆x) d −DA = d −DA a 4 4 dx x dx x + ∆x
(4.200) (4.201)
Dividing the terms in Equation 4.201 by (π/4)d2DAΔx and taking limits as Δx → 0, we get the second-order differential equation d 2CA 4kρp − CA = 0 aDA d dx 2
(4.202)
The boundary conditions are
CA = CAS At x = 0 dC A and = 0 At x = L as theflux N A = 0 at x = L (pore wall) dx
www.Ebook777.com
(4.203)
Free ebooks ==> www.ebook777.com 352
Green Chemical Engineering
The general solution to the second-order differential Equation 4.202 is CA = A1e
( 4 kρp/adDA )L( x/L)
+ A2e −
4 kρp/adDA L( x/L)
(4.204)
Define Φ=L
4kρp = Thiele modulus adDA
(4.205)
It may be noted that the Thiele modulus Φ depends on the pore dimensions, namely, pore length L and pore diameter d, and does not depend on the pellet shape and pellet size. Writing Equation 4.205 in terms of the Thiele modulus Φ, we have CA = A1e Φx/L + A2e −( Φx/L )
(4.206)
Applying the boundary conditions (4.203) at x = 0 to Equation 4.206, we have CAS = A1 + A2
(4.207)
Taking the derivative of CA with respect to x and equating dCA/dx to 0 at x = L, we have dCA dx
x=L
AΦ A Φ = 1 e Φ ( x / L) − 2 e − Φ ( x / L) =0 L L x=L
which reduces to A2e − Φ = A1e Φ
(4.208)
Solving Equations 4.207 and 4.208 for integrating constants A1 and A2, we get
A1 =
C AS e − Φ eΦ + e−Φ
(4.209)
A2 =
CAS e Φ eΦ + e−Φ
(4.210)
Substituting Equation 4.209 and Equation 4.210 for the integration constants A1 and A2 into Equation 4.206, we get CA =
CAS e − Φ e Φ( x/L ) + e Φ e − Φ( x/L ) e + e−Φ Φ
which finally reduces to
CA =
CAS cosh Φ(1 − ( x/L)) cosh Φ
www.Ebook777.com
(4.211)
Free ebooks ==> www.ebook777.com 353
Heterogeneous Reactors
Taking derivative of CA with respect to x and evaluating dCA/dx at x = 0, we get
dCA dx
x=0
C x −Φ = AS sinh Φ 1 − L x = 0 cosh Φ L dCA dx
C Φ tanh Φ = − AS L
x=0
(4.212)
The flux of A, NA at the pore mouth (x = 0) is ( N A ) = −DA N A = DA
dCA dx
x =0
CASΦ tanh Φ L
The rate of transfer of A from the bulk gas into the pore is
π D C Φ π rA = N A d 2 = A AS tanh Φ d 2 4 4 L
(4.213)
Define rA0 as the rate of transfer of A into the pore if resistance to pore diffusion is neglected. In this case, CA = CAS for all 0 ≤ x ≤ L.
(r ) = (kC o A
AS
)
ρp (πdL) a
(4.214)
By definition, effectiveness factor η is η=
rA rAo
Substituting Equations 4.213 and 4.214 for rA and rAo into the above equation, we get the final equation for η as η=
tanh Φ Φ
(4.215)
4.2.1.6 Global Rate Equation Rate equations have been derived for catalyst pellets of different shapes (slab, sphere) by combining the equation for the rate of internal pore diffusion and rate of reaction (Sections 4.2.1.1 and 4.2.1.2). This rate equation (or flux equation), which is a function of concentration of A, CAS on the external surface of the catalyst pellet, is written as
N A = ηkρp LoCAS
www.Ebook777.com
(4.216)
Free ebooks ==> www.ebook777.com 354
Green Chemical Engineering
CAg
Gas film
CAs
Catalyst pellet
Figure 4.25 Single catalyst pellet.
where L0 is the equivalent length of the catalyst pellet that is equal to L for slab, R/2 for cylinder and R/3 for sphere. Consider a catalyst pellet (Figure 4.25) of some regular shape in contact with the gas stream containing reactant A at concentration CAg. The flux of A from the bulk gas to the surface of the pellet is N A = k g (C Ag − CAS )
(4.217)
where kg: gas film mass transfer coefficient Equating Equations 4.216 and 4.217, we get N A = k g (CAg − CAS ) = ηkρp LoCAS
(4.218)
Solving Equation 4.218 for CAS, we get CAS =
kg CAg (k g + ηkρp Lo )
(4.219)
Substituting Equation 4.219 for CAS into Equation 4.216, we get the global rate equation (or flux equation) NA =
CAg [(1/k g ) + (1/ηkρp Lo )]
(4.220)
This equation is made use of in the design of catalytic reactors discussed in the following section. 4.2.2 Catalytic Reactors Catalytic reactors are broadly classified as two-phase and three-phase reactors. In twophase reactors, a single-phase fluid containing the reactant in either gas or liquid phase is passed over a fixed quantity of solid catalyst pellets or particles kept in a reaction vessel. In three-phase reactors, a multiphase fluid containing one reactant in the gas phase and the second reactant in the liquid phase is passed over solid catalysts kept in the reaction vessel. In this section, simple design equations are developed for some common types of catalytic reactors.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 355
Heterogeneous Reactors
4.2.2.1 Two-Phase Catalytic Reactors Fluid–solid contacting towers such as a packed bed or a fluidised bed are used for carrying out two-phase catalytic reactions. Packed bed reactors are used if the catalyst is in the form of solid pellets, where as fluidised bed reactors are used if the catalyst is solid particles. 4.2.2.1.1 Packed Bed Catalytic Reactor Consider a packed bed catalytic reactor (shown in Figure 4.26) in which a reaction A → B is carried out. A fluid containing the reactant A at a feed concentration CAO is passed through the bed of catalyst pellets of some regular shape and size. CAf is the exit concentration of A. The fractional conversion of A achieved in the reactor is xAf = 1 − (CAf/CAO). Define v: volumetric flow rate of fluid (m3/s) εB: porosity of the bed a: specific surface area of the catalyst pellets in the bed (m2/m3) = 1/Lo S: cross-sectional area of the bed (m2) Consider a section of the bed of length dz at a distance z from the fluid inlet. CAg is the concentration of A in the gas entering this section. dCAg is the change in concentration of A in the gas phase across the section. The flux of A from the gas phase to the catalyst pellet is given by Equation 4.220: NA =
CAg [(1/k g ) + (1/ηkρp Lo )]
υ, CAf
υ, CA + dCAg
z
dʓ
ʓ
CAg υ s
υ, CAo Figure 4.26 Schematic diagram of packed bed catalytic reactor.
www.Ebook777.com
(4.221)
Free ebooks ==> www.ebook777.com 356
Green Chemical Engineering
Taking a steady-state balance of A in the gas phase across this section Rate of transfer Rate of flow Rate of flow + of A from the gas to the of A into the section = of A out of the section catalyst in the section z z + + ∆z νCAg = [ ν(CAg + dC Ag )] + ( N A )[( a∆z)(1 − ε B )S]
(4.222) (4.223)
Rearranging Equation 4.223 and integrating it between the limits z = 0 and z = z, we get Z
CAf
νdCAg
∫ dz = − ∫ aS(1 − ε )N
0
B
CAo
(4.224) A
As the specific surface area of the pellet a = 1/Lo, the equation for the height of the tower reduces to νLo z= S(1 − ε B )
CAo
∫
CAf
dC Ag NA
(4.225)
Substituting Equation 4.221 for flux NA into Equation 4.225, we get the final equation for the calculation of tower height Z as
Z=
νLo 1 1 1 + ln S(1 − ε B ) k g ηkρp Lo 1 − x Af
(4.226)
This is the packed tower design equation used for calculating the height of the packed bed required to achieve a specified conversion xAf. Problem 4.9 Wahao et al. (1962) have reported the results of experiments conducted on a laboratoryscale fixed bed catalytic reactor to study the conversion of O-H2 to p-H2 at an isothermal condition of −196°C and at a pressure of 40 psi gauge. The catalyst used is Ni on Al2O3 in the form of 1/8” × 1/8” cylinderical pellet (surface area is 150 m2/g). The bed porosity εB = 0.33. The reaction is at first-order reversible O − H 2 p − H 2 and the rate equation is
C (− rA ) = k C A − B kmol/(s)(kg ⋅ catalayst) k
where
k = 1.1 × 10 −3 m 3 /(kg ⋅ cat)(s)
www.Ebook777.com
Free ebooks ==> www.ebook777.com 357
Heterogeneous Reactors
The equilibrium conversion of o-H2 at the specified temperature and pressure is 50.26%. The following data are reported: ρp = density of catalyst pellet = 1910 kg/m3 ρH = density of H2 at 196°C and 40 psi gauge pressure = 1.187 kg/m3 2 DH = diffusivity of H2 = 3.76 × 10−6 m2/s 2 μ = viscosity = 3.48 × 10−6(kg/ms) It is required to scale up the reactor to process 600 m3/h of fluid stream (at −196°C and 40 psi gauge pressure) containing 95% (mole) of O-H2 and achieve 95% of equilibrium conversion. The reactor diameter is 50 cm. Calculate the height of the packed bed reactor. Following correlations for packed bed hold good:
jD =
0.458 ρdp U ∈B µ
jD =
kg µ U ρDA
−0.407
2/ 3
Cylindrical catalyst pellets of 1/2″ × 1/2″ size are used in the packed bed and bed porosity εB = 0.45. The rate equation for the reversible reaction is written as (− rA ) =
k1(1 + K ) (C A − C Ae ) K
where CAe is the equilibrium concentration. The modified Thiele modulus ϕ′ is φ′ = L0
k ′ρ p k1(1 + k ) ρp = L0 k DA DA
And effectiveness factor η is η=
tanh φ′ φ′
For cylinder, L0 = R/2. The global flux equation is
NA =
C Ag (1/k g ) + (1/ηk ′ρP L0 )
(
)
where C Ag = CAg − C Ae . The height of the packed bed reactor is given by the equation
υL0 Z= S(1− ∈B )
C A 0
∫
C Af
dC Ag NA
www.Ebook777.com
Free ebooks ==> www.ebook777.com 358
Green Chemical Engineering
Z=
υL0 1 1 C A 0 + ln S(1 − ∈B ) k g ηk ′ρP L0 C Af
C A 0 C − C Ae x Ae = A0 = C Af − C Ae x Ae − x Af C Af
Z=
x Ae 1 υL0 1 + ln S(1 − ∈B ) k g ηk ′ρP L0 x Ae − x Af
Equilibrium conversion xAe = 0.5026 and equilibrium constant K is K =
x Ae 0.5026 = = 1.01 1 − x Ae 1 − 0.5026
k(1 + K ) (1.1 × 10 −3 )(2.01) = = 2.19 × 10 −3 (1.01) k
k′ =
Particle diameter dp = 1″/2 = 1.27 × 10−2 m. For cylinder L0 =
φ′ = L0
R 1.27 × 10 −2 = = 3.175 × 10 −3 m 2 4
k ′ρp (2.19 × 10 −3 )(1910) = (3.175 × 10 −3 ) = 3.348 DA (3.76 × 10 −6 ) η=
tanh φ′ = 0.298 φ′
Calculation of mass transfer coefficient kg
υ=
600 = 0.1667 m 3 /s 3600
S=
πD2 π(0.5)2 = = 0.196 m 2 4 4
υ=
v 0.1667 = = 0.85 m/s S 0.196
ReP =
ρdP U (1.187 )(1.27 × 10 −2 )(0.85) = = 3682 µ (3.48 × 10 −6 )
www.Ebook777.com
Free ebooks ==> www.ebook777.com 359
Heterogeneous Reactors
Sc =
µ (3.48 × 10 −6 ) = = 0.78 ρDA (1.187 )(3.76 × 10 −6 )
jD =
0.458 0.458 (Re p )−0.407 = (3682)−0.407 = 0.036 0.45 ∈B
kg =
jD U (0.036)(0.85) = = 0.0361 m/s (Sc)2/3 (0.78)2/3
Z=
x Ae 1 υL0 1 + ln S(1 − ∈B ) k g ηk ′ρP L0 x Ae − x Af
xAf = 0.95 xAe; x Ae 1 x − x = 1 − 0.95 = 20 Ae Af
Z=
(0.1667 )(3.175 × 10 −3 ) 1 1 + ln(20) −3 −3 (0.196)(1 − 0.45) 0.0361 (0.298)(2.19 × 10 )(1910)(3.175 × 10 )
= 4.13 m
Note: Refer MATLAB program: catreact_dsn_pckbed.m 4.2.2.1.2 Fluidised Bed Catalytic Reactor In fluidised bed catalytic reactors, catalysts in the form of small solid particles (of size www.ebook777.com 360
Green Chemical Engineering
υ, CAf Catalyst particle
υ, CA+ dCAg
z
dʓ
CAg υ
ʓ
υ, CAO Figure 4.27 Fluidised bed catalytic reactor (particulate fluidisation).
Taking the size of the catalyst particle to be very small, R → 0, the equation for bed height z gets simplified to z=
ν 1 ln S(1 − ε B )kρp 1 − x Af
(4.228)
Problem 4.10 A reagent (A) dissolved in water undergoes reaction in a fluidised bed of spherical resin particles (catalyst). Fluid flows at a rate of 55 m3/h through the reactor tube of 50 cm diameter. Resin particles are of diameter 1 mm and density ρs = 1200 kg/m3. Calculate the height of the fluidised bed required to achieve 95% conversion of the reagent. The following data are reported: ρ = density of fluid = 998 kg/m3 μ = fluid viscosity = 10−3 Ns/m2 DA = diffusivity of reagent in water = 1.62 × 10−9 m2/s k = rate constant of first-order reaction = 1.3 × 10−4 m3/(kgcat)s The following mass transfer correlation holds good for fluidised bed reactor:
Sh =
k m dp 0.81 1/2 1/3 Re p Sc = DA ∈ u ∈= ut
1/n
www.Ebook777.com
Free ebooks ==> www.ebook777.com 361
Heterogeneous Reactors
n = 4.45 Re−p0.1
Terminal settling velocity = ut =
(ρs − ρ)dp2 g 18 µ
where Rep = (ρdpu/μ) and Sc = μ/ρDA. The equation for bed height Z is R 1 1 υ + ln S(1− ∈B ) 3k g k ρP 1 − x Af
Z=
dp = 1 mm = 1 × 10 −3 m
R = 0.5 × 10 −3 m = 5 × 10 −4 m
υ=
55 = 1.528 × 10 −2 m 3/s 3600
S=
π(0.5)2 = 0.196 m 2 4
u=
v 1.528 × 10 −2 = = 0.078 m/s S 0.196
ρdpu (998)(1 × 10 −3 )(0.078) = = 77.8 Re p = (10 −3 ) µ Sc =
µ (10 −3 ) = = 619 ρDA (998)(1.62 × 10 −9 )
n = 4.45 Re−p0.1 = 4.45(77.8)−0.1 = 2.88
2
(ρs − ρ)dp g (1200 − 998)(1 × 10 −3 )2 (9.81) ut = = = 0.11 m/ss 18µ 18(10 −3 ) 1/n
1/2.88
u ∈B = ut
Sh =
0.81 1/2 1/3 Re p Sc ∈
Sh =
0.81 (77.8)1/2 (619)1/3 = 68.4 0.89
km =
0.078 = 0.11
= 0.89
(68.4)(1.62 × 10 −9 ) Sh DA = = 1.11 × 10 −4 m/s (1 × 10 −3 ) dp
www.Ebook777.com
Free ebooks ==> www.ebook777.com 362
Green Chemical Engineering
Bed height Z is Z=
Z=
R 1 1 υ + ln S(1 − ∈B ) 3k g k ρP 1 − x Af
(1.528 × 10 −2 ) (5 × 10 −4 ) 1 + ln(20) (0.196)(1 − 0.89) (3)(1.11 × 10 −4 ) (1.3 × 10 −4 )(1200)
Z = (0.708)[1.5 + 6.41](3) = 16.8 m
The reactor is quite tall. This is because the voidage fraction ∈B is very large. We can rework the design by increasing the reactor diameter. Let us take the reactor diameter to be 80 cm. S=
u=
π(0.8)2 = 0.502 m 2 4
v 1.528 × 10 −2 = = 0.0304 m/s S 0.502
ρdpu (998)(1 × 10 −3 )(0.0304) = = 30.3 Re p = (10 −3 ) µ
n = 4.45 Re−p0.1 = 4.45(30.3)−0.1 = 3.16
u ∈B = ut Sh =
km =
1/n
0.0304 = 0.11
1/3.16
= 0.67
0.81 (30.3)1/2 (619)1/3 = 56.7 0.67
(56.7 )(1.62 × 10 −9 ) ShDA = = 9.18 × 10 −5 m/s (1 × 10 −3 ) dp
Bed height Z is Z=
=
R υ 1 1 ln + S(1 − ∈B ) 3k g k ρP 1 − x Af (1.528 × 10 −2 ) (5 × 10 −4 ) 1 + ln(20) −5 −4 (0.502)(1 − 0.67 ) (3)(9.18 × 10 ) (1.3 × 10 )(1200)
= (0.0922)[1.82 + 6.41](3) = 2.3 m Note: Refer MATLAB Program: catreact_dsn_fluidbed1.m
www.Ebook777.com
Free ebooks ==> www.ebook777.com 363
Heterogeneous Reactors
υ, CAf Bubble phase (gas) υ, CA+d CAg
Dense phase (catalyst particles + gas) z
d CAg υ
CAb
CAd
Concentration profile across a single bubble υ, CAO Figure 4.28 Fluidised bed catalytic reactor (aggregate fluidisation).
Kunni–Levenspiel (K–L model) developed a mathematical model for fluidised bed catalytic reactors in which aggregate fluidisation occurs, resulting in the formation of gas– solid bubbles (Figure 4.28). Gas containing reactant A at concentration CAb rises in the form of bubbles (bubble phase) through a dense phase of solid catalyst particles immersed in a stream of gas. CAd is the concentration of A in the dense phase in contact with the bubble containing A at concentration CAb. As the bubble rises through the bed, reactant A would move from the bubble to the dense phase and would undergo reaction in the dense phase on coming into contact with the catalyst particles. Consider a section of the fluidised bed reactor of length dz at a distance z from the fluid inlet. CAb is the concentration of A in the bubbles entering the section at z and dCAb is the change in concentration of A in the bubble across the section. Define ab: specific surface area of bubbles (m2/m3) υ: volumetric flow rate of feed (m3/s) k: specific reaction rate constant S: cross-sectional area of the bed (m2) εd: volume fraction of the dense phase ρd: catalyst density in the dense phase (kg ⋅ catalyst/m3) kg: gas side mass transfer coefficient (kmol/S m2) Specific reaction rate −rA′ at the catalyst particle is − rA′ = kCAd (kmol of A converted)/(s) (kg ⋅ catalyst). In the section of the fluidised bed considered, the net rate of transfer of A from the bubble to the dense phase is
rAb = k g (C Ab − CAd )( abS∆z)
www.Ebook777.com
(4.229)
Free ebooks ==> www.ebook777.com 364
Green Chemical Engineering
The net rate of conversion of A in the dense phase is rAd = kCAd (ρd ε dS∆z)
(4.230)
As the dense phase in contact with the bubble phase is assumed to have attained steady state rAb = rAd
and equating Equations 4.229 and 4.230, we get (4.231)
k g ab (C Ab − C Ad ) = (kρd ε d )CAd
Solving Equation 4.231 for CAd, we get CAd =
k g abCAb (k g ab + kρd ε d )
(4.232)
Substituting Equation 4.232 for CAd in Equation 4.230, we get the overall global rate of transfer of A from the bubble phase to the dense phase in the section as rA =
C Ab (sdz) [(1/k g ab ) + (1/kρd ε d )]
(4.233)
Taking a molal balance of A in the bubble phase across the section, we get
Rate of transfer Rate of loss of A in the bubble phase = of A from the bubble phase to the dense in the section phase in the section (− υdCAb ) =
CAb (sdz) [(1/k g ab ) + (1/kρd ε d )]
(4.234)
Rearranging the terms in Equation 4.234 and integrating between z = 0 and z = Z, we get Z
∫ 0
1 υ 1 dz = − + S k g ab kρd ε d
CAf
∫
CAo
dCAb CAb
(4.235)
Finally, the design equation for the calculation of bed height Z reduces to
1 1 υ 1 ln Z = + S k g ab kρd ε d 1 − x Af
www.Ebook777.com
(4.236)
Free ebooks ==> www.ebook777.com 365
Heterogeneous Reactors
Problem 4.11 Gas stream containing a reacting chemical species (A) is passed through a bubbling fluidised bed catalytic reactor, at a rate of 350 m3/h. The reactor has fine catalyst particles present in the dense phase, which occupies 74% of the bed volume. The density of the catalyst in the dense phase is 89 kg ⋅ cat/m3. The reaction is first order with rate constant k = 5 × 10−3 m3/(kg ⋅ cat)(s). The bubble side mass transfer coefficient is reported as (kgab) = 1.1 s−1. The diameter of the reactor tube is 50 cm. Calculate the height of the fluidised bed reactor required to achieve 90% conversion. The design equation for calculation of bed height Z Z=
υ 1 1 1 + ln S k g ab k ρd ∈d 1 − x Af
υ=
350 = 0.0972 m/s 3600
S=
π 2 π D = (0.5)2 = 0.1963 m 2 4 4
x Af = 0.9 k g ab = 1.1 s −1
k = 5 × 10 −3 m 3 /(kg ⋅ cat)(s)
ρd = 89(kg ⋅ cat)/m 3
ε d = 0.74 Z=
(0.0972) 1 1 1 ln + (0.1963) 1.1 (5 × 10 −3 )(89)(0.74) 1 − 0.9
= (0.496) (0.91 + 3.04 )( 2.303 ) = 4.5 m
Note: Refer MATLAB program: catreact_dsn_fluidbed2.m 4.2.2.2 Three-Phase Catalytic Reactors Three-phase catalytic reactions are usually carried out in trickle bed reactors or slurry reactors. In trickle bed reactors (Figure 4.29), the catalysts in the form of pellets are placed in a packed bed and the reactant (A) present in the gas phase is passed through the bed from the bottom; the other reactant (B) in the liquid phase is passed from the top of the bed. For example, hydrodesulphurisation of petroleum oil (diesel oil) in the presence of V2O5 catalyst pellets is carried out in trickle bed reactors. The reaction is
2 O 5 (X ) H 2 ( g ) + petroleum ⋅ S(l) V → H 2S + (petroleum oil)
www.Ebook777.com
Free ebooks ==> www.ebook777.com 366
Green Chemical Engineering
(oil s) B
H2S
Catalyst pellet
H2
Desulphurised oil
Figure 4.29 Trickle bed reactor.
In slurry reactors (Figure 4.30), a slurry of liquid containing the reactant B mixed with solid catalyst particles is passed through the reaction vessel while the gas containing reactant A is bubbled through the slurry contained in the vessel. Slurry reactor is used for the hydrogenation of vegetable oil in the presence of Ni catalyst particles. The reaction is 5 (X ) → vanaspathi H 2 ( g ) + vegetable oil(l) Ni
At any particular location within the volume of the slurry reactor, one would find a gas bubble containing the reactant A and a solid catalyst particle in contact with the liquid phase containing reactant B as shown in Figure 4.31. Define CAg: concentration of A in the bulk gas phase within the bubble i CAg : concentration of A in the gas at the gas–liquid interphase i CAL concentration of A in the liquid at the gas–liquid interphase CAL: concentration of A in the bulk liquid phase CAC: concentration of A on the surface of a catalyst pellet ab: gas bubble surface area per unit reactor volume (m2/m3)
υ, CAf
υ, CAO Liquid (slurry) feed in
Liquid (slurry) feed out
Liquid slurry dV Gas bubble Solid catalyst particle Figure 4.30 Slurry reactor.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 367
Heterogeneous Reactors
Liquid phase Gas bubble CAg
Catalyst particle Gas–liquid interphase
CA
Liquid–solid interphase
CAg CAgi
CALi CAL
Liquid film
Gas film
Liquid film
CAc
Figure 4.31 Concentration profile across gas–liquid–solid interfaces in a slurry reactor.
ac: catalyst surface area per unit reactor volume (m2/m3) ρd: mass of catalyst particles per unit reactor volume (kg/m3) kg: gas film mass transfer coefficient (m/s) kl: liquid film mass transfer coefficient at the gas–liquid interface (m/s) kc: liquid film mass transfer coefficient at the liquid–solid interface (m/s) HA: Henry’s law constant Assuming reactant ‘A’ to be the limiting reactant at the reaction site (catalyst particle), the following steps are involved in the reaction of A:
1. Transfer of A from the bulk gas inside the gas bubble to the gas–liquid interphase. This happens at a rate r1:
(
i r1 = k g ab CAg − CAg
)
(4.237)
i 2. A dissolves in the liquid at the interphase and attains concentration CAL in the liquid at the gas–liquid interphase. As the gas and liquid phases are at equilibrium in the interphase, Henry’s law is assumed to hold good. i i CAg = H AC AL
www.Ebook777.com
(4.238)
Free ebooks ==> www.ebook777.com 368
Green Chemical Engineering
3. Transfer of A from the gas–liquid interphase to the bulk liquid. This happens at a rate r2:
(
i r2 = k L ab C AL − C AL
)
(4.239)
4. Transfer of A from the bulk liquid to the surface of the catalyst particle at a rate r3:
r3 = kc ac (CAL − CAC )
(4.240)
5. Conversion of A to the product at the surface of the catalyst particle and this happens at a rate r4: r4 = kρdCAC
(4.241)
As the reactor is operating at steady state, all the rates (r1, r2, r3, r4) are equal, that is, r1 = r2 = r3 = r4
(4.242)
Combining all the rate Equations 4.237, 4.239, 4.240 and 4.241 and eliminating the intermediate concentration terms from the rate expressions, we obtain the global rate equation as a function of CAg, which is the bulk concentration of A in the gas phase. The final equation for the global rate rA is rA =
CAg kmol A H A [(1/H A k g ab ) + (1/k L ab ) + (1/kc ac ) + (1/kρd )] (s)(m 3 )
(4.243)
Taking a balance of reactant A on the gas side across an elemental volume dV of the slurry reactor, we get
− υdC Ag = rA dV
(4.244)
where υ: volumetric flow rate of the gas (m3/s) dCAg: change in concentration of A in the gas phase across the elemental volume dV of the reactor Substituting Equation 4.243 for rA into Equation 4.244 and integrating between CAg = CAo and CAg = CAf, we get the design equation for the slurry reactor.
1 1 1 1 1 V = υH A + + + ln H k a k a k a k x Af ρ 1 − L b c c d A g b
(4.245)
Equation 4.245 can be used to calculate the volume V of the slurry reactor required to achieve a specified conversion xAf.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 369
Heterogeneous Reactors
Problem 4.12 A catalytic reaction between a chemical compound A in the gas phase and a compound B in the liquid phase is carried out in a slurry reactor. The reaction is represented as
A(g) + B(l) → Products
Slurry is prepared by mixing 0.05 mm diameter catalyst particles with an aqueous solution containing reactant B. This slurry is passed continuously through a stirred tank into which a gas stream containing reactant A is bubbled at the rate of 1000 m3/h. Slurry in the reaction vessel is well mixed. Bubbles rise individually in plug flow. The bubbles are uniformly distributed and each bubble is 3 mm in diameter. Gas hold-up in the vessel is Vg 0.09 m3 of gas per m3 of liquid. The slurry density of the catalyst particle is ρp = 1100 kg/m3. The slurry density of the catalyst is ρd = 80 kg of catalyst per m3 of liquid. The overall reaction is first order with respect to compound A and the rate constant is k = 1.2 × 10−2 m3/kg ⋅ cat ⋅ s. Calculate the volume required to achieve 80% conversion of A. The following data are reported: Henry’s law constant HA = 42 (kmol/m3 of gas)/(kmol/m3 of liquid) Gas side mass transfer coefficient = kg = 2.1 × 10−3 m/s Liquid side mass transfer coefficient = kL = 1.1 × 10−2 m/s Liquid to particle transfer coefficient = kc = 4.1 × 10−3 m/s The design equation for the calculation of volume V is
1 1 1 1 1 V = vH A + + + ln H k a k a k a kP 1 − x Af L b c c d A g b Diameter of particle dp = 5 × 10−5 m Diameter of bubble db = 3 × 10−3 m
P 6 ac = d m 3 /m 3 Pp dp
6 80 = = 8727 m 2 /m 3 1100 (5 × 10 −5 )
ab =
v=
of liquid
6VB 6 × (0.09) = = 180 m 2 /m 3 db (3 × 10 −3 ) 1000 = 0.2778 m 3 /s 3600
1 x Af = 0.8 ⇒ ln = 1.61 1 − x Af
www.Ebook777.com
Free ebooks ==> www.ebook777.com 370
Green Chemical Engineering
The reactor volume V is
1 1 1 ( 4.2)(2.1 × 10 −3 )(180) + (1.1 × 10 −2 )(180) + ( 4.1 × 10 −3 )(8727 ) (1.61) V = (0.2778)( 42) 1 + −2 1 2 10 80 ( . × )( ) = (18.78)[ 0.063 + 0.505 + 0.028 + 1.042] = 30.8 m 3
Exercise Problems
1. A sample containing a mixture of solid particles of three different sizes—5, 3 and 1 mm—is kept in a constant environment oven for 1 h. Under these conditions, 5 mm particles are 35% converted, 3 mm particles are 53% converted and 1 mm particles are 70% converted. Assuming that the SCM is valid i. What mechanism is rate controlling? ii. What is the time required for complete conversion of all the solid particles? (Answer: (i) Reaction is rate controlling; (ii) 7.47 h) 2. Solid particles containing a reactant B reacts with a gas stream containing reactant A in a moving grate conveyer-type reactor in a constant gas environment. The feed to the reactor is a mixture of solid particles of four different sizes. The size distribution of the solid particles is as follows: Particle Size (mm) 2 4 6 8
Weight Fraction 0.3 0.2 0.2 0.3
All the particles reside for a period of 20 min in the reactor. SCM holds good and the ash layer diffusion is rate controlling. The time taken for complete conversion of 2 mm particles is 1 h. What is the mean conversion of solid particles in the reactor? (Answer: 45.2%) 3. A mixture of solid particles of four different sizes is fed into a fluidised bed reactor, where it reacts with a stream of gas at constant environment. The mass feed rate of the solid is 10 kg/min and the mass hold-up in the reactor is 100 kgs. The size distribution of the solid particles is as follows: Particle Size (mm) 0.5 1.0 1.5 2.0
Weight Fraction 0.2 0.4 0.3 0.1
www.Ebook777.com
Free ebooks ==> www.ebook777.com 371
Heterogeneous Reactors
SCM holds good and the ash layer diffusion is rate controlling. The time taken for complete conversion of 2 mm particles is 1 h. What is the mean conversion of solid particles in the reactor? (Answer: 73.6%) 4. A fluidised bed reactor is to be designed to carry out the reaction between solid particles containing reactant B and a gas stream containing reactant A. The feed is a mixture of solid particles of four different sizes. The size distribution of the solid particles is as follows: Particle Size (mm) 0.5 1.0 1.5 2.0
Weight Fraction 0.2 0.4 0.3 0.1
SCM holds good and the reaction is rate controlling. The time taken for complete conversion of 2 mm particles is 1 h. What is the mean residence time of the solid particles in the reactor required for 80% mean conversion of solid? (Answer: 0.584 h) 5. A counter-current moving bed reactor is to be designed to carry out a reaction between solid particles containing reactant A and a gas stream containing reactant B:
A(g) + B(s) → Products Solid particles of uniform size of 10 mm diameter move from the top of the bed at a rate of 100 kgs/min counter-current to a stream of gas flowing at a rate of 400 m3/min. The bed is of 1 m diameter. The solid fraction in the bed is 0.7. The partial pressure of A in the feed is 0.3 atm. The reactor is operating at 1 atm pressure and 200°C temperature. The solid density is 4700 kg/m3 and the molecular weight of B is 120. Calculate the height of the bed required for 70% conversion of B. The results of a batch oven experiment conducted in a constant gas environment showed that 5 h was required for complete conversion of 5 mm diameter particles. SCM holds good and the reaction is rate controlling. (Answer: 8.4 m) 6. A packed bed reactor is to be designed to carry out a non-catalytic reaction between a reactant A in the gas phase and a reactant B in the liquid phase: A(g) + B(l) → Products The reaction is a fast reaction. Gas flows at a rate of 5000 m3/h counter-current to the liquid stream flowing at a rate of 1000 m3/h. Partial pressure of A in the gas inlet stream is 1 atm. The reactor operates at 5 atm pressure and 300 K temperature. Bed porosity is 0.6 and specific surface area of the packing material is 105 m2/ m3. The diameter of the bed is 1.5 m. Calculate the height of the bed required for 98% conversion of A. The following data are reported: k: reaction rate constant = 5 × 103 s−1 k Al: liquid side mass transfer coefficient = 2 × 10−3 m/s
www.Ebook777.com
Free ebooks ==> www.ebook777.com 372
Green Chemical Engineering
kg: gas side mass transfer coefficient = 1.5 × 10−8 kmol/m2 s Pa DAl: diffusivity of A in liquid = 2 × 10−8 m2/s HA: Henry’s law constant = 2 × 106 Pa/kmol (Answer: 7.83 m)
7. A reagent (A) dissolved in water undergoes reaction in a fluidised bed of spherical resin particles (catalyst) of 1.5 mm diameter. Fluid flows at a rate of 100 m3/h through the reactor tube of 75 cm diameter. The density of resin particles is 1200 kg/m3 and the density of water is 1000 kg/m3. Fluid viscosity is 10−3 Ns/m2. The diffusivity of the reagent in water is 1.62 × 10−9 m2/s. The first-order rate constant of the catalytic reaction is 3 × 10−4 m3/kg ⋅ cat ⋅ s. Calculate the height of the fluidised bed reactor required to achieve 90% conversion of the reagent. (Answer: 1.86 m)
MATLAB ® Programs List of MATLAB Programs Program Name
Description
Heterogeneous Non-Catalytic Reactors plot_xb_vs_theta_by_tau.m
Program to plot fractional conversion xb versus theta_by_tau for gas–solid reactions—shrinking core model
cal_xb_mean.m
Program to calculate mean conversion of solids xb_bar given the size distribution (batch reactor/moving grate conveyer-type reactor)
cal_xb.m
Program subroutine to calculate fractional conversion xb for the given theta_by_tau gas–solid reaction
cal_xb_mean2.m
Program to calculate mean conversion of solids xb_bar given the residence time distribution of solid particles (rotary tubular reactor)
cal_xb_mean3.m
Program to calculate mean conversion of solids xb_bar given the size distribution (fluidised bed reactor)
cal_xb_fbr.m
Program subroutine to calculate fractional conversion xb for fluidised bed reactor
fbr_mgr_dsgn.m
Program to calculate mean residence time (design problem) for specified mean fractional conversion xb_bar 1. Moving grate conveyer-type reactor 2. Fluidised bed reactor
func_xb_mgr.m
Function subroutine to calculate fractional conversion of solids xb_bar for moving grate reactor
func_xb_fbr.m
Function subroutine to calculate fractional conversion of solids xb_bar for fluidised bed reactor
mbr_dsgn.m
Design of moving bed reactor for gas–solid non-catalytic reactors
react_dsn_pckbed1.m
Program for design of packed bed non-catalytic reactor for gas–liquid reaction fast reaction—reaction between CO2 and MEA solution
react_dsn_pckbed2.m
Program for design of packed bed non-catalytic reactor for gas–liquid instantaneous reaction—reaction between HCL vapour and NaOH solution
www.Ebook777.com
Free ebooks ==> www.ebook777.com 373
Heterogeneous Reactors
MATLAB Programs PROGRAM: plot_xb_vs_theta_by_tau.m % Program to plot fractional conversion xb vs theta_by_tau % for gas solid reactions - shrinking core model clear all ; t_b_t(1) = 0 ; xb1(1) = 0 ; xb2(1) = 0 ; xb3(1) = 0 ; for i = 1:100 ; tbt = i*(1/100) ; t_b_t(i + 1) = tbt ; xb_1 = cal_xb(tbt,1) ; xb_2 = cal_xb(tbt,2) ; xb_3 = cal_xb(tbt,3) ; xb1(i + 1) = xb_1 ; xb2(i + 1) = xb_2 ; xb3(i + 1) = xb_3 ; end ; plot(t_b_t,xb1,'g',t_b_t,xb2,'r',t_b_t,xb3,'c') ; title('SHRINKING CORE MODEL'); xlabel('Theta/Tau') ; ylabel('Fractional Conversion xb') ; legend('Gas film resistance controlling','Ash layer diffusion controlling','Reaction rate controlling');
PROGRAM: cal_xb_mean.m % program to calculate mean conversion of solids xb_bar given the size % distribution (BATCH REACTOR/MOVING GRATE CONVEYER TYPE REACTOR) clear all % PROBLEM DATA %_________________________________________________________________ % size distribution % dia (mm) size_dist = [1 2 4 6
weight fraction 0.2 ; 0.3 ; 0.3 ; 0.2 ] ;
mechanism = 2 ; % 1 - gas-film resistance controlling % 2 - ash-layer diffusion controlling % 3 - reaction rate controlling theta_bar = 0.1667 ;% mean residence time or batch reaction time % batch data
www.Ebook777.com
Free ebooks ==> www.ebook777.com 374
Green Chemical Engineering
tau0 = 4 ;% time taken for complete conversion in HRS for r0 = 4 ;% particle of size diameter mm % CALCULATION %_________________________________________________________________ vec_size = size(size_dist) ; n_data = vec_size(1,1) ; xb_bar = 0 ; ws = 0 ; for i = 1:n_data r = size_dist(i,1) ; % particle size w = size_dist(i,2) ; % weight fraction if ((mechanism == 1) || (mechanism == 3)) tau = tau0*(r/r0); end ; if mechanism == 2 tau = tau0*(r/r0)^2; end ; theta_by_tau = theta_bar/tau ; xb = cal_xb(theta_by_tau,mechanism) ; xb_bar = xb_bar + xb*w ; ws = ws + w ; end ; xb_bar = xb_bar/ws ; % DISPLAY RESULTS %_________________________________________________________________ fprintf('------------------------------------------------------------\n') ; fprintf('BATCH REACTOR/MOVING GRATE CONVEYER TYPE REACTOR \n') ; fprintf('------------------------------------------------------------\n') ; fprintf('MEAN CONVERSION OF SOLIDS - SHRINKING CORE MODEL \n') ; fprintf(' \n') ; if mechanism == 1 fprintf('GAS FILM RESISTANCE IS RATE CONTROLLING \n') ; end ; if mechanism == 2 fprintf('ASH LAYER DIFFUSION IS RATE CONTROLLING \n') ; end ; if mechanism == 3 fprintf('REACTION IS RATE CONTROLLING \n') ; end ; fprintf(' \n') ; fprintf('MEAN RESIDENCE TIME/BATCH REACTION TIME : %10.4f \n',theta_bar) ; fprintf('MEAN FRACTIONAL CONVERSION OF SOLIDS : %10.4f \n',xb_bar) ; fprintf(' \n') ; fprintf('------------------------------------------------------------\n') ;
www.Ebook777.com
Free ebooks ==> www.ebook777.com Heterogeneous Reactors
375
FUNCTION SUBROUTINE : cal_xb.m % Program subroutine to calculate fractional conversion xb % for the given theta_by_tau - gas solid reaction function xb = cal_xb(theta_by_tau,mechanism) if mechanism == 1 % gas - film resistance controlling xb = theta_by_tau ; end; if mechanism == 2 % ash layer resistance controlling xb_o = 0.5 ; xb_n = 1 - ((1-((2*xb_o + theta_by_tau)/3))^1.5) ; while abs(xb_o - xb_n) > 0.00001*xb_o xb_o = xb_n ; xb_n = 1 - ((1-((2*xb_o + theta_by_tau)/3))^1.5) ; end ; xb = xb_n ; end; if mechanism == 3 % reaction rate controlling xb = 1 - (1-theta_by_tau)^3 ; end;
PROGRAM: cal_xb_mean2.m % program to calculate mean conversion of solids xb_bar given the residence % time distribution of solid particles (ROTARY TUBULAR REACTOR) clear all % PROBLEM DATA %_________________________________________________________________ % residence time distribution of solid particles % imp_tracer_data = [0 4 8 12 16 20 24 28 32 36 40 44 ; % t - time in MINS 0 1 8 20 50 100 50 24 10 5 1 0 ] ; % n - No. of tracer particles mechanism = 1 ; % 1 - gas-film resistance controlling % 2 - ash-layer diffusion controlling % 3 - reaction rate controlling % batch data tau0 = 1 ; % time taken for complete conversion in HRS for r0 = 2 ; % particle of size diameter mm tau0 = tau0*60 ; % conversion to minutes
www.Ebook777.com
Free ebooks ==> www.ebook777.com 376
Green Chemical Engineering
% CALCULATION %_________________________________________________________________ vec_size = size(imp_tracer_data) ; n_data = vec_size(1,2) ; [theta_bar sigma_sqr] = cal_mean_var(imp_tracer_data) ; E = cal_E_theta(imp_tracer_data) ; for i = 1:n_data t = E(1,i) ; theta_by_tau = t/tau0 ; xb = cal_xb(theta_by_tau,mechanism) ; x_E(1,i) = t ; x_E(2,i) = xb*E(2,i) ; end; xb_bar = trapez_integral(x_E) ; % conversion in rotary tubular reactor % DISPLAY RESULTS %_________________________________________________________________ fprintf('------------------------------------------------------------\n') ; fprintf('ROTARY TUBULAR REACTOR \n') ; fprintf('------------------------------------------------------------\n') ; fprintf('MEAN CONVERSION OF SOLIDS - SHRINKING CORE MODEL \n') ; fprintf(' \n') ; if mechanism == 1 fprintf('GAS FILM RESISTANCE IS RATE CONTROLLING \n') ; end ; if mechanism == 2 fprintf('ASH LAYER DIFFUSION IS RATE CONTROLLING \n') ; end ; if mechanism == 3 fprintf('REACTION IS RATE CONTROLLING \n') ; end ; fprintf(' \n') ; fprintf('MEAN RESIDENCE TIME/BATCH REACTION TIME : %10.4f \n',theta_bar) ; fprintf('MEAN FRACTIONAL CONVERSION OF SOLIDS : %10.4f \n',xb_bar) ; fprintf(' \n') ; fprintf('------------------------------------------------------------\n') ;
PROGRAM: cal_xb_mean3.m % program to calculate mean conversion of solids xb_bar given the size % distribution (FLUIDIZED BED REACTOR) clear all
www.Ebook777.com
Free ebooks ==> www.ebook777.com Heterogeneous Reactors
377
% PROBLEM DATA %_________________________________________________________________ % size distribution % dia (mm) weight fraction size_dist = [1 0.2 ; 1.5 0.3 ; 2 0.3 ; 3 0.2 ] ; mechanism = 3 ; % 1 - gas-film resistance controlling % 2 - ash-layer diffusion controlling % 3 - reaction rate controlling Ms = 300 ;% mass hold up Kgs ms = 30 ;% mass flow rate Kgs/min theta_bar = Ms/ms ;% mean residence time of solid in the FBR in MINS theta_bar = theta_bar/60 ;% convert mims to hours % batch data tau0 = 3 ; % time taken for complete conversion in HRS for r0 = 3 ; % particle of size diameter mm % CALCULATION %_________________________________________________________________ vec_size = size(size_dist) ; n_data = vec_size(1,1) ; xb_bar = 0 ; ws = 0 ; for i = 1:n_data r = size_dist(i,1) ;% particle size w = size_dist(i,2) ;% weight fraction if ((mechanism == 1) || (mechanism == 3)) tau = tau0*(r/r0); end ; if mechanism == 2 tau = tau0*(r/r0)^2; end ; xb = cal_xb_fbr(theta_bar,tau,mechanism) ; xb_bar = xb_bar + xb*w ; ws = ws + w ; end ; xb_bar = xb_bar/ws ; % DISPLAY RESULTS %_________________________________________________________________ fprintf('------------------------------------------------------------\n') ; fprintf('GAS SOLID FLUIDIZED BED REACTOR \n') ;
www.Ebook777.com
Free ebooks ==> www.ebook777.com 378
Green Chemical Engineering
fprintf('------------------------------------------------------------\n') ; fprintf('MEAN CONVERSION OF SOLIDS - SHRINKING CORE MODEL \n') ; fprintf(' \n') ; if mechanism == 1 fprintf('GAS FILM RESISTANCE IS RATE CONTROLLING \n') ; end ; if mechanism == 2 fprintf('ASH LAYER DIFFUSION IS RATE CONTROLLING \n') ; end ; if mechanism == 3 fprintf('REACTION IS RATE CONTROLLING \n') ; end ; fprintf(' \n') ; fprintf('MEAN RESIDENCE TIME IN HOURS : %10.4f \n',theta_bar) ; fprintf('MEAN FRACTIONAL CONVERSION OF SOLIDS : %10.4f \n',xb_bar) ; fprintf(' \n') ; fprintf('------------------------------------------------------------\n') ;
FUNCTION SUBROUTINE: cal_xb_fbr.m % program subroutine to calculate fractional conversion xb for fluidized % bed reactor function xb = cal_xb_fbr(theta_bar,tau,mechanism) if mechanism == 1 % 1 - gas-film resistance controlling xb = (theta_bar/tau)*(1-exp(-1*tau/theta_bar)) ; end ; if mechanism == 2 % 2 - ash-layer diffusion controlling theta_max = tau ; xb_exp(1,1) = 0 ; theta_by_tau = 0 ; xb0 = cal_xb(theta_by_tau,mechanism) ; xb_exp(2,1) = xb0 ; for j = 1:100 ; theta = (j-1)*theta_max/99 ; theta_by_tau = theta/tau ; xb0 = cal_xb(theta_by_tau,mechanism) ; xb_exp(1,j + 1) = theta ; xb_exp(2,j + 1) = xb0*exp(-1*theta/theta_bar); end ; integral_xb_exp = trapez_integral(xb_exp); xb = exp(-1*tau/theta_bar) + integral_xb_exp/theta_bar ; end ; if mechanism == 3 % 3 - reaction rate controlling xb = 3*(theta_bar/tau) - 6*(theta_bar/tau)^2 + 6*((theta_bar/ tau)^3)*(1-exp(-1*tau/theta_bar)) ; end ;
www.Ebook777.com
Free ebooks ==> www.ebook777.com Heterogeneous Reactors
379
PROGRAM: fbr_mgr_dsgn.m % % % %
program to calculate mean residence time (Design Problem)for specified mean fractional conversion xb_bar 1 - Moving Grate Conveyer Type Reactor 2 - Fluidized Bed Reactor
clear all global size_dist mechanism tau0 r0 % DESIGN DATA %_________________________________________________________________ reactor_type = 2 ; % 1 - moving grate conveyer type reactor % 2 - fluidized bed reactor % size distribution % dia (mm) weight fraction size_dist = [1 0.2 ; 2 0.3 ; 4 0.3 ; 6 0.2 ] ; mechanism = 3 ; % 1 - gas-film resistance controlling % 2 - ash-layer diffusion controlling % 3 - reaction rate controlling % batch data tau0 = 4 ;% time taken for complete conversion in HRS for r0 = 4 ;% particle of size diameter mm xb_bar_f = 0.80 ;% mean conversion of solids specified % CALCULATIONS %_________________________________________________________________ y0 = xb_bar_f ; x1 = 0.1 ; % theta_bar1 - initial guess value x2 = 0.3 ; % theta_bar2 - initial guess value if reactor_type == 1 % moving grate conveyer type reactor if x1 > x2 x_big = x1 ; x1 = x2 ; x2 = x_big ; end y1 = func_xb_mgr(x1);% xb_bar1 y2 = func_xb_mgr(x2);% xb_bar2 x3 = x1 + (y0 - y1)*((x2 - x1)/(y2 - y1)) ;% theta_bar3 - by linear interapolation
www.Ebook777.com
Free ebooks ==> www.ebook777.com 380
Green Chemical Engineering
y3 = func_xb_mgr(x3);% xb_bar3 x3_new = x3 + 0.1 ; % theta_bar3_new % pick up new x1 x2 while (abs(x3 - x3_new) > 0.001*x3) x3_new = x3 ; if x3 = x1) && (x3 = x2) type = 3 ; end ; if type == 1 x2 = x1 ; x1 = x3 ; end ; if type == 2 x2 = x3 ; end ; if type == 3 x1 = x2 ; x2 = x3 ; end ; y1 = func_xb_mgr(x1);% xb_bar1 y2 = func_xb_mgr(x2);% xb_bar2 x3 = x1 + (y0 - y1)*((x2 - x1)/(y2 - y1)) ;% theta_bar3 y3 = func_xb_mgr(x3);% xb_bar3 end ; theta_bar_f = x3 ; end
% of reactor_type = 1
if reactor_type == 2% fluidized bed reactor if x1 > x2 x_big = x1 ; x1 = x2 ; x2 = x_big ; end
www.Ebook777.com
Free ebooks ==> www.ebook777.com Heterogeneous Reactors
y1 = func_xb_fbr(x1);% xb_bar1 y2 = func_xb_fbr(x2);% xb_bar2 x3 = x1 + (y0 - y1)*((x2 - x1)/(y2 - y1)) ;%theta_bar3 - by linear interapolation y3 = func_xb_fbr(x3);% xb_bar3 x3_new = x3 + 0.1 ; % theta_bar3_new % pick up new x1 x2 while (abs(x3 - x3_new) > 0.001*x3) x3_new = x3 ; if x3 = x1) && (x3 = x2) type = 3 ; end ; if type == 1 x2 = x1 ; x1 = x3 ; end ; if type == 2 x2 = x3 ; end ; if type == 3 x1 = x2 ; x2 = x3 ; end ; y1 = func_xb_fbr(x1);% xb_bar1 y2 = func_xb_fbr(x2);% xb_bar2 x3 = x1 + (y0 - y1)*((x2 - x1)/(y2 - y1)) ;% theta_bar3 y3 = func_xb_fbr(x3);% xb_bar3 end ; theta_bar_f = x3 ; end % of reactor type = 2 % DISPLAY RESULTS %_________________________________________________________________ if reactor_type == 1
www.Ebook777.com
381
Free ebooks ==> www.ebook777.com 382
Green Chemical Engineering
fprintf('-------------------------------------------------------------\n') ; fprintf('DESIGN OF MOVING GRATE CONVEYER TYPE REACTOR/BATCH \n') ; fprintf('-------------------------------------------------------------\n') ; end ; if reactor_type == 2 fprintf('-------------------------------------------------------------\n') ; fprintf('DESIGN OF FLUIDIZED BED REACTOR \n') ; fprintf('-------------------------------------------------------------\n') ; end ; fprintf('CALCULATION OF MEAN RESIDENCE TIME - SHRINKING CORE MODEL \n') ; fprintf(' \n') ; if mechanism == 1 fprintf('GAS FILM RESISTANCE IS RATE CONTROLLING \n') ; end ; if mechanism == 2 fprintf('ASH LAYER DIFFUSION IS RATE CONTROLLING \n') ; end ; if mechanism == 3 fprintf('REACTION IS RATE CONTROLLING \n') ; end ; fprintf(' \n') ; fprintf('MEAN FRACTIONAL CONVERSION OF SOLIDS : %10.4f \n',xb_bar_f) ; fprintf('MEAN RESIDENCE TIME/BATCH REACTION TIME : %10.4f \n',theta_ bar_f) ; fprintf(' \n') ; fprintf('---------------------------------------------------------- \n') ;
FUNCTION SUBROUTINE: func_xb_mgr.m % function subroutine to calculate fractional conversion of solids xb_bar % for moving grate reactor function xb_bar = func_xb_mgr(theta_bar) global size_dist mechanism tau0 r0 vec_size = size(size_dist) ; n_data = vec_size(1,1) ; xb_bar = 0 ; ws = 0 ; for i = 1:n_data r = size_dist(i,1) ;% particle size w = size_dist(i,2) ;% weight fraction if ((mechanism == 1) || (mechanism == 3)) tau = tau0*(r/r0); end ;
www.Ebook777.com
Free ebooks ==> www.ebook777.com Heterogeneous Reactors
383
if mechanism == 2 tau = tau0*(r/r0)^2; end ; theta_by_tau = theta_bar/tau ; xb = cal_xb(theta_by_tau,mechanism) ; xb_bar = xb_bar + xb*w ; ws = ws + w ; end ; xb_bar = xb_bar/ws ;
FUNCTION SUBROUTINE: func_xb_fbr.m % function subroutine to calculate fractional conversion of solids xb_bar % for fluidized bed reactor function xb_bar = func_xb_fbr(theta_bar) global size_dist mechanism tau0 r0 vec_size = size(size_dist) ; n_data = vec_size(1,1) ; xb_bar = 0 ; ws = 0 ; for i = 1:n_data r = size_dist(i,1) ;% particle size w = size_dist(i,2) ;% weight fraction if ((mechanism == 1) || (mechanism == 3)) tau = tau0*(r/r0); end ; if mechanism == 2 tau = tau0*(r/r0)^2; end ; xb = cal_xb_fbr(theta_bar,tau,mechanism) ; xb_bar = xb_bar + xb*w ; ws = ws + w ; end ; xb_bar = xb_bar/ws ;
PROGRAM: mbr_dsgn.m % DESIGN OF MOVING BED REACTOR FOR GAS SOLID NONCATALYTIC REACTORS % DESIGN DATA %_________________________________________________________________ dp = 10
; % solid particle diameter in mm
www.Ebook777.com
Free ebooks ==> www.ebook777.com 384
ms = 50 vg = 200 rs = 4700 Mb = 120 eps = 0.6 P = 1 T = 250 D = 1 Pa0 = 0.2 xb0 = 0.6 b = 1
Green Chemical Engineering
; ; ; ; ; ; ; ; ; ; ;
% % % % % % % % % % %
solids flow rate Kgs/min volumetric flow rate of gas m3/min density of soild Kg/m3 molecular weight of solid reactant B solids fraction in the bed reactor pressure in ATM reactor temperature in deg C tower diameter in m partial pressure of reactant A at the inlet fractional conversion of B to be acheived stoichiometric coefficient
% Batch data tau0 = 8 ; % time in HRS for complete conversion of dp0 = 5 ; % particle of specified diameter in mm mechanism = 3 ; % 1 - gas film resistance rate controlling % 2 - ash layer diffusion rate controlling % 3 - reaction rate controlling % CALCULATIONS %_________________________________________________________________ % Estimation of controlling step rate constant from batch data tau0 = (tau0*3600) ;% conversion of Hrs to seconds rb = rs/Mb; % molal density Kgmoles/m3 Cag = (Pa0*1.013e + 5)/(8314*(T + 273)) ;% concentration of A in Kgmoles/m3 r0 = (dp0/2)/1000 ; % particle radius in m kg = (rb*r0)/(3*b*Cag*tau0) ; % mass transfer coefficient - gas film resistance controlling Da = (rb*r0^2)/(6*b*Cag*tau0);% diffsion coefficient - ash layer diffusion controlling k = (rb*r0)/(b*Cag*tau0) ; % reaction rate constant - reaction rate controlling % Calculation of bed height S = (3.14/4)*(D^2) ; % u_bar = ((vg/60)/S) ; % ms = ms/60 ; % r = (dp/2)/1000 ; %
bed cross sectional area m2 superficial gas velocity m/s solids flow rate in Kg/s particle radius in m
Ca0 = (Pa0*1.013e + 5)/(8314*(T + 273));% concentration of A (Kgmoles/m3) in reactor inlet K = ms/(3*b*Mb*eps*S) ; for i = 1:51 xb = ((i-1)/50)*xb0 ; Cag = Ca0 - (ms/(b*S*u_bar*Mb))*(xb0 - xb) ; if mechanism == 1 f_xb = (K*r)/(kg*Cag) ; end ; if mechanism == 2
www.Ebook777.com
Free ebooks ==> www.ebook777.com Heterogeneous Reactors
385
f_xb = ((K*r^2)/(Da*Cag))*((1-(1-xb)^(1/3))/((1-xb)^(1/3))) ; end ; if mechanism == 3 f_xb = ((K*r)/(k*Cag))*(1/((1-xb)^(2/3))) ; end ; mat_f_xb(1,i) = xb ; mat_f_xb(2,i) = f_xb ; end ; z = trapez_integral(mat_f_xb) ;% tower height % DISPLAY RESULTS %_________________________________________________________________ fprintf('---------------------------------------------------------- \n') ; fprintf('DESIGN OF MOVING BED REACTOR FOR GAS SOLID REACTION \n') ; fprintf('---------------------------------------------------------- \n') ; fprintf(' \n') ; if mechanism == 1 fprintf('GAS FILM RESISTANCE IS RATE CONTROLLING \n') ; end ; if mechanism == 2 fprintf('ASH LAYER DIFFUSION IS RATE CONTROLLING \n') ; end ; if mechanism == 3 fprintf('REACTION IS RATE CONTROLLING \n') ; end ; fprintf(' \n') ; fprintf('BED HEIGHT in m : %10.4f \n',z) ; fprintf('FRACTIONAL CONVERSION OF SOLIDS : %10.4f \n',xb0) ; fprintf(' \n') ; fprintf('---------------------------------------------------------- \n') ;
PROGRAM: react_dsn_pckbed1.m % Program for design of packed bed non catalytic reactor for % gas liquid reaction fast reaction - reaction % between CO2 and MEA solution clear all % INPUT DATA %_________________________________________________________________ kg = 2.639*10^-9 ; % g as side mass transfer coefficient kgmoles/m3 sec Pa 1/Hr kal = 3.889*10^-4 ; % liquid side mass transfer coefficient m/s Dal = 2.39*10^-9 ; % liquid side diffusivity of A m2/s k = 7.194*10^4 ; % reaction rate constant 1/Sec eps = 0.45 ; % bed porosity sp = 105 ; % specific surface area m2/m3
www.Ebook777.com
Free ebooks ==> www.ebook777.com 386
Ha = 4.89*10^6 ; vg = 6500 ; vl = 1000 ; Pa0 = 2 ; Paf = 0.02 ; P = 14.3 ; T = 315 ; D = 2 ;
Green Chemical Engineering
% % % % % % % %
Henry's law constant m3 Pa/Kgmoles volumetric flow rate of gas m3/hr volumetric flow rate of liquid m3/hr inlet partial pressure of A bar exit partial pressure of A bar bed pressure 14.3 bar temperature K tower diameter m
% CALCULATIONS %_________________________________________________________________ R = 8314 ; % gas law constant in J/Kgmoles K xaf = 1 - Paf/Pa0 ; % fractional conversion of A gama = sqrt(k*Dal)/kal ; % Hatta number E = gama/tanh(gama) ; % Enhancement factor vg = vg/3600 ; % gas flow rate in m3/sec S = (3.14/4)*D^2 ; % tower cross sectional area z = (vg/(R*T*S*(1-eps)*sp))*(1/kg + Ha/(E*kal))*log(1/(1-xaf)) ;% tower height % DISPLAY RESULTS %_________________________________________________________________ fprintf('---------------------------------------------------------- \n') ; fprintf('DESIGN OF PACKED BED NON CATALYTIC GAS LIQUID REACTOR - FAST REACTION \n') ; fprintf(' \n') ; fprintf('Volumetric gas flow rate vg m3/s : %10.4f \n',vg) ; fprintf('Fractional Conversion : %10.4f \n',xaf) ; fprintf('Reactor temperature K : %10.4f \n',T) ; fprintf('Bed Diameter m : %10.4f \n',D) ; fprintf(' \n') ; fprintf('Bed Height m : %10.4f \n',z) ; fprintf(' \n') ; fprintf('---------------------------------------------------------- \n') ;
PROGRAM: react_dsn_pckbed2.m % Program for design of packed bed non catalytic reactor for gas liquid % instantaneous reaction - reaction between HCL vapour and NaOH solution clear all % INPUT DATA %_________________________________________________________________ kg = 2.1*10^-9 ; % kal = 4.2*10^-4 ; % Dal_by_Dbl = 1 ; % eps = 0.45 ; % sp = 105 ; %
gas side mass transfer coefficient kgmoles/m3 sec Pa 1/Hr liquid side mass transfer coefficient m/s stant Dal = Dbl bed porosity specific surface area m2/m3
www.Ebook777.com
Free ebooks ==> www.ebook777.com 387
Heterogeneous Reactors
Ha = 2.2*10^5 ; % Henry's law constant m3 Pa/Kgmoles vg = 6500 ; % volumetric flow rate of gas m3/hr vl = 1000 ; % volumetric flow rate of liquid m3/hr Pa0 = 0.2 ; % inlet partial pressure of A bar Cb0 = 0.08 ; % inlet concentration of B in liquid Kgmoles/m3 xaf = 0.8 ; % fractional conversion of A P = 3 ; % bed pressure 14.3 bar T = 300 ; % temperature K D = 1 ; % tower diameter m b = 1 ; % stoichiometric coefficient % CALCULATIONS %_________________________________________________________________ R = 8314 ; % Paf = Pa0*(1-xaf) ; % vg = vg/3600 ; % vl = vl/3600 ; % Pa0 = Pa0*10^5 ; % Paf = Paf*10^5 ; % S = (3.14/4)*D^2 ; %
gas law constant in J/Kgmoles K exit partial pressure of A bar gas flow rate in m3/sec liquid flow rate in m3/sec inlet partial pressure of A Pascals exit partial pressure of A Pascals tower cross sectional area
dummy = vg ; dummy = dummy/R ; dummy = dummy/T ; dummy = dummy/(1-eps) ; dummy = dummy/S ; dummy = dummy/sp ; int_constant = dummy ; n_int_p = 100 ;% number of intehration points for i = 1:n_int_p Pa = Paf + ((i-1)/(n_int_p-1))*(Pa0 - Paf) ; Cbb = Cb0 - (b/(R*T))*(vg/vl)*(Pa - Paf) ; Cbb_star = b*Dal_by_Dbl*(kg/kal)*Pa ; if Cbb >= Cbb_star Na = kg*Pa ;% flux of A else Na = (Pa + Ha*Cbb/(b*Dal_by_Dbl))/((1/kg) + (Ha/kal)) ; end ; int_mat(1,i) = Pa ; int_mat(2,i) = (1/Na) ; end ; integral_val = trapez_integral(int_mat) ; z = int_constant*integral_val ;% tower height % DISPLAY RESULTS %_________________________________________________________________
www.Ebook777.com
Free ebooks ==> www.ebook777.com 388
Green Chemical Engineering
fprintf(‘---------------------------------------------------------- \n’) ; fprintf('DESIGN OF PACKED BED NON CATALYTIC GAS LIQUID REACTOR INSTANTANEOUS REACTION\n') ; fprintf(' \n') ; fprintf('Volumetric gas flow rate vg m3/s : %10.4f \n',vg) ; fprintf('Volumetric liquid flow rate vl m3/s : %10.4f \n',vl) ; fprintf('Concentration of B in liquid inlet Cb0 Kgmoles/m3 : %10.4f \n',vl) ; fprintf('Fractional Conversion : %10.4f \n',xaf) ; fprintf('Reactor temperature K : %10.4f \n',T) ; fprintf('Bed Diameter m : %10.4f \n',D) ; fprintf(' \n') ; fprintf('Bed Height m : %10.4f \n',z) ; fprintf(' \n') ;
fprintf('---------------------------------------------------------- \n') ; List of MATLAB Programs Program Name
Description
Heterogeneous Catalytic Reactors catreact_dsn_pckbed.m
Program for design of packed bed two-phase catalytic reactor O-Hydrogen to p-hydrogen in Ni on Al2O3 catalyst Rate equation (−ra) = k(Ca − Cb/K) Program for design of fluidised bed two-phase catalytic reactor particulate fluidisation (liquid–solid fluidisation) Program for design of fluidised bed two-phase catalytic reactor aggregate bubbling fluidisation (gas–solid fluidisation) Program for design of catalytic slurry (three-phase) reactor A—reactant in gas phase B—reactant in liquid phase
catreact_dsn_fluidbed1.m catreact_dsn_fluidbed2.m cat_slurry_react_dsn.m
MATLAB Programs PROGRAM: catreact_dsn_pckbed.m % Program for design of packed bed two phase catalytic reactor % o-Hydrogen to p-Hydrogen in Ni on Al2O3 catalyst % rate equation (-ra) = k(Ca - Cb/K) clear all % INPUT DATA %_________________________________________________________________ % laboratory data dp0 = 1/8 ; epsb0 = 0.33 ; k = 1.1*10^(-3) ; xae = 0.5026 ; ro_p = 1910 ; ro_a = 1.187 ;
% % % % % %
cylinderical pellet diameter in inches bed porosity reaction rate constant m3/Kg.cat S equilibrium conversion at -196 C and P = 40 PSIG pellet density Kg/m3 density of H2 (A) - Kg/m3 at -196 C and P = 40 PSIG
www.Ebook777.com
Free ebooks ==> www.ebook777.com 389
Heterogeneous Reactors
Da = 3.76*10^(-6) ; % diffusivity of H2 (A) - m2/s mu = 3.48*10^(-6) ; % viscosity Kg/m s % scale up data vg = 600 ; xa0 = 0.95 ; xaf = 0.95 ; D = 0.5 ; dp = 1/2 ; epsb = 0.45 ;
% % % % % %
gas flow rate m3/hr mole fraction of H2 (A) at inlet final conversion as percentage of equilibrium conversion reactor diamameter m cyliderical pellet diameter in inches bed porosity
% CALCULATIONS %_________________________________________________________________ % using equilibrium conversion data K = (xae/(1-xae)) ; % equilibrium constant k_dash = k*(1 + K)/K ; % modified rate constant % rate equation (-ra) = k_dash(Ca - Cae) dp = dp*(2.54*10^-2) ; % pellet diameter in m L0 = dp/4 ; % equilent length of cylinder L0 = R/2 phi_dash = L0*sqrt(k_dash*ro_p/Da) ; % modified thiele modulus eeta = tanh(phi_dash)/phi_dash ; % effectiveness factor vg = vg/3600 ; % gas flow rate m3/s S = (3.14/4)*D^2 ; % cross sectional area u_bar = vg/S ; % superfacial velocity Rep = (ro_a*dp*u_bar)/mu ; Sc = (mu/(ro_a*Da)) ; jd = (0.458/epsb)*(Rep)^(-0.407) ; kg = (jd*u_bar)/(Sc^(2/3)) ;
% Reynolds number % Schmidt number % correlation jd = (0.458/ epsb)*(Rep)^-0.407 % mass transfer coefficient m/s
xaf = xaf*xae ; constant = (vg*L0)/(S*(1-epsb)) ; z = constant*((1/kg) + (1/(eeta*k_dash*ro_p*L0)))*log(xae/(xae-xaf)) ; % DISPLAY RESULTS %_________________________________________________________________ fprintf('---------------------------------------------------------- \n') ; fprintf('DESIGN OF PACKED BED CATALYTIC REACTOR \n') ; fprintf(' \n') ; fprintf('Volumetric gas flow rate vg m3/s : %10.4f \n',vg) ; fprintf('Fractional Conversion : %10.4f \n',xaf) ; fprintf('Bed Diameter m : %10.4f \n',D) ; fprintf(' \n') ; fprintf('Bed Height m : %10.4f \n',z) ; fprintf(' \n') ; fprintf('---------------------------------------------------------- \n') ;
www.Ebook777.com
Free ebooks ==> www.ebook777.com 390
Green Chemical Engineering
PROGRAM: catreact_dsn_fluidbed1.m % Program for design of fluidized bed two phase catalytic reactor % particulate fluidization (liquid solid fluidization) clear all % INPUT DATA %_________________________________________________________________ k = 1.3*10^(-4) ; % ro_s = 1200 ; % ro_f = 998 ; % Da = 1.62*10^(-9) ; % mu = 1*10^-3 ; % vl = 55 ; % xaf = 0.95 ; % D = 0.8 ; % dp = 1 ; %
reaction rate constant m3/Kg.cat S density of solid - Kg/m3 density of fluid - Kg/m3 diffusivity of H2 (A) - m2/s fluid viscosity Kg/m s liquid flow rate m3/hr final conversion of A reactor diamameter m particle diameter in mm
% CALCULATIONS %_________________________________________________________________ % using equilibrium conversion data g = 9.81 ; dp = dp*(1*10^-3) ; R = dp/2 ; vl = vl/3600 ; S = (3.14/4)*D^2 ; u_bar = vl/S ;
% % % % % %
ut = ((ro_s - ro_f)*(dp^2)*g)/(18*mu) ; % Rep = (ro_f*dp*u_bar)/mu ; % Sc = (mu/(ro_f*Da)) ; % n = 4.45*Rep^(-0.1) ; eps = (u_bar/ut)^(1/n) ; % Sh = (0.81/eps)*(Rep^0.5)*(Sc^0.3333); % km = (Sh*Da/dp) ; %
acceleration due to gravity m2/s particle diameter in m particle radius in m liquid flow rate m3/s cross sectional area superfacial velocity terminal settling velocity Reynolds number Schmidt number bed porosity sherwood number mass transfer coefficient
constant = vl/(S*(1-eps)) ; z = constant*((R/(3*km)) + (1/(k*ro_s)))*log(1/(1-xaf)) ; % DISPLAY RESULTS %_________________________________________________________________ fprintf('---------------------------------------------------------- \n') ; fprintf('DESIGN OF FLUIDIZED BED CATALYTIC REACTOR - PARTICULATE FLUIDIZATION \n') ; fprintf(' \n') ; fprintf('Volumetric liquid flow rate vl m3/s : %10.4f \n',vl) ; fprintf('Fractional Conversion : %10.4f \n',xaf) ; fprintf('Bed Diameter m : %10.4f \n',D) ;
www.Ebook777.com
Free ebooks ==> www.ebook777.com Heterogeneous Reactors
391
fprintf(' \n') ; fprintf('Bed Height m : %10.4f \n',z) ; fprintf(' \n') ; fprintf(‘---------------------------------------------------------- \n’) ; PROGRAM: catreact_dsn_fluidbed2.m % Program for design of fluidized bed two phase catalytic reactor % Aggregate bubbling fluidization (gas solid fluidization) clear all % INPUT DATA %_________________________________________________________________ k = 5*10^(-3) ; % ro_d = 89 ; % epsd = 0.74 ; % vg = 350 ; % xaf = 0.90 ; % D = 0.5 ; % kg_ab = 1.1 ; %
reaction rate constant m3/Kg.Cat sec catalyst density in the bed - Kg. cat/m3 volume fraction of catalyst particle in dense phase liquid flow rate m3/hr final conversion of A reactor diamameter m bubble side mass transfer coefficient 1/sec
% CALCULATIONS %_________________________________________________________________ vg = vg/3600 ; % gas flow rate m3/s S = (3.14/4)*D^2 ; % cross sectional area u_bar = vg/S ; % superfacial velocity z = u_bar*((1/kg_ab) + (1/(k*ro_d*epsd)))*log(1/(1-xaf)) ; % DISPLAY RESULTS %_________________________________________________________________ fprintf(‘---------------------------------------------------------- \n’) ; fprintf('DESIGN OF FLUIDIZED BED CATALYTIC REACTOR - BUBBLING FLUIDIZATION \n') ; fprintf(' \n') ; fprintf('Volumetric liquid flow rate vg m3/s : %10.4f \n',vg) ; fprintf('Fractional Conversion : %10.4f \n',xaf) ; fprintf('Bed Diameter m : %10.4f \n',D) ; fprintf(' \n') ; fprintf('Bed Height m : %10.4f \n',z) ; fprintf(' \n') ; fprintf(‘---------------------------------------------------------- \n’) ; PROGRAM: cat_slurry_react_dsn.m % Program for design of catalytic slurry (three phase) reactor
www.Ebook777.com
Free ebooks ==> www.ebook777.com 392
Green Chemical Engineering
% A - reactant in gas phase % B - reactant in liquid phase clear all % INPUT DATA %_________________________________________________________________ dp = 0.05 ; % vg = 1000 ; % db = 3 ; % VG = 0.09 ; % ro_p = 1100 ; % ro_d = 80 ; % k = 1.2*10^-2 ; % xaf = 0.80 ; % Ha = 42 ; % liquid) kg = 2.1*10^-3 ; % kl = 1.1*10^-2 ; % kc = 4.1*10^-3 ; %
diameter of catalyst particle in mm gas flow rate m3/hr gas bubble diameter in mm gas hold up in the vessel m3 gas/m3 liquid density of catalyst particle Kg/m3 slurry density of catalyst particle Kg cat/m3 liquid reaction rate constant m3/Kg.Cat sec final conversion of A Henry's law constant (Kgmoles/m3 of gas)/(Kgmoles/m3 of gas side mass transfer coefficient m/s liquid side mass transfer coefficient m/s liquid to particle transfer coefficient m/s
% CALCULATIONS %_________________________________________________________________ vg = vg/3600 ;
% gas flow rate m3/s
dp = dp*(10^-3) ; db = db*(10^-3) ; ac = (ro_d/ro_p)*(6/dp) ; % specific surface area of catalyst m2/m3 liquid ab = (6*VG/db) ; % specific surface area of gas bubble m2/m3 liquid V = vg*Ha)*((1/(Ha*kg*ab)) + (1/(kl*ab)) + (1/(kc*ac)) + (1/(k*ro_d)))*log(1/ (1-xaf)); % reactor volume % DISPLAY RESULTS %_________________________________________________________________ fprintf('---------------------------------------------------------- \n') ; fprintf('DESIGN OF SLURRY CATALYTIC REACTOR \n') ; fprintf(' \n') ; fprintf('Volumetric gas flow rate vg m3/s : %10.4f \n',vg) ; fprintf('Fractional Conversion : %10.4f \n',xaf) ; fprintf(' \n') ; fprintf('Bed volume m : %10.4f \n',V) ; fprintf(' \n') ; fprintf('---------------------------------------------------------- \n') ;
www.Ebook777.com
Free ebooks ==> www.ebook777.com
Section II
Green Chemical Processes and Applications
www.Ebook777.com
Free ebooks ==> www.ebook777.com
www.Ebook777.com
Free ebooks ==> www.ebook777.com
5 Green Reactor Modelling From the beginning of the 1990s to the present, the research focus is on the study of the design of novel catalytic reactors. Micro-reaction engineering is an emerging field, which is rapidly developing. Several alternative micro-channel catalytic reactors have been recently introduced. The high surface-to-volume ratio, efficient heat and mass transfer characteristics and vastly improved fluid mixing allow efficient control of process parameters with improved conversions, selectivity and yields of desired products. A wide variety of other reactor configurations have also been employed with considerable success. This chapter deals with basic fundamentals of novel reactor technology and some of green reactor design softwares and their applications. Basic understanding of flow pattern in stirred-tank reactor by computational fluid dynamics and simulation of CSTR model by using ASPEN Plus were mainly presented in this chapter. Rigorous implementation of optimal policies for maximising conversion and integration of control strategies has been given importance in this decade. Performance enhancement employing computational fluid dynamics (CFD)-enabled flow modelling has received serious attention of industry and academia. The availability of superfast computing facilities has prompted the incorporation of such detailed fluid dynamical and kinetic descriptions. But increased level of phenomenological description requires accurate evaluation of larger numbers of system parameters; this becomes rather cumbersome and difficult. To circumvent these difficulties, researchers have started looking at advancement in machine learning and artificial intelligence involving data-driven models. Neural networks and genetic algorithms are increasingly employed, along with conventional first-principle models, for rational design of catalysts, their kinetics extensively exploited in chemical processes. This is mainly due to their inherent ability to approximate arbitrary complex functional relationships. Artificial neural networks have been used to formulate approximate kinetic models for biological as well as conventional chemical reactors. A simple neural network assisted by genetic algorithms was employed successfully to optimise the temperature profiles of a temperature gradient reactor for the catalytic synthesis of dimethyl ether.
5.1 Novel Reactor Technology 5.1.1 Micro-Reactor A micro-reactor is generally defined as a device consisting of a number of interconnecting micro-channels in which small quantities of reagents are manipulated, mixed and allowed to react for a specified period of time (Ehrfeld et al., 2000; Wirth, 2008). The movement of fluids within such a device can be achieved in a number of ways with the most common being mechanical micro-pumping and electro-osmotic flow, which may include electrophoresis separations. The typical cross-sectional dimensions of such micro-channels are in the range of 10–500 μm and are normally fabricated on the planer surface of substrates 395
www.Ebook777.com
Free ebooks ==> www.ebook777.com 396
Green Chemical Engineering
such as glass, polymers, ceramics and metals. Depending on the material selected, a range of fabrication methods can be used for the production of micro-channels, including photolithography and wet-etching, powder-blasting, hot embossing, injection moulding and laser micro-machining. A number of recent reviews have described the development of micro-reactors, based on the so-called ‘lab-on-a-chip’ technology, and outlined the relevance of such techniques to the field of organic synthesis (Jahnisch et al., 2004). The fundamental and practical advantages associated with micro-reactor technology are related to the current needs of the chemical industry, which is constantly searching for controllable, informative, high-throughput, environmentally friendly processes whilst retaining a high degree of chemical selectivity. 5.1.1.1 Characteristics of Micro-Reactors The unique operating characteristics of micro-reactors, compared to conventional batch reactors, include a high surface-area-to-volume ratio, enhanced heat transfer; diffusiondominated mass transfer, spatial and temporal control of reagents and products, the generation of concentration gradients and the opportunity to integrate processes and measurement systems in an automated manner. Some of characteristics are discussed here: 5.1.1.1.1 High Surface-Area-to-Volume Ratio When scaling a conventional centimeter-sized reactor down to the micron scale, the surface-to-volume ratio significantly increases to the point where the container walls can effectively become an active or influential part of the reaction or process occurring in the fluidic channel. Clearly, this attribute of micro-reactors can be viewed in a positive way and leads to the opportunity to exploit the surface-dependent performance. A relatively simple but important example of this effect is where the surface charge of the capillary is neutralised by the solution contained within it to form a charged double layer, which under the influence of an applied electric field leads to the electro-osmotic mobilisation of the solution. In more chemical applications the surfaces could represent reagents, catalysts or even physical molecular imprinted structures. 5.1.1.1.2 Enhanced Heat Transfer The high surface-to-volume ratio can also significantly improve thermal transfer conditions within micro-channels in two ways; firstly, the convective heat transfer which takes place at the solid/fluid interface is improved via an increase in heat transfer area per unit volume and, secondly, heat transfer within a small volume of fluid takes a relatively short time period to occur, enabling a thermally homogeneous state to be reached quickly. The improvement in heat transfer can certainly influence overall reaction rates and, in some cases, product selectivity. Perhaps one of the more profound effects of the efficient heat-transfer property of micro-reactors is the ability to carry potentially explosive or highly exothermic reactions in a safe way, due to the relatively small thermal mass and rapid dissipation of heat. 5.1.1.1.3 Mass Transfer Dominated by Diffusion It is well known that the flow within micro-channels is restricted to diffusive mixing under laminar flow conditions. Based on Fick’s law, the relationship between the travel distance (L) of a molecule by diffusion and time (t) can be simplified as L = (2D ∙ t)1/2 where D is the diffusion coefficient. From the above equation, it can be seen that by scaling down the dimension in which diffusive mixing occurs, a significant reduction in the time taken to achieve complete
www.Ebook777.com
Free ebooks ==> www.ebook777.com Green Reactor Modelling
397
mixing is achieved. For example, a water molecule takes 200 s to diffuse across a 1 mm wide channel, but only takes 500 ms to cross a 50 μm wide channel. This significant reduction in mixing time is beneficial for controlling reaction progress, in particular for initiating or quenching reactions in a controlled manner, enabling improvements to be made in product selectivity. 5.1.1.1.4 Spatial and Temporal Evolution of Reactions Under such diffusive laminar flow conditions, the ability to add reagents at specific locations or time leads to the unique ability to control and monitor the spatial and temporal domain of dynamic chemical processes. This attribute has some analogies with the control exerted on biochemical reactions by the micron-scale structures of living cells. Exploitation of this effect, such that a reaction well occurs in a position where the local concentration of a key intermediate is high, is a potentially valuable approach towards controlling the yield and selectivity of reactions. 5.1.1.1.5 System Integration and Automation Each of the properties of a micro-reactor outlined above does not have to be exploited independently but can be combined to provide multiple functionality within one microreactor. In this way, multi-step processes, combining a range of physical and chemical steps, can be performed in a controlled and reproducible way. In addition, the integration of in situ, real time or end of line analytical measurements can be effectively realised using micro-reactor technology, leading to rapid automated methodology. A combination of these two features will clearly create tools for the pharmaceutical and fine chemical industries, where high-throughput and information-rich techniques are constantly sought for the rapid evaluation of reaction arrays. 5.1.1.1.6 Exploiting the High Surface-to-Volume Properties of Micro-Reactors Although the rapid growth of micro-reactor technology has led to the transfer of many common synthetic reactions from batch to ‘chip’, little attention has been paid to the problems associated with the continuous purification of these reaction products. To tackle this, the incorporation of solid-supported catalysts within miniaturised flow reactors, leading to the synthesis of analytically pure compounds and aiding the development of efficient multi-step processes. Christensen et al. (1998) described the use of supported catalysts held within a borosilicate glass capillary (500 mm (i.d) × 3.0 cm (length)) in which solvent and reagents are pumped under electro-osmotic conditions. The supported catalyst was dry packed into the reactor and held in place by micro-porous silica frits. The packed capillary was primed with MeCN to remove any air, ensuring the formation of an electrical circuit; a leak-tight connection between the capillary and reagent reservoirs was achieved using polytetrafluroethylene thread seal tape. To mobilise reagents by electro-osmotic flow (from reservoir A through the packed bed to reservoir B), platinum electrodes were placed within the reservoirs and voltages applied using a high-voltage power supply (0–1000 V DC); typical applied fields of 167–333 and 0 V cm−1 were employed. To benchmark the technique against traditional stirred/shaken reactors, the base-catalysed Knoevena gel condensation of 8 α,β-unsaturated compounds was used. This was followed by the acidcatalysed protection of 15 aldehydes as their respective dimethyl acetal (Wiles et al., 2005). In all cases, high run-to-run reproducibility (94.7%). As an extension of this investigation, the incorporation of multiple-supported catalysts (a polymer-supported acid and a
www.Ebook777.com
Free ebooks ==> www.ebook777.com 398
Green Chemical Engineering
silica-supported base) into the aforementioned reactor was examined to demonstrate the two-step synthesis of 20 α,β-unsaturated compounds; again all products were obtained in excellent yield (>99.1%) and analytical purity (>99.1%). Furthermore, when performing the two-step reactions, Amberlyst-15 was recycled over 200 times and silica-supported piperazine over 1000 times, with no sign of degradation (Wiles et al., 2005). This technique has been demonstrated to be a simple and efficient approach for the incorporation of solid-supported catalysts into miniaturised flow reactors, resulting in a system suitable for the continuous flow synthesis of analytically pure compounds. Compared to traditional batch techniques, the application of miniaturised flow reactors proved advantageous, as it is possible to synthesise compounds in high yield and purity without the use of extended reaction times (min > 24 h). Additionally, the ease with which supported catalysts are recycled provides reaction reproducibility unparalleled in traditional stirred or shaken reactor vessels. Consequently, whether milligrams of a compound are required for biological evaluation (single reactor) or tonnes for the production of fine chemicals (multiple reactors), the flexibility associated with micro-reaction technology enables these differences in scale to bridge with ease. The ability to generate a large quantity of chemical reaction information through automation represents an important capability of micro-reactor systems; with this in mind, the following example describes the use of a modified HPLC system for automated reagent selection, micro-reaction and chromatographic analysis. A multi-valving system, located between two syringe pumps shown in the foreground, used in combination with an HPLC auto-sampler to allow the introduction of multiple reagents into the micro-reactor. Due to the low diffusional distances obtained in this system, compared to the use of reagent slugs, this approach is amenable to the individual introduction of a large number of reagents into the micro-reactor. Hence, the rapid loading of sample introduction loops can be performed without compromising either the reaction or analytical flow rates, offering time efficiency whilst ensuring that concentration of the sample is not reduced by excessive diffusion into the carrier solvent. In addition, high flow rates can be maintained for the chromatographic separation which would be difficult to achieve if the exit stream of the micro-reactor was directly coupled to the analytical column. The ability to independently optimise the flow in all three sections of the process is also important with respect to reagent integrity, reaction efficiency and chromatographic separation. Clearly, the system described has additional applications beyond that of a quality control technique for chemical synthesis; for example, it would be relatively simple to incorporate biological processing and/or couple the reactor set-up to other analytical instrumentation. In summary, the automated system described allows the rapid evaluation of an array of reaction conditions such as reaction time, temperature and reagent stoichiometry, enabling the production of combinatorial libraries with ease. Micro-reactors offer many advantages over conventional macro-scale reactors, particularly with respect to achieving controllable, information-rich, high-throughput, environmentally friendly and automated processes capable of generating large quantities of product with a high degree of chemical selectivity. These advantages can be attributed to the dramatic reduction in scale leading to unique operating conditions such as the spatial and temporal reagent control obtained under a non-turbulent, diffusive mixing regime and a high surface-to-volume ratio. There is no doubt that micro-reactor technology can be used as a platform for a wide range of applications such as chemical and biological analysis, chemical synthesis, materials chemistry and biotechnology—to name but a few.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 399
Green Reactor Modelling
5.1.2 Microwave Reactor Microwaves have long been used in domestic ovens, but the application of this technology in chemical research and industry has been limited by safety and reproducibility issues. Nowadays, the latest equipment allows precise and safe control of the power both in batch and continuous reactions. It enables more energy-efficient heating as well as faster and cleaner chemical reactions (Loupy, 2002; Adam, 2003). The microwave-assisted reactor has received increasing attention in recent years as a valuable alternative to the use of conductive heating for accelerating chemical reactions. With no direct contact between the chemical reactants and the energy source, microwave-assisted chemistry is energy efficient, provides fast heating rates and enables rapid optimisation of procedures. From the early experiments in domestic ovens to the use of multimodal or mono-modal instruments designed for organic synthesis, this technology has been implemented worldwide and continues to be developed. Current technology has attempted to overcome obstacles with conventional instruments by the use of continuous flow (CF) reactors that pump the reagents through a small heated coil that winds in and out of the cavity, with external temperature monitoring using a fiber-optic sensor, although alternative methods, such as using a multimode batch or CF reactor (Esveld et al., 2000; Shieh et al., 2002; Stadler et al. 2003). The principal design of a flow cell featured the need to make optimum use of the cavity and to be able to monitor the temperature of the flow cell directly using the instrument’s in-built IR sensor. To this end, a standard pressure-rated glass tube (10 mL) fitted with a custom-built steel head was filled with sand (10 g) between two drilled frits (Figure 5.1) to minimise dispersion and effectively create a lattice of micro-channels, charged with solvent (5 mL Inflow
Outflow Steel head
Dried porous frit
10 mL glass pressure tube
Sand MW
MW
Dried porous frit
IR sensor Figure 5.1 Microwave chemical flow reactor.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 400
Green Chemical Engineering
volume), sealed using PTFE washers and connected to an HPLC flow system with a backpressure regulator. The flow cell was inserted into the cavity of a self-tunable monomodal microwave synthesiser, irradiated and stabilised at the required reaction temperature through moderation of microwave power before the introduction of reagents into the reactor. This system possessed a number of advantages over commercially available coils, including simple measurement of the flow cell temperature, no additional and expensive equipment required short of an HPLC pump, and the potential to carry out heterogeneous as well as homogeneous reactions simply by immobilising a catalyst on the support in the glass tube. 5.1.3 High-Pressure Reactor Working with a high-pressure reactor fitted with a high level of control enables simulation of real process conditions for many industrially important reactions. It allows work on optimisation of an existing or a new process on a scaled down version which can be more easily translated to the actual production setup. For a new process, working under pressure can allow greater concentration of reagents and a faster reaction and thus greater throughput. Using high pressures also enables the production of superheated water, which brings important benefits to clean synthesis. This high-pressure reactor system is designed for the use of interchangeable steel pressure vessels. Safety features guarantee safe reactions under pressure. The stainless-steel reactors ensure high resistance against acids. Visual process control and monitoring is also possible under high pressure by using steel pressure vessels with sight glasses. Various low-to-high torque magnetic drives ensure efficient mixing and stirring low-to-high viscosity process media as well as excellent heat transfer. The fast action closure and vessel lift makes changing vessels quick and easy without the use of tools. This kind of reactor is designed to bridge the gap between bench-scale fuel- characterisation tests and conditions prevailing in thermochemical fuel conversion processes. It focuses on high-pressure experiments in inert atmospheres (pyrolysis), in hydrogen (hydropyrolysis and hydrogasification), as well as gasification in steam–air and steam–oxygen atmospheres. Furthermore, it examines the effects of high pressure on the morphologies and reactivities of the solid products—the chars. Gasification is a mature art and vast numbers of experiments have been done in the past to investigate the pyrolysis and gasification of coals and biomass materials. Most modern gasifier designs are based on short residence time fluidised-bed or entrained flow reactors, where heating rates are high and exposure to reaction conditions is short. Mostly, solids exit from the reactors in a matter of seconds or, at most, tens of seconds. The requirements arising from the expanded use of fluidised and entrained flow designs have substantially changed the face of solid fuel characterisation. The emerging designs of fuel characterisation tests are driven by the necessity to match rapid processing requirements. Another critical factor is the recognition that the outcomes of these tests depend on reactor configuration and reaction conditions during prior thermal breakdown, as well as the original compositions of the fuels. 5.1.4 Spinning Disk Reactor A spinning disk reactor (SDR) is a horizontally oriented circular disk plate that can be heated or cooled and rotated via an air motor at speeds up to 5000 rpm (Figure 5.2).
www.Ebook777.com
Free ebooks ==> www.ebook777.com 401
Green Reactor Modelling
Liquid feed Input (optional)
Output (optional)
Thin film Spinning disc
Temperaturecontrolled walls
Product output
Heating/ cooling fluid
Motor
Figure 5.2 Spinning disk reactor.
Surface-to-volume ratios on the disk surface are on the order of 100 m2/m3 for viscous materials and 100,000 m2/m3 for viscosity systems. The heat-transfer coefficient for this reactor may be as high as 14,000 W/m2 K and an average heat-transfer coefficient in the range of 5000–7000 W/m2 K. The SDR can also be used to perform solid-catalysed reactions by coating the surface of the disk with a solid catalyst. The residence time on the disk ranges from 0.1 to 3 s depending on the viscosity, spin rate, thus allowing for reactions with a half-life of 0.1–1 s. The rotating plate can be cooled or heated with a heat exchange fluid which is the fluid which flows inside the plate. The applied centrifugal force produces thin liquid films on the surface of the rotating disks. Reactants, which are introduced through the centre of the disk, move across the surface, forming thin film (the chemical reaction occurs during this step), and are collected on the edge of the disk. SDR was developed as an alternative to the traditional stirred tank reactor. This reactor is primarily aimed at liquid–liquid reactions with highly exothermic reactions, such as nitration, sulphonation and polymerisation. The small dimension of the film (typically 100 µm) is responsible for very high heat-transfer rates between the film and the disk as well as the high mass transfer between the liquid streams and/or between the film and the gas in the atmosphere. Additionally, SDRs provide very intense mixing in the thin liquid film and can therefore maintain uniform concentration profiles within a rapidly reacting fluid. The residence time is short and, as a result, may allow the use of higher processing temperatures. The reactor is characterised by a plug flow. It operates in a safe mode due to the small reactor hold-up and the excellent control of fluid temperature used to perform fast organic reactions and precipitations or production of nano- and micron size particles. The major drawbacks of this reactor configuration are exhibited in the challenge of overcoming a high-speed rotating system with low output. Like other miniaturised reactors, scale-up can be achieved with a numbering approach.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 402
Green Chemical Engineering
5.2 Some Reactor Design Software and Their Applications The best path to an in-depth understanding of a reactor simulation is a solid understanding and familiarity of how to arrange equations for a reaction system, but when the reactor system becomes too complicated to be simulated with a mathematical package (MATLAB, POLYMATH), then it is the turn of the process simulator package (ASPEN plus, ANSYS, ChemCAD, HYSYS, etc.) to simulate it. The chemical reactor design tool is a set of computer programs that solves the equations describing common chemical reactor models. The design of a reactor is the brainware that is an in-depth understanding of applying mass and energy balance principles to the performance of a chemical reaction taking place in a reactor. The types of reactors that can be modelled include batch reactors, continuous stirred tank reactors, plug flow reactors, plug flow reactors with axial dispersion and tubular flow reactors with radial dispersion. The most general equations describing the particular reactor are used for the base model so that any complexities can be included. It allows the student to compare many different models in a short amount of time. It can be used to investigate many different phenomena. The effects of axial and radial dispersion can be easily studied by comparing the results of the PFR model with the results of the PFR with the axial diffusion model and the two-dimensional model. Heterogeneous effects of catalyst packing can be analysed by choosing external resistance under the mass transfer resistance menu and providing the appropriate parameters. Heat transfer at the wall can be included for all reactor types. HYSYS offers another advantage for us for simulating the reactor system. It skips the steps of arranging the system of equations and reducing the work of collecting physicochemical data required to simulate a reaction system. In a HYSYS simulation, we can just pick the reactor module we want to simulate, either kinetic, conversion, or equilibrium reactor. 5.2.1 gPROMS: For Simulation and Modelling of Reactors gPROMS is a platform for high-fidelity predictive modelling for the process industries. The gPROMS is a platform for model-based engineering activities for process and equipment development and design, and optimisation of process operations. It has many major advantages over other comparable modelling software: steady-state and dynamic modelling within the same environment; multi-scale modelling; the possibility to create a reactor model that takes into account all phenomena from mass transfer in the catalyst pore to full-scale equipment effects simultaneously; the ability to apply such high-fidelity unit models within a full process flow sheet; and estimation of equipment or process empirical parameters from experimental–laboratory, pilot or operational–data, with estimates of data uncertainty for risk analysis. It is the model library for fixed-bed catalytic reaction, fluidised-bed and various polymer reactors and so on. Different tools are available in gPROMS software for simulation and modelling of various systems. Some of the following are: (i) multi-scale modelling of complex processes and phenomena. (ii) State-of-the-art model validation tools allow estimation of multiple model parameters from steady-state and dynamic experimental data, and provide rigorous model-based data analysis. (iii) The maximum amount of parameter information from the minimum number of experiments. (iv) The gPROMS– CFD Hybrid Multitubular interface provides ultimate accuracy in the modelling of
www.Ebook777.com
Free ebooks ==> www.ebook777.com Green Reactor Modelling
403
multitubular reactors by linking a CFD model of the shell-side fluid hydrodynamics to a gPROMS model of the tube-side catalytic reaction. (v) The gPROMS–CFD Hybrid Multizonal interface similarly links gPROMS and CFD models for enhanced accuracy of fluidised-bed reactor modelling, and other applications where zone-based modelling are appropriate. 5.2.2 ANSYS—Reactor Design Reactors are a crucial component of a chemical plant, and their high performance must be ensured. ANSYS is a powerful, reliable tool that complements the chemical engineering practices. It includes bringing comprehensive multi-physics capabilities to reaction engineering. ANSYS solutions can model a diverse wide variety of reactors and reactions, including gaseous and liquid, single-phase and multiphase, and homogeneous and heterogeneous, competing and parallel reactions, catalytic reactions, surface and volumetric reactions, laminar and turbulent flows, fluidised-bed reactions, multi-tube reactors, membrane reactors, micro-reactors, stirred tank reactors, fixed reactors, autoclave reactors, emulsion, hydrogenation, chlorination, polymerisation, hydro-cracking, crystallisation and precipitation and so on. Users can optimise reactor performance by better understanding the effects and impact of feed locations, vessel geometries and internals, vibrations, failures, dead spots, shear rates, resident time distributions, hot spots and particle size distributions. ANSYS delivers the diverse Water & Wastewater engineering simulation capabilities needed to help optimise their process technologies. Physical analyses include CFD, hydraulics and mass transfer predictions. Some practical challenges in water and wastewater engineering have been appearing when using ANSYS for the following purposes: minimise the size of process tanks, model fluid flows in reservoirs, optimise mixing tank rates and geometries, measure and improve disinfection efficiency, maximise oxygen transfer rates, optimise the effectiveness of various pumping systems, optimise the contributions of screening and filtration systems, improve turbine-powered aeration effectiveness, model and assess non-Newtonian fluid flows and so on. ANSYS also provides insight and a detailed understanding of the formation and dispersion of pollutants (Nox, Sox, mercury and other VOCs) for a range of flow problems, including turbulence, chemical reactions, heat and mass transfer and multiphase flows. ANSYS simulation enables engineers to study multiphase distribution, heat and mass transfer calculations, chemical kinetics and reaction of gas–liquid reactions. These include the design of plate columns, packed columns and bubble columns, a loop reactor and bioreactor development, gas-in-liquid dispersion studies and emulsion design. 5.2.2.1 Computational Fluid Dynamics CFD codes are structured around the numerical algorithms that can help tackle fluid problems. To provide easy access to their solving power, all commercial CFD packages include sophisticated user interfaces to input problem parameters and to examine the results. Hence, all codes contain three main elements: 1. Pre-processing 2. Solver 3. Post-processing
www.Ebook777.com
Free ebooks ==> www.ebook777.com 404
Green Chemical Engineering
5.2.2.1.1 Pre-Processing This is the first step in building and analysing a flow model. A pre-processor consists of the input of a flow problem by means of an operator-friendly interface and subsequent transformation of this input into a form suitable for use by the solver. The pre-processing stage involves: • Definition of the geometry of the region: The computational domain. • Grid generation: Subdivision of the domain into a number of smaller, non- overlapping subdomains (or control volumes or elements). Selection of physical or chemical phenomena that need to be modelled. 5.2.2.1.2 Definition of Fluid Properties Specification of appropriate boundary conditions at cells, which coincide with or touch the boundary. The solution of a flow problem (velocity, pressure, temperature, etc.) is defined at nodes inside each cell. The accuracy of CFD solutions is governed by the number of cells in the grid. In general, the larger the numbers of cells the better the solution accuracy. Both the accuracy of the solution and its cost in terms of necessary computer hardware and calculation time are dependent on the fineness of the grid. Efforts are underway to develop CFD codes with a (self) adaptive meshing capability. Ultimately such programs will automatically refine the grid in areas of rapid variation. 5.2.2.1.3 GAMBIT (CFD Pre-Processor) GAMBIT is a state-of-the-art pre-processor for engineering analysis. With advanced geometry and meshing tools in a powerful, flexible, tightly integrated and easy-to-use interface, GAMBIT can dramatically reduce pre-processing times for many applications. Complex models can be built directly within GAMBIT’s solid geometry modeller, or imported from any major computer-aided design/computer-aided engineering (CAD/CAE) system. Using a virtual geometry overlay and advanced cleanup tools, imported geometries are quickly converted into suitable flow domains. A comprehensive set of highly automated and size function-driven meshing tools ensures that the best mesh can be generated, whether structured, multiblock, unstructured, or hybrid. 5.2.2.1.4 Solver The CFD solver does the flow calculations and produces the results. FLUENT, FloWizard, FIDAP, CFX and POLYFLOW are some of the types of solvers. FLUENT is used in most industries. FloWizard is the first general-purpose rapid flow modelling tool for design and process engineers built by Fluent. POLYFLOW (and FIDAP) are also used in a wide range of fields, with emphasis on the materials processing industries. Two solvers FLUENT and CFX were developed independently by ANSYS and have a number of things in common, but they also have some significant differences. Both are control-volume based for high accuracy and rely heavily on a pressure-based solution technique for broad applicability. They differ mainly in the way they integrate the fluid flow equations and in their equation solution strategies. The CFX solver uses finite elements (cell vertex numerics), similar to those used in mechanical analysis, to discretise the domain. In contrast, the FLUENT solver uses finite volumes (cell-centred numerics). CFX software focuses on one approach to solve the governing equations of motion (coupled algebraic multigrid), while the FLUENT product offers several solution approaches (density-segregated- and coupled-pressure-based methods).
www.Ebook777.com
Free ebooks ==> www.ebook777.com Green Reactor Modelling
405
The FLUENT CFD code has extensive interactivity, so we can make changes to the analysis at any time during the process. This saves time and enables to refine designs more efficiently. Graphical user interface (GUI) is intuitive, which helps to shorten the learning curve and make the modelling process faster. In addition, FLUENT’s adaptive and dynamic mesh capability is unique and works with a wide range of physical models. This capability makes it possible and simple to model complex moving objects in relation to flow. This solver provides the broadest range of rigorous physical models that have been validated against industrial scale applications, so we can accurately simulate real-world conditions, including multiphase flows, reacting flows, rotating equipment, moving and deforming objects, turbulence, radiation, acoustics and dynamic meshing. The FLUENT solver has repeatedly proven to be fast and reliable for a wide range of CFD applications. The speed to solution is faster because suite of software enables us to stay within one interface from geometry building through the solution process, to post-processing and final output. The numerical solution of Navier–Stokes equations in CFD codes usually implies a discretisation method: it means that derivatives in partial differential equations are approximated by algebraic expressions which can be alternatively obtained by means of the finite-difference or the finite-element method. Otherwise, in a way that is completely different from the previous one, the discretisation equations can be derived from the integral form of the conservation equations: this approach, known as the finite volume method, is implemented in FLUENT (FLUENT User’s Guide, Vols. 1–5, Lebanon, 2001), because of its adaptability to a wide variety of grid structures. The result is a set of algebraic equations through which mass, momentum and energy transport are predicted at discrete points in the domain. In the freeboard model that is being described, the segregated solver has been chosen so the governing equations are solved sequentially. Because the governing equations are non-linear and coupled, several iterations of the solution loop must be performed before a converged solution is obtained and each of the iteration is carried out as follows:
1. Fluid properties are updated in relation to the current solution; if the calculation is at the first iteration, the fluid properties are updated consistent with the initialised solution. 2. The three momentum equations are solved consecutively using the current value for pressure so as to update the velocity field. 3. Since the velocities obtained in the previous step may not satisfy the continuity equation, one more equation for the pressure correction is derived from the continuity equation and the linearised momentum equations: once solved, it gives the correct pressure so that continuity is satisfied. The pressure–velocity coupling is made by the simple algorithm, as in FLUENT default options. 4. Other equations for scalar quantities such as turbulence, chemical species and radiation are solved using the previously updated value of the other variables; when inter-phase coupling is to be considered, the source terms in the appropriate continuous phase equations have to be updated with a discrete phase trajectory calculation. 5. Finally, the convergence of the equations set is checked and all the procedure is repeated until convergence criteria are met. The conservation equations are linearised according to the implicit scheme with respect to the dependent variable: the result is a system of linear equations (with one equation for
www.Ebook777.com
Free ebooks ==> www.ebook777.com 406
Green Chemical Engineering
each cell in the domain) that can be solved simultaneously. Briefly, the segregated implicit method calculates every single variable field considering all the cells at the same time. The code stores discrete values of each scalar quantity at the cell centre; the face values must be interpolated from the cell centre values. For all the scalar quantities, the interpolation is carried out by the second-order upwind scheme with the purpose of achieving high-order accuracy. The only exception is represented by pressure interpolation, for which the standard method has been chosen. 5.2.2.1.5 Post-processing This is the final step in CFD analysis, and it involves the organisation and interpretation of the predicted flow data and the production of CFD images and animations. Fluent’s software includes full post-processing capabilities. FLUENT exports CFD’s data to third-party post-processors and visualisation tools such as Ensight, Fieldview and TechPlot as well as to VRML formats. In addition, FLUENT CFD solutions are easily coupled with structural codes such as ABAQUS, MSC and ANSYS, as well as to other engineering process simulation tools. Thus, FLUENT is general-purpose CFD software ideally suited for incompressible and mildly compressible flows. Utilising a pressure-based segregated finite-volume method solver, FLUENT contains physical models for a wide range of applications including turbulent flows, heat transfer, reacting flows, chemical mixing, combustion and multiphase flows. FLUENT provides physical models on unstructured meshes, bringing you the benefits of easier problem setup and greater accuracy using solution adaptation of the mesh. FLUENT is a CFD software package to simulate fluid flow problems. It uses the finitevolume method to solve the governing equations for a fluid. It provides the capability to use different physical models such as incompressible or compressible, inviscid or viscous, laminar or turbulent and so forth. Geometry and grid generation is done using GAMBIT which is the pre-processor bundled with FLUENT. Owing to increased popularity of engineering work stations, many of which has outstanding graphics capabilities, the leading CFD are now equipped with versatile data visualisation tools. These include Domain geometry and grid display Vector plots Line and shaded contour plots 2D and 3D surface plots Particle tracking View manipulation (translation, rotation, scaling, etc.) 5.2.2.1.6 Advantages of CFD Major advancements in the area of gas–solid multiphase flow modelling offer substantial process improvements that have the potential to significantly improve process plant operations. Prediction of gas solid flow fields, in processes such as pneumatic transport lines, risers, fluidised-bed reactors, hoppers and precipitators are crucial to the operation of most process plants. Up to now, the inability to accurately model these interactions has limited the role that simulation could play in improving operations. In recent years, CFD software developers have focused on this area to develop new modelling methods that can simulate gas–liquid–solid flows to a much higher level of reliability. As a result, process industry
www.Ebook777.com
Free ebooks ==> www.ebook777.com Green Reactor Modelling
407
engineers are beginning to utilise these methods to make major improvements by evaluating alternatives that would be, if not impossible, too expensive or time consuming to trial on the plant floor. Over the past few decades, CFD has been used to improve process design by allowing engineers to simulate the performance of alternative configurations, eliminating guesswork that would normally be used to establish equipment geometry and process conditions. The use of CFD enables engineers to obtain solutions for problems with complex geometry and boundary conditions. A CFD analysis yields values for pressure, fluid velocity, temperature and species or phase concentration on a computational grid throughout the solution domain.
1. It provides the flexibility to change design parameters without the expense of hardware changes. It therefore costs less than laboratory or field experiments, allowing engineers to try more alternative designs than would be feasible otherwise. 2. It has a faster turnaround time than experiments. 3. It guides the engineer to the root of problems, and is therefore well suited for troubleshooting. 4. It provides comprehensive information about a flow field, especially in regions where measurements are either difficult or impossible to obtain. 5.2.2.2 CFD Modelling of Multiphase Systems This section focuses on CFD modelling of multiphase systems. Following are some examples of multiphase systems: • Bubbly flow examples: absorbers, aeration, airlift pumps, cavitations, evaporators, flotation and scrubbers. • Droplet flow examples: absorbers, atomisers, combustors, cryogenic pumping, dryers, evaporation, gas cooling and scrubbers. • Slug flow examples: large bubble motion in pipes or tanks. 5.2.2.2.1 Laminar Mixing in Stirred-Tank Reactor: Numerical Study Fluid mixing is the heart of many industrial operation such as, in spanning paper & pulp, pharmaceutical, polymer, chemical and biochemical industries. In general, industries rely heavily on fluid mixing in order to obtain consistent, high-quality products, with minimum time investment, power input and maximum efficiency. A longstanding issue in the study of mixing has been how to characterise it. In mixing there are two issues, first what to measure and how to measure it. When performing a mixing operation, the ultimate objective is to achieve a target level of homogeneity within the mixture, and to do it in the fastest, cheapest, and if possible, most elegant way. The task left to the experimentalist is how to quantify or characterise this homogenisation process. Over the years, many different methods have been employed to examine the performance of mixing flows. Early experimental methods had included gross measurements of flow characteristics, such as pressure drop, power and torque requirements, and residence time distribution; flow field investigation based on the use of probes (optical, conductimetry, etc.), non-intrusive techniques, such as dye visualisation (Akanke et al., 1986). However, high-concentration visualisation methods using dyes and direct observation only provided space-averaged information, masking many aspects of fine mixing structures.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 408
Green Chemical Engineering
Mixing is omnipresent in both technology and nature and encompasses a wide range of time and length scales. Mixing controls various environmental and industrial phenomena. In technology, mixing is of utmost importance. Often the quality of the final products is a function of the effectiveness of the mixing process. Hence, mixing plays a crucial role in the success of many engineering operations. However, its usefulness is hindered by the lack of understanding of the fundamental principles governing homogenisation processes. Subject to formal study only recently, evolving from empiricism to a semi-qualitative level, the fundamentals of mixing are at best unclear. Mixing can be carried in both laminar and turbulent regimes. In the study of laminar mixing in stirred vessels, the absence of turbulence and development of large recirculation loops make mixing performance to be ineffective. In order for fluid to mix, it must be circulated by the impeller through the entire vessel in reasonable time. In addition, the velocity of the fluid leaving the impeller must be sufficient to carry out the material in most remote parts. Therefore, determining the level of mixing and overall behaviour and performance of the mixing tanks are crucial as per future percepts from the product quality and process economics point of views. One of the most fundamental needs for the analysis of these processes from both a theoretical and industrial perspective is the knowledge of the flow structure in such mixing vessels. Often mixing is associated with presence of turbulent flows. However, it is not always feasible to operate in turbulent regime, for example, consider polymerisation reactions where due to fluid high viscosity values, achieving higher Reynolds numbers (NRe) (stirring rate) leads to large increase in energy consumption as well as higher torque requirements that may exceed equipment capabilities. In such cases, it is better to operate under laminar region. Owing to these reasons there have been adequate examples on mixing under laminar conditions in pharmaceutical, food, polymer and biotechnology industries, in the production of products such as detergents, ointments, creams, suspensions, food emulsions and so forth where mixing is to be obtained in high viscosity materials. To understand the fluid mechanics and develop rational design procedures, there have been continuous attempts over the past century. These attempts can be broadly classified in two parts, namely, experimental fluid dynamics (EFD) and CFD. Experimental investigations have contributed significantly to the better understanding of the complex hydrodynamics of stirred vessels. However, such experimental studies have obvious limitations regarding the extent of parameter space that can be studied within a time frame. In most industrial operations, high pressure, high temperature and processes with hazardous materials are often involved. With limited access during operations and, except for a few temperature or pressure measurements, there is often little data available on the structure of the flow within the vessel. The performance of any process unit is only measured in terms of the output of that unit or even some other unit farther downstream. To measure the details of operation of the unit is normally not practical. Consequently, the effects of any malfunctioning and its cause may only be observed at shut down. CFD has been adopted by a whole range of industries, including chemical, petrochemical, oil, automotive, built-environment (architecture, industrial design, building construction management, town planning), food processing and many others enabling the process engineer to begin to understand in greater detail the internal operation of individual units by relating an analysis of the flow field and other transfer processes with observed phenomena and thereby identify the cause of a problem and evaluate solutions. Moreover, it has steadily spread from research groups into the design and development departments. In short, CFD is being used as a useful engineering tool but cost-effective to aid in the understanding and design of process operation.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 409
Green Reactor Modelling
In this study, a complete analysis of a single and triple blade mixing tank in concentric and eccentric system was studied using commercial CFD software Fluent 14.0. Eight different geometries were drawn (single mixing tank concentric pitched blade; single mixing tank eccentric pitched blade; single mixing tank concentric circular solid Ruston disk blade; single mixing tank eccentric circular solid Ruston disk blade; triple mixing tank concentric pitched flat blade disk; triple mixing tank eccentric pitched flat blade disk; triple mixing tank concentric circular solid rush ton disk blade; triple mixing tank eccentric circular solid rush ton disk blade) as the geometries are well created and dimensified. Meshes was created with local tetrahedral adaptive fine and coarser using a first-order difference upwind scheme with 1.2 mesh biasing at different skewness deviations and 1.0–1.4 under relaxation factor for exactness in laminar mixing using the Quick scheme for different geometry and then they were transported to a fluent process where the flow patterns, scaled curves and contour designs were plotted so that the values of different mixing parameters were calculated under steady time conditions at different iterations. Two properties of chaotic flows make them very attractive for mixing in the laminar regime: 1. Exponential divergence of initially nearby trajectories 2. Ergodicity The former property means that two trajectories starting very close together will rapidly diverge from each other, and thereafter have totally different evolutions. Suppose x(t) is a point on a streamline at time t, and consider a nearby point x(t) + δ(t), where δ is a small separation vector of an arbitrary initial length δ(0). In chaotic flows, the ratio δ(t)/δ(0) known as the stretching of a fluid element grows as
δ(t) = δ(0) × e λt
(5.1)
where δ(t) is the separation distance between the two particles at time t. The exponential growth of distance is usually presented by the constant called short time Lyapunov exponent of the trajectory, and its asymptotic limit is a measure of the average rate of stretching at a given flow period. Chaotic flows are recognised by having positive Lyapunov experiments. The second property ‘Ergodicity’ means that as the time approaches infinity, a chaotic trajectory will explore an entire chaotic region densely. In a mixing study, this property eventually assures that every particle will visit all regions in the chaotic subdomain. The spatial position determines the amount of stretching and reorientation that a small fluid element experiences at that location. Eventually, the continuous stretching and reorientation process leads to a homogeneous distribution of materials throughout the chaotic region. In recent years, mixing strategies involving periodic and aperiodic protocols, both temporal and spatial, have been proposed to enhance mixing performance in idealised and realistic flows. Periodic protocols enhance mixing performance significantly by destroying segregated regions otherwise present in the periodic counterpart. The use of perturbations to enhance mixing has also been investigated in realistic flows. A variable-speed protocol can destroy segregated regions in stirred tanks operated under laminar conditions. By breaking temporal symmetry, widespread chaos could be achieved; the iterative alteration between different RPM values implies alternative application of two different steady flow structures.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 410
Green Chemical Engineering
Breaking spatial symmetry has also been proposed as a means of inducing chaos in stirred tanks. This could be induced by varying the angle α between the principal axis of compression or extension and the axis of rotation w. If α = 0, then the flow is symmetric and consists of nested torii above and below the impeller. However, by tilting the impeller (α > 0) and consequently geometrically perturbing the system, the flow loses rotational symmetry, and chaos arises. More recently, Alvarez et al. (2000) demonstrated that for some values of geometrical eccentricity, widespread chaos is achieved and a significant reduction in mixing time is observed with respect to concentric stirred tank systems using generic impellers. 5.2.2.2.2 The Computational Code ANSYS Fluent 14 is software which contains the broad physical modelling capabilities needed to model flow, turbulence, heat transfer and reactions. ANSYS Fluent 14 software is an integral part of the design and optimisation phases of their product development. Advanced solver technology provides fast, accurate CFD results, flexible moving and deforming meshes, and superior parallel scalability. User-defined functions allow the implementation of new user models and the extensive customisation of existing ones. The CFD code FLUENT 14 is used in the current study. It solves flow problems with structured or unstructured meshes that can be generated about complex geometries with relative ease. Supported mesh types include 3D triangular/quadrilateral, 3D tetrahedral/hexahedral/pyramid/wedge, and mixed (hybrid) meshes. FLUENT 14 also allows refining or coarsening the grid based on the flow solution. This solution-adaptive grid capability is particularly useful for accurately predicting flow fields in regions with large gradients, such as free shear layers and boundary layers. In comparison to solutions on structured or block-structured grids, this feature significantly reduces the time required to generate a ‘good’ grid. Solution-adaptive refinement makes it easier to perform grid refinement studies and reduces the computational effort required to achieve a desired level of accuracy, since mesh refinement is limited to those regions where greater mesh resolution is needed. 5.2.2.2.3 Geometry and Its Characterisation A conventional stirred tank is designed in ANSYS FLUENT 14 under a design modeller, which consists of a vessel equipped with a rotating mixer. In this work eight different types of systems were taken for numerical experiments. These include a single mixing tank concentric pitched blade, a single mixing tank eccentric pitched blade, a single mixing tank concentric circular solid Ruston disk blade, a single mixing tank eccentric circular solid Ruston disk blade, a triple mixing tank concentric pitched flat blade disk, a triple mixing tank eccentric pitched flat blade disk, a triple mixing tank concentric circular solid rush ton disk blade and a triple mixing tank eccentric circular solid rush ton disk blade. The geometric configurations of the different designs are given in Table 5.1. 5.2.2.2.4 Effect of Mesh Size Assertion The computational domain has been modelled as three distinct volumes: a large cylinder for the mixing tank impeller, blades and shaft and other volumes as inlet and outlet in some configurations. This allowed the mixing tank to be modelled with relatively coarse elements, while the smaller inlet/outlet pipes could have a much finer mesh applied as compared to the tank. If the domain had consisted of a single volume, a very large number of small elements would have been required to mesh it, as the mesh size would have to be chosen based on the size of the inlet/outlet pipes, impeller blade, shaft and tank wall. Meshing the three main volumes separately allows a dramatic reduction of the amount of
www.Ebook777.com
Single mixing tank pitched flat blade disk Single mixing tank circular solid disk Triple mixing tank pitched flat blade disk Triple mixing tank circular solid disk
Specification
Concentric Eccentric Concentric Eccentric Concentric Eccentric Concentric Eccentric
Configuration 1st order 1st order 1st order 1st order 1st order 1st order 1st order 1st order
Discretisation Scheme
Geometry Design Configurations in ANSYS 14
Table 5.1
13.639 18.507 20.663 5.316 — — — —
Tank Clearance (C), m. 28.865 29.851 23.962 27.682 25.646 29.834 43.574 39.701
Tank Bottom Width (T), m. 19.661 15.374 18.879 18.883 12.282 18.676 24.989 27.654
Impeller Diameter (Di), m. 29.502 31.447 20.663 18.076 17.329 32.584 33.705 31.371
Tank Height (H), m.
— — — — 4.8905 8.621 11.059 11.321
Clearance from 1st to 2nd
— — — — 5.111 10.056 10.311 9.2468
Clearance from 2nd to 3rd
Free ebooks ==> www.ebook777.com
Green Reactor Modelling 411
www.Ebook777.com
Free ebooks ==> www.ebook777.com 412
Green Chemical Engineering
Table 5.2 Mesh Size Distribution Relative to Discretisation Schemes Specification Single mixing tank pitched flat blade disk Single mixing tank circular solid disk Triple mixing tank pitched flat blade disk Triple mixing tank circular solid disk
Configuration
Discretisation Scheme
Total Number of Nodes
Number of Cell Elements
Maximum Skewness
Concentric Eccentric Concentric Eccentric Concentric Eccentric Concentric Eccentric
1st order 1st order 1st order 1st order 1st order 1st order 1st order 1st order
4691 5004 15,292 66,048 8917 73,502 72,066 71,794
23,013 25,039 30,326 3,64,822 46,208 4,05,198 3,97,025 3,93,524
0.9685 0.9738 0.8481 0.8453 0.9648 0.9743 0.8274 0.8432
elements in the domain, leading to realistic computational times while maintaining the accuracy of the numerical simulations. Table 5.2 presents the geometrical configurations of various types of cases present in this text. 5.2.2.2.5 Velocity Field The velocity field of a fluid is a vector field which is used to mathematically describe the motion of a fluid. The length of the flow velocity vector represents the flow speed. The flow fields obtained at Reynolds number = 130, at a rotor speed of 150 rpm, are presented in Figures 5.3 through 5.10 in the form of velocity vectors. The figures depict the velocities in the half of the vertical cross section cut at the centre of the tank and elongates. The lengths of the vectors are proportional to the magnitude of the liquid velocity. In the laminar region corresponding to Re = 130, the liquid around the impeller moves with the impeller rotation smoothly and the liquid distant from the impeller is stagnant. In addition to these, two small vortex rings exist in the flow one below the impeller plane and the other above the impeller plane. The stagnant zones which are observed in the laminar region at the centre half disappear. In this region, the resistance to impeller rotation is mainly due to viscous effects. We have also tried for higher Reynolds numbers, that is, 220, 300 and 390 and found that similar types of results are obtained with the same flow patterns. A simulation was carried out using Navier–Stokes equations for the laminar region. The results show that the overall flow pattern is regular and flow characteristics are dissimilar to the turbulent regime. 5.2.2.2.6 Variation of Maximum Vorticity with Reynolds Number The maximum vorticity of fluid elements is defined as the tendency of fluid elements to spin or circulation per unit area around a particular region either around the blade or away from the impeller at a certain position given by ‘ω.’ For CFD in a stirred tank under laminar mixing, the maximum vorticity is mainly high at the lowest zonal regimes, which are characterised by development of mixing layers enhanced by the formation of small and big spiral vortices due to instability, which is presented by the blue color regions at angular locations known as lower toroidal zone regions and as light blue spots at certain angular velocities, which shows that vortex stretching occurs at higher viscosity. This occurred for the case of circular disks in concentric as well as eccentric positions shown in Figures 5.3 through 5.6 for single mixing tanks and Figures 5.7 through 5.9 for triple mixing tanks.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 413
Green Reactor Modelling
2.30e+01 2.18e+01 2.07e+01 1.96e+01 1.84e+01 1.73e+01 1.61e+01 1.50e+01 1.38e+01 1.27e+01 1.15e+01 1.04e+01 9.23e+00 8.08e+00 6.94e+00 5.79e+00 4.64e+00 3.50e+00 2.35e+00 1.20e+00 5.79e–02
X
Y
Z
Figure 5.3 Velocity vectors of concentric single pitched flat blade mixing tank at Re = 130.
1.87e+01 1.78e+01 1.68e+01 1.59e+01 1.50e+01 1.40e+01 1.31e+01 1.22e+01 1.12e+01 1.03e+01 9.37e+00 8.43e+00 7.50e+00 6.57e+00 5.64e+00 4.71e+00 3.78e+00 2.84e+00 1.91e+00 9.80e–01 4.77e–02
Y
X
Z
Figure 5.4 Velocity vector flow field of eccentric flat blade single mixing tank at Re = 130.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 414
Green Chemical Engineering
1.61e+01 1.53e+01 1.43e+01 1.37e+01 1.29e+01 1.21e+01 1.13e+01 1.05e+01 9.70e+00 8.90e+00 8.10e+00 7.30e+00 6.50e+00 5.70e+00 4.90e+00 4.10e+00 3.30e+00 2.50e+00 1.69e+00 8.94e–01 9.28e–02
Z Y
X
Figure 5.5 Velocity vector flow field of concentric circular blade single mixing tank at Re = 130.
1.17e+01 1.11e+01 1.06e+01 9.99e+00 9.41e+00 8.83e+00 8.26e+00 7.68e+00 7.10e+00 6.52e+00 5.94e+00 5.37e+00 4.79e+00 4.21e+00 3.63e+00 3.05e+00 2.48e+00 1.90e+00 1.32e+00 7.41e–01 1.63e–01
Y
Z X
Figure 5.6 Velocity vector fields of eccentric single circular blade mixing tank at Re = 13.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 415
Green Reactor Modelling
2.41e+01 2.29e+01 2.17e+01 2.05e+01 1.93e+01 1.81e+01 1.69e+01 1.57e+01 1.45e+01 1.33e+01 1.21e+01 1.09e+01 9.68e+00 8.48e+00 7.29e+00 6.09e+00 4.89e+00 3.69e+00 2.49e+00 1.29e+00 9.64e–02
Z Y
X
Figure 5.7 Velocity vector of concentric flat blade triple mixing tank at Re = 130.
4.08e+01 3.88e+01 3.68e+01 3.47e+01 3.27e+01 3.07e+01 2.86e+01 2.66e+01 2.46e+01 2.25e+01 2.05e+01 1.85e+01 1.64e+01 1.44e+01 1.24e+01 1.03e+01 8.29e+00 6.25e+00 4.22e+00 2.18e+00 1.50e–01
Z X
Y
Figure 5.8 Velocity vector field of concentric circular triple mixing tank at Re = 130.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 416
Green Chemical Engineering
2.42e+01 2.30e+01 2.18e+01 2.06e+01 1.94e+01 1.82e+01 1.70e+01 1.58e+01 1.46e+01 1.34e+01 1.22e+01 1.10e+01 9.82e+00 8.62e+00 7.42e+00 6.22e+00 5.02e+00 3.81e+00 2.61e+00 1.41e+00 2.07e–01
Z Y
X
Figure 5.9 Velocity vector field of concentric circular triple mixing tank at Re = 130.
1.74e+01 1.65e+01 1.56e+01 1.48e+01 1.39e+01 1.30e+01 1.22e+01 1.13e+01 1.04e+01 9.58e+00 8.71e+00 7.85e+00 6.98e+00 6.12e+00 5.26e+00 4.39e+00 3.53e+00 2.66e+00 1.80e+00 9.34e–01 6.99e–02
Z Y
X
Figure 5.10 Velocity vector field of eccentric circular triple mixing tank at Re = 130.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 417
Green Reactor Modelling
This spatial instability around the disk blade is due to the inflectional nature of axial and radial velocity profiles. The vortices initially created by mixing vessels at angular velocity are linearly unstable and roll up to form coherent vortices which were pointed straight in all figures. In Fluent 14, spiral mixing layer vortices can be very well reproduced by three-dimensional CFD numerical simulations, even though Reynolds number is much lower. This shows the tendency of vortices to pair if they are close together as shown in Figure 5.10 (Table 5.3).
Table 5.3 Variation of the Maximum Vorticity with Respect to Reynolds Number Pitch Flat Blade Concentric Disk Reynolds No. (RPM)
Maximum Vorticity
Circular Concentric Disk Reynolds No. (RPM)
Maximum Vorticity
Pitched Flat-Blade 4 Impeller a. Single Mixing Tank (4 Blade) 0 150 250 350 450
17.31 108.02 181.18 298.82 500.45
0 150 250 350 450
24.12 122.42 223.63 374.51 600.13
b. Triple Mixing Tank (4 Blade) 0 150 250 350 450
16.32 112.31 193.13 314.98 551.67
0 150 250 350 450
21.08 129.61 238.71 389.17 680.23
Pitch Flat Blade Eccentric Disk Reynolds No. (RPM)
Maximum Vorticity
Circular Eccentric Disk Reynolds No. (RPM)
Maximum Vorticity
Circular Ruston Solid Disk c. Single Mixing Tank (4 Blade) 0 150 250 350 450
27.30 167.96 269.16 384.13 498.24
0 150 250 350 450
38.07 212.02 331.19 455.14 589.13
d. Triple Mixing Tank (4 Blade) 0 150 250 350 450
41.58 181.36 283.52 396.08 522.51
0 150 250 350 450
55.10 224.11 344.91 477.39 621.50
www.Ebook777.com
Free ebooks ==> www.ebook777.com 418
Green Chemical Engineering
5.2.2.2.7 Conclusions A comparative study of laminar flow in an unbaffled mixing vessel agitated by a circular solid disk rotor and a 4-blade impeller in concentric and concentric system of single and triple mixing tanks has been carried out using CFD simulations. Computational results have revealed that the solid disk rotor produces a flow field similar to the one generated by the radial flow 4-blade impeller. The solid disk can be classified as a quasi-radial flow rotor. The location of the recirculation centre is seen to be further radially away from the solid disk rotor as compared to the 4-blade impeller closer to the mid-plane for the same Reynolds number. Knowledge of this motion will help researchers to understand the motion of the isolated mixing regions in laminar mixing for understanding velocity variation, in the laminar region. The liquid around the impeller moves with the impeller rotation smoothly and the liquid distant from the impeller is stagnant. In addition to these, two small vortex rings exist in the flow one below the impeller plane and the other above the impeller plane. In this region, the resistance to impeller rotation is mainly due to viscous effects. In both cases the recirculation centre started moving towards the rotor as the Re was increased and between 130 www.ebook777.com 420
Green Chemical Engineering
Figure 5.12 Configuring setting.
4. Configuring settings (Figure 5.12): Next we have to do accounting (Figure 5.13). User name: S Suresh Account no: 01 Project ID: Chemical Project Name: CSTR 5. Specifying components: Input of reactants and products, that is, the components which are being involved (Figure 5.14). 6. Specifying property method (Figure 5.15) 7. Specifying stream 1 information (Figure 5.16) 8. Specifying stream 2 information (Figure 5.17) 9. Specifying block information (Figure 5.18) 10. Product stream phases information (Figure 5.19) 11. Reaction information (Figure 5.20) 12. Kinetic information (Figure 5.21) 13. Available reaction set (Figure 5.22) 14. Running the simulation and viewing the result (Figure 5.23) 15. Viewing output summary (Figure 5.24)
www.Ebook777.com
Free ebooks ==> www.ebook777.com Green Reactor Modelling
Figure 5.13 Accounting information.
Figure 5.14 Specifying components.
www.Ebook777.com
421
Free ebooks ==> www.ebook777.com 422
Green Chemical Engineering
Figure 5.15 Property method.
Figure 5.16 Stream 1 information.
www.Ebook777.com
Free ebooks ==> www.ebook777.com Green Reactor Modelling
Figure 5.17 Stream 2 information
Figure 5.18 Block information.
www.Ebook777.com
423
Free ebooks ==> www.ebook777.com 424
Green Chemical Engineering
Figure 5.19 Product stream phases information.
Figure 5.20 Reaction information.
www.Ebook777.com
Free ebooks ==> www.ebook777.com Green Reactor Modelling
Figure 5.21 Kinetic information.
Figure 5.22 Available reaction sets.
www.Ebook777.com
425
Free ebooks ==> www.ebook777.com 426
Green Chemical Engineering
Figure 5.23 Viewing result.
Figure 5.24 Result summary.
www.Ebook777.com
Free ebooks ==> www.ebook777.com Green Reactor Modelling
427
5.3.2 Conclusions In the above study, we have done simulation for production of cyclohexylamine (cyclo-01) in an RCSTR by hydrogenation of aniline. From the results, concluded that mass flow of vapour and liquid flow is 4416.79 kg/h and 96.51kg/h, respectively. The mole fraction of cyclo-01 is about 1.00. Reactor heat duty is −1.9290 (mm KCal/h). The residence time for reaction is 1.24 h.
www.Ebook777.com
Free ebooks ==> www.ebook777.com
www.Ebook777.com
Free ebooks ==> www.ebook777.com
6 Application of Green Catalysis and Processes The main objective of this chapter is to develop new catalysts for various environmental pollution abatement processes. A systematic approach was followed to provide insight into these practical applications. Both chemistry and reaction engineering aspects are considered. Section 6.1 presents the few general introduction on application of green catalysis and processes. Section 6.2 presents the synthesis of zeolite-X and A from fly ash, characterisation of synthesised zeolite and application of synthesised zeolite as an adsorbent for the removal of dyes. Various mathematical kinetic models are also presented to compare the reaction mechanism and intraparticle diffusion mass transfer rate of various dyes to the synthesised zeolite interface. Section 6.3 discusses synthesising Na-Y zeolite from coal fly ash by fusion followed by hydrothermal treatment. By using these two modes of heating, the time required for crystallisation has been optimised. Besides, the effect of addition of seeds has also been investigated. The improvement of crystal formation was analysed using XRD (x-ray diffraction), SEM (scanning electron microscopy), EDAX (energy-dispersive atomic x-ray analysis) and FTIR (Fourier transform infrared spectroscopy). The removal of Acid Orange 7 dye, colour and chemical oxygen demand (COD) by adopting catalytic wet peroxide oxidation (WPO) process with iron-exchanged zeolite as catalyst has been studied. Parameters like temperature, initial pH, hydrogen peroxide concentration and catalyst loading have also been studied. The dye removal efficiency using commercial Na-Y zeolite and FA Na-Y zeolite has been compared. Thermolysis has been used as an effective pretreatment method for pulp and paper mill wastewaters, composite wastewater of a cotton textile mill, petrochemical and distillery wastewater (DWW), and for the biodigester effluents of an alcohol production plant. Section 6.4, focuses on the use of different types of commercially available catalysts, CuSO4, FeCl3, FeSO4, CuO, ZnO, Mn/Cu and Mn/Ce. Time-dependent experiments were carried out to determine which adsorbents are better and to perform kinetic characterisation of the thermolysis processes. The effect of individual parameters and their interactional effects on polypropylene plant wastewater were determined experimentally and a statistical model of the process was developed. The kinetic analysis of thermolysis revealed that the process is comprised of two successive steps—an initial fast step followed by a slower second step for COD reduction. The two steps can be represented by a simple global power-law rate expression giving first order with respect to COD for both the steps. In Section 6.5, the catalyst chosen to be tested for catalytic wet air oxidation (CWAO) of DWW at atmospheric pressure and moderate temperature were inorganic as well as organic forms (CuSO4, FeCl3, ZnCl2, Al(OH)3 and synthesised zeolite).
429
www.Ebook777.com
Free ebooks ==> www.ebook777.com 430
Green Chemical Engineering
6.1 Introduction to Application of Green Catalysis and Processes Since the 1990s, the scientific community has progressively changed its approach towards dealing with regulations for environmental protection. This evolution in the chemical industries and R&D labs has led to the development of green chemistry. In the last decade, green chemistry has been widely recognised and accepted as a new means for sustainable development. Industries are often forced to pay heavy prices to meet the standards set by the pollution regulatory boards while using traditional methods of treating or recycling waste. Also, with growing environmental problems, law-making boards are now looking more critically at the possible hazardous effects of a larger number of chemical substances. Thus, the combined effect of existing environmental safety regulations, the evolving scientific understanding of previously little-known toxic chemicals and their long-term effect on the biota, and the industries’ monetary interests have turned attention from end-of-pipe cleanup to environmentally safer production processes through the green chemistry approach. A simple definition of green chemistry as given by the U.S. EPA is, ‘Use of chemistry for pollution prevention and design of chemical products and processes that are more environmentally benign’ (www.epa.gov/greenchemistry/).The growing importance now given to green chemistry can be attributed to the ability of this approach to bridge ecoefficiency and economic growth. Environmental catalysis has continuously grown in importance over the last two decades not only in terms of the worldwide catalyst market, but also as a driver of advances in the whole area of catalysis. The development of innovative ‘environmental’ catalysts is also a crucial factor towards the objective of developing a new sustainable industrial chemistry. For example, the methanol to gasoline process and biomass to biofuels (Chang and Silvestri, 1977; Suresh et al., 2013), commercialised by Mobil in New Zealand using the then newly discovered zeolite ZSM-5; this process helped to bring down the relatively high oil prices of the 1970s. Innovation in Environmental Catalysis: The extension of the use of catalysis outside traditional fields together with the basic problem, in environmental technologies, of having optimal reaction conditions, the choice of which is determined by energy and feed constraints and/or conditions defined by upstream units, implies that a very innovative effort is necessary to develop new catalytic materials, devices and solutions. It is evident that the entire field of heterogeneous catalysis as well as other industrial sectors will benefit from this research effort, not only the specific area of environmental catalysis. For example, the ordinary conditions for use of heterogeneous catalysts in chemical syntheses are in the 200–500°C temperature range (while environmental catalysts can operate sometimes at lower temperatures such as room or even lower temperatures, e.g., in the mentioned low-temperature CO oxidation catalysts in water purification technologies or in some nitrogen oxides or VOC abatement systems, where the heating of large volumes of effluents becomes too expensive) or at extremely high temperatures, 900°C or above (e.g., in catalytic combustion for gas turbines). The recent ‘European Climate Change Programme’ (ECCP) of the European community has further stimulated the need for research in using catalytic technologies for greenhouse gas emissions control (CO2, methane, N2O, halogen compounds). This area is of increasing interest for the global effect of greenhouse emissions and for the increasing pressure to find realistic solutions to the problem. Environmental catalysis research is undergoing a transition from pollution abatement to pollution prevention. Research for advanced fuel cells and catalytic combustion both
www.Ebook777.com
Free ebooks ==> www.ebook777.com Application of Green Catalysis and Processes
431
promise power generation with ultra-low emissions and are under intensive investigation worldwide. New and cleaner catalytic routes are changing the way in which bulk and fine chemicals are made. During this transitional phase, catalytic pollution abatement technology will continue to be used commercially with further improvements in effectiveness required. Emissions from the internal combustion engine will remain a focal point for new technologies that improve fuel economy and decrease emissions of greenhouse gases (i.e., CO2). Lean-burn internal combustion engines promise significant improvements in fuel economy, but the problem of NOx abatement remains to be solved. Monitoring of pollutants in extremely low concentrations in automobile exhausts, chemical processes, commercial and residential buildings is also under intense investigation using sensors that could contain catalysts. The abatement of traces of pollutants from the air using ‘passive catalysis’ is a new and exciting way to improve the quality of the air we breathe. Catalysts deposited on heat-exchanger surfaces can be utilised to decompose ambient ozone and hydrocarbons. Photocatalysis continues to show effectiveness (Gota and Suresh, 2014), but for special applications only. The zirconia-based electrochemical O2 sensor provides computer-controlled feedback for the combustion process to maintain the engine air-to-fuel ratio within a narrow range for efficient three-way catalysis. Combinations of CeO2 and ZrO2 play an integral role in providing oxygen storage capacity, which broadens the conversion efficiency for NOx, CO and HC during the rich/lean perturbations associated with the feedback control system. Truly, the automobile catalyst has resulted in the development of materials durable under extreme environments previously thought impossible in conventional catalytic processes. Further improvements, however, are still required to meet the ever-increasing stringent emission standards worldwide. Zeolites such as H-ZSM-5 are effective catalysts for room temperature conversion of methyl tert-butyl ether (MTBE) in contaminated water into biodegradable chemicals. When H-ZSM-5 zeolite is added to an aqueous solution containing MTBE, there is fast initial adsorption after which slow decay begins with formation of alcohols as the main products (t-butyl alcohol and methanol). Data indicate the practical possibility of using zeolites as catalysts for water remediation by MTBE contamination and also as a guard bed around gasoline tanks. Water remediation technologies and, in general, the entire area of the use of catalysts in wastewater purification is thus a topic that will be of increasing importance in the future. In addition to the treatment of wastewater from chemical productions, other relevant areas for zeolite use are in reduction of the environmental impact of the non-chemical sector (e.g., in the electronic, leather tanning and pulp/paper industries) and agro/food production. Recently, in continuation of our research on the synthesis and application of novel and recyclable solid catalysts, we have been exploring prepared green catalysis for different environmental applications (Gota and Suresh, 2014). A major aim of these case studies is to also describe the design and extension of the applications of green catalysts (Suresh et al., 2014).
6.2 Case Study 1: Treatment of Industrial Effluents Using Various Green Catalyses Nanoporous materials are representative candidates for various applications, taking advantage of well-defined porosity and structural integrity (Davis, 2002). Microporous ( www.ebook777.com 432
Green Chemical Engineering
and mesoporous (2–50 nm) components in nanoporous materials have been well reported in regard to their potential applications in not only environmental, pharmaceutical and electronic applications but also in the separation process, and as adsorbents, membranes and catalysts (Corma, 1997). Therefore, it is important that nanoporous materials are obtained in adjective pore sizes, accessible active sites and have well-defined porosity for applications. In this context, the microwave could be an important tool in the green chemistry approach due to its selective heating ability in reduced durations, low energy consumption and limited steps. Since zeolites were synthesised using microwave irradiation, the microwave synthesis of mesoporous materials as well as microporous materials has been investigated by many research groups (Ramaswamy et al., 2001; US Patent No. 4,778,666). Furthermore, microporous materials can be easily achieved by microwave synthesis in an efficient way by controlling particle size distribution and phase selectivity, and because of its unique morphology and enhanced crystallisation time (Park et al., 1998; Suresh et al., 2014). The current study focuses on
1. Synthesising Na-Y zeolite from coal fly ash by fusion followed by hydrothermal treatment. The synthesis has been done using two different modes of heating— conventional heating and microwave heating. Using these two modes of heating, the time required for crystallisation has been optimised. Apart from this, the effect of addition of seeds has also been investigated. The improvement of crystal formation was analysed by XRD, SEM, EDX and FTIR. 2. Studying the removal of Acid Orange 7 dye, colour and COD by adopting a catalytic WPO process with iron-exchanged zeolite as catalyst. Parameters such as temperature, initial pH, peroxide concentration and catalyst loading have been studied. 3. The dye removal efficiency using commercial Na-Y zeolite and FA Na-Y zeolite has been compared.
6.2.1 Introduction Zeolites and Their Structure: The Swedish mineralogist, Cronstedt, was the first to discover zeolites. The name derives from the Greek, and means ‘boiling stone’—so called because its behaviour when highly heated gives the appearance of boiling water within the material left the structure. Since their discovery in 1756, many different zeolite structures have been identified—some naturally occurring and some purely synthetic. Zeolite is a crystalline material and its structure consists of hydrated aluminosilicates of metals from group I and group II, in particular, sodium, potassium, magnesium and calcium. Structurally, zeolites are framework aluminosilicates based on an infinitely extending three-dimensional network of AlO4 and SiO4 tetrahedra linked to each other by sharing all of the oxygen. The structural formula of a zeolite is represented by the crystalline unit cell as
Mx/n[(AlO2) × (SiO2)y] · wH2O
where, M: cation n: valence of cation w: the number of water molecule
www.Ebook777.com
Free ebooks ==> www.ebook777.com 433
Application of Green Catalysis and Processes
y/x: the ratio of the tetrahedral silica to alumina portion [ ]: framework composition The framework contains channels and interconnected voids that are occupied by cation and water molecules. Zeolites consist of SiO2, Al2O3, alkali cation, water and other substances with varying functions from one another. Table 6.1 summarises the function of each element in zeolites. The cations are quite mobile and may usually be exchanged in varying degrees by other cations. Intra-crystalline ‘zeolitic’ water in zeolites can be removed continuously and reversibly. The first structural classification is based upon the framework topology, with distinct frameworks receiving a three-letter code (Meier et al., 1996). The frameworks for zeolites with the same code are identical. A three-letter framework-type code is assigned to zeolites and the priority in the naming of zeolites depends on the first mineral discovered in the group. This classification is useful for zeolite researchers whose major interests are in cation exchange and synthetic zeolites, but does not assist geologists attempting to name zeolite minerals (Armbruster et al., 2001). The second structural method for the classification of zeolites is described by Meier et al. (1968), based on a concept termed ‘secondary building unit’ (SBU) as shown in Figure 6.1. The primary building unit for zeolites is the tetrahedron and the SBUs are the geometric arrangements of tetrahedra (Breck et al., 1974). Quite often, these SBUs tend to control zeolite morphology. In these SBUs only the position of tetrahedral Si and Al are shown. Oxygen atoms lie near the connecting solid lines, which are not intended to mean bonds. The classification used by Breck et al. (1974) is based on the framework topology of the zeolites for which the structures are known, and it consists of seven groups, within which zeolites have a common subunit of structure that is a specific array of (Al,Si)O4 tetrahedra. In the classification, the Si–Al distribution is neglected. These subunits have been called SBUs by Meier (1968). The primary building unit for zeolites is the tetrahedron (Figure 6.1). There are many possible zeolite structures due to the large number of ways in which the SBU can be linked to form various polyhedra that, when combined, create networks of regular channels and cavities (Sulikowski et al., 1987). Gottardi proposed a classification scheme that is similar to the SBU classification of Breck et al. (1974) (Table 6.2), except that it includes some historical context of how zeolites were discovered and named. This scheme uses a combination of zeolite group names that have specific SBUs and is widely used by geologists and consists of some complex structural units of tetrahedron, whether finite or infinite, which are: (a) the chain of fibrous zeolites; (b) the single-connected 4-ring chain; (c) the double-connected 4-ring chain; Table 6.1 Element Sources in Zeolites and Their Function Source
Functions
SiO2 AlO2 OH− Alkali cation Water Organic directing agent
Primary building units of the framework Origin of the framework charge Mineraliser, guest molecule Counter-ion of framework charge Solvent, guest molecule Counter-ion of framework charge, guest molecule, template
www.Ebook777.com
Free ebooks ==> www.ebook777.com 434
Green Chemical Engineering
S4R
S6R
D4R
4-1
D6R
5-1
S8R
D8R
4-4-1
Figure 6.1 Secondary building units in zeolites (Meier, 1968).
Table 6.2 Classification Based on Breck et al. (1974) Group 1 2 3 4 5 6 7
Secondary Binding Unit (SBU) Single 4 ring, S4R Single 6 ring, S6R Double 4 ring, D4R Double 6 ring, D6R Complex 4-1, T5O10 unit Complex 5-1, T8O16 unit Complex 4-4-1, T10O20 unit
(d) the 6-ring, single or double; (e) the hexagonal sheet with handles; (f) the heulandite unit. These complex units are mostly simply connected to form the actual frameworks, but in some cases vertices, edges or also faces shared with nearby units. Zeolite pores consist of 6-, 8-, 10-, 12- and 14-membered oxygen ring systems to form tube-like structures and pores that are interconnected to each other. However, other factors such as the location, size and coordination of the extra-framework cations are also influencing pore size. 6.2.1.1 Properties of Zeolites Dehydration of Zeolites: Most zeolites can be dehydrated to some degree without major alteration of their crystal structure; they may subsequently be rehydrated, that is, absorb water from the vapour in the liquid phase (Table 6.3). However, many zeolites undergo irreversible structural changes and suffer total structural collapse.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 435
Application of Green Catalysis and Processes
Table 6.3 Some Physical Properties of Zeolites Particle size (synthetic zeolites) Thermal expansion (−183°C to 25°C) Density Hardness of crystals (mohs scale) Optical property (colour) Conductivity Dielectric
1–10 μm About 6.9 × 10−6 (zeolite A); coefficient compared to 5.2 × 10−6 (quartz) 1.9–2.3 g/cc 4–5 Colourless (presence of other metals in the zeolites adds colour) 10−8–10−4 Ω−1 cm−1 (dehydrated to fully hydrated A) Varies with temperature and water content over a wide range. For example, for zeolite ‘A’, it varies from 0.01 to 0.3. The electrical conductivity depends on a number of factors such as temperature, SiO2/Al2O3 ratio, ΔH, number of cations per unit cell, cation radius, ΔG, water molecules per unit cell, molecules per unit cell and so on NMR spectrum interprets the interchange of water molecules between sites and the transit time is small compared to residence time. Water molecules in larger zeolite cavities exhibit the same properties of isolated liquid, but for smaller zeolite cavities, they appear to cluster around anions. During dehydration, it appears that water molecules line the inside of the zeolite super cages. Cation–dipole interactions play an important role in the nature and structure of zeolitic water 0 0 Zeolite S 0298K (cal/o/gfw) ∆H 298K (kcal/gfw) (log Kf)298 (kcal/gfw) ∆G298K
Zeolitic water
Thermochemical data
Analcime Jadeite
−786.341 −719.871
56.03 31.90
−734.262 −677.206
538.228 496.405
Surface hydroxyl groups: Hydroxyl groups are necessary to terminate the faces of a zeolite crystal at positions where bonding would normally occur with adjacent tetrahedral aluminium or silicon ions within the crystal. Structural hydroxyl groups: Hydroxyl groups stretch the structure in X and Y zeolites. Hydrolysis of univalent ions: Limited hydrolysis of cations may result in some cation deficiency and replacement by hydroxyl groups as shown in Figure 6.2. Transformation Reactions—Hydrothermal: The transformation of zeolites or their recrystallisation, at elevated temperatures in the presence of water vapour, is to be distinguished from the recrystallisation reactions or transformations of zeolites to other zeolites or nonzeolite species in solution, such as solutions of strong bases. Because of thermodynamic metastability in hydrothermal magma, a zeolite may transform to another crystalline species over a period of time. Effect of Water Vapour at Elevated Temperatures—Stability of X and Y Zeolites: When exposed to steam at 350°C, sodium X zeolite loses structure and adsorption character. The partial Na+
Na+ (H2O)X O
O Si
AI
O Si
O
O AI
Si
O AI
OH
O Si
AI
Figure 6.2 Hydrolysis and hydroxyl replacement in univalent ions.
www.Ebook777.com
+ Na+ + OH–
Free ebooks ==> www.ebook777.com 436
Green Chemical Engineering
hydrogen exchange, obtained by mineral acid treatment to lower pH of zeolite in water to about 6, improves stability loss, minimises adsorption capacity and its crystalline structure is retained. The synthetic zeolites X and Y, which have the same framework topology, differ in steam stability. Zeolite Y, with Si/Al > 1.5, retains its structure and crystallinity when subjected to water vapour at 410°C. Transformations of Dehydrated Zeolites: When heated to high temperatures, the crystal structure breaks down resulting in the formation of amorphous solids and recrystallisation to non-zeolitic species. °C Example: Zeolite Y 1000 → glass
Transformation of Zeolites at High Pressures: At high pressures, zeolites transform to denser aluminosilicates. 300 ° C, 15 kilobars
For example: Zeolite Y → Zeolite P 400 ° C, 10 kilobars
→ Analcime 500 ° C, 20 kilobars
→ Jadeite
700 ° C, 15 kilobars
→ Albite + Nepheline
Reaction in Solutions—Strong Acids: It was observed that zeolites are decomposed by acids. Silicates, which are decomposed by treatment with strong acids, may be classified into two groups: (a) those that separate insoluble silica without the formation of gels and (b) those that gelatinise upon acid treatment. The general rule is that zeolites with Si/Al ratio 1.5 upon treatment with HCl decompose and precipitate silica. Strong Bases: Zeolites upon reaction with strong bases change into different species. For example, zeolite A when reacted with NaOH gives zeolite P and further reaction gives sodalite hydrate. Chelating Agents: Chelating agents like H4EDTA work in the same way as acids, dealuminating zeolites. The complete removal of aluminium with this method destroys the structure completely. The optimum level of removal for producing a thermally stable product is in the range of 25–50%. For zeolite Y, 50% removal leads to the increase in Si/Al ratio from 2.63 to 10.6. Ion Exchange of Zeolites: The ion exchange capacity of Y zeolites is less compared to that of X zeolites. Many exchange reactions do not go to completion at normal temperatures. The isotherms for exchange with the univalent cesium, ammonium and thallium, all terminate at a cation fraction, AZ, of about 0.7. The selectivity series changes with the degree of exchange. On up to 68% of exchange, the order of decreasing selectivity is Tl > Ag > Cs > Rb > NH4 > K > Na > Li 6.2.1.2 Zeolite Na-Y Synthetic zeolite Na-Y is the synthesised zeolite Y of which sodium cation neutralises the framework structure of aluminosilicate and this material is in the same group with zeolite
www.Ebook777.com
Free ebooks ==> www.ebook777.com Application of Green Catalysis and Processes
437
Table 6.4 Properties of Zeolite Y Structure Group Chemical Composition Typical oxide formula Typical unit cell contents Variations Crystallographic Data Symmetry Density Space group Unit cell volume Structural Properties Framework
SBU Void volume Cage type Framework density Effect of dehydration Largest molecule adsorbed
4 Na2OA12O3 − 4.8SiO2 − 8.9H2O Na56 [(A1O2)56(SiO2)136] · 250 H2O Na/Al 0.7–1.1; Si/Al => 1.5 to about 3 Cubic 1.92 g/cm3 Fd3 m 14,901–15,347 A3 Truncated octahedra, β-cages, linked tetrahedrally through D6R’s in arrangement like carbon atoms in diamond. Contains eight cavities ~13 A in diameter in each unit cell. D6R 0.48 cm3/cm3 β,26-hedron (II) 1.25–1.29 g/cm3 Stable and reversible (C4H9)3 N
X. Both zeolites exhibit a structure similar to naturally occurring faujasite types. The differences between these zeolites are due to the composition and other physical properties brought about by the compositional differences (Table 6.4). The Si, Al contents of zeolite Y are similar to those of faujasite, whereas zeolite X is much more aluminous. Zeolite Y exhibits a FAU (faujasite) structure that has a three-dimensional pore structure with pores running perpendicular to each other in the x, y and z planes. The pore diameter is large at 7.4 Å since the aperture is defined by a 12-member oxygen ring, and leads into a larger cavity of diameter 12 Å. The cavity is surrounded by 10 sodalite cages (truncated octahedral) connected on their hexagonal faces. Recent investigations have shown the potential of fly ash as a raw material for synthesis of various types of zeolites. The conversion of fly ash to zeolite has gained importance due to intensive research on zeolite growth in geological materials such as volcanic rock and clay minerals. High content of reactive materials such as alumino silicate makes it an interesting starting material for the synthesis of zeolite with a wide range of applications. Various methods of synthesis of zeolite from fly ash have, so far, been invented and patented. Some of the important techniques are alkali fusion followed by hydrothermal treatment (Shigemoto et al., 1993), slurry method (Grutzeck and Siemer, 1997) and molten salt method (Park et al., 2000). The fusion method is found to be the most efficient and general method for synthesis of X-type, Y-type and A-type of zeolites from a large variety of fly ash. A modified fusion process to synthesise zeolites A and X from fly ash was studied by Chang et al. (2000). It was found that the addition of aluminium hydroxide to the fused fly ash solution followed by hydrothermal treatment at 60°C produced single-phase zeolite
www.Ebook777.com
Free ebooks ==> www.ebook777.com 438
Green Chemical Engineering
A and X depending on the source of the fly ash. The result confirms that the quantity of dissolved aluminium specie is critical for the type of zeolite formed from fused fly ash. Sutarno and Arryanto (2007) synthesised faujasite from fly ash and its application for hydrocracking catalyst of heavy petroleum distillates has been studied. Faujasite was synthesised from fly ash by hydrothermal reaction in alkaline solution via a combination of reflux treatment of fly ash with HCl and fusion with NaOH. Ojha et al. (2004) synthesised X-type zeolite by alkali fusion followed by hydrothermal treatment. The synthesised zeolite was characterised using various techniques such as XRD, SEM and FTIR spectroscopy. Querol et al. (2002) synthesised zeolitic material from fly ash using two different methodologies (a) impure zeolitic material obtained by direct conversion from different fly ashes, and (b) a high-purity 4A-X zeolite blend synthesised from silica extracts obtained from Meirama fly ash. Vadapalli et al. (2010) studied solid residues resulting from the active treatment of acid mine drainage with coal fly ash, which were successfully converted to zeolite-P under mild hydrothermal treatment conditions. Scanning electron microscopy showed that the zeolite-P product was highly crystalline. The product had a high cation exchange capacity (178.7 meq/100 g) and surface area (69.1 m2/g) and has potential applications in waste water treatment. Lu et al. (2010) synthesised zeolite NaPI by a hydrothermal method from coal fly ash, the possibility of using modified zeolite NaPI as a material for removing fluorine from drinking water was studied. Fukui et al. (2003) studied the effects of NaOH concentration on the crystal structure and the reaction rate of zeolite synthesised from fly ash with a hydrothermal treatment. Zeolite Y was discovered by Breck in 1961 when his group of researchers found that it should be possible to synthesise the zeolite X structure with silica/alumina ratios as high as 4.7. Fly ash, an oxide-rich waste product from thermal power plants, can be used as raw material for different industries after proper treatment. In India, some attention has been paid to the proper utilisation of fly ash, however, only 3% of it is being utilised, mostly in the manufacture of pozzolonic cement, ready-made hollow blocks, asbestos sheets, in road embankments and for agricultural purposes. Two classes of fly ash are defined by the American Society of Testing Material (ASTM): Class F fly ash: The burning of harder, older anthracite and bituminous coal typically produces Class F fly ash. This fly ash is pozzolanic in nature, and contains less than 20% lime (CaO). Possessing pozzolanic properties, the glassy silica and alumina of Class F fly ash requires a cementing agent, such as Portland cement, quicklime or hydrated lime, with the presence of water in order to react and produce cementitious compounds. Alternatively, the addition of a chemical activator such as sodium silicate (water glass) to a Class F ash leads to the formation of a geopolymer. Class C fly ash: Fly ash produced from the burning of younger lignite or sub-bituminous coal, in addition to having pozzolanic properties, also has some selfcementing properties. In the presence of water, Class C fly ash will harden and gain strength over time. Class C fly ash generally contains more than 20% lime (CaO). Unlike Class F, self-cementing Class C fly ash does not require an activator. Alkali and sulphate (SO4) contents are generally higher in Class C fly ash. The types of zeolites formed on treatment and also the raw material compositions are very much selective to reaction parameters. The synthesis of various zeolites from fly ash and their properties mainly depend on the effect of reaction time, reaction temperature, alkalinity and fly ash composition.
www.Ebook777.com
Free ebooks ==> www.ebook777.com Application of Green Catalysis and Processes
439
Zeolites are crystalline, micro-porous, hydrated aluminosilicates that are built from an infinitely extending three-dimensional network of [SiO4]4− and [AlO4]4− tetrahedra linked to each other by the sharing of the oxygen atom. Generally, their structure can be considered as inorganic polymer built from tetrahedral TO4 units, where T is Si4+ or Al3+ ion. Each oxygen (O) atom is shared between two T atoms. Zeolite from fly ash: The disposal of coal fly ash from coal-based power plants is a problem of global concern today. In India, most of the utility thermal power and sub-bituminous coal has high ash content (30–50%) resulting in the production of a substantial quantity of fly ash. Only a small portion of this large quantity is used as raw material for concrete manufacturing and construction purposes, with the remainder being simply dumped in landfill sites. Currently, more than 90 million tons of fly ash is being generated annually in India, with 65,000 acres of land being occupied by ash ponds. Without proper disposal options, such a huge quantity of ash poses a dire threat to the environment. The possibility of using waste coal fly ash in synthesising zeolite molecular sieves is very attractive for its potential widespread applications in diverse fields. In fact, the high content of reactive materials such as aluminosilicate makes fly ash an interesting starting material for the synthesis of zeolite (Shigemoto et al., 1993). Converting fly ash into zeolites not only eliminates the disposal problem, but also turns an otherwise waste material into a marketable commodity. 6.2.1.2.1 Factors Affecting the Synthesis of Zeolites Some important factors affecting zeolite synthesis follow: Reagents: Reagents are a most obvious and significant factor in any synthesis. Purity of reagents is key to forming an appropriate product free from impurities. Zeolites, being aluminosilicates, require a source of silicon, aluminium and oxygen. Charge balancing cations are also necessary, and are usually supplied in the form of a hydroxide. Aluminium is often supplied in the form of alumina or sodium aluminate, although other sources are available. Silica sources are wide ranging, but the most commonly used are fumed silica, colloidal silica and sodium metasilicate. pH: Gel pH also plays an important role in determining the composition and structure of the zeolite formed. Zeolites are crystallised from gels with a high pH, often over 12. The pH influences the quantity of species in solution and this impacts on the rate of product formation. Reaction Vessels: As a consequence of the high pH used, standard borosilicate glass is an inappropriate reaction vessel. Leaching of silicon from the glass may occur, altering the quantity of silicon in the gel and, hence, affecting not only the Si/Al ratio, but perhaps the product formed. Durable plastic containers are more commonly used. It is necessary to thoroughly clean the containers between uses, or at least use them for one zeolite type only, as any crystals remaining from previous reactions may act as seed crystals. Ageing and Seeding: Once the gel is made, it can either be heated straightaway, or left to age at room temperature prior to use. The ageing process is said to provide a period for nuclei to form, which are the building blocks of the final crystals. Traditionally, nucleation takes place in the initial heat-up period of the gel to
www.Ebook777.com
Free ebooks ==> www.ebook777.com 440
Green Chemical Engineering
reaction temperature. However, if microwave heating is employed, the slow heatup phase is effectively eliminated, and the ageing step is beneficial. If the precursor nuclei are present already then the crystallisation stage can occur sooner and reduce the heating time necessary. Stirring: Stirring during the ageing process or reaction can cause an increase in collisions between species in solution, and prevents a local depletion of reagents around the forming crystals. In some instances this may be beneficial and lead to a reduction in reaction time through increased rates of nucleation. However, stirring may also break down existing species and stimulate production of undesired structures. For example, the synthesis of zeolite Na-X was studied with varying stirring speeds ranging from 0 to 350 rpm (Freund, 1976), which showed that increasing stirring speed resulted in decreased purity of Na-X; the purity is also compromised by the co-crystallisation of zeolite Na-P. Nucleation and Crystal Growth: Small aggregates form unstable nuclei, some of which grow large enough to become stable nuclei. Material in the solution is deposited on the stable nuclei, and these form crystallites. This process is relatively slow, as the crystals form by a condensation polymerisation. Heating Conditions: The heating conditions for the precursor gel tend to mimic those which form zeolites in nature. Naturally occurring zeolites are often found in lava flows or volcanic sediment, and so temperatures over 200°C and high pressures (>100 bar) were typically used in early synthesis. With the use of reactive alkali-metal aluminosilicate gels, however, lower temperatures and pressures can be used enabling synthesis to take place at around 100°C and under autogenous pressure. Ostwald’s law of successive transformation is very important in the consideration of zeolite synthesis. According to the law, the first phase formed during a reaction is thermodynamically the least stable, and is replaced by ever more stable phases until the most stable product is formed. However, in some instances, thermodynamically unfavourable products may persist if there is a significant activation energy barrier to the more stable phase. All zeolite structures are metastable with respect to more dense phases. 6.2.1.3 Applications of Zeolites Zeolites have a wide range of applications. The four main areas in which zeolites are applied are: Adsorbents/desiccants/separation processes: Zeolites are used as drying agents, in applications such as gas purification and in important separation processes such as n-paraffins from branched paraffins, p-xylene from its isomers and others. Catalysis: The large internal surface area of zeolites can be exploited for catalytic purposes and they can be highly selective, especially when their pore sizes are manipulated, for example by ion exchange. The role of zeolites in catalysis encompasses three different areas of selectivity that make use of the pore size. 1. Reactant selective catalysis: here reagents can only enter the zeolite and hence gain access to the catalytic site, if their size is smaller than the pore diameter.
www.Ebook777.com
Free ebooks ==> www.ebook777.com Application of Green Catalysis and Processes
441
2. Product selective catalysis: only products of the appropriate size leave the cavity. Different products have different diffusion rates out of cavities. 3. Transition state catalysis: Due to limited room in the cavity, some transition states cannot occur, this limits the reactions that may take place and ultimately affects the product. There are many advantages of zeolites over other high surface area catalysts: they can be made to be very selective (and hence give fewer by-products and a purer product), have a large number of catalytic sites per unit volume and a more regular structure, which produces more reproducible results. The reproducibility and selectivity is dependent on zeolite sample purity, as other products could form in any zeolite impurities present (as these would have different cavity sizes, allowing different reagents in and products out). The use of zeolite Y (FAU) as a catalyst in the petrochemicals industry and in fluid catalytic cracking (FCC) processes is advantageous for five reasons:
1. High activity levels 2. Low coke forming tendency 3. High organic nitrogen and NH3 resistance 4. Regenerability 5. Molecular shape selectivity
Detergents: Tonnage wise, the use of zeolites in detergent formulations is a large market with even far larger potential. Zeolite A nearly exclusively serves here as a sequestering agent to substitute phosphates. Miscellaneous: Either synthetic or natural zeolites are used in a number of applications such as:
1. Waste water treatment 2. Nuclear effluent treatment 3. Animal feed supplements 4. Soil improvement
Recently, zeolites have been used as molecular sieves for functional powders in odour removal and as plastic additives. Adsorption and adsorption processes are important fields of study in physical chemistry. They form the basis for understanding phenomena such as heterogeneous catalysis, chromatographic analysis, dyeing of textiles and clarification of various effluents. Dyes are defined as coloured substances, which when applied to fibres give them a permanent colour that is resistant to the actions of light, water and soap. Practically every dyestuff is made from either one or more of the compounds obtained by the distillation of coal tar. The chief of these are benzene (C6H6), toluene (C6H5 · CH3), naphthalene (C10H8), anthracene (C14H10), phenol (C6H5OH), cresol (C7H7OH), acridine (C13H9N) and quinoline (C9H7N). This case study describes the adsorption of methylene blue, methyl orange and safranine T over zeolite catalysts. Dyes or pigments are widely used in textile industries to colour products, creating environmentally hazardous waste. Wastewater from the dyeing and finishing operation in the textile industry are generally high in both colour and
www.Ebook777.com
Free ebooks ==> www.ebook777.com 442
Green Chemical Engineering
organic content. Colour removal from textile effluent has been the target of great attention in the last few years, not only because of its potential toxicity, but mainly due to its visibility problems. A recent estimate indicates that 20% of dyes enter the environment through effluents that result from the treatment of industrial wastewater. Existing technologies have a certain efficiency in the removal of dyes but their initial and operational costs are very high. On the other hand, low-cost technologies do not allow the desired degree of colour removal or have certain other disadvantages. Oxidation and adsorption are two major technologies that are used for wastewater treatment in the textile industry. Among oxidation methods, UV/ozone and UV/H2O2 treatments are technologies for decolourising wastewater. Adsorption is rapidly becoming a prominent method of treating aqueous effluents and has been extensively used in industrial processes for a variety of separation and purification purposes. Adsorption of dyes by zeolites has evolved into one of the most effective physical processes for the decolourisation of textile wastewater. This process has been found to be superior to other techniques for water reuse in terms of initial cost, simplicity of design, ease of operation and insensitivity to toxic substances. 6.2.2 Adsorption of Dyes onto Zeolite Although the adsorption of dyes onto zeolites has been extensively investigated, only a few studies have been reported about the adsorption of dye onto fly ash-based zeolites. Mondragon et al. (1990) investigated on the possible use of coal fly ash in general and synthesis of zeolitic material from it, in particular. But like most other investigators, they tried the hydrothermal method. Atun et al. (2011) investigated adsorption characteristics of two basic dyes, thionine and safranine T, onto fly ash and its three zeolitised products prepared at different hydrothermal conditions. Wang et al. (2006) studied adsorption over natural zeolites and synthetic zeolites, such as MCM-22, as effective adsorbents for the removal of a basic dye, methylene blue, from wastewater. Dyes: All aromatic compounds absorb electromagnetic energy, but only those that absorb light with wavelengths in the visible range (~350–700 nm) are coloured. Dyes contain chromophores, delocalised electron systems with conjugated double bonds, and auxochromes, electron-withdrawing or electron-donating substituents, which cause or intensify the colour of the chromophore by altering the overall energy of the electron system. Usual chromophores are −C = C–, −C = N–, −C = O, −N = N–, −NO2 and quinoid rings, usual auxochromes are –NH3, −COOH, −SO3H and −OH. The dye is generally applied in an aqueous solution, and may require a mordant to improve the fastness of the dye on the fibre. There are several classes of dyes such as organic dyes (acid, basic, direct, mordant, vat, reactive, disperse, sulphur, azo and food dyes) and other important dyes (leather, fluorescent, solvent, carbine dyes, etc.). These are classified according to their functional groups, derivatives, salts and so forth. Dye Classification: Based on chemical structure or chromophore, 20–30 different groups of dyes can be discerned. Azo (monoazo, disazo, triazo, polyazo), anthraquinone, phthalocyanine and triarylmethane dyes are quantitatively the most important groups. Other groups are diarylmethane, indigoid, azine, oxazine, thiazine, xanthene, nitro, nitroso, methine, thiazole, indamine, indophenol, lactone, aminoketone and hydroxyketone dyes and dyes of undetermined structure (stilbene and sulphur dyes). The vast array of commercial colourants is classified in terms of colour, structure and application method in the Colour Index (C.I.), which has been edited since 1924 (and revised every three months) by the Society of Dyers and Colourists and the American Association of Textile Chemists and Colorists. Each dye is given a C.I. generic name determined by
www.Ebook777.com
Free ebooks ==> www.ebook777.com 443
Application of Green Catalysis and Processes
its application characteristics and its colour. The C.I. discerns 15 different application classes. Some of them are: a. Acid dyes b. Reactive dyes c. Metal complex dyes d. Direct dyes e. Basic dyes f. Mordant dyes
g. Disperse dyes h. Pigment dyes i. Vat dyes j. Anionic dyes and ingrain dyes k. Solvent dyes l. Fluorescent brightners
6.2.2.1 Acid Orange 7 Dye Acid Orange 7 is of the Monoaza chemical class and its excellent chemical composition makes it suitable for various industrial applications. It is used for dyeing and printing wool, nylon and silk, and its other uses are in paper, leather, biological stain and indicator applications. Heavy metal salts of the dye are used for paper coating, and transparent pigments in tin printing and in moulding powders. Orange acid azo dyes produce an orange-pink colour. They are used to colour foods and drugs and as intermediates for making photosensitive dyes and drugs. Acid Orange 7 (acid magenta) is a mixture of sulphonated fuchsins. There are four of these compounds with three sulphonic groups in each (Figure 6.3). 6.2.2.2 Methyl Orange Dye A basic azo dye having the molecular formula C14H14N3NaO3S that is used chiefly as an acid–base indicator and of which the dilute solution is yellow when neutral and pink when acid. The structure of the methyl orange dye is given in Figure 6.4. 6.2.2.3 Methylene Blue Methylene blue is a heterocyclic aromatic chemical compound with the molecular formula C16H18N3SCl. It has many uses in a range of different fields such as biology and chemistry. O O S
Na+ –O
OH N
N
Figure 6.3 Structure of acid orange 7 dye. O N N
N
S
O
O– Na+
Figure 6.4 Structure of methyl orange dye.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 444
Green Chemical Engineering
N N
CI–
S+
N
Figure 6.5 Structure of methylene blue dye.
At room temperature it appears as a solid, odourless, dark-green powder that yields a blue solution when dissolved in water. The structure is given in Figure 6.5. 6.2.2.4 Safranine Dyes Safranines are the azonium compounds of 3,7-diamino-phenazine. They are obtained by the joint oxidation of one molecule of a para-diamine with two molecules of a primary amine; by the condensation of para-aminoazo compounds with primary amines, and by the action of para-nitrosodialkylanilines with secondary bases such as diphenylmetaphenylenediamine. The structure of safranines is given in Figure 6.6. A zeolitised fly ash product was successfully used as a low-cost adsorbent for cationic and anionic dyes. Equilibrium and kinetic results obtained in this study may be useful for designing a treatment plant for dye removal from industrial coloured effluents. Applications of Dyes: Dyes have a wide range of applications in several fields such as textile, food, medicine, electronics, etc. Some applications of the dye classes mentioned above are shown in Table 6.5. H3C
N
CH3
H2N
N+
NH2 CI–
Figure 6.6 Structure of safranine dye.
Table 6.5 Applications of Dyes Dye Acid dyes Reactive dyes Basic Direct dyes Mordant dyes Disperse dyes Vat dyes Solvent dyes Fluorescent brightners Other dye classes
Application Areas Nylon, silk, wool, paper, inks and leather Cotton, wool, silk and nylon Paper, polyacrylonitrile, modified nylon, polyester and inks Cotton, rayon, paper, leather and nylon Wool, leather and anodised aluminium Polyester, polyamide, acetate, acrylic and plastics Cotton, rayon and wool Plastics, gasoline, varnishes, lacquers, stains, inks, fats, oils and waxes Soaps and detergents, all fibres, oils, paints and plastics Food, drugs and cosmetics, electrography, direct and thermal transfer printing
www.Ebook777.com
Free ebooks ==> www.ebook777.com 445
Application of Green Catalysis and Processes
6.2.3 Catalytic WPO Wet Oxidation: Wet oxidation (WO) is a form of hydrothermal treatment. It is the oxidation of dissolved or suspended components in water using oxygen as the oxidiser. It is referred to as wet air oxidation (WAO) when air is used and when peroxide is used it is known as WPO. The oxidation reactions occur at a temperature above the normal boiling point of water (100°C) but below the critical point (374°C). More exactly, the oxidation reactions occur at temperatures between 150–320°C and at pressures from 10 to 220 bar (Imamura et al., 1999). The WO process can also be used for pretreating difficult wastewater streams, making them amenable for discharge to a conventional biological treatment plant for polishing. The process is also used for oxidation of contaminants in production liquors for recycle/reuse. Catalytic Wet Peroxide Oxidation: CWPO is similar to that of CWAO with nascent oxygen from hydrogen peroxide being used for the oxidation of toxic and non-biodegradable organic compounds. Mechanism for wet peroxide oxidation: H2O2 + (C) → 2HO* + (C)
(6.1)
H2O2 + Mn+ → HO* + OH− + M+(n+1) (6.2) ROOH + (C) → RO* + HO* + (C)
(6.3)
Reactions 6.1 and 6.3 have a collision partner (C), which can be either a molecule of water or a surface of the reactor or sediment. Reaction 6.2 occurs in the presence of transition metal species. The catalysts used depend upon the compound that has to be removed (Table 6.6). Some catalysts used for the removal of different compounds such as phenol, dye solutions. Some of zeolite synthesised methods are shown in Table 6.7. 6.2.3.1 Experimental Design Zeolite Synthesis: The synthesis of Na-Y zeolites is carried out in five steps. Fly ash is initially screened through a 355 µm mesh and the particles retained on the screen are put Table 6.6 Catalysts Used for Removal of Various Substrates in CWPO Substrate
Catalyst Used
Phenol
Azo dyes Reactive dye solutions Azo dye (Reactive Yellow 84) Organic compounds Dye wastewater Phenolic solutions
LaTil–xCuxO3 perovskite catalyst (Sotelo et al., 2004) AlFe-pillared montmorillonite (Kiss et al., 2003) Fe-SBA-15 (Martinez et al., 2007) Fe/AC (Quintanilla et al., 2007) CeO2-doped Fe2O3/γ-Al2O3 (Liu et al., 2006) Al–Cu-pillared clay (Kim et al., 2004) Fe-exchanged ultrastable Y zeolite (Catrinescu et al., 2002) Mixed (Al–Fe)-pillared clays (Barrault et al., 2000) Fe2O3/γ-Al2O3 (Liu et al., 2006) LaTil−xCuxO3 perovskite catalyst (Sotelo et al., 2004)
www.Ebook777.com
Fusion followed by hydrothermal treatment
Two-stage
Zhao et al. (1997)
Hollman et al. (1999)
Results Obtained
Zeolite Y with a maximum crystallinity of 72% was obtained in this study. Ageing proved to be a major contributor for favourable hydrothermal aluminosilicate chemistry for zeolite formation. In addition to this, seeds were added in different amounts, which enhanced the crystal formation and restarted the formation of unwanted impurities. Cation exchange capacities ranged from 3.6 to 4.3 meq/g for pure zeolites and from 2.0 to 2.5 meq/g for zeolites containing residual fly ash. They showed that pure zeolites are suitable for the removal of ammonium and heavy metal ions from wastewater.
Formation of an unreported Na aluminosilicate with approximate composition Na15Si4A13O20, and the product of fusion interacted with water, giving aluminosilicate gel, which yielded zeolite P upon hydrothermal treatment. Ageing played an important role in enhancing the hydrothermal condition during which both Si and Al in the fly ash dissolved into a basic solution and reacted to form ring-like structures, and further zeolite materials.
446
www.Ebook777.com Fly ash (500 g) was mixed with a 2 M sodium hydroxide solution and incubated at 90°C for 6 h, 24 h and so on for different stages.
Final mixture with a molar composition of 4.5Na2O:1Al2O3:7:5SiO2:104H2O and a pH of 13.55 was poured into a 500 mL autoclave, aged at 50°C for 48 h, and subsequently heated at 105°C for 48 h in a static state. Molar composition of seeds used 15Na2O:1Al2O3:15SiO2:300H2O, pH 13.55, temperature 105°C.
Fusion followed by hydrothermal treatment
Reaction Conditions Fusion at 170–180°C, hydrothermal treatment at 100°C, with and without ageing for 12 h.
Method of Synthesis
Alkaline fusion
Shigemoto et al. (1995); Singer and Berkgaut (1995) Zhao et al. (1997)
Reference
Literature for Zeolite Synthesis Methods
Table 6.7
Free ebooks ==> www.ebook777.com Green Chemical Engineering
Fusion followed by hydrothermal treatment Dialysis
Hui et al. (2006)
Tanaka et al. (2006)
Molten salt
Ho et al. (2000)
Step change of synthesis temperature during hydrothermal treatment. FA and NaOH solution added into a tube made of semipermeable membrane were pretreated in the same NaOH solution at 85°C for 24 h. After the pretreatment, the tube was removed and NaOH–NaAlO2 solution was added into the residual solution to control the SiO2/Al2O3 molar ratio of the solutions from 0.9 to 4.3. The precipitates thus formed were aged for 24 h at 85°C.
Typically, mixtures containing 0.7 g fly ash, 0.3 g base, and 1 g salt were ground into fine powder and heated to a molten state at 350 ± 5°C for various treatment periods.
The main zeolite species synthesised by the molten salt method were dependent on the types of salt mixture and raw material used. They concluded that the molten salt method is a new and alternative approach for the mass treatment of these mineral wastes at low cost, as well as for the improvement of the purity and alkalinity of zeolitic materials. Reducing the overall synthesis time while maintaining a high degree of crystallinity for the samples. When the NaOH–NaAlO2 solution was added into the solution after the pretreatment and then aged, white precipitates were yielded over the whole SiO2/Al2O3 range. At SiO2/Al2O3 = 0.9, the material formed was identified as a single-phase Na-A zeolite. The Na-X zeolite was slightly produced at SiO2/Al2O3 ≥ 1.7.
Free ebooks ==> www.ebook777.com
Application of Green Catalysis and Processes
www.Ebook777.com
447
Free ebooks ==> www.ebook777.com 448
Green Chemical Engineering
aside. The screening of fly ash is followed by calcination at 800 ± 10°C to eliminate unburnt carbon and volatile matter. A measure of 24 g of NaOH and 20 g of fly ash are taken; the NaOH in the form of pellets is ground to a fine powder using a grinder and mixed thoroughly with the fly ash. The mixture is placed in a crucible and fused at 550°C in a furnace with an increasing ramp of 30°C/10 min. The fused mixture is cooled, ground and aged for 10 h at room temperature. The sodium aluminate slurry obtained after aging is subjected to microwave heating for 15–20 min and then placed for crystallisation in an oven for 10–12 h at static state. After hydrothermal crystallisation the upper layers of the slurry are collected, cooled, washed thoroughly with deionised water followed by filtration and drying at 50–60°C for 4 h. The zeolite thus formed is powdered and stored in a dry place (Figure 6.7). CWPO of Azo Dye: This study requires a 0.5 L three-necked glass reactor, magnetic stirrer with hot plate, temperature controller, magnetic stirrer, stoppers, thermocouple and condenser. Synthetic water containing Acid Orange 7 of known concentration is put in the reactor along with hydrogen peroxide and catalyst. The temperature of the reaction m ixture is raised, using a heater, to the desired value and maintained by a PID temperature controller that has been fitted to one of the reactor necks through the thermocouple (Figure 6.8).
Calcination of fly ash at 800 ± 10ºC Grinding and mixing of FA and NaOH Fusion at 550ºC Cooling and grinding of fused mixture Aging at room temperature for 10 hrs Microwave heating for 10–15 mins Crystallisation for 10–12 hrs A A
Filteration Washing and drying (60ºC) Na-y zeolite Figure 6.7 Schematic step for Na-Y zeolite synthesis.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 449
Application of Green Catalysis and Processes
Reflux condenser
Thermocouple with temperature controller
Ruber stoppers Collection of sample Glass reactor (350 mL)
Magnetic stirrer Magnetic stirrer with heater
Figure 6.8 Experimental setup for CWPO process.
The raising of the temperature of the reaction mixture to 80°C from ambient temperature takes about 25 min. The condenser prevents loss of vapour and magnetic stirrer agitates the mixture. Hydrogen peroxide and iron-exchanged catalyst of known quantities are added to the dye solution and the reaction is carried out at 80°C; samples are taken at periodic intervals. The samples after collection are raised to pH 11 by adding 0.1 N NaOH (so that no further reaction takes place) and the residual hydrogen peroxide is removed by adding MnO2, which catalyses the decomposition of peroxide to water and oxygen. The samples after collection are settled overnight or centrifuged and then filtered to collect a clear solution. The samples thus collected are analysed for COD, colour and dye removal. Chemicals for Zeolite Synthesis: Fly ash was obtained from NTPC, Dadri, Uttarakhand. Sodium hydroxide pellets were obtained from RFCL Ltd., Mumbai. Chemicals for CWPO: Acid Orange 7 was obtained from HBR Chemicals, Sonepat, Haryana. Hydrogen peroxide (30% analytical grade), manganese dioxide, sodium hydroxide H2SO4, AgSO4 and potassium dichromate were obtained from RFCL Ltd., Mumbai. Characterisation of Na-Y Zeolite: The Na-Y zeolite synthesised from coal fly ash was characterized by XRD, SEM, EDX and FTIR spectroscopy. X-Ray Diffraction: The determination of structure of the heterogeneous catalyst was carried out using x-ray diffractometer (Bruker AXS, Diffraktometer D8, Germany) in Institute Instrumentation Centre (IIC), IIT Roorkee. The catalyst structure was confirmed by using Cu–Kα as a source and Ni as a filter. Goniometer speed was kept at 1°/min and the chart speed was 1 cm/min. The range of the scanning angle (2θ) was maintained at 5–70°. The intensity peaks indicate the values of 2θ, where Bragg’s law is applicable. The formation of compounds was tested by comparing the XRD patterns of this work with those found by other researchers as well as by using JCPDS files (1971). On the basis of Bragg’s law for constructive interference, 2d sin θ = nλ (6.4)
www.Ebook777.com
Free ebooks ==> www.ebook777.com 450
Green Chemical Engineering
When an x-ray beam hits an atom, the electrons around the atom start to oscillate at the same frequency as the incoming beam. Almost all directions have destructive interference, that is, the combining waves are out of phase and there is no resultant energy leaving the solid sample. However, the atoms in a crystal are arranged in a regular pattern and very few directions have constructive interference. The waves are in phase and well-defined x-ray beams leave the sample in various directions. Hence, a diffracted beam may be described as a beam composed of a large number of scattered rays mutually reinforcing one another. Therefore, when x-rays hit a copper target, Cu–Kα rays are emitted. These rays get diffracted between the various lattice planes of the sample and are collected by the receiver, thus giving the XRD plot. From the XRD plot that is obtained, the values of the intensities are noted for each d-spacing value. These d-spacing values are compared with the (JCPDS) powder diffraction file (PDF) and the compound (and also the composition) is identified by first the three strongest peaks and later by smaller peaks (within error). Scanning Electron Microscopy: The determination of images and composition of catalysts were done by SEM/EDAX QUANTA 200 FEG (specifications: accelerating voltage from 200 V to 30 kV and magnification up to ×1000 k) in the Institute Instrumentation Centre (IIC), IIT Roorkee. A scanning electron microscope is similar to a light microscope being used in reflection. The major difference is that instead of imaging the entire specimen at once, the electron beam is scanned back and forth over the specimen, imaging only one point at a time. The interactions of the electrons with the surface are registered, and from these data an image can be constructed. Scanning for zeolite samples is taken at different magnification and voltage of 15–25 kV to account for the crystal formation and size. EDAX: From EDAX, the elemental composition in weight percentage and atomic percentage are obtained along with the spectra for overall compositions and particular local area compositions. Fourier Transform Infra-Red Spectroscopy: The internal tetrahedra and external linkage of the zeolites formed are identified and confirmed by FTIR. The IR spectra data are taken from Ojha et al. (2004) and shown in Table 6.8. Spectrophotometer: The amount of dye present in the solution was analysed by direct reading a TVS 25 (A) Visible Spectrophotometer. The visible range absorbance at the characteristic wavelength of the sample at 486 nm was recorded to follow the progress of decolourisation during WPO. Colour: HANNA (Singapore)-made colorimeter was used for colour tests on the dye solution samples. De-ionised water was used as a blank for analysis. The filtered samples were
Table 6.8 FTIR Spectra of Zeolite Zeolite IR Assignments (Common for all Zeolites) Internal tetrahedral Asymmetric stretch 1250–950 Symmetric stretch 720–650 T-O bend 420–500 External linkage Double ring 650–500 Pore opening 300–420 Symmetric stretch 750–820 Asymmetric stretch 1050–1150 (Sharp)
www.Ebook777.com
Free ebooks ==> www.ebook777.com 451
Application of Green Catalysis and Processes
then put into vials that were compatible with the vial receptacle of the HI 93727, which was used to analyse the samples. Colour of the samples was read at a wavelength of 486 nm. The exterior of the sample vials was wiped clean and then inserted into the colorimeter. The blank was inserted first in order to adjust the reading of the colorimeter to zero. Each sample was read and the results were recorded in platinum–cobalt units. 6.2.3.2 Results and Discussions Effects of Conventional Heating, Microwave Heating and Seeding on Na-Y Formation: In this section, the results concerned with the effects of conventional heating, microwave heating and seeding on Na-Y zeolite formation are shown (Table 6.9, Figure 6.9). Effect of Conventional Heating Time: After a period of ageing of the fused mixture, the zeolitic slurry is subjected to reheating in a ‘conventional oven’ for crystallisation at different lengths of time and the formation of Na-Y zeolite is studied. The formation of Na-Y is concluded from the XRD peaks. The peaks of every sample are compared to those of standard Na-Y zeolite peaks from JCPDS. 6.2.3.2.1 Zeolite Formation Formation of Na-Y Zeolite at Different Conventional Heating Rates: From the table it is evident that as the heating time increases the number of Na-Y peaks, with maximum peaks Table 6.9 Identified Zeolite Peaks
Lin (counts)
3000
Sample
Conventional Heating Time (h)
Peaks Reported
Sample 1 Sample 2 Sample 3
10 12 14
1 8 9
Y
Y
YY Y
Y Y
YY
14 h
2000 Y Y YY Y YY 1000
Y
12 h
Y
10 h
0 0
30 2-Theta-scale
60
Figure 6.9 Peaks reported at 10, 12 and 14 h of conventional heating rate.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 452
Green Chemical Engineering
reported at 18 h of crystallisation and minimum peaks reported at 10 h of crystallisation. From this we can say that longer periods of conventional heating are required for zeolite formation. Effect of Conventional Heating Time on % Crystallinity (Based on All Peaks): The effect of conventional heating time on % crystallinity has been studied. The maximum crystallinity was for 12 h of heating and minimum for 16 h of heating. There is no particular trend in increase or decrease of % crystallinity based on all peaks (Table 6.10). Effect of Conventional Heating Time on Si/Al Ratio: The Si/Al ratio of conventional heating time has been calculated (Table 6.11). The maximum Si/Al ratio was for sample 1 3.01 and minimum for 1.56. There is no particular trend in the increase or decrease of Si/Al ratio. SEM image is shown in Figure 6.10. The chemical compositions of synthesized Na-Y zeolite are 11% (C), 42% (O), 2% (Na), 14% (Si), 5% (Fe), 5% (Al), 22% (Ti) and 2% (Br) (Figure 6.11). The SEM image and EDAX data clearly show crystal/zeolites formation and similar chemical composition of Y zeolite. Particle sizes are 1–1.5 mm and porosity is 0.28. The BET surface area of synthesised Na-Y zeolite has been found to be 456 m2/g. The XRD pattern (Figure 6.12) showed diminishing zeolite peaks along with evolution of peaks corresponding with increasing NaOH concentration. Overall, 84% crystallinity was found on the synthesised Na-Y zeolite from the XRD plot and the values of the intensities are noted for each d-spacing value. The Na-Y was present after the exchange process and the Y peaks diminished along with the rise in Na-Y peaks (Kondru et al., 2009), in the obtained zeolite iron oxide by adding NaOH and H2O2 (drop wise) at 60°C to Na-Y zeolite. The IR assignments from FTIR (Figure 6.13) remain satisfied even after iron exchanging. The internal tetrahedra and external linkage of the zeolites formed are identified and confirmed by FTIR. The IR spectra data are taken from the literature (Ojha et al., 2004). The FTIR specifications of the zeolites (common to all zeolites) are: Internal tetrahedral: asymmetric stretch 1250–950 cm−1, symmetric stretch 720–820 cm−1, T-O bend 420–500 cm−1, external linkage: double ring 650–500 cm−1, pore opening 300–420 cm−1. Similar peaks are obtained in this study. The effect of temperature, initial pH, H2O2 concentration and catalyst loading on catalytic WPO of AO7 azo dye were investigated in detail. Table 6.10 Effect of Conventional Heating Time on % Crystallinity (Based on All Peaks) Sample
% Crystallinity
Sample 1 Sample 2 Sample 3
32.4 44.6 40.6
Table 6.11 Effect of Conventional Heating Time on Si/Al ratio Sample
Si/Al Ratio
Sample 1 Sample 2 Sample 3
3.01 1.99 1.68
www.Ebook777.com
Free ebooks ==> www.ebook777.com 453
Application of Green Catalysis and Processes
(a)
WD Det HFW HV Mag 15.0 kV 2000x 9.3 mm LFD 74.60 µm
(b)
20.0 µm IIT Roorkee
(c)
Det HFW Mag WD HV 20.0 kV 8000x 10.5 mm LFD 18.65 µm
Det HFW HV Mag WD 15.0 kV 8000x 10.0 mm LFD 18.65 µm
20.0 µm IIT Roorkee
(d)
10.0 µm IIT Roorkee
EHT=15.00 kV 1 µm
WD= 25 mm Photo No, =4
Mag= 8.00 K X Detector= SE1
Figure 6.10 SEM image: (a) Fresh coal fly ash. (b) Commercial Na-Y zeolite. (c) After conventional heating of zeolite. (d) After microwave heating of zeolite.
Effect of Microwave Heating Time: After ageing the fused mixture for a given time, the zeolitic slurry is subjected to heating in a microwave oven at different lengths of times and the formation of Na-Y zeolite is studied. Effect of Microwave Heating Time on Zeolite Formation: The formation of Na-Y is concluded from the XRD peaks obtained. The peaks of every sample are compared to those of standard Na-Y zeolite peaks from JCPDS. The zeolite peaks that are identified are reported in Table 6.12. From the table it is evident that there is no specific influence on zeolite formation up to sample 4 but after that there was an increase in peaks. This shows that with longer periods
www.Ebook777.com
Free ebooks ==> www.ebook777.com 454
Green Chemical Engineering
(a)
c:\edax32\genesis\genmaps.spc 13-Mar-2009 10:17:25 1.6 LSecs : 14
1.3
1.0 KCnt
SiK AIK OK
0.7
0.3 CK 0.0
(b)
SK MgK Nak P K 1.00
2.00
CaK CaK KK BaL KK BaL 3.00
FeK Mnk FeK
Mnk
4.00 5.00 6.00 Energy (keV)
7.00
8.00
9.00
10.0
Element CK OK NaK MgK AlK SiK PK SK KK CaK BaL MnK FeK Matrix
Wt% 10.22 32.19 00.20 00.42 18.83 27.53 00.54 00.21 01.40 00.62 03.95 00.56 03.33 Correction
At% 17.96 42.44 00.18 00.37 14.72 20.67 00.37 00.14 00.76 00.32 00.61 00.22 01.26 ZAF
Element
Wt%
At%
OK
41.79
54.59
NaK
10.52
09.56
AlK
12.00
09.29
SiK
35.69
26.55
Matrix
Correction
ZAF
c:\edax32\genesis\genmaps.spc 13-Mar-2009 09:57:42 LSecs : 14 1.6
SiK
1.3
1.0
OK
KCnt AiK
0.7
Nak 0.3
0.0
1.00
2.00
3.00
4.00 5.00 6.00 Energy (keV)
7.00
8.00
9.00
10.0
Figure 6.11 EDAX image and elemental composition: (a) Fresh coal fly ash. (b) Commercial Na-Y zeolite. (c) After conventional heating of zeolite. (d) After microwave heating of zeolite.
of microwave-assisted crystallisation zeolite formation is possible. The time required for zeolite formation by microwave-assisted crystallisation is less when compared to the conventional crystallisation route (Table 6.13). Effect of Microwave Heating on Si/Al Ratio: The Si/Al ratio of microwave-assisted crystallisation had been studied. The maximum Si/Al ratio was reported for 4 h of microwave heating and minimum was 1.6 for 8 h of microwave heating (Table 6.14). There is no certain order in Si/Al ratio behaviour (see Tables 6.15 through 6.19). Effect of Temperature on Acid Orange 7 Removal: The effect of temperature on AO7 removal was studied at six different temperatures (40–90°C) keeping other parameters constant. The maximum conversion of dye is obtained at 90°C and 80°C in 4 h with maximum dye removal of 97% at 90°C. At 40°C and 50°C, the dye concentration decreases until a certain point from which there is a small increase and then it decreases and again increases and then gradually decreases with very little removal. But at 60°C, the dye concentration decreases after a small increase with some improvement in removal. At 70°C, 80°C and 90°C, the dye concentration gradually decreases with time and the removal of dye at 80°C and 90°C is almost comparable. Figure 6.14 shows the effect of temperature as a function of time, giving dye removal in terms of concentration and percent removal.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 455
Application of Green Catalysis and Processes
c:\edax32\genesis\genmaps.spc 10-June-2009 18:19:36 < Pt. 1 Spot> LSecs : 18
(c)
125 SiK 100
OK
75
AIK BrL
50
NaK CK
25
0
TiL
FeK
1.00
2.00
3.00
4.00
5.00
6.00
FeK 7.00
8.00
9.00
Element CK TiL OK NaK BrL AlK SiK FeK Matrix
Wt% 18.42 23.93 32.49 06.08 05.03 02.79 08.71 02.56 Correction
At% 31.62 10.30 41.87 05.45 01.30 02.13 06.39 00.94 ZAF
Element
Wt%
OK
21.42
38.14
NaK
08.42
10.43
BrL
08.86
03.16
AlK
09.28
09.79
SiK
21.95
22.26
TiK
10.51
06.25
FeK
19.57
09.98
Matrix
Correction
ZAF
10.00
Energy (keV)
(d)
c:\edax32\genesis\genmaps.spc 10-June-2009 16:30:37 < Pt. 1 Spot> LSecs : 17 215
SiK 172
AIK BrL
129
86
OK
43 TiL 0
TiK
Nak 1.00
2.00
3.00
4.00
TiK
5.00
FeK 6.00
FeK 7.00
8.00
9.00
10.00
At%
Energy (keV)
Figure 6.11 (Continued) EDAX image and elemental composition: (a) Fresh coal fly ash. (b) Commercial Na-Y zeolite. (c) After conventional heating of zeolite. (d) After microwave heating of zeolite.
Effect of Temperature on Colour Removal: The effect of temperature on colour removal was also studied. The results obtained for colour removal are shown as a function of time (figure is not shown here). Maximum colour removal (100%) is obtained at 90°C after 20 min and also at 80°C after 60 min. At lower temperatures colour removal is attained at a slower rate, this is the same up to 70°C, but at 80°C and 90°C, colour removal is attained at faster rates. At lower temperatures the % removal of colour is as low as 70%, whereas at higher temperatures 100% removal is obtained at shorter time periods. The plot of our experimental data did not follow zero-order kinetics, however, it fitted well for first-order kinetics. Equation 6.6 has been plotted (figures are not shown here) for dye removal. It is seen that the WAO is a two-step series process. The two rate constants, k1 and k2 for the first (fast) step and the second (slow) step, respectively, can thus be determined. The rate equation for dye removal was assumed to be a function of the concentration of the organic substrate as well as oxygen partial pressure. Since, in all the runs, air partial pressure was kept constant, the rate of reaction would invariably be a function of
www.Ebook777.com
Free ebooks ==> www.ebook777.com 456
Green Chemical Engineering
Offset Y values
2000 Y
YY
Y
Y
1000
4h
Y 2h
0
0
30
60
2-Theta-scale
Figure 6.12 Peaks reported after 2 and 4 h of microwave-assisted crystallisation.
organic concentration. We consider the rate to follow first-order reaction kinetics and try to show, through the experimental data, whether it is applicable. For a first-order reaction, we can write:
− rA = −
dCA = kC A dt
(6.5)
where CA = concentration of organic substrate (dye) Since, CA = CA0(1 − X A)
So, − CA 0
d(1 − X A ) = kC A 0 (1 − X A ) dt
So, − kdt = −
1 dX A 1 − XA
kt = −ln(1 − X A) (6.6) Equation 6.6 has been plotted in figures (not shown here) for the prepared zeolite catalyst as (−ln (1 − X A)) against time. The data exactly fit to a straight line, showing the validity of the first-order rate expression. However, there were two distinct zones: the first with a higher slope (line before 1 h reaction time) and the second with less of a slope (found after 1 h reaction time). The two zones represent a fast first-order and a slow first-order regime, respectively. The slope of these lines, which is the value of the reaction rate constant, is thus obtained and values were 0.556 h−1 (fast first-order step) and 0.03 h−1 (slow first-order step) for 313 K, 0.41 h−1 (fast first-order step) and 0.035 h−1 (slow first-order step) for 323 K, 0.556 h−1 (fast first-order step) and 0.05 h−1 (slow first-order step) for 333 K, 0.626 h−1 (fast
www.Ebook777.com
Free ebooks ==> www.ebook777.com 457
Application of Green Catalysis and Processes
(a) 1.4
Wed May 07 17:04:53 20 8 (GMT-05:00) 1.3 Wed May 07 17:05:16 2008 (GMT-05:00) 1.2 1.1
% Transmittance
1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 –0.0 3500
3000
2500 2000 Wavenumbers (cm–1)
1500
1000
500
3500
3000
2500 2000 Wavenumbers (cm–1)
1500
1000
500
(b) 5.0 4.5 4.0 3.5
% Transmittance
3.0 2.5 2.0 1.5 1.0 0.5 0.0 –0.5 –1.0 –1.5 4000
Figure 6.13 FTIR spectra: (a) Fresh coal fly ash. (b) Commercial Na-Y zeolite. (c) After conventional heating of zeolite. (d) After microwave heating of zeolite.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 458
Green Chemical Engineering
(c) 5.0 4.5
% Transmittance
4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 3500
3000
(d) 44 42 40 38 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2 4000
3500
3000
2500 2000 Wavenumbers (cm–1)
1500
1000
1500
1000
500
% Transmittance
4000
2500 2000 Wavenumbers (cm–1)
500
Figure 6.13 (Continued) FTIR spectra: (a) Fresh coal fly ash. (b) Commercial Na-Y zeolite. (c) After conventional heating of zeolite. (d) After microwave heating of zeolite.
Table 6.12 Formation of Na-Y Zeolite at Different Conventional Heating Rates Sample
Microwave Heating (min)
Conventional Heating Time (min)
Peaks Reported
Sample 1 Sample 2 Sample 3
15 15 15
105 225 345
1 5 4
www.Ebook777.com
Free ebooks ==> www.ebook777.com 459
Application of Green Catalysis and Processes
Table 6.13 Effect of Microwave Heating on % Crystallinity (Based on All Peaks) Sample
% Crystallinity
Sample 1 Sample 2 Sample 3
84 28.85 33.9
Table 6.14 Effect of Microwave Heating on Si/Al Ratio Sample
Si/Al Ratio (Molar)
Sample 1 Sample 2 Sample 3 Sample 4 Sample 5
2.06 2.28 1.9 1.6 1.83
first-order step) and 0.006 h−1 (slow first-order step) for 343 K, 0.726 h−1 (fast first-order step) and 0.065 h−1 (slow first-order step) for 353 K and 0.902 h−1 (fast first-order step) and 0.068 h−1 (slow first-order step) for 363 K, respectively. From the data, it can be seen that the rate constant increases with temperature for both the steps. An increase of rate constant with temperature for the first step is smaller than that of the second step (Figure 6.15). Arrhenius plot: The activation energy and frequency factor are determined by Arrhenius equation.
k = k0 exp (−E/RT)
(6.7)
A plot of ln k versus 1/T is shown in Figure 6.15 and the values of the frequency factor k0 and the activation energy E were determined for the two steps. The activation energy for dye removal is found to be 1.56 and 2.95 kJ/mol, for the first and the second step, respectively. 6.2.3.3 Conclusions and Recommendations 1. Zeolites can be prepared from coal fly ash, which is a source of alumino-silicates 2. Formation of zeolite peaks. 3. Formation of peaks of Y zeolite is higher when seeds are introduced before the hydrothermal crystallisation step. 4. Microwave heating of zeolitic gel enhances product formation. 5. Formation of zeolite Na-P, which is a competitive phase in the formation of Na-Y, varies with the amount of seeds added. 6. Iron exchanging for synthesised Na-Y from coal fly ash is greater compared to commercial zeolite as confirmed by XRD and EDAX results.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 460
Green Chemical Engineering
Table 6.15 The Values of the Intensities of Each d-Spacing of Y and P Zeolite by JCPDS Standard Y Zeolite
Standard P Zeolite
d(A)
Intensity
d(A)
Intensity
14.3 8.73 7.45 5.67 4.75 4.37 3.9 3.77 3.57 3.46 3.3 3.22 3.02 2.9 2.85 2.76 2.71 2.63 2.59 2.52 2.42 2.38 2.23 2.18 2.16 2.12 2.1 2.06 1.93 1.91 1.86 1.81 1.77 1.75 1.7
100 18 12 31 13 20 7 30 2 3 20 4 8 11 24 8 2 8 4 1 1 5 1 3 2 1 4 2 1 2 1 1 1 3 4
7.101
795
5.021
480
4.1
647
3.551
12
3.176
999
2.899
68
2.684 2.511 2.387 2.246
604 52 101 34
2.141
16
2.05
48
1.97
171
1.834
27
1.775
87
1.722
117
1.674
113
1.629
79
1.588
45
1.55
41
6.2.3.3.1 CWPO
1. Dye removal (97%) and colour removal (100% in 30 min) are more at 90°C but as the solution starts to vaporise, 80°C is taken as the operating temperature for dye removal (95% in 4 h), colour removal (100% in 40 min) and COD removal (65%). 2. Dye removal (97%) and colour removal (100% in 10 min).
www.Ebook777.com
Free ebooks ==> www.ebook777.com 461
Application of Green Catalysis and Processes
Table 6.16 Values of the Intensities of Each d-Spacing of Mullite and Quartz Standard Mullite JCPDS
Standard Quartz JCPDS
d(A)
Intensity
d(A)
Intensity
5.38
70
4.2453
213
3.78
20
3.3373
999
3.42
90
2.451
73
3.39
100
2.2781
74
2.88
70
2.2318
34
2.69
80
2.1226
52
2.54
90
1.9755
28
2.42
70
1.8147
109
2.4
10
1.7999
5
2.3
10
1.6686
38
2.29
80
1.6571
16
2.2
90
1.6045
2
2.19
20
1.5381
84
2.12
80
1.4507
16
2.11
40
1.4151
3
1.985
20
1.3793
52
1.916
20
1.3728
61
1.891
50
1.3688
85
1.857
10
1.2864
22
1.841
70
1.2533
25
1.836
10
1.2255
12
1.795
30
1.1977
26
1.709
60
1.1951
20
1.699
70
1.1824
21
1.696
70
1.1774
25
1.595
80
1.1504
13
1.58
60
1.139
2
1.56
30
1.1159
1
1.548
20
1.1124
2
1.523
90
1.502
10
1.484
10
1.469
10
1.461
60
1.439
80
1.42
40
1.416
50
1.39
30
1.346
40
www.Ebook777.com
Free ebooks ==> www.ebook777.com 462
Green Chemical Engineering
Table 6.17 Values of the Intensities of Each d-Spacing of Commercial Na-Y Y Stand d(A) 14.3 8.73 7.45 5.67 4.75 4.37 3.9 3.77 3.57 3.46 3.3 3.22 3.02 2.9 2.85 2.76 2.71 2.63 2.59 2.52 2.42 2.38 2.23 2.18 2.16 2.12 2.1 2.06 1.93 1.91 1.86 1.81 1.77 1.75 1.7
Commercial Na-Y d(A) ± 0.05
± 0.1
± 0.2
± 0.3
± 0.4/0.8
ERR
14.38 8.82 7.5 5.59 4.7 4.32 3.87 3.73 3.53 3.43 3.27 3.19 2.99 2.89 2.83 2.74 2.69 2.64 2.57 2.5 2.4 2.36 2.21 2.17 2.14 2.1 2.08 2.04 1.97 1.92 1.89 1.81 1.79 1.76 1.73
Com Height 2318 611 733 1690 793 1150 613 1957 395 508 1570 640 779 970 2229 836 519 431 273 234 282 541 285 447 335 273 399 360 261 267 304 224 317 317 457
3. For catalyst loading, 98.9% dye removal is obtained for 1.5 g and 100% colour removal. 6.2.3.3.2 Comparison between Fe-Exchanged Commercial Na-Y and Fe-Exchanged Synthesised Na-Y
1. Dye removal is 96% for commercial Fe Na-Y zeolite and 67.14% for Fe Na-Y synthesised from coal fly ash.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 463
Application of Green Catalysis and Processes
Table 6.18 Values of the Intensities of Each d-Spacing of Conventional Heating Conventional Heating 1 d(A)
Exact
± 0.05
± 0.1
14.3
± 0.2
± 0.3
± 0.4/0.8
14.67
8.73
No
7.45
No
5.67
No
4.75
No
4.37
No
3.9
No
3.77
No
3.57
No
3.46
No
3.3
No
3.22
No
3.02
No
2.9
No
2.85
No
2.76
No
2.71
No
2.63
No
2.59
No
2.52
No
2.42
No
2.38
No
2.23
No
2.18
No
2.16
No
2.12
No
2.1
No
2.06
No
1.93
No
1.91
No
1.86
No
1.81
No
1.77
No
1.75
No
1.7
No
Peaks [35] = 1 [Exact] + 34 [No]. 3 Strongest peaks = 1 [Exact] + 2 [No].
www.Ebook777.com
Height 752.823
Free ebooks ==> www.ebook777.com 464
Green Chemical Engineering
Table 6.19 Values of the Intensities of Each d-Spacing of Microwave Heating Microwave Heating 2 Y Stand
Mic 2
± 0.05
± 0.1
14.3 No 8.73 7.45 No 5.67 No 4.75 No 4.37 4.35 3.9 3.77 No 3.57 No 3.46 No 3.3 3.35 3.22 No 3.02 No 2.9 No 2.85 No 2.76 No 2.71 No 2.63 No 2.59 No 2.52 No 2.42 No 2.38 No 2.23 No 2.18 No 2.16 2.15 2.12 No 2.1 No 2.06 No 1.93 No 1.91 No 1.86 No 1.81 No 1.77 No 1.75 No 1.7 No Exact [35] = Exact [5] + No [30].
± 0.2
± 0.3
± 0.4/0.8
Height
8.38
328.61
4.25
220.88 214.64
318.2
152.24
2. Maximum colour removal by Fe Na-Y commercial zeolite catalyst is 100% after 4 h and by Fe Na-Y synthesised zeolite it is 70% after 4 h. 3. Maximum COD removal by Fe Na-Y commercial zeolite catalyst is 67% and by Fe Na-Y synthesised zeolite it is 46%.
6.2.3.3.3 Recommendations
1. Microwave heating of aluminosilicate slurry at the end and at the middle of crystallisation time may be studied. 2. Different exposure times of microwave heating can also be studied.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 465
Application of Green Catalysis and Processes
Temp. (°C) 40
100
50
60
70
80
90
Percent removal (dye)
80 60 40 20
0
0
100
Time (min)
200
300
Figure 6.14 Effect of temperature on dye concentration as function of time.
0 –0.5 –1
ln k
–1.5 –2
Slow step
–2.5
Fast step
–3 –3.5 –4 2.60
2.80
3.00 1000/T,
3.20
3.40
K–1
Figure 6.15 Arrhenius plot for catalytic WAO of DWW (zone 1: tR = 0–1 h and zone 2: tR = 1–8 h); catalyst: CuSO4. (From Suresh et al., 2011d.)
3. Ageing and crystallisation time can be optimised. This can be done by simultaneous heating during ageing. 4. There are various routes of hydrothermal crystallisation such as the ionothermal synthetic route, micro-emulsion-based hydrothermal route, dry gel conversion synthetic route, solvo-thermal synthetic route and so forth, which can be studied.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 466
Green Chemical Engineering
5. Synthesis at higher temperatures can be studied. 6. The removal of dye can be studied at neutral condition. This helps in catalyst reuse.
6.3 Case Study 2: Thermolysis of Petrochemical Industrial Effluent Thermolysis has been used as an effective pretreatment method for pulp and paper mill wastewaters, composite wastewater of a cotton textile mill, petrochemical wastewater, DWW and biodigester effluents from an alcohol production plant. Thermochemical precipitation is a process wherein metal salts or chemicals react with the organic and/ or inorganic substances present in the wastewater, at an elevated temperature, resulting in complexation and formation of insoluble precipitates. Thermolysis proved to be a very effective treatment of wastewater, having a high COD (in terms of mg/L), biochemical oxygen demand (BOD in terms of mg/L), benzoic acid and some amount of metals such as Co, Mn, Ca, Mg, Na and Al. Thermolysis generates sludge, which needs to be characterised, handled and managed, as it is a hazardous waste. Sludge generation is an inevitable phenomenon during physicochemical, thermochemical and biological treatment of wastewaters containing organics and inorganics. The sludge generally contains organic and inorganic substances that were present earlier in the raw wastewater and removed during thermochemical (thermolysis) treatment. The characteristics of sludge depend on the original pollution load of the treated water. Petrochemical sludge is considered to be a hazardous waste and needs proper handling and disposal, as stipulated by the Hazardous Waste (Management and Handling) Amendment Rules, 2003, Government of India. Homogeneous Catalysts: Several transition metal nitrates (such as Cu, Fe, Zn, Mn, Ni, Cr, Co) have been used as homogeneous catalysts. Copper nitrate was found to be the most effective catalyst for wet oxidation of acetic acid (Imamura, 1999). Nitrate of iron showed the second highest activity. The copper nitrate was separated in the form of CuO precipitate after the reaction. Other copper salts, such as CuCl2 and CuSO4, are fragile and some portion of these salts can be precipitated as Cu2O. LiNO3 addition is found to help in maintaining the stability of the copper ion and it also provides the activity of copper sulphate. Heterogeneous Catalysts: As problems related to the separation of homogeneous salts from wastewater were encountered, efforts are being made to develop suitable heterogeneous catalysts for wet oxidation reactions. The properties of the catalyst depend on the method of preparation, calcination temperature and surface area of the catalyst. Also, the choice of metal and support is of utmost importance for any particular industrial effluent. Several composite oxides containing Cu (e.g., Cu/Co, Cu/Co/Bi, Cu/Mn/Bi, Cu/Bi/γ-Al2O3) are found to be promising catalytic agents. Other composite oxides without copper (e.g., Bi/γAl2O3, Co/Bi, Co/Bi/γ-Al2O3, Sn/Bi, Zn/Bi, Mn/Ce) were also found to be very active catalysts. Besides this, several noble base metals (e.g., Ru, Pt, Pd and Ir) are supported in different support catalysts such as CeO2, γ-Al2O3, Na-Y-zeolite, ZrO2 and TiO2 and have been found to be very useful for the catalytic oxidation of different organic and inorganic compounds. Ceria, as support on Ru, showed the highest catalytic activity. Heterogeneous hydrophobic catalysts should be designed in such a manner that they have an affinity towards all organic compounds. They must also have a high redox ability to carry out an efficient electron transfer with pollutants. These catalysts should also be efficient in the activation of oxygen.
www.Ebook777.com
Free ebooks ==> www.ebook777.com Application of Green Catalysis and Processes
467
Garg et al. (2005) studied the removal of COD and colour from pulp and paper mill wastewater in the temperature range of 20–95°C. The homogeneous catalyst CuSO4 was found to be the most effective among various homogeneous and heterogeneous catalysts used in the study. A COD removal efficiency of 63.3% was obtained with a catalyst concentration 5 kg/m3 at pH 5. However, maximum colour removal (92.5%) was obtained at a catalyst concentration of 2 kg/m3. The effect of temperature on COD reduction was not appreciable. Kumar et al. (2008) used CuSO4, FeSO4, FeCl3, CuO, ZnO and PAC as catalysts/chemicals for the thermolysis of composite wastewater from a cotton textile mill for the removal of its COD and colour. CuSO4 at a catalyst concentration 6 kg/m3, pH 12 and temperature of 95°C was found to be the most effective chemical with ~77.9% COD removal and 92.8% colour removal. Thermolysis was followed by coagulation and flocculation. Potash alum [KAl(SO4)2 . 16H2O] at a coagulant concentration of 5 kg/m3 was found to be the best among the other coagulants tested. Coagulation of the supernatant obtained after treatment by catalytic thermolysis resulted in an overall reduction of 97.3% COD and close to 100% colour removal. Choudhari et al. (2008) treated DWW by catalytic thermolysis at 80–100°C using CuSO4, CuO, MnO2–CeO2 and ZnO as catalysts. CuO was found to be the best among all the catalysts used for COD and colour removal. At 100°C and catalyst concentration 4 kg/m3, 47% COD reduction and 68% colour reduction were found for DWW, and 61% COD removal and 78% colour removal were found for distillery biodigester effluents. 6.3.1 Source of Wastewater The wastewater was collected from the effluent treatment plant of a polypropylene plant production unit situated in northern India. The wastewater was stored at 4°C in a refrigerator in the laboratory and was subsequently used in the experiments without any dilution. All chemicals used in the experiments were of analytical reagent (AR) grade. Copper sulphate (CuSO4 ⋅ 5H2O), anhydrous ferric chloride (FeCl3) and ferrous sulphate (FeSO4 ⋅ 7H2O) were procured from M/S, RFCL, New Delhi. Analysis of Physicochemical Parameters: The wastewater characteristics such as pH, COD, BOD, total solids (TS), total dissolved solids (TDS), total suspended solids (TSS), total alkalinity and total acidity as acetic acid were determined as per standard methods (APHA). The treated wastewater samples were centrifuged (Remi Instruments, Mumbai) to obtain a clear supernatant and precipitate. The COD of the effluent, before and after treatment, was determined by the standard dichromate closed reflux method as per the standard. The COD value was assayed with a COD analyser (Aqualytic, Germany). 6.3.2 Experimental Procedure The experimental studies were carried out in a 0.5 L three-necked glass reactor at temperatures higher than the ambient temperature over a temperature range of 40–160°C. Initial pH (pH0) of the wastewater was adjusted by adding 1 N H2SO4 or 1 N NaOH, as the case warranted, to the wastewater. A 250 mL volume of wastewater was used in the reactor. The temperature of the reaction mixture was raised to the desired value using a water bath fitted with a digital temperature controller. A vertical water-cooled condenser was attached to the side neck of the reactor to prevent any loss of vapor and the middle neck was fitted with a mechanical stirrer. Thereafter, the chemical/coagulant was added to the reactor. The CuSO4 ⋅ 5H2O, FeCl3 and FeSO4 ⋅ 7H2O were used as chemicals/coagulants.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 468
Green Chemical Engineering
Petrochemical effluent (propylene plant) Analysis for COD, colour, pH pH adjustment
Coagulant/catalyst addition Temperature adjustment
Mixing for 30 min
Stand by for 2 h
Supernatant Analysis for pH, COD & colour
Effluent including sludge Rapid mixing
Settling characteristics
Filterability characteristics
Figure 6.16 Flow chart showing steps for thermochemical precipitation studies.
The FeCl3 was used in the concentration range of 1–4 kg/m3 ⋅ FeSO4 ⋅ 7H2O was also used in the concentration range of 1–4 kg/m3 ⋅ CuSO4 ⋅ 5H2O was used in the concentration range of 3–7 kg/m3. The experimental procedure consisted of three phases: a period of 5 min for the flash mixing of the chemical/coagulant at 250 rpm, followed by slow mixing at 30 rpm. In the final stage, the flocs were allowed to settle for 90 min. The reactor samples were taken out at periodic intervals and also at the end of the settling time. The COD of the supernatant was determined after centrifugation of a sample (Figure 6.16). 6.3.3 Kinetic Studies The experiments were performed at 40–160°C and catalyst mass loading of 2–5 kg/ m3. Various kinetics data were evaluated at these operating conditions. Since, to evaluate the kinetics data (rate constant and constituently activation energy), the temperature should be constant for reaction periods, kinetics data were determined when the reaction
www.Ebook777.com
Free ebooks ==> www.ebook777.com 469
Application of Green Catalysis and Processes
temperature (40–160°C) was reached. During catalytic thermolysis, two mechanisms, both in parallel but complementary to each other, take place simultaneously. The organic molecules, both smaller and larger—present in the effluent, undergo chemical and thermal breakdown, and complexation, forming insoluble particles that settle down. Further, during the thermolysis, larger molecules also undergo breakdown into smaller molecules that are soluble. Due to the formation of insoluble particles, substantial reduction in the original values of total carbon, reduced carbohydrates, lignin and proteins along with those of nitrogen, phosphates and sulphates was made. These reductions also exemplify the reduction in COD (70% reduction) of the polypropylene plant effluent. The thermolysis process of the polypropylene plant effluent can, thus, be represented as +H2O Polypropylene effluent organic → solid residue + lower molecular + heat weight organics + gas
In the presence of a catalyst, the solid residue formation gets hastened and its yield increases. The reaction equation can be written as
+ Catalyst Polypropylene effluent organic → solid residue + lower molecular + H 2O + heat weight organics + gas Organics or, + Catalyst A → B(solid) + C(a host of organics) + gas + H 2O + heat
(6.8)
The gas formation is too little to be of any significance. The global rate expression for the thermolysis can thus be written as − dCA/dt = kCCAnCwm
(6.9)
For constant catalyst loading, Equation 6.9 may be reduced to where
− dCA/dt = kCAn
k = kcCwm
(6.10)
(6.11)
Taking lumped organics, to be represented by the COD, CA may be taken as (COD), and Equation 6.11 may be written as
−d(COD)/dt = k(COD)n (6.12)
The reduction of organics has been found in first-order kinetics in most of the cases for wet oxidation (Mishra et al., 1995). Lele et al. (1989) have subsequently shown that
www.Ebook777.com
Free ebooks ==> www.ebook777.com 470
Green Chemical Engineering
the thermal pretreatment of alcohol distillery spent wash follows zero-order kinetics. Belkacemi et al. (1999) have presented first-order single-step kinetics for thermolysis of Timothy grass-based distillery wastewater. For first-order kinetics, Equation 6.12 can be represented in the form of COD conversion (X) as −ln (1 − X A ) = kt (6.13)
whereas, for zero-order kinetics,
(COD) = kt (6.14) Fitting of our experimental data with Equation 6.13 showed that the thermolysis can be adequately described by first-order kinetics. Equation 6.14 has been plotted in Figure 6.17. It is seen that the thermolysis is a two-step series process. The two rate constants, k1 and k2 for the first fast step and the second slow step, respectively, can thus be determined. The rate constants also increase with temperature, although the increase for the first step is greater than that for the second step. Thus, the ratio k1/k2 increases from its value of 2.3 at 100°C to 3.3 at 160°C. The lower values of k 2 indicate deactivation of a catalyst by carbonaceous material present in wastewater and recalcitrance to further degradation, responsible for low reaction rates. The temperature dependence of k1 and k2 are shown in Table 6.20. Assuming Arrhenius temperature dependence for the rate constant, from Equation 6.7
k = k0 exp (−E/RT)
Thus, a plot of ln k versus 1/T (Figure 6.18) gives a straight line relationship and the frequency factor k 0 and the activation energy E can be determined. The activation energy is found to be 24.12 and 16.11 kJ mol−1, for the first and the second step, respectively. The frequency factor for the first and the second step is 0.221 and 0.0413 min−1, respectively. 6.3.4 Results and Discussion Characteristics of Polypropylene Plant Wastewater: The characteristics of propylene plant wastewater as analysed by the petrochemical plant are presented in Table 6.21. The wastewater consisted of both organic and inorganic substances and was slightly acidic in nature (pH 5.3). Its COD (3520 mg/L) and BOD (1132 mg/L) were very high and the parameters were most predominant. The effect of temperature (40–160°C) on COD removal using CuSO4 ⋅ 5H2O, FeCl3 and FeSO4 ⋅ 7H2O at a dosage of 3 kg/m3 and pH 6.65 is shown in Figure 6.18. At ambient temperature, the COD removal was found to be 30.2%, 39.1% and 8.1% with CuSO4 ⋅ 5H2O, FeCl3 and FeSO4 ⋅ 7H2O, respectively. Because COD removal was found to be low, further experiments were conducted at higher temperatures (40–160°C) with different inorganic compounds. COD removal shows an increasing trend with temperature up to a certain value and then decreases. This trend is observed for all the chemicals, and shows that there is an optimum temperature at which maximum COD removal is obtained. The effect of different catalysts on thermolysis was studied in the range of 2–5 kg/m3 at 160°C (Figure 6.19). The COD reduction was found to be 63% at Cw = 3 kg/m3. It may also be seen that the rate of COD reduction increases considerably with the CuSO4 catalyst.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 471
Application of Green Catalysis and Processes
(a) 80 70
% COD reduction
60 50 40 30 20
100°C
120°C
140°C
160°C
10 0
0
50
100
150
200
250
300
350
400
Time (min) (b) 1.2 1
–ln(1 – XA)
0.8
100°C
120°C
140°C
160°C
0.6 0.4 0.2 0
0
50
100
150
200
250
300
350
400
Time (min)
Figure 6.17 Effect of temperature on COD reduction of polypropylene plant effluent during thermolysis. COD0 = 3520 mg/L, Cw = 3 kg/m3, pH0 = 6.53, P = self-pressure. (a) COD reduction with time. (b) First-order kinetics at different temperatures.
Beyond 4 kg/m3 catalyst loading, the COD reduction does not increase significantly. The effect of Cw on reaction rate constant was studied at 160°C and its kinetics are presented in Figure 6.19. Equation 6.12 may be written as ln k = ln kc + m . ln Cw (6.15) The kinetic equation for catalytic thermolysis of the polypropylene plant effluent for temperature in the range of 40–160°C, catalyst mass loading in the range of 2–5 kg m−3, and at pH0 = 6.65 may, thus, be written as
www.Ebook777.com
Free ebooks ==> www.ebook777.com 472
Green Chemical Engineering
Table 6.20 First-Order Rate Constant (k) for First and Second Steps of Catalytic Thermolysis Rate Constant versus Temperature (Catalyst Loading Cw = 3 kg/m3) Temperature (°C) 100 120 140 160
k1 (min−1)
k2 (min−1)
k1/k2
0.0011 0.0012 0.0019 0.0021
0.0004 0.0005 0.0007 0.0008
2.3 2.22 2.45 3.3
–5 –5.5
ln k (min–1)
–6
Slow step Fast step
–6.5 –7 –7.5 –8 2.4
2.5
2.6 2.7 10,000/T, (K–1)
2.8
2.9
Figure 6.18 Arrhennius plot for thermolysis of polypropylene plant effluent.
First step: (− r1 ) = −(d(COD)/dt) = 0.442 exp(−2139/T )(COD)Cw0.744
(6.16)
Second step:
(− r2 ) = −(d(COD)/dt) = 0.03762 exp(−1551/T )(COD)Cw0.187
(6.16)
where T is in K. 6.3.5 Conclusions Thermolysis is the effective process for the treatment of propylene plant effluent. A treatment in the temperature range 40–160°C and the corresponding autogenous pressures,
www.Ebook777.com
Free ebooks ==> www.ebook777.com 473
Application of Green Catalysis and Processes
Table 6.21 Typical Composition of Propylene Plant Industrial Wastewater Concentration (mg/L), Except pH
Parameters pH
5.3
COD
3520
BOD
1132
Total solid
6864
Organic nitrogen
90
P
57
Mn
5.17
SO4
7120
Mg
0.76
Na
730
Ca2+
12
Fe
10
2−
+
2+
8
Cu2+
2
Mn
2+
Colour
70
No catalyst CuSO4 FeCl3 FeSO4 CuO ZnO Mn/Cu Mn/Ce
60 50 % COD reduction
Blackish brown
40 30 20 10 0
0
50
100
150
Temperature (°C) Figure 6.19 Effect of different catalysts on COD reduction of polypropylene plant effluent. COD0 = 3520 mg/L, Cw = 3 kg/m3, tR = 6 h, T = 160°C, P = 0.1 MPa.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 474
Green Chemical Engineering
in the presence of CuO catalyst, showed its BOD and COD reduction considerably. The thermal treatment at 160°C, pH 6.65 with a Cw of 3 kg/m3 gave maximum COD reduction of about 70% from its initial value of 3520 mg/L (Table 6.20). The COD reduction is accompanied with the formation of settleable solid residues, which is enriched in carbon. The kinetic analysis of thermolysis revealed that the process is comprised of two successive steps—an initial fast step followed by a slower second step for COD reduction. The two steps can be represented by a simple global power-law rate expression giving first order with respect to COD, for both the steps (Figure 6.19).
6.4 Case Study 3: Catalytic Wet-Air Oxidation Processes Industrial pollution has been a major issue of concern for the whole world due to a sharp increase in the number of process industries and growth in population. Today, the survival of process industries is becoming increasingly dependent upon the environmental sustainability of their technologies. In this work, we have focused our attention on the wastewater discharged by a distillery. The wastewaters from this industry have high BOD, COD and colour. However, rising general awareness, stricter implementation of environmental regulations and the need to survive in a highly competitive market are slowly forcing industries to upgrade and improve practices. The choice of treatment method for a particular effluent stream is governed by factors such as the organic and inorganic constituents, their concentration, toxicity and environmental discharge standards. The WAO is used as a pre-treatment step so that the resulting solution can be treated biologically. The CWAO is an alternative of WAO techniques, which efficiently removes organics from an industrial stream using catalyst to obtain better oxidation rates at lower temperatures and pressures. Mechanism of the Reaction: The oxidation of the organic compounds takes place according to a chain reaction mechanism. The following reaction steps are involved in the WAO process:
Organic compounds + O 2 → Hydroperoxides Hydroperoxides → Alcohol Alcohols + O 2 → Ketones (or aldehydes) Ketones (or aldehydes) + O 2 → Acids Acids + O 2 → CO 2 + H 2 O
(6.17)
Actually, an organic radical R • is coupled with molecular oxygen to propagate the reaction in the WAO reaction. R • radical is originated as a result of the reaction between weakest C–H bonds and oxygen, which forms HO•2 , this HO•2 then combines with RH forming hydrogen peroxide. The hydrogen peroxide obtained decomposes readily to hydroxyl radicals due to temperature. The last reaction is a propagating step leading to oxidised species. The mechanism of WAO can be understood better according to the following reactions:
O − O + R • → ROO•
www.Ebook777.com
(6.18)
Free ebooks ==> www.ebook777.com Application of Green Catalysis and Processes
475
RH + O 2 → R • + HO •2
(6.19)
RH + HO•2 → R • + H2O 2
(6.20)
H 2 O 2 + M → 2HO• + M
(6.21)
ROO• + RH → R • + ROOH
(6.22)
As for most of the molecules’ reaction (6.22), the initiation step is a limiting step too, which depends on the temperature with an activation energy that can exceed 100 or 200 kJ/mol. That is why the WAO does not take place at room temperature, but requires high temperatures (>250°C or 300°C). As this mechanism shows the importance of free radicals, so the use of catalysts and promoters can reduce the severity of the operating conditions required for the reaction. The overall WAO mechanism includes two steps. One step has been discussed above, that is, chemical reaction between the organic matter and the dissolved oxygen. The second step involves the transfer of oxygen from a gas phase to a liquid one and the transfer of CO2 from liquid to gas phase. During designing of a wet air oxidation (WAO) reaction, it is considered that gases must be diffused rapidly within the gas phase. Li et al. (1991) presented a generalised kinetic model based on a simplified reaction scheme with acetic acid as the rate-limiting intermediate product shown below. 1 Organic Compound + O 2 k → CO 2
k1 k2
CH3COOH + O2
[Organic matter + CH 3 COOH] k2 ( k1 − k 3 ) e − k3 t + = e −( k1 + k2 ) t ( k1 + k 2 − k 3 ) [Organic matter + CH 3 COOH]0 ( k1 + k 2 − k 3 )
6.4.1 Introduction Production of ethanol from agricultural materials for use as an alternative fuel has been attracting worldwide interest because of the increasing demand for limited non-renewable energy resources and variability of oil and natural gas prices. In India, this demand is projected to go up because of a law allowing mixing of 5% ethanol with petrol and further raising this amount to 10% (The Gazette of India, 2002). Besides this, other common usages of ethanol are in the form of industrial solvents and in beverages. In India, there are a number of large-scale distilleries integrated with sugar mills. The waste products from sugar mills comprise bagasse (residue from sugarcane crushing), press mud (mud and dirt residue from juice clarification) and molasses (final residue from sugar crystallisation section). Bagasse is used in paper manufacturing and as fuel in boilers; molasses as raw material in the distillery for alcohol production while press mud has no direct industrial application (Nandy et al., 2002). The effluents from molasses-based distilleries contain large amounts
www.Ebook777.com
Free ebooks ==> www.ebook777.com 476
Green Chemical Engineering
of dark reddish-coloured molasses spent wash (MSW). In the distillation process, ethanol ranges from 5% to 12% by volume, hence it follows that the amount of waste varies from 88% to 95% by volume of the alcohol distilled. An average molasses-based distillery generates 15 L of spent wash L−1 of alcohol produced. MSW is one of the most difficult waste products to dispose of because it has a low pH, high temperature, dark reddish colour, high ash content and high percentage of dissolved organic and inorganic matter. 6.4.1.1 Alcohol Production in India India is the largest producer of sugar in the world. In terms of sugarcane production, India and Brazil are almost equally placed (Figure 6.20, Table 6.22). In Brazil, out of the total cane available for crushing, 45% goes for sugar production and 55% for the production of ethanol directly from sugarcane juice. This gives the sugar industry in Brazil additional flexibility to adjust its sugar production keeping in view the sugar price in the international market, as nearly 40% of the sugar output is exported. In India, sugar is manufactured from sugarcane; sugarcane production in India is given in Table 6.22 (Figure 6.20). There has been a steady increase in the production of alcohol in India, with the estimated production rising from 887.2 million litres in 1992–1993 to nearly 1654 million litres in 1999–2000. Surplus alcohol leads to depressed prices for both alcohol and molasses. The projected alcohol production in the country increased from 1869.7 million litres in 2002–2003 to 2300.4 million litres in 2006–2007. Thus, the surplus alcohol available in the country was expected to go up from 527.7 million litres in 2002–2003 to 822.8 million litres in 2006–2007 (Tables 6.23 and 6.24, Figure 6.21). Feed Preparation: Ethanol can be produced from a wide range of feedstock. These include sugar-based (cane and beet molasses, cane juice), starch-based (corn, wheat, cassava, rice, barley) and cellulosic (crop residues, sugarcane bagasse, wood, municipal solid wastes) materials. Indian distilleries almost exclusively use sugarcane molasses. Overall, nearly 61% of the world ethanol production is from sugar crops (Berg, 2004). The composition of molasses varies with the variety of cane, the agro climatic conditions of the region, sugar manufacturing process, and handling and storage. Molasses is diluted to about 20–25 Bx (measurement of sugar concentration in a solution) and its pH adjusted, if required, before fermentation. In India, about 90% of the molasses produced in cane sugar manufacture is consumed in ethanol production (Billore et al., 2001). Fermentation: Yeast culture is prepared in the laboratory and propagated in a series of fomenters, each about 10 times larger than the previous one. The feed is inoculated with about 10% by volume of yeast (Saccharomyces cerevisiae) inoculums. This is an anaerobic process carried out under controlled conditions of temperature and pH, wherein reducing sugars are broken down to ethyl alcohol and carbon dioxide. The reaction is exothermic. To maintain temperature between 25°C and 32°C, plate heat exchangers are used; alternatively, some units spray cooling water on the fermenter walls. Fermentation can be carried out in either batch or continuous mode (CPCB, 2003). Fermentation time for batch operation is typically 24–36 h with an efficiency of about 95%. The resulting broth contains 6–8% alcohol. The sludge (mainly yeast cells) is separated by settling and discharged from the bottom, while the cell-free fermentation broth is sent for distillation. Distillation: Distillation is a two-stage process and is typically carried out in a series of bubble cap fractionating columns. The first stage consists of the analyser column and is followed by rectification columns. The cell-free fermentation broth (wash) is preheated to
www.Ebook777.com
Free ebooks ==> www.ebook777.com 477
400
40
350
35
300
30
250
25
200
20
150
15
100
10
50
5
0
0
0
/1
8
/0
09
20
6
/0
07
20
4
/0
05
20
2
/0
03
20
0
/0
01
20
8
/9
99
19
6
/9
97
19
4
/9
95
19
2
/9
93
19
0
/9
8
/8
91
19
89
19
6
/8
87
19
85
19
Sugarcane production
Sugar million tones
Cane million tones
Application of Green Catalysis and Processes
Sugar production
Figure 6.20 Sugarcane and sugar production in India. (From Global Agricultural Information Network.)
about 90°C by heat exchange with the effluent (spent wash) and then sent to the degasifying section of the analyser column. Here, the liquor is heated by live steam and fractionated to give about 40–45% alcohol. The bottom discharge from the analyser column is the spent wash. The alcohol vapours are led to the rectification column where, by reflux action, 96% alcohol is tapped, cooled and collected. The condensed water from this stage, known as ‘spent lees’, is usually pumped back to the analyser column. Table 6.22 Sugarcane Production in Various Indian States (2001–2006) State Uttar Pradesh Maharashtra Karnataka Tamil Nadu Andhra Pradesh Gujarat Haryana Punjab UK Others Total
2001
2002
2003
2004
2005
2006
106.07 49.59 42.92 33.19 17.69 12.7 8.17 7.77 7.35 10.51 295.96
117.98 45.14 33.02 32.62 18.08 12.47 9.27 9.25 7.56 11.83 297.22
120.95 42.17 32.49 24.17 15.39 14.07 10.65 9.29 7.33 10.89 287.4
112.75 25.67 16.02 17.66 15.04 12.67 9.28 6.62 7.65 10.48 233.84
118.72 20.48 14.28 23.4 15.74 14.57 8.06 5.17 6.44 10.25 237.11
121.53 34.69 15.2 33.3 17.94 13.31 6.84 5.29 6.13 12.65 266.88
Source: Ethanol-production-india.htm. Note: All value in million tones.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 478
Green Chemical Engineering
Table 6.23 Annual Bio-Energy Potential of Distillery Effluent in Various States of India Year 1998 1999 2000 2001 2002 2003 2004 2005 2006
Molasses Production 7.00 8.02 8.33 8.77 9.23 9.73 10.24 10.79 11.36
Production of Alcohol
Industrial Use
Potable Use
Other Uses
Surplus Availability
1411.8 1654.0 1685.9 1775.2 1869.7 1969.2 2074.5 2187.0 2300.4
534.4 518.9 529.3 539.8 550.5 578.0 606.9 619.0 631.4
584.0 622.7 635.1 647.8 660.7 693.7 728.3 746.5 765.2
55.2 57.6 58.8 59.9 61.0 70.0 73.5 77.2 81.0
238.2 455.8 462.7 527.7 597.5 627.5 665.8 742.3 822.8
Source: Central Pollution Control Board (CPCB), 2003. Note: All in million litres.
Table 6.24 Yearly Alcohol Production in India State
Units
Capacity (ML/Year)
Andhra Pradesh Bihar Gujarat Karnataka Madhya Pradesh Maharashtra Punjab Tamil Nadu Uttar Pradesh Rajasthan Kerala Jammu and Kashmir Others Total
24 13 10 28 21 65 8 19 43 7 8 7 32 285
123 88 128 187 469 625 88 212 617 14 23 24 105 2703
Effluent (ML/Year) 1852 1323 1919 2799 7036 9367 1317 3178 9252 202 343 366 1854 40,508
Source: www.ethanolindia.net. Note: Process—Alcohol manufacture in distilleries consists of four main steps, namely, feed preparation, fermentation, and distillation and packaging (Figure 6.21).
Packaging: Rectified spirit (96% ethanol by volume) is marketed directly for the manufacture of chemicals such as acetic acid, acetone, oxalic acid and absolute alcohol. Denatured ethanol for industrial and laboratory use typically contains 60–95% ethanol as well as between 1% and 5% each of methanol, isopropanol, methyl isobutyl ketone (MIBK), ethyl acetate and so forth. For beverages, the alcohol is matured and blended with malt alcohol (for manufacture of whisky) and diluted to requisite strength to obtain the desired type of liquor. This is bottled appropriately in a bottling plant. Anhydrous ethanol for fuelblending applications (power alcohol) requires concentration of the ethanol to 99.5 wt% purity. The ethanol dehydration is typically done using molecular sieves.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 479
Application of Green Catalysis and Processes
Yeast
Diluted molasses
Pre-fermenter
Fermenter
CO2 Spent wash
Rectification column Spentlees Alcohol Blending and maturation
Dehydration (molecular sieve)
Potable alcohol
Power alcohol
Industrial alcohol
Figure 6.21 Process description.
6.4.1.2 Wastewater Generation and Characteristics The main source of wastewater generation is the distillation step, wherein large volumes of dark brown effluent (termed as spent wash, stillage, slop or vinasse) are generated in the temperature range of 71–81°C. The characteristics of the spent wash depend on the raw material used; also, it is estimated that 88% of the molasses constituents end up as waste. MSW has very high levels of BOD, COD, COD/BOD ratio as well as high potassium, phosphorus and sulphate content. In addition, cane MSW contains low-molecular weight compounds such as lactic acid, glycerol, ethanol and acetic acid. Table 6.25 lists the major wastewater streams generated at different stages in the alcohol manufacturing process (Table 6.26). Table 6.25 List of Major Wastewater Streams Generated at Different Stages in the Alcohol Manufacturing Process Parameter Spent wash Fermenter cleaning Fermenter cleaning Condenser cooling Floor wash Bottling plant Others
Wastewater Generation (kL/kL Alcohol)
Colour
pH
14.4 0.6 0.4 2.88 0.8 14 0.8
Dark brown Yellow Colourless Colourless Colourless Hazy Pale yellow
4.6 3.5 6.3 9.2 7.3 7.6 8.1
Source: Satyawali and Balakrishnan (2008).
www.Ebook777.com
Free ebooks ==> www.ebook777.com 480
Green Chemical Engineering
Table 6.26 Comparison of Treated Spent Wash and Effluent Quality Standards
Parameter Temperature (°C) pH BOD5 20°C (mg/L) COD (mg/L) Suspended solids (%) Total dissolved solids (inorganic) (mg/L) Oil and grease (mg/L) Sulphide (S−2) (mg/L) Chlorides as Cl− (mg/L) Total residual chlorine (mg/L) Sodium (Na+) (mg/L) Potassium (K+) (mg/L)
Spent Wash Characteristics after Primary Treatment (Ali, 2002)
Into Surface Water, Indian Standards: 2490 (1974)
On Land for Irrigation, Indian Standards: 3307 (1974)
37°C 7.0–8.5 4000–5000 25,000–30,000 1.0–1.5 —
Shall not exceed 40°C 5.5–9.0 30 250 100b 2100
Shall not exceed 40°C 5.5–9.0 100a — 200b 2100
— 700–800 2000–3000 300–500 1500–2500
10 2 1000 1.0 — —
10 — 600 600 —
Source: Central Pollution Control Board (CPCB), 2003. a When land is used for secondary treatment, BOD up to 500 mg/L is permissible. b Absolute values in mg/L.
Cane molasses also contains around 2% of a dark brown pigment called melanoidins that impart colour to the spent wash (Kalavathi et al., 2001). Melanoidins are low and high molecular weight polymers formed as one of the final products of Maillard reaction, which is a non-enzymatic browning reaction resulting from the reaction of reducing sugars and amino compounds (Martins and van Boekel, 2004). This reaction proceeds effectively at temperatures above 50°C and pH 4–7. Only 6–7% degradation of the melanoidins is achieved in the conventional anaerobic–aerobic effluent treatment process (Gonzalez et al., 2000). Due to their antioxidant properties, melanoidins are toxic to many microorganisms involved in wastewater treatment (Sirianuntapiboon et al., 2004). Apart from melanoidins, spent wash contains other colourants such as phenolics, caramel and melanin. Phenolics are more pronounced in cane molasses wastewater whereas melanin is significant in beet molasses (Godshall, 1999). Approaches Towards Water Conservation in Industries: Monitoring of water use in industries is gaining importance due to increasing competition and stringent environment norms. Water is no longer perceived as a free commodity; further, innovative technologies, along with modification of existing technologies, are employed to reduce processes water consumption. In general, reduction in industrial wastewater can be achieved through one or a combination of the following measures:
1. Process modification or change in raw materials to reduce water consumption 2. Direct reuse of wastewater 3. In-plant reuse of reclaimed wastewater 4. Use of treated wastewater for non-industrial purposes
The final choice of the measures adopted is dictated by the availability of substitute raw material and technology, nature of pollutants, purity requirement of water for reuse, competing water demands and overall treatment cost.
www.Ebook777.com
Free ebooks ==> www.ebook777.com Application of Green Catalysis and Processes
481
6.4.1.3 Wastewater Treatment Methods The choice of treatment method for a particular effluent stream is governed by factors such as the organic and inorganic constituent content, their concentration, toxicity and environmental discharge standards. The technologies available to date are mostly based on single or hybrid treatments involving one or a combination of chemical treatments, physical treatments (adsorption–separation, reverse osmosis, distillation, etc.), biological treatments (anaerobic and/or aerobic) wet oxidation (WO) and incineration. Chemical Treatment: Chemical treatment is used for pH adjustment, coagulation of colloidal impurities (using alum, FeSO4, polyelectrolytes, etc.), precipitation of dissolved pollutants (metal removal of hydroxides, carbohydrates, etc.), oxidation using (O3, ClO2, H2O2 and O2), reduction and sludge conditioning. However, chemical treatment is prohibitively costly if large volumes are to be treated. Reverse Osmosis: Reverse osmosis (RO) is a filtration method that removes many types of large molecules and ions from solutions by applying pressure to the solution when it is on one side of a selective membrane. The result is that the solute is retained on the pressurised side of the membrane and the pure solvent is allowed to pass to the other side. To be ‘selective’, this membrane should not allow large molecules or ions through the pores (holes), but should allow smaller components of the solution (such as the solvent) to pass freely. The reverse osmosis process is used for desalting of brackish water, in the food industry, in maple syrup production and so forth. This technology is not frequently used primarily due to high membrane replacement cost. Biological Treatment: Biological treatment is a method suitable for nearly all applications. However, it is necessary for the resulting sludge to be disposed of by either land filling or burning with a corresponding expenditure of energy following elaborate thickening and dewatering procedures. In spite of this, it is a popular treatment method to the extent that the wastewater that is not suitable for biotreatment due to toxicity or high organic load is treated by other means to make the final effluent suitable for biotreatment. Incineration: Incineration is a waste treatment technology that involves the combustion of organic materials and/or substances. Incineration and other high-temperature waste treatment systems are described as ‘thermal treatment’. The incineration of waste materials converts the waste into incinerator bottom ash, flue gases, particulates and heat, which can in turn be used to generate electric power. The flue gases are cleaned of pollutants before they are dispersed in the atmosphere. Wet Oxidation: Wet oxidation is a form of hydrothermal treatment. It is the oxidation of dissolved or suspended components in water using oxygen as the oxidiser. It is referred to as ‘wet air oxidation’ (WAO) when air is used. Oxidation reactions occur in superheated water at a temperature above the normal boiling point of water (100°C), but below the critical point (374°C). The system must be maintained under pressure to avoid excessive evaporation of water. This is done to control energy consumption due to the latent heat of vaporisation. It is also done because liquid water is necessary for most of the oxidation reactions to occur. Compounds that would not oxidise under dry conditions at the same temperature and pressure oxidise under wet oxidation conditions. 6.4.1.4 Drawbacks of Different Technologies A list of techniques along with their main drawbacks is given below: 1. Concentration/incineration give rise to harmful air emissions. In addition, concentration of oxygen-demanding compounds in wastewater must be adequately
www.Ebook777.com
Free ebooks ==> www.ebook777.com 482
Green Chemical Engineering
adjusted to fall within the concentration operating window required for auto thermal sustainability. 2. Anaerobic digestion with bio methane recovery is a biological treatment of which the main disadvantages are a. Large site area requirements b. Generation of large volumes of sludge with associated disposal problems c. Inherent sensitivity of microorganisms to the type of substrates and concentration of effluents often requiring dilution of effluents prior to treatment 3. No catalytic wet oxidation with steam generation followed by aerobic polishing is an aqueous-phase flameless combustion technique that is usually run under severe conditions such as elevated temperature, pressure and residence time. 6.4.1.5 Wet Air Oxidation History: The first patent of a WAO system is over 90-years old now. In 1911, Strehlenert obtained a patent for the treatment of sulphite liquor by oxidation with compressed air at 180°C. Industrial applications of the techniques started with patents granted independently to a Swedish company. The first known WAO plant was put up in 1958 by Borregaard in Norway for the treatment of sulphite liquors but was later closed down due to uneconomical operations. WAO is a well-established technique of importance for wastewater treatment, particularly toxic and highly organic wastewater. WAO involves liquid phase oxidation of organic oxidisable inorganic components at elevated temperature and pressure using a gaseous source of oxygen (usually air). The elevated pressures are required to keep water in the liquid state. Water also acts as moderant by providing a medium for heat transfer and removing excess heat by evaporation. WAO has been demonstrated to oxidise organic compounds to CO2 and other innocuous end products. The higher the temperature, the higher the extent of oxidation achieved, and the effluent contains mainly low-molecular weight oxygenated compounds, predominantly carboxylic acids. The degree of oxidation is mainly a function of temperature, oxygen partial pressure, residence time and the oxidisability of the pollutants under consideration. The oxidations depend on the treatment objective. WAO becomes self-sustaining when COD is above 20,000 mg/L. Costs can be further reduced by reducing the severity of the oxidation conditions. WAO is a pre-treatment process that increases the biodegradability of landfill leachates, settling the characteristics of sludge. Most distillery plants in India have an effluent treatment plant where biological treatment is used for the treatment of effluent. But the biological treatment method is not cost effective for treating the non-biodegradable fraction present in the effluent. Hence, it is necessary to remove that fraction so that the remaining stream can be degraded by the biological treatment, for which catalytic wet oxidation is an option that is going to be used in the near future. WAO of DWW: Effluent from distillery units is termed as dark reddish liquor due to its colour. It is highly organic in nature and contains organic matter in the form of suspended solids, colloids, BOD, COD, sulphur compounds, pulping chemical used, organic acids, chlorinated lignins, resin acids, phenolics, unsaturated fatty acids, terpenes and the like. Thus, liquor has recoverable amounts of chemicals and energy. Recovery of chemicals is necessary in order for the manufacturing units to meet local discharge standards. The WAO of black liquor is generally slow without a catalyst and requires very severe temperature and pressure condition. There has been a constant need to develop catalyst systems
www.Ebook777.com
Free ebooks ==> www.ebook777.com Application of Green Catalysis and Processes
483
capable of degrading these organic compounds at less severe conditions of temperature and pressure. Although homogeneous copper, zinc and ferric are effective in wet oxidation processes, heterogeneous catalysts are preferred since they avoid the need for further treatment to remove the toxic catalyst from the waste stream. Limitation of WAO: In the process of converting non-biodegradable waste into biodegradable carboxylic acids, different forms of intermediates are produced. To eliminate these intermediates, high temperature and high pressure are used. Corrosion can be observed due to vigorous conditions. This can be used as a pre-treatment method rather than a complete treatment plan. Advantage of WAO: The use of high temperature and pressure can be reduced by the use of catalysts. The thickness of the wall of the reactor can be reduced by using less vigorous operating conditions in the presence of a catalyst. The cost of the reactor design, preparation and maintenance can be reduced. 6.4.2 Literature Survey Imamura et al. (1982) studied the CWO of acetic acid extensively, investigating more than 30 different catalysts. The most active was a Mn/Ce (7/3) composite oxide catalyst that was prepared via the coprecipitation of MnCl2 and CeCl3. This catalyst was capable of 99.5% TOC removal under the following experimental conditions: 1 h, 247°C, [TOC]0 = 2000 ppm, [cat] = 20 mM (total metal concentration). Chowdhury and Copa (1986) suggested WAO, a process involving the treatment of aqueous streams at elevated temperature (175–320°C) and pressure (2169–20,789 kPa), as an established technology proven to be effective in the destruction of various organic and inorganic components of industrial wastewater. Especially sulphides, cyanides, thiocyanate, thiosulphate, phenols and a wide range of other toxic and hazardous organic compounds can be destroyed by WAO. They emphasised that WAO can achieve destruction exceeding 99.9% for a wide variety of toxic and hazardous organics present in industrial wastewaters. Prasad and Joshi (1987) studied the kinetics of black liquor from the kraft pulp industry in an autoclave at high temperature 120–1800°C and pressure of 0.3–1.0 MPa. More than 90% of COD reduction in 6 h was observed by them. The catalyst effect of CuO, ZnO, MnO2 and SeO2 was also evaluated. Wakabayashi and Okuwaki (1988) found that increasing alkalinity resulted in an increase in sodium acetate oxidation, using an iron powder catalyst in a nickel reactor. The nickel reactor was determined to corrode under the experimental conditions here and, hence, nickel oxide acted as a co-catalyst for the oxidation reaction. The effect of alkalinity on the CWO reaction mechanism is an example of an indirect effect on the CWO mechanism. In this mechanism, hydroxide is required to increase the rate of formation of an intermediate species with which the catalyst reacts. Pinter and Levec (1994) studied the CWAO of phenol in an aqueous solution in a semi-batch slurry reactor. A catalyst comprising ZnO, CuO and Al2O3 was found to be effective for converting phenol into non-toxic compounds via different intermediate products at pressures slightly above the atmospheric and temperatures below 130°C. Apparent activation energy for catalytic oxidation of phenol was found to be 84 kJ/mol in the temperature range of 105–130°C. Hao et al. (1994) studied the wet oxidation of red water at a high temperature of 260°C and pressure PO2 = 0.69 MPa (at 25°C). It was observed that after a 1 h run almost 25% of the total solid, 66% of the volatile solid, 97% COD and 84% TOC were removed. He also observed that the off-gas yielded a high concentration of N2 (the net increase was 4.6%), CO2 (4.3%) and CO (0.33%). The quality of the off-gas may vary as a function of WO temperatures, and must be considered in the evaluation of WO technology for the treatment
www.Ebook777.com
Free ebooks ==> www.ebook777.com 484
Green Chemical Engineering
and disposal of red water. Mishra et al. (1995) have critically reviewed the process of WAO at high temperature (125–320°C) and pressure (0.5–20 MPa) conditions for the treatment of hazardous, toxic and nonbiodegradable wastewater steams. They suggested that the process becomes self-sustaining when the effluent has a COD of 20,000 mg/L and can be a net energy producer at sufficiently high feed COD. All the information published on WAO was analysed and presented in a coherent manner. In addition to the industrial applications, some other aspects (such as various catalysts and oxidising agents) of WAO have also been discussed. Recommendations and suggestion for further research have been enlisted. The industrial applications discussed include municipal sewage sludge treatment, cyanide and nitrile wastewater treatment, distillery waste treatment, spent carbon regeneration, and energy and resource regeneration. Lin and Ho (1996) studied the treatment of resizing wastewater, a typical high strength industrial wastewater, by CWAO. They carried out the experiments to investigate the effects of temperature and catalyst dosage (CuSO4 and Cu(NO3)2) on the pollutant (COD) removal. It was observed that 80% of COD removal could be realised in an hour of the catalytic WAO process at 2000°C and 7 MPa. They also developed a kinetic model and a two-stage firstorder kinetic expression was found to well represent the treatment reaction. The correlation between the reaction rate coefficients and the temperature and catalyst dosage were also determined. Gallezot et al. (1996) and Lee and Kim (2000) reported 100% formic acid oxidation using platinum-based catalysts at www.ebook777.com Application of Green Catalysis and Processes
485
57% COD, 72% BOD, 83% TOC and 94% sulphates. WAO has been recommended as part of a combined process scheme for treating an aerobically digested spent wash. Hamoudi et al. (1999) developed a MnO2/CeO2 catalyst that they used in a WAO process for the study of phenol in terms of TOC removal. This catalyst achieved 80% TOC removal in 1 h at 80°C, using an oxygen partial pressure of 0.5 MPa. However, the actual TOC conversion (into CO2) achieved under the same conditions was only 40%. The difference in TOC removal and conversion is due to the deposition of polymeric products on the catalyst, which contributes to an approximately 40% increase in TOC removal. The polymeric products deposited on the catalyst were found to deactivate the catalyst. Dhale et al. (2000) treated wastewater from a distillery waste biogas unit and to recover acetic acid from it, selected the wet oxidative treatment after the treatment of the effluent by a thermal membrane pre-treatment process. The pre-treatment, which reduced the COD by 40% and the colour by 30%, was then followed by WO at 180–225°C and PO2 between 0.69 and 1.38 MPa. A homogeneous FeSO4 catalyst at 210°C reduced the COD by 60% within 2 h and removed 95% of the colour. This is only a slight improvement over no catalytic wet oxidation, which achieved the same result at 220°C. Adding trace amounts of hydroquinone increased COD destruction rates and also increased acid formation. The kinetics of the process followed a two-step mechanism: the rapid initial oxidation of organic substrates, followed by the slower oxidation of low-molecular weight recalcitrant compounds such as acetic acid. Chen et al. (2001) developed a Mn–Ce–O catalyst for the efficient removal of phenol TOC. This catalyst was capable of removing 80–90% of phenol TOC in 10 min at 110°C, using an oxygen partial pressure of 0.5 MPa. The percentage TOC removal achieved using this catalyst was reported to be highly dependent on the Mn/Ce ratio. At a Ce/(Mn + Ce) ratio of 1 (i.e., no manganese), there is no TOC conversion, compared to the 80–90% that is achieved using a Ce/ (Mn + Ce) ratio of 4/6. They proposed that the high activity of this Mn–Ce–O catalyst is presumably due to the following: 1. Improved oxygen storage capacity 2. Improved oxygen mobility on the surface of the catalyst 3. An electron-rich surface, which may be very important in the activation of adsorbed oxygen Zerva (2002) have critically reviewed the process of WAO at high temperatures between 180°C and 260°C and oxygen pressure 30 bar (total pressure 42–78 bar) for the treatment of industrial oily wastewater. They suggested that an increase in temperature significantly enhanced COD removal rates in the wet oxidation process. Almost 50% COD removal was achieved within only 10 min when the temperature was increased to 260°C. The oxidation rates decreased with time due to the production of resistant organic compounds, mainly acetic acid. Most compounds can be totally converted into carbon dioxide at about 250°C in the WO process with the exception of organic acids, mainly acetic acid. Ethylene glycol was the most resistant compound to wet oxidation among those contaminants contained in the wastewater. Prasad et al. (2004) studied the kinetics and mechanism of copper-catalysed WO of stripped sour water. Kinetic studies on the system showed that a two-step, first-order model comprised of fast and slow rate regions closely approximated the actual reaction. Studies on the reaction mechanism of copper-catalysed WAO revealed that the two mechanisms leading to the mineralisation
www.Ebook777.com
Free ebooks ==> www.ebook777.com 486
Green Chemical Engineering
of organics in stripped sour water occur during the heat-up period, in the absence of oxygen. These are
1. Thermal oxidative degradation and 2. Direct oxidation of the organics by copper
6.4.3 Experimental Setup and Design Chemical Oxygen Demand: The COD is the amount of oxygen needed to oxidise the waste chemically, and is of two types:
1. Biologically active, which is biological oxidised 2. Biologically inactive, which cannot be biologically oxidised
COD gives the oxygen required for the complete oxidation of both biodegradable nonbiodegradable matters Catalyst Selection: The catalysts chosen to be tested for WAO of distillery wastewater at atmospheric pressure and moderate temperature are • • • • •
CuSO4 FeCl3 ZnCl2 Zeolite Al(OH)3
Experimental Set Up and Procedure: cwao Experiments: CWAO experiments were carried out in a 0.5 L (three necks) glass reactor on a laboratory scale. The temperature in the reactor was controlled by a PI controller. The reactor contents were agitated using a magnetic stirrer (of which the stirring speed cannot be determined but intensity of stirring can be varied). The optimum concentration of various catalysts with respect to the removal of COD and colour were determined through extensive laboratory studies. The wastewater was treated in batch mode in CWAO apparatus at various catalyst dosages and analysed. During the experimental period, the DWW was invariably hot, being in the range 343–373 K and had a dark reddish colour. The COD concentration was ~160,000 mg/L. After the start of an experimental run at a desired temperature, the effluent samples were withdrawn from the reactor at definite time intervals and were subjected to COD analysis. The effect of variables such as pH (2–12), which was adjusted by the addition of 1 N H2SO4 for acidic region and 1 N NaOH for alkaline range, temperature (T = 343–373 K) and catalyst mass loading (m = 2–5 g/L) on the COD removal efficiency was studied. The time of start of treatment was considered as the ‘zero time’, when the treatment temperature was attained due to preheating of the wastewater from its ambient temperature. All the experimental runs in the reactor were carried out for the treatment time, tR = 8 h. After a test run started, samples were taken periodically during and at the end of the treatment period for analysis (Figure 6.22). 6.4.4 Results and Discussions The distillery wastewater (DWW) was obtained from Pilakhni Distillery Unit, Saharanpur. The characteristic of the DWW as obtained is given in Table 6.27.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 487
Application of Green Catalysis and Processes
Water outlet
Sand
Condenser
Water inlet
Air inlet
Thermocouple
Temp. controller
Heater
Figure 6.22 Experimental setup of CWAO. (From Suresh et al., 2011g.)
Table 6.27 Characteristic of the Distillery Wastewater COD BOD Fixed carbon Total solid Suspended solid Total hardness Chloride Alkalinity pH Total nitrogen Ash content Volatile matter
= = = = = = = = = = = =
1,58,400 mg/L 62,300 mg/L 31,500 mg/L 1,75,000 mg/L 2710 mg/L 18,000 mg/L 1100 mg/L 80 mg/L 3.96 12,000 mg/L 31,000 mg/L 1,12,000 mg/L
Several investigators studied WAO of DWW (Belkacemi et al. 1999; Chaudhari et al., 2006; Suresh et al., 2011d). The studies report the effectiveness of various catalysts, CuO, 1%Pt/Al2O3, Mn/Ce oxides and Cu(II)-exchanged Na-Y zeolite. The above studies involve temperatures in the range 453–523 K and partial pressure of 5–20 Pa, respectively. In this work we have used various inorganic catalysts (CuSO4, FeCl3, ZnCl2, Al (OH)3 ZnCl2) and one organic catalyst Cu(II)-exchanged Na-Y zeolite, respectively. By using these catalysts, we have studied the catalytic behaviour towards the COD and colour reduction of DWW. The inorganic compounds were chosen for the present studies on account of their low cost
www.Ebook777.com
Free ebooks ==> www.ebook777.com 488
Percent COD reduction
Green Chemical Engineering
80
CuSO4 ZnCl2 FeCl3 Al(OH)3 SZ Without catalyst
60 40 20 0
0
2
4
6 pH
8
10
12
Figure 6.23 Effect of pH0 on COD reduction of distillery effluent during CWAO. COD0 = 1600 mg/L: (a) T = 373 K; P = 1 atm; tR = 8 h; m = 5 g/L; v= 0.25 L/min. (From Suresh et al., 2011g.)
and ease of availability. The experimental results reported include the effect of reaction parameters, such as pH, reaction time, catalyst concentration and catalyst composition. Figure 6.23 presents the effect of pH on percent COD reduction of DWW with initial COD 1600 mg/L for different catalysts. The pH varied from 2 to 12. The COD reduction of DWW also studied for different catalysts (CuSO4, FeCl3, zeolite, Al(OH)3, Zn(Cl)2) at different pHs. It can be seen from the plot that the % COD reduction is maximum at pH 12, with 13.1% COD, 13.3% colour reduction (figure is not shown here) when no catalyst was used. Also % COD and % colour reduction were maximum at pH 12, with 56.2%, 34.375%, 21.875%, 57.57% COD and 80.4%, 56.66%, 13.33%, 88.23% colour reduction when CuSO4, FeCl3, zeolite, Zn(Cl)2 were used as a catalyst, respectively. But in the case of Al(OH)3 the colour reduction (12.8%) was maximum at pH 12, and the COD reduction (24.5) is maximum at pH 8. The % COD and % colour reduction in acidic medium were lower. And it increased with the alkalinity of the DWW. In the case of catalysts CuSO4 and FeCl3, the % COD and % colour reduction were increased marginally when the pH changed from 10 to 12. Therefore, we treated DWW at optimised pH 10 in the case of CuSO4 and FeCl3. Effects of Various Catalysts and Their Loading: Catalysts, such as CuSO4, ZnCl2, FeCl3, Al(OH)3 and SZ, were tested for CWAO of DWW (Figures 6.24a and b) at T = 373 K and P = 0.1 MPa for 8 h operation with COD0 = 1600 mg/L and m = 5 g/L. The catalysts were tested at pH = 2 value at which their performance was best. It is seen that the COD reduction is quite fast during the transient preheating period (th) and the initial 2 h pre-treatment time (tR) and, thereafter, the COD reduction proceeds very slowly. During preheating periods of the wastewater from ambient to treatment temperatures, thermal degradation/ precipitation occurs. The th increases with an increase in the treatment temperature, T. The th required for raising the temperature of the reactor and the reactor contents from the ambient temperature to the treatment temperatures, respectively. It can also be seen from Figure 6.23 shows that, for the DWW, the COD reduction is faster during the initial period (upto around 1 h or so) and proceeds slowly thereafter. During the first phase, it is expected that the large molecules in the organic substrate break down to smaller molecules and the hydrolysis of smaller molecules (in the second phase) appears to be relatively difficult. The effect of m (2–5 g/L) was studied for DWW (Figure 6.24) at T = 373 K and P = 0.1 MPa. For DWW, COD and colour reductions were 29.2%, 42.5%, 50.1% 59.8% and 45.1%, 53.2%, 78.2% 87.3% for m = 2, 3, 4 and 5 g/L of CuSO4, respectively, after 8 h of reaction. A similar trend of the maximum COD and colour reductions was obtained for ZnCl2, FeCl3, Al(OH)3 and SZ catalysts after 8 h of reaction. It can be seen that the COD and colour reductions
www.Ebook777.com
Free ebooks ==> www.ebook777.com 489
Application of Green Catalysis and Processes
Percent COD reduction
(a) 60 40 2 g/L 3 g/L 4 g/L 5 g/L
20 0
0
2
Percent colour reduction
(b) 90
4 Time (h)
6
8
60 2 g/L 3 g/L 4 g/L 5 g/L
30 0
0
2
4 Time (h)
6
8
Figure 6.24 Reduction of distillery effluent during CWAO. COD0 = 1600 mg/L; initial colour = 1500 PCU; T = 373 K; pH0 = 2; catalyst: CuSO4; P = 1 atm; tR = 8 h; v = 0.25 L/min. (a) Effect of the catalyst mass loading on COD reduction. (b) Effect of the catalyst mass loading on colour reduction. (From Suresh et al., 2011g.)
increase marginally from m = 2–4 g/L, thereafter they do not get affected significantly with the increase in m to 5 g/L. The increasing trend of COD reduction was observed with increase in m during the preheating period (Figure 6.23). Effect of Temperature: Percent COD and colour reduction as a function of reaction time at different temperatures for CuSO4 and ZnCl2 catalysts (figures are not shown here). The reaction temperatures were varied at 70°C, 85°C and 95 °C. It is observed that the % COD and colour reduction rise as the temperature is increased from 70°C to 95°C. At 95°C % COD reduction of 53%, 57.7% and colour reduction of 78% and 88% were obtained in 4 h reaction time for CuSO4 and ZnCl2 catalysts, which was followed by 48% and 52% of % COD reduction and 75% and 84% of colour reduction at 85°C, which was followed by 45% and 49% of % COD reduction and 71% and 80% of colour reduction at 70°C. The increase in % COD and colour reduction with time was faster within the first hour of the reaction (at all temperatures) than at the later step of reaction time from 1 h onwards. Reaction Kinetics: The effluent contains reduced carbohydrates, lignin, proteins and minerals. Lignin molecules contain hydroxyl and methoxyl groups and a carboxyl group. Carbohydrates contain hydroxyl and carbonium groups in their molecular structure. The lignin at acidic condition and elevated temperature undergo condensation and polymerisation (Casey, 1960; Chaudhari et al., 2008) and carbohydrates undergo hydrolysis (KirkOthmer, 1993; Chaudhari et al., 2010). Due to the reaction between various functional groups present in DWW, the organic content decreases and the catalyst accelerates the reactions. During catalytic WAO, the organic molecules, both smaller and larger, present in the effluent undergo chemical and thermal breakdown and complexation forming insoluble
www.Ebook777.com
Free ebooks ==> www.ebook777.com 490
Green Chemical Engineering
particles. At the same time, larger molecules also undergo breakdown into smaller molecules that are soluble. Due to these, the COD of the supernatant gets reduced. The formation of solid residues depends on the reaction pH, temperature and self-generated pressure. A significant amount of reductions of organic residue formation and simultaneous COD, BOD, organics such as proteins, reduced carbohydrates, lignin and so forth were obtained when the effluents were thermally treated at moderate temperature (373–413 K) and moderate pressure (0.2–0.9 MPa) (Daga et al., 1986; Lele et al., 1989; Chaudhari et al., 2008, 2010). Thus, reduction in COD is due to the reduction of organic molecules such as proteins, reduced carbohydrates, lignin and so forth. By using catalysts, the WAO process, thus, COD reduction, was found to be enhanced. In the CWAO process of DWW, impurities (organic and inorganic constituents) of effluents were converted into CO2, H2O and precipitated sludge. DWW + Catalyst + Heat CO2 + H2O + Sludge The plot of our experimental data did not follow zero-order kinetics; however, it fitted first-order kinetics well. It is seen that the WAO is a two-step series process. The two rate constants, k1 and k2 for the first (fast) step and the second (slow) step, respectively, can thus be determined. The rate equation for the COD reduction was assumed to be a function of the concentration of the organic substrate as well as oxygen partial pressure. Since the air partial pressure was kept constant in all the runs, the rate of reaction would invariably be a function of organic concentration. We consider the rate to follow first-order reaction kinetics and try to show through the experimental data whether it is applicable. The detailed theory is given in Section 6.3. Figures 6.25 and 6.26 for the CuSO4, catalyst as (−ln (1 − X A)) against time and data exactly fit to a straight line, showing the validity of the first-order rate expression. However, there were two distinct zones: the first with a higher slope (line before 1 h reaction time) and the second with less of a slope (found after 1 h reaction time). The two zones represent a fast first-order and a slow first-order regime, respectively. The slope of these lines, which is the value of a reaction rate constant, is thus obtained and values were 0.556 h−1 (fast first-order step) and 0.05 h−1 (slow first-order step) for 373 K, 0.48 h−1 (fast first-order step) and 0.035 h−1 (slow first-order step) for 358 K and 0.412 h−1 (fast first-order step) and 0.03 h−1 (slow firstorder step), respectively.
–ln(1 – XA)
0.6
0.4
343 K
0.2
358 K 373 K
0
0
0.5
1
Time (h) Figure 6.25 First-order kinetics with respect to organic substrate (zone 1: tR = 0–1 h); catalyst: CuSO4. (From Suresh et al., 2011g.)
www.Ebook777.com
Free ebooks ==> www.ebook777.com 491
Application of Green Catalysis and Processes
1
–ln(1 – XA)
0.8 0.6 0.4
343 K 358 K 373 K
0.2 0
0
2
4 Time (h)
6
8
Figure 6.26 First-order kinetics with respect to organic substrate (zone 2: tR = 1–8 h); catalyst: CuSO4. (From Suresh et al., 2011g.)
–0.5 –1
ln k
–1.5 –2 –2.5
Slow step
–3
Fast step
–3.5 –4 2.63
2.83
1000/T, K–1
3.03
Figure 6.27 Arrhenius plot for catalytic WAO of DWW (zone 1: tR = 0–1 h and zone 2: tR = 1–8 h); catalyst: CuSO4. (From Suresh et al., 2011g.)
From the data it can be seen that the rate constant increases with temperature for both the steps. Increase of rate constant with temperature for the first step is smaller than that of the second step. Arrhenius Plot: The activation energy and frequency factor are determined by the Arrhenius equation. A plot of ln k versus 1/T is shown in Figure 6.27 and the values of the frequency factor k0 and the activation energy, E were determined for the two steps. The activation energy for DWW is found to be 2.86 and 3.65 kJ/mol, for the first and the second step, respectively (Figures 6.25 through 6.27). 6.4.5 Conclusions In this case study, treatment was of typical high strength DWW by catalytic wet-air oxidation (CWAO) at atmospheric pressure and 343–373 K. Experiments were conducted to investigate the effects of temperature (T) and catalyst dosage (m) on the COD and colour removal. In this study, five catalysts were used, namely, CuSO4, ZnCl2, FeCl3, Al(OH)3 and Cu (II)-exchanged
www.Ebook777.com
Free ebooks ==> www.ebook777.com 492
Green Chemical Engineering
Na-Y zeolite (SZ). The CWAO is an effective process for treatment of DWW. Both inorganic (CuSO4, ZnCl2, FeCl3, Al(OH)3) and organic (Cu (II)-exchanged Na-Y zeolite) catalysts were found effective for the treatment. However, the CuSO4 catalyst was found to be the best among the various catalysts studied for the treatment. A maximum COD and colour reductions of 58.2% and 88.3% were observed for DWW at T = 373 K, P = 0.1 MPa, tR = 8 h, using 5 g/L CuSO4 catalyst. The CWAO is found to be a two-step process. The first (initial) step is a fast step followed by a second slower step. Both the steps are well represented by first-order kinetics. The activation energy is 2.86 and 3.65 kcal/gmol using CuSO4 catalyst.
www.Ebook777.com
Free ebooks ==> www.ebook777.com
References Abid M.S., Ammar M., Driss Z., Chtourou W. Effect of the tank design on the flow pattern generated with a pitched blade turbine. Int. J. Mech. Appl., 2012;2(1):12–19. Adib F., Bagreev A., Bandosz T.J. Analysis of the relationship between H2S removal capacity and surface properties of unimpregnated activated carbons. Environ. Sci. Technol., 2000;34:636–692. Adam D. Nature 2003;421:571. Albert H.D. III., West D.H., Tullaro N.B. Evaluation of laminar mixing in stirred tanks using a discrete-time particle-mapping procedure. Chem. Eng. Sci., 1999;55(3):667–684. Alberto S.J., Muzzio F.J. Experimental and computational study of mixing behavior in stirred tanks equipped with side entry impellers. Chemical & Biochemical Engineering, University of British Columbia, Vancouver, 2012. Anastas P.T and Warner J.C. Green Chemistry: Theory and Practice, Oxford University Press, Oxford, UK, 1998, 135+xi pages. ANSYS, Inc, Southpointe, 275 Technology Drive, Canonsburg, PA 15317. November 2011, Release 14.0, http://www.ansys.com APHA (American Public Health Association), AWWA (American Water Works Association), WPCF (Water Pollution Control Federation), Standard methods for the examination of water and wastewater. Washington, DC, USA, 1995. Aspen Plus Version 7.0 documentation, Flotran Simulation: An Introduction, 1974. ASTM Standards, Vol. 15.01, Refractories; Carbon and Graphite Products; Activated Carbon; Advanced Ceramics, ASTM D6646-01, 1998. Bakker A., Fasano J.B., Myers K.J. Effects of flow patterns on the solid distribution in a stirred tank. Proceedings of the 8th European Conference on Mixing (IChem. E Symp. Ser. No. 136), Cambridge, UK, 1994;21(23):1–8. Bakker A, Myers K.J., Ward R.W., Lee C.K. Laminar and turbulent flow pattern of the pitched flat blade turbine. J. Trans. I. Chem. E, 197;674(1):1–7. Bakshi B., Fiksel, J. The quest for sustainability: Challenges for process systems engineering. AIChE J. 2003;49(6):1350–1358. Bartholomew C.H., Farrauto R.J. Fundamentals of Industrial Catalytic Processes. Wiley-VCH Publisher, NJ, 2006, ISBN No. 978-0-471-45713-8. Belkacemi K., Larachi F., Hamoudi S., Sayari A. Catalytic wet oxidation of high strength alcoholdistillery liquors. Appl. Catal. A Gen., 2000;199:199–209. Boehm H.P., in: D.D. Eley (Ed.), Advances in Catalysis, 16th edition. Academic Press, New York, 1966, pp. 179–274. Casey J.P. Pulp and Paper Chemistry and Chemical Technology, Vol. 1, 2nd edition. Pulping and Bleaching, Interscience, New York, 1960. Chang C.D., Silvestri A.J. The conversion of methanol and other O-compounds to hydrocarbons over zeolite catalysts. J. Catal., 1977;47:249. Chaudhari P.K., Mishra I.M., Chand S. Effluent treatment for alcohol distillery: Catalytic thermal pretreatment (catalytic thermolysis) with energy recovery. Chem. Eng. J., 2008;136:14–24. Chaudhari P.K., Singh R.K, Mishra I.M., Chand S. Catalytic thermal pretreatment (catalytic thermolysis) of distillery, wastewater and bio-digester effluent of alcohol production plant at atmospheric pressure. Int. J. Chem. React. Eng., 2010;8:1–32. Christensen P.D. et al. Anal. Commun., 1998;35:341–344. Chorkendorff I., Niemantsverdriet J.W. Concepts of Modern Catalysis and Kinetics, 2nd edition. WileyVCH Publisher, NJ, 2007, 478 pp, ISBN No. 978-3-527-31672-4. Corma A. From microporous to mesoporous molecular sieve materials and their use in catalysis. Chem. Rev., 1997;97:2373. 493
www.Ebook777.com
Free ebooks ==> www.ebook777.com 494
References
Daga N.S., Prasad C.V.S., Joshi J.B. Kinetics of hydrolysis and wet air oxidation of alcohol distillery waster. Indian Chem. Eng., 1986;28:22–31. Danckwerts P.V. Continuous flow systems. Chem. Eng. Sci. 1953;2:1–13. Davis M.E. Ordered porous materials for emerging applications. Nature, 2002;417:813. Deleye L., Froment G.F. Rigorous simulation and design of columns for gas absorption and chemical reaction – I. packed columns, Computers & Chemical Engineering, 1986;10:493–504. Del Vecchio R.J., Understanding Design of Experiments. Carl Hanser Verlag, Munich, 1997. Dielot J.Y., Delaplace G, Guerin R, Brianne J.P, Leuliet C. Laminar mixing performances of a stirred tank equipped with helical ribbon agitator subjected to steady and unsteady rotational speed. Chem. Eng.Res. Design, 2008;80(4):335–344. Documentation, FLUENT 6.2, 2008. Dong L., Johansen S.T., Engh T.A. Flow induced by an impeller in an unbaffled tank—I. Experimental. Chem. Eng. Sci., 1993;49(4):549–560. Dubinin M.M., Radushkevich L.V. Equation of the characteristic curve of activated charcoal, Chem. Zentr., 1947;1:875. Ehrfeld W., Hessel V., and Löwe H. Microreactors: New Technology for Modern Chemistry, Wiley-VCH, Weinheim, Germany, 2000. Eldridge J.W., Piret E.L. Continuous-flow stirred-tank reactor system I, Design equations for homogeneous liquid phase reactions, Experimental data, Chem. Eng. Prog., 1950;46:290. El-Hendawy A.A. Carbon, 2003;41:713–722. Etemandi O., Yen T.F. Aspects of selective adsorption among oxidized sulfur compounds in fossil fuels. Energy Fuels, 2007b;21:1622–7. Esveld E., Chemat F., van Haveren. J. Chem. Eng. Technol., 2000;23:429. FLUENT User’s Guide, vols. 1–5 Lebanon, 2001. Freundlich H.M.F. Over the adsorption in solution. J. Phys. Chem., 1906;57:385–471. Gabriel A., Fernando M.J. Chaotic flow in laminar mixing in stirred vessels. Sixth International Symposium on Mixing in Industrial Processes, 2008;17(21):1–3. Garg A., Mishra I.M., Chand S. Thermochemical precipitation as a pretreatment step for the chemical oxygen demand and color removal from pulp and paper mill effluent. Ind. Eng. Chem. Res., 2005;44(7):2016–2026. Guisnet M., Ribeiro F.R. Decativation and Regeneration of Zeolites Catalyst, Catalytic Science Series, Vol. 9. World Scientific Publishing Co, Inc, 2010, 350 pp, ISBN No. 978-1-84816-637-0. www. worldscientific.com Gota K.R. and Suresh S. Preparation and its application of TiO2/ZrO2 and TiO2/Fe photocatalysts: A perspective study. Asian J. Chem., 2014;26(21). Hinshelwood C.N. The Kinetics of Chemical Change. Clarendon Press, Oxford. 1940. Ho Y.S. Second-order kinetic model for the sorption of cadmium on to tree fern: A comparison of linear and non-linear methods. Water. Res., 2006;40:119–125. Ho Y.S., McKay G. Pseudo-second order model for sorption processes. Process Biochem., 1999;34:451–465. Ho Y.S., Wase D.A.J., Forster C.F. Kinetic studies of competitive heavy metal adsorption by sphagnum moss peat. Environ. Technol., 1996;17:71–77. Hollmana G.G., Steenbruggena Jurkovicoˇva G.M.J. A two-step process for the synthesis of zeolites from coal fly ash. Fuel, 1999;78:225–1230. Hougan O.A., Watson K.M. Chemical Process Principles, Vol. III, Wiley, New York, 1943. Huang C.P. Adsorption of phosphate at the hydrous Al2O3-electrolyte interface. J. Colloid Interface Sci., 1975;53:178–186. Hui K.S., Chao C.Y.H. Effects of step-change of synthesis temperature on synthesis of zeolite 4A from coal fly ash. Microporous Mesoporous Mater., 2006;88:145–151. Imamura S. Catalytic and noncatalytic wet oxidation. Ind. Eng. Chem. Res., 1999;38:1743. Jahnisch K., Hessel V., Löwe H., and Baerns M. Angew. Chem., Int. Ed., 2004;43:406–446. Kirk-Othmer. Encyclopedia of Chemical Technology, Vol. 4, 4th edition. John Wiley, New York, 1993. Kunii D., Levenspiel O. Bubbling bed model. Ind. Eng. Chem. Fundam., 1968;7:446–452.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 495
References
Lagergren S. About the theory of so called adsorption of soluble substances. Ksver Veterskapsakad Handl, 1898;24:1–6. Langmuir I. The adsorption of gases on plane surfaces of glass, mica and platinum. J. Am. Chem. Soc., 1918;40:1361–1403. Lele S.S., Rajadhyaksha P.J., Joshi J.B. Effluent treatment for alcohol distillery: Thermal pretreatment with energy recovery. Environ. Prog., 1989;8:245–252. Leon y Leon C.A., Radovic L.R., in: P.A. Thrower (Ed.), Chemistry and Physics of Carbon, Vol. 24. Marcel Dekker, New York, 1992, pp. 213–310. Liebig J. Uber die Erscheinungen der Gahrung, Faulniss und Verwesung, und ihre Ursachen. Ann. Pharm., 1839;30:250–287. Lindemann F.A. Discussion on the radiation theory of chemical reactions. Trans. Faraday Soc., 1922;17: 598–599. Loupy A. Microwaves in Organic Synthesis, Wiley-VCH, Weinheim, Germany, 2002. Lu H., Wang B., Ban Q. Defluoridation of drinking water by zeolite NaP synthesized from coal fly ash. Energy Sources Part A, 2010;32:1509–1516. Mario A.M., Lamberto D.J., Fernando M. Computational analysis of regular chaotic and biochemical mixing in a stirred tank reactor. Chem. Eng. Sci., 2005;56(14):4887–4899. Mario A.M., Paulo A.E., Fernando M.J. Laminar mixing in eccentric stirred tank systems. Can. J. Chem. Eng., 2002;80(4):546–557. Marquardt D.W. An algorithm for least-squares estimation of nonlinear parameters. J. Soc. Ind. Appl. Math., 1963;11:431–441. Masel R.I. Chemical Kinetics and Catalysis. Wiley-VCH Publisher, 2001, ISBN No. 978-0-471-24197-3. Masoud R., Aso K., Ammar D., Abdul-Aziz A. Experimental and computational fluid dynamics (CFD) studies on mixing characteristics of a modified helical ribbon impeller. Korean J. Chem. Eng., 2010;27(4):1150–1158. Matatov-Meytel Y.I., Sheintuch M. Catalytic abatement of water pollutants. Ind. Eng. Chem. Res., 1998;37:309. Michaelis L., Menten M.L. The kinetic of invertin working, Biochem Z (in German),1913;49:333–369. Mishra V.S., Mahajani V.V., Joshi J.B. Wet air oxidation. Ind. Eng. Chem. Res., 1995;34:2–48. Montgomery D.C. Design and Analysis of Experiments. John Wiley & Sons, Inc, New York, 2001. Moreno-Castilla C., Carrasco-Marin F., Maldonado-Hodar F.J., Rivera-Utrilla J. Effects of non-oxidant and oxidant acid treatments on the surface properties of an activated carbon with very low ash content. Carbon, 1998;36:145–151. Mununga L., Hourigan K., Bakker A., Thompson M. Comparative study of flow in a mixing vessel stirred by a solid disk and four bladed impeller. 14th Australian Fluid Mechanics Conference, Adelaide University, Adelaide, Australia, 2001. Nadaniel E.A., Misici L., Ricardo P. Laminar mixing flow in stirred vessel. Chem. Eng. Sci., 2001;45(17):1–14. Ostwald W. Uber Katalyse. Ann Naturphilos, 1910;9:1–25. Park M., Choi C.L., Lim W.T., Kim M.C., Choi J., Heo N.H. Molten-salt method for the synthesis of zeolitic materials II. Characterization of zeolitic materials. Microporous Mesoporous Mater., 2000; 37:81–89. Ramaswamy V., Tripathi B., Srinivas D., Ramaswamy A.V., Cattaneo R., Prins R. Structure and redox behavior of zirconium in microporous Zr-silicalites studied by EXAFS and ESR techniques. J. Catal., 2001;200:250. Redlich O., Peterson D.L. A useful adsorption isotherm. J. Phys. Chem., 1959;63:1024–1026. Selvavathi V., Chidambaram V., Meenakshisundaram A., Sairam B., Sivasankar B. Adsorptive desulfurization of diesel on activated carbon and nickel supported systems. Catal. Today, 2009;141:99–102. Shigemoto N., Hayshi H., Miyaura K. Selective formation of Na-x zeolite from coal fly ash by fusion with sodium hydroxide prior to hydrothermal reaction. J. Mater. Sci., 1993;28:4781–4786. Shieh W.-C., Dell S., and Repie O. Tetrahedron Lett., 2002;43:5607. Singer A., Berkgaut V. Cation exchange properties of hydrothermally treated coal fly ash. Environ. Sci. Technol., 1995;29(9):1748–1753. Skelland A.H.P. Diffusional Mass Transfer. Wiley, New York, 1974.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 496
References
Stadler A., Yousefi B.H., Dallinger D., Walla P., Van der Eycken E., Kaval N., and Kappe C.O. Org. Process Res. Dev., 2003;7:707. Suresh S., Kamsonlian S., Balomajumder C., Chand S. Biosorption of Cd (II) and As (III) ions from aqueous solution by tea waste biomass. Afr. J. Environ. Sci. Technol., 2011a;5(1):1–7. Suresh S., Kamsonlian S., Majumder C.B., Chand S. Biosorption of As(v) from contaminated water onto tea waste biomass: Sorption parameters optimization, equilibrium and thermodynamic studies. J. Fut. Eng. Technol., 2011b;7l(1l). Suresh S., Kamsonlian S., Majumder C.B., Chand S. Biosorption of As(III) from contaminated water onto low cost palm bark biomass. Int. J. Curr. Eng. Technol., 2012d;2(1):153–158. Suresh S., Kamsonlian S., Ramanaiah V., Majumder C.B., Chand S., Kumar A. Biosorptive behaviour of mango leaf powder and rice husk for arsenic(III) from aqueous solutions. Int. J. Environ. Sci. Technol., 2012c;9:565–578. Suresh S., Keshav A. Textbook of Separation Processes. Studium Press (India) Pvt. Ltd., 2012, ISBN No. 978-93-80012-32-2, 1–459. Suresh S., Shankar R., Chand S. Treatment of distillery wastewater using catalytic wet air oxidation. J. Fut. Eng. Technol., 2011g;6:l. Suresh S., Srivastava V.C., Mishra I.M. Critical analysis of engineering aspects of shaken flask bioreactors. Crit. Rev. Biotechnol., 2009a;29(4):255–278. Suresh S., Srivastava V.C., Mishra I.M. Kinetic modeling and sensitivity analysis of kinetic parameters for l-glutamic acid production using Corynebacterium glutamicum. Int. J. Chem. React. Eng., 2009b;7(A89):1–14. Suresh S., Srivastava V.C., Mishra I.M. Techniques for oxygen transfer measurement in bioreactors: A review. J. Chem. Technol. Biotechnol., 2009c;84:1091–1103. Suresh S., Srivastava V.C., Mishra I.M. Adsorption of hydroquinone in aqueous solution by granulated activated carbon. J. Environ. Eng. (ASCE), 2011c;137(12):1145–1157. Suresh S., Srivastava V.C., Mishra I.M. Isotherm, thermodynamics, desorption, and disposal study for the adsorption of catechol and resorcinol onto granular activated carbon. J. Chem. Eng. Data (ACS)., 2011f;56(4):811–818. Suresh S., Srivastava V.C., Mishra I.M. Study of catechol and resorcinol adsorption mechanism through granular activated carbon characterization, pH and kinetic study. Sep. Sci. Technol., 2011d;46(11):1750–1766. Suresh S., Srivastava V.C., Mishra I.M. Studies of adsorption kinetics and regeneration of aniline, phenol, 4-chlorophenol and 4-nitrophenol by activated carbon. Chem. Ind. Chem. Eng. Q., 2012e;19(2):195–212. Suresh S., Srivastava V.C., Mishra I.M. Adsorption of catechol, resorcinol, hydroquinone and its derivatives: A review. Int. J. Energy Environ. Eng., 2012a;3:32. Soni A.B., Keshav A., Verma V., Suresh S. Removal of glycolic acid from aqueous solution using bagasse flyash. Int. J. Environ. Res., 2012;6(1):297–308. Suresh S., Vijayalakshmi G., Rajmohan B., Subbaramaiah V., Adsorption of benzene vapor onto activated biomass from cashew nut shell: Batch and column study. Recent Patents Chem. Eng., 2012b;5(2):116–133. Suresh S., Arisutha S., Sharma S.K. Production of renewable natural gas from waste biomass. J. Inst. Eng. India Ser. E, 2013;94:55–59. Suresh S., Teja K.R., and Chand S. Catalytic wet peroxide oxidation of azo dye (Acid Orange 7) using NaY zeolite from coal fly ash. Int. J. Environ. Waste Manage., 2014 (in press). Temkin M.J., Pyzhev V. Kinetics of ammonia synthesis on promoted iron catalysts. Acta Physiochim., 1940;12:327–356. Tundo P., Perosa A., Zecchini F. Methods and Reagents for Green Chemistry: An Introduction. Wiley-VCH Publisher, 2007, 314 pp, ISBN No. 978-0-470-12408-6. Turk A., Sakalis S., Lessuck J., Karamitsos H., Rago O. Ammonia injection enhances capacity of activated carbon for hydrogen sulfide and methyl mercaptan. Environ. Sci. Technol., 1989;33:1242–1245. Van Heerden C., Ind. Eng. Chem., 1953;45:1245.
www.Ebook777.com
Free ebooks ==> www.ebook777.com 497
References
Wakao N., Smith J.M., Sherwood P.W. J. Catalysis, 1962;1:62. Weber W.J., in: Physicochemical Processes for Water Quality Control. Wiley-Interscience, New York, 1972, p. 211. Weber W.J., Morris J.C. Kinetics of adsorption on carbon from solution. J. Sanit. Eng. Div. Am. Soc. Civ. Eng., 1963;89:31–39. Wiles C. et al. Tetrahedron, 2005;61:5209–5217. Wirth, T., Ed. Microreactors in Organic Synthesis and Catalysis, Wiley-VCH, Weinheim, Germany, 2008. Xu R., Pang W., Yu J., Huo Q., Chen J. Chemistry of Zeolites and Related Porous Materials. Wiley-VCH Publisher, 2007, 616 pp, ISBN No. 978-0-470-82233-3. Xue M., Chitrakar R., Sakane K., Hirotsu T., Ooi K., Yoshimura Y., Feng Q., Sumida N. J. Colloid Interface Sci., 2005;285:487. Yakoob Z., Kamruddin S.K., Hasran U.A. Experimental and numerical studies of laminar mixing in stirred tanks. CIMMA CS’08 Proceedings of the 7th WSEAS International Conference on Computational Intelligence, Man-Machine Systems and Cybernetics, 2008;978(474):149–151. Yoona H.S., Hillb D.F., Balachandra S., Adrianc R.J., Haa M.Y. Reynolds number scaling of flowing a Ruston turbine stirred tank. Mean flow, circular jet and tip vortex scaling. Chemical & Biochemical Engineering, New Brunswick, Rutgers University, 2004. Zadghaffari R., Moghaddas J.S., Ahmadlouydarab M., Revested J. Fourth International Conference on Advanced Computational Methods in Engineering. 15th Mixing Conference of (ACOMEN), University of Belgium, Europe, 2008. Zhao X.S., Lu G.Q., Zhu H.Y. Effects of ageing and seeding on the formation of zeolite Y from coal fly ash. J. Porous Mater., 1997;4:245–251.
www.Ebook777.com
Free ebooks ==> www.ebook777.com
www.Ebook777.com
Free ebooks ==> www.ebook777.com
Further Reading Armbruster T., Gunter M.E. Crystal structure of natural zeolites. Natural zeolites: Occurrence, properties, applications. In: Reviews in Mineralogy and Geochemistry 45, D.L. Bish and D.W. Ming (Eds.), Mineralogical Society of America, Washington, D.C., 2001, pp. 1–67. Atun G., Hisarh G., Kurtoglu A.E., Ayar N. A comparison of basic dye over zeolitic materials synthesized from fly ash, Journal of Hazardous Materials, 2011;187:562–573. Belkacemi K., Larachi F., Hamoudi S., Turcotte G., Sayari A., Inhibition and deactivation effects in catalytic wet oxidation of high-strength alcohol-distillary liquors. Ind. Eng. Chem. Res., 1999;38:2268–2274. Berg C. World fuel ethanol analysis and outlook. 2004. http://www.distill.com/World-Fuel-EthanolA&O-2004.html. Billore S.K., Singh N., Ram H.K., Sharma J.K., Singh V.P., Nelson R.M., Dass P. 2001. Treatment of molasses based distillery effluent ina constructed wetland in central India. Water Science and Technology, 2001:44(11–12):441–448. Breck D.W. Zeolite Molecular Sieves: Structure, Chemistry and Use, 1st Ed., John Wiley, New York, 1974, 313pp. Central Pollution Control Borard (CPCB). 2003. Environmental management in selected indusrial sectors status and needs, 97/2002-03, Ministry of Environment and Forest, New Delhi. Chen H., Sayari A., Adnot A., Larachi F. Composition-activity effects of Mn-Ce-O composites on phenol catalytic wet oxidation, Applied Catalysis B: Environmental, 2001;32:195–204. Chowdhury A.K., Copa W.C. Wet air oxidation of toxic and hazardous organics in industrial wastewaters, Ind. Chem. Eng., 1986;28:3–10. Dhale A.D., Mahajani V.V. Treatment of distillery waste after bio-gas generation: Wet oxidation. Indian J. Chem. Tech., 2000;7:11–18. Denbigh K.G., Chemical Reactor Theory: An Introduction, England, University Press, 1965. Freund E.F. Mechanism of the crystallization of zeolite x. J. Cryst. Growth, 1976;34:11–23. Froment G.F. and Bischoff K.B. Chemical Reactor Analysis and Design, John Wiley and Sons, New York, 1979. Fukui K., Nishimoto T., Takiguchi M., Yoshida H. Effects of NaOH concentration on zeolite synthesis from fly ash with a hydrothermal treatment method. J. Soc. Powder Technology, Japan. 2003;40:497–504. Fogler H.S. Elements of Chemical Reaction Engineering, Prentice Hall, USA, 2005. Gaikwad R.W., Naik P.K. Technology for the removal of sulfate from distillery wastewater. Indian Journal of Environmental Protection, 2000;20(2):106–108. Gallezot P., Laurain N., Isnard P., Catalytic wet-air oxidation of carboxylic acids on carbon-supported platinum catalysts. Applied Catalysis B: Environmental, 1996;9:L11–L17. Godshall M.A. Removal of colorants and polysaccharides and the quality of white sugar. In: Proceedings of Sixth International Symposium Organized by Association Andres Van Hook, March 1999, France, pp. 28–35. Gonzalez T., Terron, M.C., Yague S., Zapico E., Galletti G.C., Gonzalez A.E. Pyrolysis/gas chromatorgraphy/mass spectrometry monitoring of fungal-biotreated distillery wastewater using Trametes Sp. 1-62. Rapid Communications in Mass Spectrometry, 2000;14(15):1417–1424. Hamoudi S., Belkacemi K., Larachi F., Catalytic oxidation of aqueous phenolic solutions catalyst deactivation and kinetics. Chem. Engg. Sci., 1999;54:3569–3576. Hao O.J., Phull K.K., Chen J.M. Wet oxidation of red water and bacterial toxicity of treated waste. Wat. Res., 1994;28(2):283–290. Imamura S., Kinunaka H., Kawabata, N. The wet oxidation of organic compounds catalyzed by Co-Bi complex oxides, Bull. Chem. Soc. Jpn., 1982;55:3679–3680.
499
www.Ebook777.com
Free ebooks ==> www.ebook777.com 500
Further Reading
Kalavathi D.F., Uma L., Subramanian G. Degradation and metabolization of the pigment-melanoidin in a distillery effluent by the marine cyanobacterium Oscillatoria boryana DBU 92181. Enzyme and Microbial Technology, 2001;29(4–5):246–251. Kondru A.K., Kumar P., Chand S. Catalytic wet peroxide oxidation of azo dye (Congo red) using modified Y zeolite as catalyst. Journal of Hazardous Materials, 2009;166:342–347. Kumar P., Prasad B., Mishra I.M., Chand S. Decolorization and COD reduction of dyeing wastewater from a cotton textile mill using thermolysis and coagulation. Journal of Hazardous Materials, 2008;153(1/2):635–645. Lee D., Kim D., Catalytic wet air oxidation of carboxylic acids at atmospheric pressure, Catalysis Today, 2000;63:249–255. Levenspiel O., Chemical Reaction Engineering, Wiley, New York, 1972. Li L., Chen P., Gloyna E.F., Generalized kinetic model for wet oxidation of organic compounds. AIChE Journal, 1991;37(11):1687–1697. Lin S.H., Ho S.J., Catalytic wet-air oxidation of high strength industrial wastewater. Applied Catalysis B: Environmental, 1996;9:133–147. Luck F., Wet air oxidation: Past, present and future. Catalysis Today, 1999;53:81–91. Martins SIFS, Van Boekel MAJS. A kinetic model for the glucose/glycine maillard reaction pathways. Food Chemistry, 2004;90(1–2):257–269. Meier W.M. Zeolite structures. In: Molecular Sieves, Society of Chemical Industry, London, 1968, pp. 10–27. Meier W.M., Olson D.H., Baerlocher Ch. Atlas of Zeolite Structure Types, 4th Ed., Elsevier, London, 1996, 230pp. Mishra V.S., Mahajani V.V., Joshi J.B., Wet air oxidation. Ind. Eng. Chem. Res., 1995;34(1):2–48. Smith J.M. Chemical Engineering Kinetics, McGraw Hill, USA, 1970.
www.Ebook777.com
Free ebooks ==> www.ebook777.com While chemical products are useful in their own right—they address the demands and needs of the masses—they also drain our natural resources and generate unwanted pollution. Green Chemical Engineering: An Introduction to Catalysis, Kinetics, and Chemical Processes encourages minimized use of non-renewable natural resources and fosters maximized pollution prevention. This text stresses the importance of developing processes that are environmentally friendly and incorporate the role of green chemistry and reaction engineering in designing these processes.
Consisting of six chapters organized into two sections, this text:
• Covers the basic principles of chemical kinetics and catalysis
• Gives a brief introduction to classification and the various types of chemical reactors
• Discusses in detail the differential and integral methods of analysis of rate equations for different types of reactions • Presents the development of rate equations for solid catalyzed reactions and enzyme catalyzed biochemical reactions
• Explains methods for estimation of kinetic parameters from batch reactor data
• Details topics on homogeneous reactors
• Includes graphical procedures for the design of multiple reactors
• Contains topics on heterogeneous reactors including catalytic and non-catalytic reactors
• Reviews various models for non-catalytic gas–solid and gas–liquid reactions
• Introduces global rate equations and explicit design equations for a variety of non-catalytic reactors
• Gives an overview of novel green reactors and the application of CFD technique in the modeling of green reactors
• Offers detailed discussions of a number of novel reactors
• Provides a brief introduction to CFD and the application of CFD
• Highlights the development of a green catalytic process and the application of a green catalyst in the treatment of industrial effluent Comprehensive and thorough in its coverage, Green Chemical Engineering: An Introduction to Catalysis, Kinetics, and Chemical Processes explains the basic concepts of green engineering and reactor design fundamentals, and provides key knowledge for students at technical universities and professionals already working in the industry.
• Access online or download to your smartphone, tablet or PC/Mac • Search the full text of this and other titles you own • Make and share notes and highlights • Copy and paste text and figures for use in your own documents • Customize your view by changing font size and layout
WITH VITALSOURCE ® EBOOK
K15526
an informa business
www.crcpress.com
6000 Broken Sound Parkway, NW Suite 300, Boca Raton, FL 33487 711 Third Avenue New York, NY 10017 2 Park Square, Milton Park Abingdon, Oxon OX14 4RN, UK
ISBN: 978-1-4665-5883-0
90000 9 781466 558830
www.Ebook777.com
Green Chemical Engineering
Focused on practical application rather than theory, the book integrates chemical reaction engineering and green chemical engineering, and is divided into two sections. The first half of the book covers the basic principles of chemical reaction engineering and reactor design, while the second half of the book explores topics on green reactors, green catalysis, and green processes. The authors mix in elaborate illustrations along with important developments, practical applications, and recent case studies. They also include numerous exercises, examples, and problems covering the various concepts of reaction engineering addressed in this book, and provide MATLAB® software used for developing computer codes and solving a number of reaction engineering problems.
Suresh Sundaramoorthy
CHEMICAL ENGINEERING
Green Chemical Engineering An Introduction to Catalysis, Kinetics, and Chemical Processes
S. Suresh and S. Sundaramoorthy
