conservation equations and modeling of chemical and biochemical processes

CONSERVATION EQUATIONS ffND MODELING OF CHEMICfiL fiND BIOCHEMICAL PROCESSES Said S. E. M. Elnashaie Parag Garhyan Auburn University Auburn, Alabama, U.S.A. MARCEL MARCEL DEKKER, INC. NEW YORK • BASEL TM Copyright n 2003 by Marcel Dekker, Inc. All Rights Reserved. Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress. ISBN: 0-8247-0957-8 This book is printed on acid-free paper. Headquarters Marcel Dekker, Inc. 270 Madison Avenue, New York, NY 10016 tel:212-696-9000;fax:212-685-4540 Eastern Hemisphere Distribution Marcel Dekker AG Hutgasse 4, Postfach 812, CH-4001 Basel, Switzerland tel:41-61-260-6300;fax:41-61-260-6333 World Wide Web http://www.dekker.com The publisher offers discounts on this book when ordered in bulk quantities. For more information, write to Special Sales/Professional Marketing at the headquarters address above. Copyright g C 2003 by Marcel Dekker, Inc. All Rights Reserved. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage and retrieval system, without permission in writing from the publisher. Current printing (last digit): 10987654321 PRINTED IN THE UNITED STATES OF AMERICA TM Copyright n 2003 by Marcel Dekker, Inc. All Rights Reserved. CHEMICAL INDUSTRIES A Series of Reference Books and Textbooks Founding Editor HEINZ HEINEMANN 1. Fluid Catalytic Cracking with Zeolite Catalysts, Paul B. Venuto and E. Thomas Habib, Jr. 2. Ethylene: Keystone to the Petrochemical Industry, Ludwig Kniel, Olaf Winter, and Kari Stork 3. The Chemistry and Technology of Petroleum, James G. Speight 4 The Desulfunzation of Heavy Oils and Residua, James G. Speight 5. Catalysis of Organic Reactions, edited by William R. Moser 6. Acetylene-Based Chemicals from Coal and Other Natural Resources, Robert J. Tedeschi 7 Chemically Resistant Masonry, Walter Lee Sheppard, Jr. 8. Compressors and Expanders: Selection and Application for the Process Industry, Heinz P. Bloch, Joseph A. Cameron, Frank M. Danowski, Jr, Ralph James, Jr., Judson S. Sweanngen, and Marilyn E. Weightman 9. Metering Pumps. Selection and Application, James P. Poynton 10. Hydrocarbons from Methanol, Clarence D. Chang 11. Form Flotation: Theory and Applications, Ann N. Clarke and David J. Wilson 12. The Chemistry and Technology of Coal, James G. Speight 13. Pneumatic and Hydraulic Conveying of Solids, O. A. Williams 14. Catalyst Manufacture: Laboratory and Commercial Preparations, Alvin B. Stiles 15 Charactenzation of Heterogeneous Catalysts, edited by Francis Delannay 16 BASIC Programs for Chemical Engineering Design, James H. Weber 17. Catalyst Poisoning, L. Louis Hegedus and Robert W. McCabe 18. Catalysis of Organic Reactions, edited by John R. Kosak 19. Adsorption Technology A Step-by-Step Approach to Process Evaluation and Application, edited by Frank L. Slejko 20. Deactivation and Poisoning of Catalysts, edited by Jacques Oudar and Henry Wise 21. Catalysis and Surface Science: Developments in Chemicals from Meth- anol, Hydrotreating of Hydrocarbons, Catalyst Preparation, Monomers and Polymers, Photocatalysis and Photovoltaics, edited by Heinz Heinemann and Gabor A. Somorjai 22. Catalysis of Organic Reactions, edited by Robert L. Augustine TM Copyright n 2003 by Marcel Dekker, Inc. All Rights Reserved. 23. for the T. H. Tsai, J. W. Lane, and C. S. Lin 24. Temperature-Programmed Reduction for Solid Materials Character- ization, Alan Jones and Brian McNichol 25. Catalytic Cracking: Catalysts, Chemistry, and Kinetics, Bohdan W. Wojciechowski and Avelino Corma 26. Chemical Reaction and Reactor Engineering, edited by J. J. Carberry and A. Varma 27. Filtration: Principles and Practices, Second Edition, edited by Michael J. Matteson and Clyde Orr 28. Corrosion Mechanisms, edited by Florian Mansfeld 29. Catalysis and Surface Properties of Liquid Metals and Alloys, Yoshisada Ogino 30. Catalyst Deactivation, edited by Eugene E. Petersen and Alexis T. Bell 31. Hydrogen Effects in Catalysis: Fundamentals and Practical Applications, edited by Zoltan Paal and P. G. Menon 32. Flow Management for Engineers and Scientists, Nicholas P. Chere- misinoff and Paul N. Cheremisinoff 33. Catalysis of Organic Reactions, edited by Paul N. Rylander, Harold Greenfield, and Robert L. Augustine 34. Powder and Bulk Solids Handling Processes: Instrumentation and Control, Koichi linoya, Hiroaki Masuda, and Kinnosuke Watanabe 35. Reverse Osmosis Technology: Applications for High-Purity-Water Production, edited by Bipin S. Parekh 36. Shape Selective Catalysis in Industrial Applications, N. Y. Chen, William E. Garwood, and Frank G. Dwyer 37. Alpha Olefms Applications Handbook, edited by George R. Lappin and Joseph L. Sauer 38. Process Modeling and Control in Chemical Industries, edited by Kaddour Najim 39. Clathrate Hydrates of Natural Gases, E. Dendy Sloan, Jr. 40. Catalysis of Organic Reactions, edited by Dale W. Blackburn 41. Fuel Science and Technology Handbook, edited by James G. Speight 42. Octane-Enhancing Zeolitic FCC Catalysts, Julius Scherzer 43. Oxygen in Catalysis, Adam Bielanski and Jerzy Haber 44. The Chemistry and Technology of Petroleum: Second Edition, Revised and Expanded, James G. Speight 45. Industnal Drying Equipment: Selection and Application, C. M van't Land 46. Novel Production Methods for Ethylene, Light Hydrocarbons, and Aro- matics, edited by Lyle F. Albnght, Billy L. Crynes, and Siegfried Nowak 47. Catalysis of Organic Reactions, edited by William E. Pascoe 48. Synthetic Lubncants and High-Performance Functional Fluids, edited by Ronald L. Shubkin 49. Acetic Acid and Its Derivatives, edited by Victor H. Agreda and Joseph R. Zoeller 50. Properties and Applications of Perovskite-Type Oxides, edited by L. G. Tejuca and J. L. G. Fierro TM Copyright n 2003 by Marcel Dekker, Inc. All Rights Reserved. 51. d of edited by E. Robert Becker and Carmo J. Pereira 52 Models for Thermodynamic and Phase Equilibria Calculations, edited by Stanley I. Sandier 53. Catalysis of Organic Reactions, edited by John R. Kosak and Thomas A. Johnson 54. Composition and Analysis of Heavy Petroleum Fractions, Klaus H. Altgelt and Mieczyslaw M. Boduszynski 55. NMR Techniques in Catalysis, edited by Alexis T. Bell and Alexander Pines 56. Upgrading Petroleum Residues and Heavy Oils, Murray R. Gray 57. Methanol Production and Use, edited by Wu-Hsun Cheng and Harold H. Kung 58. Catalytic Hydroprocessing of Petroleum and Distillates, edited by Michael C. Oballah and Stuart S. Shin 59. The Chemistry and Technology of Coal: Second Edition, Revised and Expanded, James G. Speight 60. Lubricant Base Oil and Wax Processing, Avilino Sequeira, Jr. 61. Catalytic Naphtha Reforming: Science and Technology, edited by George J. Antos, Abdullah M. Aitani, and Jose M. Parera 62. Catalysis of Organic Reactions, edited by Mike G. Scares and Michael L. Prunier 63. Catalyst Manufacture, Alvin B. Stiles and Theodore A. Koch 64. Handbook of Grignard Reagents, edited by Gary S. Silverman and Philip E. Rakita 65 Shape Selective Catalysis in Industrial Applications: Second Edition, Revised and Expanded, N Y. Chen, William E. Garwood, and Francis G. Dwyer 66. Hydrocracking Science and Technology, Julius Scherzer and A. J. Gruia 67 Hydrotreating Technology for Pollution Control: Catalysts, Catalysis, and Processes, edited by Mario L. Occelli and Russell Chianelli 68 Catalysis of Organic Reactions, edited by Russell E. Malz, Jr. 69. Synthesis of Porous Materials: Zeolites, Clays, and Nanostructures, edited by Mario L. Occelli and Henri Kessler 70. Methane and Its Denvatives, Sunggyu Lee 71. Structured Catalysts and Reactors, edited by Andrzei Cybulski and Jacob Moulijn 72. Industnal Gases in Petrochemical Processing, Harold Gunardson 73. Clathrate Hydrates of Natural Gases: Second Edition, Revised and Expanded, E. Dendy Sloan, Jr. 74. Fluid Cracking Catalysts, edited by Mario L. Occelli and Paul O'Connor 75. Catalysis of Organic Reactions, edited by Frank E. Herkes 76. The Chemistry and Technology of Petroleum, Third Edition, Revised and Expanded, James G. Speight 77. Synthetic Lubricants and High-Performance Functional Fluids, Second Edition- Revised and Expanded, Leslie R. Rudnick and Ronald L. Shubkin TM Copyright n 2003 by Marcel Dekker, Inc. All Rights Reserved. 78. The of and Second Edition, and James G. Speight 79. Reaction Kinetics and Reactor Design: Second Edition, Revised and John B. Butt 80. Regulatory Chemicals Handbook, Jennifer M. Spero, Bella Devito, and Louis Theodore 81. Applied Parameter Estimation for Chemical Engineers, Peter Englezos and Nicolas Kalogerakis 82. Catalysis of Organic Reactions, edited by Michael E. Ford 83. The Chemical Process Industries Infrastructure: Function and Eco- nomics, James R. Couper, O. Thomas Beasley, and W. Roy Penney 84. Transport Phenomena Fundamentals, Joel L Plawsky 85. Petroleum Refining Processes, James G. Speight and Baki Ozum 86. Health, Safety, and Accident Management in the Chemical Process Industries, Ann Marie Flynn and Louis Theodore 87. Plantwide Dynamic Simulators in Chemical Processing and Control, William L. Luyben 88. Chemicial Reactor Design, Peter Harriott 89. Catalysis of Organic Reactions, edited by Dennis Morrell 90. Lubricant Additives: Chemistry and Applications, edited by Leslie R. Rudnick 91. Handbook of Fluidization and Fluid-Particle Systems, edited by Wen- Ching Yang 92. Conservation Equations and Modeling of Chemical and Biochemical Processes, Said S. E. H. Elnashaie and Parag Garhyan 93. Batch Fermentation: Modeling, Monitoring, and Control, Ah Cmar, Satish J. Parulekar, Cenk Undey, and Gulnur Birol 94. Industrial Solvents Handbook, Second Edition, Nicholas P. Chere- misinoff ADDITIONAL VOLUMES IN PREPARATION Chemical Process Engineering: Design and Economics, Harry Silla Process Engineering Economics, James R. Couper Petroleum and Gas Field Processing, H. K. Abdel-Aal, Mohamed Aggour, and M.A. Fahim Thermodynamic Cycles: Computer-Aided Design and Optimization, Chih Wu Re-Engineering the Chemical Processing Plant: Process Intensifica- tion, Andrzej Stankiewicz and Jacob A. Moulijn TM Copyright n 2003 by Marcel Dekker, Inc. All Rights Reserved. Preface We would like readers—instructors and students—to read this preface care- fully before using this book. This preface is classified into three parts: 1. Background and Basic Ideas explains the fundamentals of using a system approach as a more advanced approach to teaching chemical engineering. It also discusses very briefly how this approach allows compacting the contents of many chemical engi- neering subjects and relates them with one another in a systema- tic and easy-to-learn manner. More details on this aspect of the book are given in Chapter 1. 2. Review of Chapters and Appendices briefly describes the content s of each chapter and the educational philosophy behind choosing these materials. 3. Relation of the Book Contents to Existing Chemical Engineering Courses shows how this book can be used to cover a number of courses in an integrated manner that unfortunately is missing in many curricula today. The relation of the contents of the book to existing courses is discussed. Although our frame of reference is the curricula of the Chemical Engineering Department at Auburn University, the discussion can be applied to many curri- cula worldwide. TM Copyright n 2003 by Marcel Dekker, Inc. All Rights Reserved. 1. BACKGROUND AND BASIC IDEAS We have adopted a novel approach in the preparation of this rather revolu- tionary undergraduate-level chemical engineering textbook. It is based on the use of system theory in developing mathematical models (rigorous design equations) for different chemical and biochemical systems. After a brief introduction to system theory and its applications, the book uses the gen- eralized modular conservation equations (material and energy balances) as the starting point. This book takes as its basis the vision of chemical engineering trans- formed, as expressed in the Amundson report of 1989, in which areas new to the traditional subject matter of the discipline are explored. These new areas include biotechnology and biomedicine, electronic materials and polymers, the environment, and computer-aided pr ocess engineering, and encompass what has been labeled the BIN—Bio, Info, Nano—revolution. The book addresses these issues in a novel and imaginative way and at a level that makes it suita ble for undergraduate courses in chemical engineering. This book addresses one of the most important subjects in chemical engineering—modeling and conservation equations. These constitute the basis of any successful understanding, analysis, design, operation, and opti- mization of chemical and biochemical processes. The novel system approach used incorporates a unified and systematic way of addressing the subject, thus streamlining this difficult subject into easy-to-follow enjoyable reading. By adopting a system approach, the book deals with a wide range of subjects normally covered in a number of separate courses—mass and energy balances, transport phenomena, chemical reaction engineering, mathematical modeling, and process control. Students are thus enabled to address problems concerning physical systems, chemical reactors, and bio- chemical processes (in which microbial growth and enzymes play key roles). We strongly believe that this volume strikes the right balance between fundamentals and applications and fills a gap in the literature in a unique way. It efficiently transmits the information to the reader in a systematic and compact manner. The modular mass/energy balance equations are formu- lated, used, and then transformed into the design equ ations for a variety of systems in a simple and systematic manner. In a readily understandable way, this book relates a wide spectrum of subjects starting with material and energy balances and ending with process dynamics and control, with all the stages between. The unique system approach shows that moving from generalized material an d energy balance equations to generalized design equations is quite simple for both lumped and distributed systems. The same has been applied to homogeneous and heterogeneous systems and to reacting and nonreacting systems as well as to TM Copyright n 2003 by Marcel Dekker, Inc. All Rights Reserved. steady- and unsteady-state systems. This leads the reader gracefully and with great ease from lumped to distributed systems, from homogeneous to heterogeneous systems, from reacting to nonreacting systems, and from steady-state to unsteady-state systems. Although steady-state systems are treated, we have provided enough coverage of transient phenomena and unsteady-state modeling for students to appreciate the importance of dynamic systems. While the early part of the book is restricted to homogeneous systems, a later chapter introduces a novel systems approach and presents, in an easy-to-understand manner, the modeling of heterogeneous systems for both steady-state and unsteady-state conditions, together with a number of practical examples. Chemical and biochemical units with multiple-input multiple-output (MIMO) and with multiple reactions (MRs) for all of the above-mentioned systems are also covered. Nonreacting systems and single-input single-out- put (SISO) systems are treated as special cases of the more general MIMO, MR cases. The systems approach helps to establish a solid platform on which to formulate and use these generalized models and their special cases. As the book covers both steady - and unsteady-state situations, it logically includes a chapter on process dynamics and control that is an excellent introduction to a more advanced treatment of this topic, with special emphasis on the industrially more relevant digital control systems design. Given that all chemical/biochemical engineering processes and systems are highly nonlinear by nature, the book discusses this nonlinear behavior in some detail. All the necessary analytical and numerical tools required are included. Matrix techniques are also covered for large-dimensional systems that are common in chemical/biochemical engineering. The book also covers, in a manner that is clear and easy to understand for undergraduate chemical engineers, a dvanced topics such as multiplicity, bifurcation, and chaos to further broaden the student’s perspective. It is increasingly impor- tant for undergraduate students to think outside the conventional realm of chemical engineering, and we have shown that these phenomena are relevant to many important chemical/biochemical industrial systems. It is also shown that these phenomena cannot be neglected while designing these systems or their control loops. In the past these subjects—multiplicity, bifurcation, and chaos—have tended to be relegated to advanced research treatises. We treat them here in a manner that undergraduate students can understand and appreciate. In our fast-changing world the chemi cal/biochemical industry is also rapidly changing. Today’s chemical/biochemical engineering graduates should be exposed to training in creativity as applied to these systems. Therefore a chapter on novel configurations and modes of operations for TM Copyright n 2003 by Marcel Dekker, Inc. All Rights Reserved. two important processes is presented in the form of detailed exercises. This important chapter requires a special effort from the instructor to make it the exercise on creativity that it is meant to be. 2. REVIEW OF CHAPTERS AND APPENDICES This book presents a unified approach to the analysis of a wide range of chemical and biochemical systems. It begins with a summary of the funda- mental principles governing thermodynamics and material and energy bal- ances and proceeds to consider the mathe matical modeling of a range of systems from homogeneous steady state to heterogeneous unsteady state. A novel feature is the inclusion of the concepts surrounding chaotic systems at undergraduate level—an area of growing importance but one sadly neglected in most texts of this kind. The last chapter deals with two indu s- trial processes—reforming and fermentation—in which the foregoing prin- ciples are applied and illustrated for novel configurations and modes of operation. The useful appendices deal with many of the mathematical tech- niques such as matrix algebra, numerical methods, and the Laplace trans- form that are utilized in the book. Chapter1:SystemTheoryandChemical/Biochemical EngineeringSystems This chapter, one of the most impor tant, introduces the main components of the philosophy governing the e ntire book. It covers in a simple manner the main ideas regarding system theory and its application to chemical and biochemical systems. These systems are classified according to the principles of system theory, and this more novel classification is related to the more classical classifications. This chapter also covers the main differences between material and energy balances (inventory) and design equations, the concepts of rate processes together with their relation to state variables, and the general modeling of processes. The thermodynamic limitation of rate processes in relation to modeling and simulation is examined. A brief discussion of the new approach adopted in this book in connection with recent advances in the profession based on the Amundson report is also presented. Chapter 2: Material and Energy Balances This chapter addresses materials and energy balances for reacting (single as well as multiple reactions) and nonreacting systems in a compact way. It also covers SISO as well as MIMO systems. A generalized material and energy balance equation for a MIMO system with MRs is rigorously devel- TM Copyright n 2003 by Marcel Dekker, Inc. All Rights Reserved. [...]... types of systems—isothermal/nonisothermal, lumped/distributed, and steady-/unsteady-state A number of chemical and biochemical examples of varying degrees of complexity and unsolved problems are presented for better understanding of the concepts Chapter 7: Practical Relevance of Bifurcation, Instability, and Chaos in Chemical and Biochemical Systems This chapter covers the basic principles of multiplicity,... material and energy balance (CHEN 2100, Principles of Chemical Engineering, which covers the application of multicomponent material and energy balances to chemical processes involving phase changes and chemical reactions) Chapter 3 can be used as the basis for CHEN 3650, Chemical Engineering Analysis (which covers mathematical modeling and analytical, numerical, and statistical analysis of chemical processes) ... of systemÞ È É ¼ Time rate of change of mass inside the system Component continuity equations (component mass balances): ðFlow of moles of jth component into the systemÞ À ð Flow of moles of jth component out the systemÞ þ ðRate of formation of moles of jth component by chemical reactionsÞ ¼ ðTime rate of change of moles of jth component inside the systemÞ 1.4.2 Diffusion of Mass (Transport Law) Fick’s... Story of Chemical Engineering in Relation to System Theory and Mathematical Modeling The Present Status of Chemical Industry and Undergraduate Chemical Engineering Education System Theory and the Mathematical Modeling Approach Used in This Book 1.8.1 Systems and Mathematical Models 1.8.2 Mathematical Model Building: General Concepts 1.8.3 Outline of the Procedure for Model Building Modeling and Simulation... dynamic modeling of homogeneous and heterogeneous distributed chemical processes, feedback systems, and analog controller tuning and design) prior to the course on digital control (CHEN 6170, Digital Process Control) Chapters 3 and 4 and the first part of Chapter 8 can be used for an undergraduate course on chemical reaction engineering (CHEN 3700, Chemical Reaction Engineering, which covers design of chemical. .. numerical tools for the handling and solution of the different types of design equations, TM Copyright n 2003 by Marcel Dekker, Inc All Rights Reserved including linear and nonlinear algebraic and ordinary differential and partial differential equations 3 RELATION OF THE BOOK CONTENTS TO EXISTING CHEMICAL ENGINEERING COURSES Chapters 1 and 7 should always be included in any usage of this book Chapter 2... (Linear Dependence and Linear Independence of Multiple Reactions) 2.3.6 The Most General Mass Balance Equation (Multiple-Input, Multiple-Output, and Multiple Reactions) Solved Problems for Mass Balance Heat Effects 2.5.1 Heats of Reactions 2.5.2 Effects of Temperature, Pressure, and Phases on Heat of Reaction 2.5.3 Heats of Formation and Heats of Reaction 2.5.4 Heats of Combustion and Heats of Reaction Overall... mass, heat (energy), and momentum balance equations to obtain the necessary equations (or model equations) relating the input and output through the state variables and parameters These equations give the variation of state variables with time and/ or space 1.3.2 Solution of the Model Equations The model developed should be solved for certain inputs, design parameters, and physicochemical parameters... Professor Nabil Esmail (Dean of Engineering, Concordia University, Montreal, Canada), Professor John Yates (Chairman of the Chemical and Biochemical Engineering Department, University College, London), Professor John Grace (University of British Columbia, Canada), and Professor Gilbert Froment (Texas A & M TM Copyright n 2003 by Marcel Dekker, Inc All Rights Reserved University) I also thank Professor... 3.6.3 Nonisothermal Reactors Simple Examples for the General Equations Modeling of Biochemical Systems 3.8.1 Modeling of Enzyme Systems 3.8.2 Modeling of Microbial Systems References Problems Modeling of Distributed Systems 4.1.1 Isothermal Distributed Systems Copyright n 2003 by Marcel Dekker, Inc All Rights Reserved 4.2 4.3 5 Process Dynamics and Control 5.1 5.2 5.3 5.4 5.5 5.6 TM 4.1.2 Nonisothermal . chemical engineering modeling and conservation equations. These constitute the basis of any successful understanding, analysis, design, operation, and opti- mization of chemical and biochemical processes. The. Chemistry and Applications, edited by Leslie R. Rudnick 91. Handbook of Fluidization and Fluid-Particle Systems, edited by Wen- Ching Yang 92. Conservation Equations and Modeling of Chemical . (inventory) and design equations, the concepts of rate processes together with their relation to state variables, and the general modeling of processes. The thermodynamic limitation of rate processes