Chemical Reactor Analysis and Design Gilbert F. Froment Rijksuniversiteit Gent, Belgium Kenneth B. Bischoff University of Delaware John Wiley 8 Sons New York Chichester Brisbane Toronto Copyrrght @ 1979 by John Wlley & Sons. Inc All rights reserved. Published simultaneousiy tn Cdna Reproduction or translatron of any pan of thrs work beyond that permrtted by Sections 107 and 108 of the 1976 United States Copyright Act without the permrssion of the copyrrght owner is unlawful. Requests for permtssron or further tnformation should be addressed to the Permrsstons Department. John Wiley & Sons. Library of Congress Cataloging in Publication Data Frornent. Gilbert F. Chemical reactor analysis and design. Includes index. 1. Chemical reactors. 2. Chemical reacttons. 3. Chemical engineering. I. Bischoti. Kenneth B joint author. 11. Title. Printed in the United States of America 1098765432 To our wives: Mia and Joyce Preface This book provides a comprehensive study of chemical reaction engineering, be- ginning with the basic definitions and fundamental principles and continuing a11 the way to practical application. It emphasizes the real-world aspects of chemi- cal reaction engineering encountered in industrial practice. A rational and rigorous approach, based on mathematical expressions for the physical and chemical phenomena occurring in reactors, is maintained as far as possible toward useful solutions. However, the notions of calculus, differential equations, and statistics required for understanding the material presented in this book do not extend beyond the usual abilities of present-day chemical engineers. In addition to the practical aspects, some of the more fundamental, often more abstract, topics are also discussed to permit the reader to understand the current literature. The book is organized into two main parts: applied or engineering kinetics and reactor analysis and design. This allows the reader to study the detailed kinetics in a given "point," or local region first and then extend this to overall reactor behavior. Several special features include discussions of chain reactions (e.g., hydrocarbon pyrolysis), modem methods of statistical parameter estimation and model dis- crimination techniques, pore diffusion in complex media, genera1 models for fluid-solid reactions, catalyst deactivation mechanisms and kinetics, analysis methods for chemical processing aspects of fluid-fluid reactions. design calcula- tions for plug flow reactors in realistic typical situations (e.g., thermal cracking), fixed bed reactors, fluidized be'd reactor design, and multiphase reactor design. Several of these topics are not usually covered in chemical reaction engineering texts, but are of high current interest in applications. Comprehensive and detailed examples are presented, most of which utilize real kinetic data from processes of industrial importance and are based on the authors' combined research and consulting experience. We firmly believe, based on our experience, that this book can be taught to both undergraduate and graduate classes. If a distinction must be made between undergraduate and graduate material it should be in the extension and the depth of coverage of the chapters. But we emphasize that to prepare the student to solve the problems encountered in industry, as well as in advanced research, the approach must be the same for both levels: there is no point in ignoring the more complicated areas that do not fit into idealized schemes of analysis. Several chapters of the book have been taught for more than 10 years at the vii Rijksuniversiteit Gent, at the University of Maryland, Cornell University, and the University of Delaware. Some chapters were taught by G.F.F. at the University of Houston in 1973, at the Centre de Perfectionnement des Industries Chimiques at Nancy, France, from 1973 onwards and at the Dow Chemical Company, Terneuzen, The Netherlands in 1978. K.B.B. used the text in courses taught at Exxon and Union Carbide and also at the Katholieke Universiteit Leuven, Belgium, in 1976. Substantial parts were presented by both of us at a NATO- sponsored Advanced Study Institute on "Analysis of Fluid-Solidcatalytic Systems" held at the Laboratorium voor Petrochemische Techniek, Rijksuniversiteit, Gent, in August 1974. We thank the following persons for helpful discussions, ideas, and critiques: among these are dr. ir. L. Hosten, dr. ir. F. Dumez, dr. ir. J. Lerou, ir. J. De Geyter and ir. J. Beeckman, all from the Laboratorium voor Petrochemische Techniek of Rijksuniversiteit Gent; Prof. Dan Luss of the University of Houston and Professor W. D. Smith of the University of Rochester. Gilbert F. Froment Kenneth B. Biihoff . . . vlll PREFACE Contents Notation Greek Symbols Subscripts Superscripts xvii xxxiii xxxix xxxix Part One-Chemical Engineering Kinetics 1 Elements of Reaction Kinetics 1 .I Reaction Rate 1.2 Conversion and Extent of Reaction 1.3 Order of Reaction E,uample 1.3-1 The Rare ofan Autocaralytic Reacrion, 13 1.4 Complex Reactions Esumple 1.4-1 Comp1e.r Reaction Nertt~orks, 19 E.rattipk I .J-2 Cu~al~tic Cracking of Gusoil, 24 E.uumple 1.4-3 Rate Determinin,g Step und S~eudv-Sture Appro.uimution, 27 E.uample 1.4-4 Classicul Unimoleculur Rure Theory. 30 E.rample 1.4-5 Thermal Cracking of Efhune, 35 Example 1.4-6 Free Radical Addition Polymeri~ation Kinetics, 38 15 Influence of Temperature 42 E-\ample 1.5-1 Determination of the Actiration Enery?: 43 E.uample 1.5-2 Acticurion Energy for Comp1e.u Reuctions. 44 1.6 Determination of Kinetic Parameters 46 1.6-1 Simple Reactions 46 1.6-2 Complex Reactions 47 E.rump1e 1.6.2-1 Rure Constunr Deiermination by file Himmelblau-Jones- Bischoj'method. 50 Example 1.6.2-2 Olejin Codimerization Kinetics, 53 E.rample 1.6.2-3 Thermal Cracking of Propane, 57 1.7 Thermodynamicaily Nonideal Conditions 60 E.uumple 1.7-1 Reaction of Dilure Strong Electro!vres, 63 E-~umple 1.7-2 Pressure Eficts in Gus-Phase Reactions, 64 2 Kinetics of Heterogeneous Catalytic Reactions 2.1 Introduction 2.2 Rate Equations Exumple 2.2-1 Cnmpetitir-e Hydrogenation Reocrions. 94 E.xumple 2.2-2 Kinetics of Erhyiene O.ridur~on on a Supporred Silver Carafvsr, 101 2.3 Model Discrimination and Parameter Estimation 2.3.a Experimental Reactors 2.3.b The Differental Method for Kinetic Analysis 2.3.c The Integral Method of Kinetic Analysis 2.3.d Sequential Methods for Optimal Design of Experiments 2.3.d-1 Optimal Sequential Discrimination Exurnpie 2.3.d.l-i Model Discrimination in rhe Dehydrogeno~ion of f-Burene inro Buradiene, 121 E.rumple 2.3.d.l-I Ethanol Deh.vdrogenarion. Seqrientiul Discnminarion Using rhe Inregra! Method of'Kineric Anall~is, 125 2.3.d-2 Sequential Design Procedure for Optimal Parameter Estimation E.xumple 2.3.d.2-I Sequentiuf Descqn of Experimenrs /or Optimuf Puramerer Esrimution in n-Penfane Isomeriiur!on. Integral 'Method oJ'Kinrrlc Analysis. 129 3 Transport Processes with Fluid-Solid Heterogeneous Reactions Part I Interfacial Gradient Effects 3.1 Surface Reaction Between a Solid and a Fluid 3.2 Mass and Heat Tramfer Resistances 3.2.a Mass Transfer Coefficients 3.2.b Heat Transfer Coefficients 3.2.~ Multicomponent Diffusion in a Fluid E.~umple 3.2.c-1 Use of Mean Efectice Binarv Drffusic~ry, 149 33 Concentration or Partial Pressure and Temperature Differences Between Bulk Fluid and Surface of a Catalyst Particle E.rampfe 3.3-1 Interfaciui Gradienrs rn Erhunol Dehydrogenarion Expertments, 15 1 Part 11 Intraparticle Gradient Effects 3.4 Catalyst Internal Structure 35 Pore Diusion 3.5.a Definitions and Experimental Observations E.rcunpIe 3.5.0-1 Effect of Pore D~jiusion in the Cracking ofdlkanes on Zeolites, 164 3.5.b General Quantitative Description of Pore Diffusion x CONTENTS 3.5.c The Random Pore Model I 70 3.5.d The Pdrallrl Cross-Linked Pore Model 172 3.5.5 Pore Diifuslon with Adsorption: Surface Diffuslon: Configurational Diffusion 1 74 E.rumpie 3.S.e-1 Surface Diff~ision m Liquid-FiNed Pores, 175 3.6 Reaction with Pore Diffusion 178 3.6.a Concept of Effectiveness Factor 178 3.6.b Generalized Effectiveness Factor 182 E.xumple 3.6.6-1 Generuiized Modrclus for First-Order Reversible Reaction, 185 E.wmpfe 3.6.b-2 Effecrit,eness Facrorsfor Sucrose Inrersion in Ion E.xchunge Resms. 187 E.wmple 3.6.b-3 Methanol Synthesis, 189 3.6.c Criteria for Importance of Diffusional Limitations E.xumple 3.6.c-I Minimum Distance Ber~veen BiJw1crionuI Cutulr.st Sites for Absence of Diffusionaf Limtrurions, 192 E.rample 3.6.c-2 Use of Extended Weisz-Prurer Criterion. 196 3.6.d Combinat~on of External and Internal Diffusion Resistance 197 E.rumple 3.6.d-1 .E.rperimenrul Drferenriution Berbi~een E.~rernul und Internu[ Diffirsion Control, 199 3.7 Thermal Effects 200 3.7.a Thermal Gradients Inside Catalyst Pellets 200 3.7.b External and Internal Temperature Gradients 108 E,~umple 3.7.u-I Temperur~tre Gradients nilh Catalytic Reactions, 2 10 3.8 Complex Reactions with Pore Diffusion 214 E.rample 3.8.1 Effect oJCutalyst Purricle Size on Selecrlriiy in Burenr Dehydrogenution. 2 17 3.9 Reaction with Diffusion in Complicated Pore Structures 22 1 3.9.a Particles with Micro- and Macropores 22 1 3.9.b Parallel Cross-Linked Pores 223 3.9s Reaction with Configuritional Diffusion 224 Example 3.91-1 Cutalyiic Demerallizution (and Desu~urrzarion) o/ Heu0.v Residium Petroleum Feedsrocks, 225 4 Noncatalytic Gas-Solid Reactions 4.1 A Qualitative Discunion of Gas-Solid Reactions 4.2 A General Model with Interfacial and Intraparticle Gradients 43 A Heterogeneow iModel with Shrinking Unreacted Core Example 4.3-1 Combustion of Coke wirhin Porous Catalyst Particles, 252 4.4 Grain model Accounting Explicitly for the Structure of the Solid 45 Pore Model Acmmting Explicitly for the Structure of the Solid 4.6 Reaction Inside Nonisothermal Particles 4.7 A Concluding Remark CONTENTS xi 5 Catalyst Deactivation 5.1 Types of Catalyst Deactivation 5.2 Kinetics of Catalyst Poisoning 5.2.a Introduction 5.2.b Kinetics of Uniform Poisoning 5.2.c Shell Progressive Poisoning 5.2.d Effect of Shell Progressive Poisoning on the Selectivity of Complex Reactions 53 Kinetics of Catalyst Deactivation by Coking 5.3.a Introduction 5.3.b Kinetics of Coking 5.3.c Influence of Coking on the Selectivity 5.3.d Coking Inside a Catalyst Particle Example 5.3.d-I Coking in the Dehvdrogenution of I-Butene into Butadiene on a Chromia-Alumina Cutafvst, 294 5.3.e Determination of the Kinetics of Processes Subject to Coking Example 5.3.e-I Deh.vdrogenution of I-Burene into Butudiene, 297 6 Gas-Liquid Reactions 6.1 Introduction 6.2 Models for Transfer at a Gas-Liquid Interface 6.3 Two-Film Theory 6.3.a Single Irreversible Reaction with General Kinetics 6.3.b First-Order and Pseudo-First-Order Irreversible Reactions 6.3.c Single. Instantaneous, and Irreversible Reaction 6.3.d Some Remarks on Boundary Conditions and on Utilization and Enhancement Factors 6.3.e Extension to Reactions with Higher Orders 6.3.f Complex Reactions 6.4 Surface Renewal Theory 6.4.a Single Instantaneous Reaction 6.4.b Single Irreversible (Pseudo) First-Order Reaction 6.4.c Surface Renewal Models with Surface Elements of Limited Thickness 6.5 Experimental Determination of the Kinetics of Gas-Liquid Reactions Part Two-Analysis and Design of Chemical Reactors 7 The Fundamental Mass, Energy, and Momentum Balance Equations 7.1 Introduction 7. l .a The Continuity Equations 7.1.b The Energy Equation xii CONTENTS 7. l .c The Momentum Equation 7.2 The Fundamental Equations 7.2.a The Continuity Equations 7.2.b Simplified Forms of the "General" Continuity Equation 7.2.c The Energy Equation 7.2.d Simplified Forms of the "General" Energy Equation 8 The Batch Reactor 8.1 The Isothermal Batch Reactor Exmple 8.1-1 Example of Derivurion of a Kinetic Equation by Means oj Butch Data, 364 8.2 The Nonisothermal Batch Reactor Example 8.2-1 Hydrolysis of Acetyluted Cusror Oil Ester, 370 83 Optimal Operation Policies and Control Strategies 8.3.a Optimal Batch Operation Time Example 8.3.0-1 Optimum Conversion und iWu.~irnum Profit for u Firs!-Order Reuction, 376 8.3.b Optimal Temperature Policies E.rumple 8.3.6-1 Optimal Temperarure Trujec!orres for Firsi-Order Rerrrsible Reucrions, 378 E.uumple 8.3.b-2 Oprimum Temperature Policiestor Conseczrtice und Purullel Reuct~ons, 383 9 The Plug Flow Reactor 9.1 The Continuity, Energy, and Momentum Equations E.xump1e 9.1-1 Dericurion of u Kineric Equution from E.t-prrimenrs in un Isoihermul Tubulur Reuctor wiih Plug Flotr,. Thermul Cracking of Propune. 397 9.2 Kinetic Analysis of Nonisothermal Data Esumple 9.2-1 Dericarion ofu Rare Equurionfor rhe Thermul Crucking of Acerone from Nonisorhermul Dora, 402 93 Design of Tubular Reactors with Plug Flow E.uumple 9.3-1 An Adiubur~c Reuctor with Plug Flow Conditions, 408 E.rumple 9.3-2 Design of u Nonisothermai Reucror for Tl~ermoi Cracking of Ethane, 410 10 The Perfectly Mixed Flow Reactor 10.1 Introduction 10.2 Mass and Energy Balances 10.2.a Basic Equations 10.2.b Steady-State Reactor Design E.xumple IO.2.b-I Single Irrecersible Reaction in u Srirred Flow Reoctor, 424 CONTENTS xiii [...]... Fluidized Bed Reactors 13.1 Introduction 13.2 Fluid Catalytic Cracking CONTENTS xv 13.3 Some Features of the Design of Fluidized Bed Reactors 13.4 Modeling of Fluidized Bed Reactors E.~umple 13.4-1 iuodeling of un Acrylonitrile Reactor, 685 14 Multiphase Flow Reactors 14.1 Types of ~Multiphase Flow Reactors 14 l a Packed Columns 14.1.b Plate Columns 14.1.c Empty Columns 14.1.d Stirred Vessel Reactors 14.1.e... m Packed Beds, 48 1 I 1 1.S.b Design of a Fixed Bed Reactor According to the One-Dimensional pseudo-Homogeneous Model 1 1.5.~ Runaway Criteria E.rump1e 11.5.~- Application ofthe Firsr Runaway Criterion of 1 Van Wel~rnaere Fromenr, 490 and 11.5.d The Multibed Adiabatic Reactor 11.5.e Fixed Bed Reactors with Heat Evchange between the Feed and Effluentor between the Feed and Reacting Gases "Autothemic... 14.1.e Miscellaneous Reactors 14.2 Design iModels for Multiphase Flow Reactors 14.2.a Gas and Liquid Phase Completely Mixed 14.2.b Gas and Liquid Phase in Plug Flow 14.2.c Gas Phase in Plug Flow Liquid Phase Completely M~xed 14.2.d An Effective Diffusion Model 14.2.e A Two-Zone Model 14.2.f An Alternate Approach 14.3 Specific Design Aspects 14.3.a Packed Absorbers E.vumple 14.3.0-1 Design of u Pucked... Curbon Dio.ridr Absorption, 704 E.rumpk 14.3.~- 2Design 4spects of u Pucked Column /or rhc Absorprion of 4mmoniu in Suljuric Acid, 708 14.3.b Two-phase Fixed Bed Catalytic Reactors with Cocurrent Downflow Trickle Bed Reactors and Packed Downflow Bubble Reactors 14.3.c Two-Phase Fixed Bed Catalytic Reactors with Cocurrent L'pflow "Upflow Packed Bubble Reactors" 14.3.d Plate Columns E.\-ample 14.3.d-1... Phase Chlormarion of Merhyl Chloride, 452 11 Fixed Bed Catalytic Reactors Part I Introduction 11.1 The Importance and Scale of Fixed Bed Catalytic Processes 11.2 Factors of Progress: Technological Innovations and Increased Fundamental Insight 11.3 Factors Involved i the Preliminary Design of Fixed Bed Reactors n 11.4 Modeling of Fixed Bed Reactors Part 11 Pseudo-Homogeneous Models 11.5 The Basic OneDimensional... Bubble Reactors 14.3.g Stirred Vessel Reactors E.rump/e 14.3.g-I Design o f u Liquid-Phase o-Xj.lene Oxidurion Reactor A Stirred rank reacror B Bubble reactor, 732 Acknowledgments Author Index Subject Index xv i CONTENTS Notation Two consistent sets of &its are listed in the following pages: one that is currently the most common in engineering calculations (including, for example, m, hr, atm, kcal) and. .. increase in value of reacting mixture Weber number, p,L2 d;Q2ur amount of catalyst in bed j of a multibed adiabatic reactor cost of reactor idle time, reactor charging time reactor discharging time and of reaction time weighting factor in objective function (Sec 1.6-2) price per kmole of chemical species A j fractional conversion fractional conversion of A B.j m3 m3 kg cat kg kg cat kg $ f kg kg Sihr... Simulation of the Transient Behavior of a Reactor E.~umple1 I 8.b-1 4 Gus-Solid Reaction in u Fixed Bed Reactor, 551 11.9 One-Dimensional % I d e l Accounting for Interfacial and Intraparticle Gradients 11.9.a Model Equations Exumple 11.9.~-1Stmulur ion of u Fuuser-!Monrecaf~ni Reactor for High-Pressure Methunoi Synthesis 562 E.~ample 11.9.~-2Simulurion of an Industrial Reactor for I-Bu~ene Dehydrogenation... the reactor We have found that this greatly promotes insight into the mathematical modeling of a phenomenon Engineering units A Ab A, A, Am A, '4, reaction component heat exchange surface, packed bed side reacting species in a reaction system heat exchange surface in a batch reactor, on the side of the reaction mixture logarithmic mean of A, and A, or of Ab and A , heat exchange surface for a batch reactor. ..10.3 Design for Optimum Selectivity in Complex Reactions 10.3.a General Considerations 10.3.b Polymerization Reactions 10.4 Stability of Operation and Transient Behavior 10.4.a Stability of Operation E.rample 10.4.0-I Mulripiicity and Sfabiiity in un Adiabatic Stirred Tunk Reactor, 446 10.4.b Transient Behavior Exumple 10.4.b-I Temperalure Osciliariom in u Mixed Reactor for ihe Vapor . Solid and a Fluid 3.2 Mass and Heat Tramfer Resistances 3.2.a Mass Transfer Coefficients 3.2.b Heat Transfer Coefficients 3.2.~ Multicomponent Diffusion in a Fluid E.~umple 3.2.c-1 Use of. Diffusion 1 74 E.rumpie 3.S.e-1 Surface Diff~ision m Liquid-FiNed Pores, 175 3.6 Reaction with Pore Diffusion 178 3.6.a Concept of Effectiveness Factor 178 3.6.b Generalized Effectiveness. mass transfer coefficient referred to unit interfacial area liquid phase mass transfer coefficient referred to unit inierfacial area mass transfer coefficient (including interfacial area)