Chemical Reactions and Chemical Reactors George W. Roberts Chemical Reactions and Chemical Reactors George W. Roberts Chemical Reactions and Chemical Reactors George W. Roberts Chemical Reactions and Chemical Reactors George W. Roberts Chemical Reactions and Chemical Reactors George W. Roberts Chemical Reactions and Chemical Reactors George W. Roberts
Chemical Reactions and Chemical Reactors This page intentionally left blank Chemical Reactions and Chemical Reactors George W Roberts North Carolina State University Department of Chemical and Biomolecular Engineering � WILEY John Wiley & Sons, Inc VICE PRESIDENT AND EXECUTIVE PUBLISHER Don Fowley ASSOCIATE PUBLISHER Dan Sayre ACQUISITIONS EDITOR Jenny Welter VICE PRESIDENT AND DIRECTOR OF MARKETING Susan Elbe EXECUTIVE MARKETING MANAGER Chris Ruel SENIOR PRODUCTION EDITOR Trish McFadden DESIGNER Michael St Martine PRODUCTION MANAGEMENT SERVICES Thomson Digital Limited EDITORIAL ASSISTANT Mark Owens MARKETING ASSISTANT Chelsee Pengal MEDIA EDITOR Lauren Sapira © Taylor Kennedy/NG Image Collection COVER PHOTO Cover Description: The firefly on the cover is demonstrating the phenomenon of "bioluminescence", the production of light within an organism (the reactor) by means of a chemical reaction In addition to fireflies, certain marine animals also exhibit bioluminescence In the firefly, a reactant or substrate known as "firefly luciferin" reacts with 02 and adenosine triphosphate (ATP) in the presence of an enzyme catalyst, luciferase, to produce a reactive intermediate (a four-member cyclic perester) Firefly luciferin + ATP+ 02 Iuciferase Intermediate The intermediate then loses C02 spontaneously to form a heterocyclic intermediate known as "oxyluciferin" As formed, the oxyluciferin is in an excited state, i.e., there is an electron in an anti-bonding orbital Intermediate� Oxyluciferin* + C02 Finally, oxyluciferin decays to its ground state with the emission of light when the excited electron drops into a bonding orbital Oxyluciferin* � Oxyluciferin + hv (light) This series of reactions is of practical significance to both fireflies and humans It appears that firefly larvae use bioluminescense to discourage potential predators Some adult fireflies use the phenomenon to attract members of the opposite sex In the human world, the reaction is used to assay for ATP, a very important biological molecule Concentrations 11 M can be detected by measuring the quantity of light emitted Moreover, medical of ATP as low as 10- researchers have implanted the firefly's light-producing gene into cells inside other animals and used the resulting bioluminescense to track those cells in the animal's body This technique can be extended to cancer cells, where the intensity of the bioluminescense can signal the effectiveness of a treatment Finally, the energy released by the bioluminescense-producing reactions is almost quantitatively converted into light In contrast, only about 10% of the energy that goes into a conventional incandescent light bulb is converted into light This book was set in Times New Roman by Thomson Digital Limited and printed and bound by Hamilton Printing The cover was printed by Phoenix Color This book is printed on acid free paper @ Copyright© 2009 John Wiley & Sons, Inc All rights reserved No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc 222 Rosewood Drive, Danvers, MA 01923, website www.copyright.com Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774, (201)748-6011, fax (201)748-6008, website http://www.wiley.com/go/permissions To order books or for customer service please, call 1-800-CALL WILEY (225-5945) ISBN-13 978-0471-7 42203 Printed in the United States of America 10 Contents Reactions and Reaction Rates 1.1 Introduction 1.1.1 1 The Role of Chemical Reactions 1.1.2 Chemical Kinetics 1.1.3 Chemical Reactors 2 1.2 Stoichiometric Notation 1.3 Extent of Reaction and the Law of Definite Proportions 1.4 Definitions of Reaction Rate 1.3.1 1.4.1 Stoichiometric Notation-Multiple Reactions Species-Dependent Definition 1.4.1.1 Single Fluid Phase 1.4.1.2 Multiple Phases 9 Other Cases 1.4.1.3 Relationship between Reaction Rates of Various Species 1.4.1.4 Multiple Reactions 10 11 12 12 Reaction Rates-Some Generalizations 2.1 Rate Equations 2.2 Five Generalizations 2.3 An Important Exception Problems 17 33 33 33 Ideal Reactors 36 3.1 Generalized Material Balance 3.2 Ideal Batch Reactor 3.3 Continuous Reactors 3.4 16 16 Summary of Important Concepts 11 Species-Independent Definition Summary of Important Concepts 36 38 43 3.3.1 Ideal Continuous Stirred-Tank Reactor (CSTR) 3.3.2 Ideal Continuous Plug-Flow Reactor (PFR) 3.3.2.1 The Easy Way-Choose a Different Control Volume 3.3.2.2 The Hard Way-Do the Triple Integration Summary of Important Concepts 54 57 Sizing and Analysis of Ideal Reactors Homogeneous Reactions 4.1.1 51 54 57 Appendix Summary of Design Equations 4.1 45 49 Graphical Interpretation of the Design Equations Problems 10 (Single Reaction) Problems Heterogeneous Catalysis 1.4.2 Batch Reactors 60 63 63 63 4.1.1.1 Jumping Right In 4.1.1.2 General Discussion: Constant-Volume Systems 63 Describing the Progress of a Reaction Solving the Design Equation 68 68 71 v vi Contents 4.1.1.3 4.1.2 4.1.2.1 74 General Discussion: Variable-Volume Systems 77 Continuous Reactors 78 Continuous Stirred-Tank Reactors (CSTRs) 78 Constant-Density Systems Variable-Density (Variable-Volume) Systems 4.1.2.2 80 82 Plug-Flow Reactors Constant-Density (Constant-Volume) Systems Variable-Density (Variable-Volume) Systems 4.1.2.3 Graphical Solution of the CSTR Design Equation 4.1.2.4 Biochemical Engineering Nomenclature 82 84 86 90 4.2 Heterogeneous Catalytic Reactions (Introduction to Transport Effects) 4.3 Systems of Continuous Reactors 4.3.1 4.3.2 4.3.3 4.4 97 98 Reactors in Series 98 103 4.3.1.1 CSTRs in Series 4.3.1.2 PFRs in Series 4.3.1.3 PFRs and CSTRs in Series 103 107 Reactors in Parallel 4.3.2.1 CSTRs in Parallel 4.3.2.2 PFRs in Parallel 107 109 110 Generalizations 111 Recycle 114 Summary of Important Concepts Problems 114 Appendix Solution to Example 4-10: Three Equal-Volume CSTRs in Series Reaction Rate Fundamentals (Chemical Kinetics) 5.1 5.2 123 Significance 125 5.1.2 Definition 5.1.3 Screening Criteria 126 130 5.2.1 Open Sequences 5.2.2 Closed Sequences 130 5.3 The Steady-State Approximation (SSA) 131 Use of the Steady-State Approximation 133 5.4.1 Kinetics and Mechanism 5.4.2 The Long-Chain Approximation 136 137 5.5 Closed Sequences with a Catalyst 5.6 The Rate-Limiting Step (RLS) Approximation 138 5.6.1 Vector Representation 5.6.2 Use of the RLS Approximation 5.6.3 Physical Interpretation of the Rate Equation 5.6.4 Irreversibility Closing Comments 142 143 147 147 148 Analysis and Correlation of Kinetic Data 6.1 140 141 145 Summary of Important Concepts Problems 129 Sequences of Elementary Reactions 5.4 5.7 123 123 Elementary Reactions 5.1.1 91 Experimental Data from Ideal Reactors 6.1.1 Stirred-Tank Reactors (CSTRs) 6.1.2 Plug-Flow Reactors 6.1.2.1 154 154 155 156 Differential Plug-Flow Reactors 156 122 Contents 6.1.2.2 6.2 Integral Plug-Flow Reactors Batch Reactors 6.1.4 Differentiation of Data: An Illustration 158 162 Rate Equations Containing Only One Concentration 162 6.2.1.1 Testing a Rate Equation 6.2.1.2 Linearization of Langmuir-Hinshelwood/Michaelis-Menten 162 165 6.2.2 Rate Equations Containing More Than One Concentration 6.2.3 Testing the Arrhenius Relationship 6.2.4 Nonlinear Regression 171 Using the Integral Method 173 173 6.3.2 Linearization 6.3.3 Comparison of Methods for Data Analysis 176 Elementary Statistical Methods 6.4.1 178 First Hypothesis: First-Order Rate Equation 179 179 Residual Plots Parity Plots 6.4.1.2 177 178 Fructose Isomerization 6.4.1.1 180 Second Hypothesis: Michaelis-Menten Rate Equation Constants in the Rate Equation: Error Analysis Non-Linear Least Squares 6.4.2 186 Rate Equations Containing More Than One Concentration (Reprise) 186 Summary of Important Concepts Problems 187 188 Appendix 6-A Nonlinear Regression for AIBN Decomposition 197 Appendix 6-B Nonlinear Regression for AIBN Decomposition 198 Appendix 6-C Analysis of Michaelis-Menten Rate Equation via Lineweaver-Burke Plot Basic Calculations 201 Multiple Reactions 201 7.1 Introduction 7.2 Conversion, Selectivity, and Yield 7.3 Classification of Reactions 7.4 203 208 7.3.1 Parallel Reactions 7.3.2 Independent Reactions 7.3.3 Series (Consecutive) Reactions 7.3.4 Mixed Series and Parallel Reactions Reactor Design and Analysis 208 208 209 209 211 211 7.4.1 Overview 7.4.2 Series (Consecutive) Reactions 7.4.3 212 212 7.4.2.1 Qualitative Analysis 7.4.2.2 Time-Independent Analysis 7.4.2.3 Quantitative Analysis 7.4.2.4 Series Reactions in a CSTR 214 215 218 Material Balance on A 219 Material Balance on R 219 220 Parallel and Independent Reactions 7.4.3.1 166 169 The Integral Method of Data Analysis 6.3.1 6.4 159 The Differential Method of Data Analysis Rate Equations 6.3 157 6.1.3 6.2.1 vii Qualitative Analysis Effect of Temperature 220 221 199 181 184 viii Contents Effect of Reactant Concentrations 7.4.3.2 7.4.4 Quantitative Analysis Qualitative Analysis 7.4.4.2 Quantitative Analysis Summary of Important Concepts Problems 224 230 Mixed Series/Parallel Reactions 7.4.4.1 222 230 231 232 232 Appendix 7-A Numerical Solution of Ordinary Differential Equations 7-A.1 Single, First-Order Ordinary Differential Equation 241 241 7-A.2 Simultaneous, First-Order, Ordinary Differential Equations 251 Use of the Energy Balance in Reactor Sizing and Analysis 251 8.1 Introduction 8.2 Macroscopic Energy Balances 8.2.1 8.2.2 Single Reactors 8.2.1.2 Reactors in Series 255 Adiabatic Reactors 257 261 8.4.1 Exothermic Reactions 8.4.2 Endothermic Reactions 8.4.3 Adiabatic Temperature Change 8.4.4 Graphical Analysis of Equilibrium-Limited Adiabatic 8.4.5 Kinetically Limited Adiabatic Reactors (Batch and Plug Flow) Reactors 261 262 264 266 Continuous Stirred-Tank Reactors (General Treatment) 8.5.1 271 Simultaneous Solution of the Design Equation and the Energy Balance 272 8.5.2 Multiple Steady States 8.5.3 Reactor Stability 8.5.4 Blowout and Hysteresis 8.5.4.1 276 277 279 279 Blowout Extension 281 282 Discussion 8.5.4.2 8.8 255 Macroscopic Energy Balance for Batch Reactors 8.4 8.7 254 Macroscopic Energy Balance for Flow Reactors (PFRs and Isothermal Reactors 8.6 252 252 8.2.1.1 8.3 8.5 252 Generalized Macroscopic Energy Balance CSTRs) 8.2.3 245 Feed-Temperature Hysteresis 282 Nonisothermal, Nonadiabatic Batch, and Plug-Flow Reactors 8.6.1 General Remarks 8.6.2 Nonadiabatic Batch Reactors 284 284 Feed/Product (F/P) Heat Exchangers 8.7.1 Qualitative Considerations 8.7.2 Quantitative Analysis 285 285 286 8.7.2.1 Energy Balance-Reactor 8.7.2.2 Design Equation 288 288 8.7.2.3 Energy Balance-PIP Heat Exchanger 8.7.2.4 Overall Solution 8.7.2.5 Adjusting the Outlet Conversion 8.7.2.6 Multiple Steady States Concluding Remarks 291 294 Summary of Important Concepts 295 292 291 289 284 268 Contents Problems 296 Appendix 8-A Numerical Solution to Equation (8-26) Appendix 8-B Calculation of 302 G(T) and R(T) for "Blowout" Example Heterogeneous Catalysis Revisited 9.1 Introduction The Structure of Heterogeneous Catalysts 305 306 9.2.1 Overview 9.2.2 Characterization of Catalyst Structure 306 9.2.2.1 Basic Definitions 9.2.2.2 Model of Catalyst Structure Internal Transport 310 310 311 311 9.3.1 General Approach-Single Reaction 9.3.2 An Illustration: First-Order, Irreversible Reaction in an Isothermal, 9.3.3 Extension to Other Reaction Orders and Particle Geometries 9.3.4 The Effective Diffusion Coefficient Spherical Catalyst Particle 311 314 318 9.3.4.1 Overview 9.3.4.2 Mechanisms of Diffusion 319 Bulk (Molecular) Diffusion The Transition Region 319 320 Knudsen Diffusion (Gases) 321 323 Concentration Dependence 9.3.4.3 The Effect of Pore Size 323 325 Narrow Pore-Size Distribution Broad Pore-Size Distribution 325 326 9.3.5 Use of the Effectiveness Factor in Reactor Design and Analysis 9.3.6 Diagnosing Internal Transport Limitations in Experimental Disguised Kinetics 328 Effect of Concentration 329 329 Effect of Temperature 330 Effect of Particle Size 9.3.7 9.3.8 9.3.6.2 The Weisz Modulus 9.3.6.3 Diagnostic Experiments 331 333 335 Internal Temperature Gradients Reaction Selectivity 340 9.3.8.1 Parallel Reactions 9.3.8.2 Independent Reactions 9.3.8.3 Series Reactions External Transport 9.4.1 340 342 344 346 General Analysis-Single Reaction 9.4.1.1 9.4.1.2 326 328 Studies 9.3.6.1 315 318 Configurational (Restricted) Diffusion 9.4 304 305 9.2 ix 346 Quantitative Descriptions of Mass and Heat Transport Mass Transfer 347 Heat Transfer 347 347 First-Order, Reaction in an Isothermal Catalyst Particle-The Concept of a Controlling Step 'Y}kvlc/kc « 'Y}kvlc/kc » 349 350 348 9.4.1.3 Effect of Temperature 9.4.1.4 Temperature Difference Between Bulk Fluid and Catalyst Surface 354 353 Nomenclature fi fraction of total flow passing through vessel "i" (Chapter 10 only) fugacity of species "i" in the standard state (pressure) !? f(e) distribution function for molecular energies (molecules/energy) f(r) distribution function for pore radii (length-1) Fi molar flow rate of species "i" (moles/time) F(t) cumulative exit-age distribution function F(anq) concentration-dependent term in rate equation (units depend on reaction locus, e.g., moles/volume) or (moles/weight of catalyst) fraction of molecules with energy e, greater than e* E, greater than E* F(e>e*) F(E>E*) fraction of molecules with energy g acceleration due to gravity (length/time2) G Gi superficial mass velocity (mass/length2-time) � h hm superficial molar velocity (moles/length2-time) rate of generation of species "i" (moles/time) heat-transfer coefficient (energy/length2 -time-degree) inside heat-transfer coefficient (energy/length2-time-degree) H enthalpy (energy) H partial molar enthalpy (energy/mole) H rate of enthalpy transport (energy/time) I intercept J(t) dimensional internal-age distribution function (time-1) jo Colbumj-factor for mass transfer jH Colbumj-factor for heat transfer k rate constant (units depend on the concentration dependence of the reaction rate and on the reaction locus) Boltzmann constant (energy /molecule-absolute temperature) mass-transfer coefficient based on concentration (length/time) mass-transfer coefficient based on concentration when net molar flux = (length/ time) effective thermal conductivity of catalyst particle (energy/time-length-degree) rate constant for forward reaction mass-transfer coefficient based on partial pressure (moles/area-time-pressure) rate constant for reverse reaction rate constant on a volume of catalyst basis mass-transfer coefficient based on mole fraction (moles/length2-time) thermal conductivity (energy /time-length-degree) parameter in Eqn (2-25) (volume/mole), and in the denominator of other rate equations, e.g., Eqn (4-13) Ks constant in the Monod eqation (mass/volume) Keq equilibrium constant based on activity Kfq K� Km le equilibrium constant based on concentration (moles/volume)[...]... known chemical reactions, plus some reactions that have yet to be developed 1 For the sake of brevity, the phrase "chemical reaction" is used in the broadest possible sense throughout this book The phrase is intended to include biological and biochemical reactions, as well as organic and inorganic reactions 1 2 Chapter 1 Reactions and Reaction Rates The successful, practical implementation of a chemical. .. occurs We will approach the interactions between catalytic kinetics and heat and mass transport conceptually and qualitatively at first, and then take them head-on later in the book 1.1.3 Chemical Reactors Chemical reactions are carried out in chemical reactors Some reactors are easily recog nizable, for example, a vessel in the middle of a chemical plant or the furnace that burns natural gas or heating... information about chemical kinetics to allow the student to understand ideal xvi Preface reactors, to size ideal reactors, and to analyze the behavior of ideal reactors, in Chapters 3 and 4 Chapters 5 and 6 then return to kinetics, and treat it in more detail, and from a more fundamental point of view I use this approach because some students do not have the patience to work through Chapters 2 and 5 unless... all of these topics together, and bring them to bear on the study of Chemical Reactions and Chemical Reactors Let's begin by taking a fresh look at stoichiometry, from the standpoint of how we can use it to describe the behavior of a chemical reaction, and systems of chemical reactions 1.2 STOICHIOMETRIC NOTATION Let's consider the chemical reaction (1-A) The molecule C3H60 is propylene oxide, an important... data, and to calculate unknown quantities; 3 formulate a definition of reaction rate based on where the reaction occurs 1.1 1.1.1 INTRODUCTION The Role of Chemical Reactions Chemical reactions 1 are an essential technological element in a huge range of industries, for example, fuels, chemicals, metals, pharmaceuticals, foods, textiles, electronics, trucks and automobiles, and electric power generation Chemical. .. ideal reactors in series and parallel, and its use leads to new insights into the behavior of systems of reactors In most undergraduate reaction engineering texts, the derivation of the "design equations" for the three ideal reactors, and the subsequent discussion of ideal reactor analysis and sizing, is based exclusively on homogeneous reactions This is very unfortunate, since about 90 percent of the reactions. .. design and analysis of reactions that take place in the gas phase You may have used this stoichiometric notation in earlier courses, such as thermody namics For example, the standard Gibbs free energy change of a reaction standard enthalpy change of a reaction (Mg) (aag_) and the can be written as (1-2) and (1-3) In these equations, a