Chemical Reactions and Chemical Reactors

George W. Roberts is Professor of Chemical Engineering at North Carolina State University. He has also spent over 20 years in research and development with several industrial organizations in the Philadelphia area.

• 1. Reactions and Reaction Rates 11.1 Introduction 11.1.1 The Role of Chemical Reactions 11.1.2 Chemical Kinetics 21.1.3 Chemical Reactors 21.2 Stoichiometric Notation 31.3 Extent of Reaction and the Law of Definite Proportions 41.3.1 Stoichiometric Notation—Multiple Reactions 61.4 Definitions of Reaction Rate 81.4.1 Species-Dependent Definition 81.4.1.1 Single Fluid Phase 91.4.1.2 Multiple Phases 9Heterogeneous Catalysis 9Other Cases 101.4.1.3 Relationship between Reaction Rates of Various Species (Single Reaction) 101.4.1.4 Multiple Reactions 111.4.2 Species-Independent Definition 11Summary of Important Concepts 12Problems 122. Reaction Rates—Some Generalizations 162.1 Rate Equations 162.2 Five Generalizations 172.3 An Important Exception 33Summary of Important Concepts 33Problems 333. Ideal Reactors 363.1 Generalized Material Balance 363.2 Ideal Batch Reactor 383.3 Continuous Reactors 433.3.1 Ideal Continuous Stirred-Tank Reactor (CSTR) 453.3.2 Ideal Continuous Plug-Flow Reactor (PFR) 493.3.2.1 The Easy Way—Choose a Different Control Volume 513.3.2.2 The Hard Way—Do the Triple Integration 543.4 Graphical Interpretation of the Design Equations 54Summary of Important Concepts 57Problems 57Appendix 3 Summary of Design Equations 604. Sizing and Analysis of Ideal Reactors 634.1 Homogeneous Reactions 634.1.1 Batch Reactors 634.1.1.1 Jumping Right In 634.1.1.2 General Discussion: Constant-Volume Systems 68Describing the Progress of a Reaction 68Solving the Design Equation 714.1.1.3 General Discussion: Variable-Volume Systems 744.1.2 Continuous Reactors 774.1.2.1 Continuous Stirred-Tank Reactors (CSTRs) 78Constant-Density Systems 78Variable-Density (Variable-Volume) Systems 804.1.2.2 Plug-Flow Reactors 82Constant-Density (Constant-Volume) Systems 82Variable-Density (Variable-Volume) Systems 844.1.2.3 Graphical Solution of the CSTR Design Equation 864.1.2.4 Biochemical Engineering Nomenclature 904.2 Heterogeneous Catalytic Reactions (Introduction to Transport Effects) 914.3 Systems of Continuous Reactors 974.3.1 Reactors in Series 984.3.1.1 CSTRs in Series 984.3.1.2 PFRs in Series 1034.3.1.3 PFRs and CSTRs in Series 1034.3.2 Reactors in Parallel 1074.3.2.1 CSTRs in Parallel 1074.3.2.2 PFRs in Parallel 1094.3.3 Generalizations 1104.4 Recycle 111Summary of Important Concepts 114Problems 114Appendix 4 Solution to Example 4-10: Three Equal-Volume CSTRs in Series 1225. Reaction Rate Fundamentals (Chemical Kinetics) 1235.1 Elementary Reactions 1235.1.1 Significance 1235.1.2 Definition 1255.1.3 Screening Criteria 1265.2 Sequences of Elementary Reactions 1295.2.1 Open Sequences 1305.2.2 Closed Sequences 1305.3 The Steady-State Approximation (SSA) 1315.4 Use of the Steady-State Approximation 1335.4.1 Kinetics and Mechanism 1365.4.2 The Long-Chain Approximation 1375.5 Closed Sequences with a Catalyst 1385.6 The Rate-Limiting Step (RLS) Approximation 1405.6.1 Vector Representation 1415.6.2 Use of the RLS Approximation 1425.6.3 Physical Interpretation of the Rate Equation 1435.6.4 Irreversibility 1455.7 Closing Comments 147Summary of Important Concepts 147Problems 1486. Analysis and Correlation of Kinetic Data 1546.1 Experimental Data from Ideal Reactors 1546.1.1 Stirred-Tank Reactors (CSTRs) 1556.1.2 Plug-Flow Reactors 1566.1.2.1 Differential Plug-Flow Reactors 1566.1.2.2 Integral Plug-Flow Reactors 1576.1.3 Batch Reactors 1586.1.4 Differentiation of Data: An Illustration 1596.2 The Differential Method of Data Analysis 1626.2.1 Rate Equations Containing Only One Concentration 1626.2.1.1 Testing a Rate Equation 1626.2.1.2 Linearization of Langmuir–Hinshelwood/Michaelis–Menten Rate Equations 1656.2.2 Rate Equations Containing More Than One Concentration 1666.2.3 Testing the Arrhenius Relationship 1696.2.4 Nonlinear Regression 1716.3 The Integral Method of Data Analysis 1736.3.1 Using the Integral Method 1736.3.2 Linearization 1766.3.3 Comparison of Methods for Data Analysis 1776.4 Elementary Statistical Methods 1786.4.1 Fructose Isomerization 1786.4.1.1 First Hypothesis: First-Order Rate Equation 179Residual Plots 179Parity Plots 1806.4.1.2 Second Hypothesis: Michaelis–Menten Rate Equation 181Constants in the Rate Equation: Error Analysis 184Non-Linear Least Squares 1866.4.2 Rate Equations Containing More Than One Concentration (Reprise) 186Summary of Important Concepts 187Problems 188Appendix 6-A Nonlinear Regression for AIBN Decomposition 197Appendix 6-B Nonlinear Regression for AIBN Decomposition 198Appendix 6-C Analysis of Michaelis–Menten Rate Equation viaLineweaver–Burke Plot Basic Calculations 1997. Multiple Reactions 2017.1 Introduction 2017.2 Conversion, Selectivity, and Yield 2037.3 Classification of Reactions 2087.3.1 Parallel Reactions 2087.3.2 Independent Reactions 2087.3.3 Series (Consecutive) Reactions 2097.3.4 Mixed Series and Parallel Reactions 2097.4 Reactor Design and Analysis 2117.4.1 Overview 2117.4.2 Series (Consecutive) Reactions 2127.4.2.1 Qualitative Analysis 2127.4.2.2 Time-Independent Analysis 2147.4.2.3 Quantitative Analysis 2157.4.2.4 Series Reactions in a CSTR 218Material Balance on A 219Material Balance on R 2197.4.3 Parallel and Independent Reactions 2207.4.3.1 Qualitative Analysis 220Effect of Temperature 221Effect of Reactant Concentrations 2227.4.3.2 Quantitative Analysis 2247.4.4 Mixed Series/Parallel Reactions 2307.4.4.1 Qualitative Analysis 2307.4.4.2 Quantitative Analysis 231Summary of Important Concepts 232Problems 232Appendix 7-A Numerical Solution of Ordinary Differential Equations 2417-A.1 Single, First-Order Ordinary Differential Equation 2417-A.2 Simultaneous, First-Order, Ordinary Differential Equations 2458. Use of the Energy Balance in Reactor Sizing and Analysis 2518.1 Introduction 2518.2 Macroscopic Energy Balances 2528.2.1 Generalized Macroscopic Energy Balance 2528.2.1.1 Single Reactors 2528.2.1.2 Reactors in Series 2548.2.2 Macroscopic Energy Balance for Flow Reactors (PFRs and CSTRs) 2558.2.3 Macroscopic Energy Balance for Batch Reactors 2558.3 Isothermal Reactors 2578.4 Adiabatic Reactors 2618.4.1 Exothermic Reactions 2618.4.2 Endothermic Reactions 2628.4.3 Adiabatic Temperature Change 2648.4.4 Graphical Analysis of Equilibrium-Limited Adiabatic Reactors 2668.4.5 Kinetically Limited Adiabatic Reactors (Batch and Plug Flow) 2688.5 Continuous Stirred-Tank Reactors (General Treatment) 2718.5.1 Simultaneous Solution of the Design Equation and the Energy Balance 2728.5.2 Multiple Steady States 2768.5.3 Reactor Stability 2778.5.4 Blowout and Hysteresis 2798.5.4.1 Blowout 279Extension 281Discussion 2828.5.4.2 Feed-Temperature Hysteresis 2828.6 Nonisothermal, Nonadiabatic Batch, and Plug-Flow Reactors 2848.6.1 General Remarks 2848.6.2 Nonadiabatic Batch Reactors 2848.7 Feed/Product (F/P) Heat Exchangers 2858.7.1 Qualitative Considerations 2858.7.2 Quantitative Analysis 2868.7.2.1 Energy Balance—Reactor 2888.7.2.2 Design Equation 2888.7.2.3 Energy Balance—F/P Heat Exchanger 2898.7.2.4 Overall Solution 2918.7.2.5 Adjusting the Outlet Conversion 2918.7.2.6 Multiple Steady States 2928.8 Concluding Remarks 294Summary of Important Concepts 295Problems 296Appendix 8-A Numerical Solution to Equation (8-26) 302Appendix 8-B Calculation of G(T) and R(T) for ‘‘Blowout’’ Example 3049. Heterogeneous Catalysis Revisited 3059.1 Introduction 3059.2 The Structure of Heterogeneous Catalysts 3069.2.1 Overview 3069.2.2 Characterization of Catalyst Structure 3109.2.2.1 Basic Definitions 3109.2.2.2 Model of Catalyst Structure 3119.3 Internal Transport 3119.3.1 General Approach—Single Reaction 3119.3.2 An Illustration: First-Order, Irreversible Reaction in an Isothermal,Spherical Catalyst Particle 3149.3.3 Extension to Other Reaction Orders and Particle Geometries 3159.3.4 The Effective Diffusion Coefficient 3189.3.4.1 Overview 3189.3.4.2 Mechanisms of Diffusion 319Configurational (Restricted) Diffusion 319Knudsen Diffusion (Gases) 320Bulk (Molecular) Diffusion 321The Transition Region 323Concentration Dependence 3239.3.4.3 The Effect of Pore Size 325Narrow Pore-Size Distribution 325Broad Pore-Size Distribution 3269.3.5 Use of the Effectiveness Factor in Reactor Design and Analysis 3269.3.6 Diagnosing Internal Transport Limitations in Experimental Studies 3289.3.6.1 Disguised Kinetics 328Effect of Concentration 329Effect of Temperature 329Effect of Particle Size 3309.3.6.2 The Weisz Modulus 3319.3.6.3 Diagnostic Experiments 3339.3.7 Internal Temperature Gradients 3359.3.8 Reaction Selectivity 3409.3.8.1 Parallel Reactions 3409.3.8.2 Independent Reactions 3429.3.8.3 Series Reactions 3449.4 External Transport 3469.4.1 General Analysis—Single Reaction 3469.4.1.1 Quantitative Descriptions of Mass and Heat Transport 347Mass Transfer 347Heat Transfer 3479.4.1.2 First-Order, Reaction in an Isothermal Catalyst Particle—TheConcept of a Controlling Step 348hkvlc=kc _ 1 349hkvlc=kc _ 1 3509.4.1.3 Effect of Temperature 3539.4.1.4 Temperature Difference Between Bulk Fluid and Catalyst Surface 3549.4.2 Diagnostic Experiments 3569.4.2.1 Fixed-Bed Reactor 3579.4.2.2 Other Reactors 3619.4.3 Calculations of External Transport 3629.4.3.1 Mass-Transfer Coefficients 3629.4.3.2 Different Definitions of the Mass-Transfer Coefficient 3659.4.3.3 Use of Correlations 3669.4.4 Reaction Selectivity 3689.5 Catalyst Design—Some Final Thoughts 368Summary of Important Concepts 369Problems 369Appendix 9-A Solution to Equation (9-4c) 37610. ‘Nonideal’ Reactors 37810.1 What Can Make a Reactor ‘‘Nonideal’’? 37810.1.1 What Makes PFRs and CSTRs ‘‘Ideal’’? 37810.1.2 Nonideal Reactors: Some Examples 37910.1.2.1 Tubular Reactor with Bypassing 37910.1.2.2 Stirred Reactor with Incomplete Mixing 38010.1.2.3 Laminar Flow Tubular Reactor (LFTR) 38010.2 Diagnosing and Characterizing Nonideal Flow 38110.2.1 Tracer Response Techniques 38110.2.2 Tracer Response Curves for Ideal Reactors(Qualitative Discussion) 38310.2.2.1 Ideal Plug-How Reactor 38310.2.2.2 Ideal Continuous Stirred-Tank Reactor 38410.2.3 Tracer Response Curves for Nonideal Reactors 38510.2.3.1 Laminar Flow Tubular Reactor 38510.2.3.2 Tubular Reactor with Bypassing 38510.2.3.3 Stirred Reactor with Incomplete Mixing 38610.3 Residence Time Distributions 38710.3.1 The Exit-Age Distribution Function, E(t) 38710.3.2 Obtaining the Exit-Age Distribution from Tracer Response Curves 38910.3.3 Other Residence Time Distribution Functions 39110.3.3.1 Cumulative Exit-Age Distribution Function, F(t) 39110.3.3.2 Relationship between F(t) and E(t) 39210.3.3.3 Internal-Age Distribution Function, I(t) 39210.3.4 Residence Time Distributions for Ideal Reactors 39310.3.4.1 Ideal Plug-Flow Reactor 39310.3.4.2 Ideal Continuous Stirred-Tank Reactor 39510.4 Estimating Reactor Performance from the Exit-Age Distribution—The Macrofluid Model 39710.4.1 The Macrofluid Model 39710.4.2 Predicting Reactor Behavior with the Macrofluid Model 39810.4.3 Using the Macrofluid Model to Calculate Limits of Performance 40310.5 Other Models for Nonideal Reactors 40410.5.1 Moments of Residence Time Distributions 40410.5.1.1 Definitions 40410.5.1.2 The First Moment of E(t) 405Average Residence Time 405Reactor Diagnosis 40610.5.1.3 The Second Moment of E(t)—Mixing 40710.5.1.4 Moments for Vessels in Series 40810.5.2 The Dispersion Model 41210.5.2.1 Overview 41210.5.2.2 The Reaction Rate Term 413Homogeneous Reaction 413Heterogeneous Catalytic Reaction 41510.5.2.3 Solutions to the Dispersion Model 415Rigorous 415Approximate (Small Values of D/uL) 41710.5.2.4 The Dispersion Number 417Estimating D/uL from Correlations 417Criterion for Negligible Dispersion 419Measurement of D/uL 42010.5.2.5 The Dispersion Model—Some Final Comments 42210.5.3 CSTRs-In-Series (CIS) Model 42210.5.3.1 Overview 42210.5.3.2 Determining the Value of ‘‘N’’ 42310.5.3.3 Calculating Reactor Performance 42410.5.4 Compartment Models 42610.5.4.1 Overview 42610.5.4.2 Compartment Models Based on CSTRs and PFRs 427Reactors in Parallel 427Reactors in Series 42910.5.4.3 Well-Mixed Stagnant Zones 43110.6 Concluding Remarks 434Summary of Important Concepts 435Problems 435Nomenclature 440Index 446