Chemical Reactor Design: Mathematical Modeling and Applications

A guide to the technical and calculation problems of chemical reactor analysis, scale-up, catalytic and biochemical reactor design Chemical Reactor Design offers a guide to the myriad aspects of reactor design including the use of numerical methods for solving engineering problems. The author - a noted expert on the topic - explores the use of transfer functions to study residence time distributions, convolution and deconvolution curves for reactor characterization, forced-unsteady-state-operation, scale-up of chemical reactors, industrial catalysis, design of multiphasic reactors, biochemical reactors design, as well as the design of multiphase gas-liquid-solid reactors. Chemical Reactor Design contains several examples of calculations and it gives special emphasis on the numerical solutions of differential equations by using the finite differences approximation, which offers the background information for understanding other more complex methods. The book is designed for the chemical engineering academic community and includes case studies on mathematical modeling by using of MatLab software. This important book: - Offers an up-to-date insight into the most important developments in the field of chemical, catalytic, and biochemical reactor engineering - Contains new aspects such as the use of numerical methods for solving engineering problems, transfer functions to study residence time distributions, and more - Includes illustrative case studies on MatLab approach, with emphasis on numerical solution of differential equations using the finite differences approximation Written for chemical engineers, mechanical engineers, chemists in industry, complex chemists, bioengineers, and process engineers, Chemical Reactor Design addresses the technical and calculation problems of chemical reactor analysis, scale-up, as well as catalytic and biochemical reactor design.

Table of Contents:
Preface xiii Nomenclature xv Part I Reactor Analysis, Design, and Scale-up 1 1 Nonideal Flow 3 1.1 Introduction 3 1.2 Residence Time Distribution (RTD) Function 3 1.2.1 Measurement of the RTD 4 1.2.1.1 Pulse Input 4 1.2.1.2 Step Input 6 1.2.2 RTD Concept in Heterogeneous Systems 7 1.2.3 Characteristics of RTD 8 1.2.3.1 Mean Residence Time 9 1.2.3.2 Second and Third Moments of the RTD 10 1.3 RTD in Ideal Reactors 11 1.3.1 RTD of the Batch and PFR Reactors 11 1.3.2 RTD of an ideal CSTR 12 1.3.3 RTD of PFR/CSTR in Series 13 1.4 Modeling the Reactor with the RTD 15 1.4.1 Models with One Parameter: Tanks-in-series and Dispersion Models 15 1.4.1.1 Tanks-in-series Model 15 1.4.1.2 The Dispersion Model 18 1.4.2 Models with Two Parameters 22 1.4.2.1 Two CSTR with Exchange of Matter 22 1.4.2.2 CSTR with Dead Volume and Short Circuit 23 1.5 Other Models of Real Reactors Using CSTR and PFR 25 Bibliography 32 2 Convolution and Deconvolution of Residence Time Distribution Curves in Reactors 35 2.1 Introduction 35 2.2 Convolution 35 2.2.1 Convolution Properties 37 2.2.2 Application to a Reactor RTD 38 2.2.3 Calculating Convolution Functions 38 2.3 Deconvolution 41 2.4 Computer Program Using Matlab® (Convolution) 44 2.5 Computer Program Using MATLAB (Deconvolution) 47 2.6 Convolution of Signals in Reactors Connected in Series 50 Bibliography 55 3 Use of Transfer Function for Convolution and Deconvolution of Complex Reactor Systems 57 3.1 Introduction 57 3.2 Definition and Properties of the Transfer Function 57 3.3 Laplace Transform 58 3.3.1 Laplace Transform of Some Important Functions for Reactor Characterization 58 3.3.1.1 Ramp Function 59 3.3.1.2 Sinusoidal Function 60 3.3.1.3 Pulse Function 60 3.3.1.4 Other Functions 61 3.4 Use of Laplace Transform in Chemical Reactor Characterization 62 3.4.1 Study of the RTD in the CSTR 62 3.4.2 Study of the RTD in the PFR 65 3.5 Complex Network of Ideal Reactors 66 3.5.1 Systems in Series 67 3.5.2 Systems in Parallel 69 3.5.3 Systems with Recycle 71 3.6 Transfer Function for the Dispersion Model 81 Bibliography 85 4 Partial Differential Equations in Reactor Design 87 4.1 Introduction 87 4.2 Classification of Partial Differential Equations 87 4.3 Approximations by Finite Differences 88 4.3.1 First-order Approximation 88 4.3.2 Approximation of Second Order 89 4.4 Approaching the Problem Using Finite Differences 91 4.4.1 Explicit Method 93 4.4.2 Initial and Boundary Conditions 94 4.4.3 Stability 96 4.4.3.1 Resolution of the Selected Problem and Programming 97 4.5 Other Applications of PDE – Numerical Methods 98 4.5.1 The RTD of a Complex System 98 4.5.1.1 Boundary Conditions for Partial Differential Equations 101 4.5.2 Concentration Profile in a Reactor in Which There is Flow and Dispersion 104 4.5.3 Reaction on a Catalytic Flat Wall 106 Bibliography 110 5 Unsteady State Regime Simulation in Reactor Design 111 5.1 Introduction 111 5.2 CSTR Working in Unsteady State 111 5.3 PFR Working in Dynamic Regime (No Dispersion) 113 5.4 PFR Working in Dynamic Regime (with Dispersion) 115 5.5 Multiple Steady States in CSTR with Exothermal Reaction 118 Bibliography 125 6 Scaling and Stability of Chemical Reactors 127 6.1 Introduction 127 6.2 Scaling the Batch Tank Stirred Reactor 129 6.2.1 Temperature Control. Heat Transmission 129 6.2.2 Example of Scaling a Batch and Semi-batch Reactor 130 6.3 Rapid Exothermic Reaction in a Tubular Reactor 136 6.3.1 Study of the Stability of the Process 139 Bibliography 155 7 Forced Unsteady State Operation of Chemical Reactors 157 7.1 Introduction 157 7.2 Objectives and Types of FUSO 158 7.3 Periodic Variation of the Input 159 7.3.1 Modes of Operation 160 7.3.2 Design Strategy 162 7.3.2.1 Choice of the Entrance to Manipulate 162 7.3.2.2 Choice of Handling 162 7.3.2.3 Choice of Mode 162 7.3.3 Periodic Variation of Concentration 163 7.3.4 Periodic Variation of the Flow 164 7.3.5 Periodic Variation in Temperature 165 7.4 Periodic Flow Reversal 165 7.4.1 Operation Design 167 7.5 Operation with Variable Volume (VVO) 168 7.6 Oscillating Pressure 169 Bibliography 170 Part II Catalytic, Multiphase and Biochemical Reactor Design 173 8 Industrial Catalysis 175 8.1 Introduction 175 8.1.1 Reactors for Solid-Catalyzed Reactions 175 8.1.2 Solid Catalysts (Supports) 178 8.1.2.1 Choice of Catalyst Support 180 8.1.2.2 Comparison and Uses of Supports 180 8.1.2.3 Silica, Alumina, and Mixtures 181 8.1.2.4 Zeolites 181 8.1.2.5 Activated Carbons (ACs) 183 8.2 Industrial Preparation of Catalysts 183 8.2.1 Structure of Commercial Catalysts 184 8.2.1.1 Synthesis of Zeolites 184 8.2.1.2 Manufacturing of the Catalytic Support 185 8.2.1.3 Impregnation with Active Metals 185 8.2.2 Key Definitions in Catalysts Performance 186 8.3 Main Catalytic Processes in Industry 188 8.3.1 Acid Catalysis 190 8.3.1.1 Fluid Catalytic Cracking 191 8.3.1.2 Ethylbenzene Production 193 8.3.2 Oxidation Catalysis 194 8.3.2.1 Ethylene Oxide Production from Ethylene 194 8.3.2.2 Acrylic Acid from Acrolein 196 8.3.3 Reduction Catalysis 196 8.3.3.1 Steam Reforming of Alcohols 197 8.3.3.2 Steam Reforming of Hydrocarbons (Methane) 199 8.3.3.3 Methanation: CO/H2 to Methane 199 8.3.4 Environmental Catalysis 200 8.3.4.1 Catalytic Reactions for the Removal of Pollutants in the Exhaust Gases 201 8.3.4.2 Components of the Cleaning Systems 202 8.3.4.3 Three-Way Catalyst 202 8.3.4.4 SCR Catalyst 203 8.3.4.5 Diesel Oxidation Catalyst (DOC) 204 8.3.4.6 Diesel Particulate Filter (DPF) Catalyst 204 Bibliography 205 9 Catalytic and Multiphase Reactor Design 207 9.1 Introduction 207 9.2 Rate Equation in Catalytic Systems 208 9.2.1 Steps in the Catalytic Reaction 214 9.3 Rate Equation When Chemical Step is Limiting Reaction Rate 215 9.3.1 Mechanisms of Catalysis 215 9.3.2 Theories about Adsorption 217 9.4 Rate Expression for External Diffusion as a Limiting Step 219 9.5 Reaction Rate When Internal Diffusion is Slow 221 9.5.1 First-order Kinetics in Flat Particles 222 9.5.2 First-order Kinetics in Other Geometries 225 9.5.3 Limits of Thiele Modulus and Weisz Modulus 229 9.6 Combination of Resistances 236 9.7 Monolithic Catalytic Reactors 237 9.8 Fluid–Fluid Reactions (Catalyzed and Noncatalyzed) 245 9.8.1 Transfer Models 245 9.8.2 Two-Film Theory 247 9.8.2.1 Case A: Instantaneous Reaction 247 9.8.2.2 Analysis of the Controlling Steps: The Hatta Modulus 250 9.8.2.3 Other Cases in Fluid–Fluid Reactions: The General Rate Equation 251 9.8.3 Gas–Liquid Reactions in Solid Catalysts. General Equation 256 9.8.3.1 Estimation of the Controlling Resistance in Multiphase Systems 258 9.8.3.2 General n-th Order Kinetics 260 9.9 Design of Multiphase Reactors 261 9.9.1 Types of Flow in Multiphase Reactors 261 9.9.2 Design Models for Flow in Multiphase Reactors 262 9.9.3 Case 1: Pure Absorption (No Reaction) 263 9.9.3.1 Situation 1: Gas and Liquid Phases in Plug Flow 263 9.9.3.2 Situation 2: Gas and Liquid Phases Completely Mixed 264 9.9.3.3 Situation 3: Gas Phase in Plug Flow. Liquid Phase Completely Mixed 264 9.9.4 Case 2: Systems with Reaction 265 9.9.4.1 Situation 1: Gas and Liquid Phases in Plug Flow 265 9.9.4.2 Situation 2. Gas and Liquid as Mixed Flow 268 9.9.4.3 Situation 3. Gas in Plug Flow. Liquid Mixed Flow 269 9.9.5 Case 3. Multiphase Reactors 269 Bibliography 287 10 Biochemical Reactors 289 10.1 Introduction 289 10.2 Enzymatic Catalysis 290 10.2.1 Characteristics of Enzymatic Catalysis. The Active Center 290 10.2.2 Kinetics of Enzymatic Reactions 292 10.2.2.1 Kinetics of Reactions with a Single Substrate. Michaelis–Menten Equation 292 10.2.2.2 Meaning of the Parameters of the Michaelis Equation 293 10.2.3 Enzymatic Reactions with Inhibition 295 10.2.4 Enzymatic Reactions with More than One Substrate 296 10.2.4.1 Case 1. Enzymatic Reactions with Two Substrates by Formation of a Ternary Complex 296 10.2.4.2 Case 2. Enzymatic Reactions with Two Substrates Without Formation of a Complex 300 10.2.4.3 Strategies to Distinguish the Previous Cases 301 10.3 Microbial Kinetics 304 10.3.1 Stoichiometry of the Microbian Growth 304 10.3.2 Stoichiometry of Product Formation 304 10.3.2.1 Yields 305 10.3.2.2 Theoretical Yield Obtained from Stoichiometric Coefficients 305 10.3.3 Cell Growth, Substrate Consumption, and Product Formation 305 10.3.3.1 Kinetics of Growth 306 10.3.3.2 Kinetics of Maintenance 307 10.4 Immobilization of Enzymes and Cells: Mass Transfer Effects 310 10.4.1 Effect of Limitation by Internal Diffusion 313 10.5 Bioreactors 314 10.5.1 Continuous Stirred Tank Bioreactor (CSTB) 316 10.5.1.1 Influence of the Dilution Rate. Calculation of the Bioreactor Wash 317 10.5.1.2 Cell Recirculation 319 10.5.2 Tubular Fermenters with Flocs 319 10.5.2.1 Tubular Fermenter with Recirculation and Monod Kinetics 320 10.5.3 Fed-batch Bioreactor 320 Bibliography 325 Index 327

About the Author :
Juan A. Conesa is Professor of Chemical Engineering at the University of Alicante. His research centers on thermal decomposition of waste, both in pyrolysis and in combustion. Since 2000, he has been working on the analysis and formation and destruction of dioxins and furans in thermal decomposition systems. He is the director of the research group "Waste, Energy, Environment and Nanotechnology (WEEN)" of the University of Alicante. He has been teaching Chemical Reactor Design for more than twenty years.