Chemical reactors 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. Cover......Page 1 Title Page......Page 5 Copyright......Page 6 Contents......Page 9 Preface......Page 15 Nomenclature......Page 17 Part I Reactor Analysis, Design, and Scale‐up......Page 21 1.2 Residence Time Distribution (RTD) Function......Page 23 1.2.1.1 Pulse Input......Page 24 1.2.1.2 Step Input......Page 26 1.2.2 RTD Concept in Heterogeneous Systems......Page 27 1.2.3 Characteristics of RTD......Page 28 1.2.3.1 Mean Residence Time......Page 29 1.2.3.2 Second and Third Moments of the RTD......Page 30 1.3.1 RTD of the Batch and PFR Reactors......Page 31 1.3.2 RTD of an ideal CSTR......Page 32 1.3.3 RTD of PFR/CSTR in Series......Page 33 1.4.1.1 Tanks‐in‐series Model......Page 35 1.4.1.2 The Dispersion Model......Page 38 1.4.2.1 Two CSTR with Exchange of Matter......Page 42 1.4.2.2 CSTR with Dead Volume and Short Circuit......Page 43 1.5 Other Models of Real Reactors Using CSTR and PFR......Page 45 Bibliography......Page 52 2.2 Convolution......Page 55 2.2.1 Convolution Properties......Page 57 2.2.3 Calculating Convolution Functions......Page 58 2.3 Deconvolution......Page 61 2.4 Computer Program Using Matlab® (Convolution)......Page 64 2.5 Computer Program Using MATLAB (Deconvolution)......Page 67 2.6 Convolution of Signals in Reactors Connected in Series......Page 70 Bibliography......Page 75 3.2 Definition and Properties of the Transfer Function......Page 77 3.3.1 Laplace Transform of Some Important Functions for Reactor Characterization......Page 78 3.3.1.1 Ramp Function......Page 79 3.3.1.3 Pulse Function......Page 80 3.3.1.4 Other Functions......Page 81 3.4.1 Study of the RTD in the CSTR......Page 82 3.4.2 Study of the RTD in the PFR......Page 85 3.5 Complex Network of Ideal Reactors......Page 86 3.5.1 Systems in Series......Page 87 3.5.2 Systems in Parallel......Page 89 3.5.3 Systems with Recycle......Page 91 3.6 Transfer Function for the Dispersion Model......Page 101 Bibliography......Page 105 4.2 Classification of Partial Differential Equations......Page 107 4.3.1 First‐order Approximation......Page 108 4.3.2 Approximation of Second Order......Page 109 4.4 Approaching the Problem Using Finite Differences......Page 111 4.4.1 Explicit Method......Page 113 4.4.2 Initial and Boundary Conditions......Page 114 4.4.3 Stability......Page 116 4.4.3.1 Resolution of the Selected Problem and Programming......Page 117 4.5.1 The RTD of a Complex System......Page 118 4.5.1.1 Boundary Conditions for Partial Differential Equations......Page 121 4.5.2 Concentration Profile in a Reactor in Which There Is Flow and Dispersion......Page 124 4.5.3 Reaction on a Catalytic Flat Wall......Page 126 Bibliography......Page 130 5.2 CSTR Working in Unsteady State......Page 131 5.3 PFR Working in Dynamic Regime (No Dispersion)......Page 133 5.4 PFR Working in Dynamic Regime (with Dispersion)......Page 135 5.5 Multiple Steady States in CSTR with Exothermal Reaction......Page 138 Bibliography......Page 145 6.1 Introduction......Page 147 6.2.1 Temperature Control. Heat Transmission......Page 149 6.2.2 Example of Scaling a Batch and Semi‐batch Reactor......Page 150 6.3 Rapid Exothermic Reaction in a Tubular Reactor......Page 156 6.3.1 Study of the Stability of the Process......Page 159 Bibliography......Page 175 7.1 Introduction......Page 177 7.2 Objectives and Types of FUSO......Page 178 7.3 Periodic Variation of the Input......Page 179 7.3.1 Modes of Operation......Page 180 7.3.2.3 Choice of Mode......Page 182 7.3.3 Periodic Variation of Concentration......Page 183 7.3.4 Periodic Variation of the Flow......Page 184 7.4 Periodic Flow Reversal......Page 185 7.4.1 Operation Design......Page 187 7.5 Operation with Variable Volume (VVO)......Page 188 7.6 Oscillating Pressure......Page 189 Bibliography......Page 190 Part II Catalytic, Multiphase and Biochemical Reactor Design......Page 193 8.1.1 Reactors for Solid‐Catalyzed Reactions......Page 195 8.1.2 Solid Catalysts (Supports)......Page 198 8.1.2.2 Comparison and Uses of Supports......Page 200 8.1.2.4 Zeolites......Page 201 8.2 Industrial Preparation of Catalysts......Page 203 8.2.1.1 Synthesis of Zeolites......Page 204 8.2.1.3 Impregnation with Active Metals......Page 205 8.2.2 Key Definitions in Catalysts Performance......Page 206 8.3 Main Catalytic Processes in Industry......Page 208 8.3.1 Acid Catalysis......Page 210 8.3.1.1 Fluid Catalytic Cracking......Page 211 8.3.1.2 Ethylbenzene Production......Page 213 8.3.2.1 Ethylene Oxide Production from Ethylene......Page 214 8.3.3 Reduction Catalysis......Page 216 8.3.3.1 Steam Reforming of Alcohols......Page 217 8.3.3.3 Methanation: CO/H2 to Methane......Page 219 8.3.4 Environmental Catalysis......Page 220 8.3.4.1 Catalytic Reactions for the Removal of Pollutants in the Exhaust Gases......Page 221 8.3.4.3 Three‐Way Catalyst......Page 222 8.3.4.4 SCR Catalyst......Page 223 8.3.4.6 Diesel Particulate Filter (DPF) Catalyst......Page 224 Bibliography......Page 225 9.1 Introduction......Page 227 9.2 Rate Equation in Catalytic Systems......Page 228 9.2.1 Steps in the Catalytic Reaction......Page 234 9.3.1 Mechanisms of Catalysis......Page 235 9.3.2 Theories About Adsorption......Page 237 9.4 Rate Expression for External Diffusion as a Limiting Step......Page 239 9.5 Reaction Rate When Internal Diffusion Is Slow......Page 241 9.5.1 First‐order Kinetics in Flat Particles......Page 242 9.5.2 First‐order Kinetics in Other Geometries......Page 245 9.5.3 Limits of Thiele Modulus and Weisz Modulus......Page 249 9.6 Combination of Resistances......Page 256 9.7 Monolithic Catalytic Reactors......Page 257 9.8.1 Transfer Models......Page 265 9.8.2.1 Case A: Instantaneous Reaction......Page 267 9.8.2.2 Analysis of the Controlling Steps: The Hatta Modulus......Page 270 9.8.2.3 Other Cases in Fluid–Fluid Reactions: The General Rate Equation......Page 271 9.8.3 Gas–Liquid Reactions in Solid Catalysts. General Equation......Page 276 9.8.3.1 Estimation of the Controlling Resistance in Multiphase Systems......Page 278 9.8.3.2 General n-th Order Kinetics......Page 280 9.9.1 Types of Flow in Multiphase Reactors......Page 281 9.9.2 Design Models for Flow in Multiphase Reactors......Page 282 9.9.3.1 Situation 1: Gas and Liquid Phases in Plug Flow......Page 283 9.9.3.3 Situation 3: Gas Phase in Plug Flow. Liquid Phase Completely Mixed......Page 284 9.9.4.1 Situation 1: Gas and Liquid Phases in Plug Flow......Page 285 9.9.4.2 Situation 2. Gas and Liquid as Mixed Flow......Page 288 9.9.5 Case 3. Multiphase Reactors......Page 289 Bibliography......Page 307 10.1 Introduction......Page 309 10.2.1 Characteristics of Enzymatic Catalysis. The Active Center......Page 310 10.2.2.1 Kinetics of Reactions with a Single Substrate. Michaelis–Menten Equation......Page 312 10.2.2.2 Meaning of the Parameters of the Michaelis Equation......Page 313 10.2.3 Enzymatic Reactions with Inhibition......Page 315 10.2.4.1 Case 1. Enzymatic Reactions with Two Substrates by Formation of a Ternary Complex......Page 316 10.2.4.2 Case 2. Enzymatic Reactions with Two Substrates Without Formation of a Complex......Page 320 10.2.4.3 Strategies to Distinguish the Previous Cases......Page 321 10.3.2 Stoichiometry of Product Formation......Page 324 10.3.3 Cell Growth, Substrate Consumption, and Product Formation......Page 325 10.3.3.1 Kinetics of Growth......Page 326 10.3.3.2 Kinetics of Maintenance......Page 327 10.4 Immobilization of Enzymes and Cells: Mass Transfer Effects......Page 330 10.4.1 Effect of Limitation by Internal Diffusion......Page 333 10.5 Bioreactors......Page 334 10.5.1 Continuous Stirred Tank Bioreactor (CSTB)......Page 336 10.5.1.1 Influence of the Dilution Rate. Calculation of the Bioreactor Wash......Page 337 10.5.2 Tubular Fermenters with Flocs......Page 339 10.5.3 Fed‐batch Bioreactor......Page 340 Bibliography......Page 345 Index......Page 347 EULA......Page 353 "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, bioengineers, and process engineers, Chemical Reactor Design: Mathematical Modeling and Applications addresses the technical and calculation problems of chemical reactor analysis, scale-up, as well as catalytic and biochemical reactor design."--Page 4 of cover Reactor Analysis, Design, and Scale-up. Nonideal Flow -- Convolution and Deconvolution of Residence Time Distribution Curves in Reactors -- Use of Transfer Function for Convolution and Deconvolution of Complex Reactor Systems -- Partial Differential Equations in Reactor Design -- Unsteady State Regime Simulation in Reactor Design -- Scaling and Stability of Chemical Reactors -- Forced Unsteady State Operation of Chemical Reactors -- Catalytic, Multiphase and Biochemical Reactor Design. Industrial Catalysis -- Catalytic and Multiphase Reactor Design -- Biochemical Reactors