Chemical Reactor flnolysis

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1 Introduction to Chemical Reactor flnolysis SECOND EDITION R.E. Hayes J.P. Mmbaga ^ ^ T..,«,,.«M.iirti,im.' TECHNISCHE INFORMATIONSBIBLIOTHEK UNWERSITATSBIBLIOTHEK HANNOVER i ii ii 1 J /0\ CRC Press ycf* J Taylor & Francis Group ^ S Boca Raton London NewYork CRC Press is an imprint of the Taylor & Francis Croup, an Informa business

2 Contents About the Book Preface Acknowledgments Recommended Reading Nomenclature Authors xvii xix xxi xxiii xxvii xxxi 1 Introduction Process Development Basic Building Blocks of Chemical Reaction Engineering Outline of the Book Introduction to Chemical Reactions Rate of Reaction Classification and Types of Reactors Batch and Semibatch Operation Batch Reactor Semibatch Reactor Continuous Flow Reactors Perfectly Mixed Flow Reactor Plug Flow Reactor Classification by Number of Phases Catalytic Reactors Reactor Performance Measures Conversion Space Velocity Liquid Hourly Space Velocity Gas Hourly Space Velocity Space Time Residence Time Introduction to Rate Function Transport Phenomena in Reactors Material Balances Energy Balance Momentum Balances Coupling of Material, Energy, and Momentum Balances Numerical Methods 17 References 17 2 Thermodynamics of Chemical Reactions Basic Definitions Open and Closed Systems Thermodynamic Standard State Equations of State Ideal Gas Law 20 vii

3 viii Contents Nonideal Gas Behavior Multicomponent Mixtures Energy Changes in Systems Enthalpy Energy Change Resulting from Temperature Change: Heat Capacity Enthalpy Change with Pressure Energy Change owing to Composition Change: Heat of Reaction Computing the Enthalpy of Reaction at Other Temperatures Generalized Stoichiometric Coefficient Chemical Reaction Equilibrium Derivation of Equilibrium Constant Computing Standard Free Energy Change Temperature Dependence of Equilibrium Constant Computing Equilibrium Composition Liquid-Phase Reactions Gas-Phase Reactions Solid-Phase Reactions Equilibrium Compositions with Multiple Reactions Summary 45 Problems 45 References 47 3 Mole Balances in Ideal Reactors General Mole Balance Equation Perfectly Mixed Batch Reactor Constant-Volume Batch Reactor Variable-Volume Batch Reactor Plug Flow Reactor Plug Flow Assumptions Plug Flow Mole Balance Space Time in Plug Flow Reactor Mean Residence Time in Plug Flow Reactor Continuous Stirred Tank Reactor Space Time and Mean Residence Time in CSTR Summary of Mole Balance Equations for Three Ideal Reactors Reaction Rate in Terms of Catalyst Mass Comparison ofpfr and CSTR Performance Multiple Reactions Series Reactions Parallel Reactions Series-Parallel Reactions Multiple-Reactor Systems Plug Flow Reactors in Series Plug Flow Reactors in Parallel CSTR in Parallel CSTR in Series Minimum Total Reactor Volume for CSTR in Series 87

4 Contents ix CSTR-PFR in Series Reactors with Side Streams Further Thoughts on Defining Conversion Transient Reactor Operation Transient Plug Flow Reactor Single Transient CSTR Transient CSTR with Constant Volume Transient CSTR with Variable Volume: Semibatch Operation Transient CSTR in Series: Constant Volume Summary 112 Problems Energy Balances in Ideal Reactors Influence of Temperature on Reactor Operation Temperature Dependence of Reaction Rate Constants Effect of Temperature on Equilibrium Conversion Energy Balance for Ideal Reactors General Energy Balance Batch Reactor Constant-Volume Batch Reactor Relationship between AUR and AHR Assuming a Constant Value for Heat Capacity External Heat Transfer in CVBR Adiabatic Temperature Change for CVBR Energy Balance for CVBR Containing a Catalyst Multiple Reactions in a Batch Reactor Variable-Volume Batch Reactor Plug Flow Reactor Basic Energy Balance Equation Use of Average Heat Capacity Temperature and Concentration Profiles as Function of Reactor Length Adiabatic Operation of PFR: Adiabatic Reaction Line External Heat Transfer to PFR Multiple Reactions in PFR : Parametric Sensitivity of PFR Equilibrium Effects in PFR Equilibrium Effects in Endothermic Reactions Equilibrium Effects in Exothermic Reactions Multibed Adiabatic Reactors for Equilibrium Limited Reactions Continuous Stirred Tank Reactor Steady-State CSTR: Basic Energy Balance Adiabatic Operation of CSTR: Adiabatic Reaction Line External Heat Exchange in CSTR Multiple Reactions in CSTR Multiple Steady States in a CSTR 187

5 X Contents Transient CSTR with Energy Effects: Constant-Volume Case Semibatch Operation Summary 208 Problems 208 References Chemical Kinetics for Homogeneous Reactions General Nature of Rate Functions Reaction Mechanism Rate Expressions for Elementary Reactions Rate Expressions for Nonelementary Reactions Theoretical Analysis of Reaction Rate Collision Theory Absolute Reaction Rate Theory Temperature Dependence of Rate Constant Rate Equations for Nonelementary Reactions Unimolecular Reactions Lindeman Mechanism Steady-State Hypothesis for Lindeman Mechanism Rice-Herzfeld Mechanisms Complex Gas-Phase Reactions Rate-Determining Step Method for Deriving Rate Expressions Mechanisms and Models Experimental Methods in Rate Data Collection and Analysis Rate Data in Constant-Volume Batch Reactor Differential Method of Analysis of CVBR Data Finite Difference Formulae Fitting a Curve to the Data Determining Form of Rate Expression Power Law Models Complex Rate Expressions Integral Method of Analysis of CVBR Data Power Law Kinetics Complex Kinetics Temperature Dependence of Rate Constants Methods of Isolation and Excess Method of Isolation Method of Excess Using a CSTR to Collect Rate Data Using PFR to Collect Rate Data Summary 255 Problems Nonideal Reactor Analysis Causes of Nonideal Reactor Behavior Nonideal Behavior in CSTR Deviations from Plug Flow Performance Deviations from Perfect Mixing in Batch and Fed Batch Reactors Residence Time and Mixing 263

6 Contents xi 6.3 RTD Function Measurement of RTD RTD Function Cumulative Distribution and Washout Functions Determination offif) from Pulse Input Determination of f(t) from Step Change Means and Moments Normalized RTD Functions RTD in Ideal Reactors RTD in Perfectly Mixed CSTR RTD in Plug Flow System Modeling Multiple RTD 276 Vessel Models Parallel Plug Flow Reactors Fractional Tubularity Model Tanks-in-Series Model Extensions of Tanks in Series: Gamma Function and Fractional Tanks Backflow, Crossflow, and Side Capacity Models Theoretical Model for Laminar Flow Tubular Reactor Dispersion Model for Tubular Reactors Convection-Diffusion Equation for Tubular Reactors Taylor-Aris Dispersion Summary of RTD Mixing in Chemical Reactors Laminar and Turbulent Mixing Mixing Process: Micromixing and Macromixing Macromixing and Macrofluids 299 and Microfluids Micromixing Mixing and RTD 300 Tank Reactor Segregated Conversion in Segregated Tank Reactor 301 Flow Model General Segregated Maximum Mixedness Model Bounding Mixing Regions Summary 308 Problems 309 References Introduction to Catalysis Origins of Catalysis: Historical Perspectives Definitions and Fundamental Concepts Classification by Number of Phases Catalyst Activity and Active Sites Adsorption Selectivity and Functionality Thermodynamics Catalyst Types and Basic Structure Basic Catalyst Structure 317

7 xii Contents Supported Catalysts Metal Catalysts Deactivation Classification of Vapor-Phase Reactions Acid-Catalyzed Reactions Catalytic Cracking Alkylation Isomerization Polymerization Hydrogen Transfer Hydrogenation-Dehydrogenation Carbon Bond Saturation or Reverse Hydrogenation Dehydrogenation of Oxyorganic Compounds without of Aromatics and Aromatization 322 Water Removal Hydrogenolysis of Carbon-Oxygen or Nitrogen- Oxygen Bonds 323 of Oxides of Carbon Hydrogenolysis Hydrodesulfurization Ammonia Synthesis Oxidation Oxygen Addition Reactions Oxygenolysis Hydration and Dehydration Dehydration-Dehydrogenation Isotope Exchange Miscellaneous Basic Steps in Heterogeneous Catalytic Reactions Introduction to Catalytic Reactors Fixed Bed Reactor Fluidized Bed Reactor Reactors for Liquids and Gas/Liquid Mixtures Trickle Bed Reactor Slurry Reactor ' Summary Kinetics of Catalytic Reactions Adsorption Physical Adsorption Chemisorption Differentiating Chemical and Physical Adsorption Energetics of Adsorption Activated Chemisorption Nonactivated Chemisorption Endothermic Adsorption Dual Site Adsorption Equilibrium Adsorption Adsorption Isotherms Models for Adsorption Isotherms 338

8 Contents xiii Adsorption Isobars Adsorption Isoteres Heat of Adsorption Langmuir Adsorption Model: Detailed Consideration The Langmuir Model: Single-Component Systems Langmuir Model: Dissociative Chemisorption Langmuir Model: Multicomponent Systems, Single Site Type Models Accounting for Variable Heat of Adsorption Rate Expressions for Catalytic Reactions Langmuir-Hinshelwood-Hougen-Watson Rate Equations General Form of LHHW Reaction Models Models for Oxidation Reactions Mechanisms and Models Summary 367 Problems 367 Reference Transport Processes in Catalysis Diffusion in Bulk Phase Basics of Bulk Diffusion: Diffusion Coefficient Calculating Molecular Diffusion Coefficients in Binary Systems Total Molar Diffusive Flux in Binary System Diffusion in Multicomponent Mixtures: Generalized Pick's Law Multicomponent Diffusion in Dilute Mixtures External Mass and Heat Transfer Effects Mass and Heat Transfer Coefficients Effect of External Mass Transfer on Observed Reaction Rate Combined Heat and Mass Transfer Effect of External Transport on Selectivity Isothermal Series Reaction Parallel Isothermal Reactions Nonisothermal Reactions Diffusion in Porous Catalysts Diffusion in Catalyst Pores Effective Diffusivity Parallel Pore Model Random Pore Model Diffusion with Reaction in Porous Catalysts Effectiveness Factor Effectiveness Factor for Isothermal Flat Plate Thiele Modulus for First-Order Reaction Effectiveness Factor for First-Order Reaction in Flat Plate Asymptotic Solutions for Effectiveness Factor Effectiveness Factor for Isothermal Spherical Catalyst Pellet Effectiveness Factor for Isothermal Cylindrical Catalyst Pellet Generalized Thiele Modulus and Effectiveness Factors Effectiveness Factors for Non-First-Order Reactions 403

9 xiv Contents Nonisothermal Effectiveness Factors Solving Coupled Mole and Energy Balance Equations Solution Algorithm Using Only Initial Value Problems Effect of Internal Diffusion Limitation on Observed Kinetics Combined Internal and External Mass Transfer Resistance Summary 416 Problems 416 References Analysis of Catalytic Reactors Packed-Bed Reactor: Introduction and Overview Conservation Equations for Packed Beds Momentum Balance in Packed Beds Velocities in Packed Beds One-Dimensional Flow Ergun Equation Deriving the Ergun Equation Continuity Equation Mole and Energy Balances in Packed Beds One-Dimensional Steady-State Plug Flow Models Pseudo-Homogeneous Model for an Adiabatic-Packed Bed Steady-State Mole Balance 433 Equation Steady-State Energy Balance Equation Heterogeneous Model for an Adiabatic-Packed Bed Steady-State Mole Balance Equation for the Fluid Steady-State Mole Balance Equation for the Solid Catalyst Steady-State Energy Balance Equation for the Fluid Steady-State Energy Balance Equation for Pseudo-Homogeneous the Solid Catalyst 438 Model for a Nonadiabatic-Packed Bed Heterogeneous Model for a Nonadiabatic-Packed Bed Heat Transfer Coefficient for Nonadiabatic Reactors One-Dimensional Steady-State Axial Dispersion Models Pseudo-Homogeneous Axial Dispersion Model Mole Balance Equation Energy Balance Equation Boundary Conditions for the ID Axial Dispersion Model Heterogeneous Axial Dispersion Model Mole Balance Equations Energy Balance Equation in the Fluid Phase Energy Balance Equation for the Solid Phase Boundary Conditions Two-Dimensional Steady-State Models Pseudo-Homogeneous 2D Model Fluid Transport Mechanisms Are Dispersion Only Mole Balance Equation Energy Balance Equation Boundary Conditions Heterogeneous 2D Model 448" 447

10 Contents xv Mole Balance Equation for the Fluid Mole Balance Equation for the Solid Energy Balance Equation for the Fluid Energy Balance Equation for the Solid Boundary Conditions Transient Packed-Bed Models One-Dimensional Reactor: Pseudo-Homogeneous Case One-Dimensional Reactor: Heterogeneous Case Two-Dimensional Reactor: Pseudo-Homogeneous Case Two-Dimensional Reactor: Heterogeneous Case Transport Properties in Packed Beds Fluid/Solid Mass and Heat Transfer Coefficients Dispersion Coefficients Thermal Conductivity Bed-to-Wall Heat Transfer Coefficients Autothermal Operation of Packed Beds Fluidized-Bed Reactors Minimum Fluidization Velocity Entrainment Velocity Fluid-Bed Reactor Modeling Metal Gauze Reactors Counter Diffusive Reactor: Radiant Heaters Monolith Reactors Structure and Properties of Monoliths Analysis of Gas Phase Monolith Reactors Complete Converter Models Single Channel Models A ID Single Channel Monolith Model Reactors for Gas-Liquid-Solid Systems Slurry Reactors Trickle-Bed Reactors Summary Problems References Experimental Methods in Catalysis Kinetic Investigations Laboratory Reactor Types Experimental Tubular Reactor Isothermal Conditions Maintained in Reactor Adiabatic Operation Differential Operation Integral Operation Testing for Mass Transfer Limitations CSTR-Like Reactors Berty Reactors Carberry (Spinning Basket) Reactor Transport Limitations in Catalytic CSTR External Recycle Reactor

11 xvi Contents 11.2 Measuring Physical Properties * Calculation of Surface Area Pore Volume and Pore Size Distribution Pore Size Distribution from Capillary Condensation Data Pore Size Distribution from Mercury Porosimetry Representations of Pore Size Distribution Effective Diffusivity Electron Microscopy Transmission Electron Microscopy Scanning Electron Microscopy Surface Science Studies Summary 505 Problems 505 References 506 Appendix 1: Numerical Methods 507 Al.l Nonlinear Algebraic Equations 507 Al Convergence A1.2 Linear Algebraic Equations 510 Al.2.1 Gauss Elimination Method 511 Al.2.2 Jacobi and Gauss Seidel Iterative Methods 512 A1.3 Ordinary Differential 512 Equations Al.3.1 Single Differential Equation 512 Al.3.2 Euler's Method 513 Al.3.3 Runge-Kutta Methods 513 Al First-Order and Second Runge-Kutta Methods 514 Al Classical Fourth-Order Runge-Kutta Method 514 Al Order and Stability Function 515 Al Implicit RK Methods 516 Al.3.4 Linear Multistep Methods 516 Al Backward Differentiation Formula Methods 516 Al Predictor-Corrector Methods: Milne Method 517 Al.4 Numerical Integration 518 Al.4.1 Trapezoidal Rule 518 Al.4.2 Simpson's One-Third Rule 519 Al.4.3 Simpson's Three-Eighth Rule 519 Al.4.4 Assessment of Accuracy of above Methods 519 Al.5 Numerical Differentiation 520 A1.6 Partial Differential Equations Appendix 2: Thermodynamic Data 523 Reference 524 Appendix 3: Useful Integrals 525 Appendix 4: Numerical Software 527 A4.1 POLYMATH 527 A4.2 MATLAB 527 A4.3 COMSOL Multiphysics Index 529'

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