Chemical Reactions and Chemical Reactors

Transcription

1 Chemical Reactions and Chemical Reactors George W. Roberts North Carolina State University Department of Chemical and Biomolecular Engineering WILEY John Wiley & Sons, Inc. x

2 Contents 1. Reactions and Reaction Rates Introduction The Role of Chemical Reactions Chemical Kinetics Chemical Reactors Stoichiometric Notation Extent of Reaction and the Law of Dennite Proportions Stoichiometric Notation Multiple Reactions Definitions of Reaction Rate Species-Dependent Definition Single Fluid Phase Multiple Phases 9 Heterogeneous Catalysis 9 Other Cases Relationship between Reaction Rates of Various Species (Single Reaction) Multiple Reactions Species-Independent Definition 11 Summary of Important Concepts 12 Problems Reaction Rates Some Generalizations Rate Equations Five Generalizations An Important Exception 33 Summary of Important Concepts 33 Problems Ideal Reactors Generalized Material Balance Ideal Batch Reactor Continuous Reactors Ideal Continuous Stirred-Tank Reactor (CSTR) Ideal Continuous Plug-Flow Reactor (PFR) The Easy Way Choose a Different Control Volume The Hard Way Do the Triple Integration Graphical Interpretation of the Design Equations 54 Summary of Important Concepts 57 Problems 57 Appendix 3 Summary of Design Equations Sizing and Analysis of Ideal Reactors Homogeneous Reactions Batch Reactors Jumping Right In General Discussion: Constant-Volume Systems 68 Describing the Progress of a Reaction 68 Solving the Design Equation 71 v

3 fc General Discussion: Variable-Volume Systems Continuous Reactors Continuous Stirred-Tank Reactors (CSTRs) 78 Constant-Density Systems 78 Variable-Density (Variable-Volume) Systems Plug-Flow Reactors 82 Constant-Density (Constant-Volume) Systems 82 Variable-Density (Variable-Volume) Systems Graphical Solution of the CSTR Design Equation Biochemical Engineering Nomenclature Heterogeneous Catalytic Reactions (Introduction to Transport Effects) Systems of Continuous Reactors Reactors in Series CSTRs in Series PFRs in Series PFRs and CSTRs in Series Reactors in Parallel CSTRs in Parallel PFRs in Parallel Generalizations Recycle 111 Summary of Important Concepts 114 Problems 114 Appendix 4 Solution to Example 4-10: Three Equal-Volume CSTRs in Series Reaction Rate Fundamentals (Chemical Kinetics) Elementary Reactions Significance Definition Screening Criteria Sequences of Elementary Reactions Open Sequences Closed Sequences The Steady-State Approximation (SSA) Use of the Steady-State Approximation Kinetics and Mechanism The Long-Chain Approximation Closed Sequences with a Catalyst The Rate-Limiting Step (RLS) Approximation Vector Representation Use of the RLS Approximation Physical Interpretation of the Rate Equation Irreversibility Closing Comments 147 Summary of Important Concepts 147 Problems Analysis of Experimental Kinetic Data Experimental Data from Ideal Reactors Stirred-Tank Reactors (CSTRs) Plug-Flow Reactors Differential Plug-Flow Reactors 156

4 Contents vii Integral Plug-Flow Reactors Batch Reactors Differentiation of Data: An Illustration The Differential Method of Data Analysis Rate Equations Containing Only One Concentration Testing a Rate Equation Linearization of Langmuir-Hinshelwood/Michaelis-Menten Rate Equations Rate Equations Containing More Than One Concentration Testing the Arrhenius Relationship Nonlinear Regression The Integral Method of Data Analysis Using the Integral Method Linearization Comparison of Methods for Data Analysis Elementary Statistical Methods Fructose Isomerization First Hypothesis: First-Order Rate Equation 179 Residual Plots 179 Parity Plots Second Hypothesis: Michaelis-Menten Rate Equation 181 Constants in the Rate Equation: Error Analysis 184 Non-Linear Least Squares Rate Equations Containing More Than One Concentration (Reprise) 186 Summary of Important Concepts 187 Problems 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 Multiple Reactions Introduction Conversion, Selectivity, and Yield Classification of Reactions Parallel Reactions Independent Reactions Series (Consecutive) Reactions Mixed Series and Parallel Reactions Reactor Design and Analysis Overview Series (Consecutive) Reactions Qualitative Analysis Time-Independent Analysis Quantitative Analysis Series Reactions in a CSTR 218 Material Balance on A 219 Material Balance on R Parallel and Independent Reactions Qualitative Analysis 220 Effect of Temperature 221

5 viii Contents Effect of Reactant Concentrations Quantitative Analysis Mixed Series/Parallel Reactions Qualitative Analysis Quantitative Analysis 231 Summary of Important Concepts 232 Problems 232 Appendix 7-A Numerical Solution of Ordinary Differential Equations A.l Single, First-Order Ordinary Differential Equation A.2 Simultaneous, First-Order, Ordinary Differential Equations Use of the Energy Balance in Reactor Sizing and Analysis Introduction Macroscopic Energy Balances Generalized Macroscopic Energy Balance Single Reactors Reactors in Series Macroscopic Energy Balance for Flow Reactors (PFRs and CSTRs) Macroscopic Energy Balance for Batch Reactors Isothermal Reactors Adiabatic Reactors Exothermic Reactions Endothermic Reactions Adiabatic Temperature Change Graphical Analysis of Equilibrium-Limited Adiabatic Reactors Kinetically Limited Adiabatic Reactors (Batch and Plug Flow) Continuous Stirred-Tank Reactors (General Treatment) Simultaneous Solution of the Design Equation and the Energy Balance Multiple Steady States Reactor Stability Blowout and Hysteresis Blowout 279 Extension 281 Discussion Feed-Temperature Hysteresis Nonisothermal, Nonadiabatic Batch, and Plug-Flow Reactors General Remarks Nonadiabatic Batch Reactors Feed/Product (F/P) Heat Exchangers Qualitative Considerations Quantitative Analysis Energy Balance- Design Equation Energy Balance- Overall Solution Concluding Remarks 294 Summary of Important Concepts 295 -Reactor F/P Heat Exchang ;er Adjusting the Outlet Conversion Multiple Steady States

6 Contents ix Problems 296 Appendix 8-A Numerical Solution to Equation (8-26) 302 Appendix 8-B Calculation of G(T) and R(T) for "Blowout" Example Heterogeneous Catalysis Revisited Introduction The Structure of Heterogeneous Catalysts Overview Characterization of Catalyst Structure Basic Definitions Model of Catalyst Structure Internal Transport General Approach Single Reaction An Illustration: First-Order, Irreversible Reaction in an Isothermal, Spherical Catalyst Particle Extension to Other Reaction Orders and Particle Geometries The Effective Diffusion Coefficient Overview Mechanisms of Diffusion 319 Configurational (Restricted) Diffusion 319 Knudsen Diffusion (Gases) 320 Bulk (Molecular) Diffusion 321 The Transition Region 323 Concentration Dependence The Effect of Pore Size 325 Narrow Pore-Size Distribution 325 Broad Pore-Size Distribution Use of the Effectiveness Factor in Reactor Design and Analysis Diagnosing Internal Transport Limitations in Experimental Studies Disguised Kinetics 328 Effect of Concentration 329 Effect of Temperature 329 Effect of Particle Size The Weisz Modulus Diagnostic Experiments Internal Temperature Gradients Reaction Selectivity Parallel Reactions Independent Reactions Series Reactions External Transport General Analysis Single Reaction Quantitative Descriptions of Mass and Heat Transport 347 Mass Transfer 347 Heat Transfer First-Order, Reaction in an Isothermal Catalyst Particle The Concept of a Controlling Step 348 rik w l c /k c <C r)k v l c /k c > Effect of Temperature Temperature Difference Between Bulk Fluid and Catalyst Surface 354

7 x Contents Diagnostic Experiments Fixed-Bed Reactor Other Reactors Calculations of External Transport Mass-Transfer Coefficients Different Definitions of the Mass-Transfer Coefficient Use of Correlations Reaction Selectivity Catalyst Design Some Final Thoughts 368 Summary of Important Concepts 369 Problems 369 Appendix 9-A Solution to Equation (9-4c) "Nonideal" Reactors What Can Make a Reactor "Nonideal"? What Makes PFRs and CSTRs "Ideal"? Nonideal Reactors: Some Examples Tubulär Reactor with Bypassing Stirred Reactor with Incomplete Mixing Laminar Flow Tubulär Reactor (LFTR) Diagnosing and Characterizing Nonideal Flow Tracer Response Techniques Tracer Response Curves for Ideal Reactors (Qualitative Discussion) Ideal Plug-How Reactor Ideal Continuous Stirred-Tank Reactor Tracer Response Curves for Nonideal Reactors Laminar Flow Tubulär Reactor Tubulär Reactor with Bypassing Stirred Reactor with Incomplete Mixing Residence Time Distributions The Exit-Age Distribution Function, E(t) Obtaining the Exit-Age Distribution from Tracer Response Curves Other Residence Time Distribution Functions Cumulative Exit-Age Distribution Function, F(t) Relationship between F(t) and E(t) Internal-Age Distribution Function, I(t) Residence Time Distributions for Ideal Reactors Ideal Plug-Flow Reactor Ideal Continuous Stirred-Tank Reactor Estimating Reactor Performance from the Exit-Age Distribution The Macrofluid Model The Macrofluid Model Predicting Reactor Behavior with the Macrofluid Model Using the Macrofluid Model to Calculate Limits of Performance Other Models for Nonideal Reactors Moments of Residence Time Distributions Definitions The First Moment of E(t) 405 K

8 Contents xi Average Residence Time 405 Reactor Diagnosis The Second Moment of E(t) Mixing Moments for Vessels in Series The Dispersion Model Overview The Reaction Rate Term 413 Homogeneous Reaction 413 Heterogeneous Catalytic Reaction Solutions to the Dispersion Model 415 Rigorous 415 Approximate (Small Values of D/uL) The Dispersion Number 417 Estimating D/uL from Correlations 417 Criterion for Negligible Dispersion 419 Measurement of D/uL The Dispersion Model Some Final Comments CSTRs-In-Series (CIS) Model Overview Determining the Value of "AT Calculating Reactor Performance Compartment Models Overview Compartment Models Based on CSTRs and PFRs 427 Reactors in Parallel 427 Reactors in Series Well-Mixed Stagnant Zones Concluding Remarks 434 Summary of Important Concepts 435 Problems 435 Nomenclature 440 Index 446 <4