chemical reactor design, optimization, and scaleup

CHEMICAL REACTOR DESIGN, OPTIMIZATION, AND SCALEUP CHEMICAL REACTOR DESIGN, OPTIMIZATION, AND SCALEUP E. Bruce Nauman Rensselaer Polytechnic Institute Troy, New York McGRAW-HILL New York Chicago San Francisco Lisbon London Madrid Mexico City Milan New Delhi San Juan Seoul Singapore Sydney Toronto Copyright © 2002 by The McGraw-Hill Companies. All rights reserved. Manufactured in the United States of America. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written permission of the publisher. 0-07-139558-X The material in this eBook also appears in the print version of this title: 0-07-137753-0. All trademarks are trademarks of their respective owners. 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McGraw-Hill and its licensors do not warrant or guarantee that the functions contained in the work will meet your requirements or that its operation will be uninterrupted or error free. Neither McGraw-Hill nor its licensors shall be liable to you or anyone else for any inaccuracy, error or omission, regardless of cause, in the work or for any damages resulting therefrom. McGraw-Hill has no responsibility for the content of any information accessed through the work. Under no circumstances shall McGraw-Hill and/or its licensors be liable for any indirect, incidental, special, punitive, consequential or similar damages that result from the use of or inability to use the work, even if any of them has been advised of the possibility of such damages. This limitation of liability shall apply to any claim or cause whatsoever whether such claim or cause arises in contract, tort or other- wise. DOI: 10.1036/007139558X abc McGraw-Hill CONTENTS Preface xiii Notation xv 1. Elementary Reactions in Ideal Reactors 1 1.1 Material Balances 1 1.2 Elementary Reactions 4 1.2.1 First-Order, Unimolecular Reactions 6 1.2.2 Second-Order Reactions, One Reactant 7 1.2.3 Second-Order Reactions, Two Reactants 7 1.2.4 Third-Order Reactions 7 1.3 Reaction Order and Mechanism 8 1.4 Ideal, Isothermal Reactors 10 1.4.1 The Ideal Batch Reactor 10 1.4.2 Piston Flow Reactors 17 1.4.3 Continuous-Flow Stirred Tanks 22 1.5 Mixing Times and Scaleup 25 1.6 Batch versus Flow, and Tank versus Tube 28 Problems 30 References 33 Suggestions for Further Reading 33 2. Multiple Reactions in Batch Reactors 35 2.1 Multiple and Nonelementary Reactions 35 2.2 Component Reaction Rates for Multiple Reactions 37 2.3 Multiple Reactions in Batch Reactors 38 2.4 Numerical Solutions to Sets of First-Order ODEs 39 2.5 Analytically Tractable Examples 46 2.5.1 The nth-Order Reaction 46 2.5.2 Consecutive First-Order Reactions, A !B !C ! 47 2.5.3 The Quasi-Steady State Hypothesis 49 2.5.4 Autocatalytic Reactions 54 2.6 Variable-Volume Batch Reactors 58 2.6.1 Systems with Constant Mass 58 2.6.2 Fed-Batch Reactors 64 2.7 Scaleup of Batch Reactions 65 2.8 Stoichiometry and Reaction Coordinates 66 2.8.1 Stoichiometry of Single Reactions 66 2.8.2 Stoichiometry of Multiple Reactions 67 Problems 71 v Copyright 2002 The McGraw-Hill Companies, Inc. Click Here for Terms of Use. Reference 76 Suggestions for Further Reading 76 Appendix 2: Numerical Solution of Ordinary Differential Equations 77 3. Isothermal Piston Flow Reactors 81 3.1 Piston Flow with Constant Mass Flow 82 3.1.1 Gas-Phase Reactions 86 3.1.2 Liquid-Phase Reactions 95 3.2 Scaleup of Tubular Reactions 99 3.2.1 Tubes in Parallel 100 3.2.2 Tubes in Series 101 3.2.3 Scaling with Geometric Similarity 106 3.2.4 Scaling with Constant Pressure Drop 108 3.2.5 Scaling Down 109 3.3 Transpired-Wall Reactors 111 Problems 113 Reference 116 Suggestions for Further Reading 116 4. Stirred Tanks and Reactor Combinations 117 4.1 Continuous-Flow Stirred Tank Reactors 117 4.2 The Method of False Transients 119 4.3 CSTRs with Variable Density 123 4.3.1 Liquid-Phase CSTRs 123 4.3.2 Computation Scheme for Variable-Density CSTRs 125 4.3.3 Gas-Phase CSTRs 127 4.4 Scaleup of Isothermal CSTRs 131 4.5 Combinations of Reactors 133 4.5.1 Series and Parallel Connections 134 4.5.2 Tanks in Series 137 4.5.3 Recycle Loops 139 Problems 142 Suggestions for Further Reading 146 Appendix 4: Solution of Simultaneous Algebraic Equations 146 A.4.1 Binary Searches 146 A.4.2 Multidimensional Newton’s Method 147 5. Thermal Effects and Energy Balances 151 5.1 Temperature Dependence of Reaction Rates 151 5.1.1 Arrhenius Temperature Dependence 151 5.1.2 Optimal Temperatures for Isothermal Reactors 154 5.2 The Energy Balance 158 5.2.1 Nonisothermal Batch Reactors 160 5.2.2 Nonisothermal Piston Flow 163 5.2.3 Nonisothermal CSTRs 167 vi CONTENTS 5.3 Scaleup of Nonisothermal Reactors 173 5.3.1 Avoiding Scaleup Problems 174 5.3.2 Scaling Up Stirred Tanks 176 5.3.3 Scaling Up Tubular Reactors 179 Problems 183 References 186 Suggestions for Further Reading 186 6. Design and Optimization Studies 187 6.1 A Consecutive Reaction Sequence 187 6.2 A Competitive Reaction Sequence 202 Problems 203 Suggestions for Further Reading 205 Appendix 6: Numerical Optimization Techniques 205 A.6.1 Random Searches 206 A.6.2 Golden Section Search 207 A.6.3 Sophisticated Methods for Parameter Optimization 207 A.6.4 Functional Optimization 207 7. Fitting Rate Data and Using Thermodynamics 209 7.1 Analysis of Rate Data 209 7.1.1 Least-Squares Analysis 210 7.1.2 Stirred Tanks and Differential Reactors 212 7.1.3 Batch and Piston Flow Reactors 218 7.1.4 Confounded Reactors 224 7.2 Thermodynamics of Chemical Reactions 226 7.2.1 Terms in the Energy Balance 227 7.2.2 Reaction Equilibria 234 Problems 250 References 254 Suggestions for Further Reading 255 Appendix 7.1: Linear Regression Analysis 255 Appendix 7.2: Code for Example 7.16 258 8. Real Tubular Reactors in Laminar Flow 263 8.1 Isothermal Laminar Flow with Negligible Diffusion 264 8.1.1 A Criterion for Neglecting Diffusion 265 8.1.2 Mixing-Cup Averages 265 8.1.3 A Preview of Residence Time Theory 268 8.2 Convective Diffusion of Mass 269 8.3 Numerical Solution Techniques 272 8.3.1 The Method of Lines 273 8.3.2 Euler’s Method 275 8.3.3 Accuracy and Stability 276 8.3.4 The Trapezoidal Rule 277 8.3.5 Use of Dimensionless Variables 282 CONTENTS vii 8.4 Slit Flow and Rectangular Coordinates 285 8.5 Special Velocity Profiles 287 8.5.1 Flat Velocity Profiles 287 8.5.2 Flow Between Moving Flat Plates 289 8.5.3 Motionless Mixers 290 8.6 Convective Diffusion of Heat 291 8.6.1 Dimensionless Equations for Heat Transfer 293 8.6.2 Optimal Wall Temperatures 296 8.7 Radial Variations in Viscosity 297 8.8 Radial Velocities 301 8.9 Variable Physical Properties 303 8.10 Scaleup of Laminar Flow Reactors 304 8.10.1 Isothermal Laminar Flow 304 8.10.2 Nonisothermal Laminar Flow 305 Problems 306 References 309 Suggestions for Further Reading 309 Appendix 8.1: The Convective Diffusion Equation 310 Appendix 8.2: Finite Difference Approximations 311 Appendix 8.3: Implicit Differencing Schemes 314 9. Real Tubular Reactors in Turbulent Flow 317 9.1 Packed-Bed Reactors 318 9.2 Turbulent Flow in Tubes 327 9.3 The Axial Dispersion Model 329 9.3.1 The Danckwerts Boundary Conditions 330 9.3.2 First-Order Reactions 332 9.3.3 Utility of the Axial Dispersion Model 334 9.4 Nonisothermal Axial Dispersion 336 9.5 Numerical Solutions to Two-Point Boundary Value Problems 337 9.6 Scaleup and Modeling Considerations 344 Problems 345 References 347 Suggestions for Further Reading 347 10. Heterogeneous Catalysis 349 10.1 Overview of Transport and Reaction Steps 351 10.2 Governing Equations for Transport and Reaction 352 10.3 Intrinsic Kinetics 354 10.3.1 Intrinsic Rate Expressions from Equality of Rates 355 10.3.2 Models Based on a Rate-Controlling Step 358 10.3.3 Recommended Models 361 10.4 Effectiveness Factors 362 10.4.1 Pore Diffusion 363 10.4.2 Film Mass Transfer 366 10.4.3 Nonisothermal Effectiveness 367 10.4.4 Deactivation 369 viii CONTENTS 10.5 Experimental Determination of Intrinsic Kinetics 371 10.6 Unsteady Operation and Surface Inventories 375 Problems 376 References 380 Suggestions for Further Reading 380 11. Multiphase Reactors 381 11.1 Gas–Liquid and Liquid–Liquid Reactors 381 11.1.1 Two-Phase Stirred Tank Reactors 382 11.1.2 Measurement of Mass Transfer Coefficients 397 11.1.3 Fluid–Fluid Contacting in Piston Flow 401 11.1.4 Other Mixing Combinations 406 11.1.5 Prediction of Mass Transfer Coefficients 409 11.2 Three-Phase Reactors 412 11.2.1 Trickle-Bed Reactors 412 11.2.2 Gas-Fed Slurry Reactors 413 11.3 Moving Solids Reactors 413 11.3.1 Bubbling Fluidization 416 11.3.2 Fast Fluidization 417 11.3.3 Spouted Beds 417 11.4 Noncatalytic Fluid–Solid Reactions 418 11.5 Reaction Engineering for Nanotechnology 424 11.5.1 Microelectronics 424 11.5.2 Chemical Vapor Deposition 426 11.5.3 Self-Assembly 427 11.6 Scaleup of Multiphase Reactors 427 11.6.1 Gas–Liquid Reactors 427 11.6.2 Gas–Moving-Solids Reactors 430 Problems 430 References 432 Suggestions for Further Reading 432 12. Biochemical Reaction Engineering 435 12.1 Enzyme Catalysis 436 12.1.1 Michaelis-Menten and Similar Kinetics 436 12.1.2 Inhibition, Activation, and Deactivation 440 12.1.3 Immobilized Enzymes 441 12.1.4 Reactor Design for Enzyme Catalysis 443 12.2 Cell Culture 446 12.2.1 Growth Dynamics 448 12.2.2 Reactors for Freely Suspended Cells 452 12.2.3 Immobilized Cells 459 Problems 459 References 461 Suggestions for Further Reading 461 CONTENTS ix 13. Polymer Reaction Engineering 463 13.1 Polymerization Reactions 463 13.1.1 Step-Growth Polymerizations 464 13.1.2 Chain-Growth Polymerizations 467 13.2 Molecular Weight Distributions 470 13.2.1 Distribution Functions and Moments 470 13.2.2 Addition Rules for Molecular Weight 472 13.2.3 Molecular Weight Measurements 472 13.3 Kinetics of Condensation Polymerizations 473 13.3.1 Conversion 473 13.3.2 Number and Weight Average Chain Lengths 474 13.3.3 Molecular Weight Distribution Functions 475 13.4 Kinetics of Addition Polymerizations 478 13.4.1 Living Polymers 479 13.4.2 Free-Radical Polymerizations 482 13.4.3 Transition Metal Catalysis 487 13.4.4 Vinyl Copolymerizations 487 13.5 Polymerization Reactors 492 13.5.1 Stirred Tanks with a Continuous Polymer Phase 492 13.5.2 Tubular Reactors with a Continuous Polymer Phase 496 13.5.3 Suspending-Phase Polymerizations 501 13.6 Scaleup Considerations 503 13.6.1 Binary Polycondensations 504 13.6.2 Self-Condensing Polycondensations 504 13.6.3 Living Addition Polymerizations 504 13.6.4 Vinyl Addition Polymerizations 505 Problems 505 Reference 507 Suggestions for Further Reading 507 Appendix 13.1: Lumped Parameter Model of a Tubular Polymerizer 508 Appendix 13.2: Variable-Viscosity Model for a Polycondensation in a Tubular Reactor 512 14. Unsteady Reactors 517 14.1 Unsteady Stirred Tanks 517 14.1.1 Transients in Isothermal CSTRs 519 14.1.2 Nonisothermal Stirred Tank Reactors 527 14.2 Unsteady Piston Flow 531 14.3 Unsteady Convective Diffusion 534 Problems 534 References 538 Suggestions for Further Reading 538 15. Residence Time Distributions 539 15.1 Residence Time Theory 540 x CONTENTS 15.1.1 Inert Tracer Experiments 540 15.1.2 Means and Moments 543 15.2 Residence Time Models 545 15.2.1 Ideal Reactors and Reactor Combinations 545 15.2.2 Hydrodynamic Models 555 15.3 Reaction Yields 561 15.3.1 First-Order Reactions 562 15.3.2 Other Reactions 564 15.4 Extensions of Residence Time Theory 574 15.4.1 Unsteady Flow Systems 574 15.4.2 Contact Time Distributions 575 15.4.3 Thermal Times 575 15.5 Scaleup Considerations 576 Problems 577 References 580 Suggestions for Further Reading 580 Index 581 CONTENTS xi [...]... IN IDEAL REACTORS Material and energy balances are the heart of chemical engineering Combine them with chemical kinetics and they are the heart of chemical reaction engineering Add transport phenomena and you have the intellectual basis for chemical reactor design This chapter begins the study of chemical reactor design by combining material balances with kinetic expressions for elementary chemical. .. Use 2 CHEMICAL REACTOR DESIGN, OPTIMIZATION, AND SCALEUP Volume = V Total mass output = Qout ρout Average density = ρ ˆ Accumulation = d(Vρ) ˆ dt Total mass input = Qin ρin FIGURE 1.1 Control volume for total mass balance where Qmass is the mass flow rate and I is the mass inventory in the system We often write this equation using volumetric flow rates and volumes rather than mass flow rates and mass...PREFACE This book is an outgrowth of an earlier book, Chemical Reactor Design, John Wiley & Sons, 1987 The title is different and reflects a new emphasis on optimization and particularly on scaleup, a topic rarely covered in undergraduate or graduate education but of paramount importance to many practicing engineers The treatment of biochemical and polymer reaction engineering is also more extensive... are then solved for several simple but important types of chemical reactors More complicated reactions and more complicated reactors are treated in subsequent chapters, but the real core of chemical reactor design is here in Chapter 1 Master it, and the rest will be easy 1.1 MATERIAL BALANCES Consider any region of space that has a finite volume and prescribed boundaries that unambiguously separate the... Numerical solutions are needed for most practical problems in chemical reactor design, but sophisticated numerical techniques are rarely necessary given the speed of modern computers The goal is to make the techniques understandable and easily accessible and to allow continued focus on the chemistry and physics of the problem Computational elegance and efficiency are gladly sacrificed for simplicity Too many... spot, you will find a reasonably comprehensive treatment of reactor design, optimization and scaleup Spend a few minutes becoming comfortable with the notation (anyone bothering to read a preface obviously has the inclination), and you will find practical answers to many design problems The book is also useful for undergraduate and graduate courses in chemical engineering Some faults of the old book have... step time Interfacial area per tray Specific heat difference for reaction Standard free energy of formation Free energy of reaction Standard free energy of reaction Standard heat of formation Heat of reaction Standard heat of reaction Heat of reaction for reaction I Implied summation of heats of reaction Pressure drop Range of random change Difference in partial pressures across the interface Radial step... contact area per unit length of reactor 0 0 7.3 7.3 1.29 7.3 7.3 1.29 11.4 1.3 5.22 11.27 Abbreviations CSTR CVD MWD NEMS NPV ODE PD PDE PFR RND RTD Continuous-flow stirred tank reactor Chemical vapor deposition Molecular weight distribution Nanoelectromechanical system Net present value Ordinary differential equation Polydispersity Partial differential equation Piston flow reactor Random number with range 0... properties in CSTRs and PFRs Random searches are used for optimization and least-squares analysis These are appallingly inefficient but marvelously robust and easy to implement The method of lines is used for solving the partial differential equations that govern real tubular reactors and packed beds This technique is adequate for most problems in reactor design xiii Copyright 2002 The McGraw-Hill Companies, Inc... Vector of component concentrations (N Â 1) Concentration just before the entrance of an open reactor Concentration just after the entrance of an open reactor Concentration just before the exit of an open reactor Concentration just after the exit of an open reactor Concentration of component A in an unsteady tubular reactor Auxiliary variable, da/dz , used to convert secondorder ODEs to first order Dimensionless . CHEMICAL REACTOR DESIGN, OPTIMIZATION, AND SCALEUP CHEMICAL REACTOR DESIGN, OPTIMIZATION, AND SCALEUP E. Bruce Nauman Rensselaer Polytechnic Institute Troy,. Reaction Order and Mechanism 8 1.4 Ideal, Isothermal Reactors 10 1.4.1 The Ideal Batch Reactor 10 1.4.2 Piston Flow Reactors 17 1.4.3 Continuous-Flow Stirred Tanks 22 1.5 Mixing Times and Scaleup 25 1.6. Least-Squares Analysis 210 7.1.2 Stirred Tanks and Differential Reactors 212 7.1.3 Batch and Piston Flow Reactors 218 7.1.4 Confounded Reactors 224 7.2 Thermodynamics of Chemical Reactions 226 7.2.1 Terms