Introduction to chemical engineering computing

352 Pages·2006·6.02 MB·English

by  Bruce A. Finlayson.

INTRODUCTION TO
CHEMICAL ENGINEERING
COMPUTING
BRUCE A. FINLAYSON, PH.D.
University of Washington
Seattle, Washington
A JOHN WILEY & SONS, INC., PUBLICATION
Microsoft product screen shots reprinted with permission from Microsoft Corporation. Microsoft Excel is either
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MATLAB is a trademark of The Math Works, Inc. and is used with permission. The Math Works does not
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warrant the accuracy of the text or exercises in this book. This book’s use or discussion of MATLAB
software or related products does not constitute endorsement or sponsorship by The Math Works of a
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particular pedagogical approach or particular use of the MATLAB software.
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FEMLAB is a trademark of COMSOL AB. COMSOL product screen shots reprinted with permission from
COMSOL AB.
Copyright # 2006 by John Wiley & Sons, Inc. All rights reserved
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Library of Congress Cataloging-in-Publication Data:
Finlayson, Bruce A.
Introduction to chemical engineering computing / Bruce A. Finlayson.
p. cm.
Includes index.
ISBN-13: 978-0-471-74062-9 (cloth)
ISBN-10: 0-471-74062-4 (cloth)
1. Chemical engineering- -Data processing. I. Title.
TP184.F56 2005
0
660 .0285- -dc22
2005019351
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1
CONTENTS
Preface xiii
1 Introduction 1
Organization, 2
Algebraic Equations, 2
Process Simulation, 2
Differential Equations, 3
Appendices, 4
2 Equations of State 5
Equations of State – Mathematical Formulation, 6
Solving Equations of State Using Excel (single equation in one unknown), 8
Solution Using ‘Goal Seek’, 8
Solution Using Solver, 9
Example of a Chemical Engineering Problem Solved Using ‘Goal Seek’, 9
Solving Equations of State Using MATLAB (single equation in one unknown), 10
Example of a Chemical Engineering Problem Solved Using MATLAB, 12
Another Example of a Chemical Engineering Problem Solved Using
MATLAB, 13
Equations of State with Aspen Plus, 16
Example, 16
Specific Volume of a Mixture, 18
Chapter Summary, 22
Problems, 22
3 Vapor–Liquid Equilibrium 25
Flash and Phase Separation, 25
v
vi CONTENTS
Isothermal Flash – Development of Equations, 26
Example Using Excel, 28
Thermodynamic Parameters, 29
Example Using MATLAB, 30
Example Using Aspen Plus, 31
Nonideal Liquids – Test of Thermodynamic Model, 35
Chapter Summary, 37
Problems, 37
4 Chemical Reaction Equilibrium 41
Chemical Equilibrium Expression, 42
Example of Hydrogen for Fuel Cells, 43
Solution Using Excel, 44
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Solution Using MATLAB , 45
Chemical Equilibria with Two or More Equations, 47
Multiple Equations, Few Unknowns Using MATLAB, 48
Method 1 Using the ‘fsolve’ Command, 48
Method 2 Using the ‘fminsearch’ Function, 49
Variations in MATLAB, 50
Chemical Equilibria Using Aspen Plus, 52
Chapter Summary, 52
Problems, 52
5 Mass Balances With Recycle Streams 55
Mathematical Formulation, 56
Example Without Recycle, 58
Example With Recycle; Comparison of Sequential and Simultaneous Solution
Methods, 60
Example of Process Simulation Using Excel for Simple Mass Balances, 62
Example of Process Simulation With Excel Including Chemical Reaction
Equilibrium, 63
Example of Process Simulation With Excel Including Phase Equilibrium, 63
Did Iterations Converge?, 66
Extensions, 66
Chapter Summary, 66
Class Exercises, 67
Class Discussion, 67
Problems, 67
6 Simulation of Mass Transfer Equipment 73
Thermodynamics, 74
Example: Multicomponent Distillation With Shortcut Methods, 75
Mathematical Development, 77
Multicomponent Distillation With Rigorous Plate-to-Plate Methods, 80
Example: Packed Bed Absorption, 82
Example: Gas Plant Production Separation, 85
Chapter Summary, 87
CONTENTS vii
Class Exercise, 87
Problems (Using Aspen Plus), 87
7 Process Simulation 89
Model Library, 90
Example: Ammonia Process, 91
Utility Costs, 97
Convergence Hints, 100
Optimization, 105
Chapter Summary, 108
Class Exercise, 108
Problems, 108
8 Chemical Reactors 111
Mathematical Formulation of Reactor Problems, 112
Example: Plug Flow Reactor and Batch Reactor, 112
Example: Continuous Stirred Tank Reactor, 114
Using MATLAB to Solve Ordinary Differential Equations, 114
Simple Example, 114
Use of the ‘Global’ Command, 116
Passing Parameters, 117
Example: Isothermal Plug Flow Reactor, 118
Example: Nonisothermal Plug Flow Reactor, 121
Using FEMLAB to Solve Ordinary Differential Equations, 123
Simple Example, 124
Example: Isothermal Plug Flow Reactor, 125
Example: Nonisothermal Plug Flow Reactor, 127
Reactor Problems with Mole Changes and Variable Density, 130
Chemical Reactors with Mass Transfer Limitations, 131
Continuous Stirred Tank Reactors, 134
Solution Using Excel, 135
Solution Using MATLAB, 135
CSTR With Multiple Solutions, 136
Solutions to Multiple Equations Using MATLAB, 136
Transient Continuous Stirred Tank Reactors, 137
Chapter Summary, 141
Problems, 142
9 Transport Processes in One Dimension 147
Applications in Chemical Engineering – Mathematical Formulations, 148
Heat Transfer, 148
Diffusion and Reaction, 148
Fluid Flow, 149
Unsteady Heat Transfer, 151
Example: Heat Transfer in a Slab, 152
Example: Reaction and Diffusion, 154
viii CONTENTS
Parametric Solution, 155
Example: Flow of a Newtonian Fluid in a Pipe, 156
Example: Flow of a Non-Newtonian Fluid in a Pipe, 159
Example: Transient Heat Transfer, 162
Example: Linear Adsorption, 164
Example: Chromatography, 167
Chapter Summary, 169
Problems, 169
10 Fluid Flow in Two and Three Dimensions 175
Mathematical Foundation of Fluid Flow, 176
Navier–Stokes Equation, 176
Non-Newtonian Fluid, 177
Example: Entry Flow in a Pipe, 179
Example: Entry Flow of a Non-Newtonian Fluid, 184
Example: Flow in Microfluidic Devices, 186
Example: Turbulent Flow in a Pipe, 189
Example: Start-Up Flow in a Pipe, 191
Example: Flow Through an Orifice, 193
Example: Flow in a Serpentine Mixer, 199
Boundary Conditions, 199
Nondimensionalization, 201
Chapter Summary, 203
Problems, 203
11 Convective Diffusion Equation in Two and Three Dimensions 207
Convective Diffusion Equation, 208
Nondimensional Equations, 209
Boundary Conditions, 209
Example: Heat Transfer in Two Dimensions, 210
Example: Heat Conduction With a Hole, 213
Example: Dispersion in Microfluidic Devices, 214
Effect of Peclet Number, 215
Example: Concentration-Dependent Viscosity, 217
Example: Viscous Dissipation, 218
Example: Chemical Reactor, 221
Example: Wall Reactions, 221
Example: Mixing in a Serpentine Mixer, 222
Chapter Summary, 223
Problems, 224
Appendix A Hints When Using Excel 229
Cell Organization, 229
Cell Contents, 229
Format, 230
Comments, 230
CONTENTS ix
Pictures, Equations, Web Links, 231
Select Columns for Charts, Regression, and Printing, 231
Copy Formulas Across and Down the Spreadsheet, 231
Insert Rows and Columns, 231
Split/Freezing, 231
Iteration on, Tolerance, 232
Paste, 232
Plot – xy Scatter, Edit, Multiple Curves, Surface Plots, 233
Arrange Spreadsheet, 235
Import and Export Text Files, One Column at a Time, 236
Import and Export Text Files, Multiple Columns, 236
Export a Text File, 236
Tools, 237
Functions, 237
Matrices, 237
Excel Help, 238
Applications of Excel, 238
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Appendix B Hints When Using MATLAB 239
General Features, 239
Start the Program, 239
Screen Format, 240
Stop/Closing the Program, 240
m-Files, 241
Workspaces and Transfer of Information, 241
‘Global’ Command, 241
Display Tools, 242
Finding MATLAB Errors, 243
Debug the Program; That is, Find Your Errors, 243
Input/Output, 244
Loops, 245
Conditional Statements, 245
Timing Information, 246
Matrices, 246
Matrix Multiplication, 246
Element-by-Element Calculations, 248
Eigenvalues of a Matrix, 248
Evaluate an Integral, 248
Solve Algebraic Equations Using ‘fsolve’, 248
Solve Algebraic Equations Using ‘fzero’ or ‘fminsearch’ (both in standard
MATLAB), 249
Integrating Ordinary Differential Equations that are Initial Value
Problems, 249
Checklist for Using ‘ode45’ and Other Integration Packages, 251
Spline Interpolation, 252
Interpolate Data, Evaluate the Polynomial, and Plot the Result, 252
Plotting, 253
x CONTENTS
Plotting Results from Integration of Partial Differential Equations
Using the Method of Lines, 253
Simple Plots, 253
Add Data to an Existing Plot, 254
Dress Up Your Plot, 254
Multiple Plots, 255
Three-Dimensional Plots, 255
More Complicated Plots, 256
Use Greek Letters and Symbols in the Text, 257
MATLAB Help, 257
Applications of MATLAB, 257
Appendix C Hints When Using Aspen Plus 259
Quick Tour, 259
Start, 259
Setup, 260
Model Library, 260
Place Units on Flowsheet, 261
Connect the Units with Streams, 262
Data Entry, 262
Specify Components, 262
Specify Properties, 262
Specify the Input Streams, 263
Specify Block Parameters, 264
Run the Problem, 264
Scrutinize the Stream Table, 264
Checking Your Results, 265
Transfer the Flowsheet and Mass and Energy Balance to a
Word Processing Program, 265
Change Conditions, 266
Prepare Your Report, 266
Save Your Results, 267
Getting Help, 268
Applications of Aspen Plus, 268
Appendix D Hints When Using FEMLAB 269
Basic FEMLAB Techniques, 270
Opening Screens, 270
Equations, 270
Draw, 272
Mesh, 272
Subdomain Settings, 273
Boundary Settings, 273
Solve, 275
Postprocessing, 276
Surface Plots, 276
Contour Plots, 278
CONTENTS xi
Cross-Sectional Plots, 278
Boundary Plots, 278
Integrals, 279
Advanced Features, 280
Model Navigator, 280
Internal Boundaries, 281
Expressions, 281
Coupling Variables and Additional Geometries, 282
Applications of FEMLAB, 288
Appendix E Parameter Estimation 293
Mathematical Formulation, 293
Straight Line, 294
Straight Line Curve Fit Using Excel, 294
Plotting the Trendline, 295
Straight Line Curve Fit Using MATLAB, 295
Polynomial Regression, 296
Polynomial Regression Using Excel, 297
Polynomial Regression Using MATLAB, 298
Multiple Regression Using Excel, 298
Nonlinear Regression, 304
Nonlinear Regression Using Excel, 304
Nonlinear Regression Using MATLAB, 305
Appendix F Mathematical Methods 307
Algebraic Equations, 307
Successive Substitution, 308
Newton–Raphson, 308
Ordinary Differential Equations as Initial Value Problems, 310
Euler’s Method, 310
Runge–Kutta Methods, 311
Ordinary Differential Equations as Boundary Value Problems, 312
Finite Difference Method, 312
Finite Element Method, 314
Initial Value Methods, 317
Finite Difference Method in Excel, 317
Partial Differential Equations in Time and One Space Dimension, 317
Partial Differential Equations in Two Space Dimensions, 320
Finite Difference Method for Elliptic Equations, 321
Summary, 322
References 323
Author Index 327
Chemical Index 329
Computer Command Index 331
Subject Index 335