The problems that chemical engineers face today can no longer be answered with programs written on a case-by-case basis; computers have revolutionized the way chemical engineers design and analyze processesâ€”whether designing large units to make polyethylene or a small microreactor used to detect biological agents. This book helps identify the types of computer programs needed to solve various chemical engineering problems and ensure that the problems have been solved correctly. Each chapter contains a description of the physical problem in both general terms and mathematically, thorough step-by-step instructions, numerous examples, and comprehensive explanations for each problem and program.
Preface xv
1 Introduction 1
Organization, 2
Algebraic Equations, 3
Process Simulation, 3
Differential Equations, 3
Appendices, 4
2 Equations of State 7
Equations of Stateâ€”Mathematical Formulation, 8
Solving Equations of State Using Excel (Single Equation in One Unknown), 12
Solution Using â€śGoal Seekâ€ť, 12
Solution Using â€śSolverâ€ť, 13
Example of a Chemical Engineering Problem Solved Using â€śGoal Seekâ€ť, 13
Solving Equations of State Using MATLAB (Single Equation in One Unknown), 15
Example of a Chemical Engineering Problem Solved Using MATLAB, 16
Another Example of a Chemical Engineering Problem Solved Using MATLAB, 18
Equations of State With Aspen Plus, 20
Example Using Aspen Plus, 20
Specific Volume of a Mixture, 21
Chapter Summary, 26
Problems, 26
Numerical Problems, 28
3 Vaporâ€“Liquid Equilibria 29
Flash and Phase Separation, 30
Isothermal Flashâ€”Development of Equations, 30
Example Using Excel, 32
Thermodynamic Parameters, 33
Example Using MATLAB, 34
Example Using Aspen Plus, 35
Nonideal Liquidsâ€”Test of Thermodynamic Model, 39
NIST Thermo Data Engine in Aspen Plus, 41
Chapter Summary, 44
Problems, 44
Numerical Problems, 48
4 Chemical Reaction Equilibria 49
Chemical Equilibrium Expression, 50
Example of Hydrogen for Fuel Cells, 51
Solution Using Excel, 52
Solution Using MATLAB, 53
Chemical Reaction Equilibria with Two or More Equations, 56
Multiple Equations, Few Unknowns Using MATLAB, 56
Chemical Reaction Equilibria Using Aspen Plus, 59
Chapter Summary, 59
Problems, 60
Numerical Problems, 63
5 Mass Balances with Recycle Streams 65
Mathematical Formulation, 66
Example Without Recycle, 68
Example with Recycle; Comparison of Sequential and Simultaneous Solution Methods, 70
Example of Process Simulation Using Excel for Simple Mass Balances, 72
Example of Process Simulation Using Aspen Plus for Simple Mass Balances, 73
Example of Process Simulation with Excel Including Chemical Reaction Equilibria, 74
Did the Iterations Converge?, 75
Extensions, 76
Chapter Summary, 76
Class Exercises, 76
Class Discussion (After Viewing Problem 5.10 on the Book Website), 76
Problems, 77
6 Thermodynamics and Simulation of Mass Transfer Equipment 85
Thermodynamics, 86
Guidelines for Choosing, 89
Property Method Selection Assistant, 89
Thermodynamic Models, 90
Example: Multicomponent Distillation with Shortcut Methods, 91
Multicomponent Distillation with Rigorous Plate-to-Plate Methods, 95
Example: Packed Bed Absorption, 97
Example: Gas Plant Product Separation, 100
Example: Water Gas Shift Equilibrium Reactor with Sensitivity Block and Design Specification Block, 102
Chapter Summary, 106
Class Exercise, 106
Problems (using Aspen Plus), 106
7 Process Simulation 109
Model Library, 110
Example: Ammonia Process, 110
Development of the Model, 112
Solution of the Model, 115
Examination of Results, 115
Testing the Thermodynamic Model, 118
Utility Costs, 118
Greenhouse Gas Emissions, 120
Convergence Hints, 120
Optimization, 122
Integrated Gasification Combined Cycle, 125
Cellulose to Ethanol, 126
Chapter Summary, 128
Class Exercise, 128
Problems, 128
Problems Involving Corn Stover and Ethanol, 131
8 Chemical Reactors 137
Mathematical Formulation of Reactor Problems, 138
Example: Plug Flow Reactor and Batch Reactor, 138
Example: Continuous Stirred Tank Reactor, 140
Using MATLAB to Solve Ordinary Differential Equations, 140
Simple Example, 140
Use of the â€śGlobalâ€ť Command, 142
Passing Parameters, 143
Example: Isothermal Plug Flow Reactor, 144
Example: Nonisothermal Plug Flow Reactor, 146
Using Comsol Multiphysics to Solve Ordinary Differential Equations, 148
Simple Example, 148
Example: Isothermal Plug Flow Reactor, 150
Example: Nonisothermal Plug Flow Reactor, 151
Reactor Problems with Mole Changes and Variable Density, 153
Chemical Reactors with Mass Transfer Limitations, 155
Plug Flow Chemical Reactors in Aspen Plus, 158
Continuous Stirred Tank Reactors, 161
Solution Using Excel, 162
Solution Using MATLAB, 163
CSTR with Multiple Solutions, 163
Transient Continuous Stirred Tank Reactors, 164
Chapter Summary, 168
Problems, 169
Numerical Problems (See Appendix E), 174
9 Transport Processes in One Dimension 175
Applications in Chemical Engineeringâ€”Mathematical Formulations, 176
Heat Transfer, 176
Diffusion and Reaction, 177
Fluid Flow, 178
Unsteady Heat Transfer, 180
Introduction to Comsol Multiphysics, 180
Example: Heat Transfer in a Slab, 181
Solution Using Comsol Multiphysics, 181
Solution Using MATLAB, 184
Example: Reaction and Diffusion, 185
Parametric Solution, 186
Example: Flow of a Newtonian Fluid in a Pipe, 188
Example: Flow of a Non-Newtonian Fluid in a Pipe, 190
Example: Transient Heat Transfer, 193
Solution Using Comsol Multiphysics, 193
Solution Using MATLAB, 195
Example: Linear Adsorption, 196
Example: Chromatography, 199
Pressure Swing Adsorption, 203
Chapter Summary, 204
Problems, 204
Chemical Reaction, 204
Chemical Reaction and Heat Transfer, 205
Mass Transfer, 207
Heat Transfer, 207
Electrical Fields, 207
Fluid Flow, 208
Numerical Problems (See Appendix E), 213
10 Fluid Flow in Two and Three Dimensions 215
Mathematical Foundation of Fluid Flow, 217
Navierâ€“Stokes Equation, 217
Non-Newtonian Fluid, 218
Nondimensionalization, 219
Option One: Slow Flows, 219
Option Two: High-Speed Flows, 220
Example: Entry Flow in a Pipe, 221
Example: Entry Flow of a Non-Newtonian Fluid, 226
Example: Flow in Microfluidic Devices, 227
Example: Turbulent Flow in a Pipe, 230
Example: Start-Up Flow in a Pipe, 233
Example: Flow Through an Orifice, 235
Example: Flow in a Serpentine Mixer, 239
Microfluidics, 240
Mechanical Energy Balance for Laminar Flow, 243
Pressure Drop for Contractions and Expansions, 245
Generation of Two-Dimensional Inlet Velocity Profiles for Three-Dimensional Simulations, 246
Chapter Summary, 249
Problems, 249
11 Heat and Mass Transfer in Two and Three Dimensions 259
Convective Diffusion Equation, 260
Nondimensional Equations, 261
Example: Heat Transfer in Two Dimensions, 262
Example: Heat Conduction with a Hole, 264
Example: Convective Diffusion in Microfluidic Devices, 265
Example: Concentration-Dependent Viscosity, 268
Example: Viscous Dissipation, 269
Example: Chemical Reaction, 270
Example: Wall Reactions, 272
Example: Mixing in a Serpentine Mixer, 272
Microfluidics, 274
Characterization of Mixing, 276
Average Concentration along an Optical Path, 276
Peclet Number, 276
Example: Convection and Diffusion in a Three-Dimensional T-Sensor, 278
Chapter Summary, 280
Problems, 280
Steady, Two-Dimensional Problems, 280
Heat Transfer with Flow, 283
Reaction with Known Flow, 284
Reaction with No Flow, 285
Solve for Concentration and Flow, 286
Numerical Problems, 289
Appendix A HintsWhen Using ExcelÂ® 291
Introduction, 291
Calculation, 292
Plotting, 293
Import and Export, 294
Presentation, 294
Appendix B HintsWhen Using MATLABÂ® 297
General Features, 298
Screen Format, 298
Stop/Closing the Program, 299
m-files and Scripts, 299
Workspaces and Transfer of Information, 300
â€śGlobalâ€ť Command, 300
Display Tools, 301
Classes of Data, 301
Programming Options: Input/Output, Loops, Conditional Statements, Timing, and Matrices, 302
Input/Output, 302
Loops, 303
Conditional Statements, 303
Timing Information, 304
Matrices, 304
Matrix Multiplication, 304
Element by Element Calculations, 305
More Information, 306
Finding and Fixing Errors, 306
Eigenvalues of a Matrix, 307
Evaluate an Integral, 307
Spline Interpolation, 307
Interpolate Data, Evaluate the Polynomial, and Plot the Result, 308
Solve Algebraic Equations, 309
Using â€śfsolveâ€ť, 309
Solve Algebraic Equations Using â€śfzeroâ€ť or â€śfminsearchâ€ť (Both in Standard MATLAB), 309
Integrate Ordinary Differential Equations that are Initial Value Problems, 309
Differential-Algebraic Equations, 311
Checklist for Using â€śode45â€ť and Other Integration Packages, 311
Plotting, 312
Simple Plots, 312
Add Data to an Existing Plot, 312
Dress Up Your Plot, 312
Multiple Plots, 313
3D Plots, 313
More Complicated Plots, 314
Use Greek Letters and Symbols in the Text, 314
Bold, Italics, and Subscripts, 314
Other Applications, 315
Plotting Results from Integration of Partial Differential Equations Using Method of Lines, 315
Import/Export Data, 315
Import/Export with Comsol Multiphysics, 318
Programming Graphical User Interfaces, 318
MATLAB Help, 318
Applications of MATLAB, 319
Appendix C Hints When Using Aspen PlusÂ® 321
Introduction, 321
Flowsheet, 322
Model Library, 322
Place Units on Flowsheet, 323
Connect the Units with Streams, 323
Data, 323
Setup, 324
Data Entry, 324
Specify Components, 325
Specify Properties, 325
Specify Input Streams, 326
Specify Block Parameters, 326
Run the Problem, 327
Scrutinize the Stream Table, 327
Checking Your Results, 328
Change Conditions, 328
Report, 328
Transfer the Flowsheet and Mass and Energy Balance to a Word Processing Program, 328
Prepare Your Report, 328
Save Your Results, 329
Getting Help, 329
Advanced Features, 329
Flowsheet Sections, 329
Mass Balance Only Simulations and Inclusion of Solids, 330
Transfer Between Excel and Aspen, 331
Block Summary, 331
Calculator Blocks, 331
Aspen Examples, 332
Molecule Draw, 332
Applications of Aspen Plus, 334
Appendix D HintsWhen Using Comsol MultiphysicsÂ® 335
Basic Comsol Multiphysics Techniques, 336
Opening Screens, 336
Equations, 337
Specify the Problem and Parameters, 337
Physics, 339
Definitions, 339
Geometry, 339
Materials, 340
Discretization, 341
Boundary Conditions, 341
Mesh, 342
Solve and Examine the Solution, 342
Solve, 342
Plot, 342
Publication Quality Figures, 343
Results, 343
Probes, 344
Data Sets, 344
Advanced Features, 345
Mesh, 345
Transfer to Excel, 346
LiveLink with MATLAB, 347
Variables, 348
Animation, 349
Studies, 349
Help with Convergence, 349
Help with Time-Dependent Problems, 350
Jump Discontinuity, 350
Help, 351
Applications of Comsol Multiphysics, 351
Appendix E Mathematical Methods 353
Algebraic Equations, 354
Successive Substitution, 354
Newtonâ€“Raphson, 354
Ordinary Differential Equations as Initial Value Problems, 356
Eulerâ€™s Method, 356
Rungeâ€“Kutta Methods, 357
MATLAB and ode45 and ode15s, 357
Ordinary Differential Equations as Boundary Value Problems, 358
Finite Difference Method, 359
Finite Difference Method in Excel, 360
Finite Element Method in One Space Dimension, 361
Initial Value Methods, 363
Partial Differential Equations in time and One Space Dimension, 365
Problems with Strong Convection, 366
Partial Differential Equations in Two Space Dimensions, 367
Finite-Difference Method for Elliptic Equations in Excel, 367
Finite Element Method for Two-Dimensional Problems, 368
Summary, 370
Problems, 370
References 373
Index 379