BRUCE A. FINLAYSON, PhD, is Rehnberg Professor Emeritus of Chemical Engineering in the Department of Chemical Engineering of the University of Washington. He is also a former president of the American Institute of Chemical Engineers (AIChE). Among his many accolades and honors, Dr. Finlayson is a recipient of the AIChE’s prestigious William H. Walker Award and an elected member of the National Academy of Engineering.

1 Introduction 1

Organization, 2

Algebraic Equations, 3

Process Simulation, 3

Differential Equations, 3

Appendices, 4

2 Equations of State 7

Equations of State—Mathematical Formulation, 8

Solving Equations of State Using Excel (Single Equation in One Unknown), 12

Solution Using “Goal Seek”, 12

Solution Using “Solver”, 13

Example of a Chemical Engineering Problem Solved Using “Goal Seek”, 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 Vapor–Liquid Equilibria 29

Flash and Phase Separation, 30

Isothermal Flash—Development of Equations, 30

Example Using Excel, 32

Thermodynamic Parameters, 33

Example Using MATLAB, 34

Example Using Aspen Plus, 35

Nonideal Liquids—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

Properties Environment | Home | Methods 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 “Global” 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 Engineering—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

Navier–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 Excel® 291

Introduction, 291

Calculation, 292

Plotting, 293

Import and Export, 294

Presentation, 294

Appendix B HintsWhen Using MATLAB® 297

General Features, 298

Screen Format, 298

Stop/Closing the Program, 299

m-files and Scripts, 299

Workspaces and Transfer of Information, 300

“Global” 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 “fsolve”, 309

Solve Algebraic Equations Using “fzero” or “fminsearch” (Both in Standard MATLAB), 309

Integrate Ordinary Differential Equations that are Initial Value Problems, 309

Differential-Algebraic Equations, 311

Checklist for Using “ode45” 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 Plus® 321

Introduction, 321

Flowsheet, 323

Model Library, 323

Place Units on Flowsheet, 324

Connect the Units with Streams, 324

Data, 324

Setup, 324

Data Entry, 325

Specify Components, 325

Specify Properties, 325

Specify Input Streams, 326

Specify Block Parameters, 326

Run the Problem, 326

Scrutinize the Stream Table, 327

Checking Your Results, 328

Change Conditions, 328

Report, 329

Transfer the Flowsheet and Mass and Energy Balance to a Word Processing Program, 329

Prepare Your Report, 329

Save Your Results, 330

Getting Help, 330

Advanced Features, 330

Flowsheet Sections, 330

Mass Balance Only Simulations and Inclusion of Solids, 331

Transfer Between Excel and Aspen, 331

Block Summary, 331

Calculator Blocks, 332

Aspen Examples, 334

Molecule Draw, 334

Applications of Aspen Plus, 334

Appendix D HintsWhen Using Comsol Multiphysics® 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

Newton–Raphson, 354

Ordinary Differential Equations as Initial Value Problems, 356

Euler’s Method, 356

Runge–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

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