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Table of Contents 3 Preface 14 Chapter 1. Introduction 19 Organization 20 Algebraic Equations 21 Process Simulation 21 Differential Equations 21 Appendices 23 Chapter 2. Equations of State 24 Equation of state - mathematical formulation 25 Solving equations of state Using Excel (Single equation in one unknown) 28 Solution using 'Goal seek' 28 Solution using 'Solver' 29 Example of a chemical engineering problem solved using 'Goal Seek' 30 Solving equations of state using MATLAB(r) (Single equation in one unknown) 31 Example of a chemical engineering problem solved using MATLAB 33 Another example of a chemical engineering problem solved using MATLAB 35 Equations of state with Aspen Plus 37 Specific volume of a mixture 39 Chapter summary 42 Problems 43 Chapter 3. Vapor-liquid Equilibria 45 Flash and phase separation 45 Isothermal flash - development of equations 47 Example using Excel 48 Thermodynamic parameters 49 Example using MATLAB 52 Example using Aspen Plus 53 Non-ideal liquids - test of thermodynamic model 56 Chapter summary 58 Problems 58 Chapter 4. Chemical Reaction Equilibria 63 Chemical equilibrium expression 64 Example of hydrogen for fuel cells 65 Solution with Excel 66 Solution using MATLAB 67 Chemical equilibria with two or more equations 71 Multiple equations, few unknowns with MATLAB 71 Method 1 using the 'fsolve' command 71 Method 2 using the 'fminsearch' function 73 Variations in MATLAB 74 Chemical Equilibria with Aspen Plus 75 Chapter summary 76 Problems 76 Chapter 5. Mass Balances with Recycle Streams 79 Mathematical formulation 79 Example without recycle 81 Example with recycle; comparison of sequential and simultaneous solution methods 83 Example of process simulation using Excel for simple mass balances 85 Example of process simulation using Excel including chemical reaction equilibrium 86 Example of process simulation using Excel including phase equilibrium 88 Chapter summary 90 Class exercises 91 Class discussion 91 Problems 91 Chapter 6. Simulation of Mass Transfer Equipment 98 Thermodynamics 99 Example: multicomponent distillation with shortcut methods 102 Mathematical development 103 Example: multicomponent distillation with rigorous plate-to-plate methods 108 Example: packed bed absorption 109 Example: gas plant product separation 110 Chapter summary 111 Class exercise 111 Problems (using Aspen Plus) 111 Chapter 7. Process Simulation 114 Model library 115 Example: Ammonia process 115 Utility costs 120 Convergence hints 121 Optimization 124 Chapter summary 125 Class exercise 125 Problems 125 Chapter 8. Chemical Reactors 128 Mathematical formulation of reactor problems 129 Example: plug flow reactor and batch reactor 130 Example: continuous stirred tank reactor (CSTR) 132 Using MATLAB to solve ordinary differential equations 132 Simple example 132 Use of the 'global' command 134 Passing parameters 136 Example: isothermal plug flow reactor 137 Example: non-isothermal flow reactor 140 Using FEMLAB to solve ordinary differential equations 143 Simple example 144 Example: isothermal plug flow reactor 145 Example: non-isothermal flow reactor 147 Reactor problems with mole changes and variable density 151 Chemical reactors with mass transfer limitations 153 Continuous stirred tank reactors (CSTR) 157 Solution using Excel 158 Solution using MATLAB 159 CSTR with multiple solutions 159 Solutions to multiple equations using MATLAB 160 Transient continuous stirred tank reactors (CSTR) 161 Chapter summary 165 Problems 165 Chapter 9. Transport Process in 1D 171 Applications in chemical engineering - mathematical foundation 172 Heat transfer 172 Diffusion and reaction 172 Fluid flow 174 Unsteady heat transfer 176 Example: Heat transfer in a slab 177 Example: Reaction and diffusion 179 Parametric solution 180 Flow of a Newtonion fluid in a pipe 181 Example: Flow of a Non-Newtonion in a pipe 182 Example: Transient Heat Transfer 184 Example: Liinear Adsorption 185 Example: Chromatography 189 Chapter summary 191 Problems 192 Chapter 10. Fluid Flow in 2D and 3D 197 Mathematical foundation of fluid flow 199 Navier-Stokes equation 199 Non-Newtonian fluid 201 Example: Entry flow in a pipe 201 Example: Entry flow of a non-Newtonian fluid 205 Example: Flow in microfluidic devices 207 Example: Turbulent flow in a pipe 209 Example: Start-up flow in a pipe 211 Example: Flow through an orifice 213 Example: Flow in a serpentine mixer 217 Boundary conditions 218 Non-dimensionalization 221 Chapter summary 221 Problems 222 Chapter 11. Convective Diffusion Equation in 2D and 3D 225 Convective diffusion equation 226 Non-dimensional equations 227 Boundary conditions 228 Example: heat transfer in two dimensions 229 Example: heat conduction with a hole 230 Example: dispersion in microfluidic devices 231 Effect of Peclet number 233 Example: concentration-dependent viscosity 234 Example: viscous dissipation 235 Example: chemical reactor 237 Example: wall reactions 238 Example: mixing in a serpentine mixer 238 Chapter summary 239 Problems 240 Appendix A. Hints when using Excel 245 Cell organization, Cell contents 245 Format , Comments, Pictures, equations, web links 246 Select columns for charts, regression and printing 247 Copy formulas across and down the spreadsheet, Insert rows and columns 247 Split/freezing, Iteration on, tolerance 248 Paste, Plot - xy scatter, edit, multiple curves, surface plots 249 Arrange spreadsheet, Import and export text files, one column at a time 250 Import and export text files, multiple columns, Export a text file 251 Tools , Functions, Matrices, Excel help, Applications of Excel 252 Appendix B. Hints when using MATLAB(r) 254 General features 254 Start the program, Screen format 254 Stop/Closing the program , m-files, Workspaces and transfer of information 255 'Global' command 256 Display tools 257 Finding MATLAB errors 258 Debug the program, i.e. find your errors 259 Input/Output, Loops 260 Conditional statements 261 Timing information 262 Matrices 263 Matrix multiplication 2644 Element by element calculations 265 Eigenvalues of a matrix 265 Evaluate an integral 265 Solve algebraic equations using 'fsolve' 266 Solve algebraic equations using 'fzero' or 'fminsearch' (both in standard MATLAB) 266 Integrating ordinary differential equations that are initial value problems 267 Checklist for using 'ode45' and other integration packages 269 Spline interpolation 270 Interpolate data, evaluate the polynomial, plot the result 270 Plotting 271 Plotting results from integration of partial differential equations using method of lines 271 Simple plots, Add data to an existing plot, Dress up your plot 272 Multiple plots 273 3D plots, More complicated plots 274 Use Greek letters and symbols in the text 275 Matlab help 276 Applications of MATLAB 277 Appendix C. Hints when using Aspen Plus 278 Quick Tour; Start 278 Setup, Model library, Place units on flowsheet 279 Connect the units with streams, data entry, Specify components 280 Specify properties, Specify the input streams, Specify block parameters 281 Run the problem 281 Scrutinize the stream table, Checking your results 282 Transfer the flowsheet and mass and energy balance to a word processing program 282 Change conditions, Prepare your report 283 Save your results, Getting help, Applications of Aspen Plus 284 Appendix D. Hints when using FEMLAB 285 Basic FEMLAB techniques 286 Opening screens, Equations 286 Draw 287 Mesh, Subdomain settings, Boundary settings 288 Solve 289 Postprocessing 289 Surface plots 289 Contour plots, Cross-sectional plots, Boundary plots 290 Integrals 291 Advanced features 291 Model navigator 291 Internal boundaries, Expressions 292 Coupling variables and additional geometries 292 Applications of FEMLAB 294 Appendix E. Parameter Estimation 296 Mathematical formulation 296 Straight line 297 Straight line curve fit using Excel 297 Plotting the trendline 298 Straight line curve fit using MATLAB 298 Polynomial Regression 299 Polynomial regression using Excel 299 Polynomial regression using MATLAB 300 Multiple Regression using Excel 300 Nonlinear Regression 303 Nonlinear regression using Excel 304 Nonlinear regression using MATLAB 305 Appendix F. Mathematical Methods 307 Algebraic Equations 307 Successive substitution 307 Newton-Raphson 328 Secant method 329 Ordinary differential equations as initial value problems 330 Euler's method 331 Runge-Kutta methods 332 Implicit methods 332 Differential-algebraic equations 333 Ordinary differential equations as boundary value problems 334 Finite difference method 334 Finite element method 335 Initial value methods 338 Finite difference method in Excel 338 Partial differential equations in time and one space dimension 339 Partial differential equations in two space dimensions 341 Finite difference methods for elliptic equations in Excel 342 Summary 343

Library of Congress Subject Headings for this publication:

Chemical engineering -- Data processing.