## Description

* Problem Solving in Chemical and Biochemical Engineering with POLYMATH™, Excel, and MATLAB®, Second Edition*, is a valuable resource and companion that integrates the use of numerical problem solving in the three most widely used software packages: POLYMATH, Microsoft Excel, and MATLAB. Recently developed POLYMATH capabilities allow the automatic creation of Excel spreadsheets and the generation of MATLAB code for problem solutions. Students and professional engineers will appreciate the ease with which problems can be entered into POLYMATH and then solved independently in all three software packages, while taking full advantage of the unique capabilities within each package. The book includes more than 170 problems requiring numerical solutions.

This greatly expanded and revised second edition includes new chapters on getting started with and using Excel and MATLAB. It also places special emphasis on biochemical engineering with a major chapter on the subject and with the integration of biochemical problems throughout the book.

#### General Topics and Subject Areas, Organized by Chapter

- Introduction to Problem Solving with Mathematical Software Packages

- Basic Principles and Calculations

- Regression and Correlation of Data

- Introduction to Problem Solving with Excel

- Introduction to Problem Solving with MATLAB

- Advanced Problem-Solving Techniques

- Thermodynamics

- Fluid Mechanics

- Heat Transfer

- Mass Transfer

- Chemical Reaction Engineering

- Phase Equilibrium and Distillation

- Process Dynamics and Control

- Biochemical Engineering

#### Practical Aspects of Problem-Solving Capabilities

- Simultaneous Linear Equations

- Simultaneous Nonlinear Equations

- Linear, Multiple Linear, and Nonlinear Regressions with Statistical Analyses

- Partial Differential Equations (Using the Numerical Method of Lines)

- Curve Fitting by Polynomials with Statistical Analysis

- Simultaneous Ordinary Differential Equations (Including Problems Involving Stiff Systems, Differential-Algebraic Equations, and Parameter Estimation in Systems of Ordinary Differential Equations)

#### The Book's Web Site (http://www.problemsolvingbook.com)

- Provides solved and partially solved problem files for all three software packages, plus additional materials

- Describes discounted purchase options for educational version of POLYMATH available to book purchasers

- Includes detailed, selected problem solutions in Maple™, Mathcad®, and Mathematica™

## Table of Contents

*Prefacexv *

### Chapter 1 Problem Solving with Mathematical Software Packages 1

1.1 Efficient Problem Solving--The Objective of This Book 1

1.2 From Manual Problem Solving to Use of Mathematical Software 2

1.3 Categorizing Problems According to the Solution Technique Used 5

1.4 Effective Use of This Book 10

1.5 Software Usage with This Book 12

1.6 Web-Based Resources for This Book 13

### Chapter 2 Basic Principles and Calculations15

2.1 Molar Volume and Compressibility Factor from Van Der Waals Equation 15

2.2 Molar Volume and Compressibility Factor from Redlich-Kwong Equation 19

2.3 Stoichiometric Calculations for Biological Reactions 20

2.4 Steady-State Material Balances on A Separation Train 23

2.5 Fitting Polynomials and Correlation Equations to Vapor Pressure Data 25

2.6 Vapor Pressure Correlations for Sulfur Compounds in Petroleum 33

2.7 Mean Heat Capacity of N-Propane 34

2.8 Vapor Pressure Correlation by Clapeyron and Antoine Equations 36

2.9 Gas Volume Calculations Using Various Equations of State 38

2.10 Bubble Point Calculation for an Ideal Binary Mixture 41

2.11 Dew Point Calculation for an Ideal Binary Mixture 44

2.12 Bubble Point and Dew Point for an Ideal Multicomponent Mixture 45

2.13 Adiabatic Flame Temperature in Combustion 46

2.14 Unsteady-State Mixing in a Tank 49

2.15 Unsteady-State Mixing in a Series of Tanks 52

2.16 Heat Exchange in a Series of Tanks 53

References 56

### Chapter 3 Regression and Correlation of Data57

3.1 Estimation of Antoine Equation Parameters Using Nonlinear Regression 57

3.2 Antoine Equation Parameters for Various Hydrocarbons 61

3.3 Correlation of Thermodynamic and Physical Properties of N-Propane 62

3.4 Temperature Dependency of Selected Properties 72

3.5 Heat Transfer Correlations from Dimensional Analysis 73

3.6 Heat Transfer Correlation of Liquids in Tubes 79

3.7 Heat Transfer in Fluidized Bed Reactor 80

3.8 Correlation of Binary Activity Coefficients Using Margules Equations 81

3.9 Margules Equations for Binary Systems Containing Trichloroethane 86

3.10 Rate Data Analysis for A Catalytic Reforming Reaction 87

3.11 Regression of Rate Data-Checking Dependency Among Variables 89

3.12 Regression of Heterogeneous Catalytic Rate Data 93

3.13 Variation of Reaction Rate Constant with Temperature 94

3.14 Calculation of Antoine Equation Parameters Using Linear Regression 95

References 100

### Chapter 4 Problem Solving with Excel 101

4.1 Molar Volume And Compressibility From Redlich-Kwong Equation 101

4.2 Calculation Of The Flow Rate In A Pipeline 110

4.3 Adiabatic Operation Of A Tubular Reactor For Cracking Of Acetone 119

4.4 Correlation Of The Physical Properties Of Ethane 128

4.5 Complex Chemical Equilibrium By Gibbs Energy Minimization 144

References 152

### Chapter 5 Problem Solving with MATLAB 153

5.1 Molar Volume and Compressibility from Redlich-Kwong Equation 153

5.2 Calculation of the Flow Rate in a Pipeline 165

5.3 Adiabatic Operation of a Tubular Reactor for Cracking of Acetone 173

5.4 Correlation of the Physical Properties of Ethane 182

5.5 Complex Chemical Equilibrium by Gibbs Energy Minimization 195

Reference 202

### Chapter 6 Advanced Techniques in Problem Solving 203

6.1 Solution of Stiff Ordinary Differential Equations 203

6.2 Stiff Ordinary Differential Equations in Chemical Kinetics 206

6.3 Multiple Steady States in a System of Ordinary Differential Equations 207

6.4 Iterative Solution of Ode Boundary Value Problem 209

6.5 Shooting Method for Solving Two-Point Boundary Value Problems 218

6.6 Expediting the Solution of Systems of Nonlinear Algebraic Equations 223

6.7 Solving Differential Algebraic Equations--DAEs 226

6.8 Method of Lines for Partial Differential Equations 229

6.9 Estimating Model Parameters Involving Odes Using Fermentation Data 235

References 242

### Chapter 7 Thermodynamics 243

7.1 Compressibility Factor Variation from Van Der Waals Equation 243

7.2 Compressibility Factor Variation from Various Equations of State 248

7.3 Isothermal Compression of Gas Using Redlich-Kwong Equation of State 251

7.4 Thermodynamic Properties of Steam from Redlich-Kwong Equation 255

7.5 Enthalpy and Entropy Departure Using the Redlich-Kwong Equation 258

7.6 Fugacity Coefficients of Pure Fluids from Various Equations of State 263

7.7 Fugacity Coefficients for Ammonia--Experimental and Predicted 265

7.8 Flash Evaporation of an Ideal Multicomponent Mixture 267

7.9 Flash Evaporation of Various Hydrocarbon Mixtures 271

7.10 Correlation of Activity Coefficients with the Van Laar Equations 272

7.11 Vapor Liquid Equilibrium Data from Total Pressure Measurements I 274

7.12 Vapor Liquid Equilibrium Data from Total Pressure Measurements II 279

7.13 Complex Chemical Equilibrium 280

7.14 Reaction Equilibrium at Constant Pressure or Constant Volume 281

References 282

### Chapter 8 Fluid Mechanics283

8.1 Laminar Flow of a Newtonian Fluid in a Horizontal Pipe 283

8.2 Laminar Flow of Non-Newtonian Fluids in a Horizontal Pipe 289

8.3 Vertical Laminar Flow of a Liquid Film291

8.4 Laminar Flow of Non-Newtonian Fluids in a Horizontal Annulus 294

8.5 Temperature Dependency of Density and Viscosity of Various Liquids 297

8.6 Terminal Velocity of Falling Particles 299

8.7 Comparison of Friction Factor Correlations for Turbulent Pipe Flow 301

8.8 Calculations Involving Friction Factors for Flow in Pipes 303

8.9 Average Velocity in Turbulent Smooth Pipe Flow from Maximum Velocity 306

8.10 Calculation of the Flow Rate in a Pipeline 307

8.11 Flow Distribution in a Pipeline Network 309

8.12 Water Distribution Network 313

8.13 Pipe and Pump Network 315

8.14 Optimal Pipe Length for Draining a Cylindrical Tank in Turbulent Flow 317

8.15 Optimal Pipe Length for Draining a Cylindrical Tank in Laminar Flow 320

8.16 Baseball Trajectories as a Function of Elevation 322

8.17 Velocity Profiles for a Wall Suddenly Set in Motion--Laminar Flow 325

8.18 Boundary Layer Flow of a Newtonian Fluid on a Flat Plate 328

References 332

### Chapter 9 Heat Transfer 333

9.1 One-Dimensional Heat Transfer Through a Multilayered Wall 333

9.2 Heat Conduction in a Wire With Electrical Heat Source and Insulation 338

9.3 Radial Heat Transfer by Conduction with Convection at Boundaries 344

9.4 Energy Loss from an Insulated Pipe 346

9.5 Heat Loss Through Pipe Flanges 347

9.6 Heat Transfer from a Horizontal Cylinder Attached to a Heated Wall 352

9.7 Heat Transfer from a Triangular Fin355

9.8 Single-Pass Heat Exchanger with Convective Heat Transfer on Tube Side 357

9.9 Double-Pipe Heat Exchanger361

9.10 Heat Losses from an Uninsulated Tank Due to Convection 365

9.11 Unsteady-State Radiation to a Thin Plate 368

9.12 Unsteady-State Conduction within a Semi-Infinite Slab 370

9.13 Cooling of a Solid Sphere in a Finite Water Bath 373

9.14 Unsteady-State Conduction in Two Dimensions 378

References 382

### Chapter 10 Mass Transfer 383

10.1 One-Dimensional Binary Mass Transfer in a Stefan Tube 383

10.2 Mass Transfer in a Packed Bed with Known Mass Transfer Coefficient 389

10.3 Slow Sublimation of a Solid Sphere 391

10.4 Controlled Drug Delivery by Dissolution of Pill Coating 396

10.5 Diffusion with Simultaneous Reaction in Isothermal Catalyst Particles 400

10.6 General Effectiveness Factor Calculations for First-Order Reactions 404

10.7 Simultaneous Diffusion and Reversible Reaction in a Catalytic Layer 406

10.8 Simultaneous Multicomponent Diffusion of Gases 413

10.9 Multicomponent Diffusion of Acetone and Methanol in Air 418

10.10 Multicomponent Diffusion in a Porous Layer Covering a Catalyst 419

10.11 Second-Order Reaction with Diffusion in Liquid Film 421

10.12 Simultaneous Heat and Mass Transfer in Catalyst Particles 423

10.13 Unsteady-State Mass Transfer in a Slab 428

10.14 Unsteady-State Diffusion and Reaction in a Semi-Infinite Slab 434

10.15 Diffusion and Reaction in a Falling Laminar Liquid Film 438

References 444

### Chapter 11 Chemical Reaction Engineering 445

11.1 Plug-Flow Reactor with Volume Change during Reaction 445

11.2 Variation of Conversion with Reaction Order in a Plug-Flow Reactor 450

11.3 Gas Phase Reaction in a Packed Bed Reactor with Pressure Drop 453

11.4 Catalytic Reactor with Membrane Separation 455

11.5 Semibatch Reactor with Reversible Liquid Phase Reaction 458

11.6 Operation of Three Continuous Stirred Tank Reactors in Series 462

11.7 Differential Method of Rate Data Analysis in a Batch Reactor 465

11.8 Integral Method of Rate Data Analysis in a Batch Reactor 467

11.9 Integral Method of Rate Data Analysis--Bimolecular Reaction 468

11.10 Initial Rate Method of Data Analysis 470

11.11 Half-Life Method for Rate Data Analysis 471

11.12 Method Of Excess for Rate Data Analysis in a Batch Reactor 474

11.13 Rate Data Analysis for a CSTR476

11.14 Differential Rate Data Analysis for a Plug-Flow Reactor 477

11.15 Integral Rate Data Analysis for a Plug-Flow Reactor 479

11.16 Determination of Rate Expressions for a Catalytic Reaction 481

11.17 Packed Bed Reactor Design for a Gas Phase Catalytic Reaction 485

11.18 Catalyst Decay in a Packed Bed Reactor Modeled by a Series Of CSTRs 488

11.19 Design for Catalyst Deactivation in a Straight-Through Reactor 491

11.20 Enzymatic Reactions in a Batch Reactor496

11.21 Isothermal Batch Reactor Design for Multiple Reactions 498

11.22 Material and Energy Balances on a Batch Reactor 502

11.23 Operation of a Cooled Exothermic CSTR504

11.24 Exothermic Reversible Gas Phase Reaction in a Packed Bed Reactor 509

11.25 Temperature Effects with Exothermic Reactions 512

11.26 Diffusion with Multiple Reactions in Porous Catalyst Particles 514

11.27 Nitrification Of Biomass in a Fluidized Bed Reactor 516

11.28 Sterilization Kinetics and Extinction Probabilities in Batch Fermenters 519

References 521

### Chapter 12 Phase Equilibria and Distillation523

12.1 Three Stage Flash Evaporator for Recovering Hexane from Octane 523

12.2 Non-Ideal Vapor-Liquid and Liquid-Liquid Equilibrium 527

12.3 Calculation of Wilson Equation Coefficients from Azeotropic Data 535

12.4 Van Laar Equations Coefficients from Azeotropic Data 541

12.5 Non-Ideal Vle from Azeotropic Data Using the Van Laar Equations 542

12.6 Fenske-Underwood-Gilliland Correlations for Separation Towers 544

12.7 Fenske-Underwood-Gilliland Correlations in Depropanizer Design 550

12.8 Rigorous Distillation Calculations for a Simple Separation Tower 551

12.9 Rigorous Distillation Calculations for Hexane-Octane Separation Tower 558

12.10 Batch Distillation of a Water-Ethanol Mixture 559

12.11 Dynamics Of Batch Distillation of Fermenter Broth 563

References 564

### Chapter 13 Process Dynamics and Control 565

13.1 Modeling the Dynamics of First- and Second-Order Systems 565

13.2 Dynamics of a U-Tube Manometer 572

13.3 Dynamics and Stability of an Exothermic CSTR 574

13.4 Fitting a First-Order Plus Dead-Time Model to Process Data 576

13.5 Dynamics and Control of a Flow-Through Storage Tank 580

13.6 Dynamics and Control of a Stirred Tank Heater 586

13.7 Controller Tuning Using Internal Model Control (IMC) Correlations 593

13.8 First Order Plus Dead Time Models for Stirred Tank Heater 596

13.9 Closed-Loop Controller Tuning-The Ziegler-Nichols Method 597

13.10 Pi Controller Tuning Using the Auto Tune Variation "ATV" Method 600

13.11 Reset Windup in a Stirred Tank Heater 603

13.12 Temperature Control and Startup of a Nonisothermal CSTR 604

13.13 Level Control of Two Interactive Tanks 605

13.14 Pi Control of Fermenter Temperature 609

13.15 Insulin Delivery to Diabetics Using Pi Control 612

References 615

### Chapter 14 Biochemical Engineering 617

14.1 Elementary Step and Approximate Models for Enzyme Kinetics 617

14.2 Determination and Modeling Inhibition for Enzyme-Catalyzed Reactions 622

14.3 Bioreactor Design with Enzyme Catalysts--Temperature Effects 626

14.4 Optimization of Temperature in Batch and CSTR Enzymatic Reactors 628

14.5 Diffusion with Reaction in Spherical Immobilized Enzyme Particles 630

14.6 Multiple Steady States in a Chemostat with Inhibited Microbial Growth 635

14.7 Fitting Parameters in the Monod Equation for a Batch Culture 638

14.8 Modeling and Analysis of Kinetics in a Chemostat 640

14.9 Dynamic Modeling of a Chemostat 643

14.10 Predator-Prey Dynamics of Mixed Cultures in a Chemostat 647

14.11 Biokinetic Modeling Incorporating Imperfect Mixing in a Chemostat 650

14.12 Dynamic Modeling of a Chemostat System with Two Stages 652

14.13 Semicontinuous Fed-Batch and Cyclic-Fed Batch Operation 655

14.14 Optimization of Ethanol Production in a Batch Fermenter 658

14.15 Ethanol Production in a Well-Mixed Fermenter with Cell Recycle 660

14.16 Dynamic Modeling of an Anaerobic Digester 663

14.17 Start-Up and Control of an Anaerobic Digester 668

References 672