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More About This Textbook
Overview
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
Practical Aspects of ProblemSolving Capabilities
The Book's Web Site (http://www.problemsolvingbook.com)
Product Details
Related Subjects
Meet the Author
Michael B. Cutlip is an emeritus professor in the Department of Chemical, Materials, and Biomolecular Engineering at the University of Connecticut. He is a coauthor of POLYMATH. His research interests include chemical and electrochemical reaction engineering.
Mordechai Shacham is the Benjamin H. Swig Professor in the Department of Chemical Engineering at the BenGurion University of the Negev. He is a coauthor of POLYMATH . His research interests include analysis, modeling, regression of data, applied numerical methods, and prediction and consistency analysis of physical properties.
Read an Excerpt
This book provides extensive problemsolving instruction and suggestions, numerous examples, and many complete and partial solutions in the main subject areas of chemical and biochemical engineering and related disciplines. Problem solutions are clearly developed using fundamental principles to create mathematical models. An equationoriented approach that enables computerbased problem solving on personal computers is utilized. Efficient and effective problem solving is introduced employing numerical methods for linear equations, nonlinear equations, ordinary and partial differential equations, linear and nonlinear regressions, and polynomial curve fitting. Basic to advanced problem solving is covered utilizing a novel integrated approach with three widely used mathematical software packages: POLYMATH, Excel, and MATLAB. Readers may choose to focus on one or more of these software packages or utilize another mathematical software package.
The book and a dedicated web site (http://www.problemsolvingbook.com) furnish all necessary problem information, software files, and additional enrichment materials. For advanced applications, unique software tools are provided for solving complex problems such as parameter estimation in dynamic systems and solution of constrained systems of algebraic equations.
Intended Audience
This book is intended for individuals who are interested in solving problems in chemical and biochemical engineering and in related fields by using mathematical software packages on personal computers. It can serve as a textbook for students in conjunction with college and universitylevel courses, and it can be a companion reference book for individual students. For professionals, it can be an invaluable reference book that also allows extensive selfstudy in problem solving using the most widely used software packages.
Background
Prior to the introduction of the personal computers and mathematical software packages in the early 1980's, desktop calculations for engineering problem solving were mainly carried out with handheld calculators. Sometimes mainframe computers were utilized, which required source code programming. Since then the emphasis has gradually moved to computerbased (or computerenhanced) problem solving or CBPS on desktop or notebook computers. By the time the first edition of this book was published in 1999, it became evident that CBPS can be a very important, or possibly the most important, application of the computer in scientific and engineering education and in industrial practice.
The first edition of this book provided examples to the use of CBPS in core chemical engineering subject areas using the POLYMATH software package. Shortly after the publication of the first edition, we carried out several comparison studies in order to determine what types of software packages should be included in the "toolbox" of the engineering student and the practicing engineer that would enable the effective and efficient solution of practical problems. We arrived at the conclusion that three types of software are needed. There is a need for a numerical problem solver, such as POLYMATH, that accepts the model equations close to their mathematical forms and provides their numerical solution with very minimal user intervention. Additionally, there is also a need to be able to use spreadsheet software, such as Excel, because of its wide use in business and industry. Software like Excel is also used for the organization and presentation of information in tabular and graphical forms and for database managementrelated operations. Software packages that support programming, such as MATLAB, are needed to implement algorithms which are required in graduate research and advanced mathematics, programming, control, and numerical analysis courses.
It is increasingly important for today's engineering student and forwardlooking engineering professionals to be proficient in the use of several software packages, and thus we greatly expanded the book so that it now includes solutions in Excel and MATLAB, in addition to POLYMATH. New problems have been introduced that demonstrate how the special capabilities of each of these packages can best be utilized for efficient and effective problem solving.
The POLYMATH Numerical Computation Package
The POLYMATH package provides convenient solutions to most numerical analysis problems, including the problems that are presented in this book. We authored and published the first PC version of POLYMATH in 1984, and it has been in use since then in over one hundred universities and selected industrial sites world wide. The version available at the time of the publication of the book, POLYMATH 6.1, was released in 2006. This package contains the following programs:
Ordinary Differential Equations Solver
Nonlinear Algebraic Equations Solver
Linear Algebraic Equations Solver
Polynomial, Multiple Linear, and Nonlinear Regression Program
The programs are extremely easy to use, and all options are menu driven. Equations are entered in standard form with userdefined notation. Results are presented in graphical or tabular form. A sophisticated calculator and a general unit conversion utility are available within POLYMATH.
The new and unique capability of the latest POLYMATH to automatically export any problem to Excel and MATLAB with a single keypress is extensively utilized within this book. Automatic export to Excel includes all intrinsic functions and logical variables. A POLYMATH ODE_Solver AddIn is included for solving ordinary differential equations in Excel. Upon export to MATLAB, the equations are ordered in the computational sequence, the intrinsic functions and logical statements are converted, and a MATLAB function is generated. Template files to run the functions are available in the HELP section of POLYMATH or from the book's web site.
Current information on the latest POLYMATH software is available from http://www.polymathsoftware.com.
Many departments and some universities have obtained site licenses for POLYMATH. These licenses allow installation in all computer labs, and individual copies can be provided to all students, faculty and staff for use on personal computers. Detailed information is available from academic@polymathsoftware.com
Use of This Book
This book is intended to serve as a companion text for the engineering student, the faculty instructor, or the practicing engineer. The instructions in the practical use of mathematical software package on representative problems from most chemical and biochemical engineering subject areas provide direct insight into problem setup and various practical aspects of numerical problem solving. For the undergraduate student at the early stages of his/her studies, the book can serve as the textbook for learning to categorize the problems according to the numerical methods that should be used for efficient and effective solutions. It provides basic instruction in the use of three popular and widely used software packages: POLYMATH, Excel, and MATLAB. Emphasis is on setting up problems and effectively obtaining the necessary solutions.
In addition to providing general numerical solving capabilities, the text gives problems in most subject areas so that it can serve as a reference book in most courses, as it provides example problems that can be illustrative of problems that may be assigned in the various courses. The book also provides help with problem solving in advanced level for problems often encountered in undergraduate and graduate research such as nonlinear regression, parameter estimation in differential systems, solving twopoint boundary value problems and partial differential equations, constrained equation solving, and optimization.
For the practicing engineer, the book serves as resource book in computerbased problem solving. It provides a solid foundation in problem solving and can develop basic and advanced skills in the utilization of spreadsheets. Practical problems illustrate various problem solving approaches that can be implemented for problem formulation, problem solving, analysis, presentation of results, and documentation. Of particular interest is the coverage of the correlation and regression of data with statistical analysis. All of the book's problems can be solved with the Excel spreadsheet software that is widely used in industry.
Engineering faculty can use the book to introduce numerical methods into an individual course, a sequence of courses, or an entire departmental curriculum. This book provides supplementary problems that can be assigned to students in order to introduce numerical problem solving which is avoided in most textbooks. Many of the problems can be easily extended to openended problem solving so that critical thinking skills can be developed. The numerical solutions can be used to answer many "what if" type questions so that students can be encouraged to think about the implications of the problem solutions. The book can also be used as a companion textbook for an introductory computer programming course or a comprehensive course in numerical analysis.
Book Organization
All the chapters of the book, except the introductory Chapter 1, are built around problems that serve to provide practical applications in a particular subject area. Most of the problems presented in the book have the same general format for the convenience of the reader. The concise problem topic is followed by a listing of the engineering concepts demonstrated by the problem. Then the numerical methods utilized in the solution are indicated just before the detailed problem statement. Each of the problems presents the detailed equations and parameter values that are necessary for solution, including the appropriate units in a variety of systems, with Systeme International d'Unites (SI) being the most commonly used. Because of the wide variety of problems posed in this book, the notation used has been standardized according to one of the major Prentice Hall textbooks in the various subject areas whenever possible. Physical properties are either given directly in the problem or in the appendices.
The book is divided into two parts. In the first part, which includes the first six chapters, subjects of general interest are presented, some on an introductory level and some on an advanced level. In Chapter 1, Introduction, the history of CBPS is briefly reviewed and guidelines are provided for categorizing problems according to the numerical techniques that should be used for their solution. Chapter 2, Basic Principles and Calculations, serves a dual purpose. The chapter introduces the reader to the subject material that is typically taught in a first chemical engineering course (in most universities called Material and Energy Balance, or Stoichiometry). Additionally, this chapter demonstrates the use of POLYMATH for solving simple problems belonging to the main categories discussed in the book, namely single nonlinear algebraic equations, systems of linear algebraic equations, linear and polynomial regression, and systems of ordinary differential equations (ODEs).
In Chapter 3, Regression and Correlation of Data, the application of POLYMATH for analysis and regression of data using advanced statistical techniques is demonstrated. Chapter 4, Problem Solving with Excel, introduces the reader to the engineering and scientific problem solving capabilities of Excel using problems belonging to the same categories as in Chapter 2. The automatic export capabilities of POLYMATH to Excel are discussed. More advanced topics such as solution of systems of nonlinear algebraic equations (NLEs) and optimization with constraints (nonlinear programming) are also presented.
In Chapter 5, Problem Solving with MATLAB, MATLAB is used to solve the problems presented in Chapter 4. The capability of POLYMATH to automatically generate MATLAB mfiles are presented and provided templates for MATLAB problem solutions are demonstrated and utilized. In Chapter 6, Advanced Techniques in Problem Solving, the problem solutions deal with advanced topics such as twopoint boundary value problems, systems of differentialalgebraic equations, partial differential equations, and parameter estimation in systems of differential equations.
The second part of the book (Chapters 7 through 14) is organized according to the particular subject areas such as Thermodynamics (Chapter 7), Fluid Mechanics (Chapter 8), and so forth. The content of these chapters is presented in the typical order of coverage in college or universitylevel courses.
New Content in the Second Edition
The contents of the book were almost doubled by adding six new chapters to the eight chapters of the first edition. The introductory Chapter 1 was added in order to help the reader in a very critical step of the problem solving—the characterization of the problem in terms of the solution method that has to be used.
After studying and verifying the importance of various software packages in effective and efficient problem solving, the two chapters dealing with the use of Excel and MATLAB were added. These chapters also introduce the new capability of the POLYMATH software to automatically convert a problem solution into Excel worksheets and MATLAB mfiles. This considerably shortens the learning curve associated with the initial use of these packages.
Since the first edition was published, biochemical engineering has gained importance and is now being taught in most colleges and universities. The new biochemical engineering chapter and selected problems in other chapters provide a wide selection of problems in this important subject area. New chapters on "Phase Equilibria and Distillation" (Chapter 12) and "Process Dynamics and Control" (Chapter 13) have been added.
Companion Web Site
Readers of the book are encouraged to make full use of the companion web site that will be maintained and extended by the book's authors. This web site, http://www.problemsolvingbook.com/ , enables downloads of program files which are used in the various book chapters for the three software packages: POLYMATH, Excel, and MATLAB. Additional educational problems, learning resources, corrections and updates to this book, and new materials are provided.
The web site also allows book owners to purchase and immediately download the latest POLYMATH software at significant discounts from the already highly discounted POLYMATH Educational version software. This enables book users to have the very latest software at very reasonable cost.
Instructors who are using the book have special access to all problems as well as substantial educational and enrichment materials through the companion web site. This include suggestions as to the book use in individual courses, sequences of courses, and throughout a departmental curriculum. Details about this access are provided in Chapter 1 from the authors.
Chemical and Biochemical Engineering Departments
Academic departments are encouraged to consider adopting this book during the first introductory course in chemical and/or biochemical engineering and then utilizing the book as a supplement for many of the following courses in the curriculum. This allows an integrated approach to the use of numerical methods throughout the curriculum. This approach can be helpful in satisfying the ABET requirements for appropriate computer use in undergraduate studies.
A first course in numerical methods can also utilize many of the problems as relevant examples. In this application, the book will supplement a standard numerical methods textbook. Students will find the problems in this book to be more interesting than the strictly mathematical or simplified problems presented in many standard numerical analysis textbooks.
Table of Contents
Prefacexv
Chapter 1 Problem Solving with Mathematical Software Packages 1
1.1 Efficient Problem SolvingThe 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 WebBased 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 RedlichKwong Equation 19
2.3 Stoichiometric Calculations for Biological Reactions 20
2.4 SteadyState 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 NPropane 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 UnsteadyState Mixing in a Tank 49
2.15 UnsteadyState 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 NPropane 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 DataChecking 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 RedlichKwong 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 RedlichKwong 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 TwoPoint Boundary Value Problems 218
6.6 Expediting the Solution of Systems of Nonlinear Algebraic Equations 223
6.7 Solving Differential Algebraic EquationsDAEs 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 RedlichKwong Equation of State 251
7.4 Thermodynamic Properties of Steam from RedlichKwong Equation 255
7.5 Enthalpy and Entropy Departure Using the RedlichKwong Equation 258
7.6 Fugacity Coefficients of Pure Fluids from Various Equations of State 263
7.7 Fugacity Coefficients for AmmoniaExperimental 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 NonNewtonian Fluids in a Horizontal Pipe 289
8.3 Vertical Laminar Flow of a Liquid Film291
8.4 Laminar Flow of NonNewtonian 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 MotionLaminar 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 OneDimensional 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 SinglePass Heat Exchanger with Convective Heat Transfer on Tube Side 357
9.9 DoublePipe Heat Exchanger361
9.10 Heat Losses from an Uninsulated Tank Due to Convection 365
9.11 UnsteadyState Radiation to a Thin Plate 368
9.12 UnsteadyState Conduction within a SemiInfinite Slab 370
9.13 Cooling of a Solid Sphere in a Finite Water Bath 373
9.14 UnsteadyState Conduction in Two Dimensions 378
References 382
Chapter 10 Mass Transfer 383
10.1 OneDimensional 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 FirstOrder 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 SecondOrder Reaction with Diffusion in Liquid Film 421
10.12 Simultaneous Heat and Mass Transfer in Catalyst Particles 423
10.13 UnsteadyState Mass Transfer in a Slab 428
10.14 UnsteadyState Diffusion and Reaction in a SemiInfinite Slab 434
10.15 Diffusion and Reaction in a Falling Laminar Liquid Film 438
References 444
Chapter 11 Chemical Reaction Engineering 445
11.1 PlugFlow Reactor with Volume Change during Reaction 445
11.2 Variation of Conversion with Reaction Order in a PlugFlow 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 AnalysisBimolecular Reaction 468
11.10 Initial Rate Method of Data Analysis 470
11.11 HalfLife 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 PlugFlow Reactor 477
11.15 Integral Rate Data Analysis for a PlugFlow 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 StraightThrough 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 NonIdeal VaporLiquid and LiquidLiquid 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 NonIdeal Vle from Azeotropic Data Using the Van Laar Equations 542
12.6 FenskeUnderwoodGilliland Correlations for Separation Towers 544
12.7 FenskeUnderwoodGilliland Correlations in Depropanizer Design 550
12.8 Rigorous Distillation Calculations for a Simple Separation Tower 551
12.9 Rigorous Distillation Calculations for HexaneOctane Separation Tower 558
12.10 Batch Distillation of a WaterEthanol 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 SecondOrder Systems 565
13.2 Dynamics of a UTube Manometer 572
13.3 Dynamics and Stability of an Exothermic CSTR 574
13.4 Fitting a FirstOrder Plus DeadTime Model to Process Data 576
13.5 Dynamics and Control of a FlowThrough 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 ClosedLoop Controller TuningThe ZieglerNichols 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 EnzymeCatalyzed Reactions 622
14.3 Bioreactor Design with Enzyme CatalystsTemperature 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 PredatorPrey 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 FedBatch and CyclicFed Batch Operation 655
14.14 Optimization of Ethanol Production in a Batch Fermenter 658
14.15 Ethanol Production in a WellMixed Fermenter with Cell Recycle 660
14.16 Dynamic Modeling of an Anaerobic Digester 663
14.17 StartUp and Control of an Anaerobic Digester 668
References 672
Appendix A 673
Appendix B 679
Appendix C 695
Appendix D 697
Appendix E 703
Appendix F 705
Index 709
Preface
Book Overview
This book provides extensive problemsolving instruction and suggestions, numerous examples, and many complete and partial solutions in the main subject areas of chemical and biochemical engineering and related disciplines. Problem solutions are clearly developed using fundamental principles to create mathematical models. An equationoriented approach that enables computerbased problem solving on personal computers is utilized. Efficient and effective problem solving is introduced employing numerical methods for linear equations, nonlinear equations, ordinary and partial differential equations, linear and nonlinear regressions, and polynomial curve fitting. Basic to advanced problem solving is covered utilizing a novel integrated approach with three widely used mathematical software packages: POLYMATH, Excel, and MATLAB. Readers may choose to focus on one or more of these software packages or utilize another mathematical software package.
The book and a dedicated web site (http://www.problemsolvingbook.com) furnish all necessary problem information, software files, and additional enrichment materials. For advanced applications, unique software tools are provided for solving complex problems such as parameter estimation in dynamic systems and solution of constrained systems of algebraic equations.
Intended Audience
This book is intended for individuals who are interested in solving problems in chemical and biochemical engineering and in related fields by using mathematical software packages on personal computers. It can serve as a textbook for students in conjunction with college and universitylevel courses, and it can be a companion reference book for individual students. For professionals, it can be an invaluable reference book that also allows extensive selfstudy in problem solving using the most widely used software packages.
Background
Prior to the introduction of the personal computers and mathematical software packages in the early 1980's, desktop calculations for engineering problem solving were mainly carried out with handheld calculators. Sometimes mainframe computers were utilized, which required source code programming. Since then the emphasis has gradually moved to computerbased (or computerenhanced) problem solving or CBPS on desktop or notebook computers. By the time the first edition of this book was published in 1999, it became evident that CBPS can be a very important, or possibly the most important, application of the computer in scientific and engineering education and in industrial practice.
The first edition of this book provided examples to the use of CBPS in core chemical engineering subject areas using the POLYMATH software package. Shortly after the publication of the first edition, we carried out several comparison studies in order to determine what types of software packages should be included in the "toolbox" of the engineering student and the practicing engineer that would enable the effective and efficient solution of practical problems. We arrived at the conclusion that three types of software are needed. There is a need for a numerical problem solver, such as POLYMATH, that accepts the model equations close to their mathematical forms and provides their numerical solution with very minimal user intervention. Additionally, there is also a need to be able to use spreadsheet software, such as Excel, because of its wide use in business and industry. Software like Excel is also used for the organization and presentation of information in tabular and graphical forms and for database managementrelated operations. Software packages that support programming, such as MATLAB, are needed to implement algorithms which are required in graduate research and advanced mathematics, programming, control, and numerical analysis courses.
It is increasingly important for today's engineering student and forwardlooking engineering professionals to be proficient in the use of several software packages, and thus we greatly expanded the book so that it now includes solutions in Excel and MATLAB, in addition to POLYMATH. New problems have been introduced that demonstrate how the special capabilities of each of these packages can best be utilized for efficient and effective problem solving.
The POLYMATH Numerical Computation Package
The POLYMATH package provides convenient solutions to most numerical analysis problems, including the problems that are presented in this book. We authored and published the first PC version of POLYMATH in 1984, and it has been in use since then in over one hundred universities and selected industrial sites world wide. The version available at the time of the publication of the book, POLYMATH 6.1, was released in 2006. This package contains the following programs:
Ordinary Differential Equations Solver
Nonlinear Algebraic Equations Solver
Linear Algebraic Equations Solver
Polynomial, Multiple Linear, and Nonlinear Regression Program
The programs are extremely easy to use, and all options are menu driven. Equations are entered in standard form with userdefined notation. Results are presented in graphical or tabular form. A sophisticated calculator and a general unit conversion utility are available within POLYMATH.
The new and unique capability of the latest POLYMATH to automatically export any problem to Excel and MATLAB with a single keypress is extensively utilized within this book. Automatic export to Excel includes all intrinsic functions and logical variables. A POLYMATH ODE_Solver AddIn is included for solving ordinary differential equations in Excel. Upon export to MATLAB, the equations are ordered in the computational sequence, the intrinsic functions and logical statements are converted, and a MATLAB function is generated. Template files to run the functions are available in the HELP section of POLYMATH or from the book's web site.
Current information on the latest POLYMATH software is available from http://www.polymathsoftware.com.
Many departments and some universities have obtained site licenses for POLYMATH. These licenses allow installation in all computer labs, and individual copies can be provided to all students, faculty and staff for use on personal computers. Detailed information is available from academic@polymathsoftware.com
Use of This Book
This book is intended to serve as a companion text for the engineering student, the faculty instructor, or the practicing engineer. The instructions in the practical use of mathematical software package on representative problems from most chemical and biochemical engineering subject areas provide direct insight into problem setup and various practical aspects of numerical problem solving. For the undergraduate student at the early stages of his/her studies, the book can serve as the textbook for learning to categorize the problems according to the numerical methods that should be used for efficient and effective solutions. It provides basic instruction in the use of three popular and widely used software packages: POLYMATH, Excel, and MATLAB. Emphasis is on setting up problems and effectively obtaining the necessary solutions.
In addition to providing general numerical solving capabilities, the text gives problems in most subject areas so that it can serve as a reference book in most courses, as it provides example problems that can be illustrative of problems that may be assigned in the various courses. The book also provides help with problem solving in advanced level for problems often encountered in undergraduate and graduate research such as nonlinear regression, parameter estimation in differential systems, solving twopoint boundary value problems and partial differential equations, constrained equation solving, and optimization.
For the practicing engineer, the book serves as resource book in computerbased problem solving. It provides a solid foundation in problem solving and can develop basic and advanced skills in the utilization of spreadsheets. Practical problems illustrate various problem solving approaches that can be implemented for problem formulation, problem solving, analysis, presentation of results, and documentation. Of particular interest is the coverage of the correlation and regression of data with statistical analysis. All of the book's problems can be solved with the Excel spreadsheet software that is widely used in industry.
Engineering faculty can use the book to introduce numerical methods into an individual course, a sequence of courses, or an entire departmental curriculum. This book provides supplementary problems that can be assigned to students in order to introduce numerical problem solving which is avoided in most textbooks. Many of the problems can be easily extended to openended problem solving so that critical thinking skills can be developed. The numerical solutions can be used to answer many "what if" type questions so that students can be encouraged to think about the implications of the problem solutions. The book can also be used as a companion textbook for an introductory computer programming course or a comprehensive course in numerical analysis.
Book Organization
All the chapters of the book, except the introductory Chapter 1, are built around problems that serve to provide practical applications in a particular subject area. Most of the problems presented in the book have the same general format for the convenience of the reader. The concise problem topic is followed by a listing of the engineering concepts demonstrated by the problem. Then the numerical methods utilized in the solution are indicated just before the detailed problem statement. Each of the problems presents the detailed equations and parameter values that are necessary for solution, including the appropriate units in a variety of systems, with Systeme International d'Unites (SI) being the most commonly used. Because of the wide variety of problems posed in this book, the notation used has been standardized according to one of the major Prentice Hall textbooks in the various subject areas whenever possible. Physical properties are either given directly in the problem or in the appendices.
The book is divided into two parts. In the first part, which includes the first six chapters, subjects of general interest are presented, some on an introductory level and some on an advanced level. In Chapter 1, Introduction, the history of CBPS is briefly reviewed and guidelines are provided for categorizing problems according to the numerical techniques that should be used for their solution. Chapter 2, Basic Principles and Calculations, serves a dual purpose. The chapter introduces the reader to the subject material that is typically taught in a first chemical engineering course (in most universities called Material and Energy Balance, or Stoichiometry). Additionally, this chapter demonstrates the use of POLYMATH for solving simple problems belonging to the main categories discussed in the book, namely single nonlinear algebraic equations, systems of linear algebraic equations, linear and polynomial regression, and systems of ordinary differential equations (ODEs).
In Chapter 3, Regression and Correlation of Data, the application of POLYMATH for analysis and regression of data using advanced statistical techniques is demonstrated. Chapter 4, Problem Solving with Excel, introduces the reader to the engineering and scientific problem solving capabilities of Excel using problems belonging to the same categories as in Chapter 2. The automatic export capabilities of POLYMATH to Excel are discussed. More advanced topics such as solution of systems of nonlinear algebraic equations (NLEs) and optimization with constraints (nonlinear programming) are also presented.
In Chapter 5, Problem Solving with MATLAB, MATLAB is used to solve the problems presented in Chapter 4. The capability of POLYMATH to automatically generate MATLAB mfiles are presented and provided templates for MATLAB problem solutions are demonstrated and utilized. In Chapter 6, Advanced Techniques in Problem Solving, the problem solutions deal with advanced topics such as twopoint boundary value problems, systems of differentialalgebraic equations, partial differential equations, and parameter estimation in systems of differential equations.
The second part of the book (Chapters 7 through 14) is organized according to the particular subject areas such as Thermodynamics (Chapter 7), Fluid Mechanics (Chapter 8), and so forth. The content of these chapters is presented in the typical order of coverage in college or universitylevel courses.
New Content in the Second Edition
The contents of the book were almost doubled by adding six new chapters to the eight chapters of the first edition. The introductory Chapter 1 was added in order to help the reader in a very critical step of the problem solvingthe characterization of the problem in terms of the solution method that has to be used.
After studying and verifying the importance of various software packages in effective and efficient problem solving, the two chapters dealing with the use of Excel and MATLAB were added. These chapters also introduce the new capability of the POLYMATH software to automatically convert a problem solution into Excel worksheets and MATLAB mfiles. This considerably shortens the learning curve associated with the initial use of these packages.
Since the first edition was published, biochemical engineering has gained importance and is now being taught in most colleges and universities. The new biochemical engineering chapter and selected problems in other chapters provide a wide selection of problems in this important subject area. New chapters on "Phase Equilibria and Distillation" (Chapter 12) and "Process Dynamics and Control" (Chapter 13) have been added.
Companion Web Site
Readers of the book are encouraged to make full use of the companion web site that will be maintained and extended by the book's authors. This web site, http://www.problemsolvingbook.com/ , enables downloads of program files which are used in the various book chapters for the three software packages: POLYMATH, Excel, and MATLAB. Additional educational problems, learning resources, corrections and updates to this book, and new materials are provided.
The web site also allows book owners to purchase and immediately download the latest POLYMATH software at significant discounts from the already highly discounted POLYMATH Educational version software. This enables book users to have the very latest software at very reasonable cost.
Instructors who are using the book have special access to all problems as well as substantial educational and enrichment materials through the companion web site. This include suggestions as to the book use in individual courses, sequences of courses, and throughout a departmental curriculum. Details about this access are provided in Chapter 1 from the authors.
Chemical and Biochemical Engineering Departments
Academic departments are encouraged to consider adopting this book during the first introductory course in chemical and/or biochemical engineering and then utilizing the book as a supplement for many of the following courses in the curriculum. This allows an integrated approach to the use of numerical methods throughout the curriculum. This approach can be helpful in satisfying the ABET requirements for appropriate computer use in undergraduate studies.
A first course in numerical methods can also utilize many of the problems as relevant examples. In this application, the book will supplement a standard numerical methods textbook. Students will find the problems in this book to be more interesting than the strictly mathematical or simplified problems presented in many standard numerical analysis textbooks.