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Problem Solving in Chemical and Biochemical Engineering with POLYMATH,

Book 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

  1. Copyright
    1. Dedication
  2. Prentice Hall PTR International Series in the Physical and Chemical Engineering Sciences
  3. Preface
    1. Book Overview
    2. Intended Audience
    3. Background
    4. The POLYMATH Numerical Computation Package
    5. Use of This Book
    6. Book Organization
    7. New Content in the Second Edition
    8. Companion Web Site
    9. Recommendation for Book Use in Various Courses
    10. Chemical and Biochemical Engineering Departments
    11. Acknowledgments
  4. 1. Problem Solving with Mathematical Software Packages
    1. 1.1. Efficient Problem Solving—The Objective of This Book
    2. 1.2. From Manual Problem Solving to Use of Mathematical Software
    3. 1.3. Categorizing Problems According to the Solution Technique Used
      1. (a) Consecutive Calculations
      2. (b) System of Linear Algebraic Equations
      3. (c) One Nonlinear (Implicit) Algebraic Equation
      4. (d) Multiple Linear and Polynomial Regressions
      5. (e) Systems of First-Order Ordinary Differential Equations (ODEs) – Initial Value Problems
      6. (f) System of Nonlinear Algebraic Equations (NLEs)
      7. (g) Higher Order ODEs
      8. (h) Systems of First-Order ODEs—Boundary Value Problems
      9. (i) Stiff Systems of First-Order ODEs
      10. (j) Differential-Algebraic System of Equations (DAEs)
      11. (k) Partial Differential Equations (PDEs)
      12. (l) Nonlinear Regression
      13. (m) Parameter Estimation in Dynamic Systems
      14. (n) Nonlinear Programming (Optimization) with Equity Constraints
    4. 1.4. Effective Use of This Book
    5. 1.5. Software Usage with This Book
    6. 1.6. Web-Based Resources for This Book
    7. General References
  5. 2. Basic Principles and Calculations
    1. 2.1. Molar Volume and Compressibility Factor from Van Der Waals Equation
      1. 2.1.1. Concepts Demonstrated
      2. 2.1.2. Numerical Methods Utilized
      3. 2.1.3. Problem Statement
      4. 2.1.4. Solution
    2. 2.2. Molar Volume and Compressibility Factor from Redlich-Kwong Equation
      1. 2.2.1. Concepts Demonstrated
      2. 2.2.2. Numerical Methods Utilized
      3. 2.2.3. Problem Statement
    3. 2.3. Stoichiometric Calculations for Biological Reactions
      1. 2.3.1. Concepts Demonstrated
      2. 2.3.2. Numerical Methods Utilized
      3. 2.3.3. Problem Statement
      4. 2.3.4. Solution (Partial)
    4. 2.4. Steady-State Material Balances on a Separation Train
      1. 2.4.1. Concepts Demonstrated
      2. 2.4.2. Numerical Methods Utilized
      3. 2.4.3. Problem Statement
      4. 2.4.4. Solution (Partial)
    5. 2.5. Fitting Polynomials and Correlation Equations to Vapor Pressure Data
      1. 2.5.1. Concepts Demonstrated
      2. 2.5.2. Numerical Methods Utilized
      3. 2.5.3. Problem Statement
        1. Polynomial Regression Expression
      4. 2.5.4. Solution
        1. (a) Data Correlation by a Polynomial
        2. (b) Clapeyron Equation Data Correlation
        3. (c) Riedel Equation Data Correlation
        4. (d) Comparison of Data Correlations
    6. 2.6. Vapor Pressure Correlations for Sulfur Compounds in Petroleum
      1. 2.6.1. Concepts Demonstrated
      2. 2.6.2. Numerical Methods Utilized
      3. 2.6.3. Problem Statement
    7. 2.7. Mean Heat Capacity of n-Propane
      1. 2.7.1. Concepts Demonstrated
      2. 2.7.2. Numerical Methods Utilized
      3. 2.7.3. Problem Statement
      4. 2.7.4. Solution (Suggestions)
        1. Approach (1)
        2. Approach (2)
    8. 2.8. Vapor Pressure Correlation by Clapeyron and Antoine Equations
      1. 2.8.1. Concepts Demonstrated
      2. 2.8.2. Numerical Methods Utilized
      3. 2.8.3. Problem Statement
      4. 2.8.4. Solution (Partial)
    9. 2.9. Gas Volume Calculations using Various Equations of State
      1. 2.9.1. Concepts Demonstrated
      2. 2.9.2. Numerical Methods Utilized
      3. 2.9.3. Problem Statement
        1. Ideal Gas
        2. van der Waals equation
        3. Soave-Redlich-Kwong equation
        4. Peng-Robinson[7] equation
        5. Beattie-Bridgeman[4] equation
      4. 2.9.4. Solution (Partial)
    10. 2.10. Bubble Point Calculation for an Ideal Binary Mixture
      1. 2.10.1. Concepts Demonstrated
      2. 2.10.2. Numerical Methods Utilized
      3. 2.10.3. Problem Statement
      4. 2.10.4. Solution
    11. 2.11. Dew Point Calculation for an Ideal Binary Mixture
      1. 2.11.1. Concepts Demonstrated
      2. 2.11.2. Numerical Methods Utilized
      3. 2.11.3. Problem Statement
      4. 2.11.4. Solution (Partial)
    12. 2.12. Bubble Point and Dew Point for an Ideal Multicomponent Mixture
      1. 2.12.1. Concepts Demonstrated
      2. 2.12.2. Numerical Methods Utilized
      3. 2.12.3. Problem Statement
      4. 2.12.4. Solution
    13. 2.13. Adiabatic Flame Temperature in Combustion
      1. 2.13.1. Concepts Demonstrated
      2. 2.13.2. Numerical Methods Utilized
      3. 2.13.3. Problem Statement
      4. 2.13.4. Solution
    14. 2.14. Unsteady-State Mixing in a Tank
      1. 2.14.1. Concepts Demonstrated
      2. 2.14.2. Numerical Methods Utilized
      3. 2.14.3. Problem Statement
      4. 2.14.4. Solution
    15. 2.15. Unsteady-State Mixing in a Series of Tanks
      1. 2.15.1. Concepts Demonstrated
      2. 2.15.2. Numerical Methods Utilized
      3. 2.15.3. Problem Statement
    16. 2.16. Heat Exchange in a Series of Tanks
      1. 2.16.1. Concepts Demonstrated
      2. 2.16.2. Numerical Methods Utilized
      3. 2.16.3. Problem Statement
      4. 2.16.4. Solution
    17. References
  6. 3. Regression and Correlation of Data
    1. 3.1. Estimation of Antoine Equation Parameters Using Nonlinear Regression
      1. 3.1.1. Concepts Demonstrated
      2. 3.1.2. Numerical Methods Utilized
      3. 3.1.3. Excel Options and Functions Demonstrated
      4. 3.1.4. Problem Definition
        1. Nonlinear Regression
          1. (a) Nonlinear Regression of the Antoine Equation
          2. (b) Overall Variance for the Antoine Equation
          3. (c) Residuals Plot for the Antoine Equation
          4. (d) Precision of Data and Appropriateness of Antoine Equation
    2. 3.2. Antoine Equation Parameters for Various Hydrocarbons
      1. 3.2.1. Concepts Demonstrated
      2. 3.2.2. Numerical Methods Utilized
      3. 3.2.3. Excel Options and Functions Demonstrated
    3. 3.3. Correlation of Thermodynamic and Physical Properties of n-Propane
      1. 3.3.1. Concepts Demonstrated
      2. 3.3.2. Numerical Methods Utilized
      3. 3.3.3. Excel Options and Functions Demonstrated
      4. 3.3.4. Problem Definition
        1. (a) Heat Capacity for a Gas
        2. (b) Thermal Conductivity
        3. (c) Liquid Viscosity
        4. (d) Heat of Vaporization
    4. 3.4. Temperature Dependency of Selected Properties
      1. 3.4.1. Concepts Demonstrated
      2. 3.4.2. Numerical Methods Utilized
      3. 3.4.3. Excel Options and Functions Demonstrated
    5. 3.5. Heat Transfer Correlations from Dimensional Analysis
      1. 3.5.1. Concepts Demonstrated
      2. 3.5.2. Numerical Methods Utilized
      3. 3.5.3. Excel Options and Functions Demonstrated
      4. 3.5.4. Problem Definition
        1. Confidence Intervals
        2. Residual Plots
        3. Comparison of Variances
        4. Possible Interdependency of Variables
        5. Final Correlation
    6. 3.6. Heat Transfer Correlation of Liquids in Tubes
      1. 3.6.1. Concepts Demonstrated
      2. 3.6.2. Numerical Methods Utilized
      3. 3.6.3. Excel Options and Functions Demonstrated
      4. 3.6.4. Problem Definition (Comment)
    7. 3.7. Heat Transfer in Fluidized Bed Reactor
      1. 3.7.1. Concepts Demonstrated
      2. 3.7.2. Numerical Methods Utilized
      3. 3.7.3. Excel Options and Functions Demonstrated
    8. 3.8. Correlation of Binary Activity Coefficients Using Margules Equations
      1. 3.8.1. Concepts Demonstrated
      2. 3.8.2. Numerical Methods Utilized
      3. 3.8.3. Excel Options and Functions Demonstrated
      4. 3.8.4. Problem Definition
        1. (a) Linear Regression of Excess Gibbs Energy Equation
        2. (b) Nonlinear Regression for Sum of Equations (3-30) and (3-31)
        3. (c) Compare the Results of the Regressions in (a) and (b)
    9. 3.9. Margules Equations for Binary Systems Containing Trichloroethane
      1. 3.9.1. Concepts Demonstrated
      2. 3.9.2. Numerical Methods Utilized
      3. 3.9.3. Excel Options and Functions Demonstrated
    10. 3.10. Rate Data Analysis for a Catalytic Reforming Reaction
      1. 3.10.1. Concepts Demonstrated
      2. 3.10.2. Numerical Methods Utilized
      3. 3.10.3. Excel Options and Functions Demonstrated
    11. 3.11. Regression of Rate Data–Checking Dependency Among Variables
      1. 3.11.1. Concepts Demonstrated
      2. 3.11.2. Numerical Methods Utilized
      3. 3.11.3. Excel Options and Functions Demonstrated
      4. 3.11.4. Problem Definition
        1. (a) Regression of Rate Expressions
        2. (b) Comparison of Rate Models
        3. (c) Checking for Correlation of Variables
        4. (d) Significance of any Correlation among the Regression Variables
    12. 3.12. Regression of Heterogeneous Catalytic Rate Data
      1. 3.12.1. Concepts Demonstrated
      2. 3.12.2. Numerical Methods Utilized
      3. 3.12.3. Excel Options and Functions Demonstrated
    13. 3.13. Variation of Reaction Rate Constant with Temperature
      1. 3.13.1. Concepts Demonstrated
      2. 3.13.2. Numerical Methods Utilized
      3. 3.13.3. Excel Options and Functions Demonstrated
    14. 3.14. Calculation of Antoine Equation Parameters Using Linear Regression
      1. 3.14.1. Concepts Demonstrated
      2. 3.14.2. Numerical Methods Utilized
      3. 3.14.3. Excel Options and Functions Demonstrated
        1. Multiple Linear Regression
      4. 3.14.4. Problem Definition
    15. References
  7. 4. Problem Solving with Excel
    1. 4.1. Molar Volume and Compressibility from Redlich-Kwong Equation
      1. 4.1.1. Concepts Demonstrated
      2. 4.1.2. Numerical Methods Utilized
      3. 4.1.3. Excel Options and Functions Demonstrated
      4. 4.1.4. Problem Definition
      5. 4.1.5. Solution
    2. 4.2. Calculation of the Flow Rate in a Pipeline
      1. 4.2.1. Concepts Demonstrated
      2. 4.2.2. Numerical Methods Utilized
      3. 4.2.3. Excel Options and Functions Demonstrated
      4. 4.2.4. Problem Definition
      5. 4.2.5. Equations and Numerical Data
      6. 4.2.6. Solution
    3. 4.3. Adiabatic Operation of a Tubular Reactor for Cracking of Acetone
      1. 4.3.1. Concepts Demonstrated
      2. 4.3.2. Numerical Methods Utilized
      3. 4.3.3. Excel Options and Functions Demonstrated
      4. 4.3.4. Problem Definition
      5. 4.3.5. Equations and Numerical Data
      6. 4.3.6. Solution (Partial)
    4. 4.4. Correlation of the Physical Properties of Ethane
      1. 4.4.1. Concepts Demonstrated
      2. 4.4.2. Numerical Methods Utilized
      3. 4.4.3. Excel Options and Functions Demonstrated
      4. 4.4.4. Problem Definition
      5. 4.4.5. Solution
    5. 4.5. Complex Chemical Equilibrium by Gibbs Energy Minimization
      1. 4.5.1. Concepts Demonstrated
      2. 4.5.2. Numerical Methods Utilized
      3. 4.5.3. Excel Options and Functions Demonstrated
      4. 4.5.4. Problem Definition
      5. 4.5.5. Solution
    6. References
  8. 5. Problem Solving with MATLAB
    1. 5.1. Molar Volume and Compressibility from Redlich-Kwong Equation
      1. 5.1.1. Concepts Demonstrated
      2. 5.1.2. Numerical Methods Utilized
      3. 5.1.3. MATLAB Options and Functions Demonstrated
      4. 5.1.4. Problem Definition
      5. 5.1.5. Solution
    2. 5.2. Calculation of the Flow Rate in a Pipeline
      1. 5.2.1. Concepts Demonstrated
      2. 5.2.2. Numerical Methods Utilized
      3. 5.2.3. MATLAB Options and Functions Demonstrated
      4. 5.2.4. Problem Definition
      5. 5.2.5. Solution
    3. 5.3. Adiabatic Operation of a Tubular Reactor for Cracking of Acetone
      1. 5.3.1. Concepts Demonstrated
      2. 5.3.2. Numerical Methods Utilized
      3. 5.3.3. MATLAB Options and Functions Demonstrated
      4. 5.3.4. Problem Definition
      5. 5.3.5. Solution
    4. 5.4. Correlation of the Physical Properties of Ethane
      1. 5.4.1. Concepts Demonstrated
      2. 5.4.2. Numerical Methods Utilized
      3. 5.4.3. MATLAB Options and Functions Demonstrated
      4. 5.4.4. Problem Definition
      5. 5.4.5. Solution
    5. 5.5. Complex Chemical Equilibrium by Gibbs Energy Minimization
      1. 5.5.1. Concepts Demonstrated
      2. 5.5.2. Numerical Methods Utilized
      3. 5.5.3. MATLAB Options and Functions Demonstrated
      4. 5.5.4. Problem Definition
      5. 5.5.5. Solution
        1. Input Parameters for conles
        2. Output Parameters for conles
    6. Reference
  9. 6. Advanced Techniques in Problem Solving
    1. 6.1. Solution of Stiff Ordinary Differential Equations
      1. 6.1.1. Concepts Demonstrated
      2. 6.1.2. Numerical Methods Utilized
      3. 6.1.3. Problem Statement
      4. 6.1.4. Solution
    2. 6.2. Stiff Ordinary Differential Equations in Chemical Kinetics
      1. 6.2.1. Concepts Demonstrated
      2. 6.2.2. Numerical Methods Utilized
      3. 6.2.3. Problem Statement
    3. 6.3. Multiple Steady States in a System of Ordinary Differential Equations
      1. 6.3.1. Concepts Demonstrated
      2. 6.3.2. Numerical Methods Utilized
      3. 6.3.3. Problem Statement
      4. 6.3.4. Solution (Partial)
    4. 6.4. Iterative Solution of an ODE Boundary Value Problem
      1. 6.4.1. Concepts Demonstrated
      2. 6.4.2. Numerical Methods Utilized
      3. 6.4.3. Problem Statement
      4. 6.4.4. Solution
        1. (a) Secant Method—POLYMATH Solution
        2. (a) Secant Method—MATLAB Solution
        3. (b) False Position Method—POLYMATH Solution
        4. (b) False Position Method—MATLAB Solution
    5. 6.5. Shooting Method for Solving Two-Point Boundary Value Problems
      1. 6.5.1. Concepts Demonstrated
      2. 6.5.2. Numerical Methods Utilized
      3. 6.5.3. Problem Statement
      4. 6.5.4. Solution (Partial)
        1. Solving Higher Order Ordinary Differential Equations
        2. Shooting Method—Trial and Error
        3. Secant Method for Boundary Condition Convergence
    6. 6.6. Expediting the Solution of Systems of Nonlinear Algebraic Equations
      1. 6.6.1. Concepts Demonstrated
      2. 6.6.2. Numerical Methods Utilized
      3. 6.6.3. Problem Statement
      4. 6.6.4. Solution and Partial Solution
        1. Expediting the Solution of Nonlinear Equations
    7. 6.7. Solving Differential Algebraic Equations—DAEs
      1. 6.7.1. Concepts Demonstrated
      2. 6.7.2. Numerical Methods Utilized
      3. 6.7.3. Problem Statement
      4. 6.7.4. Solution (Partial)
        1. Approach 1
        2. Approach 2
    8. 6.8. Method of Lines for Partial Differential Equations
      1. 6.8.1. Concepts Demonstrated
      2. 6.8.2. Numerical Methods Utilized
      3. 6.8.3. Problem Statement
        1. The Numerical Method of Lines
        2. Surface Boundary Condition
      4. 6.8.4. Solution
    9. 6.9. Estimating Model Parameters Involving ODEs Using Fermentation Data
      1. 6.9.1. Concepts Demonstrated
      2. 6.9.2. Numerical Methods Utilized
      3. 6.9.3. Problem Statement (Adapted from Constantinides[15])
      4. 6.9.4. Solution
    10. References
  10. 7. Thermodynamics
    1. 7.1. Compressibility Factor Variation from van der Waals Equation
      1. 7.1.1. Concepts Demonstrated
      2. 7.1.2. Numerical Methods Utilized
      3. 7.1.3. Problem Statement
      4. 7.1.4. Solution
        1. (a)–(d) Approach 1
        2. (a)–(d) Approach 2
    2. 7.2. Compressibility Factor Variation from Various Equations of State
      1. 7.2.1. Concepts Demonstrated
      2. 7.2.2. Numerical Methods Utilized
      3. 7.2.3. Problem Statement
        1. Additional Information and Data
          1. The Virial Equation of State
      4. 7.2.4. Solution (Suggestions)
    3. 7.3. Isothermal Compression of Gas Using Redlich-Kwong Equation of State
      1. 7.3.1. Concepts Demonstrated
      2. 7.3.2. Numerical Methods Utilized
      3. 7.3.3. Problem Statement
        1. Additional Information and Data
          1. Redlich-Kwong Equation of State
      4. 7.3.4. Solution (Partial)
        1. Change of Variable to Allow Decreasing Independent Variable in ODEs
    4. 7.4. Thermodynamic Properties of Steam from Redlich-Kwong Equation
      1. 7.4.1. Concepts Demonstrated
      2. 7.4.2. Numerical Methods Utilized
      3. 7.4.3. Problem Statement
        1. Additional Information and Data
      4. 7.4.4. Solution (Partial)
    5. 7.5. Enthalpy and Entropy Departure Using the Redlich-Kwong Equation
      1. 7.5.1. Concepts Demonstrated
      2. 7.5.2. Numerical Methods Utilized
      3. 7.5.3. Problem Statement
        1. Additional Information and Data
      4. 7.5.4. Solution (Partial)
        1. Calculational Approach
    6. 7.6. Fugacity Coefficients of Pure Fluids from Various Equations of State
      1. 7.6.1. Concepts Demonstrated
      2. 7.6.2. Numerical Methods Utilized
      3. 7.6.3. Problem Statement
        1. Additional Information and Data
          1. van der Waals
          2. Redlich-Kwong
          3. Peng-Robinson
      4. 7.6.4. Solution (Comments)
    7. 7.7. Fugacity Coefficients for Ammonia—Experimental and Predicted
      1. 7.7.1. Concepts Demonstrated
      2. 7.7.2. Numerical Methods Utilized
      3. 7.7.3. Problem Statement
        1. Additional Information and Data
      4. 7.7.4. Solution (Suggestions)
    8. 7.8. Flash Evaporation of an Ideal Multicomponent Mixture
      1. 7.8.1. Concepts Demonstrated
      2. 7.8.2. Numerical Methods Utilized
      3. 7.8.3. Problem Statement
        1. Additional Information and Data
      4. 7.8.4. Solution (Partial)
    9. 7.9. Flash Evaporation of Various Hydrocarbon Mixtures
      1. 7.9.1. Concepts Demonstrated
      2. 7.9.2. Numerical Methods Utilized
      3. 7.9.3. Problem Statement
      4. 7.9.4. Solution (Suggestion)
    10. 7.10. Correlation of Activity Coefficients with the Van Laar Equations
      1. 7.10.1. Concepts Demonstrated
      2. 7.10.2. Numerical Methods Utilized
      3. 7.10.3. Problem Statement
      4. 7.10.4. Solution (Suggestions)
    11. 7.11. Vapor Liquid Equilibrium Data from Total Pressure Measurements I
      1. 7.11.1. Concepts Demonstrated
      2. 7.11.2. Numerical Methods Utilized
      3. 7.11.3. Problem Statement
        1. Additional Information and Data
      4. 7.11.4. Solution
    12. 7.12. Vapor Liquid Equilibrium Data from Total Pressure Measurements II
      1. 7.12.1. Concepts Demonstrated
      2. 7.12.2. Numerical Methods Utilized
      3. 7.12.3. Problem Statement
      4. 7.12.4. Solution (Suggestions)
    13. 7.13. Complex Chemical Equilibrium
      1. 7.13.1. Concepts Demonstrated
      2. 7.13.2. Numerical Methods Utilized
      3. 7.13.3. Problem Statement
      4. 7.13.4. Solution (Suggestions)
    14. 7.14. Reaction Equilibrium at Constant Pressure or Constant Volume
      1. 7.14.1. Concepts Demonstrated
      2. 7.14.2. Numerical Methods Utilized
      3. 7.14.3. Problem Statement
      4. 7.14.4. Solution (Suggestions)
    15. References
  11. 8. Fluid Mechanics
    1. 8.1. Laminar Flow of a Newtonian Fluid in a Horizontal Pipe
      1. 8.1.1. Concepts Demonstrated
      2. 8.1.2. Numerical Methods Utilized
      3. 8.1.3. Problem Statement
      4. 8.1.4. Solution
        1. Division by Zero
        2. Boundary Condition Convergence
    2. 8.2. Laminar Flow of Non-Newtonian Fluids in a Horizontal Pipe
      1. 8.2.1. Concepts Demonstrated
      2. 8.2.2. Numerical Methods Utilized
      3. 8.2.3. Problem Statement
      4. 8.2.4. Solution (Suggestions)
    3. 8.3. Vertical Laminar Flow of a Liquid Film
      1. 8.3.1. Concepts Demonstrated
      2. 8.3.2. Numerical Methods Utilized
      3. 8.3.3. Problem Statement
      4. 8.3.4. Solution (Suggestions)
        1. (a) and (b)
    4. 8.4. Laminar Flow of Non-Newtonian Fluids in a Horizontal Annulus
      1. 8.4.1. Concepts Demonstrated
      2. 8.4.2. Numerical Methods Utilized
      3. 8.4.3. Problem Statement
      4. 8.4.4. Solution (Suggestion)
        1. (a)–(c)
    5. 8.5. Temperature Dependency of Density and Viscosity of Various Liquids
      1. 8.5.1. Concepts Demonstrated
      2. 8.5.2. Numerical Methods Utilized
      3. 8.5.3. Problem Statement
      4. 8.5.4. Solution (Partial)
    6. 8.6. Terminal Velocity of Falling Particles
      1. 8.6.1. Concepts Demonstrated
      2. 8.6.2. Numerical Methods Utilized
      3. 8.6.3. Problem Statement
        1. Additional Information and Data
      4. 8.6.4. Solution for Water
    7. 8.7. Comparison of Friction Factor Correlations for Turbulent Pipe Flow
      1. 8.7.1. Concepts Demonstrated
      2. 8.7.2. Numerical Methods Utilized
      3. 8.7.3. Problem Statement
      4. 8.7.4. Solution (Suggestions)
    8. 8.8. Calculations Involving Friction Factors for Flow in Pipes
      1. 8.8.1. Concepts Demonstrated
      2. 8.8.2. Numerical Methods Utilized
      3. 8.8.3. Problem Statement
      4. 8.8.4. Solution (Partial)
    9. 8.9. Average Velocity in Turbulent Smooth Pipe Flow from Maximum Velocity
      1. 8.9.1. Concepts Demonstrated
      2. 8.9.2. Numerical Methods Utilized
      3. 8.9.3. Problem Statement
    10. 8.10. Calculation of the Flow Rate in a Pipeline
      1. 8.10.1. Concepts Demonstrated
      2. 8.10.2. Numerical Methods Utilized
      3. 8.10.3. Problem Statement
        1. Additional Information and Data
      4. 8.10.4. Solution (Suggestions)
    11. 8.11. Flow Distribution in a Pipeline Network
      1. 8.11.1. Concepts Demonstrated
      2. 8.11.2. Numerical Methods Utilized
      3. 8.11.3. Problem Statement
        1. Additional Information and Data
        2. Balance on Node 1
        3. Balance on Node 2
        4. Balance on Node 3
        5. Balance on Node 4
        6. Summation on Loop I
        7. Summation on Loop II
        8. Summation on Loop III
    12. 8.12. Water Distribution Network
      1. 8.12.1. Concepts Demonstrated
      2. 8.12.2. Numerical Methods Utilized
      3. 8.12.3. Problem Statement
      4. 8.12.4. Solution (Suggestions)
    13. 8.13. Pipe and Pump Network
      1. 8.13.1. Concepts Demonstrated
      2. 8.13.2. Numerical Methods Utilized
      3. 8.13.3. Problem Statement
        1. Additional Information and Data
      4. 8.13.4. Solution (Suggestions)
    14. 8.14. Optimal Pipe Length for Draining a Cylindrical Tank in Turbulent Flow
      1. 8.14.1. Concepts Demonstrated
      2. 8.14.2. Numerical Methods Utilized
      3. 8.14.3. Problem Statement
        1. Additional Information and Data
      4. 8.14.4. Solution (Suggestions)
    15. 8.15. Optimal Pipe Length for Draining a Cylindrical Tank in Laminar Flow
      1. 8.15.1. Concepts Demonstrated
      2. 8.15.2. Numerical Methods Utilized
      3. 8.15.3. Problem Statement
      4. 8.15.4. Solution (Suggestions)
    16. 8.16. Baseball Trajectories as a Function of Elevation
      1. 8.16.1. Concepts Demonstrated
      2. 8.16.2. Numerical Methods Utilized
      3. 8.16.3. Problem Statement
        1. Additional Information and Data
      4. 8.16.4. Solution (Suggestions)
        1. Retaining a Value when a Condition Is Satisfied
    17. 8.17. Velocity Profiles for a Wall Suddenly Set in Motion—Laminar Flow
      1. 8.17.1. Concepts Demonstrated
      2. 8.17.2. Numerical Methods Utilized
      3. 8.17.3. Problem Statement
      4. 8.17.4. Solution (Suggestions)
    18. 8.18. Boundary Layer Flow of a Newtonian Fluid on a Flat Plate
      1. 8.18.1. Concepts Demonstrated
      2. 8.18.2. Numerical Methods Utilized
      3. 8.18.3. Problem Statement
        1. Boundary Layer Thickness
        2. Drag Force Due to Skin Friction
      4. 8.18.4. Solution (Partial)
    19. References
  12. 9. Heat Transfer
    1. 9.1. One-Dimensional Heat Transfer Through a Multilayered Wall
      1. 9.1.1. Concepts Demonstrated
      2. 9.1.2. Numerical Methods Utilized
      3. 9.1.3. Problem Statement
      4. 9.1.4. Solution (Partial)
    2. 9.2. Heat Conduction in a Wire with Electrical Heat Source and Insulation
      1. 9.2.1. Concepts Demonstrated
      2. 9.2.2. Numerical Methods Utilized
      3. 9.2.3. Problem Statement
      4. 9.2.4. Solution (Partial)
    3. 9.3. Radial Heat Transfer by Conduction with Convection at Boundaries
      1. 9.3.1. Concepts Demonstrated
      2. 9.3.2. Numerical Methods Utilized
      3. 9.3.3. Problem Statement
        1. Additional Information and Data
      4. 9.3.4. Solution (Suggestions)
    4. 9.4. Energy Loss from an Insulated Pipe
      1. 9.4.1. Concepts Demonstrated
      2. 9.4.2. Numerical Methods Utilized
      3. 9.4.3. Problem Statement
    5. 9.5. Heat Loss Through Pipe Flanges
      1. 9.5.1. Concepts Demonstrated
      2. 9.5.2. Numerical Methods Utilized
      3. 9.5.3. Problem Statement
      4. 9.5.4. Solution (Partial)
    6. 9.6. Heat Transfer from a Horizontal Cylinder Attached to a Heated Wall
      1. 9.6.1. Concepts Demonstrated
      2. 9.6.2. Numerical Methods Utilized
      3. 9.6.3. Problem Statement
        1. Additional Information and Data
          1. Modeling Equations for Heat Transfer
          2. Equation for Heat Rate into Rod
      4. 9.6.4. Solution (Suggestions)
    7. 9.7. Heat Transfer from a Triangular Fin
      1. 9.7.1. Concepts Demonstrated
      2. 9.7.2. Numerical Methods Utilized
      3. 9.7.3. Problem Statement
    8. 9.8. Single-Pass Heat Exchanger with Convective Heat Transfer on Tube Side
      1. 9.8.1. Concepts Demonstrated
      2. 9.8.2. Numerical Methods Utilized
      3. 9.8.3. Problem Statement
        1. Additional Information and Data
          1. Average Temperature Driving Force
          2. Log Mean Temperature Driving Force
          3. Local Temperature Driving Force
      4. 9.8.4. Solution (Partial)
        1. (a) and (b)
    9. 9.9. Double-Pipe Heat Exchanger
      1. 9.9.1. Concepts Demonstrated
      2. 9.9.2. Numerical Methods Utilized
      3. 9.9.3. Problem Statement
        1. Additional Information and Data
          1. Cocurrent or Parallel Flow
          2. Overall Heat Transfer Coefficients
          3. Heat Transfer within the Shell
          4. Countercurrent Flow
      4. 9.9.4. Solution (Suggestions)
    10. 9.10. Heat Losses from an Uninsulated Tank Due to Convection
      1. 9.10.1. Concepts Demonstrated
      2. 9.10.2. Numerical Methods Utilized
      3. 9.10.3. Problem Statement
        1. Additional Information and Data
          1. Natural Convection
          2. Forced Convection
      4. 9.10.4. Solution (Suggestions)
        1. (a) Calm Air
        2. (b) Windy Conditions
    11. 9.11. Unsteady-State Radiation to a Thin Plate
      1. 9.11.1. Concepts Demonstrated
      2. 9.11.2. Numerical Methods Utilized
      3. 9.11.3. Problem Statement
        1. Additional Information and Data
    12. 9.12. Unsteady-State Conduction within a Semi-Infinite Slab
      1. 9.12.1. Concepts Demonstrated
      2. 9.12.2. Numerical Methods Utilized
      3. 9.12.3. Problem Statement
      4. 9.12.4. Solution (Suggestions)
        1. (a) and (b)
    13. 9.13. Cooling of a Solid Sphere in a Finite Water Bath
      1. 9.13.1. Concepts Demonstrated
      2. 9.13.2. Numerical Methods Utilized
      3. 9.13.3. Problem Statement
      4. 9.13.4. Solution (Partial)
        1. Boundary Condition at Surface of the Sphere
        2. Boundary Condition at Center of the Sphere
        3. Numerical Solution
    14. 9.14. Unsteady-State Conduction in Two Dimensions
      1. 9.14.1. Concepts Demonstrated
      2. 9.14.2. Numerical Methods Utilized
      3. 9.14.3. Problem Statement
        1. The Numerical Method of Lines
      4. 9.14.4. Solution (Partial)
    15. References
  13. 10. Mass Transfer
    1. 10.1. One-Dimensional Binary Mass Transfer in a Stefan Tube
      1. 10.1.1. Concepts Demonstrated
      2. 10.1.2. Numerical Methods Utilized
      3. 10.1.3. Problem Statement
        1. Mass Balance on Component A within Diffusion Path
        2. Fick’s Law for Binary Diffusion
        3. Final Equations and Boundary Conditions
        4. Analytical Solution
          1. Additional Information and Data
      4. 10.1.4. Solution (Partial with Suggestions)
        1. (a), (b), and (c)
    2. 10.2. Mass Transfer in a Packed Bed with Known Mass Transfer Coefficient
      1. 10.2.1. Concepts Demonstrated
      2. 10.2.2. Numerical Methods Utilized
      3. 10.2.3. Problem Statement
        1. Additional Information and Data
      4. 10.2.4. Solution (Suggestions)
    3. 10.3. Slow Sublimation of a Solid Sphere
      1. 10.3.1. Concepts Demonstrated
      2. 10.3.2. Numerical Methods Utilized
      3. 10.3.3. Problem Statement
        1. Additional Information and Data
          1. Diffusion
          2. Mass Transfer Coefficient
      4. 10.3.4. Solution (Partial with Suggestions)
    4. 10.4. Controlled Drug Delivery by Dissolution of Pill Coating
      1. 10.4.1. Concepts Demonstrated
      2. 10.4.2. Numerical Methods Utilized
      3. 10.4.3. Problem Statement (Adapted from Fogler,[4] p. 600)
        1. Additional Information and Data
      4. 10.4.4. Solution (Suggestions)
    5. 10.5. Diffusion with Simultaneous Reaction in Isothermal Catalyst Particles
      1. 10.5.1. Concepts Demonstrated
      2. 10.5.2. Numerical Methods Utilized
      3. 10.5.3. Problem Statement
        1. Analytical Solution
      4. 10.5.4. Solution (Partial)
        1. (a) and (b) Sphere
          1. Division by Zero
          2. Boundary Condition Convergence
        2. (c) Cylinder
    6. 10.6. General Effectiveness Factor Calculations for First-Order Reactions
      1. 10.6.1. Concepts Demonstrated
      2. 10.6.2. Numerical Methods Utilized
      3. 10.6.3. Problem Statement
    7. 10.7. Simultaneous Diffusion and Reversible Reaction in a Catalytic Layer
      1. 10.7.1. Concepts Demonstrated
      2. 10.7.2. Numerical Methods Utilized
      3. 10.7.3. Problem Statement
        1. Material Balances on A and B within the Porous Layer
        2. Fick’s Law for Binary Diffusion
      4. 10.7.4. Solution (Suggestions)
        1. (a) Implicit Finite Difference (IFD) Solution
          1. Effectiveness Factor Calculation
          2. Results
        2. (b) Shooting Technique Solution
          1. Effectiveness Factor Calculation
          2. Split Boundary Value Solution
          3. Initial Condition Estimate for NA
          4. Results
        3. (c) Comparison of Solution Methods
    8. 10.8. Simultaneous Multicomponent Diffusion of Gases
      1. 10.8.1. Concepts Demonstrated
      2. 10.8.2. Numerical Methods Utilized
      3. 10.8.3. Problem Statement
        1. Additional Information and Data
      4. 10.8.4. Solution
        1. (a) and (b)
        2. Optimization of NA and NB
    9. 10.9. Multicomponent Diffusion of Acetone and Methanol in Air
      1. 10.9.1. Concepts Demonstrated
      2. 10.9.2. Numerical Methods Utilized
      3. 10.9.3. Problem Statement
    10. 10.10. Multicomponent Diffusion in a Porous Layer Covering a Catalyst
      1. 10.10.1. Concepts Demonstrated
      2. 10.10.2. Numerical Methods Utilized
      3. 10.10.3. Problem Statement
      4. 10.10.4. Solution (Suggestions)
        1. (a) and (b)
        2. (c) and (d)
    11. 10.11. Second-Order Reaction with Diffusion in Liquid Film
      1. 10.11.1. Concepts Demonstrated
      2. 10.11.2. Numerical Methods Utilized
      3. 10.11.3. Problem Statement
    12. 10.12. Simultaneous Heat and Mass Transfer in Catalyst Particles
      1. 10.12.1. Concepts Demonstrated
      2. 10.12.2. Numerical Methods Utilized
      3. 10.12.3. Problem Statement
        1. Simplification of Heat Transfer Equations
        2. Nonisothermal Effectiveness Factor
        3. Common Dimensionless Variables
      4. 10.12.4. Solution (Suggestions)
    13. 10.13. Unsteady-State Mass Transfer in a Slab
      1. 10.13.1. Concepts Demonstrated
      2. 10.13.2. Numerical Methods Utilized
      3. 10.13.3. Problem Statement
        1. The Numerical Method of Lines
        2. Boundary Condition for Exposed Surface
        3. Boundary Condition for Insulated Surface (No Mass Flux)
        4. Initial Concentration Profile
      4. 10.13.4. Solution (Partial)
        1. (a), (b), and (c)
    14. 10.14. Unsteady-State Diffusion and Reaction in a Semi-Infinite Slab
      1. 10.14.1. Concepts Demonstrated
      2. 10.14.2. Numerical Methods Utilized
      3. 10.14.3. Problem Statement
      4. 10.14.4. Solution (Partial)
    15. 10.15. Diffusion and Reaction in a Falling Laminar Liquid Film
      1. 10.15.1. Concepts Demonstrated
      2. 10.15.2. Numerical Methods Utilized
      3. 10.15.3. Problem Statement
      4. 10.15.4. Solution (Partial)
        1. Boundary Conditions
        2. Numerical Solution
    16. References
  14. 11. Chemical Reaction Engineering
    1. 11.1. Plug-Flow Reactor with Volume Change During Reaction
      1. 11.1.1. Concepts Demonstrated
      2. 11.1.2. Numerical Methods Utilized
      3. 11.1.3. Problem Statement
      4. 11.1.4. Solution (Partial)
        1. Graphical Comparison of Results
        2. Tabulated Results
    2. 11.2. Variation of Conversion with Reaction Order in a Plug-Flow Reactor
      1. 11.2.1. Concepts Demonstrated
      2. 11.2.2. Numerical Methods Utilized
      3. 11.2.3. Problem Statement
      4. 11.2.4. Solution (Partial)
    3. 11.3. Gas Phase Reaction in a Packed Bed Reactor with Pressure Drop
      1. 11.3.1. Concepts Demonstrated
      2. 11.3.2. Numerical Methods Utilized
      3. 11.3.3. Problem Statement
      4. 11.3.4. Solution (Partial)
        1. Suggestions
    4. 11.4. Catalytic Reactor with Membrane Separation
      1. 11.4.1. Concepts Demonstrated
      2. 11.4.2. Numerical Methods Utilized
      3. 11.4.3. Problem Statement
      4. 11.4.4. Solution (Equations)
    5. 11.5. Semibatch Reactor with Reversible Liquid Phase Reaction
      1. 11.5.1. Concepts Demonstrated
      2. 11.5.2. Numerical Methods Utilized
      3. 11.5.3. Problem Statement
      4. 11.5.4. Solution (Partial)
    6. 11.6. Operation of Three Continuous Stirred Tank Reactors in Series
      1. 11.6.1. Concepts Demonstrated
      2. 11.6.2. Numerical Methods Utilized
      3. 11.6.3. Problem Statement
      4. 11.6.4. Solution
        1. (a) – (c)
    7. 11.7. Differential Method of Rate Data Analysis in a Batch Reactor
      1. 11.7.1. Concepts Demonstrated
      2. 11.7.2. Numerical Methods Utilized
      3. 11.7.3. Problem Statement
      4. 11.7.4. Solution (Suggestions)
    8. 11.8. Integral Method of Rate Data Analysis in a Batch Reactor
      1. 11.8.1. Concepts Demonstrated
      2. 11.8.2. Numerical Methods Utilized
      3. 11.8.3. Problem Statement
    9. 11.9. Integral Method of Rate Data Analysis—Bimolecular Reaction
      1. 11.9.1. Concepts Demonstrated
      2. 11.9.2. Numerical Methods Utilized
      3. 11.9.3. Problem Statement
    10. 11.10. Initial Rate Method of Data Analysis
      1. 11.10.1. Concepts Demonstrated
      2. 11.10.2. Numerical Methods Utilized
      3. 11.10.3. Problem Statement
    11. 11.11. Half-Life Method for Rate Data Analysis
      1. 11.11.1. Concepts Demonstrated
      2. 11.11.2. Numerical Methods Utilized
      3. 11.11.3. Problem Statement
      4. 11.11.4. Solution (Suggestions)
    12. 11.12. Method of Excess for Rate Data Analysis in a Batch Reactor
      1. 11.12.1. Concepts Demonstrated
      2. 11.12.2. Numerical Methods Utilized
      3. 11.12.3. Problem Statement
    13. 11.13. Rate Data Analysis for a CSTR
      1. 11.13.1. Concepts Demonstrated
      2. 11.13.2. Numerical Methods Utilized
      3. 11.13.3. Problem Statement
    14. 11.14. Differential Rate Data Analysis for a Plug-Flow Reactor
      1. 11.14.1. Concepts Demonstrated
      2. 11.14.2. Numerical Methods Utilized
      3. 11.14.3. Problem Statement
    15. 11.15. Integral Rate Data Analysis for a Plug-Flow Reactor
      1. 11.15.1. Concepts Demonstrated
      2. 11.15.2. Numerical Methods Utilized
      3. 11.15.3. Problem Statement
    16. 11.16. Determination of Rate Expressions for a Catalytic Reaction
      1. 11.16.1. Concepts Demonstrated
      2. 11.16.2. Numerical Methods Utilized
      3. 11.16.3. Problem Statement
      4. 11.16.4. Solution (Suggestions and Partial Results)
        1. Model 3
    17. 11.17. Packed Bed Reactor Design for a Gas Phase Catalytic Reaction
      1. 11.17.1. Concepts Demonstrated
      2. 11.17.2. Numerical Methods Utilized
      3. 11.17.3. Problem Statement
      4. 11.17.4. Solution (Partial with Suggestions)
    18. 11.18. Catalyst Decay in a Packed Bed Reactor Modeled by a Series of CSTRs
      1. 11.18.1. Concepts Demonstrated
      2. 11.18.2. Numerical Methods Utilized
      3. 11.18.3. Problem Statement
      4. 11.18.4. Partial Solution
    19. 11.19. Design for Catalyst Deactivation in a Straight-Through Reactor
      1. 11.19.1. Concepts Demonstrated
      2. 11.19.2. Numerical Methods Utilized
      3. 11.19.3. Problem Statement
      4. 11.19.4. Solution
        1. (a) No Deactivation
        2. (b) Deactivation
          1. Coking
          2. Sintering
          3. Poisoning
          4. POLYMATH Solution
    20. 11.20. Enzymatic Reactions in a Batch Reactor
      1. 11.20.1. Concepts Demonstrated
      2. 11.20.2. Numerical Methods Utilized
      3. 11.20.3. Problem Statement
      4. 11.20.4. Solution (Suggestions)
    21. 11.21. Isothermal Batch Reactor Design for Multiple Reactions
      1. 11.21.1. Concepts Demonstrated
      2. 11.21.2. Numerical Methods Utilized
      3. 11.21.3. Problem Statement
      4. 11.21.4. Solution (Suggestions)
    22. 11.22. Material and Energy Balances on a Batch Reactor
      1. 11.22.1. Concepts Demonstrated
      2. 11.22.2. Numerical Methods Utilized
      3. 11.22.3. Problem Statement
      4. 11.22.4. Solution (Suggestions)
    23. 11.23. Operation of a Cooled Exothermic CSTR
      1. 11.23.1. Concepts Demonstrated
      2. 11.23.2. Numerical Methods Utilized
      3. 11.23.3. Problem Statement
      4. 11.23.4. Solution (Partial)
        1. Mole balance on CSTR for reactant A
        2. Energy balance on the reactor
        3. Energy balance on the cooling jacket
    24. 11.24. Exothermic Reversible Gas Phase Reaction in a Packed Bed Reactor
      1. 11.24.1. Concepts Demonstrated
      2. 11.24.2. Numerical Methods Utilized
      3. 11.24.3. Problem Statement
        1. Additional Information
    25. 11.25. Temperature Effects with Exothermic Reactions
      1. 11.25.1. Concepts Demonstrated
      2. 11.25.2. Numerical Methods Utilized
      3. 11.25.3. Problem Statement
    26. 11.26. Diffusion with Multiple Reactions in Porous Catalyst Particles
      1. 11.26.1. Concepts Demonstrated
      2. 11.26.2. Numerical Methods Utilized
      3. 11.26.3. Problem Statement
    27. 11.27. Nitrification of Biomass in a Fluidized Bed Reactor
      1. 11.27.1. Concepts Demonstrated
      2. 11.27.2. Numerical Methods Utilized
      3. 11.27.3. Problem Statement (adapted from Tanaka et al.[12] and Dunn et al.[13])
        1. Balances on Stages of the Fluidized Sand Reactor
        2. Balances on the Oxygen Absorber
    28. 11.28. Sterilization Kinetics and Extinction Probabilities in Batch Fermenters
      1. 11.28.1. Concepts Demonstrated
      2. 11.28.2. Numerical Methods Utilized
      3. 11.28.3. Problem Statement
    29. References
  15. 12. Phase Equilibria and Distillation
    1. 12.1. Three Stage Flash Evaporator for Recovering Hexane from Octane
      1. 12.1.1. Concepts Demonstrated
      2. 12.1.2. Numerical Methods Utilized
      3. 12.1.3. Problem Statement
        1. Additional Information and Data
      4. 12.1.4. Solution (Partial)
    2. 12.2. Non-Ideal Vapor-Liquid and Liquid-Liquid Equilibrium
      1. 12.2.1. Concepts Demonstrated
      2. 12.2.2. Numerical Methods Utilized
      3. 12.2.3. Problem Statement
        1. Additional Information and Data
      4. 12.2.4. Solution
        1. (a1) Calculation of the Bubble Point Temperature and the Composition of the Two Liquid Phases
        2. (a2) Calculation of the Dew Point Temperature and the Composition of the Liquid Phase
        3. (b) Isothermal Flash Calculations in the Two Phase Region
    3. 12.3. Calculation of Wilson Equation Coefficients from Azeotropic Data
      1. 12.3.1. Concepts Demonstrated
      2. 12.3.2. Numerical Methods Utilized
      3. 12.3.3. Problem Statement
      4. 12.3.4. Solution: System Ethanol (1) and n-Hexane (2)
    4. 12.4. Van Laar Equations Coefficients from Azeotropic Data
      1. 12.4.1. Concepts Demonstrated
      2. 12.4.2. Numerical Methods Utilized
      3. 12.4.3. Problem Statement
      4. 12.4.4. Solution (Suggestion)
    5. 12.5. Non-Ideal VLE from Azeotropic Data Using the Van Laar Equations
      1. 12.5.1. Concepts Demonstrated
      2. 12.5.2. Numerical Methods Utilized
      3. 12.5.3. Problem Statement
      4. 12.5.4. Solution Suggestions
    6. 12.6. Fenske-Underwood-Gilliland Correlations for Separation Towers
      1. 12.6.1. Concepts Demonstrated
      2. 12.6.2. Numerical Methods Utilized
      3. 12.6.3. Problem Statement
        1. Additional Information and Data
      4. 12.6.4. Solution
      5. 12.6.5. Solution
    7. 12.7. Fenske-Underwood-Gilliland Correlations in Depropanizer Design
      1. 12.7.1. Concepts Demonstrated
      2. 12.7.2. Numerical Methods Utilized
      3. 12.7.3. Problem Statement
    8. 12.8. Rigorous Distillation Calculations for a Simple Separation Tower
      1. 12.8.1. Concepts Demonstrated
      2. 12.8.2. Numerical Methods Utilized
      3. 12.8.3. Problem Statement
        1. Additional Information and Data
      4. 12.8.4. Solution
        1. Problem Specification and Condenser Calculations
        2. Stage 1 Calculations
        3. Stage 2 and 3 Calculations
        4. Calculated Results (Partial Solution)
    9. 12.9. Rigorous Distillation Calculations for Hexane-Octane Separation Tower
      1. 12.9.1. Concepts Demonstrated
      2. 12.9.2. Numerical Methods Utilized
      3. 12.9.3. Problem Statement
        1. Additional Information and Data
      4. 12.9.4. Solution (Suggestion)
    10. 12.10. Batch Distillation of a Water-Ethanol Mixture
      1. 12.10.1. Concepts Demonstrated
      2. 12.10.2. Numerical Methods Utilized
      3. 12.10.3. Problem Statement
        1. Additional Information and Data
      4. 12.10.4. Solution (Partial)
    11. 12.11. Dynamics of Batch Distillation of Fermenter Broth
      1. 12.11.1. Concepts Demonstrated
      2. 12.11.2. Numerical Methods Utilized
      3. 12.11.3. Problem Statement
      4. 12.11.4. Solution (Suggestions)
    12. References
  16. 13. Process Dynamics and Control
    1. 13.1. Modeling the Dynamics of First- and Second-Order Systems
      1. 13.1.1. Concepts Demonstrated
      2. 13.1.2. Numerical Methods Utilized
      3. 13.1.3. Problem Statement
        1. First-Order Systems
        2. Second-Order Systems
      4. 13.1.4. Solution (Partial)
    2. 13.2. Dynamics of a U-Tube Manometer
      1. 13.2.1. Concepts Demonstrated
      2. 13.2.2. Numerical Methods Utilized
      3. 13.2.3. Problem Statement
      4. 13.2.4. Solution (Partial)
    3. 13.3. Dynamics and Stability of an Exothermic CSTR
      1. 13.3.1. Concepts Demonstrated
      2. 13.3.2. Numerical Methods Utilized
      3. 13.3.3. Problem Statement
      4. 13.3.4. Solution (Partial)
        1. Dynamic mole balance on CSTR for reactant A
        2. Dynamic energy balance on the reactor
        3. Dynamic energy balance on the cooling jacket
    4. 13.4. Fitting a First-Order Plus Dead-Time Model to Process Data
      1. 13.4.1. Concepts Demonstrated
      2. 13.4.2. Numerical Methods Utilized
      3. 13.4.3. Problem Statement
        1. First-Order Plus Dead-Time Model (FOPDT Model)
      4. 13.4.4. Solution (Partial)
        1. (a) First-Order Plus Dead Time-Model
    5. 13.5. Dynamics and Control of a Flow-Through Storage Tank
      1. 13.5.1. Concepts Demonstrated
      2. 13.5.2. Numerical Methods Utilized
      3. 13.5.3. Problem Statement
        1. Linearization of a Nonlinear Function
        2. Deviation Variables
        3. Basic Proportional and Integral (PI) Control
        4. Numerical Solution of Control Equations
        5. Analytical Solution of Control Equations
      4. 13.5.4. Solution (Partial Solution and Suggestions)
        1. (a) Effect of Model Linearization
        2. (b) PI Control of Liquid Level
    6. 13.6. Dynamics and Control of a Stirred Tank Heater
      1. 13.6.1. Concepts Demonstrated
      2. 13.6.2. Numerical Methods Utilized
      3. 13.6.3. Problem Statement
        1. Modeling and Control Equations
      4. 13.6.4. Solution
        1. (a) Open Loop Performance
        2. (b) Closed-Loop Performance
        3. (c) Closed-Loop Performance for KC = 500
        4. (d) Closed Loop Performance for Proportional Control
        5. (e) Closed-Loop Performance with Limits on q
    7. 13.7. Controller Tuning Using Internal Model Control (IMC) Correlations
      1. 13.7.1. Concepts Demonstrated
      2. 13.7.2. Numerical Methods Utilized
      3. 13.7.3. Problem Statement
      4. 13.7.4. Solution (Partial with Suggestions)
    8. 13.8. First Order Plus Dead Time Models for Stirred Tank Heater
      1. 13.8.1. Concepts Demonstrated
      2. 13.8.2. Numerical Methods Utilized
      3. 13.8.3. Problem Statement
      4. 13.8.4. Solution (Suggestions)
        1. (a) and (b)
    9. 13.9. Closed-Loop Controller Tuning–The Ziegler-Nichols Method
      1. 13.9.1. Concepts Demonstrated
      2. 13.9.2. Numerical Methods Utilized
      3. 13.9.3. Problem Statement
      4. 13.9.4. Solution (Partial)
    10. 13.10. PI Controller Tuning Using the Auto Tune Variation “ATV” Method
      1. 13.10.1. Concepts Demonstrated
      2. 13.10.2. Numerical Methods Utilized
      3. 13.10.3. Problem Statement
      4. 13.10.4. Solution (Partial)
    11. 13.11. Reset Windup in a Stirred Tank Heater
      1. 13.11.1. Concepts Demonstrated
      2. 13.11.2. Numerical Methods Utilized
      3. 13.11.3. Problem Statement
      4. 13.11.4. Solution (Suggestion)
    12. 13.12. Temperature Control and Startup of a Nonisothermal CSTR
      1. 13.12.1. Concepts Demonstrated
      2. 13.12.2. Numerical Methods Utilized
      3. 13.12.3. Problem Statement
    13. 13.13. Level Control of Two Interactive Tanks
      1. 13.13.1. Concepts Demonstrated
      2. 13.13.2. Numerical Methods Utilized
      3. 13.13.3. Problem Statement (Adapted from Corripio[8])
      4. 13.13.4. Solution (Partial)
    14. 13.14. PI Control of Fermenter Temperature
      1. 13.14.1. Concepts Demonstrated
      2. 13.14.2. Numerical Methods Utilized
      3. 13.14.3. Problem Statement (adapted from Dunn et al.[9])
      4. 13.14.4. Solution (Comments and Suggestions)
    15. 13.15. Insulin Delivery to Diabetics Using PI Control
      1. 13.15.1. Concepts Demonstrated
      2. 13.15.2. Numerical Methods Utilized
      3. 13.15.3. Problem Statement
    16. References
  17. 14. Biochemical Engineering
    1. 14.1. Elementary Step and Approximate Models for Enzyme Kinetics
      1. 14.1.1. Concepts Demonstrated
      2. 14.1.2. Numerical Methods Utilized
      3. 14.1.3. Problem Statement
        1. Elementary Step Model
        2. Michaelis-Menten and Quasi-Steady-State Models
      4. 14.1.4. Solution (Partial)
        1. (a)–(c)
    2. 14.2. Determination and Modeling Inhibition for Enzyme-Catalyzed Reactions
      1. 14.2.1. Concepts Demonstrated
      2. 14.2.2. Numerical Methods Utilized
      3. 14.2.3. Problem Statement
      4. 14.2.4. Solution (Partial)
    3. 14.3. Bioreactor Design with Enzyme Catalysts—Temperature Effects
      1. 14.3.1. Concepts Demonstrated
      2. 14.3.2. Numerical Methods Utilized
      3. 14.3.3. Problem Statement
    4. 14.4. Optimization of Temperature in Batch and CSTR Enzymatic Reactors
      1. 14.4.1. Concepts Demonstrated
      2. 14.4.2. Numerical Methods Utilized
      3. 14.4.3. Problem Statement
      4. 14.4.4. Solution (Suggestions)
    5. 14.5. Diffusion with Reaction in Spherical Immobilized Enzyme Particles
      1. 14.5.1. Concepts Demonstrated
      2. 14.5.2. Numerical Methods Utilized
      3. 14.5.3. Problem Statement
      4. 14.5.4. Solution (Partial)
    6. 14.6. Multiple Steady States in a Chemostat with Inhibited Microbial Growth
      1. 14.6.1. Concepts Demonstrated
      2. 14.6.2. Numerical Methods Utilized
      3. 14.6.3. Problem Statement
      4. 14.6.4. Solution (Suggestions)
    7. 14.7. Fitting Parameters in the Monod Equation for a Batch Culture
      1. 14.7.1. Concepts Demonstrated
      2. 14.7.2. Numerical Methods Utilized
      3. 14.7.3. Problem Statement
    8. 14.8. Modeling and Analysis of Kinetics in a Chemostat
      1. 14.8.1. Concepts Demonstrated
      2. 14.8.2. Numerical Methods Utilized
      3. 14.8.3. Problem Statement
      4. 14.8.4. Solution (Suggestions)
    9. 14.9. Dynamic Modeling of a Chemostat
      1. 14.9.1. Concepts Demonstrated
      2. 14.9.2. Numerical Methods Utilized
      3. 14.9.3. Problem Statement
      4. 14.9.4. Solution (Partial plus Suggestions)
    10. 14.10. Predator-Prey Dynamics of Mixed Cultures in a Chemostat
      1. 14.10.1. Concepts Demonstrated
      2. 14.10.2. Numerical Methods Utilized
      3. 14.10.3. Problem Statement
    11. 14.11. Biokinetic Modeling Incorporating Imperfect Mixing in a Chemostat
      1. 14.11.1. Concepts Demonstrated
      2. 14.11.2. Numerical Methods Utilized
      3. 14.11.3. Problem Statement
        1. Steady-State Substrate Balance on Volume V1
        2. Steady-State Substrate Balance on Volume V2
        3. Steady-State Cell Balance on Volume V1
        4. Steady-State Cell Balance on Volume V2
        5. Overall Steady-State Material Balance for Product
    12. 14.12. Dynamic Modeling of a Chemostat System with Two Stages
      1. 14.12.1. Concepts Demonstrated
      2. 14.12.2. Numerical Methods Utilized
      3. 14.12.3. Problem Statement
        1. Dynamic Cell Mass Balance on Stage 1
        2. Dynamic Substrate Mass Balance on Stage 1
        3. Dynamic Product Mass Balance on Stage 1
        4. Dynamic Cell Mass Balance on Stage 2
        5. Dynamic Substrate Mass Balance on Stage 2
        6. Dynamic Product Mass Balance on Stage 2
        7. Overall Production Rate
    13. 14.13. Semicontinuous Fed-Batch and Cyclic-Fed Batch Operation
      1. 14.13.1. Concepts Demonstrated
      2. 14.13.2. Numerical Methods Utilized
      3. 14.13.3. Problem Statement
    14. 14.14. Optimization of Ethanol Production in a Batch Fermenter
      1. 14.14.1. Concepts Demonstrated
      2. 14.14.2. Numerical Methods Utilized
      3. 14.14.3. Problem Statement
      4. 14.14.4. Problem Statement
    15. 14.15. Ethanol Production in a Well-Mixed Fermenter with Cell Recycle
      1. 14.15.1. Concepts Demonstrated
      2. 14.15.2. Numerical Methods Utilized
      3. 14.15.3. Problem Statement
        1. Overall Material Balance on Cells
        2. Cell Balance on Fermenter
        3. Overall Material Balance on Substrate
        4. Substrate Balance on Fermenter
        5. Overall Material Balance on Product
        6. Product Balance on Fermenter
        7. Average Volumetric Productivity
        8. Production Rate
        9. Problem Details
    16. 14.16. Dynamic Modeling of an Anaerobic Digester
      1. 14.16.1. Concepts Demonstrated
      2. 14.16.2. Numerical Methods Utilized
      3. 14.16.3. Problem Statement
        1. Continuous Digester Model at Standard Operating Conditions
        2. Liquid Volume
        3. Gas Phase
        4. Steady-State Operation
      4. 14.16.4. Solution Suggestions
    17. 14.17. Start-Up and Control of an Anaerobic Digester
      1. 14.17.1. Concepts Demonstrated
      2. 14.17.2. Numerical Methods Utilized
      3. 14.17.3. Problem Statement
      4. 14.17.4. Solution Suggestions
    18. References
  18. A.
    1. Useful Constants
      1. Ideal Gas
      2. Stefan-Boltzmann
    2. Useful Conversion Factors
      1. Temperature
      2. Mass
      3. Length
      4. Area
      5. Volume
      6. Force
      7. Pressure
      8. Molar Volume and Density
      9. Acceleration of Gravity
      10. Thermodynamics
      11. Fluid Dynamics
      12. Heat Transfer
      13. Mass Transfer
    3. Useful Finite Difference Approximations
    4. Error Functions
    5. Student’s t-Distribution
  19. B.
    1. Data Tables
  20. C.
    1. Vapor-Liquid Equilibrium Data Tables
  21. D.
    1. Miscellaneous Data Tables
  22. E.
    1. Physical and Transport Properties
  23. F.
    1. Physical Property Data for Ethane
  24. Problems Listed by Subject Areas