Chemical Engineering Computation with MATLAB

Cover
Half Title
Title Page
Copyright Page
Contents
Preface
Acknowledgments
Author
1. Introduction to MATLABⓇ
	1.1. Starting MATLAB
		1.1.1. Entering Commands in the Command Window
		1.1.2. help Command
		1.1.3. Exiting MATLAB
	1.2. Operations and Assignment of Variables
		1.2.1. Errors in Input
		1.2.2. Aborting Calculations
	1.3. Vectors and Matrices
		1.3.1. Vectors
		1.3.2. Matrices
		1.3.3. Complex Number
		1.3.4. Suppression of Screen Output
	1.4. Numerical Expressions
	1.5. Managing Variables
		1.5.1. clear Command
		1.5.2. Computational Limitations and Constants
		1.5.3. "whos" Command
	1.6. Symbolic Operations
		1.6.1. Creation of Symbolic Variables
		1.6.2. Substitution in Symbolic Equations
	1.7. Code Files
		1.7.1. Script Code Files
		1.7.2. Adding Comments
		1.7.3. Function Code Files
	1.8. Functions
		1.8.1. Built-In Functions
		1.8.2. User-Defined Functions
	1.9. Loops
		1.9.1. If Statement
		1.9.2. For Loop
	1.10. Graphics
		1.10.1. Plotting with ezplot
		1.10.2. Modifying Graphs
		1.10.3. Graphing with plot
		1.10.4. Plotting Multiple Curves
		1.10.5. Three-Dimensional Plots
	1.11. Ordinary Differential Equations
	1.12. Code File Examples
		1.12.1. Population Growth Model
		1.12.2. Random Fibonacci Sequence
		1.12.3. Generation of a 3D Object
	1.13. Simulink®
		1.13.1. Simulink Blocks
		1.13.2. Creation of a Simple Simulink Model
	Bibliography
2. Numerical Methods with MATLABⓇ
	2.1. Linear Systems
		2.1.1. Gauss Elimination Method
		2.1.2. Gauss-Seidel Method
		2.1.3. Conjugate Gradient Method
		2.1.4. Use of MATLAB Built-In Functions
	2.2. Nonlinear Equations
		2.2.1. Polynomial Equations
		2.2.2. Zeros of Nonlinear Equations
			2.2.2.1. Bisection Method
			2.2.2.2. False Position Method
			2.2.2.3. Newton-Raphson Method
			2.2.2.4. Secant Method
			2.2.2.5. Muller Method
		2.2.3. Solution of Nonlinear Equations of Several Variables
			2.2.3.1. Newton-Raphson Method
			2.2.3.2. Secant Method
			2.2.3.3. Fixed-Point Iteration Method for Nonlinear Systems
		2.2.4. Use of MATLAB Built-In Functions
	2.3. Regression Analysis
		2.3.1. Introduction to Statistics
			2.3.1.1. Elementary Statistics
			2.3.1.2. Probability Distribution
		2.3.2. Generation of Random Numbers
		2.3.3. Linear Regression Analysis
		2.3.4. Polynomial Regression Analysis
			2.3.4.1. Data Fitting by Least-Squares Method
			2.3.4.2. Use of MATLAB Built-In Functions
		2.3.5. Transformation of Nonlinear Functions to Linear Functions
	2.4. Interpolation
		2.4.1. Polynomial Interpolation
		2.4.2. Lagrange Method
		2.4.3. Newton Method
		2.4.4. Cubic Splines
		2.4.5. Use of MATLAB Built-In Functions
			2.4.5.1. Polynomial and Cubic Spline Regression
			2.4.5.2. Interpolation in One Dimension
			2.4.5.3. Interpolation in Multiple Dimensions
	2.5. Differentiation and Integration
		2.5.1. Differentiation
		2.5.2. Integration
			2.5.2.1. Definite Integrals
			2.5.2.2. Multiple Integrals
	2.6. Ordinary Differential Equations
		2.6.1. Initial-Value Problems
			2.6.1.1. Explicit Euler Method
			2.6.1.2. Implicit Euler Method
			2.6.1.3. Heun Method
			2.6.1.4. Runge-Kutta Methods
			2.6.1.5. nth-Order ODE
			2.6.1.6. Use of MATLAB Built-In Functions
		2.6.2. Boundary-Value Problems
		2.6.3. Differential Algebraic Equations (DAEs)
	2.7. Partial Differential Equations
		2.7.1. Classification of Partial Differential Equations
			2.7.1.1. Classification by Order
			2.7.1.2. Classification by Linearity
			2.7.1.3. Classification of Linear 2nd-Order Partial Differential Equations
			2.7.1.4. Classification by Initial and Boundary Conditions
		2.7.2. Solution of Partial Differential Equations by Finite Difference Methods
			2.7.2.1. Parabolic PDE
			2.7.2.2. Hyperbolic PDE
			2.7.2.3. Elliptic PDE
		2.7.3. Method of Lines
		2.7.4. Use of the MATLAB Built-In Function pdepe
	2.8. Historical Development of Process Engineering Software
	Problems
		Linear Systems
		Nonlinear Equations
		Regression Analysis
		Interpolation
		Differentiation and Integration
		Ordinary Differential Equations
		Partial Differential Equations
	References
3. Physical Properties
	3.1. Water and Steam
		3.1.1. Division of Pressure-Temperature Range
		3.1.2. Property Equations
			3.1.2.1. Parameters and Auxiliary Equations
			3.1.2.2. Basic Equation for Region 1
			3.1.2.3. Basic Equation for Region 2
			3.1.2.4. Basic Equation for Region 3
			3.1.2.5. Basic Equation for Region 4
			3.1.2.6. Basic Equations for Region 5
		3.1.3. Properties of Saturated Steam
		3.1.4. Calculation of H2O Properties by MATLAB Programs
			3.1.4.1. Properties of H2O
			3.1.4.2. Properties of Saturated H2O
	3.2. Humidity
		3.2.1. Relative Humidity
		3.2.2. Absolute Humidity
	3.3. Density of Saturated Liquids
		3.3.1. Yaws Correlation
		3.3.2. COSTALD Method
		3.3.3. Gunn-Yamada Method7
	3.4. Viscosity
		3.4.1. Viscosity of Liquids
		3.4.2. Viscosity of Gases
	3.5. Heat Capacity
		3.5.1. Heat Capacity of Liquids
			3.5.1.1. Polynomial Correlation
		3.5.1.2. Rowlinson-Bondi Method
		3.5.2. Heat Capacity of Gases
	3.6. Thermal Conductivity
		3.6.1. Thermal Conductivity of Liquids
		3.6.2. Thermal Conductivity of Gases
	3.7. Surface Tension
		3.7.1. Surface Tension of Liquids
		3.7.2. Surface Tension by Correlations
	3.8. Vapor Pressure
		3.8.1. Antoine Equation
		3.8.2. Extended Antoine Equation
		3.8.3. Wagner Equation
		3.8.4. Hoffmann-Florin Equation
		3.8.5. Rarey-Moller Equation
		3.8.6. Vapor Pressure Estimation by Correlations
	3.9. Enthalpy of Vaporization
		3.9.1. Watson Equation
		3.9.2. Pitzer Correlation
		3.9.3. Clausius-Clapeyron Equation
	3.10. Heat of Formation for Ideal Gases
	3.11. Gibbs Free Energy
	3.12. Diffusion Coefficients
		3.12.1. Liquid-Phase Diffusion Coefficients
		3.12.2. Gas-Phase Diffusion Coefficients
	3.13. Compressibility Factor of Natural Gases
	Problems
	References
4. Thermodynamics
	4.1. Equation of State
		4.1.1. Virial State Equation
		4.1.2. Lee-Kesler Equation
		4.1.3. Cubic Equations of State
		4.1.4. Thermodynamic State Models
	4.2. Thermodynamic Properties of Fluids
		4.2.1. Enthalpy Change
		4.2.2. Departure Function
			4.2.2.1. Departure Function from the Virial Equation of State
			4.2.2.2. Departure Function from the VDW (van der Waals) Equation of State
			4.2.2.3. Departure Function from the RK (Redlich-Kwong) Equation of State
			4.2.2.4. Departure Function from the SRK (Soave-Redlich-Kwong) Equation of State
			4.2.2.5. Departure Function from the PR (Peng-Robinson) Equation of State
		4.2.3. Enthalpy of Mixture
	4.3. Fugacity Coefficient
		4.3.1. Fugacity Coefficients of Pure Species
		4.3.2. Fugacity Coefficient of a Species in a Mixture
			4.3.2.1. Fugacity Coefficient from the Virial Equation of State
			4.3.2.2. Fugacity Coefficient from the Cubic Equations of State
			4.3.2.3. Fugacity Coefficient from the van der Waals Equation of State
	4.4. Activity Coefficient
		4.4.1. Activity Coefficient Models
			4.4.1.1. Wilson equation
			4.4.1.2. van Laar equation
		4.4.2. Activity Coefficients by the Group Contribution Method
			4.4.2.1. UNIQUAC Method
			4.4.2.2. UNIFAC Method
	4.5. Vapor-Liquid Equilibrium
		4.5.1. Vapor-Liquid Equilibrium by Raoult's Law
		4.5.2. Vapor-Liquid Equilibrium by Modified Raoult's Law
			4.5.2.1. Dew Point and Bubble Point Calculations
			4.5.2.2. Flash Calculation by the Modified Raoult's Law
		4.5.3. Vapor-Liquid Equilibrium Using Ratio of Fugacity Coefficients
			4.5.3.1. Dew Point and Bubble Point Calculations38
			4.5.3.2. Flash Calculations Using Fugacity Coefficients
	4.6. Vapor-Liquid-Liquid Equilibrium
	Problems
	References
5. Fluid Mechanics
	5.1. Laminar Flow
		5.1.1. Reynolds Number
		5.1.2. Flow in a Horizontal Pipe
		5.1.3. Laminar Flow in a Horizontal Annulus
		5.1.4. Vertical Laminar Flow of a Falling Film
		5.1.5. Falling Particles
	5.2. Friction Factor
	5.3. Flow of Fluids in Pipes
		5.3.1. Friction Loss
		5.3.2. Equivalent Length of Various Fittings and Valves
		5.3.3. Excess Head Loss
		5.3.4. Pipe Reduction and Enlargement
		5.3.5. Overall Pressure Drop
		5.3.6. Pipeline Network
	5.4. Flow through a Tank
		5.4.1. Open Tank
		5.4.2. Enclosed Tank
	5.5. Flow Measurement: Orifice and Venturi Meter
	5.6. Flow of Non-Newtonian Fluids
		5.6.1. Velocity Profile
		5.6.2. Reynolds Number
		5.6.3. Friction Factor
	5.7. Compressible Fluid Flow in Pipes
		5.7.1. Critical Flow and the Mach Number
		5.7.2. Compressible Isothermal Flow
		5.7.3. Choked Flow
	5.8. Two-Phase Flow in Pipes
		5.8.1. Flow Patterns
		5.8.2. Pressure Drop
		5.8.3. Corrosion and Erosion
		5.8.4. Vapor-Liquid Two-Phase Vertical Downflow
		5.8.5. Pressure Drop in Flashing Steam Condensate Flow
	5.9. Flow through Packed Beds
	Problems
	References
6. Chemical Reaction Engineering
	6.1. Characteristics of Reaction Rates
		6.1.1. Estimation of Reaction Rate Constant and Reaction Order
		6.1.2. Reaction Equilibrium
		6.1.3. Reaction Conversion
		6.1.4. Series Reactions
	6.2. Continuous-Stirred Tank Reactors (CSTRs)
		6.2.1. Concentration Changes with Time
		6.2.2. Nonisothermal Reaction
		6.2.3. Multiple Reactions in a CSTR
	6.3. Batch Reactors
		6.3.1. Estimation of Batch Reaction Parameters
		6.3.2. Semibatch Reactors
	6.4. Plug-Flow Reactors
		6.4.1. Isothermal Plug-Flow Reactor
		6.4.2. Nonisothermal Plug-Flow Reactor
		6.4.3. Adiabatic Reaction in a Plug-Flow Reactor
	6.5. Catalytic Reactors
		6.5.1. Characteristics of Catalytic Reaction
		6.5.2. Diffusion and Reaction in a Catalyst Pellet
		6.5.3. Catalytic Reactions in a Packed-Bed Reactor
		6.5.4. Packed-Bed Reactor with Axial Mixing
		6.5.5. Oxidation of SO2 in a Packed-Bed Reactor
		6.5.6. Straight-Through Transport Reactor
		6.5.7. Steady-State Nonisothermal Reactions
	6.6. Cracking and Polymerization
		6.6.1. Cracking Reaction
		6.6.2. Polymerization of Methyl Methacrylate (MMA)
	6.7. Microreactors
	6.8. Membrane Reactors
	6.9. Biochemical Reaction: Cell Growth Models
	Problems
	References
7. Mass Transfer
	7.1. Diffusion
		7.1.1. One-Dimensional Diffusion
		7.1.2. Multi-Component Diffusion in Gases
		7.1.3. Diffusion from a Sphere
		7.1.4. Mass Transfer Coefficient
		7.1.5. Diffusion in Isothermal Catalyst Particles
		7.1.6. Unsteady-State Diffusion in a One-Dimensional Slab
		7.1.7. Diffusion in a Falling Laminar Film
	7.2. Evaporation
		7.2.1. Single-Effect Evaporators
		7.2.2. Vaporizers
		7.2.3. Multiple-Effect Evaporators
	7.3. Absorption
		7.3.1. Absorption by Tray Column
		7.3.2. Momentum and Mass Transfer in the Absorption Column
		7.3.3. Packed-Bed Absorber
			7.3.3.1. Packed-Bed Column Diameter
			7.3.3.2. Packed-Bed Column Height
	7.4. Binary Distillation
		7.4.1. McCabe-Thiele Method
		7.4.2. Ideal Binary Distillation
	7.5. Multi-Component Distillation: Shortcut Calculation
		7.5.1. Fenske-Underwood-Gilliland Method
			7.5.1.1. Fenske Equation: The Minimum Number of Stages
			7.5.1.2. Underwood Equation: The Minimum Reflux
			7.5.1.3. Gilliland's Correlation
			7.5.1.4. Feed Stage Location
			7.5.1.5. Determination of the Number of Stages by the Smoker Equation
	7.6. Rigorous Steady-State Distillation Calculations
		7.6.1. Equilibrium Stage
		7.6.2. Rigorous Distillation Model: MESH Equations
		7.6.3. Tridiagonal Matrix Method
		7.6.4. Bubble Point (BP) Method
	7.7. Differential Distillation
	7.8. Filtration
	7.9. Membrane Separation
		7.9.1. Complete-Mixing Model for Gas Separation
		7.9.2. Cross-Flow Model for Gas Separation
	Problems
	References
8. Heat Transfer
	8.1. One-Dimensional Heat Transfer
		8.1.1. Heat Transfer in a One-Dimensional Slab
		8.1.2. Heat Transfer through Multilayers of Slabs and Cylinders
		8.1.3. Heat Transfer in a Wire
		8.1.4. Heat Loss through Pipe Flanges
		8.1.5. Heat Transfer in a Laminar Flow through a Cylinder
	8.2. Multidimensional Heat Conduction
		8.2.1. Unsteady-State Heat Conduction
		8.2.2. Method of Lines
		8.2.3. Steady-State Heat Conduction
	8.3. Heat Exchangers
		8.3.1. Log-Mean Temperature Difference
		8.3.2. Simplified Heat Exchanger Calculation,
			8.3.2.1. Heat Duty
			8.3.2.2. Overall Heat Transfer Coefficient
			8.3.2.3. Tube-Side Heat Transfer Coefficient
			8.3.2.4. Shell-Side Heat Transfer Coefficient
			8.3.2.5. Pressure Drop in the Tube Side
			8.3.2.6. Pressure Drop in the Shell Side
		8.3.3. Rigorous Heat Exchanger Calculation
			8.3.3.1. Tube-Side Heat Transfer Coefficient
			8.3.3.2. Shell-Side Heat Transfer Coefficient
			8.3.3.3. Pressure Drop in the Tube Side
			8.3.3.4. Pressure Drop in the Shell Side
			8.3.3.5. Heat Exchanger Calculation Procedure
		8.3.4. Double-Pipe Heat Exchanger
	Problems
	References
9. Process Control
	9.1. Laplace Transform and Transfer Function
		9.1.1. Laplace Transform and Inverse Laplace Transform
		9.1.2. Partial Fraction Expansion
		9.1.3. Representation of the Transfer Function
	9.2. Block Diagrams
	9.3. State-Space Representation
	9.4. Process Dynamics
		9.4.1. Dynamics of 1st-Order Processes
		9.4.2. Dynamics of 2nd-Order Processes
		9.4.3. Dynamics of Complex Processes
			9.4.3.1. Higher-Order Processes
			9.4.3.2. Lead/Lag
			9.4.3.3. Time Delay
	9.5. Dynamics of Feedback Control Loops
		9.5.1. Simple Feedback Control Loops
			9.5.1.1. Servo Problem
			9.5.1.2. Regulator Problem
		9.5.2. Control of a Continuous-Stirred Tank Heater
	9.6. Stability of Feedback Control Systems
	9.7. Frequency Response Analysis
		9.7.1. Bode Diagram
		9.7.2. Nyquist Diagram
		9.7.3. Nichols Chart
		9.7.4. Gain and Phase Margins
	Problems
	References
10. Optimization
	10.1. Unconstrained Optimization
		10.1.1. Fibonacci Method
		10.1.2. Golden Section Method
		10.1.3. Brent's Quadratic Fit Method
		10.1.4. Shubert-Piyavskii Method
		10.1.5. Steepest Descent Method
		10.1.6. Newton's Method
		10.1.7. Conjugate Gradient Method
		10.1.8. Quasi-Newton Method
	10.2. Linear Programming
		10.2.1. Formulation of Linear Programming Problems
		10.2.2. Simplex Method
		10.2.3. Two-Phase Simplex Method
		10.2.4. Interior Point Method
	10.3. Constrained Optimization
		10.3.1. Rosen's Gradient Projection Method
		10.3.2. Zoutendijk's Feasible Direction Method
		10.3.3. Generalized Reduced Gradient (GRG) Method
		10.3.4. Sequential Quadratic Programming (SQP) Method
	10.4 Direct Search Methods
		10.4.1. Cyclic Coordinate Method
		10.4.2. Hooke-Jeeves Pattern Search Method
		10.4.3. Rosenbrock's Method
		10.4.4. Nelder-Mead's Simplex Method
		10.4.5. Simulated Annealing (SA) Method
		10.4.6. Genetic Algorithm (GA)
	10.5. Mixed-Integer Programming
		10.5.1. Zero-One Programming Method
		10.5.2 Branch-and-Bound Method
	10.6. Use of MATLAB Built-In Functions
		10.6.1. Unconstrained Optimization
			10.6.1.1. fminsearch
			10.6.1.2. fminunc
			10.6.1.3. fminbnd
			10.6.1.4. lsqnonlin
		10.6.2. Constrained Optimization
			10.6.2.1. lsqlin
			10.6.2.2. fmincon
			10.6.2.3. fminimax
			10.6.2.4. quadprog
		10.6.3. Linear and Mixed-Integer Programming Problems
			10.6.3.1. linprog
			10.6.3.2. intlinprog
	Problems
	References
11. Computational Intelligence
	11.1. Fuzzy Systems
		11.1.1. Membership Functions
		11.1.2. Fuzzy Arithmetic Operations
		11.1.3. Defuzzification
		11.1.4. Fuzzy Inference Systems
			11.1.4.1. Mamdani Fuzz Inference System (FIS) Objects
			11.1.4.2. Creation of an FIS Object Using the mamfis Function
			11.1.4.3. Creation of an FIS Object Using the genfis Function
			11.1.4.4. Creation of an FIS Object Using Fuzzy Logic Designer
	11.2. Artificial Neural Networks
		11.2.1. Neural Network Models
		11.2.2. Function Fitting Neural Networks
			11.2.2.1. Construction and Training of a Function Fitting Network
			11.2.2.2. Creation and Training of a Feed-forward Network
			11.2.2.3. Creation and Training of a Cascade Network
		11.2.3. Regression Fitting
			11.2.3.1. Regression Models
			11.2.3.2. Data Fitting
	11.3. Support Vector Machines
		11.3.1. Fundamentals of Support Vector Machines
		11.3.2. Creation of Regression Models Using fitrsvm
		11.3.3. Creation of Regression Models Using fitrlinear
	Problems
	References
Index