Computational techniques for process simulation and analysis using MATLAB /

Bibliographic Details
Main Author:	Kaisare, Niket S. (Author)
Corporate Author:	ProQuest (Firm)
Format:	eBook
Language:	English
Published:	Boca Raton, FL : CRC Press, [2018]
Subjects:	MATLAB. Chemical processes > Mathematical models. Chemical processes > Computer simulation. Electronic books.
Online Access:	Connect to the full text of this electronic book

Table of Contents:

Machine generated contents note: 1.1.Overview
1.1.1.A General Model
1.1.2.A Process Example
1.1.3.Analysis of Dynamical Systems
1.2.Structure Of A MATLAB® Code
1.2.1.Writing Our First MATLAB® Script
1.2.2.MATLAB® Functions
1.2.3.Using Array Operations in MATLAB®
1.2.4.Loops and Execution Control
1.2.5.Section Recap
1.3.Approximations And Errors In Numerical Methods
1.3.1.Machine Precision
1.3.2.Round-Off Error
1.3.3.Taylor's Series and Truncation Error
1.3.4.Trade-Off between Truncation and Round-Off Errors
1.4.Error Analysis
1.4.1.Convergence and Stability
1.4.2.Global Truncation Error
1.5.Outlook
ch. 2 Linear Algebra
2.1.Introduction
2.1.1.Solving a System of Linear Equations
2.1.2.Overview
2.2.Vector Spaces
2.2.1.Definition and Properties
2.2.2.Span, Linear Independence, and Subspaces
2.2.3.Basis and Coordinate Transformation
2.2.3.1.Change of Basis
Note continued: 2.2.4.Null (Kernel) and Image Spaces of a Matrix
2.2.4.1.Matrix as Linear Operator
2.2.4.2.Null and Image Spaces in MATLAB®
2.3.Singular Value Decomposition
2.3.1.Orthonormal Vectors
2.3.2.Singular Value Decomposition
2.3.3.Condition Number
2.3.3.1.Singular Values, Rank, and Condition Number
2.3.3.2.Sensitivity of Solutions to Linear Equations
2.3.4.Directionality
2.4.Eigenvalues And Eigenvectors
2.4.1.Orientation for This Section
2.4.2.Brief Recap of Definitions
2.4.3.Eigenvalue Decomposition
2.4.4.Applications
2.4.4.1.Similarity Transform
2.4.4.2.Linear Differential Equations
2.4.4.3.Linear Difference Equations
2.5.Epilogue
Exercises
ch. 3 Ordinary Differential Equations: Explicit Methods
3.1.General Setup
3.1.1.Some Examples
3.1.2.Geometric Interpretation
3.1.3.Euler's Explicit Method
3.1.4.Euler's Implicit Method
3.1.5.Stability and Step-Size
Note continued: 3.1.5.1.Stability of Euler's Explicit Method
3.1.5.2.Error and Stability of Euler's Implicit Method
3.1.6.Multivariable ODE
3.1.6.1.Nonlinear Case
3.2.Second-Order Methods: A Journey Through The Woods
3.2.1.Some History
3.2.2.Runge-Kutta (RK-2) Methods
3.2.2.1.Derivation for RK-2 Methods
3.2.2.2.Heun's Method
3.2.2.3.Other RK-2 Methods
3.2.3.Step-Size Halving: Error Estimate for RK-2
3.2.4.Richardson's Extrapolation
3.2.5.Other Second-Order Methods (*)
3.2.5.1.Trapezoidal Rule: An Implicit Second-Order Method
3.2.5.2.Second-Order Adams-Bashforth Methods
3.2.5.3.Predictor-Corrector Methods
3.2.5.4.Backward Differentiation Formulae
3.3.Higher-Order Runge-Kutta Methods
3.3.1.Explicit Runge-Kutta Methods: Generalization
3.3.2.Error Estimation and Embedded RK Methods
3.3.2.1.MATLAB® Solver ode 23
3.3.3.The Workhorse: Fourth-Order Runge-Kutta
3.3.3.1.Classical RK-4 Method(s)
Note continued: 3.3.3.2.Kutta's 3/8th Rule RK-4 Method
3.4.MATLAB® ODE45 Solver: Options And Parameterization
3.5.Case Studies And Examples
3.5.1.An Ideal PFR
3.5.1.1.Simulation of PFR as ODE-IVP
3.5.1.2.Numerical Integration for PFR Design
3.5.1.3.Comparison of ODE-IVP with Integration
3.5.2.Multiple Steady States: Nonisothermal CSTR
3.5.2.1.Model and Problem Setup
3.5.2.2.Simulation of Transient CSTR
3.5.2.3.Step Change in Inlet Temperature
3.5.3.Hybrid System: Two-Tank with Heater
3.5.4.Chemostat: Preview into "Stiff" System
3.6.Epilogue
Exercises
ch. 4 Partial Differential Equations in Time
4.1.General Setup
4.1.1.Classification of PDEs
4.1.2.Brief History of Second-Order PDEs
4.1.3.Classification of Second-Order PDEs and Practical Implications
4.1.3.1.Elliptic PDE
4.1.3.2.Hyperbolic PDE
4.1.3.3.First-Order Hyperbolic PDEs
4.1.3.4.Parabolic PDE
4.1.4.Initial and Boundary Conditions
Note continued: 4.2.A Brief Overview Of Numerical Methods
4.2.1.Finite Difference
4.2.2.Method of Lines
4.2.3.Finite Volume Methods
4.2.4.Finite Element Methods
4.3.Hyperbolic PDE: Convective Systems
4.3.1.Finite Differences in Space and Time
4.3.1.1.Upwind Difference in Space
4.3.1.2.Forward in Time Central in Space (FTCS) Differencing
4.3.1.3.Lax-Friedrichs Scheme
4.3.1.4.Higher-Order Methods
4.3.2.Crank-Nicolson: Second-Order Implicit Method
4.3.2.1.Preview of Numerical Solution
4.3.3.Solution Using Method of Lines
4.3.3.1.MoL with Central Difference in Space
4.3.3.2.MoL with Upwind Difference in Space
4.3.4.Numerical Diffusion
4.4.Parabolic PDE: Diffusive Systems
4.4.1.Finite Difference in Space and Time
4.4.2.Crank-Nicolson Method
4.4.3.Method of Lines Using MATLAB® ODE Solvers
4.4.3.1.MoL with Central Difference in Space
4.4.4.Methods to Improve Stability
4.5.Case Studies And Examples
Note continued: 4.5.1.Nonisothermal Plug Flow Reactor
4.5.2.Packed Bed Reactor with Multiple Reactions
4.5.3.Steady Graetz Problem: Parabolic PDE in Two Spatial Dimensions
4.5.3.1.Heat Transfer in Fluid Flowing through a Tube
4.5.3.2.Effect of Velocity Profile
4.5.3.3.Calculation of Nusselt Number
4.6.Epilogue
Exercises
ch. 5 Section Wrap-Up: Simulation and Analysis
5.1.Binary Distillation Column: Staged ODE Model
5.1.1.Model Description
5.1.2.Model Equations and Simulation
5.1.3.Effect of Parameters: Reflux Ratio and Relative Volatility
5.2.Stability Analysis For Linear Systems
5.2.1.Motivation: Linear Stability Analysis of a Chemostat
5.2.1.1.Phase Portrait at the Steady State
5.2.1.2.Trivial Steady State and Analysis
5.2.2.Eigenvalues, Stability, and Dynamics
5.2.2.1.Dynamics When Eigenvalues Are Real and Distinct
5.2.2.2.An Example
5.2.2.3.Summary
5.2.3.Transient Growth in Stable Linear Systems
Note continued: 5.2.3.1.Defining Normal and Nonnormal Matrices
5.2.3.2.Analysis of Nonnormal Systems
5.3.Combined Parabolic PDE With ODE-IVP: Polymer Curing
5.4.TIme-varying inlet conditions and process disturbances
5.4.1.Chemostat with Time-Varying Inlet Flowrate
5.4.2.Zero-Order Hold Reconstruction in Digital Control
5.5.Simulating System With Boundary Constraints
5.5.1.PFR with Temperature Profile Specified
5.6.Wrap-Up
Exercises
ch. 6 Nonlinear Algebraic Equations
6.1.General Setup
6.1.1.A Motivating Example: Equation of State
6.2.Equations In Single Variable
6.2.1.Bisection Method
6.2.2.Secant and Related Methods
6.2.2.1.Regula-Falsi: Method of False Position
6.2.2.2.Brent's Method
6.2.3.Fixed Point Iteration
6.2.4.Newton-Raphson in Single Variable
6.2.5.Comparison of Numerical Methods
6.3.Newton-Raphson: Extensions And Multivariate
6.3.1.Multivariate Newton-Raphson
6.3.2.Modified Secant Method
Note continued: 6.3.3.Line Search and Other Methods
6.4.MATLAB® Solvers
6.4.1.Single Variable Solver: fzero
6.4.2.Multiple Variable Solver: fsolve
6.5.Case Studies And Examples
6.5.1.Recap: Equation of State
6.5.2.Two-Phase Vapor-Liquid Equilibrium
6.5.2.1.Bubble Temperature Calculation
6.5.2.2.Dew Temperature Calculation
6.5.2.3.Generating the T-x-y Diagram
6.5.3.Steady State Multiplicity in CSTR
6.5.4.Recap: Chemostat
6.5.5.Integral Equations: Conversion from a PFR
6.5.5.1.First-Order Kinetics
6.5.5.2.Complex Kinetics
6.6.Epilogue
Exercises
ch. 7 Special Methods for Linear and Nonlinear Equations
7.1.General Setup
7.1.1.Ordinary Differential Equation-Boundary Value Problems
7.1.2.Elliptic PDEs
7.1.3.Outlook of This Chapter
7.2.Tridiagonal And Banded Systems
7.2.1.What Is a Banded System?
7.2.1.1.Tridiagonal Matrix
7.2.2.Thomas Algorithm a.k.a TDMA
7.2.2.1.Heat Conduction Problem
Note continued: 7.2.2.2.Thomas Algorithm
7.2.3.ODE-BVP with Flux Specified at Boundary
7.2.4.Extension to Banded Systems
7.2.5.Elliptic PDEs in Two Dimensions
7.3.Iterative Methods
7.3.1.Gauss-Siedel Method
7.3.2.Iterative Method with Under-Relaxation
7.4.Nonlinear Banded Systems
7.4.1.Nonlinear ODE-BVP Example
7.4.1.1.Heat Conduction with Radiative Heat Loss
7.4.2.Modified Successive Linearization-Based Approach
7.4.3.Gauss-Siedel with Linearization of Source Term
7.4.4.Using fsolve with Sparse Systems
7.5.Examples
7.5.1.Heat Conduction with Convective or Radiative Losses
7.5.2.Diffusion and Reaction in a Catalyst Pellet
7.5.2.1.Linear System and Thiele Modulus
7.5.2.2.Langmuir-Hinshelwood Kinetics in a Pellet
7.6.Epilogue
Exercises
ch. 8 Implicit Methods: Differential and Differential Algebraic Systems
8.1.General Setup
8.1.1.Stiff System of Equation
8.1.1.1.Stiff ODE in Single Variable
Note continued: 8.1.2.Implicit Methods for Distributed Parameter Systems
8.1.3.Differential Algebraic Equations
8.2.Multistep Methods For Differential Equations
8.2.1.Implicit Adams-Moulton Methods
8.2.2.Higher-Order Adams-Moulton Method
8.2.3.Explicit Adams-Bashforth Method
8.2.4.Backward Difference Formula
8.2.5.Stability and MATLAB® Solvers
8.2.5.1.Explicit Adams-Bashforth Methods
8.2.5.2.Implicit Euler and Trapezoidal Methods
8.2.5.3.Implicit Adams-Moulton Methods of Higher Order
8.2.5.4.BDF/NDF Methods
8.2.5.5.MATLAB® Nonstiff Solvers
8.2.5.6.MATLAB® Stiff Solvers
8.3.Implicit Solutions For Differential Equations
8.3.1.Trapezoidal Method for Stiff ODE
8.3.1.1.Adaptive Step-Sizing
8.3.1.2.Multivariable Example
8.3.2.Crank-Nicolson Method for Hyperbolic PDEs
8.3.2.1.Exploiting Sparse Structure for Efficient Simulation
8.4.Differential Algebraic Equations
8.4.1.An Introductory Example
Note continued: 8.4.1.1.Direct Substitution
8.4.1.2.Formulating and Solving a DAE
8.4.2.Index of a DAE and More Examples
8.4.2.1.Example 2: Pendulum in Cartesian Coordinate System
8.4.2.2.Example 3: Heterogeneous Catalytic Reactor
8.4.3.Solution Methodology: Overview
8.4.3.1.Solving Algebraic Equation within ODE
8.4.3.2.Combined Approach
8.4.4.Solving Semiexplicit DAEs Using ode15s in MATLAB®
8.5.Case Studies And Examples
8.5.1.Heterogeneous Catalytic Reactor: Single Complex Reaction
8.5.2.Flash Separation/Batch Distillation
8.6.Epilogue
Exercises
ch. 9 Section Wrap-Up: Nonlinear Analysis
9.1.Nonlinear Analysis Of Chemostat: "Transcritical" Bifurcation
9.1.1.Steady State Multiplicity and Stability
9.1.2.Phase-Plane Analysis
9.1.3.Bifurcation with Variation in Dilution Rate
9.1.4.Transcritical Bifurcation
9.2.Nonisothermal CSTR: "Turning-Point" Bifurcation
9.2.1.Steady States: Graphical Approach
Note continued: 9.2.2.Stability Analysis at Steady States
9.2.3.Phase-Plane Analysis
9.2.4.Turning-Point Bifurcation
9.3.Limit Cycle Oscillations
9.3.1.Oscillations in Linear Systems
9.3.2.Limit Cycles: van der Pol Oscillator
9.3.2.1.Relaxation vs. Harmonic Oscillations
9.3.3.Oscillating Chemical Reactions
9.4.Simulation Of Methanol Synthesis In Tubular Reactor
9.4.1.Steady State PFR with Pressure Drop
9.4.1.1.Reaction Kinetics
9.4.1.2.Input Parameters and Initial Processing
9.4.1.3.Steady State PFR Model
9.4.2.Transient Model
9.5.Trajectory Of A Cricket Ball
9.5.1.Solving the ODE for Trajectory
9.5.2.Location Where the Ball Hits the Ground
9.5.3.Animation
9.6.Wrap-Up
Exercises
ch. 10 Regression and Parameter Estimation
10.1.General Setup
10.1.1.Orientation
10.1.2.Some Statistics
10.1.3.Some Other Considerations in Regression
10.2.Linear Least Squares Regression
Note continued: 10.2.1.Fitting a Straight Line
10.2.2.General Matrix Approach
10.2.3.Goodness of Fit
10.2.3.1.Maximum Likelihood Solution
10.2.3.2.Error and Coefficient of Determination
10.3.Regression In Multiple Variables
10.3.1.General Multilinear Regression
10.3.2.Polynomial Regression
10.3.3.Singularity and SVD
10.4.Nonlinear Estimation
10.4.1.Functional Regression by Linearization
10.4.2.MATLAB® Solver: Linear Regression
10.4.3.Nonlinear Regression Using Optimization Toolbox
10.5.Case Studies And Examples
10.5.1.Specific Heat: Revisited
10.5.2.Antoine's Equation for Vapor Pressure
10.5.2.1.Linear Regression for Benzene
10.5.2.2.Nonlinear Regression for Ethylbenzene
10.5.3.Complex Langmuir-Hinshelwood Kinetic Model
10.5.3.1.Case 1: Experiments Performed at Single Concentration of B
10.5.3.2.Case 2: Experiments Performed at Different Initial Concentrations of B
Note continued: 10.5.4.Reaction Rate: Differential Approach
10.6.Epilogue
10.6.1.Summary
10.6.2.Data Tables
Exercises.