Chemical Engineering Analysis and Optimization Using MATLAB

Weiguo Xie, PhD, is a Professor of Chemical Engineering at the University of Minnesota, Duluth, MN, USA. He has previously held faculty appointments in UK and Australian universities. He has authored over 100 scientific publications, with particular expertise in mathematical modeling, simulation, optimization, and related subjects. Sam Toan, PhD, is an Associate Professor of Chemical Engineering at the University of Minnesota, Duluth, MN, USA. He has nearly a decade of experience teaching engineering courses focused on MATLAB and has authored over 60 scientific publications. Richard Davis, PhD, is a Jean G. Blehart Distinguished Professor of Chemical Engineering at the University of Minnesota, Duluth, MN, USA. He has over three decades of experience teaching and researching computational methods, focusing on process modeling and simulation, energy conversion, chemical process safety, and environmental management.

• Preface xiAbout the Companion Website xiii1 Introduction to Modeling 11.1 Numerical Methods 31.1.1 Linear vs. Nonlinear Equations 51.1.2 Standard Features of Numerical Methods 61.1.3 Significant Figures and Computer Round-Off Error 71.2 Mathematical Model Building 121.2.1 Laws of Conservation 141.2.2 Lumped vs. Distributed Systems 161.2.3 Degrees of Freedom 231.2.4 Dimensionless Equations 231.2.5 Stochastic vs. Deterministic Modeling 241.2.6 Model Verification and Validation 241.3 Expert Problem-Solvers 252 MATLAB Skill Preparation 272.1 Introduction 272.1.1 MATLAB User Interface 272.1.2 MATLAB File Extensions 292.2 Some Useful MATLAB Commands and Functions 332.2.1 MATLAB Commands 332.2.2 MATLAB Functions 332.3 Vector and Matrix Operations 392.3.1 Vector Operations 392.3.2 Matrix Operations 402.4 Loops & Conditional Statements 422.5 Solving Equations 432.5.1 Linear and Nonlinear Equations and Systems 442.6 Optimization Toolbox 462.6.1 Minimization vs. Maximization Problems 462.6.2 Optimization Solvers 46Problems 493 Model Fitting and Spline Functions 513.1 Introduction 513.1.1 Linear Equations 523.1.1.1 Linear Models 523.1.1.2 Model Linearization 523.1.2 Algebraic Nonlinear Models 533.1.2.1 Nonlinear Models 533.1.2.2 Solution Methods for Nonlinear Problems 533.1.3 Model Fitting 553.1.3.1 Least Squares Procedure 553.1.3.2 Regression Analysis 553.1.4 Spline Functions 573.1.4.1 Linear Interpolation 573.1.4.2 Polynomial Interpolation 573.1.4.3 Cubic Spline Interpolation 583.2 Curve Fitting Toolbox in MATLAB 583.2.1 Two Ways to Curve Fitting 583.2.2 An Example of Using Curve Fitting App 593.2.2.1 Open the Curve Fitting App in Command Window 593.2.2.2 Selecting Data and the Default Linear Model 603.2.2.3 Selecting Better Models 603.3 Model Fitting via Optimization Algorithms 653.4 Spline Functions for Complex Models 653.4.1 Spline Interpolation in MATLAB – interp1 663.4.2 Spline Interpolation in MATLAB – interp2 683.5 Application in Chemical Engineering 693.5.1 Using Linear Equations 693.5.2 Using Nonlinear Equations 723.6 Summary 75Problems 764 Optimization 794.1 Optimization Overview and Solver Options 794.1.1 What Is Optimization? 794.1.2 Built-In Function and MATLAB’s Toolbox for Optimization 804.2 Extreme Value Problem 824.2.1 Unconstrained Functions 824.2.2 Constrained Functions 924.3 Linear Programming 934.3.1 Standard Procedure of Linear Programming 944.3.2 Solving Linear Programming in MATLAB 954.4 Quadratic Programming 964.4.1 Standard Procedure of Quadratic Programming 964.4.2 Solving Quadratic Programming in MATLAB 974.5 Nonlinear Programming 984.6 Application in Chemical Engineering 1004.6.1 Reaction Kinetics Optimization 1004.6.2 Reaction Productivity Optimization 1014.6.3 Refinery Economics 1034.6.4 Chemical Production Optimization 1054.6.5 Productivity Profit Optimization 1074.6.6 Catalyst System Design Optimization 1084.6.7 Reaction Kinetic 1094.7 Summary 110Problems 1105 Enhanced Optimization 1155.1 Introduction 1155.1.1 Differences Among Optimization Solvers in MATLAB 1155.1.2 The Differences in Algorithms 1165.2 Enhanced Optimization Through Treatment of Constraints on the Search Region 1195.2.1 Lagrange Method 1195.2.1.1 Method of Lagrange Multiplier 1195.2.1.2 Method of Optimizing S Function 1245.2.2 Convert Inequality Constraints to Equality Constraints 1265.2.3 Penalty Function Method 1285.2.4 Enhanced Constraints Method 1335.3 Application in Chemical Engineering 1355.3.1 Optimization of a Three-Stage Compressor 1355.3.2 Productivity Profit Optimization 1385.3.3 Optimization for the Operation of a Continuous Stirred Tank Reactor (cstr) 1405.4 Summary 145Problems 1456 Global Optimization 1476.1 Introduction 1476.1.1 Local vs. Global Optima 1476.1.2 Four Standard Heuristic Techniques (Often Incorporate Randomization) 1486.2 Global Optimization Toolbox in MATLAB 1516.2.1 Global Optimization Solvers in MATLAB 1516.2.2 The Differences in the Syntax of the Solvers 1526.3 The Selection of Global Optimization Methods 1566.3.1 Based on Constraints 1566.3.2 Based on the Number of Variables 1596.3.3 Based on Computational Time 1626.4 Application in Chemical Engineering 1666.4.1 Optimization of a Three-Stage Compressor 1666.4.2 Productivity Profit Optimization 1726.4.3 Optimization for the Operation of a Continuous Stirred Tank Reactor (cstr) 1796.5 Summary 186Problems 1867 Optimal Experimental Design 1897.1 Introduction 1897.1.1 Experimental Design 1897.1.2 Experimental Error 1907.1.2.1 Random Error 1907.1.2.2 Systematic Error 1927.2 Design of Experiments (DOE) 1927.2.1 Statistical Design of Experiments 1927.2.2 MATLAB Functions for the Design of Experiments 1937.2.3 Orthogonal Experimental Design 1967.3 Model Building with Experimental Data 2007.3.1 The Relationships Among M Values vs. Three Factors 2017.3.2 The Power Relationships and Multiplication used for Model Building 2037.3.3 The Model Fitting to Determine the Unknown Parameters 2037.4 Application in Chemical Engineering 2087.4.1 Experimental Design for Nanoparticle-Reinforced Silica Gels 2087.4.2 Experimental Design for Turbulence Model Development of a Flotation Cell 2117.4.2.1 The Relationships Among M Values vs. Four Factors 2127.4.2.2 The Power Relationships and Multiplication Used for Model Building 2167.4.2.3 The Model Fitting to Determine the Unknown Parameters 2177.5 Summary 220Problems 2208 Data Statistics 2238.1 Introduction 2238.1.1 Data Types 2238.1.2 Physical Units 2268.1.3 Dimensional Analysis 2288.1.4 Some Dimensionless Groups 2288.1.5 Buckingham Pi Method 2318.1.6 Model Analysis 2328.2 Data Statistics Toolbox in MATLAB 2348.2.1 Statistics and Machine Learning Toolbox 2348.2.2 Statistics Visualization 2348.2.2.1 Scatter Plots 2348.2.2.2 Box Plots 2358.2.2.3 Distribution Plots 2368.2.3 Analysis of Variance 2388.2.3.1 One-Way ANOVA 2388.2.3.2 ANOVA with Multiple Responses 2388.2.4 Regression 2418.2.5 Principal Component Analysis 2488.3 Application in Chemical Engineering 2508.3.1 Application of Buckingham Pi (π) Method for a Flotation Rate Model 2508.3.2 Statistics Visualization for Particle Size Distributions 2518.4 Summary 261Problems 2629 Complex Equation Systems 2659.1 Introduction 2659.1.1 Dynamic Systems 2659.1.2 Lump Parameter System and Distributed Parameter System 2669.2 Ordinary Differential Equations (ODEs) 2679.2.1 ODEs for Dynamic Systems 2679.2.2 Higher-Order ODEs 2679.2.3 Numerical Integration and Differentiation 2689.2.4 Numerical Method to Solve ODEs 2719.2.4.1 Euler’s Explicit Method 2719.2.4.2 Euler’s Implicit Method 2749.2.4.3 Runge–Kutta Methods 2769.2.4.4 Finite-Difference Method 2779.2.5 MATLAB ODE Solvers 2799.3 Partial Differential Equation Toolbox in MATLAB (PDE) 2839.3.1 Forms of Equations Can Be Solved 2839.3.2 MATLAB PDE Solver pdepe 2849.4 Application in Chemical Engineering 2889.4.1 Complex Chemical Reactions 2889.4.2 Liquid Level Response 2899.4.3 Plane Poiseuille Flow 2929.5 Summary 295Problems 29510 Process Integration and Optimization 29910.1 Introduction 29910.1.1 Process Simulators 29910.1.2 Flowsheet Simulation and Design 30010.2 Process Integration and Optimization 30010.2.1 Process Models 30010.2.2 Simulating Novel Processes and Equipment 30010.2.3 Physical and Chemical Property Estimation 30310.2.4 Process Optimization 30510.3 Application in Chemical Engineering 30510.3.1 Introduction to Solvent Extraction 30510.3.2 Ternary Diagram (Partially Soluble Ternary Systems) 30610.3.3 Ternary Diagram – One Equilibrium Stage 30610.3.4 Ternary Diagram – Cross-Current Two Stages Solvent Extraction 31010.3.5 Ternary Diagram – Counter-Current Two Stages Solvent Extraction 31010.3.6 Ternary Diagram – Counter-Current N Stages Solvent Extraction 31310.3.7 Case Study – Cross-Current Multistages Solvent Extraction 31410.4 Summary 331Problems 331References 333Index 335