Process Modeling and Simulation for Chemical Engineers (eBook)

Theory and Practice

Simant R. Upreti (Autor)

eBook Download: PDF

2017
John Wiley & Sons (Verlag)
978-1-118-91465-6 (ISBN)

Infos

This book provides a rigorous treatment of the fundamental concepts and techniques involved in process modeling and simulation. The book allows the reader to:

(i)         Get a solid grasp of 'under-the-hood' mathematical results

(ii)        Develop models of sophisticated processes

(iii)       Transform models to different geometries and domains as appropriate

(iv)       Utilize various model simplification techniques

(v)        Learn simple and effective computational methods for model simulation

(vi)       Intensify the effectiveness of their research

Modeling and Simulation for Chemical Engineers: Theory and Practice begins with an introduction to the terminology of process modeling and simulation. Chapters 2 and 3 cover fundamental and constitutive relations, while Chapter 4 on model formulation builds on these relations. Chapters 5 and 6 introduce the advanced techniques of model transformation and simplification. Chapter 7 deals with model simulation, and the final chapter reviews important mathematical concepts.

Presented in a methodical, systematic way, this book is suitable as a self-study guide or as a graduate reference, and includes examples, schematics and diagrams to enrich understanding. End of chapter problems with solutions and computer software available online at www.wiley.com/go/upreti/pms_for_chemical_engineers are designed to further stimulate readers to apply the newly learned concepts.

Simant Ranjan Upreti, Department of Chemical Engineering, Ryerson University, Toronto, Canada

Inhalt

Cover 1
Title Page 5
Copyright 6
Dedication 7
Contents 9
Preface 15
Notation 17
Chapter 1 Introduction 23
1.1 System 23
1.1.1 Uniform System 24
1.1.2 Properties of System 24
1.1.3 Classification of System 25
1.1.4 Model 25
1.2 Process 25
1.2.1 Classification of Processes 26
1.2.2 Process Model 27
1.3 Process Modeling 28
1.3.1 Relations 29
1.3.2 Assumptions 29
1.3.3 Variables and Parameters 30
1.4 Process Simulation 31
1.4.1 Utility 31
1.4.2 Simulation Methods 32
1.5 Development of Process Model 33
1.6 Learning about Process 35
1.7 System Specification 36
Bibliography 38
Exercises 38
Chapter 2 Fundamental Relations 39
2.1 Basic Form 39
2.1.1 Application 41
2.2 Mass Balance 43
2.2.1 Microscopic Balances 43
2.2.2 Equation of Change for Mass Fraction 45
2.3 Mole Balance 46
2.3.1 Microscopic Balances 46
2.3.2 Equation of Change for Mole Fraction 47
2.4 Momentum Balance 48
2.4.1 Convective Momentum Flux 49
2.4.2 Total Momentum Flux 50
2.4.3 Macroscopic Balance 51
2.4.4 Microscopic Balance 53
2.5 Energy Balance 55
2.5.1 Microscopic Balance 55
2.5.2 Macroscopic Balance 57
2.6 Equation of Change for Kinetic and Potential Energy 60
2.6.1 Microscopic Equation 60
2.6.2 Macroscopic Equation 62
2.7 Equation of Change for Temperature 63
2.7.1 Microscopic Equation 63
2.7.2 Macroscopic Equation 64
2.A Enthalpy Change from Thermodynamics 66
2.B Divergence Theorem 70
2.C General Transport Theorem 72
2.D Equations in Cartesian, Cylindrical and Spherical Coordinate Systems 75
2.D.1 Equations of Continuity 76
2.D.2 Equations of Continuity for Individual Species 76
2.D.3 Equations of Motion 77
2.D.4 Equations of Change for Temperature 78
Bibliography 79
Exercises 79
Chapter 3 Constitutive Relations 81
3.1 Diffusion 81
3.1.1 Multicomponent Mixtures 82
3.2 Viscous Motion 82
3.2.1 Newtonian Fluids 83
3.2.2 Non-Newtonian Fluids 84
3.3 Thermal Conduction 85
3.4 Chemical Reaction 85
3.5 Rate of Reaction 87
3.5.1 Equations of Change for Moles 88
3.5.2 Equations of Change for Temperature 89
3.5.3 Macroscopic Equation of Change for Temperature 91
3.6 Interphase Transfer 93
3.7 Thermodynamic Relations 94
3.A Equations in Cartesian, Cylindrical and Spherical Coordinate Systems 96
3.A.1 Equations of Continuity for Binary Systems of Constant Density and Diffusivity 96
3.A.2 Equations of Motion for Newtonian Fluids of Constant Density and Viscosity 97
3.A.3 Equations of Change for Temperature in Non-Reactive, Non-Viscous Dissipative Systems of Constant Density and Thermal Conductivity 98
References 99
Bibliography 99
Exercises 100
Chapter 4 Model Formulation 101
4.1 Lumped-Parameter Systems 102
4.1.1 Isothermal CSTR 102
4.1.2 Flow through Eccentric Reducer 105
4.1.3 Liquid Preheater 106
4.1.4 Non-Isothermal CSTR 109
4.2 Distributed-Parameter Systems 112
4.2.1 Nicotine Patch 112
4.2.2 Fluid Flow between Inclined Parallel Plates 115
4.2.3 Tapered Fin 118
4.2.4 Continuous Microchannel Reactor 121
4.2.5 Oxygen Transport to Tissues 125
4.2.6 Dermal Heat Transfer in Cylindrical Limb 128
4.2.7 Solvent Induced Heavy Oil Recovery 130
4.2.8 Hydrogel Tablet 134
4.2.9 Neutron Diffusion 139
4.2.10 Horton Sphere 141
4.2.11 Reactions around Solid Reactant 144
4.3 Fluxes along Non-Linear Directions 149
4.3.1 Saccadic Movement of an Eye 150
4.A Initial and Boundary Conditions 153
4.A.1 Initial Condition 153
4.A.2 Boundary Condition 153
4.A.3 Periodic Condition 154
4.B Zero Derivative at the Point of Symmetry 155
4.C Equation of Motion along the Radial Direction in Cylindrical Coordinates 156
References 159
Exercises 159
Chapter 5 Model Transformation 161
5.1 Transformation between Orthogonal Coordinate Systems 161
5.1.2 Differential Elements 164
5.1.3 Vector Representation 165
5.1.4 Derivatives of Unit Vectors 166
5.1.5 Differential Operators 168
5.2 Transformation between Arbitrary Coordinate Systems 177
5.2.1 Transformation of Velocity 177
5.2.2 Transformation of Spatial Derivatives 178
5.2.3 Correctness of Transformation Matrices 178
5.3 Laplace Transformation 183
5.3.1 Examples 184
5.3.2 Properties of Laplace Transforms 186
5.3.3 Solution of Linear Differential Equations 190
5.4 Miscellaneous Transformations 200
5.4.1 Higher Order Derivatives 200
5.4.3 Change of Independent Variable 201
5.4.4 Semi-Infinite Domain 201
5.4.5 Non-Autonomous to Autonomous Differential Equation 202
5.A Differential Operators in an Orthogonal Coordinate System 202
5.A.1 Gradient of a Scalar 202
5.A.2 Divergence of a Vector 203
5.A.3 Laplacian of a Scalar 206
5.A.4 Curl of a Vector 206
References 208
Bibliography 208
Exercises 208
Chapter 6 Model Simplification and Approximation 211
6.1 Model Simplification 211
6.1.1 Scaling and Ordering Analysis 212
6.1.2 Linearization 215
6.2 Model Approximation 222
6.2.1 Dimensional Analysis 223
6.2.2 Model Fitting 226
6.A Linear Function 242
6.B Proof of Buckingham Pi Theorem 243
6.C Newton’s Optimization Method 245
References 246
Bibliography 246
Exercises 247
Chapter 7 Process Simulation 249
7.1 Algebraic Equations 249
7.1.1 Linear Algebraic Equations 249
7.1.2 Non-Linear Algebraic Equations 258
7.2 Differential Equations 263
7.2.1 Ordinary Differential Equations 264
7.2.2 Explicit Runge–Kutta Methods 264
7.2.3 Step-Size Control 268
7.2.4 Stiff Equations 269
7.3 Partial Differential Equations 275
7.3.1 Finite Difference Method 277
7.4 Differential Equations with Split Boundaries 285
7.4.1 Shooting Newton–Raphson Method 286
7.5 Periodic Differential Equations 290
7.5.1 Shooting Newton–Raphson Method 290
7.6 Programming of Derivatives 293
7.7 Miscellanea 296
7.7.1 Integration of Discrete Data 296
7.7.2 Roots of a Single Algebraic Equation 298
7.7.3 Cubic Equations 300
7.A Partial Pivoting for Matrix Inverse 303
7.B Derivation of Newton–Raphson Method 303
7.B.1 Quadratic Convergence 304
7.C General Derivation of Finite Difference Formulas 306
7.C.1 First Derivative, Centered Second Order Formula 307
7.C.2 Second Derivative, Forward Second Order Formula 308
7.C.3 Third Derivative, Mixed Fourth Order Formula 309
7.C.4 Common Finite Difference Formulas 311
References 313
Bibliography 313
Exercises 313
Chapter 8 Mathematical Review 317
8.1 Order of Magnitude 317
8.2 Big-O Notation 317
8.3 Analytical Function 317
8.4 Vectors 318
8.4.1 Vector Operations 319
8.4.2 Cauchy–Schwarz Inequality 324
8.5 Matrices 324
8.5.1 Terminology 325
8.5.2 Matrix Operations 326
8.5.3 Operator Inequality 327
8.6 Tensors 328
8.6.1 Multilinearity 328
8.6.2 Coordinate-Independence 328
8.6.3 Representation of Second Order Tensor 329
8.6.4 Einstein or Index Notation 330
8.6.5 Kronecker Delta 332
8.6.6 Operations Involving Vectors and Second Order Tensors 332
8.7 Differential 340
8.7.1 Derivative 340
8.7.2 Partial Derivative and Differential 340
8.7.3 Chain Rule of Differentiation 341
8.7.4 Material and Total Derivatives 343
8.8 Taylor Series 344
8.8.1 Multivariable Taylor Series 345
8.8.2 First Order Taylor Expansion 345
8.9 L’Hopital’s Rule 348
8.10 Leibniz’s Rule 348
8.11 Integration by Parts 349
8.12 Euler’s Formulas 349
8.13 Solution of Linear Ordinary Differential Equations 349
8.13.1 Single First Order Equation 349
8.13.2 Simultaneous First Order Equations 350
Bibliography 354
Index 355
EULA 364

Produkt-Details

• Erscheint lt. Verlag: 5.4.2017
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Chemie ► Technische Chemie
• Themenwelt: Technik ► Umwelttechnik / Biotechnologie
• Schlagworte: chemical engineering • Chemie • Chemische Verfahrenstechnik • Chemistry • Computational Chemistry • Computational Chemistry & Molecular Modeling • Computational Chemistry u. Molecular Modeling • heat transfer • Industrial Chemistry • mass transfer • model simplification • model simulation • model transformation • momentum transfer • Process dynamics • Process Modelling • Process Simulation • Prozessmodell • Technische u. Industrielle Chemie • Transport Processes
• ISBN-10: 1-118-91465-1 / 1118914651
• ISBN-13: 978-1-118-91465-6 / 9781118914656