Analysis of Kinetic Reaction Mechanisms (eBook)

Contents 6
Chapter 1: Introduction 11
References 13
Chapter 2: Reaction Kinetics Basics 15
2.1 Stoichiometry and Reaction Rate 15
2.1.1 Reaction Stoichiometry 15
2.1.2 Molecularity of an Elementary Reaction 19
2.1.3 Mass Action Kinetics and Chemical Rate Equations 20
2.1.4 Examples 24
2.2 Parameterising Rate Coefficients 28
2.2.1 Temperature Dependence of Rate Coefficients 28
2.2.2 Pressure Dependence of Rate Coefficients 30
2.2.3 Reversible Reaction Steps 36
2.3 Basic Simplification Principles in Reaction Kinetics 38
2.3.1 The Pool Chemical Approximation 38
2.3.2 The Pre-equilibrium Approximation 39
2.3.3 Rate-Determining Step 40
2.3.4 The Quasi-Steady-State Approximation (QSSA) 40
2.3.5 Conserved Properties 42
2.3.6 Lumping of Reaction Steps 43
References 44
Chapter 3: Mechanism Construction and the Sources of Data 48
3.1 Automatic Mechanism Generation 48
3.2 Data Sources 55
References 57
Chapter 4: Reaction Pathway Analysis 62
4.1 Species Conversion Pathways 62
4.2 Pathways Leading to the Consumption or Production of a Species 65
References 68
Chapter 5: Sensitivity and Uncertainty Analyses 70
5.1 Introduction 70
5.2 Local Sensitivity Analysis 72
5.2.1 Basic Equations 72
5.2.2 The Brute Force Method 75
5.2.3 The Green Function Method 76
5.2.4 The Decoupled Direct Method 77
5.2.5 Automatic Differentiation 78
5.2.6 Application to Oscillating Systems 79
5.3 Principal Component Analysis of the Sensitivity Matrix 80
5.4 Local Uncertainty Analysis 83
5.5 Global Uncertainty Analysis 84
5.5.1 Morris Screening Method 85
5.5.2 Global Uncertainty Analysis Using Sampling-Based Methods 88
5.5.3 Sensitivity Indices 95
5.5.4 Fourier Amplitude Sensitivity Test 97
5.5.5 Response Surface Methods 99
5.5.5.1 Gaussian Process Emulator Methods 101
5.5.5.2 Polynomial Chaos Expansion Methods 101
5.5.5.3 High-Dimensional Model Representation Methods 104
5.5.6 Moment-Independent Global Sensitivity Analysis Methods 109
5.6 Uncertainty Analysis of Gas Kinetic Models 110
5.6.1 Uncertainty of the Rate Coefficients 111
5.6.2 Characterisation of the Uncertainty of the Arrhenius Parameters 115
5.6.3 Local Uncertainty Analysis of Reaction Kinetic Models 120
5.6.4 Examples of the Application of Uncertainty Analysis to Methane Flame Models 123
5.6.5 Applications of Response Surface Techniques to Uncertainty Analysis in Gas Kinetic Models 128
5.6.6 Handling Correlated Inputs Within Global Uncertainty and Sensitivity Studies 132
5.7 Uncertainty Analysis in Systems Biology 133
Uncertainty Analysis: General Conclusions 137
References 142
Chapter 6: Timescale Analysis 154
6.1 Introduction 154
6.2 Species Lifetimes and Timescales 155
6.3 Application of Perturbation Theory to Chemical Kinetic Systems 161
6.4 Computational Singular Perturbation Theory 169
6.5 Slow Manifolds in the Space of Variables 172
6.6 Timescales in Reactive Flow Models 178
6.7 Stiffness of Reaction Kinetic Models 180
6.8 Operator Splitting and Stiffness 184
References 186
Chapter 7: Reduction of Reaction Mechanisms 192
7.1 Introduction 193
7.2 Reaction Rate and Jacobian-Based Methods for Species Removal 194
7.2.1 Species Removal via the Inspection of Rates 194
7.2.2 Species Elimination via Trial and Error 195
7.2.3 Connectivity Method: Connections Between the Species Defined by the Jacobian 196
7.2.4 Simulation Error Minimization Connectivity Method 197
7.3 Identification of Redundant Reaction Steps Using Rate-of-Production and Sensitivity Methods 198
7.4 Identification of Redundant Reaction Steps Based on Entropy Production 201
7.5 Graph-Based Methods 202
7.5.1 Directed Relation Graph Method 202
7.5.2 DRG-Aided Sensitivity Analysis 206
7.5.3 DRG with Error Propagation 207
7.5.4 The Path Flux Analysis Method 209
7.5.5 Comparison of Methods for Species Elimination 210
7.6 Optimisation Approaches 211
7.6.1 Integer Programming Methods 211
7.6.2 Genetic Algorithm-Based Methods 215
7.6.3 Optimisation of Reduced Models to Experimental Data 217
7.6.4 Application to Oscillatory Systems 218
7.7 Species Lumping 219
7.7.1 Chemical Lumping 220
7.7.2 Linear Lumping 226
7.7.3 Linear Lumping in Systems with Timescale Separation 231
7.7.4 General Nonlinear Methods 233
7.7.5 Approximate Nonlinear Lumping in Systems with Timescale Separation 235
7.7.6 Continuous Lumping 236
7.7.7 The Application of Lumping to Biological and Biochemical Systems 238
7.8 The Quasi-Steady-State Approximation 240
7.8.1 Basic Equations 241
7.8.2 Historical Context 242
7.8.3 The Analysis of Errors 243
7.8.4 Further Recent Approaches to the Selection of QSS-Species 247
7.8.5 Application of the QSSA in Spatially Distributed Systems 248
7.8.6 Practical Applications of the QSSA 249
7.9 CSP-Based Mechanism Reduction 251
7.10 Numerical Reduced Models Derived from the Rate Equations of the Detailed Model 253
7.10.1 Slow Manifold Methods 254
7.10.2 Intrinsic Low-Dimensional Manifolds 256
7.10.3 Application of ILDM Methods in Reaction Diffusion Systems 260
7.10.4 Thermodynamic Approaches for the Calculation of Manifolds 262
7.11 Numerical Reduced Models Based on Geometric Approaches 266
7.11.1 Calculation of Slow Invariant Manifolds 266
7.11.2 The Minimal Entropy Production Trajectory Method 268
7.11.3 Calculation of Temporal Concentration Changes Based on the Self-Similarity of the Concentration Curves 268
7.12 Tabulation Approaches 269
7.12.1 The Use of Look-Up Tables 270
7.12.2 In Situ Tabulation 272
7.12.3 Controlling Errors and the Invariant Constrained Equilibrium Pre-image Curve (ICE-PIC) Method 276
7.12.4 Flamelet-Generated Manifolds 279
7.13 Numerical Reduced Models Based on Fitting 280
7.13.1 Calculation of Temporal Concentration Changes Using Difference Equations 281
7.13.2 Calculation of Concentration Changes by Assuming the Presence of Slow Manifolds 283
7.13.3 Fitting Polynomials Using Factorial Design 284
7.13.4 Fitting Polynomials Using Taylor Expansions 285
7.13.5 Orthonormal Polynomial Fitting Methods 285
7.13.6 High-Dimensional Model Representations 290
7.13.7 Artificial Neural Networks 291
7.13.8 Piecewise Reusable Maps (PRISM) 295
7.14 Adaptive Reduced Mechanisms 296
References 300
Chapter 8: Similarity of Sensitivity Functions 322
8.1 Introduction and Basic Definitions 322
8.2 The Origins of Local Similarity and Scaling Relationships 325
8.3 The Origin of Global Similarity 331
8.4 Similarity of the Sensitivity Functions of Biological Models 334
8.5 The Importance of the Similarity of Sensitivity Functions 339
References 344
Chapter 9: Computer Codes for the Study of Complex Reaction Systems 345
9.1 General Simulation Codes in Reaction Kinetics 345
9.2 Simulation of Gas Kinetics Systems 347
9.3 Analysis of Reaction Mechanisms 350
9.4 Investigation of Biological Reaction Kinetic Systems 352
9.5 Global Uncertainty Analysis 355
References 357
Chapter 10: Summary and Concluding Remarks 360
Index 365