1;Contents;6 2;Chapter 1: Introduction;11 2.1;References;13 3;Chapter 2: Reaction Kinetics Basics;15 3.1;2.1 Stoichiometry and Reaction Rate;15 3.1.1;2.1.1 Reaction Stoichiometry;15 3.1.2;2.1.2 Molecularity of an Elementary Reaction;19 3.1.3;2.1.3 Mass Action Kinetics and Chemical Rate Equations;20 3.1.4;2.1.4 Examples;24 3.2;2.2 Parameterising Rate Coefficients;28 3.2.1;2.2.1 Temperature Dependence of Rate Coefficients;28 3.2.2;2.2.2 Pressure Dependence of Rate Coefficients;30 3.2.3;2.2.3 Reversible Reaction Steps;36 3.3;2.3 Basic Simplification Principles in Reaction Kinetics;38 3.3.1;2.3.1 The Pool Chemical Approximation;38 3.3.2;2.3.2 The Pre-equilibrium Approximation;39 3.3.3;2.3.3 Rate-Determining Step;40 3.3.4;2.3.4 The Quasi-Steady-State Approximation (QSSA);40 3.3.5;2.3.5 Conserved Properties;42 3.3.6;2.3.6 Lumping of Reaction Steps;43 3.4;References;44 4;Chapter 3: Mechanism Construction and the Sources of Data;48 4.1;3.1 Automatic Mechanism Generation;48 4.2;3.2 Data Sources;55 4.3;References;57 5;Chapter 4: Reaction Pathway Analysis;62 5.1;4.1 Species Conversion Pathways;62 5.2;4.2 Pathways Leading to the Consumption or Production of a Species;65 5.3;References;68 6;Chapter 5: Sensitivity and Uncertainty Analyses;70 6.1;5.1 Introduction;70 6.2;5.2 Local Sensitivity Analysis;72 6.2.1;5.2.1 Basic Equations;72 6.2.2;5.2.2 The Brute Force Method;75 6.2.3;5.2.3 The Green Function Method;76 6.2.4;5.2.4 The Decoupled Direct Method;77 6.2.5;5.2.5 Automatic Differentiation;78 6.2.6;5.2.6 Application to Oscillating Systems;79 6.3;5.3 Principal Component Analysis of the Sensitivity Matrix;80 6.4;5.4 Local Uncertainty Analysis;83 6.5;5.5 Global Uncertainty Analysis;84 6.5.1;5.5.1 Morris Screening Method;85 6.5.2;5.5.2 Global Uncertainty Analysis Using Sampling-Based Methods;88 6.5.3;5.5.3 Sensitivity Indices;95 6.5.4;5.5.4 Fourier Amplitude Sensitivity Test;97 6.5.5;5.5.5 Response Surface Methods;99 6.5.5.1;5.5.5.1 Gaussian Process Emulator Methods;101 6.5.5.2;5.5.5.2 Polynomial Chaos Expansion Methods;101 6.5.5.3;5.5.5.3 High-Dimensional Model Representation Methods;104 6.5.6;5.5.6 Moment-Independent Global Sensitivity Analysis Methods;109 6.6;5.6 Uncertainty Analysis of Gas Kinetic Models;110 6.6.1;5.6.1 Uncertainty of the Rate Coefficients;111 6.6.2;5.6.2 Characterisation of the Uncertainty of the Arrhenius Parameters;115 6.6.3;5.6.3 Local Uncertainty Analysis of Reaction Kinetic Models;120 6.6.4;5.6.4 Examples of the Application of Uncertainty Analysis to Methane Flame Models;123 6.6.5;5.6.5 Applications of Response Surface Techniques to Uncertainty Analysis in Gas Kinetic Models;128 6.6.6;5.6.6 Handling Correlated Inputs Within Global Uncertainty and Sensitivity Studies;132 6.7;5.7 Uncertainty Analysis in Systems Biology;133 6.8;Uncertainty Analysis: General Conclusions;137 6.9;References;142 7;Chapter 6: Timescale Analysis;154 7.1;6.1 Introduction;154 7.2;6.2 Species Lifetimes and Timescales;155 7.3;6.3 Application of Perturbation Theory to Chemical Kinetic Systems;161 7.4;6.4 Computational Singular Perturbation Theory;169 7.5;6.5 Slow Manifolds in the Space of Variables;172 7.6;6.6 Timescales in Reactive Flow Models;178 7.7;6.7 Stiffness of Reaction Kinetic Models;180 7.8;6.8 Operator Splitting and Stiffness;184 7.9;References;186 8;Chapter 7: Reduction of Reaction Mechanisms;192 8.1;7.1 Introduction;193 8.2;7.2 Reaction Rate and Jacobian-Based Methods for Species Removal;194 8.2.1;7.2.1 Species Removal via the Inspection of Rates;194 8.2.2;7.2.2 Species Elimination via Trial and Error;195 8.2.3;7.2.3 Connectivity Method: Connections Between the Species Defined by the Jacobian;196 8.2.4;7.2.4 Simulation Error Minimization Connectivity Method;197 8.3;7.3 Identification of Redundant Reaction Steps Using Rate-of-Production and Sensitivity Methods;198 8.4;7.4 Identification of Redundant Reaction Steps Based on Entropy Production;201 8.5;7.5 Graph-Based Methods;202 8.5.1;7.5.1 Directed Relation Graph Method;202 8.5.2;7.5.2 D