Turányi - Tomlin: Analysis of Kinetic Reaction Mechanisms


Tamás Turányi and Alison S. Tomlin
Analysis of kinetic reaction mechanisms

Springer, 2014

with 1025 references


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Chemical processes in many fields of science and technology, including combustion, atmospheric chemistry, environmental modelling, process engineering, and systems biology, can be described by detailed reaction mechanisms consisting of numerous reaction steps. This book describes methods that are applicable in all these fields. Topics addressed include: how sensitivity and uncertainty analyses allow the calculation of the overall uncertainty of simulation results and the identification of the most important input parameters, the ways in which mechanisms can be reduced without losing important kinetic and dynamic detail, and the application of reduced models for more accurate engineering optimizations. This monograph is invaluable for researchers and engineers dealing with detailed reaction mechanisms, but is also useful for graduate students of related courses in chemistry, mechanical engineering, energy and environmental science and biology.




Chapter 2: Reaction Kinetics Basics

Abstract This chapter provides an introduction to the basic concepts of reaction kinetics simulations. The level corresponds mainly to undergraduate teaching in chemistry and in process, chemical and mechanical engineering. However, some topics are discussed in more detail and depth in order to underpin the later chapters. The section “parameterising rate coefficients” contains several topics that are usually not present in textbooks. For example, all reaction kinetics textbooks discuss the pressure dependence of the rate coefficients of unimolecular reactions, but usually do not cover those of complex-forming bimolecular reactions. The chapter contains an undergraduate level introduction to basic simplification principles in reaction kinetics. The corresponding sections also discuss the handling of conserved properties in chemical kinetic systems and the lumping of reaction steps.

You may download here the complete text of Chapter 2.



1        Introduction.. 2

2        Reaction kinetics basics2

2.1     Stoichiometry and reaction rate.. 2

2.1.1       Reaction stoichiometry

2.1.2       Molecularity of an elementary reaction2

2.1.3       Mass action kinetics and chemical rate equations2

2.1.4       Examples2

2.2     Parameterising rate coefficients2

2.2.1       Temperature dependence of the rate coefficients2

2.2.2       Pressure dependence of the rate coefficients2

2.2.3       Reversible reaction steps2

2.3     Basic simplification principles in reaction kinetics2

2.3.1       The pool chemical approximation2

2.3.2       The pre-equilibrium approximation2

2.3.3       Rate determining step2

2.3.4       The quasi-steady-state approximation (QSSA) 2

2.3.5       Conserved properties2

2.3.6       Lumping of reaction steps2

3        Mechanism construction and the sources of data.. 2

3.1     Automatic mechanism generation.. 2

3.2     Data sources2

4        Reaction pathway analysis2

4.1     Species conversion pathways2

4.2     Pathways leading to the consumption or production of a species2

5        Sensitivity and uncertainty analyses2

5.1     Introduction.. 2

5.2     Local sensitivity analysis2

5.2.1       Basic equations2

5.2.2       The brute force method2

5.2.3       The Green function method2

5.2.4       The decoupled direct method2

5.2.5       Automatic differentiation2

5.2.6       Application to oscillating systems2

5.3     Principal component analysis of the sensitivity matrix.. 2

5.4     Local uncertainty analysis2

5.5     Global uncertainty analysis2

5.5.1       Morris’ screening method2

5.5.2       Global uncertainty analysis using sampling based methods2

5.5.3       Sensitivity indices2

5.5.4       Fourier Amplitude Sensitivity Test (FAST) 2

5.5.5       Response Surface Methods (RSMs) 2

5.5.6       Moment-independent global sensitivity analysis methods2

5.6     Uncertainty analysis of gas kinetic models2

5.6.1       Uncertainty of the rate coefficients2

5.6.2       Characterization of the uncertainty of the Arrhenius parameters2

5.6.3       Local uncertainty analysis of reaction kinetic models2

5.6.4       Examples of the application of uncertainty analysis to methane flame models2

5.6.5       Applications of  response surface techniques to uncertainty analysis in gas kinetic models2

5.6.6       Handling correlated inputs within global uncertainty and sensitivity studies2

5.7     Uncertainty analysis in systems biology.. 2

5.8     Uncertainty analysis: general conclusions2

6        Time-scale analysis2

6.1     Introduction.. 2

6.2     Species lifetimes and time-scales2

6.3     Application of perturbation theory to chemical kinetic systems2

6.4     Computational singular perturbation (CSP) theory.. 2

6.5     Slow manifolds in the space of variables2

6.6     Time-scales in reactive flow models2

6.7     Stiffness of reaction kinetic models2

6.8     Operator Splitting and Stiffness2

7        Reduction of reaction mechanisms2

7.1     Introduction.. 2

7.2     Reaction rate and Jacobian based methods for species removal.. 2

7.2.1       Species removal via the inspection of rates2

7.2.2       Species elimination via trial and error

7.2.3       Connectivity method: connections between the species defined by the Jacobian2

7.2.4       Simulation Error Minimization Connectivity Method (SEM-CM) 2

7.3     Identification of redundant reaction steps using rate-of-production and sensitivity methods  2

7.4     Identification of redundant reaction steps based on entropy production.. 2

7.5     Graph Based Methods2

7.5.1       Directed Relation Graph (DRG) method2

7.5.2       DRG-aided sensitivity analysis (DRGASA) 2

7.5.3       DRG with error propagation (DRGEP) 2

7.5.4       The Path Flux Analysis (PFA) method2

7.5.5       Comparison of methods for species elimination2

7.6     Optimisation Approaches2

7.6.1       Integer programming methods2

7.6.2       Genetic algorithm (GA) based methods2

7.6.3       Optimisation of reduced models to experimental data2

7.6.4       Application to oscillatory systems2

7.7     Species Lumping.. 2

7.7.1       Chemical Lumping2

7.7.2       Linear lumping2

7.7.3       Linear lumping in systems with time-scale separation2

7.7.4       General nonlinear methods2

7.7.5       Approximate nonlinear lumping in systems with time-scale separation2

7.7.6       Continuous lumping2

7.7.7       The application of lumping to biological and biochemical systems2

7.8     The quasi-steady-state approximation (QSSA) 2

7.8.1       Basic equations2

7.8.2       Historical context 2

7.8.3       The analysis of errors2

7.8.4       Further recent approaches to the selection of QSS-species2

7.8.5       Application of the QSSA in spatially distributed systems2

7.8.6       Practical applications of the QSSA2

7.9     CSP-based mechanism reduction.. 2

7.10        Numerical reduced models derived from the rate equations of the detailed model   2

7.10.1          Slow manifold methods2

7.10.2          Intrinsic low -dimensional manifolds (ILDMs) 2

7.10.3          Application of ILDM methods in reaction diffusion systems2

7.10.4          Thermodynamic approaches for the calculation of manifolds2

7.11        Numerical reduced models based on geometric approaches2

7.11.1          Calculation of slow invariant manifolds (SIMs) 2

7.11.2          The minimal entropy production trajectory method (MEPT) 2

7.11.3          Calculation of temporal concentration changes based on the self similarity of the concentration curves2

7.12        Tabulation approaches 2

7.12.1          The use of look-up tables2

7.12.2          In situ tabulation2

7.12.3          Controlling errors and the invariant constrained equilibrium pre-image curve (ICE-PIC) method2

7.12.4          Flamelet generated manifolds2

7.13        Numerical reduced models based on fitting2

7.13.1          Calculation of temporal concentration changes using difference equations2

7.13.2          Calculation of concentration changes by assuming the presence of slow manifolds2

7.13.3          Fitting polynomials using factorial design2

7.13.4          Fitting polynomials using Taylor expansions2

7.13.5          Orthonormal polynomial fitting methods2

7.13.6          High-dimensional model representations (HDMRs) 2

7.13.7          Artificial neural networks2

7.13.8          Piecewise reusable maps (PRISM) 2

7.14        Adaptive reduced mechanisms2

8        Similarity of sensitivity functions2

8.1     Introduction and basic definitions2

8.2     The origins of local similarity and scaling relationships2

8.3     The origin of global similarity.. 2

8.4     Similarity of the sensitivity functions of biological models2

8.5     The importance of the similarity of sensitivity functions2

9        Computer codes for the study of complex reaction systems2

9.1     General simulation codes in reaction kinetics2

9.2     Simulation of gas kinetics systems2

9.3     Analysis of reaction mechanisms2

9.4     Investigation of biological reaction kinetic systems2

9.5     Global uncertainty analysis2

10      Summary and concluding remarks2

11      Index.. 2

12      Literature.. 2


activation temperature

active mode

Active Thermochemical Table (ATcT)

ACUCHEM program

adaptive chemistry

adaptive reduced mechanism


analytical solution

ANOVA decomposition

approximate slow invariant manifold (ASIM)

Arrhenius equation

Arrhenius plot

artificial neural network (ANN)

ASIM. see Approximate Slow Invariant Manifold

automatic differentiation

automatic differentiation in FORTRAN. see ADIFOR

autonomous system of ODEs

backward reaction

bath gas

bimolecular reaction

binary search tree (BST)

Bodenstein-principle. see quasi-steady-state approximation

branching ratio

brute force method

Cantera program

CARM program package

cell cycle

channel ratio

characteristic timescale


chemical explosive mode analysis (CEMA)

Chemical Kinetics Simulator (CKS) program

chemical lumping

CHEMKIN program package

circadian clock models

cluster analysis

collision efficiency

Common Representative Intermediates (CRI) mechanism

complementary set of species

complex-forming bimolecular reaction

computational singular perturbation (CSP)

connectivity method (CM)

conserved moiety

conserved property

consistent mechanism

constrained equilibrium manifold (CEM)

constrained species lumping

continuous species

COPASI program

CSP. see computational singular perturbation theory

CSP Importance Index

CSP Participation Index

CSP Pointer

DAKOTA program package

data collaboration

DDM. see decoupled direct method

decoupled direct method

direct method

DRG method

DRG with error propagation (DRGEP)

DRG-aided sensitivity analysis (DRGASA)

DRGEP-aided sensitivity analysis (DRGEP-ASA)

dynamic adaptive chemistry (DAC)

dynamical dimension

E-CELL code

ellipsoid of accuracy (EOA)

empirical low-dimensional manifold (ELDM)

equivalence ratio

exact-steady-state adaptive chemistry (ESAC)

EXGAS code

explicit methods for the solution of ODEs

extended Arrhenius equation

external species

fall-off region

family method

fast equilibrium approximation. see pre-equilibrium approximation

fast equivalent operational model (FEOM)

fast variable

FGM. see flamelet generated manifolds

first order sensitivity index

flame prolongated ILDM (FPI)

flamelet generated manifolds (FGM)

FlameMaster program

flow-controlled chemistry tabulation (FCCT) method

Flux balance analysis (FBA)

FluxViewer program

forward reaction

Fourier Amplitude Sensitivity Test (FAST)

FPI. see Flamelet Prolongated ILD

functional principal component analysis (fPCA)

functional sensitivity analysis

Gaussian error propagation rule

Gaussian process emulator methods

genetic algorithm (GA)

genetic regulatory network (GRN) model

GeneWays code

Gepasi program

global error

global sensitivity analysis

global similarity

global uncertainty analysis

greedy approach

Green function

GUI-HDMR program

half life

HDMR. see high-dimensional model representation

heuristics-aided quantum chemistry (HAQC) methodology

high-dimensional model representation (HDMR)

Horner representation


implicit methods for the solution of ODEs

important feature

important species

impulse parametric sensitivity analysis (iPSA)

in situ adaptive tabulation (ISAT)

induction period

information-theoretic sensitivity analysis

initial concentration sensitivity coefficient. see Green function

internal species

invariant constrained equilibrium edge preimage curve (ICE-PIC) method

irreversible reaction step

ISAT. see in situ adaptive tabulation

KEGG database

KINAL program package

KINALC program

kinetic reaction mechanism

kinetic simplification principles

kinetic system of ODEs

Kintecus program

KPP program

laminarSMOKE program

Latin hypercube sampling

law of mass action

level of importance (LOI) index


Lindemann approach

linear species lumping

living species

local error

local similarity

local uncertainty analysis

log p formalism

LOGEsoft code

LOI. see level of importance index

Lotka-Volterra model

lumped reaction mechanism


MAMOX code

mass action kinetics

Master Chemical Mechanism (MCM)

Mechacut program

MECHMOD program

MEPT. see minimal entropy production trajectory method

metabolism network

method of invariant grid (MIG)

method of invariant manifold (MIM)

MIG. see method of invariant grid

MIM. see method of invariant manifold

minimal entropy production trajectory (MEPT) method


modified Arrhenius equation

molecular signal transfer


moment-independent global sensitivity analysis methods

Monte Carlo uncertainty analysis

Morris’ method

multichannel reactions

NASA polynomials

necessary species

negative cross effect

Network of Computed Reaction Enthalpies to Atom-Based Thermochemistry (NEAT)

NF-kB signalling pathway

NO relaxation approach (NORA) method

nominal parameter set

nonautonomous system of ODEs

nonlinear species lumping

nonreactive collisions

normalised sensitivity coefficient

odd oxygen species

on-the-fly mechanism reduction

operator splitting

optimal artificial neural network (OANN)

orthonormal polynomials

oscillating reactions

overall order of a reaction

overall reaction equation

overall sensitivity

pairwise mixing stirred reactor (PMSR)

partial equilibrium approximation. see pre-equilibrium approximation

Path Flux Analysis (PFA) method

PCAF-method. see principal component analysis of matrix F

PCAS method. see principal component analysis of matrix S

phase response curve (PRC)

phase space

physiologically based pharmacokinetic (PBPK) model

pool chemical approximation

pool component approximation. see pool chemical approximation

PottersWheel toolbox for MATLAB

pre-equilibrium approximation (PEA)

PREP-SPOP program package

PrIMe collaboration

principal component analysis (PCA) of the composition space

principal component analysis of matrix F (PCAF)

principal component analysis of matrix S (PCAS)

production rate

proper orthogonal decomposition (POD)

proper species lumping

pseudo-first-order approximation

QSSA. see quasi-steady-state approximation

quasi-steady-state approximation (QSSA)

radial design method

Range Identification and Optimization Tool (RIOT) code

rate coefficient

rate constant. see rate coefficient

rate determining step

rate-controlled constrained equilibrium method (RCCE)

rate-of-production analysis

RCARM code

RCCE. see rate-controlled constrained equilibrium method

reachable species

reaction channel

reaction invariant. see conserved property

reaction mechanism

reaction order with respect to a species

reaction pathway analysis

reaction rate

reaction step

reaction-diffusion manifold (REDIM) method


ReactionKinetics program

redundant species


response surface methods (RSMs)

reversible reaction step

rkmGen program

RMG code

SaSAT program

SBML data format

SBML Toolbox for MATLAB

SBML-PET program

SBML-PET-MPI program

SBML-SAT program

scaling law

screening methods

second order sensitivity index

self-organising map (SOM)

SEM program package

seminormalised sensitivity coefficient

sensitivity analysis

sensitivity analysis based (SAB) method

sensitivity coefficient

sensitivity index

sensitivity matrix

SIM. see slow invariant manifold

SimBiology toolbox for MATLAB

SimLab program package

simulated annealing optimisation

simulation error

Simulation Error Minimization Connectivity Method (SEM-CM)

skeletal model reduction

slow invariant manifold (SIM)

slow manifold

slow variable

stiff system of differential equations

stiffness index

stiffness ratio

stochastic kinetic modelling

stoichiometric coefficient

stoichiometric equation

stoichiometric matrix

SUNDIALS program package

symbolic solution

Systems Biology Toolbox for MATLAB

Systems Biology Workbench program

Tenua program


THERM code

third body

time scale

Titan, the moon of Saturn

total sensitivity index


Troe parameterisation

uncertainty analysis

uncertainty parameter f

unimolecular reaction

variable volume tabulated homogeneous chemistry (VVTHC) approach

WINPP/XPP program


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Typo found:

original:             Ranzi, E., Frassoldati, A., Granata, S., Faravelli, T.: Wide-range kinetic modeling study of the pyrolysis, partial oxidation, and combustion of heavy n-alkanes. Ind. Eng. Chem. Res. 44, 5170-5183 (2004)    
corrected:         Ranzi, E., Frassoldati, A., Granata, S., Faravelli, T.: Wide-range kinetic modeling study of the pyrolysis, partial oxidation, and combustion of heavy n-alkanes. Ind. Eng. Chem. Res. 44, 5170-5183 (2004)

p. 293
original:          Bilger, R.W.: On reduced mechanisms 
corrected:      Bilger, R.W.,
Stårner, S.H., Kee, R.J.:  On reduced mechanisms 

p. 297
original:            Gicquel, O., Ribert, O., Darabiha, N., Veynante, D.: Tabulation of complex chemistry based on self-similar behavior of laminar premixed flames. Combust. Flame 146, 649–664 (2006)
corrected:        Ribert, G., Gicquel, O., Darabiha, N., Veynante, D.: Tabulation of complex chemistry based on self-similar behavior of laminar premixed flames. Combust. Flame 146, 649–664 (2006)