Chapter 10 Conventional Asymptotics and Computational Singular Perturbation for Simplified Kinetics Modelling

Generally speaking, the chemical kinetics of any reaction system can potentially be very complex. Even though the investigator may only be interested in a few species, the reaction model almost always involves a much larger number of species. Some of the species involved are often referred to as radicals with a special meaning: they are usually reactants of low concentrations which are believed to be important intermediaries in the whole reaction scheme. A large number of elementary reactions can occur among the species; some of these reactions are fast and some are slow. The aim of simplified kinetics modelling is to derive the simplest reaction system which nevertheless retains the essential features of the full reaction system. The conventional technique [1] is to systematically apply the so-called steady-state approximation to the appropriate radicals, the partial-equilibrium approximation to the fast reactions, and to ignore the very slow (and therefore unimportant) reactions. The investigator is responsible for identifying what are the appropriate radicals, which are the fast elementary reactions, and which are the very slow ones by making intelligent order of magnitude estimates using information gathered from detailed examination of available data. A skilled and knowledgeable chemical kineticist is usually needed, and the results obtained are expected to be valid only in some limited domain of initial and operating conditions in some limited interval of time. The successful derivation of a simplified chemical kinetics model by conventional methodology thus depends considerably on the experience, intuition and judgement of the investigator.