Reduction of Reaction Mechanisms

Abstract

Increases in both chemical kinetics knowledge and the capacity of computers have led to the availability of very large detailed kinetic mechanisms for many problems. These mechanisms may contain up to several thousand species and several ten thousand reaction steps. For computational reasons, however, large mechanisms still cannot be used in spatially 2D or 3D computational fluid dynamics simulations, where the applied mechanism typically requires less than 100 species. Also, within such large mechanisms, the key processes can be masked by the presence of many reaction steps of only marginal importance. A first step to reducing the size of a kinetic mechanism is to identify species and reaction steps which do not need to be included in order to accurately predict the key target outputs of the model. Such methods lead to so-called ``skeletal'' schemes. This chapter discusses many different methods for the identification of redundant species and reaction steps within a mechanism, including those based on sensitivity and Jacobian analyses, the comparison of reaction rates, trial and error and calculated entropy production. Another family of methods for the development of skeletal schemes is based on the investigation of reaction graphs. We discuss here the directed relation graph (DRG) method and its derivatives, and the path flux analysis (PFA) method. Mechanism reduction may be also based on optimisation methods which minimise an objective function related to the simulation error between the full and reduced models, subject to a set of constraints (e.g. numbers of species required). Integer programming and genetic algorithm-based methods have been used for such an optimisation and are discussed here. From these skeletal schemes, subsequent reductions can be achieved via either species or reaction lumping. Chemical and mathematical approaches to lumping are discussed with applications in combustion, atmospheric and biological systems. Reduction methods based on timescale separation are then introduced starting with the classic quasi-steady-state approximation (QSSA). Computational singular perturbation (CSP) methods are then described as a means of informing the derivation of analytically reduced models. Further efficiency gains can also be obtained by using a numerical approximation of a function in place of more traditional descriptions of chemical source terms within simulation models. The generation of such numerical reduced models can be based on the original differential equations and the thermodynamics of the problem or deduced from the simulation results. Using any of these methods, the applied function has to meet special requirements, such as the need to be evaluated quickly and to provide an accurate approximation. We discuss a series of approaches, tabulation methods, artificial neural networks (ANNs) and various types of polynomials, that all have been tested and applied within the context of kinetic modelling.