Finding redundant species

The primary stage in finding an appropriate submechanism is the determination of redundant species. Species of chemical mechanisms can be classified into three categories. The reproduction of the concentration profiles of important species is the aim of the modelling process. Important species might, for example, include reaction products or initial reactants. Other species, termed necessary species, have to be present in the model to enable the accurate reproduction of the concentration profiles of important species, temperature profiles or other important reaction features. The remaining species are redundant species. If redundant species are on the lefthand side of a reaction, this reaction can then be eliminated from the mechanism without any effect on the output of the model. If such a species is on the righthand side, then the reaction may or may not be deleted. Even if the reaction has to be retained, the redundant species can be deleted from the list of products of the reaction. Of course the latter can only be done if preservation of atoms or mass is not a formal requirement for the mechanism. 

An alternative method is based on the investigation of the Jacobian of the kinetic system of odes, J = df/dc. A species may be considered redundant if its concentration change has no significant effect on the rate of production of important species. An element of the normed Jacobian (3 ln/,)/(3 In Cy) shows the fractional change of the rate of production of species i caused by the fractional change of the concentration of species j. The influence of the change of the concentration of species i on the rate of production of an A-membered group of important species can be taken into account by the sum of squares of normalized Jacobian elements, 

The first method requires several simulations of different reduced models as each species is eliminated. The number of simulations is of the order of the number of species. Using this method the effect of species elimination on important features can be obtained directly in a quantitative way. The second method requires a single simulation of the original model where the Jacobian is calculated from the concentrations at several reaction times. Therefore, this method is more efficient and can be applied automatically, but cannot be used to investigate the effects on important features such as ignition time. 

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Finding a subset of a reaction mechanism with identical applicability to the full mechanism, should be the final step of every mechanism generation, and the first step of any mechanism reduction work. However, most published mechanisms contain plenty of species and reactions which are redundant over the range of experimental conditions they are intended to cover. A systematic search for redundant species is almost never carried out, and redundant species are usually identified either accidentally or on the basis of detailed chemical knowledge of the mechanism studied. Two techniques are described here which allow the identification of redundant species in a systematic way. 

Thus, it is concluded that six stretching and nine bending vibrations are distributed as indicated in Eqs. 1.98 and 1.100, respectively. Although the method given above is simpler than that of Sec. 1.8, caution must be exercised with respect to the bending vibrations whenever redundancy is involved. In such a case, comparison of the results obtained from both methods is useful in finding the species of redundancy. 

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