Redundant reactions

Once the necessary species have been found, the second step in reducing a mechanism is the elimination of its non-important reactions. A classical and reliable method is the comparison of the contribution of reaction steps to the production rate of necessary species. A description of this method - without the pre-selection of redundant species - is given by Wamatz [4, 93]. A more recent application of this technique for methane flames is presented in [94]. According to this method a reaction is redundant if its contribution to the production rate of each necessary species is small. This rule sounds simple and obvious but there are, however, several drawbacks and pitfalls. First, the reaction contributions have to be considered at several reaction times (or at several heights in the case of steady flames). Second, all reaction contributions to each necessary species have to be considered, and it is not easy to analyze such huge matrices. The threshold of unimportance will vary from time to time, and from species to species. Applying a uniform threshold for each time and species (e.g., minimum 5% contribution) can either result in redundant reactions being left in the scheme, or an over-simplified mechanism. 

From the redundant species analysis it is clear that all reactions which consume H2O2 and O3 are redundant and can be removed automatically from the mechanism. In order to identify other redundant reactions the techniques of rate sensitivity analysis coupled with a principal component analysis of the resulting matrix can be used. The principal component analysis of the rate sensitivity matrix containing only the remaining important and necessary species will reveal the important reactions leading to reduced mechanisms applicable at various ambient temperatures. In principle it may be possible to produce a reduced scheme which models non-isothermal behaviour from analysis carried out on an isothermal model. An isothermal system is easier to model since thermodynamic and heat-transfer properties can be excluded from the calculations. However,... 

Comparison of reaction rates, called rate-of-production analysis, is a frequently applied technique and is the basis of limiting the size of a newly created mechanism. However, this technique requires a lot of manual effort. Algebraic rate sensitivities are the partial derivatives of production rates with respect to rate parameters. These measures are equal to normed reaction rate contributions. Inspection of algebraic rate sensitivities, based on either the sum of squares of the coefficients (overall sensitivities) or principal component analysis, is a simpler and more automatic way for the identification of redundant reactions than that based on rate-of-production analysis. 

Generally, local concentration sensitivities are used for finding the parameters that have to be known with high precision, and for the identification of rate-limiting steps. An important achievement in the field of sensitivity analysis has been the introduction of principal component analysis as a method for the interpretation of the large amount of information contained in the sensitivity matrix. In the future, a more wide-spread application of principal component analysis is expected for the interpretation of concentration sensitivity results. This would help the extraction of further mechanistic details, or could be used for the detection of redundant reactions. The calculation of initial concentration sensitivities is very useful in some cases, but most simulation packages cannot calculate these sensitivities and there is no sign that such a feature will be incorporated. 

An overview of the methods used previously in mechanism reduction is presented in Tomlin et al. (1997). The present work uses a combination of existing methods to produce a carbon monoxide-hydrogen oxidation scheme with fewer reactions and species variables, but which accurately reproduces the dynamics of the full scheme. Local concentration sensitivity analysis was used to identify necessary species from the full scheme, and a principle component analysis of the rate sensitivity matrix employed to identify redundant reactions. This was followed by application of the quasi-steady state approximation (QSSA) for the fast intermediate species, based on species lifetimes and quasi-steady state errors, and finally, the use of intrinsic low dimensional manifold (ILDM) methods to calculate the mechanisms underlying dimension and to verify the choice of QSSA species. The origin of the full mechanism and its relevance to existing experimental data is described first, followed by descriptions of the reduction methods used. The errors introduced by the reduction and approximation methods are also discussed. Finally, conclusions are drawn about the results, and suggestions made as to how further reductions in computer run times can be achieved. 

Further simplification is possible by eliminating the redundant reactions, through principal components analysis (PCA) of the rate sensitivity matrix, F, which has elements... 

Identification of Redundant Reaction Steps Using Rate-of-Production and... 

Another method for removing redundant reaction steps is the principal component analysis of matrix F PCAF), where V=[dfjdxk (Turmyi et al. 1989 Tomlin et al. 1992 Borger et al. 1992 Heard et al. 1998 Carslaw et al. 1999 Zsely and Turanyi 2001 Bahlouli et al. 2014). Here the sensitivity of the net rates of production of species to changes in the input parameters is investigated. Using the PCAF method, the objective function has the following form ... 

All of the previous methods identify redundant reactions via the inspection of the reaction rates or by the study of sensitivity matrices deduced from the kinetic system of differential equations. A very different approach is the application of thermodynamic functions for the identification of redundant reactions. This approach has common features with the derivation of numerical reduced models based on thermodynamics reasoning (see Sect. 7.10.4). 

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