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Research and reduction of mathematical model of chemical reaction by Sobol’ method
The technique of simplification of mathematical model of a chemical reaction by reducing the number of steps of the reaction scheme, based on an analysis of sensitivity to changes in the objective function of the model parameters, is proposed. The reduced scheme of model reaction of formaldehyde oxidation is received. Functional characterizes the measure of proximity to the calculated values for the initial kinetic reaction scheme and the scheme resulting disturbance of its parameters. The advantage of this technique is the ability to analyze complex kinetic schemes and reduction of kinetic models to a size suitable for practical use. The results of computational experiments under different reaction conditions can be included in the functional and thus to receive the reduce scheme, which is consistent the detailed scheme for the desired range of conditions. Sensitivity analysis of the functional model allows to identify those parameters, which provide the largest (or smallest) the contribution to the result of the process simulation. The mathematical model can contain parameters, which change of values do not affect the qualitative and quantitative description of the process. The contribution of these parameters in the functional value won’t be of great importance. Thus it can be eliminated from consideration, which do not serve for modeling kinetic curves substances. The kinetic scheme of formaldehyde oxidation, the detailed mechanism which includes 25 stages and 15 substances, were investigated using this method. On the basis of the local and global sensitivity analysis, the most important stage of the process that affect the overall dynamics of the target concentrations of the reaction. The reduced scheme of model reaction of formaldehyde oxidation is received. This scheme also describes the behavior of the main substances, as detailed scheme, but has a much smaller number of reaction stages. The results of the comparative analysis of modeling of formaldehyde oxidation on detailed and reduced schemes are given. Computational aspects of the problems of chemical kinetics by Sobol’ global method an example of this reaction are specified. The comparison results are local, global and total sensitivity indices are given.
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International Interdisciplinary Conference "Mathematics. Computing. Education"