The Approximation of the Chemical Reaction Rate by Solving the Integral Equation

Abstract

The paper discusses possible methods of approximation of the chemical reaction rate con- stant for the range of values that lie outside of the experimental temperature range: direct approximation of chemical reaction rate constants obtained by pro- cessing experimental values; approximation based on an analytical model of dependence of the integrated process cross-section on energy; and approximation based on the direct solution of the chemical reaction rate constant equation with arbitrary dependence of the integrated process cross-section on energy. The second-order reactions CH4 + M ! CH3 + H + M, CH3 +M! CH2 +H +M, CH3 +M! CH +H2 +M were explored. To solve the integrated equation, the variational Tikhonov's regularization method was used. It was shown that this method allowed both estimating the threshold energy value and re-establishing the cross- section form. By using the calculated cross-section we can obtain estimated chemical reaction rate constants over a wide temperature range. The data obtained can be used in various calculations in applied elds, in particular, in hypersonic gas dynamics problems, as well as for lling information system databases.