Numerical algorithm for finding the optimal composition of the reacting mixture on the basis of the reaction kinetic model

Abstract

The results of developing an algorithm for searching for optimal initial concentrations of substances in a chemical reaction are presented. The algorithm combines a combination of optimization methods with the theoretical foundations of modeling chemical reactions in terms of constructing their kinetic models. A mathematical description of the dynamics of the concentrations of reactants over time is presented in the form of a system of ordinary differential equations the initial conditions of which are specified by the values of the initial concentrations of the reactants. The problem of determining the optimal composition of the reacting mixture is formulated in general terms. The problem contains restrictions imposed on the values of the initial concentrations of substances and on their initial total concentration. To solve the problem, the penalty method and the Hooke–Jeeves method were used. A penalty function is described that allows one to reduce the original problem to a problem without restrictions. A step-by-step algorithm for searching for optimal initial concentrations of a chemical reaction is formulated. A computational experiment was carried out for the catalytic reaction of aminomethylation of thiols using tetramethylmethanediamine. A kinetic model of the reaction is presented on the basis of which an optimization problem is formulated to find the values of the initial concentrations of reagents to obtain the highest yield of the target product at the end of the reaction. The optimal initial concentrations of the starting substances were calculated for different reaction durations and at different temperatures. The developed numerical algorithm for determining the optimal initial concentrations of reagents takes into account the physicochemical features of the problem and can be used in the study of complex chemical reactions containing a large number of initial and intermediate substances. Its use makes it possible to determine the patterns of a chemical reaction at the stage of a computer experiment, without resorting to laboratory experiments, which significantly saves the material and time costs of the researcher.

Keywords

• optimal initial concentrations
• penalty method
• hooke-jeeves method
• reaction kinetic model