Numerical Algorithm for Finding the Optimal Composition of the Reacting Mixture on the Basis of the Reaction Kinetic Model

Abstract

The results of development of an algorithm for searching for optimal initial concentrations of substances in a chemical reaction are presented. The algorithm combines 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 involves 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 are 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 is 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 the reagents to obtain the highest yield of the target product at the end of the reaction. The optimal initial concentrations of the starting substances are calculated for different reaction durations and at different temperatures. The developed numerical algorithm for determining the optimal initial concentrations of the 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, thus providing significant savings in time and material costs.