THE INTERVAL METHODS ON EVALUATION OF MOLECULAR CHARACTERISTICS FOR SOLUTION OF THE DIRECT PROBLEMS IN CHEMICAL KINETICS
The paper presents a method for constructing a two-sided estimation of the solution for the direct problem of chemical kinetics. The basic methodology and algorithm for reducing the original system of differential equations to a modified form under the conditions of the interval nature of the kinetic parameters and the concentration of reagents are described. The main idea of the method for constructing a two-sided estimation of the solution for the direct problem of chemical kinetics is to carry out preliminary analysis for isotonicity and antitonicity of the right-hand sides of the equations in the system and the formation of a modified system of differential equations, depending on the results of the analysis of functions. The described methodology and algorithm were tested on the example of isoprene polymerization in the presence of a neodymium-containing catalytic complex used in the industrial production of polyisoprene. The main kinetic mechanism of the process is described, a mathematical model is drawn up, represented by a system of differential equations, and the model is modified for the case of an interval nature of the initial concentration of reagents. To solve the presented systems of ordinary differential equations, a Python program was developed using the Jupiter Notebook tool, which simplifies the visualization of the results. Two-sided estimates of conversion and averaged molecular characteristics were obtained under conditions of the interval nature of the concentration of diisobutylaluminum hydride, which acts as a molecular weight regulator, and the fraction of active sites of the catalyst. The effect of unwinding the obtained interval values is demonstrated for the case of solving the original system of differential equations by the implicit Euler method, modified by replacing arithmetic operations with the corresponding interval analogs. The results obtained demonstrate that two-sided methods make it possible to indicate the boundaries of the region, where a solution of the problem may be obviously found.