MATHEMATICAL MODELING OF TECHNOLOGICAL PROCESSES OF CATALYTIC CLEANING

Abstract

This article presents an overview that shows how different mathematical models of catalytic purification processes are used today. Among them, numerical methods of analysis for solving differential equations or their systems have proved to be the best. An important feature of the mathematical description, which contains ordinary differential equations, is the need to specify the initial conditions. Differential equations in partial derivatives are used to mathematically describe the dynamics of objects with distributed parameters or stationary modes for objects with parameters distributed over several coordinates. For these equations, when describing the dynamics of the object, along with the initial conditions, you must also specify the boundary conditions, which in the general case are functions of time. For stationary objects, which are described by equations in partial derivatives, set only the boundary conditions. Problems with equations in partial derivatives, as a rule, are of the greatest complexity, and in most cases the solution of each specific problem requires serious work. The method of transition to nonstationary problems, which were approximated by systems of finite equations, was used in the works on solving differential equations. The possibility of performing mathematical processing of experimental data using graphical methods and apparatus for interpolating the function is shown. It was found that the numerical solution of the boundary value problem for modeling heat, mass and moisture exchange in soil massifs taking into account catalytic microparticles or nanoparticles was found using the finite difference method. It is proved that it is better to use a one-dimensional three-temperature mathematical model for modeling nonstationary regimes in a stationary adiabatic adsorption-catalytic approximation. A similar one-dimensional mathematical model can be used to describe the process of filtering a suspension of solid particles through a porous tissue filter. The kinetic regularities of the process of catalytic hydrotreating of atmospheric gas oil on the catalyst KF-905-1.3Q were established using a reliable mathematical model suitable for forecasting and optimizing the most important indicators of the quality of atmospheric gas oil. Thus, the possibility of preliminary sorption treatment of wastewater from soy milk production with sorbents obtained from agricultural waste was investigated, the prospects of using these reagents using the method of interpolation polynomials were shown. A mathematical model for the system in dynamic modes of operation was also demonstrated, which confirmed the adequacy of the developed model of the real control system by the technological process of catalytic gas purification. It is shown how, with the help of Lagrange interpolation polynomials, it is possible to construct analytical expressions that describe the dependence of the change in the physicochemical parameters of the wastewater on the reagent concentration.