[en] The article deals with the problem associated with the process of ion-exchange filtration of ionized liquid solutions from heavy ionic compounds emitted from production facilities. To carry out a comprehensive study of the above mentioned process, the paper presents a mathematical tool - a mathematical model and its numerical algorithm for conducting a computational experiment on a computer and the results of the above calculations, as well as conclusions related to them. For numerical integration, the task of suppressing small-scale oscillation is added to the term with some numerical parameter - the coefficient of 'artificial viscosity', and the nonlinear terms of the equation are linearized by the Bellman-Calaba quasi linearization method. (author)

[en] The paper presents a mathematical model in the form of a second-order nonlinear differential equation with initial and boundary conditions and a numerical method for solving the problem based on the finite-difference method of the technological process of filtration of low-concentration suspensions to determine the ranges of variation of the ion-exchange filter parameters, as well as the results of computational experiments. When developing a mathematical model, the following main filter parameters and physico-mechanical properties of solutions (liquids) were taken into account: filtration rate, rate of sedimentation of gel particles on the pores of the filter, filter porosity, filter layer thickness, kinetic coefficient, dynamic viscosity coefficient and outlet concentration of the suspension. The developed mathematical model and a numerical solution method allow determining the deposition rate of gel particles in the pores of the filter, the outlet concentration of the solution and changes in the concentration of the driving solution of the ion-exchange filter. (paper)