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Solution of an urgent problem related to technological process of filtering and dehydration of liquid solutions from fine particles and undesirable ionic compounds is discussed in the paper. There was developed a mathematical model and numerical algorithm taking into account the key factors and parameters that significantly affect considered processes. The problems related to the determination of the key parameters and their variation ranges are solved in the paper. Based on the analysis of conducted numerical experiments, the conclusions are formulated that serve as the basis for making appropriate management decisions.

Impact Factor:ISRA (India) = 1.344 ISI (Dubai, UAE) = 0.829 GIF (Australia) = 0.564 JIF = 1.500 SIS (USA) = 0.912 РИНЦ (Russia) = 0.207 ESJI (KZ) = 3.860 SJIF (Morocco) = 2.031 ICV (Poland) = 6.630 PIF (India) = MATHEMATICAL MODEL AND NUMERICAL ALGORITHM FOR SOLVING THE PROBLEM OF ION EXCHANGE FILTERING OF LIQUIDS Abstract: A detailed analytical review of scientific papers related to the process of modeling the nonstationary technological process of filtering ionic solutions from fine particles and ionic compounds is given in the paper. To study the technological process of filtering ionic solutions, depending on their physico-chemical properties and operating modes of the filtering unit, a mathematical model, a numerical algorithm and

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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.