Solution of an actual problem related to the process of filtration and dehydration of liquid and ionic solutions from gel particles and heavy ionic compounds is considered in the paper. This technological process is realized during the preparation and cleaning of chemical solutions, drinking water, pharmaceuticals, liquid fuels, products for public use, etc. For the analysis, research, determination of the main parameters of the technological process and operating modes of filter units and for support in managerial decision-making, a mathematical model is developed. Using the developed model, a series of computational experiments on a computer is carried out. The results of numerical calculations are illustrated in the form of graphs. Based on the analysis of numerical experiments, the conclusions are formulated that serve as the basis for making appropriate managerial decisions.