Mathematical Modeling of the Water Purification Process Taking Into Account the Inverse Effect of the Process Characteristics on the Characteristics of the Environment

Abstract

This paper considers and solves the issues of taking into account the inverse effect of process characteristics (liquid concentration and sediment contamination) on the environment characteristics (porosity, filtration, diffusion, mass transfer, etc.) on the example of liquid purification in magnetic and sorption filters. An algorithm for numerical-asymptotic approximation of the corresponding model problem solution is obtained, which is described by a system of non-linear singularly perturbed differential equations of the type "convection-diffusion-mass transfer". Appropriate ratios (formulas) are effective for optimizing the water treatment process and increasing the treatment system productivity as a whole (allow to determine the filter protective time, the filter size, etc.) in cases of convective predominance and sorption components of the corresponding process over diffusion and desorption which occurs in the vast majority of filter systems. On this basis, a corresponding computer experiment was conducted, the results of which show the proposed model advantages in comparison with classical.