A Mathematical Modelling of Solid Particles Transport in Two-Zone Porous Media with Non-Linear Kinetics of Deposition

Abstract

The processes of transport of various pollutants in porous media are of great practical importance. Such contaminants can be solid colloidal particles suspended in the carrier fluid. In the process of transfer, particles can be deposited in pores, which significantly change the permeability and porosity characteristics of the medium. The heterogeneity of porous media considerably affects the transfer of these particles. One of the macroscopically inhomogeneous media is zonal inhomogeneous media, consisting of several zones with different characteristics. In such media, generalized mathematical models have not yet been developed that take into account the zonal inhomogeneity of the medium, various linear and nonlinear, reversible and irreversible kinetics of deposition of solid particles from the liquid into the pore space, etc. In this work, a model is generalized for the transfer of solid particles in a two-zone porous medium. In this work, a mathematical model is considered for colloidal particles transport process in a two-zone porous medium and both the zones having the reversible retentions of particles with different characteristics (parameters). It is shown that the nonlinear kinetics of particle deposition, other parameters being equal, leads to an intensification of particle deposition in pores. As the index n decreases from unity, the rate of particle deposition increases in both zones of the medium. As a consequence, the concentration of suspended particles in the mobile fluid in both zones decreases.