Simulation of the Motion of a Mixture of Liquid and Solid Particles in Porous Media with Regard to Internal Suffosion

Abstract

The mathematical model of isothermal internal soil erosion is studied without regard for deformation of the porous medium. Soil particles are removed from the flow region when a certain velocity of filtration is reached. As the mathematical model of the problem, the mass conservation equations for water, moving solid particles and stationary porous skeleton are used along with an analog of Darcy's law for water and moving solid particles and a relation for the intensity of suffosion aquifer. The moving soil particles are considered to be an individual phase with its own filtration rate determined in solving the problem. This assumption makes it possible to construct the closed model. The algorithm of numerical solution of the initial boundary-value problem of groundwater filtration in which the internal soil erosion is taken into account is proposed. The numerical test calculations are carried out. The calculation results correlate well with the experimental data.