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Transfer of Particles in a Porous Medium

Y. V. Osipov, Associate professor of the Department of applied
mathematics, candidate of phys. and math. sciences, Associate professor;
S.P. Zotkin, Associate professor of the Department of applied
mathematics, candidate of tech. sciences, Associate professor
Moscow State University of Civil Engineering
(National Research University)

Abstract. Construction of buildings and structures on loose ground requires preliminary measures to strengthen the base. One of the methods for creating a solid foundation is to inject a liquid concrete solution into the porous soil under pressure. A fluid with concrete grains spreads in the pores of the rock and, solidifying, strengthens the soil. The problem of suspension filtration in a porous medium is studying the transfer and deposition of small solid particles transported by the fluid flow in a porous soil. A filtration model, based on the size­exclusion mechanism of particles capture in a porous medium, is considered: the particles freely pass through large­diameter pores and get stuck in the pore throats, smaller than the particles diameter. A suspension with a constant concentration of suspended particles is injected into the porous medium that does not contain any suspended and retained particles. The concentrations front of the suspended and retained particles moves at a constant velocity from the inlet to the outlet of the porous medium. At the front, the concentration of suspended particles has a discontinuity. The most intensive filtration and particles deposition occur at the porous medium inlet. Deep bed filtration of a monodisperse suspension in a porous medium is described by a hyperbolic quasilinear system of the first­order equations ­ the equation of the mass transfer of suspended and retained particles and the equation of kinetic deposit growth rate. It is assumed that the growth rate of the deposit is proportional to the concentration of suspended particles in the suspension. In this paper an asymptotic solution near the porous medium inlet is constructed. The distance from the inlet serves as a small parameter of the asymptotic expansion. The asymptotic solution is compared with the exact solution for the linear filtration coefficient. Numerical calculations show that as the number of asymptotic terms increases, its accuracy improves significantly.
Key words: filtration, suspension, porous medium, suspended and retained particles, filtration coefficient, asymptotics.

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