Asymptotics of the filtration problem for suspension in porous media

Vestnik MGSU 1/2015
  • Kuzmina Ludmila Ivanovna - Higher School of Economics Department of Applied Mathematics, Moscow Institute of Electronics and Mathematics, Higher School of Economics, 20 Myasnitskaya str., Moscow, 101000, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Osipov Yuri Viktorovich - Moscow State University of Civil Engineering (National Research University) (MGSU) Candidate of Physical and Mathematical Sciences, Associate Professor, Department of Computer Science and Applied Mathematics, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoe Shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 54-62

The mechanical-geometric model of the suspension filtering in the porous media is considered. Suspended solid particles of the same size move with suspension flow through the porous media - a solid body with pores - channels of constant cross section. It is assumed that the particles pass freely through the pores of large diameter and are stuck at the inlet of pores that are smaller than the particle size. It is considered that one particle can clog only one small pore and vice versa. The particles stuck in the pores remain motionless and form a deposit. The concentrations of suspended and retained particles satisfy a quasilinear hyperbolic system of partial differential equations of the first order, obtained as a result of macro-averaging of micro-stochastic diffusion equations. Initially the porous media contains no particles and both concentrations are equal to zero; the suspension supplied to the porous media inlet has a constant concentration of suspended particles. The flow of particles moves in the porous media with a constant speed, before the wave front the concentrations of suspended and retained particles are zero. Assuming that the filtration coefficient is small we construct an asymptotic solution of the filtration problem over the concentration front. The terms of the asymptotic expansions satisfy linear partial differential equations of the first order and are determined successively in an explicit form. It is shown that in the simplest case the asymptotics found matches the known asymptotic expansion of the solution near the concentration front.

DOI: 10.22227/1997-0935.2015.1.54-62

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