Inverse Filtration Problem of a Bidisperse Suspension

P. 585–593.

Liudmila I. Kuzmina, Osipov Y.

Filtration problems of suspensions and colloids in porous media are considered when designing tunnels and underground structures. To strengthen weak soil, a liquid solution is injected into the rock, the particles of which are filtered in the pores and distributed far from the well. A deep bed filtration model of 2-particle suspension in a porous material is considered. The purpose of the work is to determine the model parameters from the measured outlet concentration of suspended particles. Using an explicit solution to the direct filtration problem on the concentration front, the inverse problem is reduced to a system of nonlinear algebraic equations, which is a special case of the moment problem. The system is solved by passing to a canonical basis in the space of symmetric polynomials. Conditions for the existence of a solution are obtained. An explicit solution is constructed. The inverse filtration problem of a suspension with particles of two types is solved, determining the initial partial concentrations and filtration coefficients.

Keywords: highly porous mediums, Deep bed filtration, inverse problem, analytical solution

In book

Proceedings of the 10th International Conference on Civil Engineering

Singapore: Springer, 2024.