Inverse Problem For A Linear Filtration Function

Abstract

The article is devoted to an important task of underground hydro-mechanics-filtration of suspension in a porous medium. One-dimensional long-term deep filtration of a monodisperse suspension in a homogeneous porous medium is considered. For a one-dimensional macroscopic model with a linear filtration function, an asymptotic solution is constructed near the concentration front of suspended and retained particles. On the basis of explicit asymptotic formulas, the inverse filtration problem is studied : finding the filtration function for a given concentration of suspended particles at the outlet of a porous medium. It is revealed that the least squares method is an effective way to determine the model parameters. It is shown that the calculated parameters are close to the coefficients of the model, and the asymptotics well approximates the numerical solution. The proposed numerical - asymptotic method makes it possible to calculate the linear filtration function using laboratory experiments and adjust the model to specific field conditions. It is concluded that the next stage in solving the inverse filtration problem is to determine unknown parameters of a nonlinear filtration function that depends on three or more constants. To do this, it is needed to modify the methods presented in this paper.