Determining the Lengmur Coefficient of the Filtration Problem

Abstract

Filtration of suspension in a porous medium is actual in the construction of tunnels and underground structures. A model of deep bed filtration with size-exclusion mechanism of particle capture is considered. The inverse filtration problem - finding the Langmuir coefficient from a given concentration of suspended particles at the porous medium outlet is solved using the asymptotic solution near the concentrations front. The Langmuir coefficient constants are obtained by the least squares method from the condition of best approximation of the asymptotics to exact solution. It is shown that the calculated parameters are close to the coefficients of the model, and the asymptotics well approximates the exact solution

Asymptotics of the Filtration Problem With Almost Constant Coefficients

“…Analytical methods allow to obtain exact and asymptotic solutions and their dependence on parameters. This makes it possible to fine-tune experiments and to solve inverse filtration problems [17][18][19].…”

“…Analytical methods allow to obtain exact and asymptotic solutions and their dependence on parameters. This makes it possible to fine-tune experiments and to solve inverse filtration problems [17][18][19]. The classical filtration model assumes that the properties of the porous medium do not change with the formation of deposit.…”

Analysis of the Filtration Problem by Bitwise Search Method

“…Calculation using an explicit difference scheme allows you to quickly make calculations, but the presence of discontinuities significantly complicates finding a solution. If an exact solution in an implicit closed form or its asymptotics is known, it is used to numerically calculate the solution in an explicit form [21,22]. For the problem of filtering a bidisperse suspension in a porous medium, an exact implicit solution is obtained.…”