Global Asymptotics of the Filtration Problem in a Porous Medium

Abstract

Filtration of the suspension in a porous medium is important when strengthening the soil and creating watertight partitions for the constructi on of tunnels and underground structures. A model of deep bed filtration with variable porosity and fractional flow, and a size-exclusion mechanism of particle retention are considered. A global asymptotic solution is constructed in the entire domain in which the filtering process takes place. The obtained asymptotics is close to the numerical solution.

Numerical methods for solving improper problems of filtration theory

“…Therefore, we restrict ourselves to deriving formulas for calculating the functional derivatives from dJ 2 according to required parameters. In obtaining expressions for the functional derivatives, use the technique given in [18][19][20][21][22][23][24].…”

“…Because of conditions (21) and (23), the first term in (28) is equal to zero. Now we transform the fourth term of the right-hand side of (21):…”

“…Due to (21) and (23) the first term on the right-hand side of (29) is zero. Thus, taking into account the transformations carried out, expression (22) is transformed to the following form:…”