Numerical Study of Suspension Filtration Model in Porous Medium with Modified Deposition Kinetics

Abstract

Filtration is one of the most used technologies in chemical engineering. Development of computer technology and computational mathematics made it possible to explore such processes by mathematical modeling and computational methods. The article deals with the study of suspension filtration in a porous medium with modified deposition kinetics. It is suggested that deposition is formed in two types, reversible and irreversible. The model of suspension filtration in porous media consists of the mass balance equation and kinetic equations for each type of deposition. The model includes dynamic factors and multi-stage deposition kinetics. By using the symmetricity of porous media, the higher dimensional cases are reduced to the one-dimensional case. To solve the problem, a stable, effective and simple numerical algorithm is proposed based on the finite difference method. Sufficient conditions for stability of schemes are found. Based on numerical results, influences of dynamic factors on solid particle transport and deposition characteristics are analyzed. It is shown that the dynamic factors mainly affect the profiles of changes in the concentration of deposition of the active zone.

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].…”

“…Due to condition (24), the first term in (27) is equal to zero. We transform the third term on the right-hand side of (22):…”