Mathematical modeling of the process of fluid filtration through a multi-layer filtering element - Vecherkovskaya, Anastasia; Popereshnyak, Svitlana (Technology audit and production reserves, 2017)
The paper presents a mathematical model of the fluid filtration process in a porous medium. The mathematical model of fluid filtration in a porous medium is based on the equation of continuity and the Darcy law for a hollow porous cylinder. The porous cylinder consists of three materials having different mechanical and filtration properties, made of polypropylene fibers by extrusion, consisting of seven layers. Filtration is described by different types of research laws that establish the relationship between a velocity vector of the fluid filtration and the field of pressure. There are several ways to describe mathematically the process of filter colmatation. Present work considers a single-component model of the flow of suspension through a porous medium. An analysis of this model revealed that it can be implemented in the presence of empirical coefficients that take into account porosity of the sediment deposited on the walls of a porous space, linear functions that describe adsorption and desorption of precipitation on the pore walls, as well as functional dependences for the permeability of filter and the viscosity of suspension. An efficient technique to calculate complex models is to apply parallel programming methods, which make it possible to split calculations into streams performed on the basis of supercomputers, clusters, and other high-performance computing systems. The proposed method for organizing distributed calculations for a finite-element filter model could be used to construct a hydrodynamic model of the filtration process, as well as its program implementation, which is planned in the future.