# porous medium

## 3D model and numerical algorithm for gas filtration in porous media

The article presents a three-dimensional mathematical model of the gas filtration process in porous media and a numerical algorithm for solving the initial-boundary value problem.  The developed model is described using the nonlinear differential equation in partial derivatives with the appropriate initial and boundary conditions.  The proposed mathematical apparatus makes it possible to carry out hydrodynamic calculations taking into account changes in the main factors affecting the process under consideration: permeability, porosity, and thickness of layers, gas recovery coefficient, visc

## Investigation of drying the porous wood of a cylindrical shape

In the presented study, the mathematical model for drying the porous timber beam of a circular cross-section under the action of a convective-heat nonstationary flow of the drying agent is constructed.  When solving the problem, a capillary-porous structure of the beam is described in terms of a quasi-homogeneous medium with effective coefficients, which are chosen so that the solution in a homogeneous medium coincides with the solution in the porous medium.  The influence of the porous structure is taken into account by introducing into the Stefan–Maxwell equation the effective binary inte

## Mathematical modeling of fluid flows through the piecewise homogeneous porous medium by R-function method

The stationary fluid flow through a piecewise homogeneous porous medium is considered under the assumption that Darcy's law holds.  The mathematical model of this problem is defined as an elliptic equation for the stream function, supplemented by the second-type boundary conditions at the water boundaries and the first-type boundary conditions at the impervious to liquid boundaries.  The problem statement also includes the conditions of conjugation at the separation line between two soils and the unknown value of fluid discharge, which can be established from the additional integral ratio.

## The gas filtration in complex porous media with stagnant zones

The process of gas filtration in a porous medium depending on its structure is modeled in the paper.  The presence of pores of various sizes leads to the formation of flow and stagnation zones, which affect both the pressure distribution in the medium and the active gas mass.  The obtained results make it possible to determine the proportion of the flow zones volume and the exchange coefficient between the flow and stagnant zones.