Mathematical model and numerical algorithms to analyze gas filtration process in a porous medium

Abstract

Abstract The paper deals with the problem of gas filtration process in a porous medium using a mathematical model of an object; the model is described by a nonlinear partial differential equation and the corresponding boundary and internal conditions. The paper presents the main stages in construction of mathematical model of the process of gas filtration in porous media, taking into account the changes in hydrodynamic parameters of the object of study. To solve the above problem, the following numerical methods have been used: local-one-dimensional schemes and longitudinal-transverse direction schemes. To solve the problem of nonlinear gas filtration in a porous medium, several methods of constructing an iterative process have been checked. To study the responses of the principal parameters of the process, a series of computational experiments on a computer, their analyses and conclusions are given in the paper.