Numerical homogenization of the gas filtration problem

Abstract

The non-stationary gas flow equation in homogeneous and heterogeneous media is considered. Areas of this type are often encountered when considering gas production processes from a gas-bearing reservoir. The heterogeneous structure of the reservoir can strongly affect the extraction processes. For the numerical solution of the problem under consideration, we construct an approximation of the equations on a coarse grid using the numerical averaging method. The method allows us to solve the problem using less computational power and in a shorter time. A numerical comparison of the results of solving the model problem is carried out in a two-dimensional domain for the cases of linear and nonlinear variants of the equations, as well as in a homogeneous and heterogeneous medium. The finite element solution on a fine mesh was taken as a reference solution. The computational realization was performed using the FEniCS library. The construction of the geometric computational domain was performed in the program Gmsh. Paraview and the Matplotlib library in Python were used for data visualization.