An Approximate Analytical Solution of the Problem of Fluid Filtration in the Multilayer Porous Medium

Abstract

This paper deals with a mathematical problem statement of unsteady fluid flow in heterogeneous porous media with various hydrogeological characteristics. In order to solve the problem the authors developed an approximate analytical method. The method allows multidimensional differential equation in partial derivatives describing the process of fluid filtration in layered porous media to become one-dimensional differential equation. There was obtained a calculation formula for determining the process of mass transfer between the layers, depending on the operating modes of production wells and hydrogeological parameters of filtration layers. The model and the algorithm can be used as a mathematical support for the processes of development of oil and gas fields.

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

“…Based on the above, to integrate problem ( 7)-( 10), we introduce a uniform mesh in x, y, z and t [9][10][11][12][13][14][15]:…”

“…Replacing the differential operators in equation (10*) with finite-difference operators and using the scheme of longitudinal-transverse direction along Ox, we obtain [9][10][11][12][13][14][15]:…”