Numerical Study of the Process of Unsteady Filtration of a Fluid in Interacting Porous Pressure Layers

Abstract

A review of the fundamental studies conducted in 2010 - 2020 is given in the article to develop a mathematical model related to the fluid and gas filtration processes in porous media. To conduct a comprehensive study of the process of unsteady filtration of fluid in multi-layer porous pressure media and to make a management decision, a mathematical model described by a system of partial differential equations with corresponding initial and boundary conditions and a conservative numerical algorithm were developed. On the basis of the developed software of the problem posed, computational experiments were conducted on a computer; the calculation results were presented in the form of tables and graphical objects. The schemes of location and capacity of vertical drainage wells to protect irrigated and non-irrigated areas from flooding were proposed on the basis of the developed software. Using the proposed mathematical tool, it is possible to obtain the prognostic groundwater levels for any area for the required period of time, considering a number of factors, for example, the formation heterogeneity in plan, the gradient of the permeability barrier, and other hydrogeological, hydro-technical, and natural conditions; to calculate the capacity and optimal drilling pattern of vertical drainage wells to protect the territory and to develop oil and gas fields.