A Numerical Method for Solving the Problem of Gas Filtration in an Interconnected Three Layer Porous Medium Based on an Opaque Finite Difference Scheme

In this article, a mathematical model of the parabolic type has been developed, which makes it possible to investigate and predict complex processes occurring in interconnected inhomogeneous porous media of gas fields with sluggish conductive layers between each of the three layers. The mathematical model is made into a dimensionless boundary value problem, and a cross-sectional opaque scheme is used. The quasilinear method was applied to the nonlinear terms of the system of equations, and the system of equations was solved by the finite difference method. Based on the mathematical model, a numerical algorithm was developed, and computer programs were created to calculate the main indicators of the development of gas fields. Calculation results are presented numerically and graphically. These results show the pressure distribution in the formations and the pressure drop dynamics in the wells at different values of the weak permeability coefficients. Based on the obtained results, it is possible to perform calculations on various parameters to increase the efficiency in the development of gas fields. Also, it is possible to analyze and predict oil and gas fields through software created on the basis of numerous models and algorithms developed in the article.