In this work, computer simulation of filtration processes based on the laws of hydrodynamics is considered. The adequacy of the developed models was verified by conducting a series of computational experiments. Created mathematical and software serves the purpose of research, forecasting and decision-making in the development and design of oil and gas fields.

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.

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The article presents a three-dimensional mathematical model of the gas filtration process in porous media and a numerical algorithm for solving the initial-boundary value problem. The developed model is described using the nonlinear differential equation in partial derivatives with the appropriate initial and boundary conditions. The proposed mathematical apparatus makes it possible to carry out hydrodynamic calculations taking into account changes in the main factors affecting the process under consideration: permeability, porosity, and thickness of layers, gas recovery coefficient, viscosity, etc. Computer implementation of the model provides an opportunity to solve practical problems of analysis and forecasting of the gas production process under various conditions of impact on the productive reservoir, as well as making decisions on the development of existing and design of new gas fields.

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