# DEVELOPMENT OF THE MATHEMATICAL MODEL OF A «RESERVOIR-GAS WELL» SYSTEM

Presents mathematical models of steady and unsteady isothermal gas filtration. For the case of pressure distribution in the bottomhole formation zone around a single well, a numerical model of gas filtration is constructed that approximates the boundary value problem by an implicit four-point scheme using a propulsion method, under the assumption of consistency of gas density and viscosity, permeability and elastic capacity of the rock. The presented model allows to calculate and predict the change in pressure distribution in the area around the well. For the numerical model obtained, an algorithm for the computer model has been developed. Using a computer model, the pressure distribution for the well, which drains the initially undisturbed formation within 30 days, is calculated. Graphs of the distribution of the pressure field, obtained when using a computer model, are given. In the simulation, boundary conditions of the first and second kind are adopted for the feed and bottom hole contours, respectively. The results obtained can be applied to the development of control systems for gas production facilities aimed at rational use of the reservoir energy and increasing the gas recovery factor.

**Authors:** S. E. Abramkin, S. E. Dushin, D. D. Sirota

**Direction:** Informatics, Computer Technologies And Control

**Keywords:** Model of unsteady gas filtration, numerical model of gas filtration, computer model of gas filtration, distribution of pressure in a homogeneous gas reservoir

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