Mathematical modeling and numerical algorithm for the gas displacement by water in an inhomogeneous porous medium

Abstract The problems associated with the development of gas fields bounded by aquifer systems are considered in the paper in order to increase gas recovery and determine the key parameters of the reservoir for further development. To conduct a comprehensive study of the process under consideration, a computer model has been developed that is described by a differential equation with variable coefficients under corresponding initial and boundary conditions and moving boundaries. An arbitrarily defined region is converted to a standard one using the dummy region method. Functional dependences of the parameters of porosity and permeability are constructed by the method of local approximation given at some defined points in the reservoir for each nodal point. An algorithm is developed for solving the problem using the methods of longitudinal-transverse scheme and the flow option of the sweep method. The results are shown as isolines. In this paper, an attempt is made to prove that in the practice of fluid production it is advisable to introduce development technology based on inhomogeneous formation parameters. Numerical experiments have shown that using this technology wide opportunities appear for finding highly effective design solutions for fields development.

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