This paper is devoted to the development and investigation of methods of mathematical and computer simulation of the process of fluid filtration in a porous medium. The methods of numerical solution of the problems of the filtration theory of build-up of conditions in the catchment and discharge areas boundaries, identification of filtration-capacitive parameters of the effective formation and determination of free (unknown) boundaries and creation of computational algorithms for analysis and forecast of technological indicators of oil and gas fields are considered. Methods and models of continuum mechanics, filtration theories, and methods for solving ill-defined problems, numerical modeling and computer programming were used. ApproxiNumericalmate methods for solving direct and inverse problems of filtration theory, mathematical models for single-phase isothermal filtration of a gas mixture in a horizontal formation at small concentration gradients of components, studying the properties of self-similar solutions, as well as numerical solving the problem of identifying the capacitive parameters of the water-bearing stratum.

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