Abstract
A mathematical model, methods and algorithms for the numerical solution of problems of joint gas-water filtration in porous media are considered. The mathematical model of the process of non-stationary joint gas-water filtration in a porous medium is described by a system of nonlinear differential equations of parabolic type. In the numerical solution of the boundary value problem of gas displacement by water in a porous medium, the differential sweeping method is used for systems of differential-difference equations. The system of differential-difference equations with respect to the gas pressure function is nonlinear, therefore, an iterative method is used for it, based on the method of quasilinearization of nonlinear terms. Computational algorithms and software have been developed for conducting computational experiments to study unsteady processes of gas filtration in porous media. The results of the developed software, as well as the results of computational experiments in a graphical form in visual form are given.
Highlights
The development of highly viscous gas fields always raises the problem of lowering the recovery gas and lowering the reservoir pressure
The mathematical model of the process of non-stationary joint gas-water filtration in a porous medium is described by a system of nonlinear differential equations of parabolic type
In the numerical solution of the boundary value problem of gas displacement by water in a porous medium, the differential sweeping method is used for systems of differential-difference equations
Summary
The development of highly viscous gas fields always raises the problem of lowering the recovery gas and lowering the reservoir pressure. The paper presents a numerical models, computational algorithms and software for the investigation of gas filtration in porous media to identify key indicators of gas fields [14]. The software is based on the finitevolume approach to approximation of the partial differential equations describing fluid motion and accompanying physical processes It provides explicit and implicit methods for time integration of these equations. A lot of work is being done in this direction to design the processes of exploitation of oil and gas fields, to develop mathematical models of nonstationary processes of filtering heterogeneous liquids and algorithms for studying non-linear gas and hydrodynamic processes, to evaluate key indicators using modern computer technologies, as well as to create automated software. To determine indicators of gas field development, taking into account heterogeneity of the formation, arbitrary location of multi-debit wells, uneven progress of the gas-water interface, etc. integration of differential equations of transient gas and water filtration is necessary under the corresponding initial, internal, and boundary conditions
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