MODEL RADIAL APPROXIMATIONS OF FILTERING BASED ON THE GREEN'S FUNCTIONS

Abstract

The article discusses the problem of approximating solutions of differential equations describing the process of a two-dimensional fluid flow in porous media. The approximation is presented as a combination of radial basis functions based of the Green's function used to solve the Poisson equation with variable coefficients in the case of steady state filtration and parabolic equations in the transient regime. To illustrate the effectiveness of the proposed approximation obtained by the field pressure distribution in the reservoir with a network of injection and production wells. Comparing of approximated pressure and design points to a satisfactory accuracy of the results. It is revealed that the obtained model of approximation of the stationary filtration equation using Green as the basis functions provides the root-mean-square deviation of the approximated pressure from the calculated one at the level of 0.95 - 1.05 %. This type of basis functions is used in constructing approximating models for non-stationary modes of multiphase filtration. The maximum deviations are observed precisely in these cells, where the most abrupt (peak) pressure changes occur. The Neumann's boundary conditions, as follows from the presented results, are satisfied. It should be noted that the Neumann boundary conditions, especially for all boundaries, are the most complicated computational case. To approximate the nonstationary solution of the filtration equation, the Green function is used, which is shown as a product of two parts: one part only depends exponentially on time; the second part depends only on the spatial coordinates. The use of the background intensity of the sources made it possible to build approximators for the possibilities of non-stationary transformation of the intensity of the sources even with a non-zero equilibrium of the intensities.