Mathematical modeling of two-phase compressible fluid filtration based on modified adaptive method of minimum amendments

Abstract

The work objective is to build and investigate the modified adaptive method of minimum amendments (MAMMA) which is destined for the numerical simulation of the two-phase compressible fluid filtration in porous media. This approach allows overcoming the known use limitations of other methods of the finite-difference equations solution, such as: crucial differential pressures acting on the oil-and-water bearing formation; and the compressibility of the medium at the considerable gas content in the oil phase. An approximation method - an explicit one for defining the function of water saturation, and an implicit one for the pressure function computation - is selected as the research basis. When setting the initial boundary value problem and its sampling, the process of the two-phase compressible fluid filtration in the space-dimensional domain with the lateral area bounded below by the subface of stratum, and above - by the bed top, is considered. A two-layer iterative method of the variational type - a modified method of minimal amendments adapted for solving finite-difference equations of the two-phase compressible fluid with a non-selfadjoint operator under the most general assumptions on the properties of the grid-problem operator is built. It is shown that a MAMMA has the asymptotic convergence rate characteristic of the “classical” alternate triangular method that does not use the Chebyshev acceleration technique and can be applied to the problems with a self-adjoint operator. Numerical experiments have confirmed the high efficiency of MAMMA. It is established that to achieve the specified accuracy, the number of iterations at the MAMMA reduces to 3-20 times as compared to the method of Seidel and the overrelaxation method.