Abstract
Summary Singular value decomposition (SVD) is one of the powerful methods for matrix computing. The SVD method can be used as a method of extracting patterns from a matrix and as a method of compressing large matrices. This approach can be used to solve hydrodynamic problems for increasing oil recovery of (multiphase flow in anisotropic porous media). There is a known problem in determining the permeability of porous medium. Permeability is one of the important characteristics of the oil reservoir, which greatly affects the flooding of the porous medium and the oil recovery coefficient. Known common methods can determine the value of permeability only in individual sections of the porous medium, while the value in the remaining sections remains unknown. When simulating such problems on large sizes of the computational grid, the matrix of permeability values - Kabs will turn out to be large and sparse. In this regard, the task is to analytically analyze the Kabs matrix, namely, to find the singular values of the Kabs matrix to determine the condition number of the linear operator. The value of the condition number affects the existence of a solution to the original system of the equation and to the accuracy of the solution to solve the oil recovery problem. This article discusses the application of the SVD algorithm for calculating the eigenvalues/unit values/vectors of a large sparse matrix in oil extraction problems in anisotropic porous media.