Mathematical modeling of well operation in the case of two-dimensional filtration in an anisotropic heterogeneous layer

Abstract

A flat (two-dimensional) problem has been posed on the mathematical modeling of well in an anisotropic inhomogeneous reservoir of soil with separate anisotropy and heterogeneity when the power contour is arbitrary. The considered well completely opens the formation with its working part (filter). Such a well is called perfect. The permeability of the soil is characterized by a second-rank tensor whose components are modeled by a power function of the coordinates. With a homeomorphic affine transformation of coordinates, this problem is reduced to a canonical form which greatly simplifies its study. An analytical solution of the problem of well production with an elliptical power contour is obtained in the final form as well as in the case when the power contour is removed to infinity. In the general case, the problem is reduced to a system of integral equations and the integral relation. The results were obtained in the general case using the discrete singularities method. The influence on the flow rate of anisotropy, heterogeneity of the reservoir and the shape of the power contour was studied.