Numerical modeling of the performance of a well with an arbitrary piecewise-smooth external boundary in an anisotropic heterogeneous reservoir

The extraction of oil and gas from productive reservoirs complex geological structures is constantly increasing. Thus, it obvious that reliable mathematical models able to manage such porous media are particular interest. In this paper, a model filtration flow well located in an anisotropic heterogeneous soil formation, with piecewise-smooth external contour, numerically studied. permeability soil, as medium, characterized by second-rank tensor. Soil heterogeneity modeled power function one the coordinates. We consider case positive exponent. solution stated boundary problem operation reservoir causes significant difficulties associated complicated form basic equation. formulation reduced canonical form, which greatly simplifies solution. To do this, we turn on auxiliary plane using homeomorphic (affine) transformation. system includes Fredholm type integral equation relation. results were obtained discrete singularity method. It was found algorithm convergence slightly better under weak anisotropy. influence anisotropy production rectangular assessed. can change rate compared isotropic soil. Permeability tensor components main diagonal have major impact This method be used solve different problems fluid medium.