Modeling of Filtration Processes in Media with Extended Horizontal Drains and Sources

Abstract

Filtration problems with drains and sources are considered in the porous media, where the drains and sources are modeled by delta-functions. Depending on coefficient magnitudes compared to the microscale parameter, three filtering modes are identified and described for the filtration problems. This classifies and simulates possible modes, for example, of modern oil production in problem wells, at least for the model inhomogeneous porous media under consideration. In all these cases, asymptotic approximations of solutions to such problems are obtained. Estimates of the accuracy of such asymptotic approximations are also presented. The estimates are necessary for computer simulation for the filtration problems with suitable accuracy. In turn, this makes it possible, instead of a direct (for example, numerical) solution to a rather complex problem for small microscales, to solve a simpler homogenized problem and receive a description of processes with guaranteed accuracy.