Upscaling of Well Singularities in the Flow Transport through Heterogeneous Porous Media

Abstract

We consider the steady flow transport through highly heterogeneous porous media driven by extraction wells. We develop a new upscaling technique lumping the small-scale details of the medium property into a few representative macroscopic parameters on a coarse scale, which preserve the large-scale behavior of the medium and are more appropriate for simulations. The method is based on the recently introduced over-sampling multiscale finite element method and on the introduction of new base functions that locally resolve the well singularities. Numerical experiments are carried out for flow transport in both periodic and randomly generated log-normal permeabilities to demonstrate the efficiency and accuracy of the proposed method.