Large-Scale Properties for Flow through a Stratified Medium: A Discussion of Various Approaches

The determination of effective properties or pseudo-functions for two-phase flow through heterogeneous porous media is a problem of central importance in petroleum engineering (reservoir simulation). Our purpose was to compare published theories by performing test case studies. The test case corresponded to the waterflooding of a two-strata heterogeneous medium. Generalized Darcy’s equations were solved by using a black-oil reservoir simulator. Several simulations were performed by varying the filtration velocity and the relative importance of gravity effects versus capillary and viscous effects. Based on an extensive literature survey, two fundamental methods were essentially tested: the large-scale averaging method and an application of the fine-grid to coarse-grid method.