Capillary Limit Effective Two-Phase Properties for 3D Media

Abstract

Abstract The paper describes an approximate method to compute effective relative permeabilities and capillary pressure for 3D heterogeneous porous media. The method is based on the self-consistent approximation, and works in the capillary (quasi-static, low velocity) limit. The method needs as input data for the individual rock types making up the heterogeneous medium, their relative occurrence, and information related to the ratio between vertical and horizontal length scales of the heterogeneities. No actual realization of the heterogeneous medium is needed. The method is computationally very efficient. Example effective properties are given, demonstrating capillary trapping, and the tensorial nature of effective relative permeabilities. The accuracy of the self-consistent approximation is known to be quite satisfactory for most heterogeneity types. We have also studied the applicability of the capillary limit, using numerical simulation. At typical reservoir rates, the capillary limit appears to be valid only for heterogeneities at the sub-meter scale.