Effective Relative Permeabilities and Capillary Pressure for 1D Heterogeneous Media

Abstract

The paper gives an analytical construction of effective two-phase parameters for 1D heterogeneous porous media, and studies their properties. We base the computation of effective parameters on analytical solutions for steady-state saturation distributions. Special care has to be taken with respect to saturation and pressure discontinuities at the intersection between different rocks. The ensuing effective relative permeabilities and capillary pressure will be functions of rate, flow direction, fluid viscosities, and spatial scale of the heterogeneities. The applicability of the effective parameters in dynamic displacement situations is demonstrated, by comparing fine-gridded simulations in heterogeneous media with simulations in their homogeneous (effective) counterparts. Performance is quite satisfactory, even with strong fronts present. Also, we report experiments studying the applicability of capillary limit parameters outside the strict limit.