Effect of Heterogeneity on Buckley-Leverett Displacement

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Abstract
The Buckley-Leverett (B-L) equation has been routinely used for the description of immiscible displacement in laboratory operations, and for parameter estimation and prediction. The recent resurgence of interest on effects of heterogeneity, however, has led to a serious challenge of the validity of many of the traditional theories. For the case of B-1 displacement, most studies have examined heterogeneity effects originating from viscous fingering phenomena. In this paper we present a numerical investigation of the effects of capillary heterogeneity, induced by a variation of the permeability in the direction of displacement. It is shown that for a medium of rapid enough permeability variation, the associated capillary effect is not negligible, even at the relatively high rates, where the B-1 theory is typically valid. This effect manifests itself as a position-dependent addition to the fractional flow curve, and contrary to ordinary capillary effects, it is not limited to the saturation shock front. We study the resulting equation for a variety of heterogeneity forms, including uncorrelated and correlated variations. It is found that, although it has a negligible effect on the recovery variables, heterogeneity affects significantly the saturation profiles. The latter closely follow the permeability variation at the points of heterogeneity, and conform to the B-L predictions, otherwise. The saturation response is found to be higher for more unfavorable mobility, oil-wet conditions and for less spatially correlated heterogeneity. The results may be useful in the interpretation of laboratory saturation profiles, in the identification of heterogeneity, and in the estimation of parameters such as relative permeabilities, in heterogeneous systems. Introduction

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