Geostatistical Analysis of Water Saturation in Heterogeneous Unsaturated Media under Capillary-Gravity Equilibrium

Abstract

This study investigates the spatial distribution of water content and the upscaling of capillary pressure-saturation curves in heterogeneous porous media under static conditions. It extends the work of (1990) to randomly heterogeneous formations characterized within a geostatistical framework. Lab-scale capillary pressure-saturation curves are normalized using the Leverett “J” function and are represented by a Corey-Brooks power model. These curves, giving saturation as a function of capillary pressure, are parametrized in terms of permeability, porosity and irreducible water saturation. Simulated cross-sectional fields of these three coregionalized variables are generated using geostatistical methods. The corresponding saturation fields are then calculated from the parameter fields and the capillary pressure field, using the capillary pressure-saturation model. Under static conditions, capillary pressures at any elevation above the phreatic surface are uniform and are given by the equilibrating gravity forces. A series of numerical experiments are used to investigate the effect of parameter heterogeneity on the spatial distribution of water saturations. Results show that, in heterogeneous media, uniform capillary pressures give rise to sharp discontinuities in saturation. For each simulated saturation field, megascopic-scale capillary pressure-saturation curves are obtained by averaging saturation over horizontal layers within the field. These upscaled curves are found to reduce to the same non-dimensional form when normalized using a Leverett “J” function approach. This result indicates a promising direction for further research on upscaling of capillary pressure-saturation relationships.