Effective properties of two‐phase flow in heterogeneous aquifers

Abstract

The spectral perturbation approach is employed to predict the field‐scale relative permeabilities and the variance of capillary pressure and saturation under steady two‐phase flow conditions. The theoretical analysis treats stationary three‐dimensional variations in pressure and flow produced as a result of spatial variations of permeability and two‐phase flow characteristics. The analysis is developed in a general form that is applied to different commonly used two‐phase flow characterizations, and results are illustrated for two‐phase flow characteristics corresponding to those observed at the Borden site in Canada. For gravity‐driven flow in horizontally layered aquifers, both nonwetting phase flow (dense nonaqueous phase liquid (DNAPL) flow) and wetting phase flow (water, unsaturated flow) show effective vertical relative permeabilities that are substantially decreased in comparison with those corresponding to a homogeneous system. The resulting saturation‐dependent anisotropy of effective permeability is substantially larger for DNAPL flow than for the case of unsaturated flow. The Leverett scaling characterization frequently used in Monte Carlo simulations is shown to underestimate system anisotropy owing to omission of variability of the parameter governing the slope in the capillary pressure–saturation function. Application of the Brooks‐Corey characterization of the relative permeability resulted in significantly greater anisotropy than with the van Genuchten characterization. In contrast to the strong influence of heterogeneity predicted in the case of effective permeabilities, the effective capillary pressure characteristic (mean capillary pressure versus mean saturation curve) is only weakly influenced by heterogeneity.