Upscaling of Two-Phase Flow Processes in Porous Media

Intrinsic heterogeneities influence the multi-phase flow behavior of a dense non-aqueous phase liquids (DNAPL) infiltrating into a natural soil. Typically, we cannot resolve the scale of these heterogeneities so that upscaling techniques are required. The choice of the appropriate upscaling method depends on the averaging scale, since the relative importance of capillary and gravity forces change with scale. We present an easy and quick upscaling approach for cases in which the flow on the length-scale of heterogeneities is dominated by capillary forces.

The approach is based on a percolation model and a single-phase flow-averaging method. We apply the upscaling approach to experimental data of a DNAPL infiltration into a sandbox with artificial sand lenses. The anisotropy of the structure results in anisotropic flow which is amplified by the nonlinear behavior of multi-phase flow. The residual saturation depends on the direction of flow, and the anisotropy ratio of the effective permeability is a function of the DNAPL saturation. Furthermore, it appears necessary to regard the relative permeability-saturation relationship as a tensor property rather than a scalar. The overall flow behavior simulated by the upscaled model agrees well with simulations accounting for the distinct lenses and the experimental data.