Spatially Variable Relative Permeability in Heterogeneous Multiphase Systems

The rate of DNAPL migration through porous media is dependent, in part, on relative permeability constitutive relationships, which describe the saturation and saturation-history dependence of nonwetting phase permeability at the macroscopic scale. Gerhard and Kueper (2003) demonstrate that accurate prediction of DNAPL migration rates requires detailed knowledge of hysteretic relative permeability functions including their curvature and endpoints. To date, the difficulty of measuring hysteretic relative permeability functions has resulted in limited data and conflicting opinions on their shape, magnitude, and significance. This study established a database of parameters that define hysteretic relative permeability-saturation relationships for a range of porous media. Relative permeability - saturation curves were generated for sands of varying mean particle diameter using a macroscopic-scale flow cell. The relative permeability of HFE-7500 (a low solubility, low volatility, non-reactive DNAPL) was measured in a DNAPL-water system as a function of aqueous saturation and saturation history. Best-fit comprehensive constitutive relationships exhibit trends in the functional parameters that are sensitive to porous media properties. Typical numerical simulations of multiphase flow in heterogeneous porous media assume homogeneity with respect to relative permeability functions. In this study, the significance of the observed variation in the shape and end-point locations of the relative permeability-saturation curves was examined through a series of numerical simulations. Simulations of a fixed volume DNAPL release were conducted using a spatially correlated, random permeability field. Simulations assuming homogeneity of relative permeability were compared to those employing the determined functional dependence of relative permeability on porous media properties. The results of the simulations illustrate the sensitivity of the rate of nonwetting phase migration and the ultimate extent of a DNAPL release to the spatial variability of relative permeability properties.