PNNL

Abstract

We compare two methods for determining the upscaled water characteristics and saturation-dependent anisotropy in the unsaturated hydraulic conductivity. In both approaches an effective medium approximation is used to reduce a porous medium of M textures to an equivalent homogenous medium. The first approach is based on in which the moisture-based Richards’ flow equation is treated as a nonlinear Fokker-Plank equation. Model parameters are derived from the spatial moments of an infiltrating water plume in a manner similar to that used for the convective dispersion equation. The gravity term, dKz(?)/d(?), which is analogous to the vertical convective velocity, is inferred from the temporal evolution of the vertical location of the plume centroid and allows calculation of the upscaled Kz(?). As with the dispersion tensor, the rate of change of the second spatial moment in 3D space is related to the water diffusivity tensor D(?) from which the upscale K(?) is calculated. In the second approach, parameter scaling is used first to reduce the number of parameters to be estimated by a factor M. Upscaled parameters are then optimized by inverse modeling of a field-scale injection test to produce K(?) and a pore connectivity tensor, L. Parameters for individual textures are finally inferred from the optimized parameters by inverse scaling using scale factors determined a priori. Parameter scaling reduced the inversion time by a factor of M2. Both methods produced upscaled K(?) that show saturation dependent anisotropy. Flow predictions with the STOMP simulator, parameterized with the upscaled parameters were compared with field observations. Predictions based on the first method were only able to capture the mean plume behavior. The second method reduced the mean squared residual by nearly 90% compared to local-scale and upscaled parameters from the forts method. The Pacific Northwest National Laboratory is operated for the U.S. Department of Energy by Battelle under Contract DE-AC05-76RL01830.