Non-Gaussian effects on hydraulic conductivity upscaling in unsaturated porous media via direct averaging (2019)
Hydraulic conductivity is a key parameter governing groundwater flow processes. In this work, hydraulic conductivity was upscaled with the objective of assessing the optimal value of the p-power parameter (of the power averaging upscaling approach) that minimizes the discrepancy between the capillary pressure calculated with fine hydraulic conductivity fields, and the capillary pressure computed with upscaled fields in a two-dimensional unsaturated infiltration problem. The analyses were framed in a probabilistic context, where hydraulic conductivity is conceptualized as a random process in space. Values of p in the interval [-1,1] to scale the hydraulic conductivity under four different infiltration rates were tested. Gaussian and non-Gaussian random hydraulic conductivity fields were analyzed. An optimum p between geometric and harmonic means was found for all the infiltration rates. As a result, the optimum p-power can diminish the capillary pressure error almost to the half, depending on the infiltration rate of the problem and the employed fields.