Effective properties for flow in heterogeneous porous media

Modeling of groundwater flow and chemical transport calls for a good characterization of heterogeneity of soil properties. The effects of variabilities of soil properties at local scale on the mean behavior of heterogeneous flows were investigated via Monte Carlo method. Assuming log-normal distribution of conductivity and capillary pressure head being a stochastic process, the mean behavior model defined by effective properties was derived to predict the mean behavior of heterogeneous flows. Effective parameters were evaluated numerically and were parameterized in terms of statistics of randomly distributed soil properties and flow characteristics. Monte Carlo simulations were performed to reveal the mean behaviors of steady unsaturated gravity flows, transient areal source infiltration and transient point source infiltration in heterogeneous porous media. The most important findings include (a) the effective conductivity is between the geometric mean and the arithmetic mean, (b) the effective conductivity is time dependent. The derivation of a mean behavior model and the capability of parametrizing the effective properties make it possible to use current deterministic models to predict the mean behavior with minimum changes in the constitutive relations, specifically adding the dependence on the flow characteristic to the K-S-P relations. The mean model derived in this study was applied to a field site, good agreement was found between the model prediction and field data.