Scale Dependence of Effective Hydraulic Conductivity Distributions in 3D Heterogeneous Media: A Numerical Study

Upscaling procedures and determination of effective properties are of major importance for the description of flow in heterogeneous porous media. In this context, we study the statistical properties of effective hydraulic conductivity (Keff) distributions and their dependence on the coarsening scale. First, we focus on lognormal stationary isotropic media. Our results suggest that Keff is lognormally distributed independently on the coarsening scale. The scale dependence of the mean and variance of Keff are in agreement with recent analytical derivations obtained using coarse graining filtering techniques. In the second part, we focus on binary media, analysing the dependence of Keff distributions on the coarsening scale and also on the high-K facies volume fraction p. When p is near the percolation threshold pc, the decrease of the normalized variance with the coarsening scale is remarkably (102 times) slower compared to the situation in which p far from pc, but also compared to the cases of lognormal media studied before. This result permits to assess the degree of difficulty that systems with p near pc pose for upscaling procedures. Also we point out in terms of Keff statistics the relative influence of the coarsening scale and of the high-K facies connectivity.