Equivalent hydraulic conductivity of three-dimensional heterogeneous porous media: An upscaling study based on an experimental stratigraphy

A critical issue facing large scale numerical simulation models is the estimation of representative hydraulic conductivity to account for the unresolved sub-grid-scale heterogeneity. In this study, two experiment-based hydraulic conductivity models offer a test case to evaluate this parameter. Each model contains a different heterogeneity pattern with connectivity characteristics that cannot be captured by univariate and bivariate statistics. A three-dimensional numerical upscaling method was developed to compute an equivalent conductivity full tensor for each model. The equivalent conductivities were compared to direct averages of local conductivities and to an effective conductivity predicted by several analytical methods. For each model, ln K variances up to 16 were evaluated. The impact of variance on both upscaled conductivity and three fluid flow connectivity factors was assessed. Results suggest: (1) the upscaling method gave reliable results comparable to an established method which only gives the diagonal components, (2) for both aquifer models, when ln K variances are low (less than 1.0), all analytical methods evaluated are nearly equally accurate; however, when variance becomes higher, the analytical methods of were found to provide robust estimates of equivalent conductivities, despite possible violation of the multiGaussian assumption, (3) fluid flow characteristics in each model were significantly impacted by increasing variance, which can result in flow channeling in the lateral direction and increasing global anisotropy ratios of the equivalent conductivity, and (4) geometric connectivity, as analyzed by a percolation cluster analysis, indicates the importance of such features in focusing flow, in addition to the effects of high variance.