Representative hydraulic conductivity of hydrogeologic units: Insights from an experimental stratigraphy

r a 200 .007 .: +1 734 mich.ed Summary A critical issue facing groundwater flow models is the estimation of representative hydraulic conductivity assigned to the model units. In this study, an experimentbased, high-resolution hydraulic conductivity map offers a test case to evaluate this parameter. Various hydrogeological units are distinguished, each is of irregular shape with distinct heterogeneity pattern created by physical sedimentation. Extending a previous study which used numerical upscaling to compute equivalent conductivities for these units (at two upscaling scales) [Zhang, Y., Gable, C.W., Person, M., 2006. Equivalent hydraulic conductivity of an experimental stratigraphy – implications for basin-scale flow simulations. Water Resources Research 42, W05404. doi:10.1029/2005WR004720], this study compares them with local statistics and effective conductivities predicted by a stochastic theory. Results suggest that for a system with moderate lnK variance (4.07) and low topographic slope ( 1 ), the arithmetic mean (KA) provides a good estimate for the maximum principal component (Kmax) of the equivalent conductivity. The minimum principal component (Kmin) lies between the harmonic and geometric means: its closeness to the geometric mean is affected by heterogeneity pattern and upscaling scale. Using Kmax (alternatively, the arithmetic mean), geometric mean, and ln(K) variance, the stochastic theory predicts a Kmin that is consistent with the up-scaled value. Similarly, knowing Kmin, Kmax predicted by theory is also consistent with the up-scaled value. For most deposits (some with variance greater than 1), a low-variance version of the theory is more accurate than a high-variance version. However, the increase of topographic slope (to 4 ) and total lnK variance (to 16) result in increased deviation of Kmax from KA. High variance also results in significantly larger anisotropy ratio, possibly due to the dominance of