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

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Abstract

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 (K eff) distributions and their dependence on the coarsening scale. First, we focus on lognormal stationary isotropic media. Our results suggest that K eff is lognormally distributed independently on the coarsening scale. The scale dependence of the mean and variance of K eff 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 K eff distributions on the coarsening scale and also on the high-K facies volume fraction p. When p is near the percolation threshold p c, the decrease of the normalized variance with the coarsening scale is remarkably (102 times) slower compared to the situation in which p far from p c, 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 p c pose for upscaling procedures. Also we point out in terms of K eff statistics the relative influence of the coarsening scale and of the high-K facies connectivity.

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  1. A. Boschan

    Present address: Grupo de Medios Porosos, CONICET, CABA, Paseo Colón 850, Buenos Aires, Argentina

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  1. IFP Energies Nouvelles, Rueil Malmaison, France

    A. Boschan & B. Nœtinger

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Boschan, A., Nœtinger, B. Scale Dependence of Effective Hydraulic Conductivity Distributions in 3D Heterogeneous Media: A Numerical Study. Transp Porous Med 94, 101–121 (2012). https://doi.org/10.1007/s11242-012-9991-2

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