Use of power-averaging for quantifying the influence of structure organization on permeability upscaling in on-lattice networks under mean parallel flow

International audienceWe numerically assess the relevance of power-averaging as a means for permeability upscaling on a variety of 2D and 3D, dense and sparse on-lattice networks. The power-average exponent \omega determined on a realization basis converges with the system size within the range of scales explored for all cases. Power-averaging is strictly valid only for the 2D dense square case for which \omega is equal to 0 with a numerical precision of 0.01 both for the lognormal and log-uniform permeability distributions consistently with the theoretical proof of Matheron [1967]. For all other cases, the variability of \omega with the local permeability distribution variance \sigma^2 is non negligible but remains small. It is equal to 0.09 for sparse networks and 0.14 for dense networks representing respectively 4.5% and 7% of the full possible range of \omega values. Power-averaging is not strictly valid but gives an estimate of upscaling at a few percents. \omega depends slightly on the local permeability distribution shape beyond its variance but mostly on the morphological network structures. Most of the morphological control on upscaling for on-lattice structures is local and topological and can be explained by the dependence on the average number of neighbour by points (effective coordination number) within the following structure (backbone)

Upscaling permeability and characterizing flow channeling in complex media

International audienceIn a first step, we numerically assess the relevance of power-averaging as a means for permeability upscaling on a variety of 2D and 3D, dense and sparse and on-lattice and off-lattice structures. Power averaging consists in finding the most determinant moment of the permeability distribution for upscaling. The moment order is the power-average exponent . We show that power-averaging is strictly valid only for 2D isotropic systems as proved rigorously by Matheron [1967]. It is however a good approximation at a maximum accuracy of 7% for all other tested systems. In more complex fracture networks, we use power-averaging as a way to better understand the key factors controlling upscaling. We find that the power-average exponent can be linked to a local effective coordination number associated to a global evaluation of the density of the flowing structure. In a second step, we propose two new indicators for channeling based on the Lagrangian correlations of velocity for both porous and fractured media. The first one characterizes the channel typical scale and the second one characterizes the inter-channel distance. We relate the dependence of these indicators on geometrical key properties of the structure. We finally seek for finer understandings on the relations between upscaling and flow channeling

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