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Use of power-averaging for quantifying the influence of structure organization on permeability upscaling in on-lattice networks under mean parallel flow
Abstract : We 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).
Cited literature [45 references]
https://hal.inria.fr/inria-00537053
Contributor : Géraldine Pichot <>
Submitted on : Thursday, February 4, 2016 - 3:06:05 PM
Last modification on : Thursday, January 14, 2021 - 11:45:53 AM
Long-term archiving on: : Saturday, November 12, 2016 - 9:11:56 AM
Contributor : Géraldine Pichot <>
Submitted on : Thursday, February 4, 2016 - 3:06:05 PM
Last modification on : Thursday, January 14, 2021 - 11:45:53 AM
Long-term archiving on: : Saturday, November 12, 2016 - 9:11:56 AM
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