Upscaling permeability and characterizing flow channeling in complex media

Abstract : In 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.