Equivalent Hydraulic Conductivity, Connectivity and Percolation in 2D and 3D Random Binary Media
Résumé
The equivalent hydraulic conductivity () relates the spatial averages of flux and head gradient in a block of heterogeneous media. In this article, we study the influence of connectivity on of media samples composed of a high conductivity () and a low conductivity () facies. The facies is characterized by a proportion , and also by two connectivity parameters: a connectivity structure type (no, low, intermediate, high), and a correlation integral scale .The probability distribution of , and the critical value of at which percolation occurs (), are studied as a function of these connectivity parameters. The distribution of is Gaussian in all cases, so the results are presented in terms of the geometric mean () and the variance ().Both quantities show a data collapse if expressed as a function of (for the variance , notably, even if 2D and 3D data are plotted together). In 3D, when a connectivity structure exists, is always greater than when no structure exists, and increases (while decreases) as increases. The same is observed in 2D, except for the low connectivity structure type (i.e. when the facies is disconnected), that shows an unprecedented behaviour: is greater in the absence of structure, and decreases ( increases) as increases. Our results show that any influence of connectivity on is well accounted for simply by a shift in the percolation threshold , and then, suggest that is controlled mainly by the proximity to percolation.