Effective Hydraulic Conductivity of Three-Dimensional Heterogeneous Formations of Lognormal Permeability Distribution: The Impact of Connectivity

Uniform mean flow takes place in a 3-D heterogeneous formation of normal hydraulic logconductivity Y=lnK. The aim of the study is to derive the dependence of the horizontal Kefhand vertical Kefveffective conductivities on the structural parameters of hydraulic conductivity and investigate the impact of departure from multi-Gaussianity on Kef, by numerical simulations of flow in formations that share the same pdf and covariance of Y but differ in the connectivity of classes of Y. The main result is that for the extreme models of connected and disconnected high Y zones the ratio between the effective conductivities in isotropic media is much smaller than in 2-D. The dependence of Kefh and Kefvupon the logconductivity variance and the anisotropy ratio is compared with existing approximations (first-order, Landau-Matheron conjecture, self-consistent approximation). Besides the theoretical interest, the results offer a basis for empirical relationships to be used in applications.