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 (Formula presented.). The aim of the study is to derive the dependence of the horizontal K_efh and vertical K_efv effective conductivities on the structural parameters of hydraulic conductivity and investigate the impact of departure from multi-Gaussianity on K_ef, 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 (Formula presented.) and K_efv upon 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.