Effective conductivity of isotropic highly heterogeneous formations: Numerical and theoretical issues

We consider three-dimensional uniform flow in heterogeneous porous media characterized by a spatially variable hydraulic conductivity K(x) ; the latter is considered as a stationary random function of lognormal distribution (mean ln K_G and variance σ_Y² of Y= ln K) and of finite integral scale I_Y. We investigate the effective conductivity Kef of such formation by adopting a structural model of cubical inclusions that tessellate the space. The domain is large compared to I_Y. The dependence of K_ef/K_G upon σ_Y² is determined by numerical simulations that are performed in parallel employing 2.5 10⁹ cells. This technical note focuses on numerical issues in media with strong heterogeneity: domain discretization and the averaging scheme for the intercell conductivity. The effective conductivity is also derived using the self-consistent approximation.