Effective conductivity of isotropic highly heterogeneous formations: Numerical and theoretical issues. Issue 2 (4th February 2013) - Jankovic, Igor; Fiori, Aldo; Dagan, Gedeon
Key Points: Effective conductivity is studies through accurate 3D numerical simulations Kef is similar to the one predicted by the self‐consistent approximation Kef may depend on the higher order correlations of K Abstract : [1] 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 KG and variance σ Y 2 of Y = ln K ) and of finite integral scale IY . We investigate the effective conductivity K ef of such formation by adopting a structural model of cubical inclusions that tessellate the space. The domain is large compared to IY . The dependence of K ef / KG upon σ Y 2 is determined by numerical simulations that are performed in parallel employing 2.5 × 10 9 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.