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


Corresponding author: A. Fiori, Dipartimento di Scienza dell'Ingegneria Civile, Faculty of Engineering, Università di Roma Tre, via Volterra 62, I-00146 Rome, Italy. (aldo@uniroma3.it)


[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 inline image of Y = ln K) and of finite integral scale IY. 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 IY. The dependence of Kef/KG upon inline image 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.