Effective permeability of porous media containing branching channel networks.

We study the effective permeability of two-dimensional binary systems characterized by a network of branching channels embedded in a uniform matrix material. Channels are assigned a higher permeability than the surrounding matrix and, therefore, serve as preferential pathways for fluid migration. The channel networks are constructed using a nonlooping invasion percolation model. We perform extensive numerical flow simulations to determine the effective permeability tensor of channel-matrix systems with broadly varying network properties. These computed effective permeabilities are then used to systematically investigate the factors that control the permeability upscaling process. The upscaling framework adopted for this study is based on spatial power averaging. We determine the scaling behavior of the averaging exponent omega by analyzing its dependence on three characteristic properties of the channel-matrix system: (i) the channel-matrix permeability contrast; (ii) the fractal dimension of the channel network, df; and (iii) the average tortuosity of spanning paths on the network backbone, tau. The behavior of and the corresponding component of effective permeability in each principal direction (parallel and perpendicular to the network-spanning direction) are compared. The permeability anisotropy ratio is shown to be a clear function of key system properties.