Effective permeability of fractured porous media with power-law distribution of fracture sizes

The permeability of geological formations which contain fractures with a power-law size distribution is addressed numerically by solving the coupled Darcy equations in the fractures and in the surrounding porous medium. Two reduced parameters are introduced which allow for a unified description over a very wide range of the fracture characteristics, including their shape, density, size distribution, and possibly size-dependent permeability. Two general models are proposed for loose and dense fracture networks, and they provide a good representation of the numerical data throughout the investigated parameter range.