[1] Flow in fractured porous media was first investigated by and by means of the double-porosity model. A direct, exact, and complete numerical solution of the flow in such media is given in this paper for arbitrary distributions of permeabilities in the porous matrix and in the fracture network. The fracture network and the porous matrix are automatically meshed; the flow equations are discretized by means of the finite volume method. This code has been so far applied to incompressible fluids and to statistically homogeneous media which are schematized as spatially periodic media. Some results pertaining to random networks of polygonal fractures are presented and discussed; they show the importance of the percolation threshold of the fracture network and possibly of the porous matrix. Moreover, the influence of the fracture shape can be taken into account by means of the excluded volume.

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.

Two-phase flow in fractured porous media is investigated by means of a direct and complete numerical solution of the generalized Darcy equations in a three-dimensional discrete fracture description. The numerical model applies to arbitrary fracture network geometry, and to arbitrary distributions of permeabilities in the porous matrix and in the fractures. It is used here in order to obtain the steady-state macroscopic relative permeabilities of random fractured media. Results are presented as functions of the mean saturation and are discussed in comparison with simple models.

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