Quasi-steady two-equation models for diffusive transport in fractured porous media: large-scale properties for densely fractured systems

When dealing with the macroscopic behavior of a fractured porous medium, one is faced with the problem of computing the large-scale parameters from the fracture network properties. In particular, when the retained model is the quasi-steady two-equation model, three effective coefficients have to be estimated. This upscaling problem has been reviewed using a volume averaging method by Quintard and Whitaker. As a result, a closed form of the macroscopic model was obtained with associate closure problems that can be used for the determination of the required parameters. In this paper, we use the corresponding problems to study and discuss the behavior of the effective properties of 2D densely fractured systems. First, the emphasis is put on the large-scale fracture permeability tensor, which is related to the degree of interconnection of the fractures combined to the effect of matrix diffusion. Secondly, the exchange coefficient is considered, in particular, its dependence on the matrix blocks geometry. Finally, we compare our approach with numerous techniques currently proposed in the literature.