ABSTRACT: Flow in fractured porous media is investigated by a direct, exact and complete numerical solution of the flow equations for arbitrary distributions of permeabilities in the porous matrix and in the fracture network. For single phase flow, the macroscopic permeability of the network has been systematically computed; the main parameters are the fracture density, the ratio between the characteristic fracture and porous medium permeabilifies. Some results are presented and discussed; they show the importance of the percolafion threshold of the fracture network and possibly of the porous matrix. The same work is underway for twophase flow. The unsteady non-linear equations are solved in the same general setting. The method of solution is presented, together with illustrative simulation results.
INTRODUCTION Consider a set of permeable fractures embodied in a permeable porous solid matrix. When a fluid is flowing through such a medium, the fractures and the porous matrix interact. Historically, this complex situation was first addressed by Barenblatt & Zheltoy 0960) and Barenblatt et al. 0960); though these papers motivated many further works, progress in this area has been slow and so far no complete solution of this problem for any fracture network and for any permeability distribution in the porous matrix has been described to the best of our knowledge in the literature.
Warren & Root (1963) modeled a fractured porous rock as an idealized system made up of identical rectangular porous parallelepipeds separated by an orthogonal network of fractures. Flow is assumed to take place in the fracture network which is fed by the porous blocks. This sort of model was further developed by Odeh (1965). All these equations have been thoroughly studied in the literature with many different boundary conditions (van Golf-Racht 1982, Chen 1989, Chen 1990 and Pinder 1993). Other possible approaches have also been presented by Adler & Thovert 0999). The most important is probably the multiscale analysis of flow through fractured porous media, initiated by Aifantis (1980) and extended by Arbogast (1990), Levy 0988, 1990) and Panfilov (1990,1994).
The purpose of this paper is to briefly present the methodology and the first results obtained in the determination of the single-phase permeability of fractured porous media. It is a significant extension of our previous paper on the permeability of fractured media Koudina et al. (1998). In addition, a further extension to two-phase flow is presented, with a set of illustrative results.