Analysis of a Multiple-porosity Model for Single-phase Flow through Naturally Fractured Porous Media

A model for single-phase flow in porous media that are hierarchically fissured in regular patterns was derived by a recursive asymptotic expansion technique in [16] and part of [24]. This work rigorously justifies that model. Through recursive homogenization, we extend the doubleporosity model in [5], which has one fracture system and a matrix (rock) block system, to a triple-porosity model that has two levels of fracture systems and a matrix block system. See [9, 22] for an introduction to homogenization theory. Then, a multiple-porosity model with N levels of fracture systems and a matrix block system is derived, resulting in a general (N + 1)-scale model. A dual-porosity concept was first introduced in [8, 25] using a specific transmissibility function (see [7]) for the interaction of the matrixfracture flow. For petroleum-reservoir engineering problems, a new treatment of the coupling of the flow through the fracture system with that in the matrix system was introduced over the past two decades in [2, 3, 4, 5, 6, 13, 14, 17, 18, 19]. The models discussed in this work are based on these ideas. Our focus on the nested levels of fracture systems is appropriate for further studies on high-level nuclear waste transport