Derivation of a multiple‐porosity model of single‐phase flow through a fractured porous medium via recursive homogenization

Abstract

A derivation of a multiple‐porosity model for the flow of a single‐phase, slightly compressible fluid in a multiscale, naturally‐fractured reservoir is presented using recursive homogenization theory. The model was rigorously derived by the authors under different assumptions on the flow in relation to the geometry of the medium. In the earlier work, a recursive assumption on the flow at each level was made in order to treat certain internal boundary conditions. In the present work, the model is derived using reasonable assumptions for the geometry of the medium as well as the physics of the flow.