Modelling of steady-state fluid flow in 3D fractured isotropic porous media: application to effective permeability calculation

In this paper, 3D steady-state fluid flow in a porous medium with a large number of intersecting fractures is derived numerically by using collocation method. Fluid flow in the matrix and fractures is described by Darcy's law and Poiseuille's law, respectively. The recent theoretical development presented a general potential solution to model the steady-state flow in fractured porous media under a far-field condition. This solution is a hypersingular integral equation with pressure field in the fracture surfaces as the main unknown. The numerical procedure can resolve the problem for any form of fractures and also takes into account the interactions and the intersection between fractures. Once the pressure field and then the flux field in fractures have been determined, the pressure field in the porous matrix is computed completely. The basic problem of a single fracture is investigated, and a semi-analytical solution is presented. Using the solution obtained for a single fracture, Mori-Tanaka and self-consistent schemes are employed for upscaling the effective permeability of 3D fractured porous media. Copyright (c) 2012 John Wiley & Sons, Ltd.