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

Minh-Ngoc Vu (1) , Ahmad Pouya (1) , Darius Seyedi (2)

1 cermes - Géotechnique
2 BRGM - Bureau de Recherches Géologiques et Minières (BRGM)

In this paper, 3D steady-state fluid flow in a porous medium with many intersecting fractures is derived numerically by using collocation method. Fluid flow, in the matrix and fractures, are described by Darcy's law and Poisseuille'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 upscalling the effective permeability of 3D fractured porous media.

Domaines: Mécanique des matériaux [physics.class-ph]; Mécanique des matériaux [physics.class-ph]; Génie civil

Minh-Ngoc Vu, Ahmad Pouya, Darius Seyedi. Modelling of steady-state fluid flow in 3D fractured isotropic porous media: Application to effective permeability calculation. International Journal for Numerical and Analytical Methods in Geomechanics, 2013, 37 (14), pp.2257-2277. ⟨10.1002/nag.2134⟩. ⟨hal-00795809⟩