Numerical modelling of steady-state flow in 2D cracked anisotropic porous media by singular integral equations method

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

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

The equations governing plane steady-state flow in heterogeneous porous media containing curved-line intersecting cracks (Pouya and Ghabezloo 2010) and the potential solution obtained for these equations are considered here. The theoretical results are first completed for the mass balance at crack intersections points. Then, a numerical procedure based on a singular integral equations method is described concretely to derive this solution for cracked materials. Closed-form expressions of elementary integrals for special choice of collocation points lead to a very quick and easy numerical method. It is shown that this method can be applied efficiently to the study of the steady state flow in cracked materials with anisotropic matrix permeability and a dense distribution of curved-line intersecting cracks. Some applications of this method to the permeability of cracked materials are given.

Mots clés: porous media; cracks; steady state flow; singular integral equations; effective permeability

Domaines: Mécanique des matériaux [physics.class-ph]; Mécanique des matériaux [physics.class-ph]; Sciences de la Terre

Ahmad Pouya, Minh-Ngoc Vu. Numerical modelling of steady-state flow in 2D cracked anisotropic porous media by singular integral equations method. Transport in Porous Media, 2012, 93 (3), pp.475-493. ⟨10.1007/s11242-012-9968-1⟩. ⟨hal-00790536v2⟩