Effective Permeability of Media with a Dense Network of Long and Micro Fractures

Jean-François Barthélémy (1)

1 IFPEN - IFP Energies nouvelles

This article presents a new methodology to estimate the effective permeability of random fractured media of any anisotropy containing both microfractures and a large number of long fractures crosscutting the representative volume element. The fractures are replaced by fictitious permeable materials for which the tangential permeability is deduced from a Poiseuille flow. A self-consistent scheme is proposed to derive the macroscopic permeability. On the one hand, the contribution of long fractures to the effective permeability writes by simple superposition of the fracture tangential permeabilities. On the other hand, the contribution of microfractures needs to resort to auxiliary problems requiring the computation of second-order Hill (or Eshelby) tensors related to ellipsoids embedded in an anisotropic matrix, for which a complete procedure is detailed. The effect of the microfracture normal permeability is put in evidence in the upscaling scheme and analyzed. In particular, it is shown that it must be chosen large enough to allow the connections between families. Examples are finally developed and compared to numerical simulations in the 2D case.

Mots clés: anisotropic effective permeability; self-consistent scheme; fracture permeability; double scale fracture network

Domaines: Matériaux et structures en mécanique [physics.class-ph]

Jean-François Barthélémy. Effective Permeability of Media with a Dense Network of Long and Micro Fractures. Transport in Porous Media, 2009, 76 (1), pp.153-178. ⟨10.1007/s11242-008-9241-9⟩. ⟨hal-01977047⟩