Theoretical and numerical study of the steady‐state flow through finite fractured porous media

Abstract

International audienceThis paper investigates the two-dimensional flow problem through an anisotropic porous medium containing several intersecting curved fractures. First, the governing equations of steady-state fluid flow in a fractured porous body are summarized. The flow follows Darcy's law in matrix and Poiseuille's law in fractures. An infinite transversal permeability is considered for the fractures. A multi-region boundary element method is used to derive a general pressure solution as a function of discharge through the fractures and the pressure and the normal flux on the domain boundary. The obtained solution fully accounts for the interaction and the intersection between fractures. A numerical procedure based on collocation method is presented to compute the unknowns on the boundaries and on the fractures. The numerical solution is validated by comparing with finite element solution or the results obtained for an infinite matrix. Pressure fields in the matrix are illustrated for domains containing several interconnected fractures, and mass balance at the intersection points is also checked

Responses of chemically active and naturally fractured shale under time‐dependent mechanical loading and ionic solution exposure

“…Such fracture property differences are not studied in this paper. For the case of open and closed fractures, numerical methods can be found in previous studies …”

Effects of fractal surface roughness and lithology on single and multiphase flow in a single fracture: An experimental investigation

“…They include the attempts on modelling two-phase flow using a 3-D discrete fracture description (Bogdanov et al, 2003), characterization of the permeability behaviour for isotropic and anisotropic fracture networks (Mourzenko et al, 2011), and an investigation of 3-D steady-state and 2-D flow through porous medium with intersecting fractures (Vu et al, 2013(Vu et al, , 2014. Even modelling single and multiphase in fracture networks requires the inclusion of roughness and its effects on flow characteristics of a single fracture.…”

Development of Embedded Element Technique for Permeability Analysis of Cracked Porous Media

“…The case of intersecting cracks might be more interesting to us. Here consider a 6 m long square domain with nine intersecting cracks [30]. The model boundary condition and its corresponding CE and EE meshes are shown in Figure 11.…”