In the present work, we address the issue of groundwater flow in fractured porous media submitted to local or regional stress-state variations. Due to the increasing pore pressure fluid, the size and aperture distribution of the fractures are modified resulting in the formation of preferential flow channels within the geological formation. The numerical approach proposed in this paper is a fully coupled hydro-mechanical model in saturated conditions involving single-phase flow both in fractures and the porous matrix. The extended finite element method (XFEM) is employed to model fracture dynamic and fluid flow assuming fracture cutting through the elements.
Faults or fractures play a key role as preferential pathways for migration of pollutants or circulation of mineralizing fluids in geological subsurface reservoirs. In case of local stress variations, fracture orientation and permeability may change and new ones may occur. Due to the relevance of these channels for the assessment of flow and solute transport in geological formations, modeling their behavior with time is highly suitable for environmental, geotechnical, petroleum and mining applications. Here a new numerical modeling approach, hereafter referred to as the XFEM-HM (Extended Finite Element Method for Hydro Mechanical processes) method, is proposed to model the complex processes involved and provide an accurate dynamic description of the geological reservoir that evolves with time.
The formulation of the XFEM-HM model is based on the governing balance equations of coupled hydromechanical processes for fully saturated porous media. A zero-thickness finite element is used to model the fracture (Cornec et al., 2003; Carrier et al., 2012).
The XFEM-HM model takes into account (Adachi et al., 2008):
preferential fluid flow inside and through the fracture depending on its aperture;
fluid exchanges between rock formation and fracture;
fracture dynamics (initiation, opening or closure);
porous medium deformation due to the fluid pressure inside the fracture.
The eXtended Finite Element Method (XFEM) (Belytschko et al., 1999; Moës et al., 1999) is used for spatial discretization of the above problem close to the fracture within the porous medium. The XFEM method, based on the partition of unity (Melenk et al., 1996) overcomes the mesh dependences of the fracture representation by enriching the classical finite element approximation of the displacement and pore pressure fields with additional degrees of freedom (dof). Especially, the geometry does not need to be updated with each time step and the edge-elements do not have to match the fracture walls. Discontinuity of those fields is directly taken into account in the constitutive equations.