Modeling Fractures and Barriers as Interfaces for Porous Flow with Extended Finite-Element Method

Abstract

Fractures and barriers exist in hydrocarbon reservoirs. It is essential to evaluate the influence of fractures and barriers on porous flow in many research domains like petroleum engineering and disposal of nuclear waste. Fractures can play the role of highly conductive channels in the flow fields, while barriers can act as the walls blocking fluids. The extended finite-element method (XFEM) is effective in addressing the porous flow problems involving arbitrary geometries of fractures and barriers that do not need to conform to the mesh. This paper uses the XFEM to deal with the discontinuity problems of porous flow caused by highly permeable fractures, lowly permeable fractures, and impermeable barriers. The authors further improve the previous fracture-matrix transfer flow equations by differentiating the pressure at the fracture center from the average pressure in the fracture cross section, and finally combine the fracture-matrix transfer flow equations with a boundary layer theory to better model fluid flow in the case of anisotropically permeable fractures. Numerical results demonstrate that the XFEM is effective and applicable in solving the discontinuity problems of porous flow due to barriers and fractures. In addition, the introduction of the boundary layer can improve the accuracy in modeling anisotropically permeable fractures in which the tangential permeability is far larger than the normal permeability.