An Extended Finite Element Model for Fluid Flow in Fractured Porous Media

Abstract

This paper proposes a numerical model for the fluid flow in fractured porous media with the extended finite element method. The governing equations account for the fluid flow in the porous medium and the discrete natural fractures, as well as the fluid exchange between the fracture and the porous medium surrounding the fracture. The pore fluid pressure is continuous, while its derivatives are discontinuous on both sides of these high conductivity fractures. The pressure field is enriched by the absolute signed distance and appropriate asymptotic functions to capture the discontinuities in derivatives. The most important advantage of this method is that the domain can be partitioned as nonmatching grid without considering the presence of fractures. Arbitrarily multiple, kinking, branching, and intersecting fractures can be treated with the new approach. In particular, for propagating fractures, such as hydraulic fracturing or network volume fracturing in fissured reservoirs, this method can process the complex fluid leak-off behavior without remeshing. Numerical examples are presented to demonstrate the capability of the proposed method in saturated fractured porous media.

Transverse and longitudinal fluid flow modelling in fractured porous media with non‐matching meshes

“…The first permeability condition is considered here and the pressure distribution along a vertical section through the centre, from bottom to top of the model, is shown in Figure 12a. According to the figure, the results agree well with those obtained by [50] with a DFM model, and fracture mapping with a mesh‐free model and FEM, and also with the results reported by [51] using XFEM. For the second permeability condition, that is, , , and a domain without discontinuity, the fluid pressure distributions along the vertical section through the centre of the domain are shown in Figure 12b.…”

Deformation Behavior between Hydraulic and Natural Fractures Using Fully Coupled Hydromechanical Model with XFEM

“…The fluid exchange items or leak between the fractures and the surrounding matrix rock can then be vanished by adding the equivalent integrals of the matrix rock and fractures, which have the same absolute value but opposite signs. Thus, it becomes unnecessary to explicitly express the fluid exchange items or leak [16][17][18]: …”

“…This presents a typical weak discontinuous problem. Similar to the interpolation of displacement field, the pressure field can be interpolated as [16,18] …”

Coupling mixed hybrid and extended finite element methods for the simulation of hydro-mechanical processes in fractured porous media

“…These properties improve computational efficiency greatly and make XFEM a promising approach for solving complex problems with fractures at reasonable computing costs. Recently, XFEM has been increasingly applied to the simulation of HM processes in fractured domains (Khoei et al, 2012;Lamb et al, 2013;Liu et al, 2015;Shao et al, 2014a;Yan et al, 2018;Zeng and Yao, 2015;Zheng and Luo, 2015). In several previous studies, XFEM has been used for solving the mechanical equations, combined with the FVM for fluid flow.…”