Embedded Finite Element formulation for fluid flow in fractured porous medium

The presence of discontinuities, such as fractures or geological faults, can significantly influence the fluid flow in a porous medium. In general, the discontinuities can act as preferential flow paths. However, depending on their aperture and filling material, they can act as barriers to fluid flow. To model these different possibilities, this paper presents an embedded approach in the context of the finite element method to model the presence of discontinuities inside a porous medium in transient analyses. The formulation is attractive since it does not require the mesh used to discretize the porous medium to conform to the discontinuities. The derivation of the formulation is based on the Strong Discontinuity Approach by enriching the pressure field of the finite element with a Heaviside function. The enriched part of the pressure field is discretized based on the pressure jumps evaluated at the nodes where the discontinuity intersects the finite element. The discontinuity internal pressure is taken as an independent field, allowing the modeling of high pressures inside the discontinuity. A strategy to condense the discontinuity internal pressure degrees of freedom is presented. Numerical examples are presented showing the flexibility of the formulation to capture the influence of discontinuities on the fluid flow in porous medium. The results obtained with the proposed formulation are compared with interface element models, showing a good agreement between the two approaches.