An improved embedded finite element formulation for investigating fluid flow behavior in fractured porous media

Resumo

Discontinuities, such as fractures and geological faults, are present in several geological models where a fluid flow analysis is performed. In cases where the discontinuity filling material has a lower permeability than the matrix, this discontinuity will act as a barrier to fluid flow in the porous media. On the other hand, fluid flow is enhanced in the absence of filling material or in the highly porous case. Embedded formulations have become attractive to model discontinuities over the last decades since they do not require mesh conformity. However, the literature lacks a formulation fully developed in the context of the Finite Element Method capable of modeling discontinuities that act like barriers to fluid flow in transient problems. This paper presents an improved embedded finite element formulation to investigate fluid flow behavior in fractured porous media. The proposed approach includes additional degrees-of-freedom representing the pressure drop between fracture surfaces and the fluid pressure within the fracture. Single-phase flow is considered. Darcy’s law governs fluid flow through the porous media, while the cubic law of parallel plates controls the fluid flow inside the fracture channel. A numerical
example comparing the results with a model with interface elements modeling the discontinuity is compared to
the embedded formulation. The numerical results demonstrate the capability and limitations of the proposed
approach to capture the influence of discontinuities on fluid flow behavior in porous media.