Modeling the hydrodynamic behavior of fractures and barriers in porous media using coupling finite elements

Abstract

Fractures, vugs and barriers are geological structures that strongly affect the fluid flow in porous media. While the first two lead to the formation of preferential flow paths, the latter blocks the flow and induces discontinuities in the pressure field. The difference in scale between these structures and the porous medium can be significant and, therefore, appropriate numerical models are required to take into account their interactions. In the context of the finite element method, this work presents a methodology to couple equi-dimensional and independent meshes (i.e., non-matching meshes) of geological structures and the porous medium by using coupling finite elements (CFEs), which are able to connect the meshes via a penalty method that ensures the continuity of the pressure field. This technique is easy to implement and does not require any special formulation, since the shape functions of the CFE are the ones used in conventional finite elements. Moreover, the addition of the CFE does not increase the number of degrees of freedom of the problem. In order to show that the technique has great potential to capture the main phenomena related to the fluid flow problem in a porous medium, 2D single-phase flow numerical experiments were conducted by considering different geological structures, geometries and boundary conditions, with incompressible fluid. The methodology was validated by comparing the results obtained with several DFM methods available in the literature as well as considering matching meshes between matrix and fracture. The results showed that the proposed coupling scheme applied to equi-dimensional meshes is adequate to reproduce the influence of geological formations such as fractures, vugs and barriers on the hydrodynamic behavior of fluids in porous media.