An embedded discrete fracture model based on the use of coupling finite elements for modeling fluid flow in naturally fractured porous media. - Borges, Livia Fernanda Araujo (2021)
Petroleum is a natural occurrence of hydrocarbons and inorganic impurities, usually presented in a liquid or gas phase in a system. Some reservoirs rock which stores the hydrocarbon can be separated between two domains: the porous medium and the fracture network which may creates preferential channels that change the equivalent permeability of the medium. Many numerical models have been proposed to simulate fluid flow in naturally fractured reservoirs, however, the representation of the complex geometric characteristics of the fracture network is still an issue nowadays. In this sense, this work proposes an embedded discrete fracture model based on the use of coupling finite elements (CFEs) for modeling fluid flow in naturally fractured porous media. The proposed model is able to couple the initially independent non-matching and overlapping meshes from the fractures and rock matrix via CFEs to enforce the continuity of the pressure field between the meshes through a penalty parameter. The main advantage of the use of this approach is that the implementation of CFEs does not require additional degrees of freedom or special integration procedures for coupling the non-matching meshes. Three sets of 2D numerical examples are performed to validate the proposed approach for modeling the steady-state flow in fractured porous medium. The first set of numerical examples focused on the influence of the natural fractures position and the penalty parameter magnitude. In the second set of examples, a study of mesh refinement is performed considering fracture intersections in order to assess the capability of the proposed model to account for the contribution of each discontinuity to the pressure field. The last set of numerical examples presents the simulation of a complex naturally fractured porous medium with vug pore spaces. In conclusion with the results obtained: (i) the coarse meshes presents good results in comparison with refined meshes; (ii) a ratio of porous media and fracture elements between 1 and 2 is acceptable for better results; and (iii) and an specific value of the penalty parameter is applied to predict better behavior of fluid flow in porous medium. Furthermore, the results are in good agreement with reference solutions (the numerical results obtained in previous studies) and the proposed approach demonstrated to be able to capture the main phenomena associated with the fluid transport in fractured porous media.