Multiscale hybrid-mixed finite element method for flow simulation in fractured porous media

Abstract

The multiscale hybrid-mixed (MHM) method is applied to the numerical approximation of two-dimensional matrix fluid flow in porous media with fractures. The two-dimensional fluid flow in the reservoir and the one-dimensional flow in the discrete fractures are approximated using mixed finite elements. The coupling of the two-dimensional matrix flow with the one-dimensional fracture flow is enforced using the pressure of the one-dimensional flow as a Lagrange multiplier to express the conservation of fluid transfer between the fracture flow and the divergence of the one-dimensional fracture flux. A zero-dimensional pressure (point element) is used to express conservation of mass where fractures intersect. The issuing simulation is then reduced using the MHM method leading to accurate results with a very reduced number of global equations. A general system was developed where fracture geometries and conductivities are specified in an input file and meshes are generated using the public domain mesh generator GMsh. Several test cases illustrate the effectiveness of the proposed approach by comparing the multiscale results with direct simulations.