A robust fully mixed finite element model for flow and transport in unsaturated fractured porous media

Abstract

A fully mixed finite element (MFE) model is developed for nonlinear flow and transport in unsaturated fractured porous media with matrix-fracture and fracture-fracture fluid and mass exchanges. The model is based on the discrete fracture matrix (DFM) approach and assumes cross-flow equilibrium in the fractures. The MFE method is employed for the spatial discretization of both flow and transport on the 2D-matrix elements as well as on the 1D-fracture elements. An upwind scheme is employed to avoid unphysical oscillations in the case of advection dominant transport. The temporal discretization is performed using high-order time integration methods and efficient automatic time-stepping schemes via the MOL.Two test problems dealing with flow and mass transport in saturated and unsaturated fractured porous media are simulated to show the validity of the new model by comparison against (i) a 1D-2D Comsol finite element model and (ii) a 2D-2D Discontinuous Galerkin (DG) model where both fractures and matrix continua are discretized with small 2D mesh elements. The robustness and efficiency of the developed 1D-2D MFE model are then investigated for a challenging problem dealing with infiltration of contaminated water into an initially dry soil involving a fracture network.The new model yields stable results for advection-dominated and advection-dispersion transport configurations. Further, the results of the 1D-2D MFE model are in very good agreement with those of the 2D-2D DG model for both configurations. The simulation of infiltration of contaminated water into a dry fractured soil shows that the 1D-2D MFE model is within 15 times more efficient than the 2D-2D DG model, which confirms the high benefit of using robust and efficient DFM models for the simulation of flow and transport in fractured porous media.