Grid convergence of variable-density flow simulations in discretely-fractured porous media

Grid convergence in space and time of variable-density flow in fractured-porous rock is systematically assessed. Convergence of the flow simulation is attained using both uniform and adaptive time-stepping. This contrasts to variable-density flow in unfractured porous media where grid convergence variable-density flow problems is almost never achieved. At high discretization levels, the number of fingers in fractured-porous rock is no longer influenced by spatial-temporal grid discretization, which is not the case in unfractured porous media. However, similar to unfractured porous media, the number of fingers in fractured-porous media varies at low discretization levels. Simulated convective pattern and penetration depth of the dense plume in fractured rock depend more on spatial discretization than on temporal discretization. The appropriate spatial-temporal grid is then used to examine some aspects of mixed convection in fractured-porous rock, characterized by the mixed convection number M. The critical mixed convection number M_c = 46 represents the transition between forced and free convection in fractured porous media, which is much higher than M_c = 1 in unfractured porous media. Thus, for mixed convective flow problems, the value of M_c is not a sufficient indicator to predict the convective mode (free convection-forced convection), and the presence of vertical fractures must be included in the prediction of convective flow modes.