Um método híbrido de elementos finitos aplicado a deslocamentos miscíveis em meios porosos heterogêneos

We study incompressible miscible displacements in heterogeneous porous media with adverse mobility ratios in order to understand the influence of these parameters on the oil reservoir recovery processes. This problem is mathematically modeled by a coupled system of nonlinear partial differential equations. Through a backward finite difference scheme in time, a sequentially implicit time-stepping algorithm that uncouples the system at each time-step is defined. A Stabilized Dual Hybrid Mixed (SDHM) method is employed for computing velocity field and pressure approximations, involving the conservation of mass and Darcy's law. Finally, the SUPG (Streamline Upwind Petrov-Galerkin) is used to approximate the concentration equation. The good performance of the proposed approach is verified via numerical simulations where it is analyzed the influence of the properties of porous media on the oil reservoir recovery.