A MODIFIED FLOW ORIENTATION SCHEME COUPLED WITH A ROBUST MPFA-DIAMOND FOR THE SOLUTION OF TWO-PHASE FLOW IN HIGHLY ANISOTROPIC PETROLEUM RESERVOIRS (Revista Interdisciplinar de Pesquisa em Engenharia, 2017)
In this paperwe simulate two-phase flow in anisotropic petroleum reservoirs. The IMPES procedure is used to solve the coupling between pressure and saturation equations. The pressure equation is discretized by a robust Multipoint Flux Approximation Method with a Diamond-type support. This formulation is capable of reproducing piecewise linear solutions exactly and deals with anisotropic media. To solve the saturation equation a Modified Flow Oriented Scheme (M-FOS) is proposed. This alternative computes the multidimensional numerical fluxes using higher order accuracy in space. This formulation explicitly takes into account the angular distortion of the computational mesh by means of an adaptive weight that tunes the multidimensional character of the formulation according to the grid distortion. A recently devised Multidimensional Limiting Process is adopted in this paper to control the spurious oscillations in higher order approximation. This strategy guarantees monotone solutions and can be used with any polygonal mesh. Finally, an efficient entropy fix strategy, originally proposed in magneto-dynamics context, is also employed in order to produce convergent solutions. The performance of this set of numerical schemes is verified by solving some relevant benchmark problems, where we observe that the Grid Orientation Effects are clearly diminished by using this M-FOS framework.