A MPFA METHOD USING HARMONIC POINTS COUPLED TO A MULTIDIMENSIONAL OPTIMAL ORDER DETECTION METHOD (MOOD) FOR THE SIMULATION OF OIL-WATER DISPLACEMENTS IN PETROLEUM RESERVOIRS - Contreras, Fernando R. L.; Souza, Marcio R. A.; Lyra, Paulo R. M.; Carvalho, Darlan K. E. (Revista Interdisciplinar de Pesquisa em Engenharia, 2017)
In this paper, our main goal is to present a non-classical MPFA method coupled with a high order finite volume method for the simulation of oil water displacements in heterogeneous and anisotropic petroleum reservoirs using general polygonal meshes. The governing equations are solved using the IMPES (IMplicit Pressure and Explicit Saturation) strategy, where the elliptic pressure equation is discretized by a linear Multipoint Flux Approximation method using Harmonic points (MPFA-H) capable to handle strongly heterogeneous and anisotropic media. Besides, to approximate the advective term that characterizes the hyperbolic saturation equation, we use the Multidimensional Optimal Order Detection (MOOD) method. This technique is based in an “a posteriori” limitation procedure, i.e., the limitation procedure is done after the calculation of “candidate solutions” only where necessary to guarantee certain physical properties such as monotonicity. To show the potential of our finite volume formulation, we solve some benchmark problems found in literature.