Numerical Simulation of Oil and Water Displacements in Petroleum Reservoirs using a Multipoint Flux Approximation Method Coupled to a Flux Corrected Transport with a Flow Oriented Formulation

Resumo

The numerical modeling of multiphase and multicomponent flow in oil reservoirs poses a great
challenge and demands the development of robust and computationally efficient numerical formulations. Common
reservoir simulators are based on the combination of the classical Two Point Flux Approximation (TPFA) for the
discretization of diffusive fluxes and the First Order Upwind (FOU) method for the discretization of the advective
fluxes in the fluid flow equations. In certain cases, particularly for high mobility ratios between the injected and
the resident fluids, the numerical solution may strongly depend on the alignment between the flow and the
computational grid, this is known as the grid orientation effect (GOE). This effect is linked to the anisotropic
distribution in the truncation error associated to the numerical approximation of the transport term. Another
problem occurs when non monotonic solutions are obtained whenever using highly distorted meshes. Besides, the
standard TPFA method may not converge at all to an adequate solution when the grid is non k-orthogonal. In this
context, in the present paper, our main goal is present a full cell centered finite volume formulation for the
numerical simulation of oil-water displacements in oil reservoirs using a segregate formulation in general
unstructured and non k-orthogonal 2D meshes. For the discretization of the diffusive fluxes, we use a Multipoint
Flux Approximation based in Harmonic Points (MPFA-H) and for the discretization of the transport term, we
present a modified version of the 2nd order Flux Corrected Transport (FCT) approach to reduce artificial numerical
diffusion and we also use a Flow Oriented Scheme (FOS) in the computation of the low-order approximations
used in our modified FCT scheme. The FOS philosophy consists in using weights that are properly adapted to the
flow direction, turning our scheme into a truly multidimensional approximation in order to reduce GOE. Our
strategy was tested against one benchmark problem available in literature, producing very accurate results with
reduced artificial numerical diffusion and GOE.