Comparative Study of Different Numerical Alternatives for Modeling Two-Phase Flows in Naturally Fractured Reservoirs

Resumo

Two-phase flows of water and oil in heterogeneous and anisotropic porous media can be described by
a system of nonlinear partial differential equations that comprises an elliptic pressure equation and a hyperbolic
saturation equation coupled through the total velocity field. These problems are difficult to model, due to
physical and geometric complex features of oil reservoirs, which can include fractures, inclined layers and
directional wells. In such cases, it is important to use formulations that can deal with full permeability tensors on
unstructured grids. Here, we present a comparative study of different numerical formulations in the context of

modeling two-phase flows in naturally fractured reservoirs. Our simulation tool incorporates different Finite-
Volume Methods with Multi-Point Flux Approximation (MPFA) schemes to obtain implicitly the solution of the

pressure equation. Among the different MPFA approaches we used some non-conventional alternatives proposed
by our research group, namely: MPFA with a diamond stencil (MPFA-D); MPFA with a quasi-local stencil
(MPFA-QL); MPFA with harmonic points (MPFA-H) and the Nonlinear Finite Volume Method that Preserves
Positivity (NLFV-PP). A Hybrid-Grid Method (HyG) was employed to model the fractures and the classical
First Order Upwind Method (FOUM) was adopted to solve the saturation equation applied in its implicit version.