Multidimensional transport for reservoir simulation is typically solved by applying 1D numerical methods in each spatial coordinate direction. This approach is simple, but the disadvantage is that numerical errors become highly correlated with the underlying computational grid. In many real-field applications this can result in strong sensitivity to grid design for the computed saturation/composition fields, but also for critical integrated data such as breakthrough times. To increase robustness of simulators, especially for adverse mobility ratio flows that arise in gas injection and other EOR processes, it is therefore of much interest to design truly multi-D schemes for transport that remove, or at least strongly reduce, the sensitivity to grid design.

We present a new upwind biased truly multi-D family of schemes for multi-phase transport capable of handling counter-current flow arising from gravity. The proposed family of schemes has four attractive properties: applicability within a variety of simulation formulations with varying levels of implicitness; extensibility to general grid topologies; compatibility with any finite volume flow discretization; and provable stability (monotonicity) for multi-phase transport. The family is sufficiently expressive to include several previously developed multi-D schemes, such as the narrow scheme, in a manner appropriate for general purpose reservoir simulation.

A number of water flooding problems in homogeneous and heterogeneous media demonstrate the robustness of the method as well as reduced transverse (cross-wind) diffusion and grid orientation effects.

You can access this article if you purchase or spend a download.