We present a multi-point flux approximation (MPFA) scheme for simulation of 3-D multi-phase flow on adapted grids. It is an extension of the VCMP (Variable Compact Multi-Point) scheme, which constructs stencils that are locally adapted to flow through transmissibility upscaling. The proposed integration of upscaling, MPFA stencil selection and gridding leads to an optimized flow discretization that can accurately resolve full-tensor effects, is compact, and leads to low upscaling errors.

The grid adaptivity is driven by both upscaling, in a pre-processing stage, and by solution gradients during run-time. During transmissibility upscaling, the grid is refined to resolve important flow features such as high permeability flow paths. During run-time, we refine the grid locally, as needed, to accurately resolve saturation fronts, and coarsen once the front passes. We do not employ downscaling techniques, but compute transmissibilities for the newly refined regions using the upscaling methodology that can be effectively applied to localized regions.

The numerical tests presented in this paper show that the method leads to higher upscaling accuracy as compared to commonly used upscaling methods. On average, error in total flow is reduced by a factor of two, and the fine-scale velocity field is resolved with greater accuracy as well. They also illustrate that saturation fronts can be resolved accurately using single-phase upscaling only by employing VCMP on adapted grids.

The combined strategy promises to significantly improve the workflow of coarse-scale modeling for flow simulations such as those routinely performed in the industry.

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