Incorporation of Global Effects in Two-phase Upscaling for Modeling Flow and Transport with Full-tensor Anisotropy

Upscaling is often applied to coarsen highly-detailed geological descriptions. The upscaling of multiphase flow functions is challenging due to their strong dependency on global flow effects. In this work, we present two approaches to generate upscaled two-phase flow functions with global flow effects incorporated. In global two-phase upscaling, the upscaled two-phase functions are directly computed from global fine-scale two-phase solutions. In a new adaptive local-global two-phase upscaling approach, local boundary conditions (for both pressure and saturation) are determined from time-dependent global coarse-scale solutions. This avoids solving global fine-scale two-phase flow. In both approaches, the upscaled two-phase flow functions are adapted to a specific flow scenario, thus providing more accurate coarse models than the use of generic flows. The methods are applied to heterogeneous permeability fields with full-tensor anisotropy. We demonstrate the impact of full-tensor effects on the global flow dependency in two-phase upscaling. It is also shown that the full-tensor effects in two-phase flow are appropriately accounted for by the upscaled two-phase functions with the global flow effects incorporated. The use of those upscaled functions in conjunction with a two-point flux approximation can effectively capture the two-phase crossflow due to the full-tensor anisotropy on the coarse scale.