Time-of-flight (TOF)-based two-phase upscaling for subsurface flow and transport

Subsurface formations are characterized by heterogeneity over multiple length scales, which can have a strong impact on flow and transport. In this paper, we present a new upscaling approach, based on time-of-flight (TOF), to generate upscaled two-phase flow functions. The method focuses on more accurate representations of local saturation boundary conditions, which are found to have a dominant impact (in comparison to the pressure boundary conditions) on the upscaled two-phase flow models. The TOF-based upscaling approach effectively incorporates single-phase flow and transport information into local upscaling calculations, accounting for the global flow effects on saturation, as well as the local variations due to subgrid heterogeneity. The method can be categorized into quasi-global upscaling techniques, as the global single-phase flow and transport information is incorporated in the local boundary conditions. The TOF-based two-phase upscaling can be readily integrated into any existing local two-phase upscaling framework, thus more flexible than local-global two-phase upscaling approaches developed recently. The method was applied to permeability fields with different correlation lengths and various fluid-mobility ratios. It was shown that the new method consistently outperforms existing local two-phase upscaling techniques, including recently developed methods with improved local boundary conditions (such as effective flux boundary conditions), and provides accurate coarse-scale models for both flow and transport.