Optimization-based upscaling for gravity segregation with 3D capillary heterogeneity effects

Multiphase flow driven by gravity and capillary forces occurs in various applications pertaining to aquifers, the vadoze zone and hydrocarbon reservoirs. In particular, these processes have been under investigation for modeling CO₂ migration in geosequestration applications. Solving such multiscale problems can be extremely computationally demanding and therefore upscaling is often employed. However, a recent study by Rabinovich and Cheng, 2020 showed that implementation of conventional upscaling methods fails to reproduce fine-grid simulations of gravity-capilary driven flow. This work presents a new upscaling method based on an effective property formula for permeability (k), power law averaging in the capillary limit for relative permeability, and an optimization approach for capillary pressure (P_c). The new method is tested on various example cases and coarse-grid simulations are shown to match fine-grid ones with sufficient accuracy. The challenge of upscaling the flows is found to be related to entry pressure trapping and the optimization upscaled P_c is shown to have a unique structure allowing to model the trapping. The method is global, requiring a fine-grid simulation for calibration of the optimized parameters. However, we show that the method reduces computational time dramatically if calibrated parameters are used in cases in which the fine-grid solution is unknown, such as for varying k realizations.