Nonlinear non-local multicontinua upscaling

In the past, many well-known linear and nonlinear upscaling tools have been developed, as mentioned earlier. Single-phase upscaling methods include permeability upscaling [84, 154, 252, 419] and many multiscale techniques [19, 27, 101, 190, 247, 324, 344]). Nonlinear upscaling methods, e.g., known as pseudo-relative permeability approach [42, 84, 292], computes nonlinear relative permeability functions based on single cell two-phase flow computations. It is known that these nonlinear approaches lack robustness and they are processes dependent [165, 167]. To overcome these difficulties, one needs a better understanding of nonlinear upscaling methods, which is our goal.