A Rate-Dependent Upscaling Framework for REV Saturation Functions in Dual-Porosity Media

Summary Simulating multi-phase flow at length scale larger than measured scale has been an active topic for decades. In this study, we address the numerical challenges associated with estimating effective relative permeability and capillary pressure (usually known as saturation functions) of dual porosity systems. Specifically, we introduce a modified version of periodic boundary conditions applied in steady-state upscaling workflow. Our modification is based on mirror-periodic boundary conditions as a reasonable choice overcoming short failings introduced through direct application of periodic boundary conditions. This modification can be seamlessly coupled with previous approaches handling force balance spectrum from capillary limit to viscous limit. In addition, the resultant relative permeability is a tensor allowing for modeling complex geometrical configurations. The approach is demonstrated through estimation of effective multi-phase parameters of bioturbated strata model.