Appropriate choice of average pressure for upscallng relative permeability in dynamic flow conditions

A new macroscale pressure definition is investigated through a series of upscaling calculations for two-phase flow in porous media. This definition is taken from previous theoretical work by the authors and aims at correcting for systematic subscale heterogeneities including those generated by nonlinear dependencies on (heterogeneous) saturation distributionsTraditional intrinsic phaseaveraged pressure leads to nonmonotone and multivalued upscaled constitutive functions (e.g., discontinuous upscaled-relative-permeabilities exceeding unity). Using both analytical and numerical calculations, the new macroscale pressure definition is shown to lead to better-behaved upscaled functions.