Dynamic Relative Permeabilities for Partially Saturated Porous Media Accounting for Viscous Coupling Effects: An Analytical Solution

Abstract We present an analytical model to compute frequency-dependent relative permeability functions for partially saturated porous media accounting viscous coupling effects. For this, we consider the oscillatory motion of two immiscible fluid phases and solve Navier–Stokes equations at pore scale using suitable interface conditions between fluids. These calculations are combined with generalized two-phase flow Darcy obtain corresponding upscaled macroscopic fluxes. By means analog consisting a bundle cylindrical capillaries in which fluids distributed concentric manner, find closed expressions complex-valued frequency- saturation-dependent functions. allow direct assessment effects on all frequencies saturations. Our results show that significantly affect characteristics inertial regimes. Dynamic permeabilities affected by densities viscosities. Moreover, may induce critical dynamic curves, characteristic cannot be addressed extending classic definition scenarios effective The theoretical derivations presented this work have implications estimation interpretation seismic seismoelectric responses media.