Relative permeability scaling from pore-scale flow regimes

The development of predictive tools to model multiphase flow through porous media is critical to petroleum recovery and carbon sequestration. Although features in the topology of the flowing phases at the pore-scale (i.e., the pore-scale flow regimes) have been recently revealed by X-ray microtomography, they are still not captured by routinely used macro-scale models (i.e., Darcy's law). In fact, relative permeabilities are just fitted with empirical correlations and a fundamental understanding of their scaling behavior with respect to in-situ saturation, viscosity ratio, and capillary number is still missing. We tackle this problem by proposing a theoretical framework that allows one to formulate the relative permeabilities of the wetting and non-wetting phase in real 3-D porous media while accounting for pore-scale flow regimes (i.e., ganglia flow, connected pathway). We also discuss the scaling behavior of the fractional flow and provide a detailed validation against data from numerical simulations and experiments available in the literature. The data set used for the validation covers a wide range of systems, ranging from brine-CO2 to oil-water flows. We also test our theory on two-phase water-steam systems at conditions typical of geothermal reservoirs.