Relative Permeability (RP): Has anything to do with Darcy’s Law?

RP: Most important and least understood property (we only have a limited number of well-characterized studies on RP)

RP: Manifestation of complicated pore-level displacement physics along with the characteristics of fluid-fluid and fluid-solid interactions

RP: The actual measurement poses a real challenge

(a)By using laboratory-scale experiments using representative rock-fluid systems

(3-phase RP is almost exorbitantly difficult, costly & time-consuming);

(For a given rock-fluid system and under fixed experimental conditions, RPs are not unique functions of phase saturations, but would depend upon saturation history)

(The problem of saturation history in 3-phase flows is more convoluted since there are 2 independent phase saturations, increasing the number of process paths significantly)

(We have more than 2 saturation histories in 3-phase flow, as the saturation of each phase may increase, or, decrease, or, may remain unchanged) OR,

(b) By using Empirical Correlations; OR,

(c) By using Physically-based Pore-Scale Models

(d) (b) & (c) require high-quality experimental data for development and validation

Even if we assume the Reservoir to be Water-Wet, RP of the most wetting-phase remains to be independent of saturation history, however, the RPs of the intermediate-wetting and the most non-wetting phases remain significantly affected by saturation history.