Concept of relative permeability

Concept of relative permeability If two fluids flow simultaneously in a porous medium, the permeability of each fluid is reduced by the presence of the other one! P1 Fluid 1 Fluid 1 Fluid 2 Fluid 2 P2 k1 and k2 are effective permeabilities and modified by saturations of the fluids

rel perm vs. saturation Curvatures kr is called relative permeability and depends on saturation (also rock type and geometry and fluid properties) Curvatures End-points

Different demonstrations

Log scale

General comments on rel perms Relative permeabilities only provide the general description of the process not the mechanism! It is a very simple tool to describe multi-phase flow in porous media Often used as fitting parameters in history-matching exercises Absolute permeability does not depend on wettability while rel perms do Like capillary pressure there are two drainage rel perms and imbibition rel perms

Gas-oil relative permeability Gas flows above a critical gas saturation (Sgc) When pressure drops below bubble point pressure, gas bubbles appear in oil, however they must coalesce and form a gas phase before gas can really move Sgc = 0 – 8%

Capillary end effect

Capillary end effect Capillary pressure end effect gives rise to increasing wetting phase saturation towards outlet of the core

Determination of relative permeability Steady-state method: Fluids are injected with fixed flowrate into core until equilibrium is reached. Unsteady-state method:

Empirical correlations Corey: Brooks-Corey:

Normalizing oil relative permeability data Slope is no kro Log scale Son, log scale

Normalizing water relative permeability data End point, krw0 Slope is nw krw Log scale Swn, log scale

Model Fit

Estimation of Sor We choose Sor that gives straight line kro Log scale Son, log scale

Different wettabilities wettability no nw krw0 Water-wet 2-3 4-6 0.1-0.4 Intermediate 3-5 2-4 0.5-0.9 Oil wet 6-8 1.5-3 0.8-1.0