1. Concept of relative permeability

2. 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

3. 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

4. Different demonstrations

5. Log scale

6. 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

7. 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%

8. Capillary end effect

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

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

11. Empirical correlations
Corey:
Brooks-Corey:

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

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

14. Model Fit

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

16. Different wettabilities
wettability no nw
krw0
Water-wet
2-3
4-6
Intermediate
3-5
2-4
Oil wet
6-8
1.5-3