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**Concept of relative permeability**

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**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

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**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

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**Different demonstrations**

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Log scale

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**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

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**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%

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Capillary end effect

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

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**Determination of relative permeability**

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

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**Empirical correlations**

Corey: Brooks-Corey:

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**Normalizing oil relative permeability data**

Slope is no kro Log scale Son, log scale

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**Normalizing water relative permeability data**

End point, krw0 Slope is nw krw Log scale Swn, log scale

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Model Fit

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**Estimation of Sor We choose Sor that gives straight line kro Log scale**

Son, log scale

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**Different wettabilities**

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

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