concept of relative permeability. if two fluids flow simultaneously in a porous medium, the...
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Concept of relative permeability
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Concept of relative permeability
1 11
1
k A Pq
L
If two fluids flow simultaneously in a porous medium, the permeability of each fluid is reduced by the presence of the other one!
Fluid 1
Fluid 2Fluid 2
Fluid 1P1
P2
2 22
2
k A Pq
L
k1 and k2 are effective permeabilities and modified by saturations of the fluids
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rel perm vs. saturation
r
kk
K
kr is called relative permeability and depends on saturation (also rock type and geometry and fluid properties)
End-points
Curvatures
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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:
0 wnrw rw ek k S 0 1 no
ro ro ek k S
1
w wc
eor wc
S SS
S S
Brooks-Corey:
2 30
/rw rw ek k S 2 2 1
0 1 1 /ro ro e ek k S S
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Normalizing oil relative permeability data
1
1
w or
onwi or
S SS
S S
kroLog scale
Son, log scale
Slope is no
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Normalizing water relative permeability data
1
w wi
wnwi or
S SS
S S
krwLog scale
Swn, log scale
Slope is nw
End point, krw0
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Model Fit
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70
Water Saturation, fraction
Rel
ativ
e Pe
rmea
bilit
ies,
fra
ctio
n
Water
Oil
Water Fit
Oil Fit
0.00
0.01
0.10
1.00
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70
Water Saturation, fraction
Rel
ativ
e Pe
rmea
bilit
ies,
fra
ctio
nWater
Oil
Water Fit
Oil Fit
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Estimation of Sor
1
1
w or
onwi or
S SS
S S
kroLog scale
Son, log scale
We choose Sor that gives straight line
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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