concept of relative permeability. if two fluids flow simultaneously in a porous medium, the...
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Concept of relative permeability
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
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
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:
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
Normalizing oil relative permeability data
1
1
w or
onwi or
S SS
S S
kroLog scale
Son, log scale
Slope is no
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
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
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
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
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