Introduction to
Effective Permeability
and
Relative Permeability
r
i
k
Review: Absolute Permeability
o
d
e
h
S
Absolute permeability: is the permeability of a
porous medium saturated with a single fluid
(e.g. Sw=1)
a
s
m
a
h
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Absolute permeability can be calculated from
the steady-state flow equation (1D Linear,
Horizontal Flow; Single Phase; Darcy Units):
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E
.
r
k
A
p
D
.f q
L
ro
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Multiphase Flow in Reservoirsk
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Commonly, reservoirs contain 2 or 3S
fluids
d
e
Water-oil systems
m
a
Oil-gas systems
h
o
Water-gas systems M
a
s
Three phase systems
(water, oil, and gas)
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E
To evaluate multiphase
systems, must
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considerDthe effective and relative
.
f
permeability
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Effective Permeability
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k
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h
Effective permeability: is a measure of
the conductance of a porous medium
for one fluid phase when the medium is
saturated with more than one fluid.
m
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h
o
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The porous medium can have a distinct and
measurable conductance to each phase present in
the medium
.
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E
a
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Effective permeabilities:
f
ro
(ko, kg, kw)
Effective Permeability
ko A o
qo
o L
Oil
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i
k
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h
Steady state, 1D, linear flow
equation (Darcy units):
d
e
m
a
qn = volumetric flow rate for a
specific phase, n
k w A w h A = flow area
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Water qw
w LM = flow potential drop for
Gas
f
ro
s
i
Ek A
q gr.
D
.
a
s
g L
phase, n (including pressure,
gravity and capillary pressure
terms)
n = fluid viscosity for phase n
L = flow length
r
i
Relative Permeability is the ratio of the effectivek
o
permeability of a fluid at a given saturation
to some
h
S
base permeability
d
e as:
Base permeability is typically defined
m
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h
o
M
a
s
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D
.
f
o
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Relative Permeability
absolute permeability, k
air permeability, kair
effective permeability to non-wetting phase at irreducible wetting
phase saturation [e.g. ko(Sw=Swi)]
because definition of base permeability varies, the definition
used must always be:
confirmed before applying relative permeability data
noted along with tables and figures presenting relative
permeability data
Relative Permeability
Oil
kro( 0.5, 0.3)
ko ( 0.5,0.3)
k
m
a
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e
h
k w( 0o.5,0.3)
Water k rw( 0.5, 0.3) M
k
a
s
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k g ( 0.5,0.3)
.
krgr( 0.5,0.3)
Gas D
k
.f
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P
r
i
k
o
h
So =0.5
Sw =0.3
Sg = 0.2
r
i
Relative Permeability Functions
k
o
h
S
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e
m
a
h
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M
a
s
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E
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r
D
.
f
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Relative Permeability (fraction)
Imbibition Relative Permeability
1.00
Wettability and direction of
saturation change must be
considered
drainage, or
imbibition
kro @ Swi
0.80
Two-Phase Flow
Region
0.60
Base used to normalize this
relative permeability curve is
ko @ Swi
Oil
0.40
0.20
krw @ Sor
Water
0.20
0.40
0.60
0.80
Water Saturation (fraction)
1.00
As Sw increases, kro decreases
and krw increases until
reaching residual oil
saturation
1.0
0.8
0.6
a
s
Oil
0.4
0.2
.
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D
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Water
20
f
ro
40
s
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E
60
80
100
Relative Permeability, Fraction
Relative Permeability, Fraction
Effect of Wettability
for Increasing Sw
d
e
1.0
o
h
m
a
0.8
h
o
r
i
k
0.6
Oil
0.4
Water
0.2
20
40
60
80
Water Saturation (% PV)
Water Saturation (% PV)
Strongly Water-Wet Rock
Strongly Oil-Wet Rock
100
Water flows more freely
Higher residual oil saturation (typical)
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Factors Affecting Relative Permeabilities
o
Fluid saturations
d
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h
S
h
o
m
a
Geometry of the pore spaces and pore
size distribution
Wettability
.
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D
.
s
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E
a
s
Fluid saturation history (i.e., imbibition
or drainage)
f
ro
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Characteristics of Relativek
o
h
Permeability Functions
S
d
e for
Relative permeability is unique
m
a
different rocks and fluids
h
o
Relative permeability
M affects the flow
characteristicssa
of reservoir fluids.
s
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Relative permeability
affects the
E
.
r
recovery
efficiency
of
oil
and/or
gas.
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.
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o
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P
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Applications of
o
h
Relative Permeability Functions
m
a
d
e
Reservoir simulation
h
Flow calculationsothat involve
M
multi-phase flow
in reservoirs
a
s
s
i
Estimation
of residual oil (and/or
E
.
r
gas) saturation
D
.
f
o
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