Difference between revisions of "Relative Permeability"

Latest revision as of 17:35, 2 April 2022

Brief

Relative Permeability is the ratio of the effective permeability to base oil permeability measured at connate water saturation^[1].

k_{ro}(S_w) = k_o(S_w)/k_o(S_{wc})

k_{rw}(S_w) = k_w(S_w)/k_o(S_{wc})

where

k_{ro}(S_w) =

Oil relative permeability at the given water saturation Sw, fraction

k_{rw}(S_w) =

Water relative permeability at the given water saturation Sw, fraction

k_o(S_w) =

Effective oil permeability at the given water saturation Sw, mD

k_w(S_w) =

Effective water permeability at the given water saturation Sw, mD

k_o(S_{wc}) =

Effective oil permeability at the connate water saturation, mD

S_{wc} =

Connate water saturation, fraction

Related definitions

Relative permeability curves are the relationships between the k_ro and k_rw vs S_w. Corey correlation is a useful approximation for the rel. perm. curves.

Effective permeability - oil, water, gas phase permeability when more than one phase is present. Depends on fluids saturations.

Absolute permeability - permeability of the core sample when saturated with one liquid. Independent of fluid. Dependent on pore throat sizes.

Example

Determine the Relative Permeability using the following data^[1]:
Core dimensions: A=2 cm2, L=3 cm. PVT: water viscosity = 1 cP, oil viscosity = 3 cP, Bw=1 cc/cc, Bo=1.2 cc/cc.

Absolute permeability

Core is at 100% water and qw=0.553 cc/sec:

Using Darcy's law:

k_{abs} = \frac{0.553*1*1*3}{2*2} = 0.415 D = 415 mD

Same core at 100% oil and qo=0.154 cc/sec:

k_{abs} = \frac{0.154*1.2*3*3}{2*2} = 0.415 D = 415 mD

Effective permeability

Same core at 70% water and 30% oil and qw=0.332 cc/sec and qo=0.0184 cc/sec:

k_w(S_w=0.7)= \frac{0.332*1*1*3}{2*2} = 0.249 D = 249 mD

k_o(S_w=0.7)= \frac{0.0184*1.2*3*3}{2*2} = 0.049 D = 50 mD

Same core at 30% connate water and 70% oil and qw=0 cc/sec and qo=0.123 cc/sec:

k_w(S_{wc}=0.3)= \frac{0*1*1*3}{2*2} = 0 D = 0 mD

k_o(S_{wc}=0.3)= \frac{0.123*1.2*3*3}{2*2} = 0.332 D = 332 mD

SInce Sw=0.3 is connate water saturation, ko=332mD is the effective base permeability.

Relative permeability

Core at 70% water and 30% oil:

k_{rw}(S_w=0.7) = \frac{249}{332} = 0.75

k_{ro}(S_w=0.7) = \frac{50}{332} = 0.15

Core at 30% connate water and 70% oil:

k_{rw}(S_w=0.3) = \frac{0}{332} = 0

k_{ro}(S_w=0.3) = \frac{332}{332} = 1

References

↑ ^1.0 ^1.1 Wolcott, Don (2009). Applied Waterflood Field Development. Houston: Energy Tribune Publishing Inc.

[DW-1] 1.0 ^1.1 Wolcott, Don (2009). Applied Waterflood Field Development. Houston: Energy Tribune Publishing Inc.

[1]

@@ Line 5: / Line 5: @@
 [[Relative Permeability]] is the ratio of the effective permeability to base oil permeability measured at connate water saturation<ref name=DW/>.
-:<math> k_{ro} = k_o/k_{oS_{wc}}</math>
+:<math> k_{ro}(S_w) = k_o(S_w)/k_o(S_{wc})</math>
-:<math> k_{rw} = k_w/k_{oS_{wc}}</math>
+:<math> k_{rw}(S_w) = k_w(S_w)/k_o(S_{wc})</math>
 where
-:<math> k_{ro} =</math> Oil relative permeability, fraction
+:<math> k_{ro}(S_w) =</math> Oil relative permeability at the given water saturation Sw, fraction
-:<math> k_{rw} =</math> Water relative permeability, fraction
+:<math> k_{rw}(S_w) =</math> Water relative permeability at the given water saturation Sw, fraction
-:<math> k_o =</math> Effective water permeability, mD
+:<math> k_o(S_w) =</math> Effective oil permeability at the given water saturation Sw, mD
-:<math> k_w =</math> Effective water permeability, mD
+:<math> k_w(S_w) =</math> Effective water permeability at the given water saturation Sw, mD
-:<math> k_{oS_{wc}} =</math> Effective oil permeability at irreducible oil saturation, mD
+:<math> k_o(S_{wc}) =</math> Effective oil permeability at the connate water saturation, mD
 :<math> S_{wc} =</math> Connate water saturation, fraction
-===Related definitions===
+==Related definitions==
+'''Relative permeability curves''' are the relationships between the k<sub>ro</sub> and k<sub>rw</sub> vs S<sub>w</sub>. Corey correlation is a useful approximation for the rel. perm. curves.
 '''Effective permeability''' - oil, water, gas phase permeability when more than one phase is present. Depends on fluids saturations.
@@ Line 47: / Line 50: @@
 Same core at 30% connate water and 70% oil and qw=0 cc/sec and qo=0.123 cc/sec:
-:<math> k_w(S_w=0.3)= \frac{0*1*1*3}{2*2} = 0 D = 0 mD </math>
+:<math> k_w(S_{wc}=0.3)= \frac{0*1*1*3}{2*2} = 0 D = 0 mD </math>
-:<math> k_o(S_w=0.3)= \frac{0.123*1.2*3*3}{2*2} = 0.332 D = 332 mD </math>
+:<math> k_o(S_{wc}=0.3)= \frac{0.123*1.2*3*3}{2*2} = 0.332 D = 332 mD </math>
+SInce Sw=0.3 is connate water saturation, ko=332mD is the effective base permeability.
-SInce S3=0.3 is connate water saturation, ko is effective base permeability.
 === Relative permeability===
-In this case the mobility of water is 15 times higher than the mobility of water.
+Core at 70% water and 30% oil:
+:<math> k_{rw}(S_w=0.7) = \frac{249}{332} = 0.75 </math>
+:<math> k_{ro}(S_w=0.7) = \frac{50}{332} = 0.15 </math>
+Core at 30% connate water and 70% oil:
+:<math> k_{rw}(S_w=0.3) = \frac{0}{332} = 0 </math>
+:<math> k_{ro}(S_w=0.3) = \frac{332}{332} = 1 </math>
 ==See Also==
 *[[Mobility Ratio]]
-*[[HCPV]]
-*[[STOIIP]]
-*[[VRR]]
-*[[Pattern]]
-*[[Block]]
 *[[Mature Water Flood Analysis]]

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