Difference between revisions of "Relative Permeability"

Revision as of 16:50, 30 March 2022

Brief

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

k_{ro} = k_o/k_{oS_{wc}}

k_{rw} = k_w/k_{oS_{wc}}

where

k_{ro} =

Oil relative permeability, fraction

k_{rw} =

Water relative permeability, fraction

k_o =

Effective water permeability, mD

k_w =

Effective water permeability, mD

k_{oS_{wc}} =

Effective oil permeability at irreducible oil saturation, mD

S_{wc} =

Connate water saturation, fraction

Related definitions

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% water and 70% oil and qw=0 cc/sec and qo=0.123 cc/sec:

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

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

Relative permeability

In this case the mobility of water is 15 times higher than the mobility of water.

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 26: / Line 26: @@
 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:
@@ Line 35: / Line 37: @@
 :<math> k_{abs} = \frac{0.154*1.2*3*3}{2*2} = 0.415 D = 415 mD </math>
+=== Effective permeability===
 Same core at 70% water and 30% oil and qw=0.332 cc/sec and qo=0.0184 cc/sec:
@@ Line 46: / Line 50: @@
 :<math> k_o(S_w=0.3)= \frac{0.123*1.2*3*3}{2*2} = 0.332 D = 332 mD </math>
+=== Relative permeability===
 In this case the mobility of water is 15 times higher than the mobility of water.

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