Difference between revisions of "Relative Permeability"

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==Brief==
 
==Brief==
  
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[[Relative Permeability]] is the ratio of the effective permeability to base oil permeability measured at connate water saturation.
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[[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
 
where
  
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:<math> k_{ro} =</math> Oil relative permeability, fraction
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:<math> k_{ro}(S_w) =</math> Oil relative permeability at the given water saturation Sw, fraction
−
:<math> k_{rw} =</math> Water relative permeability, fraction  
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:<math> k_{rw}(S_w) =</math> Water relative permeability at the given water saturation Sw, fraction  
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:<math> k_o =</math> Effective water permeability, mD  
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:<math> k_o(S_w) =</math> Effective oil permeability at the given water saturation Sw, mD  
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:<math> k_w =</math> Effective water permeability, mD
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:<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
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:<math> k_o(S_{wc}) =</math> Effective oil permeability at the connate water saturation, mD
 
:<math> S_{wc} =</math> Connate water saturation, fraction
 
:<math> S_{wc} =</math> Connate water saturation, fraction
 +
 +
==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.
 +
 +
'''Absolute permeability''' - permeability of the core sample when saturated with one liquid. Independent of fluid. Dependent on pore throat sizes.
  
 
==Example==
 
==Example==
−
Determine the [[Mobility Ratio]] using the following data<ref name=DW/>:<BR>
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Determine the [[Relative Permeability]] using the following data<ref name=DW/>:<BR>
−
Core is at 70% water and 30% oil saturation. Water phase permeability is 248 mD, oil phase permeability is 50 mD. Water viscosity is 1 cP, oil viscosity is 3 cP.  
+
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===
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 +
Core is at 100% water and qw=0.553 cc/sec:
 +
 
 +
Using [[Darcy's law]]:
  
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:<math> M = \frac{248/1}{50/3} =15 </math>
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:<math> k_{abs} = \frac{0.553*1*1*3}{2*2} = 0.415 D = 415 mD </math>
  
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In this case the mobility of water is 15 times higher than the mobility of water.
+
Same core at 100% oil and qo=0.154 cc/sec:
 +
 
 +
:<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:
 +
 
 +
:<math> k_w(S_w=0.7)= \frac{0.332*1*1*3}{2*2} = 0.249 D = 249 mD </math>
 +
:<math> k_o(S_w=0.7)= \frac{0.0184*1.2*3*3}{2*2} = 0.049 D = 50 mD </math>
 +
 
 +
Same core at 30% connate water and 70% oil and qw=0 cc/sec and qo=0.123 cc/sec:
 +
 
 +
:<math> k_w(S_{wc}=0.3)= \frac{0*1*1*3}{2*2} = 0 D = 0 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.
 +
 
 +
=== Relative permeability===
 +
 
 +
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==
 
==See Also==
 
*[[Mobility Ratio]]
 
*[[Mobility Ratio]]
−
*[[HCPV]]
+
 
−
*[[STOIIP]]
 
−
*[[VRR]]
 
−
*[[Pattern]]
 
−
*[[Block]]
 
 
*[[Mature Water Flood Analysis]]
 
*[[Mature Water Flood Analysis]]
  

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 kro and krw vs Sw. 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

See Also

References

  1. ↑ 1.0 1.1 Wolcott, Don (2009). Applied Waterflood Field DevelopmentPaid subscription required. Houston: Energy Tribune Publishing Inc. 


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