Difference between revisions of "Relative Permeability"
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:<math> k_{ro}(S_w) = k_o(S_w)/k_o(S_{wc})</math> | :<math> k_{ro}(S_w) = k_o(S_w)/k_o(S_{wc})</math> | ||
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:<math> k_{rw}(S_w) = k_w(S_w)/k_o(S_{wc})</math> | :<math> k_{rw}(S_w) = k_w(S_w)/k_o(S_{wc})</math> | ||
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:<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. | ||
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'''Effective permeability''' - oil, water, gas phase permeability when more than one phase is present. Depends on fluids saturations. | '''Effective permeability''' - oil, water, gas phase permeability when more than one phase is present. Depends on fluids saturations. | ||
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Same core at 30% connate water and 70% oil and qw=0 cc/sec and qo=0.123 cc/sec: | Same core at 30% connate water and 70% oil and qw=0 cc/sec and qo=0.123 cc/sec: | ||
| − | :<math> k_w( | + | :<math> k_w(S_{wc}=0.3)= \frac{0*1*1*3}{2*2} = 0 D = 0 mD </math> |
| − | :<math> k_o( | + | :<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 Sw=0.3 is connate water saturation, ko=332mD is the effective base permeability. | ||
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:<math> k_{rw}(S_w=0.3) = \frac{0}{332} = 0 </math> | :<math> k_{rw}(S_w=0.3) = \frac{0}{332} = 0 </math> | ||
:<math> k_{ro}(S_w=0.3) = \frac{332}{332} = 1 </math> | :<math> k_{ro}(S_w=0.3) = \frac{332}{332} = 1 </math> | ||
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==See Also== | ==See Also== | ||
*[[Mobility Ratio]] | *[[Mobility Ratio]] | ||
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*[[Mature Water Flood Analysis]] | *[[Mature Water Flood Analysis]] | ||
Latest revision as of 17:35, 2 April 2022
Contents
Brief
Relative Permeability is the ratio of the effective permeability to base oil permeability measured at connate water saturation[1].
where
Oil relative permeability at the given water saturation Sw, fraction
Water relative permeability at the given water saturation Sw, fraction 
Effective oil permeability at the given water saturation Sw, mD 
Effective water permeability at the given water saturation Sw, mD
Effective oil permeability at the connate water saturation, mD
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:
Same core at 100% oil and qo=0.154 cc/sec:
Effective permeability
Same core at 70% water and 30% oil and qw=0.332 cc/sec and qo=0.0184 cc/sec:
Same core at 30% connate water and 70% oil and qw=0 cc/sec and qo=0.123 cc/sec:
SInce Sw=0.3 is connate water saturation, ko=332mD is the effective base permeability.
Relative permeability
Core at 70% water and 30% oil:
Core at 30% connate water and 70% oil:
See Also
References
- ↑ 1.0 1.1
Wolcott, Don (2009). Applied Waterflood Field Development
. Houston: Energy Tribune Publishing Inc.
