Relative Permeability

Brief

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

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

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

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:
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

• Mobility Ratio

• Mature Water Flood Analysis