Relative Permeability

Brief

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

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

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

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:
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.

See Also

• Mobility Ratio
• HCPV
• STOIIP
• VRR
• Pattern
• Block
• Mature Water Flood Analysis