Introduction to

Three PhaseRelative Permeability

Ternary Diagrams

• Because So+Sw+Sg=1, we can use a ternary diagram to represent three phase saturations, and plot values of relative permeability as the independent variable.

– Two of the three saturations are independent

• We can plot in 2-D space using two independent (not same direction) coordinates

Ternary Diagrams

• Plot Point for:

Sw=0.30

So=0.25

Sg=0.45

0.00 So 1.00

0.00

S

g

1.00

Three Phase Relative Permeability

• Saturation plotted on ternary diagram

• Lines show constant krw

– parallel to water saturation lines

• krw is function only of water saturation

• for water wet, water is in smallest pores

Three Phase Relative Permeability

• Saturation plotted on ternary diagram

• Lines show constant krg

– approximately parallel to gas saturation lines

• krg is primarily a function of gas saturation

• gas is in largest pores

Three Phase Relative Permeability• Saturation plotted on ternary

diagram

• Lines show constant kro

– not parallel to any saturation lines

• kro is function of both water and gas saturation

• pore size distribution

–water: smallest

–gas: largest

–oil: intermediate size pores

Three Phase Relative Permeability• Lines show constant kro

– not parallel to any saturation lines

• At low gas saturation, kro is a primarily function of oil saturation

• At low water saturation, kro is primarily a function of gas saturation

Three Phase Relative Permeability• Three phase flow occurs over a limited range of three phase

saturations

– outside this range, two phase or single phase flow occurs

Application ofThree Phase Relative Permeability

• Three phase relative permeability data is needed whenever we wish to consider reservoir flow with all three phases present– Three phase lab data is expensive and time consuming– Two phase data is much more common– Many methods have been developed to calculate three phase relative permeability from two

phase curves (water/oil curve and oil/gas curve)

Modeling ofThree Phase Relative Permeability

• Stones Method II– An accepted industry standard

– krg obtained from gas/oil two phase curve as function of Sg

– krw obtained from oil/water two phase curve as function of Sw

– kro for three phase flow obtained from both two phase curves as function of Sg and Sw

– krow, kro from oil/water

– krwo, krw from oil/water

– krog, kro from gas/oil

– krgo, krg from gas/oil

rgorworgorogrworowro kkkkkkk