1. Introduction to Three Phase Relative Permeability
Effective and Relative Permeabilities 1
Introduction to Three Phase Relative Permeability

2. 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

3. Ternary Diagrams Plot Point for: Sw=0.30 So=0.25 Sg=0.45 0.00 Sg 1.00

4. 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

5. 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

6. 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

7. 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

8. 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

9. Application of Three 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)

10. Modeling of Three 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