Introduction to Three Phase Relative Permeability

1
Introduction toThree PhaseRelative Permeability
2
Ternary Diagrams

• Because SoSwSg1, 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
• Sw0.30
• So0.25
• Sg0.45

0.00 Sg
1.00
0.00 So
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 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)

10
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