Transcript Effective and Relative Permeabilities

Introduction to
Three Phase
Relative 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
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 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)
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
k ro  k row  k rwo k rog  k rgo  k rwo  k rgo
–
–
–
–
krow, kro from oil/water
krwo, krw from oil/water
krog, kro from gas/oil
krgo, krg from gas/oil