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
