The Effect of Saturation History on Three-Phase Relative Permeability: An Experimental Study

We investigate the effect of different saturation histories relevant to various oil displacement processes (including secondary and tertiary gas injections) on three-phase gas/oil/brine relative permeabilities of water-wet sandstone. It is found that three-phase water (wetting phase) relative permeability is primarily a function of water saturation and shows no dependency upon saturation history. Three-phase gas (nonwetting phase) relative permeability is also a function of gas saturation as well as the direction of gas saturation change. Three-phase relative permeability to oil (intermediate-wetting phase) appears to depend on all phase saturations, and saturation history have no significant impact on it. Three-phase oil relative permeability shows weak sensitivity to initial oil saturation prior to gas injection. The functional forms of oil relative permeability with saturation, particularly at low oil saturations, are also examined. It is observed that, at high oil saturations where networks of oil-filled elements govern oil flow, oil relative permeability exhibits a quartic form with oil saturation ðkro / SoÞ whereas, at low oil saturations where flow is believed to be controlled by layer drainage, it shows a quadratic form ðkro / SoÞ. The quadratic form of three-phase oil relative permeability is consistent with the theoretical interpretation of layer drainage at the pore scale.