Calculation of Imbibition Relative Permeability for Two- and Three-Phase Flow From Rock Properties

Abstract

Relative permeability functions are developed for both two- and three-phasesystems with the saturation changes in the imbibition direction.An empirical relation between residual nonwetting-phase saturationafter water imbibition and initial nonwetting-phase saturations isfound from published data. From this empirical relation, expressionsare obtained for trapped and mobile nonwetting-phase saturationswhich are used in connection with established theory relating relativepermeability to pore-size distribution. The resulting equations yieldrelative permeability as a function of saturation having characteristicsbelieved to be representative of real systems. The relative permeabilityof water-wet rocks for both two- and three-phase systems, with thesaturation change in the imbibition direction, may be obtained bythis method after properly selecting two rock properties: the residualnonwetting-phase saturation after the complete imbibition cycle,and the capillary pressure curve.