Modeling nonwetting-phase relative permeability accounting for a discontinuous nonwetting phase

A model Par the wetting and nonwetting-phase constitutive relationships is presented. The nonwetting-phase relative permeability in the model is a function of the degree of continuous nonwetting-phase saturation. Different formulations of the continuous nonwetting-phase model were evaluated by comparison of calculated anti measured air permeabilities as well as discontinuous air saturations. A Brooks and Corey-Burdine type formulation of the nonwetting phase relative permeability was more accurate than the corresponding van Genuchten-Mualem equation. Estimated discontinuous air saturations were higher for drying than for wetting, thus reflecting hysteresis in the water-retention smd relative air permeability functions. The continuous nonwetting-phase model provided a much better prediction of relative air permeabilities than a formulation that neglects the presence of a discontinuous nonwetting phase. Three emergence point model for the nonwetting-phase relative permeability provided a good approximation of the continuous nonwetting-phase model.