Modeling Nonwetting‐Phase Relative Permeability Accounting for a Discontinuous Nonwetting Phase

Abstract

Abstract A model for 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 and 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 and 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. The emergence point model for the nonwetting‐phase relative permeability provided a good approximation of the continuous nonwetting‐phase model.