Effective parameterizations of three nonwetting phase relative permeability models

Describing convective nonwetting phase flow in unsaturated porous media requires knowledge of the nonwetting phase relative permeability. This study was conducted to formulate and derive a generalized expression for the nonwetting phase relative permeability via combining with the Kosugi water retention function. This generalized formulation is then used to flexibly investigate the Burdine, Mualem, and Alexander and Skaggs models’ prediction accuracy for relative nonwetting phase permeability. The model and data comparison results show that these three permeability models, if used in their original form, but applied to the nonwetting phase, could not predict the experimental data well. The optimum pore tortuosity and connectivity value is thus obtained for the improved prediction of relative nonwetting phase permeability. As a result, the effective parameterization of (a; b; g) parameters in the modified Burdine, modified Mualem, and modified Alexander and Skaggs permeability models were found to be (2.5, 2, 1), (2, 1, 2), and (2.5, 1, 1), respectively. These three suggested models display the highest accuracy among the nine relative permeability models investigated in this study. However, the corresponding discontinuous nonwetting phase and the liquid film flow should be accounted for in future for the improved prediction of nonwetting phase relative permeability at very high and very low water saturation range, respectively.