A comparison of relative nonwetting-phase permeability models

We compared three groups of models commonly used to describe the dependence of relative nonwetting-phase permeability on phase saturation in porous media and tested the capability of these models to predict relative air permeabilities using two experimental data sets. The first group of models is purely empirical, involving no fitting parameters. In models of the second type, denoted here as geometry-based models, relative nonwetting-phase permeability is derived from the wetting-phase retention curve on the basis of an idealized concept of pore space geometry. According to these models, nonwetting-phase permeability should vary over the full range of saturation and should be a function of total nonwetting-phase saturation. In models of the third type this variation is limited to a narrower range based on the concept that only part of the nonwetting phase contributes to permeability and assuming that the relationship between the "effective" saturation of this continuous nonwetting phase can be described by the same mathematical functions as between total nonwetting-phase saturation and relative permeability in the geometry-based models. Since this implies some kind of analogy, we refer to this group of models as "analogy-based." We found that matching the saturation at which nonwetting-phase permeability emerges, i.e., the emergence point, is crucial for the description or prediction of relative nonwetting-phase permeability in the range of high wetting-phase saturations. Using analogy-based models which were derived from the geometry-based models by simply rescaling the effective saturation range to fit this endpoint, predictions were found to depend sensitively on whether the Burdine or the Mualem model was chosen to relate the permeability function to the retention curve. Differences between these two approaches were found to be primarily due to the different exponents in the tortuosity term. When we made this parameter flexible and determined it by curve-fitting from measured data, we obtained very good fits of experimental air permeabilities.