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 me dia and tested the capability of these models to predict relative air perme abilities using two experimental data sets. The first group of models is pu rely empirical, involving no fitting parameters. In models of the second ty pe, denoted here as geometry-based models, relative nonwetting-phase permea bility is derived from the wetting-phase retention curve on the basis of an idealized concept of pore space geometry. According to these models, nonwe tting-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 conc ept that only part of the nonwetting phase contributes to permeability and assuming that the relationship between the "effective" saturation of this c ontinuous nonwetting phase can be described by the same mathematical functi ons as between total nonwetting-phase saturation and relative permeability in the geometry-based models. Since this implies some kind of analogy, we r efer to this group of models as "analogy-based." We found that matching the saturation at which nonwetting-phase permeability emerges, i.e., the emerg ence point, is crucial for the description or prediction of relative nonwet ting-phase permeability in the range of high wetting-phase saturations. Usi ng analogy-based models which were derived from the geometry-based models b y simply rescaling the effective saturation range to fit this endpoint, pre dictions were found to depend sensitively on whether the Burdine or the Mua lem model was chosen to relate the permeability function to the retention c urve. Differences between these two approaches were found to be primarily d ue to the different exponents in the tortuosity term. When we made this par ameter flexible and determined it by curve-fitting from measured data, we o btained very good fits of experimental air permeabilities.