Comparison of relative permeability–fluid saturation–capillary pressure relations in the modelling of non-aqueous phase liquid infiltration in variably saturated, layered media

The characteristic functions relating relative permeabilities and capillary pressures to fluid saturations (kr–S–Pc models) are of great importance for the modelling of sub-surface multi-phase flow and transport. In order to test their performance and to identify their important parameters, four well-known three-phase kr–S–Pc models have been tested against published experimental data on non-aqueous phase liquid (NAPL) migration in the unsaturated zone. Both homogenous systems and systems with embedded heterogeneities have been analysed.The results show that although there are differences between predictions based on the different models, all models exhibit some common problems and it is not obvious that any one model is more accurate than the other three. However, with the inclusion of a non-linear NAPL tortuosity factor, both the Brooks–Corey–Burdine and van Genuchten–Mualem models yield excellent fits to experimental data.For NAPLs with non-zero spreading coefficients no exact theory currently exists for scaling two-phase capillary pressure–saturation functions to three-phase systems. Different ways of applying the Parker et al. [Parker JC, Lenhard RJ, Kuppusamy T. A parametric model for constitutive properties governing multi-phase flow in porous media. Water Resour Res 1987;23:618–24] scaling method have therefore been tested. It was found that since the NAPL–gas capillary pressure function has the strongest influence on NAPL migration, the scaling procedure should focus on accuracy in this function.