Comparison of relative permeability-saturation-pressure parametric models for infiltration and redistribution of a light nonaqueous-phase liquid in sandy porous media

To test and evaluate the ability of commonly used constitutive relations for multifluid flow predictions, results of numerical flow and transport simulations are compared to experimental data. Three quantitative experiments were conducted in 1-m-long vertical columns. The columns were filled with either a uniform sand, a sand with a broad particle-size distribution, or with a layered system where a layer of a course-textured uniform sand was placed in an otherwise finer-textured uniform sand. After establishing variably water-saturated conditions, a pulse of a light nonaqueous-phase liquid (LNAPL) was injected uniformly at a constant rate. Water and LNAPL saturations were measured as a function of time and elevation with a dual-energy gamma-radiation system. The infiltration and redistribution of the LNAPL were simulated with nonhysteretic and hysteretic parametric relative permeability-saturation-pressure (k-S-P) models. The models were calibrated using two-phase air-water retention data and an established scaling theory. The nonhysteretic Brooks-Corey k-S-P model, which utilizes the Burdine relative permeability model, yielded predictions that closely matched the experimental data. Use of the nonhysteretic and hysteretic k-S-P models, based on the van Genuchten S-P relations and k-S relations derived from the Mualem relative permeability model, did not agree as well with the experimental data as those obtained with the Brooks-Corey k-S-P model. Explanations for the differences in performance of the three tested parametric k-S-P models are proposed.