Relative permeability characteristics necessary for simulating DNAPL infiltration, redistribution, and immobilization in saturated porous media

Abstract

This study presents a relative permeability-saturation (kr-S) constitutive model that incorporates the critical phenomena necessary for simulating the rates of nonwetting fluid infiltration, redistribution, and immobilization in a saturated porous medium. To develop a model validation data set, the migration of a dense, nonaqueous phase liquid (DNAPL) pool within a one-dimensional, 1 m tall, saturated sandpack was monitored under alternating drainage and imbibition conditions. A light transmission/image analysis system, able to distinguish between connected-phase and residual nonwetting phase (NWP) in the apparatus, measured the elevation of the top of the connected-phase DNAPL pool as a function of time. Light transmission calibration curves, correlating fluid saturation to transmitted color at the macroscopic scale, were found to exhibit a functional dependence on saturation history that must be taken into account. Applying the calibration curves to captured images of the experiment provided a continuous sequence of fluid saturation profiles. Numerical simulations of the bench-scale experiment, using model parameters measured independently at the macroscopic scale, predict within measurement uncertainty the observed timescales of DNAPL migration and immobilization. Additional simulations reveal that model validation for imbibition processes depends on properly accounting for NWP kr-S hysteresis, including imbibition function curvature and the abrupt extinction of NWP relative permeability.