Critical Phenomena of Nonwetting Fluid Infiltration, Redistribution, and Immobilization in Saturated Porous Media

This study presents a capillary pressure-relative permeability-saturation (Pc-kr-S) constitutive model that incorporates the key characteristics necessary for simulating the infiltration, redistribution, and immobilization of nonwetting fluid 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 measured the evolution of the interface between mobile and residual DNAPL as well as providing a continuous sequence of fluid saturation profiles. The terminal pressure is demonstrated to be the minimum sustainable capillary pressure for imbibing nonwetting fluid, below which continuity cannot be sustained and complete residual is formed. A ratio of terminal to entry pressure of approximately 0.6 is found to apply at both bench and macroscopic scales, and to be independent of porous media and fluid properties. Numerical simulations of the bench-scale experiments, using model parameters obtained independently from measured local scale Pc-kr-S hysteretic curves, predict, within measurement uncertainty, the observed equilibrium pool heights and rates of DNAPL migration and immobilization. Constitutive models that do not incorporate both an entry and a terminal capillary pressure, such as those based upon the standard van Genuchten function, are unable to reproduce the observed equilibrium pool heights. Constitutive models that do not properly incorporate nonwetting phase relative permeability hysteresis, including appropriate function curvature and the abrupt extinction of relative permeability at the terminal pressure, are unable to reproduce the observed rates of DNAPL migration and immobilization.