Capillary Pressure Characteristics Necessary for Simulating DNAPL Infiltration, Redistribution, and Immobilization in Saturated Porous Media

This study presents a capillary-pressure saturation (PC-S) constitutive model that incorporates the capillary phenomena necessary for simulating the spatial distribution of nonwetting fluid migrating in a saturated porous medium. To develop a model validation data set, a sequence of dense, nonaqueous phase liquid (DNAPL) pools were emplaced, under alternating drainage and imbibition conditions, in a one-dimensional, 1 m tall, saturated sand pack. A light transmission/image analysis system successfully distinguished between connected-phase and residual nonwetting fluid in the apparatus, thereby permitting the accurate measurement of DNAPL pool heights. These heights are found to depend on the nonzero capillary pressure across the fluid-fluid interface at the top of the pool. The terminal pressure is demonstrated to be the minimum sustainable capillary pressure in connected-phase nonwetting fluid experiencing imbibition, below which residual is formed. Additional bench-scale experiments demonstrate that a nonwetting phase pool will penetrate an underlying capillary barrier when the entry pressure is exceeded and that the resulting infiltration will terminate when the capillary pressure at the barrier reduces to the terminal pressure. At the macroscopic scale the terminal pressure corresponds to the extinction saturation (i.e., zero nonwetting phase flow) at the inflection point on the imbibition PC-S curve. 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. The developed PC-S constitutive model, which extends the Brooks-Corey function to incorporate the terminal pressure, successfully predicted the behavior observed in the laboratory experiments. Constitutive models that do not incorporate both an entry and a terminal pressure, such as those based upon the standard van Genuchten function, are demonstrated to be unable to predict the observed equilibrium DNAPL pool heights in homogeneous media or above capillary barriers

Relative Permeability Characteristics Necessary for Simulating DNAPL Infiltration, Redistribution, and Immobilization in Saturated Porous Media

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

Influence of Constitutive Model Parameters on the Predicted Migration of DNAPL in Heterogeneous Porous Media

This study examines the influence of constitutive models and their parameters on predictions of the spatial and temporal distribution of a finite release of a dense, nonaqueous phase liquid (DNAPL) into a two-dimensional, spatially correlated random permeability field. The base case simulation employed a comprehensive constitutive model that was validated against relevant one-dimensional laboratory experiments. The base case was perturbed in the course of nine individual simulations, where each simulation examined the consequences of simplifying a single model characteristic. None of the nine subsequent simulations was able to reproduce, within ±10%, the spatial and temporal migration characteristics of the nonwetting fluid body at late time predicted by the base case. Capillary pressure-saturation relationships that do not incorporate specific displacement and terminal pressures are demonstrated to severely overpredict the spatial extent of nonwetting fluid advancement. This suggests that van Genuchten-based models may not be suitable for predicting DNAPL migration in saturated porous media. Not accounting for any one of hysteresis, nonwetting phase trapping, or the proper curvature or end-point values of the nonwetting phase imbibition relative permeability curve profoundly influenced the time predicted for all nonwetting fluid movement to cease. The practical implication of this study is that an appropriate, comprehensive constitutive model, characterized with suitable parameter values, is necessary to accurately simulate a complete DNAPL release below the water table in both space and time

Field Scale Impacts of Spatially Correlated Relative Permeability in Heterogeneous Multiphase Systems

Two-dimensional numerical simulations of two-phase (DNAPL-water) flow in spatially correlated random fields demonstrate the influence of nonwetting phase (NWP) relative permeability–saturation (kr,N–SW) relationships correlated to porous media intrinsic permeability (k). Both the volume of porous media invaded by the NWP and the length of time during which the NWP is migrating are under predicted if kr,N–k correlation is not accounted for in the model formulation. Not accounting for the kr,N–k correlation resulted in under predicting the volume of porous media invaded by up to approximately 10%, which is likely not significant for many practical applications. However, not accounting for the kr,N–k correlation resulted in under predicting field scale migration times by up to a factor of 4, which is likely significant in that the migration times are on the order of years to several decades for the DNAPL (1,2-DCE) considered in this study. The under prediction of migration times was greater for lower permeability aquifers