The influence of field-scale heterogeneity on the infiltration and entrapment of dense nonaqueous phase liquids in saturated formations

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Abstract

Numerical simulations are used for the systematic exploration of the migration and entrapment of dense nonaqueous phase liquids (DNAPLs) in heterogeneous formations. Ensembles of realizations of random, spatially correlated permeability fields are generated and employed in model simulations of a spill event. Statistical techniques are then used to quantify the sensitivity of model predictions to input parameters, thereby identifying the parameters or processes that may be of primary importance in the determination of organic liquid distributions in heterogeneous systems. Results of the study indicate that the most critical factors in modeling organic entrapment include the spill release rate, reliable estimates of the mean, variance, and vertical correlation scale of the formation permeability, and an accurate representation of the correlation between the capillary pressure–saturation function and the permeability. In contrast, the hydraulic gradient and cross-correlation of residual saturations with permeabilities are found to have only minor influence on organic liquid distributions in such heterogeneous formations.

Introduction

The migration and entrapment of organic liquids in the subsurface has been a subject of active research in recent years, primarily due to the critical impact of subsurface organic liquid entrapment on long-term groundwater quality (Abriola, 1989; Mercer and Cohen, 1990; Kueper et al., 1993). Of particular concern is the behavior of dense nonaqueous phase liquids (DNAPLs) which frequently migrate under pressure and gravity forces to depths beneath the water table, where they may pool on less permeable layers and become entrapped as an immobile residual (Schwille, 1988). The presence of DNAPLs at hazardous waste sites has been well documented (e.g., Faust, 1985; Schwille, 1988; Mercer and Cohen, 1990). Major sources of DNAPL waste are dry cleaning and industrial degreasing operations, both of which primarily use chlorinated hydrocarbons. Trichloroethylene, tetrachloroethylene (PCE), and 1,1,1-trichloroethane are some of the more commonly used degreasers, and are among those compounds most frequently detected at contaminated sites identified by the CERCLA national priorities list. Because DNAPLs usually exhibit low aqueous solubility and are typically difficult to detect and relatively inaccessible in natural formations, they represent a highly persistent source of environmental contamination, posing unique challenges to environmental remediation efforts (National Research Council, 1994). The problem of DNAPL remediation is made more complex in heterogeneous natural formations, in which formation variability can cause highly irregular distributions of DNAPLs in the subsurface (Essaid et al., 1993; Kueper et al., 1993). An improved understanding of the migration and entrapment of DNAPLs, particularly in heterogeneous subsurface systems, should aid in the characterization of contaminant sources in the field and in the assessment of the performance of remedial technologies.

Many properties related to the prediction of multiphase flow typically vary spatially in natural porous media over several scales. These scales range from: (1) the molecular level, at which surface properties may influence wettability, (2) to the scale of individual pores (microscale) at which topology influences entrapment behavior, (3) to the macroscale, at which the flow can be modeled using continuum concepts, and (4) to the megascopic or field scale at which variability in properties may be described as trends which vary over meters or even kilometers (Bear, 1972; Freeze and Cherry, 1979). The work presented in this paper defines heterogeneity as spatial variability in parameters which occurs at scales in the macroscopic to megascopic range, or in the range of centimeters to meters.

Numerous studies have presented conceptual and mathematical models for multiphase flow in porous media (e.g., Abriola, 1989; Kueper and Frind, 1991a; Kaluarachchi and Parker, 1992). While such mathematical models were typically developed for heterogeneous systems, most model applications have been restricted to homogeneous systems. More recently, the application of multiphase modeling approaches to heterogeneous formations has been undertaken (Kueper and Frind, 1991aKueper and Frind, 1991b; Essaid and Hess, 1993; Kueper and Gerhard, 1995). These studies have highlighted the importance of variability of permeability and capillary parameters on organic liquid spreading.

Kueper and Frind (1991b) and Essaid and Hess (1993) demonstrated the application of multiphase flow simulators in conjunction with a random field generator (Mantoglu and Wilson, 1982) to predictions for a spatially correlated heterogeneous parameter field. Their results indicated a significant influence of heterogeneity on the spreading of infiltrating organic liquid spills, even for relatively low degrees of heterogeneity such as that observed at the Borden site, a stratified, sandy aquifer formation located at the Canadian Air Forces Base in Borden, Ontario. In these studies, the intrinsic permeability, k, was treated as the primary heterogeneous variable, described statistically with a lognormal distribution (Hoeksema and Kitanidis, 1985; Sudicky, 1986; Hess et al., 1992). In example simulations, correlation of capillary pressure and relative permeability parameters to the primary k variable was shown to have a signficant effect on the degree of spreading observed. Field observations, both of existing spills and of controlled releases of dense organics, provide some experimental verification of the trend of increased spreading with heterogeneity observed in these numerical studies. In general, a relatively small degree of horizontal bedding has been observed to result in a pronounced preferential lateral migration of organic (Essaid et al., 1993; Kueper et al., 1993). Such behavior can be reproduced by numerical simulators only when heterogeneity in permeability and capillary pressure parameters is incorporated (Kueper and Frind, 1991b; Essaid and Hess, 1993).

Experiments performed at the column scale give strong evidence for the dependence of residual wetting and nonwetting phase saturations on the pore-scale properties of the medium, such as particle and pore-throat diameters (Hoag and Marley, 1986; Kia, 1988; Mayer and Miller, 1992; Powers, 1992). Since pore-scale topology also influences macroscale permeability, it is likely that observed macro-scale variability in residual saturations will be linked to variability in permeability. The influence of spatially variable residual wetting and nonwetting phase saturations on predictions of multiphase flow and entrapment has not been systematically examined to date.

The influence of source size and strength on the infiltration rate and conformation of an organic liquid spill was explored by Kueper and Gerhard (1995), through the use of multiple realization simulations of a permeability field. Infiltration rates were found to be highly variable, depending strongly on the size of the source relative to the correlation structure of the permeability field. The wide variability among individual predictions for different realizations observed by Kueper and Gerhard (1995) suggests that single-realization simulations may give little insight into expected mean model behavior. Thus, a comprehensive exploration of the interplay between heterogeneity and other model input parameters will, in general, require a multiple realization approach.

Given the demonstrable effect of formation heterogeneity described above and the broad range of parameters which might be considered spatially heterogeneous in natural media, there exists a clear need to identify the parameters which exert primary control over the migration of organic liquids in typical field spill scenarios. To date, a systematic study of the effect of heterogeneity on organic liquid distribution and entrapment has not been undertaken. An enhanced understanding of the processes governing flow and entrapment in heterogeneous systems will make it possible to determine those critical to the modeling of such systems and to identify key parameters which must be estimated for model application. To this end, a series of multiphase flow simulations is undertaken in the present work to explore infiltration and redistribution of a DNAPL in a heterogeneous formation. The influence of heterogeneity in material properties is considered, in terms of variance and correlation structure. Statistical methods are used to analyze the sensitivity of model predictions to both input parameters and parametric models for ensembles of realizations of spatially correlated random permeability fields. An analysis of the variance of output metrics of the model is used to identify primary effects which control model behavior.

Section snippets

Mathematical formulation

Migration of a spill of a dense organic liquid in a water saturated porous medium can be described by two (organic (o), water (w)) phase mass balance equations incorporating a modified Darcy's law expression for the specific discharge (Abriola, 1989):t[φsβρβ]=·ρβkkμβ·(Pβ−ρβgz)+Qβwhere β=o,w denotes the liquid phase, φ is the porosity of the medium, sβ is the saturation of phase β, ρβ is the density of the phase [M L−3], k is the permeability tensor [L2], k is the relative permeability

Parameter variability

The hydraulic properties of soils have long been recognized as stochastic quantities, or quantities which vary spatially with an element of randomness (Russo and Bressler, 1981; Hoeksema and Kitanidis, 1985). Of primary research interest in recent years has been the hydraulic conductivity, which has frequently been shown to be well described statistically using either normal or exponential distributions for ln(K) (Sudicky, 1986; Woodbury and Sudicky, 1991). The hydraulic conductivity in aquifer

Base simulation scenario

In order to explore the behavior of a typical organic spill in a heterogeneous setting, a base simulation scenario was defined describing a release of PCE in a field-scale domain. The base scenario is comprised by a 5×10 m vertical cross-section of a saturated, sandy aquifer having the permeability distribution and spatial correlation characteristics of the Borden aquifer (Fig. 1). A summary of the input parameters used in the base simulations is presented in Table 1. The relatively mild degree

Statistical methods

While a single simulation of the type presented in Fig. 4 provides a quantitative description of NAPL flow and entrapment in a particular heterogeneous system, a more meaningful description of spill behavior in a heterogeneous system requires examination of a series of spills conducted in different manifestations, or realizations, of the permeability field. A set of four sample simulation results is shown in Fig. 5, illustrating the variability in model output among realizations. A sufficiently

Simulation results

The statistical approach outlined above makes it possible to identify important model input parameters or parametric representations by quantifying the variability which each contributes to the model output. It was found that analysis of model behavior for 15 to 20 realizations of the generated permeability field (i=15–20) gives a stable estimate of variance of model output parameters. An example is presented in Fig. 6, in which the variance of spreading is estimated for the Swiss formation

Conclusions

This study was performed to explore the sensitivity of numerical model predictions of dense NAPL migration and entrapment to physical parameter variation in a sandy porous medium exhibiting well-defined structural heterogeneity. A simulator incorporating heterogeneity in a number of potentially significant parameters was used to simulate DNAPL infiltration in a medium with the lognormal permeability distribution and spatial correlation structure of the Borden formation. Numerous simulations

Acknowledgements

Funding for this research was provided by the Office of Research and Development, US Environmental Protection Agency under Grant R815710 to the Great Lakes and Mid-Atlantic Hazardous Substance Research Center. Partial funding for HSRC research activities was also provided by the Michigan Department of Natural Resources. Additional funding was provided by the National Science Foundation under Grant EID-9023090. The research described in this article has not been subject to Agency review and,

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