Convergence of DNAPL Source Strength Functions with Site Age

Nov 20, 2009 - These authors concluded that site age combined with the effects of field-scale heterogeneities in travel time and DNAPL content distrib...
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Environ. Sci. Technol. 43, 9374–9379

Convergence of DNAPL Source Strength Functions with Site Age X. CHEN AND J.W. JAWITZ* Soil and Water Science Department, University of Florida, Gainesville, Florida 32611

Received July 14, 2009. Revised manuscript received November 4, 2009. Accepted November 6, 2009.

Dissolution of dense nonaqueous phase liquid (DNAPL) source zones can be accurately predicted based on appropriate characterization of the source zone architecture, which controls the rate of mass discharge or source strength function. However, the architecture changes temporally as the source zone mass is depleted by dissolution. To generalize comparisons between contaminated sites with different porewater velocities or contaminant solubilities, site age is defined in terms of the fraction of contaminant mass that has been eluted from the source zone by aqueous dissolution. Here changes in DNAPL architecture during dissolution of a source zone were measured by light transmission visualization in laboratory flow chambers. Architectures measured at ages corresponding to initial conditions, 20, 50, and 90% mass removal were used in an equilibrium streamtube (EST) model to accurately predict subsequent dissolution. It is shown both experimentally and theoretically that as DNAPL contaminated sites age, fractional reductions in contaminant discharge and mass converge to become equal, regardless of the initial architecture. This behavior is a consequence of convergence from lognormal to exponential behavior. Analysis of errors in dissolution predictions suggests that the age of many contaminated sites is likely sufficient that architecture and source strength function characterization may not be necessary as it can be assumed with reasonable accuracy that future dissolution will follow an exponential decay model.

Introduction Aquifer heterogeneity and contaminant architecture are important factors controlling dense nonaqueous phase liquid (DNAPL) dissolution dynamics. Appropriate characterization of these parameters can facilitate prediction of DNAPL source zone dissolution behavior. Several simple models have been introduced to describe source zone dissolution behavior (1-8). The parameters of these models are related either mechanistically or empirically to source zone architecture. Here architecture refers to the combined effects of heterogeneity of both the porous media and the contaminant spatial distribution. The former can be assumed as an intrinsic property that is temporally invariant and insensitive to minor effects such as relative permeability changing with DNAPL content. However, the contaminant spatial distribution does change as mass is removed from the system. Therefore model parameters describing DNAPL architecture are a function of the age of the contaminated site, where age is defined here as the fraction of the initial source zone mass that is present at the time of characterization. * Corresponding author phone: 352-392-1951, x203; fax: 352-3923902; e-mail: [email protected]. 9374

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The temporal evolution of DNAPL dissolution is usually described with a concentration vs time breakthrough curve (BTC). In recognition of the technical difficulty of complete mass removal, even with aggressive treatment, recent studies have emphasized the effect of partial mass removal on fluxaveraged concentration exiting the source zone (3, 4, 6, 9-11). Water flow is often assumed to be steady-state such that changes in flux-averaged concentration are equivalent to changes in mass discharge or flux across a control plane at the downgradient source zone boundary. Consistent with previous work (1, 3), we define fractional reductions in source zone mass and downgradient flux, Rm and Rj, as ratios of the change in mass and flux to their initial values at the time of characterization. At the initial time considered (such as contaminant release or initial characterization) Rm ) Rj ) 0, and these parameters increase with site age until reaching final values of one when the source zone has been completely removed. For relatively homogeneous architectures even large reductions in contaminant mass may result in only marginally reduced flux. Such conditions are deemed “unfavorable” for reduction of risk from contaminant mass removal. It has been shown that greater architecture heterogeneity leads to more favorable conditions (3, 10, 12). That is, for a given percentage removal of contaminant mass, the resulting reduction in discharge increases with heterogeneity. Jawitz et al. (3) quantified this effect using an analytical relationship between fractional reductions in flux, Rj, and mass, Rm, based on a Lagrangian definition of source zone architecture heterogeneity. In this framework the travel time and trajectory-integrated DNAPL content distributions are jointly considered as a reactive travel time distribution, and the statistics of this distribution control the dissolution behavior. Further, because these properties can be measured directly, dissolution can be predicted with a simple analytical expression that is a function primarily of the reactive travel time distribution standard deviation, σlnτ. Successful applications have been demonstrated for DNAPL architectures of varying heterogeneity in both laboratory experiments and numerical modeling exercises (1, 2, 12, 13) However, it is emphasized that the reactive travel time distribution changes during dissolution. Thus, both the measures of architecture heterogeneity and the resulting predicted Rj(Rm) relationship depend on the site age at the time of characterization. Jawitz et al. (3) showed analytically that as dissolution progressed, Rj(Rm) for the remaining mass became more favorable for homogeneous architectures, with the opposite trend for very heterogeneous architectures. Moderately heterogeneous architectures did not change significantly during dissolution. With continued mass depletion, all cases converged to a condition of approximately equal fractional flux reduction for a given mass reduction. These authors concluded that site age combined with the effects of field-scale heterogeneities in travel time and DNAPL content distributions will place many real contaminated sites in the midrange of the family of Rj(Rm) curves, with near equivalent flux reduction for a given mass reduction. The convergence to a 1:1 relationship between changes in discharge and mass has been shown to correspond to exponential decay in source zone concentration, C(t) (4, 8, 10):

(

C(t) ) C0exp -

vdAC0 t M0

)

(1)

where vd is the average Darcy velocity, A is cross-sectional area, and C0 is the flux-averaged contaminant concentration 10.1021/es902108z

 2009 American Chemical Society

Published on Web 11/20/2009

FIGURE 1. Change in PCE saturation with time, based on LTV analysis, for all five experiments. Low-permeability zones (hatched areas) are shown only in the initial view (0 PV). Frame dimensions 30 × 20 cm. at the source zone control plane corresponding to source zone mass M0 at an initial time of characterization that could be at any time during the history of the source zone. These authors have described this condition as a special case of a general power function model to describe the change in source zone mass discharge, or source strength function:

( )

M(t) C(t) ) C0 M0

Γ

(2)

where Γ is an empirical measure of the architecture heterogeneity that must be calibrated to site-measured dissolution data. The special case of Γ ) 1 is equivalent to exponential decay in source discharge and mass (1:1 correspondence). Lacking theoretical linkage to measurable site characteristics, Γ ) 1 has been proposed or otherwise assumed as a “middle-of-the road” approach (4, 6) and to facilitate development of analytical solutions (8, 10). DiFilippo and Brusseau (14) analyzed field data from 21 source-zone remediation projects representing 12 different sites and studied the Rj(Rm) curves by fitting Γ using eq 2. The Γ values for the majority of the data (almost 85%) were reported between 0.5 and 2, and nearly one-third fell on the 1:1 line. These authors did not assess the relative contributions of DNAPL architecture and site age to the observed Rj(Rm) behavior. This paper seeks to provide a link between the empirical source strength functions in common use and the mechanistic Lagrangian model that is based on measurable, but age-dependent, site characteristics. This work extends our previous theoretical site age analysis (3) with laboratory experiments to understand how source zone architecture changes with mass depletion. Further, while our previous work showed evidence for convergence of Rj(Rm) to 1:1

behavior with site age, here we develop the theoretical explanation for why this behavior can be expected. This theoretical foundation is used to provide guidance related to the expected BTC prediction errors arising from broadly assuming 1:1 behavior even in the absence of sufficient data to characterize source strength function.

Laboratory Experiments Five DNAPL dissolution experiments were conducted with surfactant flushing tests (2% Tween-80/water) in a twodimensional flow chamber packed with porous media and contaminated by tetrachloroethylene (PCE, Acros spectrophotometric grade, 99+%). The flow chamber was constructed of two 5.5 mm thick glass sheets clasped on a U-shape 1.5-cm square aluminum tubing frame, resulting in a 30 × 20 × 1.7 cm experimental chamber (13). Well characterized 20/30 mesh Accusand (16) was introduced into the chamber and lower-permeability 40/60 sand was interspersed heterogeneously as layers into the otherwise homogeneous coarser sand. The measured bulk densities of the packings were ∼1.7 g/cm3 with porosities ∼0.35. Teflon tape was applied to the porous media-air interface to minimize DNAPL volatilization. The PCE was injected into the upper portion of the domain at 0.5-1.5 mL/min by a syringe pump to create different architectures (Figure 1). Observed redistribution of the PCE was complete approximately 24 h after injection. Following redistribution, approximately 20 pore volumes (PVs) of surfactant solution were continuously pumped through the chamber until either more than 95% of the PCE was removed or the effluent concentration was lower than the gas VOL. 43, NO. 24, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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TABLE 1. Comparison of Initial, Pre-Remediation NAPL Architecture Characterization by Tracer and LTV Methods for All Five Experimentsa EST model parameters PCE mass (mL) injected exp exp exp exp exp

1 2 3 4 5

12.0 9.32 4.40 8.25 3.20

µlnSˆ

σlnSˆ

rRMSE

σlnτ

LTV

tracer

Γ

LTV

tracer

LTV

tracer

LTV

tracer

EST

Γ)1

10.7 9.62 4.19 8.14 3.29

13.0 9.85 4.24 8.30 3.75

1.62 1.30 1.10 0.76 0.46

-4.15 -4.10 -4.75 -3.86 -4.60

-4.02 -3.93 -4.70 -3.78 -4.48

1.25 1.12 0.94 0.66 0.33

1.30 0.98 0.92 0.57 0.38

1.19 1.02 0.76 0.58 0.33

1.25 0.89 0.78 0.62 0.36

0.15 0.12 0.18 0.17 0.15

0.94 0.66 0.20 0.58 0.71

a The rRMSE values are based on comparison between measured dissolution data and EST and exponential decay models.

chromatography analytical detection limit (∼1 mg/L). Solubility of PCE in the surfactant solution, Cs, was approximately 8600 mg/L. Preremediation tracer tests were conducted to characterize the DNAPL architecture at flow rates between 0.2 and 0.5 PV/h using methods described elsewhere (13). Methanol was applied as the nonpartitioning tracer, and 2,4-dimethyl-3pentanol (Acros, 99%) was the partitioning tracer. Light transmission visualization (LTV) was used to study how the DNAPL architecture changed during dissolution, with images collected every 1-2 PVs during dissolution. Although typically limited to laboratory-scale application for thin flow cells, LTV methods present the advantages of nonintrusive and nondestructive measurement and capability of providing both local and instantaneous DNAPL distribution mapping directly. The LTV method employed a dyed water phase, which avoided assumptions regarding the structure of phase interfaces and uncertainties associated with differential solubilization of DNAPL and DNAPL-phase dye (17) (further method details in the Supporting Information (SI)).

Dissolution Modeling Jawitz et al. (3) proposed an equilibrium streamtube (EST) model based on conceptualizing a porous medium as a collection of noninteracting streamtubes (15, 18) to predict DNAPL dissolution. In this framework, the trajectorySN is DNAPL integrated DNAPL content (k S)k SNη/θ, where k saturation, η is porosity, and θ is water content) is integrated along the flowpath through the source zone for each streamtube. The distribution of k S values for all streamtubes describes the DNAPL spatial distribution. Note that while k SN exhibits a range of [0,1], the range for k S is [0, ∞], which is consistent with the common probability distributions, such as log-normal and gamma, that may be used to characterize the heterogeneity of this parameter (3). The reactive travel time,τ ) t(1 + FNSˆ/Cs), where t is nonreactive travel time and FN is DNAPL density, is defined as the dissolution/flushing duration required to deplete DNAPL from a streamtube. The overall dissolution behavior is controlled by the distribution of τ values for all streamtubes (3). The τ distribution parameters µlnτ and σlnτ are determined from the measured characteristics of the t and k S distributions as shown in SI eqs SI-1-SI-4. The τ distribution parameters were obtained from preflushing tracer tests, and LTV data were also used to estimate the critical parameter σln kS at different times as dissolution progressed. For the latter method, horizontal straight flow trajectories were assumed and DNAPL contents were summed along pixel rows (1, 12). In the absence of partitioning tracer data for estimating both travel time and DNAPL content variability, Fure et al. (12) obtained good prediction of the DNAPL dissolution behavior by assuming the travel time variability to be zero. 9376

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In a suite of numerical modeling exercises, Basu et al. (1) found σlnτ to be relatively insensitive to σlnt. Thus, in this paper σlnt was assumed zero and the equation for σlnτ was simplified as described in SI eqs SI-5 and SI-6. This assumption results in an underestimation of σlnτ that was found to not significantly affect the results, as described below. The flux averaged concentration at time since the contaminant release, t, can then be related as simply (adapted from 1, 12): Cf(t) ) fcCs(1 - fQ,c) ) fcCsmτ0(t, ∞)

(3)

where fc is the fraction of the streamtubes that are contaminated, which can be estimated as the ratio of the initial flux-averaged concentration to the aqueous solubility of the contaminant, and fQ,c is the fraction of the total flow that is discharged from the clean zone. The latter term can be calculated from the frontally truncated zeroth moment of the τ distribution, mτ0(t,∞), where t and ∞ represent the upper and lower limits for the moment integral (19).

Results and Discussion Initial DNAPL Distribution and Dissolution Prediction. The preremediation (0 PVs of surfactant flushed) source zone PCE saturation distributions for the five experiments are shown in the first column of Figure 1. The PCE architecture varied due to the different injection rates of PCE and structures of layers. The ratio of PCE mass determined from LTV analysis to the known injection amount were between 0.89 and 1.03 for the five experiments. Similar accuracy in mass estimates was obtained from the partitioning tracer tests (Table 1). The value of σln kS estimated from moment analysis of partitioning tracers was within 5% of the LTVbased value (Table 1). These results indicate that LTV methods can be applied as an alternative to tracer tests for characterizing DNAPL architecture. The changes in DNAPL distribution at 2 and 10 PVs are also shown for the five experiments in Figure 1. Different experiments achieved different mass removal for the same flushing duration. For example, after 10 PV flushing, the removal ranged from 60% for experiment 1 to nearly 100% for experiment 5. No DNAPL was observed in previously clean locations, which indicated that no obvious mobilization occurred during the flushing process. Architecture heterogeneity increases with σlnτ (3), thus the initial conditions in experiments 1-5 were decreasingly heterogeneous (Table 1). Measured BTCs and Rj(Rm) curves illustrative of different degrees of heterogeneity are shown in Figure 2 for experiments 2, 3, and 5. Predicted BTCs based on the EST model (eq 3) are also compared in Figure 2a. The average relative root-mean-square error (rRMSE, SI SI-7) between the complete BTCs predicted by the streamtube model and the experimental data was 0.15 ( 0.02 for five experiments (Table 1). Note that the dissolution prediction

FIGURE 2. (a) Measured BTCs and LTV-based EST model predictions (solid lines) for representative experiments 2, 3, and 5. Dashed lines are exponential model predictions based on LTV characterization of aged conditions at Rm ) {0.2,0.5,0.9}. Empty circles indicate these new initial conditions. (B) Evolution of Rj(Rm) with age.

FIGURE 3. (a) Convergence of σlnτ with mass removal for all five experiments, and (b) convergence of CV to 1 with mass removal for the distal portion of the zeroth moment of reactive travel time distribution. The value of σlnτ,0 is the reactive travel time distribution standard deviation under initial conditions (Rm ) 0). rRMSEs were within 8% of these values when the σlnt measured by the nonpartitioning tracer was used (rather than assuming this value ) 0), consistent with prior findings (1). As shown in Table 1, the BTC prediction errors obtained from assuming first order decay (Γ ) 1) were significantly higher than from the EST model for the most heterogeneous and most homogeneous architectures (experiments 1 and 5), but were similar for those in the midrange (experiment 3). Also shown in Table 1 are posterior best-fit values of Γ from fitting eq 2 to the measured Rj(Rm) curves. The LTV images captured at dissolution times corresponding to 0.2, 0.5, and 0.9 PCE mass removal were analyzed to obtain new σlnτ values which were taken as the initial condition for predicting subsequent dissolution. Both the heterogeneous and homogeneous cases converged to oneto-one Rj(Rm) behavior as dissolution progressed (Figure 2b), as predicted by theoretical considerations (compare to Figure 6 of ref 3). Experiments 2, 3, and 5 are shown as representative cases, the other experiments behaved similarly. The change in LTV-measured σlnτ with mass removal is shown in Figure 3a for all five experiments. The initial conditions for the more-homogeneous experiment 5 (σlnτ

)0.33) were relatively unfavorable for flux reduction compared to the more-heterogeneous experiment 1 (σlnτ ) 1.19). But σlnτ varied continuously during dissolution and after 50% of the mass was removed, σlnτ converged to between 0.5 and 0.9 for all five experiments (Figure 3a). When 90% of the initial mass had been removed the range of values for σlnτ had narrowed to 0.73 ( 0.05 (the value for Rm ) 0.9 in experiment 1 was unavailable due to the longevity of source zone in this highly heterogeneous case and the experiment was stopped after 20 PV of flushing, corresponding to 72% mass removal). Explanation of Convergence Behavior with Site Age. The EST model is based on log-normal distributions of travel time, DNAPL content, and reactive travel time. In this framework, increasing DNAPL architecture heterogeneity is quantified as increased variance of the lognormally distributed reactive travel times. Both experimental (12) and numerical (1) studies have supported the concept of lognormally distributed reactive travel times to characterize the DNAPL source zone architecture and predict dissolution. In the EST framework, as dissolution progresses streamtubes with increasing τ values are sequentially cleaned. Thus, VOL. 43, NO. 24, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 4. Relative root-mean-square error (rRMSE) between the BTC predictions based on the EST and exponential models, shown as a function of architecture heterogeneity (σlnτ) and site age (Rm). Each point is also labeled for reference with the number of pore volumes of surfactant flushing required to achieve a given Rm in these experiments. the source zone dissolution process can be conceptualized as a progressive truncation of the reactive travel time distribution, and quantified specifically as the progressive truncation of the zeroth moment of the log-normal τ distribution as shown in eq 3. Here we show that as the frontal portion of the zeroth moment of a log-normal distribution is truncated, the remaining distal or tail portion converges to an exponential distribution. Because exponential decay of source zone mass and discharge leads to a one-to-one Rj(Rm) relationship, it therefore follows that the source strength functions of all lognormally distributed architectures can be expected to converge with site age to one-to-one Rj(Rm) and exponential decay in discharge. The EST model framework enables a theoretical linkage between site characteristics and the site age (time or mass removed) required to reach this stage. That such behavior has been observed at many sites (14) may be an indication of the relatively high site ages of many contaminated sites. A characteristic of the exponential distribution is that the coefficient of variation (ratio of standard deviation to mean), CV ) 1. The CV of a truncated distribution can be calculated based on the truncated moment equations developed by Jawitz (19) (see SI). When an exponential distribution is progressively frontally truncated, the mean remains equal to the standard deviation, and thus the CV of the distal portion of the truncated distribution is not a function of truncation point. However, the CV of the distal portion of the truncated zeroth moment of a log-normal distribution is a function of truncation point. SI eqs SI-9-SI-12 were used to numerically determine the CV as a function of mass removal of reactive travel time distributions using the σlnτ measured from experiments 1-5 (Figure 4). For the initial condition (t ) 0), m0τ (t,∞) was high-variance (CV > 1) for the more-heterogeneous cases of experiments 1 and 2 (σlnτ ) 1.19 and 1.02), while the more-homogeneous cases (σlnτ ) 0.33 or 0.58) were low variance (initial CV < 1). For experiment 3 with σlnτ ) 0.76, initial CV was close to 1. The CV for more-heterogeneous cases decreased with increasing Rm, whereas the morehomogeneous cases showed the opposite trend (Figure 3b). For both heterogeneous and homogeneous cases, the CV of 9378

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mτ0(t,∞) linearly converged to 1 with mass removal, consistent with exponential decay. Implications for Field Site Management. Based on the above analyses, it is concluded that at sites with disparate degrees of DNAPL architecture heterogeneity, aqueous dissolution will eventually converge to exponential source zone mass loss, which corresponds to one-to-one Rj(Rm) and Γ ) 1. Under such conditions, the only site characteristics needed to accurately predict future dissolution behavior using eqs 1 and 2 are average Darcy velocity, and current source zone mass and flux-averaged discharge concentrations. Here we examine the errors associated with broadly assuming exponential decay when actual site age and heterogeneity may not yet have supported convergence to this behavior. At ages corresponding to 0.20, 0.50, and 0.90 PCE mass removed, eq 1 was applied to predict future dissolution for the five experiments described here. For the examples shown in Figure 2a, these exponential model BTC predictions are compared to the BTCs predicted from the EST model computed using the initial (Rm ) 0) σlnτ value. The differences between these predictions (quantified as rRMSE) were affected both by initial σlnτ value and mass removal (Figure 4). For a given mass removal, the discrepancy was minimal for initial σlnτ ≈ 0.8 (initially close to one-to-one Rj(Rm)) but increased as σlnτ either increased (more heterogeneous) or decreased (more homogeneous). When Rm ) 0, the first order decay model was not consistent with the EST model for either the most heterogeneous or homogeneous cases (experiments 2 and 5). For the more heterogeneous case, the exponential distribution overpredicted the dissolution initially followed by significant under-prediction of the BTC tail, with the converse for the relatively homogeneous case. The rRMSEs for Rm ) 0 in Figure 4 indicated that for newly contaminated sites the first order decay model is only applicable to conditions within a relatively narrow range of heterogeneities. As dissolution progressed (increasing PVs and Rm), the exponential model converged to the EST model for both heterogeneous and homogeneous cases (Figure 2a). For example, the rRMSEs between these models for experiments 2 and 5 decreased to {0.44, 0.33, 0.08} and {0.66, 0.31, 0.07} for Rm ) {0.2,0.5,0.9}. Thus, the tail of the EST model is well fitted by first order decay for both heterogeneous and homogeneous cases. It was also observed that once Rj(Rm) converged to oneto-one, dissolution continued as first order decay. Experiment 3 was designed to investigate the change in source zone architecture during dissolution when the initial Rj(Rm) was already near one-to-one. The σlnτ value remained within 0.70 ( 0.06 and the RMSEs between EST model and first order decay model were less than 0.18 and remained low throughout dissolution. For experiments 2 and 4, after 20% of the initial mass was removed, σlnτ remained at 0.85 ( 0.07 and 0.66 ( 0.08, respectively, and the Rj(Rm) curves persisted around the 1:1 line. For experiment 1, σlnτ was reduced from 1.20 to below 0.90 and remained between 0.7 and 0.9 after 50% mass removal. For the more homogeneous experiment 5, σlnτ increased from 0.33 to 0.60 and remained between 0.5 and 0.7 after 50% mass removal. Note that for the power function model, 0.5 < Γ < 2 has been regarded as the central section of the Rj(Rm) plot and close to the 1:1 line (4), and ˆ these correspond to 0.5 < σlnτ < 1.0 (for λ ) FNµ1S/Cs ≈ 6, where ˆ µ1S is the domain-average trajectory integrated DNAPL content) (3). For the experiments presented here, after 90% of the initial mass was removed, the exponential model predicted future dissolution with rRMSEs of less than 0.1 compared to the EST model, except the initially highly heterogeneous case (experiment 1) with rRMSE ) 0.2. Under the most homogeneous initial conditions, rRMSE was reduced to 0.3 after

only 50% mass removal. Note that age defined in terms of source mass reduction is translatable to other contaminants but when considering the age of field sites in terms of years or PVs of natural gradient flow, higher solubility DNAPLs will of course age faster. The relatively low-solubility DNAPL used in this research (PCE) is expected to have greater longevity compared to higher solubility DNAPLs such as TCE. Also, at sites with multicomponent NAPLs (rather than the single component case examined here), where individual components are preferentially solubilized according to Raoult’s law (20), site age will vary depending on the component of interest. Further, other changes to the DNAPL such as film formation or polymerization (21) that may occur during the many years likely required to remove significant DNAPL mass by aqueous dissolution were not considered here. Characterization of contaminated sites to estimate source strength function, which is a measure of the degree of heterogeneity of DNAPL architecture, facilitates prediction of future dissolution behavior. However, it is suggested that at many older contaminated sites the significant fractions of the initial DNAPL mass that have been eluted from the soure zone are likely sufficient to have already entered the exponential dissolution phase. At such sites, characterization of source strength function may not be necessary as it can be assumed with reasonable accuracy that future dissolution will follow an exponential decay model.

Acknowledgments This study was funded by grant ER-1613 from SERDP (Strategic Environmental Research and Development Program), which is a collaborative effort involving the U.S. EPA, U.S. DOE, and U.S. DOD.

Supporting Information Available Details of the LTV method, statistics of the reactive travel time distribution, definition of rRMSE, and derivation of CV of a truncated distribution. This material is available free of charge via the Internet at http://pubs.acs.org.

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(5) Parker, J. C.; Park, E. Modeling field-scale dense nonaqueous phase liquid dissolution kinetics in heterogeneous aquifers Water Resour. Res. 2004, 40, 5, WR05109, DOI: 10.1029/ 2003WR002807. (6) Rao, P. S. C.; Jawitz, J. W.; Enfield, C. G.; Falta, R. W.; Annable, M. D.; Wood, A. L. Technology integration for contaminated site Remediation: Cleanup goals and performance criteria. In Groundwater Quality 2001: Natural and Enhanced Restoration of Groundwater Pollution; Thornton, S., Oswald, S., Eds.; IAHS Publ. 273: Sheffield, U.K., 2001; 571-578. (7) Suchomel, E. J.; Pennell, K. D. Reductions in contaminant mass discharge following partial mass removal from DNAPL source zones Environ. Sci. Technol. 2006, 40, 19, 6110-6116, DOI: 10.1021/es060298e. (8) Zhu, J.; Sykes, J. F. Simple screening models of NAPL dissolution in the subsurface. J. Contam. Hydrol. 2004, 72, 1-4, 245-258, DOI: 10.1016/j.jconhyd.2003.11.002. (9) Sale, T. C.; McWhorter, D. B. Steady state mass transfer from single-component dense nonaqueous phase liquids in uniform flow fields. Water Resour. Res. 2001, 37, 2, 393-404. (10) Falta, R. W.; Rao, P. S.; Basu, N. Assessing the impacts of partial mass depletion in DNAPL source zones I. Analytical modeling of source strength functions and plume response. J. Contam. Hydrol., 2005, 78, 4, 259-280, DOI: 10.1016/j.jconhyd.2005.05.010. (11) Soga, K.; Page, J. W. E.; Illangasekare, T. H. A review of NAPL source zone. Remediation efficiency and the mass flux approach. J. Hazard. Mater. 2004, 110, 1-3, 13-27, DOI: 10.1016/ j.jhazmat.2004.02.034. (12) Fure, A. D.; Jawitz, J. W.; Annable, M. D. DNAPL source depletion: Linking architecture and flux response. J. Contam. Hydrol. 2006, 85, 3-4, 118-140, DOI: 10.1016/j.jconhyd. 2006.01.002. (13) Chen, X.; Jawitz, J. W. Reactive tracer tests to predict DNAPL dissolution dynamics in laboratory flow chambers Environ. Sci. Technol. 2008, 42, 14, 5285-5291, DOI: 10.1021/es7029653. (14) Difilippo, E. L.; Brusseau, M. L. Relationship between mass-flux reduction and source-zone mass removal: analysis of field data. J. Contam. Hydrol. 2008, 98, 1-2, 22-35, DOI: 10.1016/ j.jconhyd.2008.02.004. (15) Jawitz, J. W.; Annable, M. D.; Demmy, G. G.; Rao, P. S. C. Estimating non-aqueous phase liquid spatial variability using partitioning tracer higher temporal moments. Water Resources Research 2003, 39, 7, 1192, DOI: 10.1029/2002WR001309. (16) Schroth, M. H.; Ahearn, S. J.; Selker, J. S.; Istok, J. D. Characterization of miller-similar silica sands for laboratory hydrologic studies. Soil Sci. Soc. Am. J. 1996, 60, (5, 1331–1339. (17) Wang, H. G.; Chen, X.; Jawitz, J. W. Locally-calibrated light transmission visualization methods to quantify nonaqueous phase liquid mass in porous media. J. Contam. Hydrol. 2008, 102, 1-2, 29-38, DOI: 10.1016/j.jconhyd.2008.05.003. (18) Cvetkovic, V.; Dagan, G.; Cheng, H. Contaminant transport in aquifers with spatially variable hydraulic and sorption properties. Proc. R. Soc. A 1998, 454, 2173–2207. (19) Jawitz, J. W. Moments of truncated continuous univariate distributions Adv. Water Resour. 2004, 27, 3, 269-281, DOI: 10.1016/j.advwatres.2003.12.002. (20) Rivett, M. O.; Feenstra, S. Dissolution of an Emplaced Source of DNAPL in a Natural Aquifer Setting Environ. Sci. Technol. 2005, 39, 2, 447-455, DOI: 10.1021/es040016f. (21) Peters, C. A.; Wammer, K. H.; Wammer, C. D. Knightes Multicomponent NAPL Solidification Thermodynamics. Transport in Porous Media 2000, 38 (1-2), 57–77.

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