VZJ
HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS
QUICK SEARCH:   [advanced]


     

Published online 8 October 2007
Published in Vadose Zone J 6:725-734 (2007)
DOI: 10.2136/vzj2006.0108
© 2007 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
This Article
Right arrow Abstract Freely available
Right arrow Figures Only
Right arrow Full Text (PDF) Free
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Similar articles in this journal
Right arrow Similar articles in Web of Science
Right arrow Alert me to new issues of the journal
Right arrow Download to citation manager
Right arrow reprints & permissions
Citing Articles
Right arrow Citing Articles via Google Scholar
Google Scholar
Right arrow Articles by Moreno-Barbero, E.
Right arrow Articles by Illangasekare, T. H.
Right arrow Search for Related Content
PubMed
Right arrow Articles by Moreno-Barbero, E.
Right arrow Articles by Illangasekare, T. H.
GeoRef
Right arrow GeoRef Citation
Agricola
Right arrow Articles by Moreno-Barbero, E.
Right arrow Articles by Illangasekare, T. H.
Related Collections
Right arrow Effective Parameters
Right arrow Inverse Procedures/Parameter Estimation
Right arrow Experiment Design

ORIGINAL RESEARCH

Intermediate-Scale Investigation of Nonaqueous-Phase Liquid Architecture on Partitioning Tracer Test Performance

Elena Moreno-Barberoa,d,*, Yongcheol Kimb, Satawat Saentonc and Tissa H. Illangasekarea

a Center of Experimental Studies of Subsurface Environmental Processes (CESEP), Environmental Science and Engineering, Colorado School of Mines, Golden, CO 80401
b Korea Institute of Geoscience and Mineral Resources, 30 Gajeong-dong, Yuseong-gu Daejeon 305-350, South Korea
c Dep. of Geological Sciences, Faculty of Science, Chiang Mai Univ., 239 Huaykaew Rd., Tumbon Suthep, Amper Muang, Chiang Mai 50200, Thailand
d ARCADIS U.S., 630 Plaza Dr., Ste. 200, Highlands Ranch, CO 80129
* Corresponding author (elena.moreno-barbero{at}arcadis-us.com).

All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.


Received 30 July 2006.



   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 Materials and Methods
 Data Analysis
 Conclusions
 REFERENCES
 
Partitioning interwell tracer tests (PITTs) have been proposed as a tool to characterize source zones of waste sites with chemicals entrapped in the form of nonaqueous-phase liquids (NAPLs). This technique has the potential to be applied to NAPL source characterization of both the vadose and saturated zones, but the recent applications have been primarily focused on dense NAPLs (DNAPLs) entrapped below the water table. This study presents an intermediate-scale experiment to investigate the applicability of the technique to heterogeneous sites with complex NAPL entrapment architecture. Tracer experiments were conducted in an intermediate-scale test tank (4.87 by 1.21 by 0.05 m) with heterogeneity defined using the geostatistical parameters of a spatially correlated random field. Tetrachloroethene (PCE), a DNAPL, was spilled into the heterogeneous packing and was allowed to distribute naturally, creating zones of both residual and pooled entrapment. The saturation distribution of the DNAPL was determined in situ using a gamma attenuation system. Once the saturation distribution was characterized, a set of tracer tests was conducted. Results of this study demonstrate how the inversion of the tracer breakthrough concentrations provided valuable information to establish the validity of the use of equilibrium partition coefficients in situations where tracer partitioning might be controlled by nonequilibrium behavior. While our previous work quantified the estimation error introduced by the assumption of equilibrium partitioning in tracer data analysis, this study demonstrated that more accurate NAPL estimates can be obtained using effective partition coefficients in combination with inverse modeling methods upscaled for more realistic heterogeneous settings.

Abbreviations: 6M2H, 6-methyl-2-heptanol • BTC, breakthrough curve • DMP, 2,2-dimethyl-3-pentanol • DNAPL, dense nonaqueous-phase liquid • NAPL, nonaqueous-phase liquid • PCE, tetrachloroethene • PITT, partitioning interwell tracer test


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
Materials and Methods
 Data Analysis
 Conclusions
 REFERENCES
 
Chlorinated solvents in the form of DNAPLs exist at a large number of hazardous waste sites. The distribution of DNAPLs is controlled by fingering (Held and Illangasekare, 1995), preferential channeling, and heterogeneity of the subsurface formation (Kueper and Frind, 1991). All of these factors increase the complexity of NAPL movement and subsequent entrapment (Schwille, 1988; Kueper et al., 1989; Illangasekare et al., 1995; Oostrom et al., 1999).

Due to the complexity of entrapment architecture, the tasks of delineating and characterizing source zones have become a challenge when selecting and implementing effective remediation schemes. Traditional soil coring methods present difficulties in resolving the spatial distribution of NAPL from discrete samples (Dai et al., 2001). Considering the heterogeneity of the subsurface, it is highly unlikely that the interpolation of core data will reproduce the distribution of contaminants.

The importance and prevalence of the DNAPL problems at many waste sites have driven the need to investigate new techniques for source zone characterization. The partitioning interwell tracer technique (PITT) was modified by Jin et al. (1995) for detecting and characterizing the distribution of NAPL contaminants in subsurface environments from a technique originally developed by petroleum engineers in enhanced oil recovery (Allison et al., 1991). The PITT has been used at both the laboratory and field scales to detect and characterize NAPL source zones in the subsurface (Jin et al., 1995; Nelson and Brusseau, 1996; Annable et al., 1998; Cain et al., 2000; Meinardus et al., 2002). The method involves the injection of a set of reactive and nonreactive tracers that travel through the source zone located between injection and extraction wells. The transport of the reactive tracers is delayed with respect to the nonreactive tracers due to partitioning into and out of the DNAPL phase. If equilibrium conditions are present, the retardation depends only on the DNAPL saturation and the partition coefficient of the tracer (Kp). The entrapped DNAPL saturation can then be calculated using the following expression (Jin et al., 1995):

Formula 1[1]
where SN is NAPL saturation and R is retardation. The validity of the equilibrium assumption (Valocchi, 1985) to tracer behavior has been explored by several researchers (Imhoff and Pirestani, 2004; Jalbert et al., 2003) and depends on the tracer's residence time being sufficient to achieve equilibrium concentrations in both water and nonaqueous liquid phases. Equilibrium concentrations in both aqueous and nonaqueous phases depend on Kp as described by the following relationship:

Formula 2[2]
where Ci,N represents the concentration of tracer i in the NAPL phase, and Ci,w is the concentration of that same tracer in water.

The deviation from equilibrium behavior is reflected as a mass transfer limitation. Several researchers have explored the effect of mass transfer limitations on tracer performance. Willson et al. (2000) evaluated mass transfer limitation effects comparing local equilibrium and rate models in combination with laboratory experiments and concluded that a greater understanding of the tracer limitations in the field scale is necessary. Dai et al. (2001) evaluated the sole influence of entrapment architecture (pools vs. residuals) on estimation errors using one-dimensional columns. Results from their study suggested that improvement on PITT data interpretation could be achieved with the use of kinetic data assessment models. Jalbert et al. (2003) developed a dual-domain model where a fraction (F) of the NAPL consists of instantaneous sites where equilibrium partitioning occurs and a fraction (1 – F) consists of rate-limited sites. Jawitz et al. (2003) used binary models to express higher tracer moments that can be used to estimate NAPL spatial distribution. A strong agreement was found between the measured and expected fractions of the tracer-swept zone that contained NAPL. Imhoff and Pirestani (2004) also compared single- and dual-domain models to interpret the data obtained from a set of one-dimensional experiments. Although both modeling approaches were capable of matching experimental data, the input parameters necessary to use them are normally unknown in the field. In addition, the effect of mass transfer limitations on the estimation accuracy of these models has not been quantified. In a recent study, Moreno-Barbero and Illangasekare (2005) evaluated the importance of NAPL saturation on the performance of a partitioning tracer test. The effects of flow bypassing and nonequilibrium partitioning behavior were considered.

This investigation attempts to further evaluate the effect of soil and NAPL heterogeneity and nonequilibrium partitioning in more complex settings and proposes an alternative method for interpretation. The intermediate scale allows small-scale processes to be manifested at a larger scale in a controlled environmental setting (Lenhard et al., 1995). An intermediate-scale tank packed with well-characterized sand was used as an artificial two-dimensional test aquifer. The tank dimensions were 4.87 by 1.21 by 0.05 m. A spatially correlated random field with known geostatistical parameters was generated to design the heterogeneity field to pack the tank. The exact aquifer properties were known, and associated instrumentation of the test tank allowed the in situ determination of the exact DNAPL architecture, so the tracer performance could be evaluated for different test conditions.

The objective of this experimental study was to generate accurate data to evaluate the applicability and limitations of the partitioning tracer technique and the methods of analysis to determine DNAPL saturations in heterogeneous source zones. Previous studies investigated the influence of pool morphology on the partitioning tracer test performance and evaluated estimation errors associated with high saturation zones. The study presented here focuses on upscaling these findings to source zones with more complex DNAPL architecture. Previous work (Moreno-Barbero and Illangasekare, 2006) quantified the magnitude of PITT estimation errors in the case of an isolated pool. This study was designed to evaluate estimation errors and validate an alternate method to moment analysis to interpret tracer breakthrough concentration data under more realistic heterogeneous settings using experimental data generated in an intermediate-scale test system.

The PITT techniques have also been applied in the vadose zone with the use of partitioning gas tracers (Deeds et al., 1999). Although in this study, the PITT was evaluated for saturated-zone conditions, the findings in general will be of value for evaluating the impact of heterogeneity and nonequilibrium conditions on tracer behavior for both vadose and saturated zones.


   Materials and Methods
TOP
 ABSTRACT
 INTRODUCTION
 Materials and Methods
Data Analysis
 Conclusions
 REFERENCES
 
Because the purpose of this investigation was to evaluate the PITT under heterogeneous conditions, packing configuration and procedures were designed to capture some of the complexities of heterogeneous field sites. The turning bands method (Mantoglou and Wilson, 1982; Tompson et al., 1989) was used to generate a spatially correlated random field defining the permeability distribution. The geostatistical parameters of the random field were: mean of lognormal hydraulic conductivity (K) of 4.18 m/d, variance of 1.22, horizontal correlation length of 0.508 m, and vertical correlation length of 0.0508 m. The theoretical, continuous hydraulic conductivity field was then discretized into five categories (or bins) that correspond to five well-characterized Unimin test sands used in our previous studies (Barth et al., 2001). The relevant properties of all of the test sands are given in Table 1.


View this table:
[in this window]
[in a new window]

  		TABLE 1. Physical properties of sands used (Saba, 1999; Barth et al., 2001).

 
Out of the 20 realizations generated with the selected geostatistical parameters, a realization that was expected to produce a heterogeneous DNAPL source zone containing both residual and pools was selected for packing the tank. A theoretical analysis of the estimation performance of the PITT for all of these realizations was reported in Moreno-Barbero and Illangasekare (2005). The configuration chosen for this experimental study contained zones within the target source area for DNAPL injection that were likely to produced a complex entrapment morphology while minimizing the possibility of vertical DNAPL migration to the bottom of the tank. This achieved an acceptable vertical distribution of DNAPL in the source zone for testing while protecting the bottom of the tank from DNAPL that could deteriorate the seals, thereby producing leaks.

Upstream of the source zone, a short tank length was packed homogeneously with coarse no. 8 sand. The tracers were injected into this high-permeability zone to create a uniform tracer to enter the source zone. Six pairs of vertical sampling and monitoring port arrays were placed for aqueous sampling and head measurement, and one array within the upstream homogeneous zone was used for tracer injection. Each array had 40 sampling and monitoring ports spaced vertically, 2.54 cm apart. Constant-head end reservoirs at both ends were used to maintain a constant hydraulic head difference, and a hydraulic gradient of 0.001 was used in all experiments. Figure 1 shows a schematic of the intermediate-scale test tank.


Figure 1
View larger version (41K):
[in this window]
[in a new window]

  		FIG. 1. Schematic of the flow cell. The permeability field is represented on the top; the locations of the sampling ports are specified on the bottom.

 
The tank was filled by hand according to the packing design of the random field. Sand volumes of approximately 80 mL were placed into the tank following the discretization that corresponds to the selected random field. A 5-cm polyvinyl chloride (PVC) pipe with screens emplaced at the ends was used to place each batch of sand type into its specified location. In this manner, individual sand lenses approximately 15 cm long and 1 cm high were created in the test tank. Dropping the sand through the PVC pipe as the pipe was moved laterally along a 15-cm track avoided a discrete "blocky" geometry and established more realistic sand contacts. The resulting individual sand units were tapered at their boundaries without sharp vertical texture interfaces (Fig. 2 ). Water-saturated conditions were maintained during packing by maintaining the water level approximately 5 cm above the top layer. A total of 2800 cells were packed in 100 horizontal layers and 28 vertical columns.


Figure 2
View larger version (107K):
[in this window]
[in a new window]

  		FIG. 2. Intermediate-scale tank and details of the heterogeneous packing.

 
After packing, water was flushed through the tank; a series of tracer experiments was conducted once the steady-state flow condition was achieved. The chronology of all of these activities is presented in Table 2, and a description of all of the PITT experiments follows.


View this table:
[in this window]
[in a new window]

  		TABLE 2. Chronology of experimental tasks.

 
Initial Scanning of the Test Tank
Gamma-ray attenuation was used for the determination of the PCE saturation distribution within the tank. The gamma system used in this work was placed on a computer-automated gantry system for precise positioning within a 10.7-m-long and 1.5-m-high vertical plane. The position of the motor-controlled gantry was set and recorded automatically using a LabVIEW-based data acquisition system (National Instruments Corp., Austin, TX). Collimated beams of gamma energy were produced by two sealed radioisotope sources: 7.4 GBq of 241Am with a primary peak at 60 keV and 1.85 GBq of 137Cs with a primary peak at 662 keV. The relative strengths of the two gamma sources can be tuned through selective filtering to provide maximum accuracy and precision for the simultaneous measurement of water and NAPL saturations. A more detailed description and operation of these methods can be found in Saba (1999). The gamma-ray attenuation system was used to scan the source zone before and after the PCE spill. It took approximately 7 d to scan the source zone area (an area of approximately 70 by 60 cm).

Pre-spill Tracer Test
A background tracer test was conducted primarily to evaluate retardation of the conservative tracers due to other mechanisms, such as sorption to the porous medium. With this test, it was also possible to: (i) check the uniformity of tracer injection through all the ports; (ii) optimize design parameters such as flow rate, injection duration, sampling frequency, and total sampling time; and (iii) obtain a set of conservative tracer data for calibration of transport parameters needed in modeling.

During the test, the effluent rate was continuously measured at the tank outlet to verify steady-state flow conditions throughout the experiment. Hydraulic head distribution in the tank was monitored using a differential pressure transducer that provided readings at 48 different locations distributed throughout the test domain.

The transducer was connected to a head reservoir (used as a reference) and to a solenoid controller. This controller was connected to 48 ports in the tank. LabVIEW software has been developed to automatically control the selector switch and to provide sequential input to the transducer from all 48 ports. The output (voltage) was converted into head measurements using a linear fit created from calibration data.

A mixture of 2,2-dimethyl-3-pentanol (DMP), n-hexanol, and 6-methyl-2-heptanol (6M2H) (all from Sigma-Aldrich Corp., St. Louis, MO) was used as the partitioning tracer solution. Selection criteria of the tracers were based on general guidelines defined by Young et al. (1999) and on their partition coefficients (low enough to allow a reasonable time for breakthrough and high enough to ensure separation between partitioning and nonpartitioning tracers). Bromide (from NaBr) was selected as the conservative tracer.

A solution of 500 mg/L of DMP, 300 mg/L of 6M2H, 300 mg/L of hexanol, and 500 mg/L of NaBr was injected into the upstream tank using a multisyringe pump located in the center of the homogeneous zone. The pump used 32 injection ports that were set to create a total injection rate of 8 mL/min during a total injection time of 10 h. The water flow rate through the tank was controlled using the two constant-head reservoirs connected to each end of the tank.

After tracer injection, samples were collected manually at 29 ports located at six different vertical arrays downstream from the source zone (Fig. 1) during a total experimental time of 2 d. To reduce the required sample volume, 0.2-mL inserts were placed in 1.5-mL vials. A total of 596 samples were collected during the experiment in gas chromatography autosampler vials, and partitioning tracer concentrations were analyzed using a flame ionization detector. After analysis of partitioning tracers, Br– concentrations were analyzed using ion chromatography (IC).

Creation of Tetrachloroethene Source Zone
Tetrachloroethene was used as the test DNAPL for these experiments (Sigma-Aldrich Corp.). It was dyed with a small fraction of Sudan IV (0.01%) to allow visual observation through the transparent wall of the test cell. Table 3 lists the relevant physicochemical properties of PCE.


View this table:
[in this window]
[in a new window]

  		TABLE 3. Physicochemical properties of tetrachloroethene (PCE).

 
Once the porous media were packed in the tank and steady-state flow was established through the tank, the PCE source zone was created. A Mariotte bottle was used to inject PCE under a constant head. To avoid lateral migration of the contaminant beyond the area scanned during background gamma scanning, the PCE was injected at five different vertical locations in the same vertical array, each of them located at a different depth. During injection, the flow rate and the volume of PCE injected were monitored using an electronic scale. A total volume of 586.7 mL was injected, and the DNAPL was allowed to achieve static conditions.

The PCE spread downward and laterally within the coarser layers around the injection ports until it reached the finer layers (no. 110 sand), where it spread laterally.

Scanning 1
To evaluate the effect of the entrapment architecture on the performance of the partitioning tracer test, it was necessary to determine the actual PCE saturation distribution in the source zone. After the spill and once static conditions were achieved, a second gamma-ray scan was conducted. Results from Scanning 0 and Scanning 1 were combined to obtain NAPL saturation (Saba, 1999). Figure 3 compares a digital image of distribution of PCE and the contours of saturations determined using the gamma attenuation system.


Figure 3
View larger version (31K):
[in this window]
[in a new window]

  		FIG. 3. Final distribution of tetrachloroethene and saturation contours obtained from gamma attenuation.

 
Partitioning Interwell Tracer Test 1
After injection of PCE and scanning of the source zone, flow conditions were reestablished, and the second partitioning tracer test (PITT 1) was conducted using the same design parameters applied in PITT 0. The aqueous samples were collected in 1.5-mL vials with 0.2-mL inserts, then capped and stored for gas and ion chromatography analysis. A total of 900 vials was collected during this experiment. The total time of the experiment was increased to 4 d, because a delay in partitioning tracer transport was anticipated due to the presence of the DNAPL.


   Data Analysis
TOP
 ABSTRACT
 INTRODUCTION
 Materials and Methods
 Data Analysis
Conclusions
 REFERENCES
 
Observed Tracer Behavior
The results of temporal moment analysis of PITT 0 showed no background retardation of any of the tracers in the system. Breakthrough curves (BTCs) also showed that the tracer injection system was generating the appropriate flow patterns in the test domain, such that a uniform tracer front was created in the homogeneous zone before entering the heterogeneous source zone. The locations of the injection and extraction ports were found to be optimal for subsequent tests because the tracers swept the area where the source zone was expected to be created after the DNAPL spill. The data from PITT 0 also showed the influence of heterogeneity as reflected by the variability in the shapes of the BTC constructed using data from the ports placed along the same vertical section.

Before the analysis of tracer data using method of moments, the BTCs were examined qualitatively to evaluate signatures or features that contain information about the vertical DNAPL architecture of the system. Results of PITT 1 demonstrated the presence of DNAPL. During data analysis, the ion chromatography experienced some technical difficulties, which caused the loss of some Br– samples. This technical problem resulted in two Br– BTCs that are nonexistent or incomplete (A26 and A31).

The BTCs obtained during PITT 1 in Array A are presented in Fig. 4 . All of the sampling locations on this vertical array captured some retardation of the partitioning tracers, indicating the presence of high-saturation zones of PCE. Tailing observed in A16 and A17 indicates that the DNAPL was not distributed uniformly because a uniform distribution would produce a simple offset (Brooks et al., 2002; Jawitz et al., 2003). This feature could also be the result of nonequilibrium conditions that reflect permeability contrasts in the source zone. These permeability contrasts control the local velocities, and tracers may not have been in contact with the DNAPL for a sufficient time to partition with all of the DNAPL mass. Tracers only partition to the DNAPL located in the transition zone of the pools, as described in the conceptual model developed in Moreno-Barbero and Illangasekare (2006). This conceptual-pool model suggested a range of saturations varying from full to residuals within the pool. These variable saturations produced a nonuniform velocity field within the pool, resulting in the tracer primarily migrating through the low NAPL saturation zones and bypassing zones of relatively higher NAPL saturations. In these scenarios of tracer interaction in zones of high heterogeneity, the retardation is reflected in the tail of the BTC and may not be entirely captured due to the detection limit of the analytical instruments. The BTC tail was extrapolated using an exponential decay function (Annable et al., 1998). The BTCs are plotted in Fig. 3 in both natural and semilog scale to show the trend at low concentrations.


Figure 4
View larger version (52K):
[in this window]
[in a new window]

  		FIG. 4. Breakthrough curves collected in array A; the x axis represents time (minutes) and the y axis represents concentration (C/C0). DMP is 2,2-dimethyl-3-pentanol; HEX is n-hexanol; 6M2H is 6-methyl-2-heptanol; BR is NaBr.

 
The issue of tailing becomes more problematic as the distance from the source zone increases with the dilution of the tracer plume due to dispersion. It becomes impossible to capture the tailing effect when the concentrations fall below detection limits. In the downstream Array F (located at 3.5 m from the source zone), the retardation becomes very small compared with what is observed in Array A (at 0.5 m from the source zone) due to mixing and dilution of tracers. Based on these results, in general, it can be concluded that, as the sampling distance from the source zone increased, the information contained in the BTCs on the NAPL architecture decreased.

Method of Moment Analysis
After qualitative analysis of the BTCs, arrival times of all of the tracers were calculated using numerical integration. The average saturation can be obtained using Eq. [1]. For the sampling ports that did not contain sufficient Br– observations, hexanol concentrations were used as the reference to calculate retardation values, as described in Jin et al. (1995).

Because hexanol was used as a reference tracer in the BTCs that lack Br– data and 6M2H seems to deviate more from equilibrium conditions due to its high Kp (see Moreno-Barbero and Illangasekare, 2006), the DMP data set was selected for quantitative analysis. The highest R computed for DMP in Array A was 3.9 and the lowest 1.1; this variability demonstrates the different response of the partitioning tracer to the vertical NAPL architecture. As expected, with increasing distance from the source zone, the retardation values were smaller because the signal attenuated due to dispersion, and the increasing swept volume resulted in a lower average saturation. In Array F, the highest R computed was 1.4. Figure 5 shows the comparison between method-of-moment estimates and the gamma-measured distribution of PCE. Underestimation of the saturations by the method of moments is potentially caused by flow-bypassing mechanisms and rate-limited partitioning. The results presented here compared the saturation estimated using partitioning tracer data from each sampling port located at a certain vertical depth within the source zone with the in situ saturation measured using the gamma system at that same depth. Errors in the saturation estimates from tracer data collected at a given sampling location may also be the result of the flow lines passing through a NAPL mass that may not necessarily remain horizontal to pass through the sampling port at the same depth. Divergence of flow lines can be expected due to the heterogeneity of the formation. In Arrays A, B, and C, the signals contained some information about the vertical architecture. Conversely, results obtained at Arrays D, E, and F (located farther downstream) did not contain adequate information about the DNAPL vertical distribution. In arrays located at a distance >2 m from the source zone, the heterogeneity controlled the mixing, thus losing the information contained in the downstream signals to estimate entrapped NAPL saturations.


Figure 5
View larger version (31K):
[in this window]
[in a new window]

  		FIG. 5. Actual tetrachloroehtene (PCE) saturation (Sn; line) at depth z and PCE saturation calculations using moments (dots).

 
Inverse Modeling Analysis to Determine Source Zone Architecture
The finite difference groundwater model MODFLOW (Harbaugh et al., 2000) was used to simulate flow through the test tank. This model can work in conjunction with MT3DMS (Zheng and Wang, 1999) to simulate transport. The DNAPL phase and the partitioning behavior were incorporated in the transport using the preprocessor MODTRACER (Saenton, 2003).

The test aquifer was discretized into a finite-difference grid system that consisted of 106 layers, 154 columns, and two rows. Observed effluent rate, water pressures, and tracer concentrations before the DNAPL spill were used to calibrate the flow and transport parameters of the model. An inversion procedure based on nonlinear least-square regression was designed to estimate the entrapment saturations from the observed BTCs. The inversion code PEST (Doherty, 1994) was used to estimate the average NAPL saturations in horizontal planes that were treated as unknowns.

Initial Inverse Modeling Setup
The inverse modeling formulation was designed to use the relative concentrations of partitioning and conservative tracer BTC data collected at Arrays A, B, and C as observations. The parameters to be estimated were defined to be seven value saturations in horizontal planes (S1–S7). For N observation points in each array, the source zone was discretized into N different zones, each with a constant saturation value (Saenton, 2003). Figure 6 shows the reconceptualization of the source zone for inverse modeling.


Figure 6
View larger version (42K):
[in this window]
[in a new window]

  		FIG. 6. Reconceptualization of the source zone area for parameter estimation; S1 through S7 are value saturations in horizontal planes.

 
Parameter estimation is an iterative process; in each of the iterations, the simulated and observed tracer concentrations were compared. The evaluation of the objective function (sum of all squared residuals) and the parameter changes allows the inverse model to determine if a new iteration is necessary and, if so, the entire process is repeated. Nonlinear regression begins with starting parameter values, so it is necessary to input an initial set of saturations for the seven areas. In this case, results from method-of-moments analysis of Array A data were used as the initial guess of saturation values.

It is obvious that the high degree of heterogeneity of the domain created a more complicated source zone than the one reconceptualized for inverse modeling, as seen from the saturation values obtained from gamma attenuation. Only the information that was observed during the PITT was used in the inversion, however, which created a more simplistic source zone due to the limited information available from tracer tests. The purpose was to determine if this information is sufficient to characterize the location of "hotspots" that produce dissolved mass and the main features of the source zone. After parameter estimation, results from the inversion were compared with the saturation distribution obtained from gamma attenuation.

The DNAPL architecture obtained by inverse modeling and its comparison with in situ determined values is represented in Fig. 7 . Results from inverse modeling approximately fit the saturation distribution obtained from gamma attenuation. The saturations, however, were still underestimated.


Figure 7
View larger version (15K):
[in this window]
[in a new window]

  		FIG. 7. Comparison of the saturation distribution obtained from inverse modeling and actual data (center of layer is in centimeters).

 
The BTCs at the end of the simulation were compared with the experimental data to evaluate whether the model mimics the long tailing observed in the experimental tracer responses. Figure 8 shows how the simulated Br– data fit well into the experimental data. Both curves show the same time for breakthrough as well as the same degree of spreading. The DMP simulated values did not produce a good fit, however, when equilibrium was assumed in the analysis. Even though a certain degree of discrepancy is expected (the zonation of the saturation in the model does not match exactly the real saturation distribution observed in Fig. 3), the simulated DMP BTCs show a single offset instead of the asymmetric and long-tailed curve observed in the experiments. If local equilibrium is not attained, local-equilibrium-based models will predict a breakthrough response that occurs too late and exhibits small dispersion (Valocchi, 1985). This is an indication that the model is not capturing the behavior of the tracers, and this error could affect final results.


Figure 8
View larger version (22K):
[in this window]
[in a new window]

  		FIG. 8. Experimental (obs) and simulated (mod) breakthrough curves for 2,2-dimethyl-3-pentanol (DMP) and NaBr for Ports A16 and A17.

 
In an attempt to overcome these problems, effective partition coefficients (Kpe) were incorporated in the inversion analysis.

Incorporation of Effective Partition Coefficients
The issue of nonequilibrium was addressed using a method proposed by Valocchi (1985) and adopted in Moreno-Barbero and Illangasekare (2006) to assess the deviation from equilibrium of observed partitioning tracer BTCs. The differences between the simulated and experimental BTCs for DMP are reflected in the computed values of moments. Considering that the numerical models provide a BTC that represents local equilibrium and that the experimental data represent a BTC under nonequilibrium behavior, the deviation from equilibrium conditions could be measured using the second moment of the two data sets. The fractional change ({varepsilon}2) in the second central moment is defined as

Formula 3[3]
where superscripts K and E refer to the kinetic (i.e., nonequilibrium) and equilibrium models, respectively, and µ2 refers to the second central moment.

If the fractional change of the second moment is calculated for the BTCs collected and simulated at all the ports, large {varepsilon}2 values are obtained, representing large deviations from equilibrium. To relax the condition of equilibrium, Kpe obtained in batch experiments were substituted for the equilibrium values. These values were applied to the areas that were subject to nonequilibrium behavior represented by high values of fractional changes in the second central moments. After the range of Kpe with time was obtained for each tracer, a Kpe was applied to each zone depending on the deviation from equilibrium quantified by the second moments.

This kinetic batch experiment follows the same procedure used in equilibrium batch tests, except that the partitioning process is stopped at discrete time intervals (15 min and 1, 2, 6, 12, and 24 h) by separating the aqueous and NAPL phases. The last time period of 24 h corresponded to the equilibration time that was determined in previous batch experiments reported by Moreno-Barbero and Illangasekare (2006). Figure 9 shows three distinctive zones based on the deviation from equilibrium. The values of the equilibrium partitioning were modified with Kpe for the zones that correspond to BTCs A16, A17, and A31. Values of Kpe = 25, 20, and 25 were applied to Zones S3, S4, and S7, respectively, based on the deviation from equilibrium.


Figure 9
View larger version (19K):
[in this window]
[in a new window]

  		FIG. 9. Tracer partition coefficient (Kp) as a function of time for 2,2-dimethyl-3-pentanol (DMP).

 
After evaluation of the fractional change of the second moment, the Kpe obtained for DMP (Fig. 9) was applied to the inversion analysis. With the incorporation of Kpe, the model not only produced a source zone closer to the actual value (Fig. 10 ), it also provided a higher quality regression (smaller sum of squared residuals).


Figure 10
View larger version (15K):
[in this window]
[in a new window]

  		FIG. 10. Comparison of saturation distribution between actual tetrachloroethene distribution and results from inverse modeling with the effective partition coefficient, Kpe.

 
One of the advantages in this correction method is that, even though the exact value of Kpe is not known for each situation, it allows determination of DNAPL distribution for the best- and worst-case scenarios. That is, if equilibrium is assumed in the analysis, the underestimation will reach its highest value. Conversely, if a value of Kpe = 10 (far from the equilibrium condition) is used in the analysis, the maximum value for the saturation at that location will be obtained. In this way, the method can provide a range of saturation values to account for the errors caused by the local equilibrium assumption.


   Conclusions
TOP
 ABSTRACT
 INTRODUCTION
 Materials and Methods
 Data Analysis
 Conclusions
REFERENCES
 
This was a combined experimental and numerical study to evaluate the influence of heterogeneity on tracer performance in settings that resemble heterogeneous sites. Because previous work by Moreno-Barbero and Illangasekare (2006) demonstrated that extraction wells provide underestimation of the mass under conditions of heterogeneity, only multilevel samplers were used in this study. Multilevel sampling (Sillan et al., 1998) is also the only sampling method that can potentially provide information about the vertical architecture.

After collecting tracer BTCs, method of moments was conducted to determine DNAPL saturation. This method offers limited information about the vertical distribution of DNAPL. It underestimated entrapped NAPL mass due to the nonequilibrium behavior and the limitations of the tracer solution in accessing the entire source zone.

Despite the computational effort that inverse modeling requires compared with the method of moments, it allows an integrated interpretation of the tracer behavior in the system. Results of this study demonstrate how the inversion exercise provided valuable information to support evaluation of the validity and limitations of using equilibrium partition coefficients in situations where tracer partitioning is controlled by nonequilibrium behavior. Estimated values of saturation via inversion with Kpe will correct the effect of nonequilibrium partitioning. This method does not, however, account for underestimation caused by hydrodynamic inaccessibility of the tracers to all DNAPL mass in high saturation zones that are found in pools. The tracers do not respond to certain zones of the pool that are not accessed due to low aqueous permeabilities resulting from high saturations.

Even though method of moment analysis has several limitations under conditions of heterogeneity, it is still a simple procedure that should always be applied to BTC data analysis. It is also a necessary step for the inverse modeling procedure, which requires an initial guess of the saturation distribution.

This inverse modeling procedure was tested for a two-dimensional setting, whereas in field situations, flow and transport conditions are all three dimensional. Extrapolation of these findings to field conditions needs further study. It is also important to recognize that, due to the two-dimensional nature of the experiment, the pools created here will be thicker than what would be found in the field due to spreading in the third dimension. The "thicker" DNAPL morphology created in this two-dimensional setting could have led to larger estimation errors than what might be expected in the field.


   ACKNOWLEDGMENTS
 
This work was funded by the Department of Education GAANN program, the National Science Foundation Award EAR-0107095, and the Strategic Environmental Research and Development Program (SERDP).


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 Materials and Methods
 Data Analysis
 Conclusions
 REFERENCES
 





This Article
Right arrow Abstract Freely available
Right arrow Figures Only
Right arrow Full Text (PDF) Free
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Similar articles in this journal
Right arrow Similar articles in Web of Science
Right arrow Alert me to new issues of the journal
Right arrow Download to citation manager
Right arrow reprints & permissions
Citing Articles
Right arrow Citing Articles via Google Scholar
Google Scholar
Right arrow Articles by Moreno-Barbero, E.
Right arrow Articles by Illangasekare, T. H.
Right arrow Search for Related Content
PubMed
Right arrow Articles by Moreno-Barbero, E.
Right arrow Articles by Illangasekare, T. H.
GeoRef
Right arrow GeoRef Citation
Agricola
Right arrow Articles by Moreno-Barbero, E.
Right arrow Articles by Illangasekare, T. H.
Related Collections
Right arrow Effective Parameters
Right arrow Inverse Procedures/Parameter Estimation
Right arrow Experiment Design

HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS
The SCI Journals Agronomy Journal Crop Science
Journal of Natural Resources
and Life Sciences Education		 Soil Science Society of America Journal
Journal of Plant Registrations Journal of
Environmental Quality		 The Plant Genome