The use of mass depletion–mass flux reduction relationships during pumping to determine source zone mass of a reactive brominated-solvent DNAPL

Journal of Contaminant Hydrology 144 (2013) 122–137

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The use of mass depletion–mass flux reduction relationships during pumping to determine source zone mass of a reactive brominated-solvent DNAPL C.D. Johnston a, b,⁎, G.B. Davis a, b, T.P. Bastow a, M.D. Annable c, M.G. Trefry a, b, A. Furness a, Y. Geste a, R.J. Woodbury a, P.S.C. Rao d, S. Rhodes e a b c d e

CSIRO Land and Water, Private Bag No. 5, Wembley, Western Australia, 6913, Australia School of Earth and Environment, University of Western Australia, Nedlands, Australia Environmental Engineering Sciences, University of Florida, PO Box 116450, Gainesville, Florida, 32611-6450 ,USA School of Civil Engineering, Purdue University, West Lafayette, Indiana, 47907-2051 ,USA Rio Tinto, 120 Collins Street, Melbourne, Victoria, 3000, Australia

a r t i c l e

i n f o

Article history: Received 16 August 2012 Received in revised form 12 November 2012 Accepted 16 November 2012 Available online 24 November 2012 Keywords: Brominated solvent DNAPL Source zone PITT Mass depletion Mass flux reduction Groundwater Contamination

a b s t r a c t Mass depletion–mass flux relationships usually applied to a groundwater plume were established at field scale for groundwater pumped from within the source zone of a dense non-aqueous phase liquid (DNAPL). These were used as part of multiple lines of evidence in establishing the DNAPL source mass and architecture. Simplified source mass-dissolved concentration models including those described by exponential, power, and error functions as well as a rational mass equation based on the equilibrium stream tube approach were fitted to data from 285 days of source zone pumping (SZP) from a single well which removed 152 kg of dissolved organics from a multi-component, reactive brominated solvent DNAPL. The total molar concentration of the source compound, tetrabromoethane and its daughter products was used as a single measure of contaminant concentration to relate to source mass. A partitioning inter-well tracer test (PITT) conducted prior to the SZP provided estimates of groundwater travel times, enabling parameterisation of the models. After accounting for capture of the down-gradient dissolved plume, all models provided a good fit to the observed data. It was shown that differentiation between models would only emerge after appreciably more pumping from the source zone. The model fits were not particularly sensitive to the exponent parameters and variance of groundwater travel time. In addition, the multicomponent nature of the DNAPL did not seem to affect the utility of the models for the period examined. Estimates of the DNAPL mass prior to the start of SZP from the models were greatest where the log of the variance of travel time was used explicitly in the source depletion models (mean 295 kg) compared to where the associated power exponent and variance was fitted freely (mean 258 kg). The estimates of source mass were close to that of 220 kg determined from the PITT. In addition to the PITT, multi-level groundwater sampling from within the source zone provided important supporting information for developing the conceptual model of the source zone. It is concluded that SZP may be an effective and relatively simple means for characterising DNAPL source zones. Crown Copyright © 2012 Published by Elsevier B.V. All rights reserved.

1. Introduction ⁎ Corresponding author at: CSIRO Land and Water, Private Bag No. 5, Wembley, Western Australia, 6913, Australia. Tel.: + 61 8 93336328; fax: + 61 8 93336211. E-mail address: [email protected] (C.D. Johnston).

Characterising the mass of dense non-aqueous phase liquid (DNAPL) contaminants in aquifers and the emission of dissolved organic chemicals from DNAPL sources remains a challenge for those dealing with contaminated sites and

0169-7722/$ – see front matter. Crown Copyright © 2012 Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jconhyd.2012.11.005

C.D. Johnston et al. / Journal of Contaminant Hydrology 144 (2013) 122–137

protecting groundwater quality. The challenges arise from a variety of factors. Prime amongst them are the complexity and unpredictability of the distribution of DNAPL in the subsurface after being released. This has severe implications in how the mass and architecture of DNAPL can be reliably determined (here we use architecture to describe the threedimensional spatial distribution as well the pore-scale distribution of the DNAPL in blobs, ganglia and pools in the aquifer). In turn, this impinges on the certainty of predicting the magnitude and longevity of risks posed by the DNAPL contaminant, particularly from the flux of dissolved constituents of the DNAPL source, as well as determining the most efficient and effective means of managing and remediating the source contaminants. The difficulty of making direct observations of the distribution of DNAPL saturations in heterogeneous aquifers has spawned indirect techniques such as partitioning tracer tests (Annable et al., 1998; Brooks et al., 2002; Jawitz et al., 2000; Jin et al., 1995; Kim et al., 1997; Meinardus et al., 2002) to give estimates of average DNAPL saturation, DNAPL mass and, to a certain extent, DNAPL architecture including the ratio of the interfacial area to DNAPL volume. By de-convoluting the quantitative interaction of the partitioning tracers integrated over relatively large volumes of the aquifer compared to core sampling, for instance, problems of extreme heterogeneity of DNAPL distribution at a fine scale may be overcome. This is not to say that partitioning tracer tests do not also have limitations, some directly attributable to aquifer and DNAPL heterogeneity as well as DNAPL morphology (Illman et al., 2010; Meinardus et al., 2002; Moreno-Barbero and Illangasekare, 2006). Such heterogeneity may affect accessibility of the tracers to the DNAPL and cause more complex kinetic interactions between the tracers and DNAPL where the DNAPL exists in thick pools (Moreno-Barbero and Illangasekare, 2006). One of the key objectives of determining the mass and architecture of DNAPL contaminants is to be able to predict the concentrations and fluxes of dissolved constituents. An ability to predict these concentrations and fluxes over time is critical to the assessment of the longevity of risk and the formulation of an appropriate site management and remediation action plan. It is rare for the DNAPL distribution and aquifer structure to be known to a sufficient level of detail for reliable predictions to be made from DNAPL dissolution and reactive transport simulators. Thus, there has been an increasing level of interest in developing more general relationships between DNAPL source mass and the concentration/flux of dissolved DNAPL constituents in natural groundwater flow emanating from source zones. Sale and McWhorter (2001) investigated the nature and form of the relationship with a semi-analytical mass transfer model in which analytical solutions were superimposed (denoted the MASST approach). This was followed by efforts seeking more general relationships (Basu et al., 2008; Chen and Jawitz, 2009; Falta et al., 2005; Jawitz et al., 2005; Parker and Falta, 2008; Parker and Park, 2004; Rao et al., 2002; Zhang et al., 2008; Zhu and Sykes, 2004). Some of these are based on a statistical description of the heterogeneity of groundwater flow velocity or dissolution times within the source zone (Basu et al., 2008; Jawitz et al., 2005; Zhang et al., 2008). Other empirical functional relationships have been proposed between contaminant concentration and source mass, most notably a power function (e.g. Falta et

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al., 2005; Rao et al., 2002; Zhu and Sykes, 2004). Parker and Park (2004) also postulated the Damkohler model which simplified to the power function model under certain conditions. However Chen and Jawitz (2009), Christ et al. (2010) and DiFilippo and Brusseau (2011) inferred from bench-scale flow cell experiments and numerical models that the exponent parameter in these models was not constant over the course of source dissolution and there was a need to account for changes in DNAPL distribution characteristics within the aquifer. The research presented here, combined and compared the use of a partitioning inter-well tracer test (PITT) and a novel application of the source mass–dissolved mass flux relationship under conditions of pumping from the source zone to estimate source mass on an unusual, reactive brominated DNAPL (tetrabromoethane). The research has focussed on using information gained from the PITT in relation to groundwater velocity distribution at the field scale in a heterogeneous, layered aquifer to test a range of functional relationships that have been proposed between source mass and dissolved concentration/flux. As well as their ability to predict observed concentrations and fluxes of dissolved DNAPL constituents, an evaluation was made of how specific functional relations differed in terms of the extrapolated time history of dissolved contaminants from the source zone. An important extension to previous work is the evaluation and application of such relationships to pumped groundwater from the source zone, rather than the more usual application to concentration/flux in natural groundwater flow. In addition, other than the extreme density (specific gravity 2.99), the brominated DNAPL is novel in that it undergoes a series of abiotic and biotic transformations in groundwater. Here, a simple, pragmatic approach was tested to deal with multi-component speciation and transformations in the DNAPL and dissolved phases. 2. The setting 2.1. The genesis of the contamination The field site was a former industrial facility that had used the dense solvent tetrabromoethane (TBA) for mineral separation. At the site, a plume of dissolved brominated organic daughter products and bromide (Patterson et al., 2007) was discovered in the underlying aquifer systems threatening to discharge to a nearby small open drainage channel, come stream, and sensitive estuarine ecosystem. Investigations indicated that TBA had leaked from a waste collection system, contaminating the aquifer for some period prior to its discovery. 2.2. The brominated organic contaminants Tetrabromoethane has appreciable water solubility (700 mg/ L, Patterson et al., 2007) and in groundwater undergoes debromination through rapid abiotic transformation to TriBE. Patterson et al. (2007) studied the transformation pathways and kinetics and indicated the abiotic transformation of TBA to tribromoethene (TriBE) had a first-order half life of around 0.2 days. As a result, TBA was not observed down-gradient of the presumed source zone. As a corollary, the presence of TBA in groundwater indicates the very close proximity of a DNAPL source. Tribromoethene was shown to degrade biotically with a

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first-order half life of approximately 96 days. Degradation pathways to cis- and trans-dibromoethene (c-DBE and t-DBE) and bromoacetylene (BA) were suggested. In turn, very slow transformations of c-DBE, t-DBE to vinyl bromide (VB) were shown or inferred. In these cases however, first-order half lives were greater than 220 days. Other relevant properties of the brominated compounds are shown in Table 1.

2.3. The aquifer system The Site is located on the Swan Coastal Plain (Playford et al., 1976), in suburban Perth, Western Australia. The ground surface in the immediate area of the presumed TBA release is at around 8.6 m Australian Height Datum (AHD). Here, the superficial sediments are subdivided into the upper, intermediate and lower aquifers. These closely correspond to the hydrogeological units described by Davidson (1995). The upper aquifer incorporates the relatively high permeability Bassendean Sand unit (8.6 to 3.8 m AHD) along with the underlying Guildford Formation (centred around 3 m AHD). The Guildford Formation is clayey in places and mostly acts as an aquitard between the upper and intermediate aquifers. The intermediate aquifer (2.7 to − 7.8 m AHD) is comprised of sands and silts of the Gnangara Sands Formation with mainly silty fine sand facies. However coarser sand layers are encountered, particularly near the base of the unit. The underlying Ascot formation, composed of silts and clays, acts as an important aquitard between the intermediate and lower aquifers. The water table is at around 3–3.5 m below ground in the Bassendean Sands of the upper aquifer. Heads are generally directed downwards from the upper to intermediate aquifer. Contamination from the TBA has only ever been observed in the upper and intermediate aquifers and at the time of these studies was largely absent from the upper aquifer.

3. Field methods The field study consisted of three separate parts: 1) Coring and installation of multi-level samplers; 2) the PITT; and 3) source zone pumping (SZP). However, the PITT and SZP used common infrastructure and sampling techniques. These are described below. Specific field methodology for the conduct of the PITT and SZP are discussed separately.

Fig. 1. Layout of pumping wells and multi-level sampling wells used for the PITT and SZP together with the location of cored profiles.

3.1. Pumping and monitoring wells Three continuous cores were collected from near the presumed source of the TBA release to establish the detailed stratigraphy prior to well placement. Pumping (injection and extraction) wells were placed in a five-spot pattern centred close to the assumed release of TBA (Fig. 1) roughly orientated with groundwater flow. The wells were screened over 9 m encompassing the majority of the intermediate aquifer (see Fig. 2). A grout seal was placed across the aquitard layer between the upper and intermediate aquifer. Eight multi-level (ML) sampling installations, two on each of the rays emanating from the central pumping well (Fig. 1), were also emplaced. Individual screens were 1 m long, 10 mm diameter, slotted aluminium tubing and connected to the surface with 4.8-mm diameter nylon tubing. The multi-level sampling screens were strategically placed in regard to the profile stratigraphy (Fig. 2). 3.2. Soil and groundwater sampling The three continuous cores to the base of the intermediate aquifer were collected by a direct push technique and cut into

Table 1 Properties of brominated compounds referred to in the study. Compound

Abbrev.

Molecular wt (g mol−1)

Density (kg m−3)

Solubility (mg L−1)

Solubility (μM L−1)

1,1,2,2-Tetrabromoethane† Tribromoethene† cis-1,2-Dibromoethene†ˆ trans-1,2-Dibromoethene†ˆ Bromoacetylene Vinyl bromide†

TBA TriBE c-DBE t-DBE BA VB

345.65 264.74 185.85 185.85 104.93 106.95

2966 2710 2246 2246

700 1200 8910 8910

2000 4500 47900 47900

1493

7600

71000

Sources: † Patterson et al. (2007). ˆ Same properties assumed for cis- and trans-dibromoethene.

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Fig. 2. Location of pumping wells and multi-level sampling screens in relation to stratigraphy in the section A–A′. Aquitards are shaded grey, dashed lines indicate facies boundaries in core P1.

100-mm sections for analysis. Subsamples were extracted with ether–acetone solvent spiked with two internal standards and analysed by gas chromatography–mass spectrometry (GC–MS) to determine contents of the brominated organic compounds. The brominated organics occurring as DNAPL was calculated from the total content assuming the dissolved fraction could be calculated from Raoult's Law (Mackay et al., 1991). The remainder of the core sections were used to determine the total liquid content, dry bulk density and porosity. Samples of groundwater from multi-level installations and pumping wells were collected in syringes after first purging the lines of stagnant water. The samples were immediately extracted into hexane (containing an internal standard) in the field before GC–MS analyses in the laboratory. Bromide concentrations in groundwater were determined by liquid chromatography using a conductivity detector. 3.3. Partitioning inter-well tracer test The PITT was conducted by injecting domestic mains water into the central well (C3) and extracting equally from the four surrounding wells. The constant total extraction rate of 0.55 L s − 1 was 1.7 times the injection rate of 0.32 L s − 1. After establishing the injection and extraction, 7 m 3 of an aqueous tracer solution containing methanol, hexanol, 2-methyl-1-hexanol and octanol was injected. Injection of mains water and extraction of groundwater continued for a further 19 days after the tracer solution. Batch tests were used to determine the partitioning coefficients of the alcohols between TBA and water in order to estimate average TBA saturation from the observed tracer retardation. The extracted groundwater was periodically sampled to follow the breakthrough of alcohol tracers. Eighty percent or greater of the injected tracers was recovered. Similar sampling

was done from the multi-level installations. Relative retardation of the alcohol tracers was determined from a moment analysis of their breakthrough at the extraction wells. Methanol was confirmed as a non-partitioning tracer and used as a reference (common inorganic tracers were at too-high natural abundance). Because of truncated time series, average groundwater flow velocity and retardation of the alcohols at the multi-level sampling screens were determined by fitting to a one-dimensional advection-dispersion equation. In addition, concentrations of brominated organics were determined in groundwater from the multi-level installations and pumping wells on three occasions over the course of the test. 3.4. Source zone pumping Source zone pumping was conducted from the central well C3 at a nominally constant rate which averaged 0.30 L s −1 (standard deviation 0.009 L s −1) for a run time of 252 days and then at 0.17 L s −1 for a further 33 days. The pumping was punctuated by a small number of stoppages for maintenance. The most significant of these were: a 5-day stoppage after 60 days run time; a 12-day stoppage after 139 days run time; and a 7-day stoppage after 231 days run time. The extracted groundwater was periodically sampled and analysed for brominated organics. Bromide was only analysed over the later part of the pumping sequence. Groundwater samples were collected from the multi-level installations after 57 and 216 days run time and analysed for brominated organics. 4. Field results 4.1. DNAPL mass and distribution from the PITT The most direct indication of the presence and saturation of DNAPL was gained from the three cores. The vertical

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distribution of DNAPL saturation, Sn, is presented in Fig. 3 for Profiles 1 and 2 (no significant DNAPL saturations were calculated for Profile 3). The DNAPL mass of brominated organics is reported in Table 2. The DNAPL was composed of 51–60% TBA by mass with the remainder being TriBE. On a molar basis, the TBA had a molar fraction of 0.44–0.54 in the DNAPL. The vertical distribution of Sn is dominated by spikes around −5.9 m AHD in both profiles and at −4.4 m AHD in Profile 1. The magnitude of Sn was low, with a maximum value 0.044, averaged over the 0.1-m sampling interval at −4.4 m AHD in Profile 1. Profile 1 showed that DNAPL saturations measured in the upper part of the intermediate aquifer were very low — a maximum of 0.001 at 1.1 m AHD. Significant dissolved phase concentrations of TriBE (up to 50% of solubility), and in some instances TBA (up to 20% of solubility) suggest the close proximity of DNAPL in other parts of the profiles. This is the case for the interval 0 to 3 m AHD in both Profiles 1 and 2 as well as around −4 m AHD in Profile 2. The DNAPL tended to occur adjacent to soil texture boundaries as was mostly found in fine-textured materials. The inferred distribution of DNAPL within the intermediate aquifer based on the retardation of partitioning tracers in the four multi-level installations at 2 m from the injection well during the PITT was similar to the core data. The correspondence was not exact, particularly for the upper part of the intermediate aquifer. Complications in interpreting these data included the 3 orders of magnitude range of apparent groundwater velocities leading to incomplete (or no) breakthrough of tracers. The concentration of TBA in groundwater in the profile under ambient conditions prior to the PITT (23 August 2007) and on 13 September 2007 near the end of the PITT (Fig. 4) adds further support to the sporadic distribution of DNAPL in the aquifer. In making the comparison between the core data and that from groundwater sampling during the PITT, account needs to be made of vertical flow induced by downward hydraulic gradients (as much as 0.1). A key observation is that there is little evidence for DNAPL being present outside the area swept by the PITT and was

Table 2 Estimates of combined DNAPL and dissolved mass of brominated compounds in cored profiles and DNAPL mass (in parenthesis). Location TBA TriBE c-DBE (kg m−2) (kg m−2) (kg m−2)

t-DBE (kg m−2)

Total (kg m−2)

Profile1

0.047 (0.006) 0.034 (0.005) 0.0087

10.0 (9.14) 5.11 (4.40) 0.0253

Profile2 Profile3

4.82 (4.65) 2.71 (2.64) 0

5.09 (4.48) 2.31 (1.75) 0.0032

0.087 (0.009) 0.059 (0.007) 0.013

most likely to have been within a 2-m radius of the central injection well. Analysis of the retardation of the partitioning tracers monitored in the four extraction wells suggested average DNAPL saturation of around 3–6 × 10 −4 within the swept volumes. This suggests that a volume of around 70 L TBA was present — equivalent to a mass of around 220 kg. This estimate is in line with what may be inferred from both the cored profiles (the average Sn over the length of core in the intermediate aquifer was 0.0004) and retardation at multi-level screens (average Sn was 0.0004 for the 41 screens in the intermediate aquifer in which tracers were detected). An important caveat in the DNAPL mass estimate is that the multi-levels indicated that some of the slowest flow paths would not have been sampled by the tracers and therefore are not included in the estimates from the extraction wells.

4.2. Indications from the PITT of DNAPL source depletion The sampling of the pumped groundwater enabled a coarse estimate of the average mass flux and total mass of brominated compounds extracted during the PITT (Table 3). The total mass discharge rate (1.4 kg day−1) and mass extracted (28 kg) were significant in relation to the mass estimated to be in the source zone. These mass fluxes corresponded to 5.14 mol of brominated organics per day and a total of 102 mol of brominated organics over the course of the PITT test. This suggested that extended pumping from the source zone may

Fig. 3. Vertical distribution of the estimated DNAPL saturation, Sn, in cored profiles.

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a)

b)

Fig. 4. Concentration of brominated organics in groundwater sampled from multi-level installations on — a) 23 August 2007, under ambient conditions prior to the PITT; and b) 13 September 2007, 15 days after the start of injection for the PITT. Locations relative to the central well (C3) are shown schematically. Concentrations of brominated organics are plotted against the sampled screened intervals. The concentration of TBA, TriBE and other measured brominated organics are indicated within the total concentration. The multi-level screens are indicated by hatched rectangles and the grey filled areas indicate the nominal location of aquitards defining the intermediate aquifer. “N.S.” indicates no sample.

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Table 3 Estimated mass flux of brominated compounds removed from extraction wells over the course of the PITT. Screen

TBA (kg day−1)

TriBE (kg day−1)

c-DBE (kg day−1)

t-DBE (kg day−1)

BA (kg day−1)

VB (kg day−1)

Total (kg day−1)

PITT2 PITT3 PITT4 PITT5 Total

0.221 0.029 0.020 0.173 0.442

0.216 0.053 0.082 0.560 0.911

0.0065 0.0031 0.0079 0.0242 0.0418

0.0042 0.0017 0.0039 0.0148 0.0247

0.00003 0.00001 0.00013 0.00259 0.00277

0.00001 0.00002 0.00003 0.00022 0.00028

0.447 0.087 0.114 0.775 1.423

achieve mass reductions over a suitably short time to enable further evaluation and confirmation of the source mass. 4.3. Concentrations and fluxes of brominated compounds during SZP The molar concentration and relative abundance of brominated compounds observed in the groundwater extracted from C3 over the course of the SZP are presented in Fig. 5. Total organic brominated compound concentration decreased from a maximum 173 μM L −1 to 38 μM L −1. As shown, TBA and TriBE were co-dominant and had changing relative abundance over the course of pumping. Combined, the minor constituents c-DBE, t-DBE, BA and VB never constituted more than 8.5% of the total molar concentration and for most of the period they accounted for 2.5–4%. A fairly rapid decline in concentration over the first 28 days of pumping is likely due to removal of resident groundwater initially in the source zone and in the down-gradient dissolved plume equilibrated to former natural flow conditions. Further evidence of the capture and extraction of previously derived groundwater is seen in the rate of decline of TriBE compared to TBA. 4.3.1. Capture of the down-gradient plume The extent to which groundwater from the dissolved plume down-gradient of the source was captured and incorporated into the groundwater pumped from the source zone was quantified using groundwater modelling (see Appendix A). This showed that by 30 days after the start of pumping, the fraction of the pumped water coming from the dissolved plume, fplume, reduces to around 0.15. This fraction reduces to 0.08 at 75 days of pumping and decreases slowly after that. The change in fplume over the duration of pumping is very much less than the observed change in the concentration of brominated compounds — excluding this as a dominant factor in the time trend of concentration in pumped groundwater. 4.3.2. Mass transfer limitations An important feature of the concentration time series is the general lack of evidence of mass transfer limitations. Mass transfer limitations in the partitioning between phases is usually manifested in the increase of dissolved concentrations in the mobile phase (groundwater) immediately after flow interruptions or as changing concentrations with changing flow rates. The 5-day stoppage at 60 days run time seems the only event to have provoked such an increase in concentration (Fig. 5). Perhaps most telling however, was the lack of any

change in concentrations for the nearly halved extraction rate for the period after 252 days run time.

4.3.3. Relative abundance of brominated organics Key questions are the source of the dissolved TriBE seen in the extracted groundwater and the processes behind the changing relative abundance of TBA and TriBE. The results from the core analyses indicate that the DNAPL would have been contributing both TBA and TriBE directly to the dissolved phase as well as some fraction of the aqueous-phase TriBE being contributed by contemporary debromination of the TBA. A further complication is the likely presence of noncontemporaneous (with the pumping) generated TriBE from existing groundwater down-gradient of the source zone. The concentration of Br − in the pumped groundwater also suggests that the aqueous-phase TriBE is only partially from the debromination of aqueous phase TBA. The average molar ratio of Br −:TriBE was around 0.4 to 0.5. However, the interpretation is complicated because, whilst the Br − accumulates from aqueous-phase transformations, the extracted TBA and TriBE will continue to equilibrate to the DNAPL it contacts.

4.4. Supporting information from sampling multi-levels The multi-level installations were sampled twice during the source zone pumping, on 24 November 2008 after 57 days of continuous pumping and extraction of 33 pore volumes (PV — the estimated volume, 45.4 m 3 of groundwater in the intermediate aquifer within 2 m of the pumping well), and 18 May 2009 after 216 days of continuous pumping and extraction of 122 PV. The total mass flux of brominated organics decreased from 4.5 to 2.0 mol PV−1 over this period. Results from the groundwater sampling are shown in Fig. 6. When compared to the groundwater sampling under ambient conditions prior to the PITT (Fig. 4), Fig. 6 indicates major reductions in concentrations within the source zone. There was great similarity in the distribution of concentrations for the two sampling dates although reductions in concentrations were seen for the later sampling. Concentrations about halved but these were for relatively low concentrations. Those locations with the highest concentrations showed the least proportionate reduction. Some changes in the relative abundance of the brominated organics were also seen when compared to that prior to the PITT. TBA persisted at higher relative abundance in the upper part of the profile at ML1 and in the lower profile at ML5. Also

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a)

129

depletion models) were evaluated against the source zone pumping data. These are summarised in Table 4 and described in more detail below. The models are casts in terms of the concentration time series Cs(t) or, in the case of the Rational model, the dissolved mass flux, Jm(t), pumped from the source zone. All incorporate the initial mass in the source zone, M0, the initial dissolved concentration, Cs,0, and/or mass flux, Jm,0, and a parameter (Γ, β, and σlog τ) reflecting the rate of depletion (except for the exponential function where this is implicit, i.e. Γ=1). 5.1. Background to the source depletion models

b)

5.1.1. Power function models Rao et al. (2002) amongst others originally proposed that the relative mass flux of a dissolved NAPL in groundwater across a control plane in the aquifer perpendicular to groundwater flow over time was related to the relative NAPL mass in the source zone by a power function, represented by: J m ðt Þ ¼ J m;0


 Mðt Þ Γ M0

ð1Þ

where t is time, Jm,0 is the initial mass flux, M is the mass in the source zone, M0 is the initial mass and Γ is the power parameter. Here the mass flux in groundwater is given by: J m ðt Þ ¼ qw Acp C s ðt Þ Fig. 5. (a) Concentration, C, of brominated organics and Br− and (b) relative abundance, C′, of brominated organics in pumped groundwater as a function of pumping time. Vertical dashed lines indicate major shut down of the pump (see text).

evident is the disappearance of brominated organics other than TBA and TriBE. Fig. 7 shows the flux weighted average concentrations, C f , for six sampling dates from before the PITT and up to during the SZP. Flux weighted concentrations were computed by assuming the computed groundwater velocities, ϑw, at each of the sampling screens during the PITT was indicative of the local volumetric flux density. Fig. 7 is revealing of the location and composition of the DNAPL source, in particular, the increase in the concentration and relative abundance of TBA during the PITT. Combined with the much reduced concentrations observed during the extraction of the SZP, this isolates the main DNAPL source to within 2 m of well C3. Both C f and the relative abundance of the brominated compounds in the multi-levels during the SZP deviates from that observed in the extracted groundwater. This adds more weight of evidence that the volume within 2 m of the well C3 as being more determinant of the concentrations observed in the pumped groundwater. 5. Models describing source depletion Four published relationships between the source mass depletion and dissolved mass flux/concentration (source

ð2Þ

where qw is the average specific flux of groundwater, Acp is the cross-sectional area of the control plane, and Cs is the average flux weighted concentration in groundwater leaving the source across the control plane. The power function relationship of Eq. (1) can be presented equivalently in terms of the average concentration Cs and NAPL mass (see Falta et al., 2005): C s ðt Þ ¼ C s;0




 Mðt Þ Γ M0

ð3Þ

As presented by Falta et al. (2005), an explicit expression of the mass of DNAPL in the source zone as a function of time can be derived using the power function given by Eq. (1). For the case where there is no biotic and abiotic transformation of the compound, the analytical formulation of the mass flux as a function of time follows directly:   Γ J m;0 ðΓ−1Þ ð1−Γ Þ J m ðt Þ ¼ J m;0 1 þ t M0

ð4Þ

Eq. (4) allows estimation of the initial mass flux, Jm,0, and initial mass, M0, from the time series of mass flux where estimates of Γ are available. It also follows that the dissolved concentration from the source follows the same relationship, that is:   Γ J m;0 ðΓ−1Þ ð1−Γ Þ C s ðt Þ ¼ C s;0 1 þ t M0

ð5Þ

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The special case of Γ = 1 leads to a simple exponential form for the mass flux (and source zone concentration) over time.
 J m;0 J m ðt Þ ¼ J m;0 exp − t M0

ð6Þ


 J m;0 t C s ðt Þ ¼ C s;0 exp − M0

ð7Þ

both flux, Rj = 1 − Jm(t)/Jm,0, and mass, Rm = 1 − M(t)/M0. In examining the relationship between Rj and Rm as a function of the standard deviation of the natural log of reactive travel time, σlog τ, through the source zone, they found that a power function relationship, similar to Eq. (1) could only be used as a good approximation where σlog τ ≤ 0.7. In this region of modest standard deviations of reactive travel time, they found the relationship: 1

Again, Eqs. (6) and (7) allow estimation of the initial mass flux, Jm,0, and initial mass, M0 where the mass flux approximates an exponentially decreasing function of time. 5.1.2. Stream-tube models Jawitz et al. (2005) and others (e.g. Basu et al., 2008; Zhang et al., 2008) have sought to base the relationship between discharging mass flux and NAPL mass on characteristics of flow within the aquifer using the distribution of reactive travel time through the source zone. The reactive travel time is essentially the time it takes for NAPL to be removed from a discrete flow tube in the aquifer. This particular approach has been termed equilibrium streamtube modelling. Jawitz et al. (2005) formulated the functional relationship in terms of the fractional reduction of

Rj ¼ ðRm Þα

ð8Þ

where  1:22 α ¼ 1:31 σ logτ

ð9Þ

It should be noted that Eq. (8) can also be written in the form:
1 J m ðt Þ M ðt Þ α ¼ 1− 1− J m;0 M0

ð10Þ

emphasising that there is a difference between the power parameters of Eqs. (1) and (8), and indeed the form of the functional relationship.

Fig. 6. Concentration of brominated organics in groundwater sampled from multi-level installations on 23 November 2008 and 19 May 2009 during the SZP. Locations relative to the central well (C3) are shown schematically. Concentrations of brominated organics are plotted against the sampled screened intervals. The concentration of TBA, TriBE and other measured brominated organics are indicated within the total concentration. The multi-level screens are indicated by hatched rectangles and the grey filled areas indicate the nominal location of aquitards defining the intermediate aquifer. “N.S.” indicates no sample.

C.D. Johnston et al. / Journal of Contaminant Hydrology 144 (2013) 122–137

131

Thus Jm is expressed as a rational function of Μ (the cumulative recovered mass) in Eq. (13) with parameters M0, Jm,0 and β. Note too that Eq. (13) can be rearranged to yield: Jm M0 1 þ β J m;0 ¼ Μ 1− JJ m

ð14Þ

m;0

This indicates a linear dependence of M0 on β. 5.1.3. Error function model Jawitz et al. (2005) also noted that the reactive travel time for the dissolution of a NAPL source may be assumed to follow a log normal distribution. In this case, the fractional reduction in dissolved mass flux and concentration would follow a cumulative distribution in the form of an error function via: Fig. 7. Flux averaged concentration, C f , of brominated organics in groundwater from multi-level installations 2 m from well C3 on different dates during the PITT and SZP. Note the x-axis is not quantitative.

" J m ðt Þ ¼ 0:5 1−erf J m;0

logt−μ logτ pffiffiffi 2 σ logτ

!# ð15Þ

and: For the cases where σlog τ > 0.7, Jawitz et al. (2005) proposed an alternative empirical rational function relationship between the mass flux reduction and reduction in NAPL mass:   R ð1 þ βÞ Rj ¼ m 1 þ βRm

ð11Þ

" C s ðt Þ ¼ 0:5 1−erf C s;0

logt−μ logτ pffiffiffi 2 σ logτ

!# ð16Þ

Here, μlog τ is the mean of the logarithm of the reactive travel time. 5.2. Explicit estimation of model parameters

where  4:50 β ¼ 1:03 σ logτ

ð12Þ

Eq. (11) is not readily amenable to being solved to give Jm as an explicit, closed-form function of time and thereby allow identification of M0 and Jm,0 by the fitting of a time series of observations (as is possible with the power function model). However, in this case it is possible to identify M0 and Jm,0 by fits to the relationship between Jm and the cumulative recovered mass, Μ. Noting that the mass remaining in the source zone, M, is given by M = M0 − Μ and simplifying, Eq. (11) leads to: " J m ¼ J m;0

#

1− MΜ

ð13Þ

0

1 þ β MΜ

0

The reactive travel time, σlog τ, which is used directly in the Error Function model, has also been used to estimate Γ in the case of the Power Function model and β for the Rational model. This offers the prospect of direct parameter estimation from independent observations rather than fitting these rate-of-depletion parameters. 5.2.1. Estimates of the reactive travel time Neither the PITT nor the later pumping from the central extraction well provide direct estimates of the distribution of the reactive travel time (i.e. times for dissolution of the NAPL). However, the PITT did present the distribution of groundwater travel times from the central injection well to a lateral distance of 2 m which appeared to encompass most of the DNAPL source. The computed groundwater travel times, τ, over this distance had a lognormal distribution with a standard

Table 4 Source depletion models used to describe the concentration, Cs(t), and mass flux, Jm(t), of brominated organics pumped from the source zone. Name

Expression

Parameters

Power function

h i Γ J ðΓ−1Þ ð1−Γ Þ C s ðt Þ ¼ C s;0 1 þ m;0M0 t

Cs,0

M0

Exponential

  J C s ðt Þ ¼ C s;0 exp − Mm;00 t

Cs,0

M0



Jm,0

M0

β

Cs,0

M0

μlog τ

Rational J m ðt Þ ¼ J m;0 Error function

Μ ðt Þ

1− M



Γ

0 Μ ðt Þ

1þβ M

0


 logt−μ C s ðt Þ ¼ 0:5C s;0 1−erf pffiffi2 σ logτ logτ

σlog τ

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C.D. Johnston et al. / Journal of Contaminant Hydrology 144 (2013) 122–137

Fig. 8. Fits to the observed concentrations using the power function relationship for different observation periods (see text) and comparing fitting of the power function exponent, Γ, with the use of Γ=2.063 calculated from the estimated σlog τ =1.14.

deviation σlog τ = 1.14 and μlog τ = 4.14 (travel time in hours, N = 23). Although not strictly equivalent, the observed value of σlog τ for groundwater flow velocity provides at least a starting point for predictions of the source mass reduction based on the functions defined in terms of reactive travel time. The standard deviation of the reactive travel time would differ from that of the groundwater travel time according to the correlation between DNAPL saturation/mass and hydraulic conductivity of the flow paths.

Fig. 10. Fits to the observed molar mass flux using the rational function model for different observation periods (see text) and comparing fitting of the parameter, β, with the use of β = 1.857 calculated from the estimated σlog τ = 1.14.

relationship between Jm/Jm,0 and M/M0 provided the desired estimate of Γ equal to 2.063.

5.3. Model fits

5.2.2. Estimates of depletion model parameters from reactive travel time Estimates of the parameters β and Γ from the stream tube approach were made as described above. The parameter β was calculated directly from Eq. (12) and yielded a value of 1.857. To find a value of Γ for the power function model, Eq. (11) was used (with the directly calculated value of β) to derive the relationship Rj(Rm) and hence the relationship between Jm/Jm,0 and M/M0. The exponent of the best power function fit to this

For the fitting of the various source depletion models, the combined/total molar concentration and molar mass flux of brominated compounds was used. For the models that describe the time series of concentration and mass, pumped pore volumes (PV) of groundwater was used as a surrogate for time. As used previously, 1 PV was defined as the estimated volume (45.4 m3) of groundwater in the intermediate aquifer within 2 m of the pumping well. This particular radius matches the distance over which the travel time distribution was characterised as well as being the distance within which most of the DNAPL mass appeared to be located. In the case of the rational model, the molar mass flux was redefined as the molar mass per pore volume pumped (i.e. per volume) instead of per day (i.e. per time).

Fig. 9. Fits to the observed concentrations using the exponential function relationship (Power function with Γ = 1) for different observation periods (see text).

Fig. 11. Fits to the observed concentrations using the Error function relationship for different observation periods (see text) and comparing fitting of σ, with the use of σ from the estimated σlog τ =1.14.

C.D. Johnston et al. / Journal of Contaminant Hydrology 144 (2013) 122–137 Table 5 Parameter values determined from the fitting of power function and exponential models along with the coefficient of determination (R2). Errors of the parameter are shown in parenthesis. Fitting range (PV)

Γ

Power function model 17–43 1.464 17–143 2.063 44–143 2.109 44–143 2.063 17–153 1.550 17–153 2.063 44–153 1.572 44–153 2.063 Exponential model 17–143 1 (0) 44–143 1 (0) 17–153 1 (0) 44–153 1 (0)

(0.693) (0) (2.054) (0) (0.582) (0) (0.803) (0)

C0 (μM L−1)

M0 (kg)

137 142 128 127 138 142 123 129

(8) (4) (19) (5) (7) (3) (12) (5)

254 320 333 328 265 320 272 325

131 112 130 112

(3) (4) (3) (3)

205 210 208 211

Fitting range (PV)

σ

(75) (10) (228) (8) (62) (8) (87) (6)

0.9607 0.9601 0.9571 0.9571 0.9675 0.9670 0.9642 0.9640

17–143 17–143 44–143 44–143 17–153 17–153 44–153 44–153

1.081 1.14 1.257 1.14 1.102 1.14 1.148 1.14

(5) (4) (4) (3)

0.9590 0.9546 0.9651 0.9628

Table 6 Parameter values determined from the fitting of the rational model along with the coefficient of determination (R2). Errors of the parameter are shown in parenthesis. Fitting range (PV)

β

17–143 17–143 44–143 44–143 17–153 17–153 44–153 44–153

0.363 1.857 0.769 1.857 0.440 1.857 0.476 1.857

(0.474) (0) (1.096) (0) (.394) (0) (0.61) (0)

Jm0 (M PV−1)

M0 (kg)

6.47 7.36 6.28 7.20 6.52 7.41 6.01 7.34

224 294 256 296 229 290 243 290

(0.42) (0.22) (1.09) (0.29) (0.36) (0.19) (0.72) (0.24)

Table 7 Parameter values determined from the fitting of the Error function model along with the coefficient of determination (R2). Errors of the parameter are shown in parenthesis.

R2

In all, the models were fitted over four different observation periods. This was to examine the effects of including some of the earlier observations whilst a greater contribution of the dissolved flux may have come from the down-gradient plume as well as the effect of including later observations where pumping rate had been appreciably reduced. Observations prior to 28 days of pumping (equivalent to 17 pore volumes) were excluded from all fits. In other fits, early observations up to 76 days (equivalent to 44 pore volumes) were excluded. The pumping rate was reduced after 252 days of pumping, at which time 143 pore volumes had been pumped. All of the source depletion models gave reasonably good fits to the observed concentration/flux data within the particular fitted ranges (Figs. 8–11). The coefficient of determination (R2) varied from 0.955 to 0.969 over all the fits presented here (see Tables 5–7). For each of the depletion models, the fits were clearly differentiated by the inclusion/exclusion of the early data in the range of 17–44 pore volumes. Those fits incorporating these data gave higher predictions of concentrations and fluxes for observations up to about 80 pore volumes. However, the differentiation was not as strong in the case of the rational model. Part of the differentiation can be attributed to the spike in concentrations immediately following the pumping interruption at 35 pore volumes. Even so, it is notable that those fits to the later times series under-predict observation of

R2 (25) (11) (45) (11) (19) (8) (25) (8)

0.9591 0.9533 0.9571 0.9562 0.9661 0.9609 0.9643 0.9620

133

μ

(0.137) (0) (0.349) (0) (0.113) (0) (0.211) (0)

4.481 4.440 4.482 4.610 4.474 4.445 4.588 4.597

R2

C0 M0 (μM L−1) (kg) (0.100) (0.047) (0.411) (0.058) (0.092) (0.037) (0.235) (0.045)

121 124 118 109 122 124 110 109

(7) (3) (29) (4) (7) (3) (17) (4)

257 270 306 279 263 271 279 277

(24) (52) (7) (55) (30) (54) (12) (56)

0.9626 0.9623 0.9570 0.9567 0.9689 0.9688 0.9640 0.9640

concentration/flux immediately prior to this interruption. Importantly, all the model predictions grossly under-predict concentrations observed prior to 17 pore volumes of pumped groundwater. This initial period is where the greatest contributions from the capture of the pre-existing dissolved plume were expected. An important feature is that the inclusion of the reducedpumping rate data (that >143 pore volumes) seems entirely consistent with the depletion functions established from the fitting of the models to data up to the time that pumping rate was reduced. This gives further justification (based on assuming no difference in mass transfer kinetics) for including these reduced-pumping rate data into the process of identifying the appropriateness of the different models and their parameter values. Overall, it is difficult to choose any particular source depletion model as a superior performer in describing the observed data over the fitting period. Where all parameters were fitted, there was essentially no difference in the R2. The Error function model had a slightly higher average R2 (0.963) with the rational model having the lowest average (0.962). Where the estimated σlog τ was used to specify model parameters, the range in R2 was greater, the Error function model again had an average R2 of 0.963 whilst the rational function model had average R2 = 0.958. The special case of the exponential function had an average R2 of 0.960. Even from a more qualitative point of view, no model stands out as superior. 5.3.1. Model parameters The model parameters gained from fitting the source depletion models to the observed data are summarised in Tables 5–7. These, including the source mass, are discussed in more detail below. 5.3.1.1. Power function. Where Γ was included as a fitting parameter, its estimated value was mostly appreciably less (Table 5) than the value of Γ estimated from σlog τ (2.063). However, when fitted to data over the range 44–143 pore volumes, a similar value of 2.109 was derived from the fit to the data. The large error associated with this estimate is notable. Otherwise, the estimated Γ was insensitive to the fitting range, and varied from 1.464 to 1.572. In terms of the estimated initial mass, M0, the value of Γ estimated from σlog τ generally gave higher estimates of the initial mass present (Table 5). Values of 254–272 kg where Γ

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was a fitting parameter compared to values of 320 – 328 kg where Γ was set to the value estimated from σlog τ. Again, the exception to this was where Γ was fitted to observed data over the range 44–143 pore volumes, in which case the estimate for M0, 333 kg, reflected the greater estimated (fitted) value of Γ. However, the error associated with this particular estimate of M0 was also large. 5.3.1.2. Exponential model. The various estimates of M0 from the exponential model fits for different observation ranges are remarkably similar, varying from 205 to 211 kg. Indeed, given the errors associated with the estimates, none could be considered to be significantly different to the mean value of 208 kg. 5.3.1.3. Rational model. For the rational model, values of β derived as part of the model fitting processes, 0.363–0.769, were much lower than that of 1.857 estimated from σlog τ (see Table 6). The impression is that the fits to the observed data were not so sensitive to β which is highlighted by their relatively large estimation errors — typically greater than the estimated value. Of the fitted values of β, that fitted to data over the range 44–143 pore volumes stood out as being much higher (0.769) and having a much greater estimation error (1.096) compared to those from the other three estimates of β. This translated to a higher estimate of the initial mass (256 kg) compared to the other rational models where β was fitted (224–243 kg). The estimates of M0 where β was set to 1.857 were higher again, ranging from 290 to 296 kg. 5.3.1.4. Error function. For the Error function model, the fitted value of σ and inferred value of M0 for the data range 44–143 pore volumes again produced higher values than the other fitting ranges and had larger estimation errors (Table 7). Ignoring this particular value of σ, it is notable that the values of σ derived from the fitting of the model were relatively close to that estimated from the distribution of tracer travel times in the aquifer. Fitted values of 1.081–1.148 compared to the value of σ = 1.14 from groundwater tracer travel times. This similarity was reflected in the estimates of the initial mass. Estimates of 257–279 kg where σ was fitted compared to 270–279 kg where σ was set to 1.14. 5.3.2. Estimates of DNAPL mass from depletion models Where conservative selections were made to minimise any effect of capturing the down-gradient plume, estimates of the source mass ranged from 208 to 325 kg (with mean 267 kg) for the 14 models and fitting schemes considered. This was impressively close to the estimate of 220 kg made from the PITT. The uncertainty of the fitted estimates of initial DNAPL mass was also relatively small, typically around 6% although it did range up to 32%. DNAPL mass estimates were greatest where the log of the variance of travel time was used explicitly in the source depletion models (271–325 kg, mean 295 kg) compared to where the associated power exponent and variance was fitted freely (229 – 279 kg, mean 258 kg). This follows from the smaller inferred variance and power function exponents identified through fitting to the concentration data.

5.3.3. Simplifying the multi-component nature of the contaminants From a pragmatic viewpoint, the simplification of reducing the multi-component contaminant to a single species based on molar concentrations appeared to be successful. Here the success was measured by the predictability of the observed data and the consistency of the estimates of DNAPL mass with those from the PITT and core samples. This simplification is based on the contaminants stemming from the sequential debromination of the TBA parent, thus preserving molar mass. However, perhaps a little surprising is that the success of the simplification is despite the difference in the solubility of the dominant TBA and TriBE. The evidence from various data is that the DNAPL was a mixture of TBA and TriBE. Preferential dissolution of TriBE is expected from its greater solubility and otherwise inferred from the increased relative abundance of TBA. This could decrease the rate of dissolution of the DNAPL as a whole over time and this would detract from the validity of the source depletion approach. On the other hand, degradation of the TBA in the aqueous phase could be expected to increase the rate of dissolution of TBA (Carr et al., 2000; Chu et al., 2007; Cope and Hughes, 2001) and the repartitioning of the TriBE to the DNAPL would maintain its mole fraction in the DNAPL (Ramsburg et al., 2010, 2011). Both factors could mitigate appreciable changes in the solubility of the DNAPL. 5.3.4. Forward prediction and model discrimination Extrapolation of the models to further pumping from the source zone shows differences in their predictions (Fig. 12). This gives further information on the period of pumping that may be required to be able to discriminate between the models. The fits shown are to data over the range 44–153 PV. Fig. 12 shows an increasing deviation of the exponential function when compared to both the other power function and the Error function fits. The extrapolations suggest that observable differences between the models should emerge after 200–300 PV pumped. It appears that it would be much harder to discriminate between the other power function and error function fits, even in the longer term. Observable differences between the power functions with fitted Γ (= 0.476) and Γ = 1.857 calculated from σlog τ would only seem to emerge after about 300 PV. By 500 PV, the predicted

Fig. 12. Extrapolated concentration time series of brominated compounds in pumped groundwater according to model fits to the observed data (fits to data 44–153 PV).

C.D. Johnston et al. / Journal of Contaminant Hydrology 144 (2013) 122–137

concentrations are only 20% different (7.8 c.f. 9.6 μM L − 1). The Error function model is intermediate to the two Power function models shown. As such, it will be difficult to distinguish from the Power function models until very long pumping times. It is possible to reconstruct a time history of pumped concentrations from the fitted rational models where the recovered mass is matched to a particular observed concentration at a certain pumped pore volume. The time series of predicted concentration calculated in this way is shown for comparison in Fig. 12. This shows that the C(tD) relationships for different β diverge fairly strongly when extrapolated for continued pumping. These relationships also bracket those for the Power and Error functions. A clear discrimination between the rational models with different β should be rendered within a further 50–100 PV of pumping. Discrimination of the rational model with fitted β (=0.476) from those of the Power functions and Error function seems likely to be possible after about 350 PV. Another important aspect of the extrapolation of the models is the timing required to achieve a specified concentration or mass flux. A useful comparison is that of the pumped pore volumes to achieve a pumped concentration of 10 μM L − 1 (tD,10). This concentration is approximately a further 4-fold reduction on the observed field concentrations at the end of pumping and a 10–20 fold reduction from the concentrations at the start of pumping. Estimates of tD,10 ranged from 341 to 509 PV and had a median value of 453 PV. Notably the exponential function produced the lowest estimate of tD,10 (341 PV). Where the defining parameters Γ, σ and β were fitted, tD,10 varied over the narrower range of 397 to 455 PV with a mean and median value around 430 PV. 5.3.5. Constancy of source-depletion model parameters A feature of the models evaluated was the ability to describe the experiment data with constant parameters. Other laboratory and numerical evaluation has highlighted the need to vary parameter values as the architecture of the source NAPL varies over the course of its depletion (DiFilippo and Brusseau, 2011). Christ et al. (2010) particularly showed this may be the case for mixed architecture where the DNAPL distribution becomes dominated by pools within the aquifer. Chen and Jawitz (2009) also argue that parameters will vary according to the stage of dissolution of the source and that ultimately the depletion model will assume an exponential form. The inference from the present study is that the source zone has indeed reached or is close to the stage of being well aged. There is supporting evidence for this in the distribution of DNAPL in cores. This was shown by the absence of DNAPL from higher permeability zones and its presence in lower-permeability intervals of the intermediate aquifer. As indicated above, it may still require considerable further depletion from the source to confirm that the dissolved concentration is indeed following an exponential decrease, rather than some other functional relationship. 5.3.6. Comparative data requirements The source depletion analysis was efficient in its data requirements, based in this case on a relatively low intensity sampling program albeit over an extended period. The

135

efficiency is based around similar approaches like the integral pump test (Bauer et al., 2004; Bayer-Raich et al., 2004; Bockelmann et al., 2001) which integrate over a volume of the aquifer appropriate for management. From the evidence of equilibrium dissolution within the source zone, this approach also seems to have avoided the potential uncertainty of the interaction of partition tracers with DNAPL sources in thick pools and heterogeneous aquifer systems that are associated with partitioning inter-well tracer tests (Moreno-Barbero and Illangasekare, 2006) in this particular instance. In addition, the usual extreme intensity of sampling required for a PITT is avoided. However, supporting information from elements of the PITT in terms of the spatial distribution of groundwater velocity and contaminant concentrations were valuable in the overall interpretations but ultimately were not a necessary element of establishing the mass depletion–mass flux relationships. 6. Conclusions The poorly documented release history, complex and novel chemistry of a brominated solvent contaminant and the heterogeneity of the aquifer system provided an appreciable challenge to characterising the DNAPL mass and architecture at the study site. However, the pragmatic approach of applying simplified source depletion models to contaminant concentrations in pumped groundwater during source zone pumping was shown to provide valuable information on the source zone mass. When coupled with measurements of in situ groundwater concentrations from multi-levels within the aquifer, further information on the complex architecture of the source DNAPL in the heterogeneous aquifer was able to be identified. Information gained from tracer injection through the same well used for source zone pumping as part of a partitioning inter-well tracer test proved to be a valuable adjunct to the analyses of the source zone depletion pumping data. When viewed as a whole, these various data enabled a reliable conceptual site model to be established which allowed confidence to be placed in the outcomes from source zone depletion modelling. In itself, the source depletion analysis was efficient in its data requirements. The mass flux-source depletion models considered performed well in describing the decreasing concentration with pumped volume. The method appeared robust in the sense that the goodness of fit was similar and estimates of critical parameters such as the initial DNAPL mass present were consistent. The model fits were surprisingly insensitive to the exponent used in the power function fits over the range of the observed data. From extrapolation, it was evident that it would only be after appreciably greater reductions in source mass/pumped concentration that discrimination between the values of the exponent, and therefore model, could be made. Only at this time would an evaluation of whether or not an independent estimate of the variance of the reactive travel time would warrant the effort of independently obtaining such a value. This may well be justified where the approach of the dissolved mass flux or concentration to a preset target is an important remediation endpoint or management criterion. Longer observation would also be warranted to elucidate those issues of the effect of changing DNAPL composition on the overall dissolution rate and the potential effects of changing DNAPL architecture on depletion model parameters.

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A key outcome was the consistency of the estimates of the DNAPL mass between the source depletion models as well as its correspondence to estimates from the PITT. These multiple lines of evidence provide confidence in the interpretations at the site stemming from a robust conceptual site model. An important aspect of the use of the mass depletion models was to exclude early data and the influence of the capture of the dissolved plume. Acknowledgements We express our deep appreciation to Barry Goodridge for his efforts in maintaining the pumping and treatment system along with the support of Pieter Swart. We also thank David Reynolds, Dave Thomas, Keely Mundle, and Julia Horgan for their assistance and support. Brad Patterson also provided valuable insights into the chemistry of the brominated compounds. Appendix A. Evaluating the capture of the down-gradient plume A relatively simple, two-dimensional-in-plan, numerical groundwater model was used to further evaluate how the capture of the down-gradient dissolved plume may have influenced the pumped concentrations. The simulator Feflow (Diersch, 2004) was used for predicting steady state flow under pumped conditions where the aquifer was assumed uniform and isotropic, constant saturated thickness and where a regional groundwater flow was maintained by fixed heads distant from the pumping well. The hydraulic conductivity (1.4 m day−1) was taken from the analysis of the confined aquifer response during pumping, the porosity (0.344) was taken from core sample measurements, the regional hydraulic gradient (0.012) was taken from direct observations and the pumping rate (0.30 L s−1) was the average for the first 252 days of pumping. A rectangular-in-plan plume the width of the source zone was assumed to emanate from the source. In the case simulated here, the fraction of the pumped water from the plume, fplume(t), is given by integrating the specific volumetric flux of groundwater normal to the isochrone, qwn(x,y), over the arc length, ℓp; t ðx; yÞ, of the isochrone passing through the plume at any given time and comparing it to the total volumetric flux of groundwater being pumped, Qw,total:

f plume ðt Þ ¼

∮ ℓp;t qwn ðx; yÞ d ℓ Q w;total

17

The time series of fplume(t) calculated in this way is shown in Fig. 13. Fig. 13 shows a sharp drop from the initial stage where all the extracted water was part of the dissolved plume and within the DNAPL source zone prior to the start of pumping (fplume(t) = 1), to where the isochrones move outside the DNAPL source zone. References Annable, M.D., Rao, P.S.C., Hatfield, K., Graham, W.D., Enfield, C.G., 1998. Partitioning tracers for measuring residual NAPLs for field-scale test results. J. Environ. Engineering 124, 498–503.

Fig. 13. Computed time series of the fraction of the pumped water sourced from within the dissolved-phase plume, fplume(t).

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