Influence of porous medium and NAPL distribution heterogeneities on partitioning inter-well tracer tests: a laboratory investigation

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Abstract

The inter-well partitioning tracer test seemingly provides an attractive way of investigating the presence of non-aqueous phase liquids (NAPLs) in aquifers. Although the feasibility of this rather new technique has been tested in the field, only few laboratory experiments have been performed to test its validity at scales greater than the column scale. In this study, a partitioning tracer test was conducted in a nominally two-dimensional, intermediate-scale flow cell containing a tetrachloroethene (PCE) spill. Tracer breakthrough curves were obtained at 14 sampling ports and an extraction well containing three outlets. Estimated PCE contents resulting from the tracer technique were compared to PCE saturations obtained at 800 locations by gamma radiation. An inverse procedure, based on the two-site, non-equilibrium convection–dispersion equation, was used in addition to the moment method for sampling port data analysis. Although the inverse procedure produced slightly better results than the moment method, the tracer technique generally underestimated the amount of DNAPL contained in our aquifer model. Notably, our results showed that the pooled part of the DNAPL spill was not detected. This was attributed to the low aqueous phase permeability within the DNAPL pool in combination with rate-limited partitioning of the tracers into the DNAPL. Our analysis indicate a general difficulty for the tracer technique to detect NAPL located in pools or large lenses.

Introduction

The partitioning tracer method was first extensively used in the petroleum industry (Cooke, 1971, Tang, 1992), but has recently gained interest among environmental engineers and scientists (Jackson and Pickens, 1994, Jin et al., 1995, James et al., 1997, Annable et al., 1998). The method is intended to estimate amounts of a non-aqueous phase liquids (NAPLs) present in aquifers. The technique involves the use of a partitioning and a non-partitioning tracer which are simultaneously injected into an aquifer by means of an injection well. The partitioning tracer is soluble in the NAPL present in the aquifer as well as in the carrier solution, whereas the non-partitioning tracer is soluble only in the ambient ground water. Although Wise et al. (1999) demonstrated that partitioning isotherms for commonly used tracers are non-linear, it is customary, at low tracer concentration, to consider a linear relationship between non-aqueous (cn) and aqueous phase tracer concentration (ca) at equilibrium, i.e.cnca=K(the notation list explains all symbols and gives their dimensions). When a partitioning and a non-partitioning tracer are injected into an aquifer simultaneously, the non-partitioning tracer molecules move with the ground water without interacting with the NAPL, while the partitioning tracer molecules move back and forth between the aqueous and non-aqueous phase (Jin et al., 1995). Consequently, the partitioning tracer transport is delayed compared to that of the non-partitioning tracer. The ratio of the partitioning tracer arrival time (tp) and the non-partitioning tracer arrival time (tnp) at an extraction or observation well may be referred to as the retardation factor R. Assuming Eq. (1) to be valid at all times and locations in the porous medium (local equilibrium assumption, see Valocchi (1985)), the retardation factor can be related to the average NAPL saturation (Jin et al., 1995). Although the reader is referred to Jin et al. (1995) for a mathematical development of the relationship between R and NAPL saturation, it can also be derived upon from a probabilistic point of view. If a partitioning tracer molecule has a probability of 1/R to be in the aqueous phase at a given location at any given time, then the partitioning tracer will take R times as long as the non-partitioning tracer to travel a given distance (Jury and Roth, 1990). Therefore, the retardation factor is the ratio of the total mass of partitioning tracer per pore volume and the mass of the partitioning tracer in the aqueous phase, also per pore volume (the non-aqueous phase is not moving). Hence,R=tptnp=ct(1−Sn)ca=(1−Sn)ca+Sncn(1−Sn)ca=1+KSn1−Snwhich leads toSn=R−1R−1+KTraditionally, R is estimated by direct calculation of partitioning and non-partitioning tracer arrival times. The moment method is typically used to obtain these arrival times from breakthrough curves in response to a pulse input as stated, e.g. for the partitioning tracer by:tp(x)=0tca(x,t)dt0ca(x,t)dtIn the above expression the breakthrough time corresponds to the time at which half of the tracer mass has arrived at the observation location. For a step input with the concentration of the aqueous tracer changing from c0 to 0, the arrival time is equated to the normalized surface under the breakthrough curve:tp(x)=0ca(x,t)c0dtFor a step input with the aqueous tracer concentration changing from 0 to c0, the arrival time istp(x)=0c0−ca(x,t)c0dtThe expressions stated so far are based on the local equilibrium assumption. However, it can be shown (Harvey and Gorelick, 1995) that Eq. (2) is theoretically still valid under non-equilibrium conditions and for a non-uniform NAPL distribution. In that case, Eq. (2) gives the average retardation factor along the streamline passing through a sampling point (port) or for that region of the aquifer associated with the aqueous phase that is intercepted by an extraction well. Therefore, the partitioning tracer technique can theoretically be carried out without knowledge of the NAPL and/or the partitioning tracer exchange rate distribution. In this paper, we investigated the validity of this assertion by studying the cumulated influence of non-equilibrium conditions and NAPL non-uniformity on a partitioning tracer test performed in an intermediate-scale flow cell.

A repercussion of non-equilibrium tracer partitioning on breakthrough curves is the so-called tailing, i.e. in response to a pulse input, the breakthrough curve of the partitioning tracer shows a long-lasting decrease in tracer concentration. Other factors contributing to tailing are non-uniform NAPL distributions, permeability contrasts, and dilution effects. Especially the presence of NAPL pools or lenses, where greatly reduced aqueous phase permeabilities exist, would seem to contribute to long-term tailing. Tailing creates uncertainty in the numerical integration of the curve or, in case of missing tail data, results in an underestimation of the arrival time. To overcome this drawback when applying the moment method, Annable et al. (1998) extrapolated missing tail data assuming empirical exponential decay. In an attempt to limit tailing-induced errors in the estimation of retardation factors, and to determine to what extent our partitioning tracer test was under the influence of non-equilibrium partition, we analyzed breakthrough curves with a fitting procedure taking into account the kinetics of tracer transfer between the aqueous and non-aqueous phase. We made use of the non-dimensional form of the one-dimensional, non-equilibrium convection–dispersion equation (CDE) for modeling transport of the partitioning tracer, as suggested by Hatfield et al. (1993). The method was easily implemented since analytical solutions for the non-dimensional CDE and curve fitting procedures are readily available (Parker and van Genuchten, 1984, Toride et al., 1995). The results of this technique and the moment method were compared to actual saturation values determined by gamma radiation scanning.

Following a NAPL spill into an aquifer, the NAPL is likely to exist in different forms. It will not only exist in residual form, but also as ganglia, lenses, and pools of different sizes. These different forms will have different exchange properties with respect to tracers present in the aqueous phase. In an attempt to incorporate the influence of different NAPL occurrences in our aquifer model, we considered a two-site partitioning model as the basis of an inverse analysis of partitioning tracer breakthrough curves (Brusseau, 1992, Hatfield et al., 1993, Nkeddi-Kizza et al., 1984, Cussler, 1984, van Genuchten and Wagenet, 1989, Sardin et al., 1991). Analogous to the earlier developed two-site model (Selim et al., 1976) for solid–liquid interactions, we assumed a fraction F of the NAPL to consist of instantaneous sites, where equilibrium conditions exist, and a fraction (1−F) of rate-limited sites, for which first-order mass transfer between aqueous and non-aqueous phase was adopted. The basic premise of this approach is to capture partitioning tracer exchange phenomena for which no mathematical descriptions are yet available, especially those related to heterogeneities (Nelson et al., 1999). Considering no adsorption on solid particles, the one-dimensional convection–dispersion equation, describing transport of a tracer partitioning into residual NAPL at saturation Sn, can then be expressed as(1−Sn)cat+Sncn1t+Sncn2t=(1−Sn)D2cax2−(1−Sn)vcaxcn1=FKcacn2t=α[(1−F)Kca−cn2]These equations were obtained following the argument presented by van Genuchten and Wagenet (1989) for describing two-site adsorption on solid surfaces. , , are similar to submodel 3 of Hatfield et al. (1993), except that we make use of NAPL saturation and a liquid–liquid partitioning coefficient (K), while these authors chose to formulate their model in terms consistent with adsorption on solid surfaces. We would like to point out that the above model does not include any description of exchange between potential zones of immobile water and bulk ground water flow. It was assumed that the influence of immobile water on tracer transport was limited, and that it could be incorporated in the value of the dispersion coefficient D, following the approach of Passioura (1971).

Using the following non-dimensional variablesT=vtLX=xLP=vLDC1=cac0C2=cn2(1−F)Kc0R=1+KSn(1−Sn)RF=1+FKSn(1−Sn)β=RFRω=α(1−β)RLvthe transport equations take the form:βRC1T+(1−β)RC2T=1P2C1X2C1X(1−β)RC2T=ω(C1−C2)The convection–dispersion equation for the partitioning tracer is thus available in the non-dimensional, classical form used for physical and chemical non-equilibrium (Nkeddi-Kizza et al., 1984, Leij and Toride, 1998). The model used herein (special case of model 4 of Brusseau (1992); submodel 3 of Hatfield et al. (1993)) is thus equivalent to the two-site adsorption model first proposed by Selim et al., 1976, Cameron and Klute, 1977 and to the model describing solute transport in sorptive and aggregated porous media presented by van Genuchten and Wierenga (1976). The reader should notice that when no instantaneous sites are considered (F=0, =1), the form of the model we used further reduces to the non-equilibrium adsorption model of Lapidus and Amundson (1952) and to the mobile–immobile water model of Coats and Smith (1964). The choice of a two-site model is supported by experimental work of Augustijn et al., 1991, Hatfield et al., 1993, who demonstrated that , can successfully describe transport of partitioning tracers in sand columns containing a rather uniform residual NAPL. The two-site model was subsequently implemented in a fully inverse fitting procedure to estimate parameters such as NAPL amounts and transfer rates between the aqueous and organic phase. Even though the NAPL saturation was not uniform during our experiments, it was believed that an inverse procedure using , would be successful in estimating meaningful retardation factors. Support to our approach was presented by Leij and Dane (1991), who concluded that tracer retardation depends only on the amount of absorption and not on the absorption distribution. The procedure, which only uses partitioning and non-partitioning tracer breakthrough curve information, was thus tested as an alternative to the classical moment method. Five parameters, other than L and c0, are needed to model the partitioning tracer transport according to , : v, D, R, β, and ω. Because the non-partitioning tracer is unaffected by the presence of the NAPL, its transport can be used to independently obtain values for the pore water velocity and the dispersion coefficient, which are physical properties that also apply to the partitioning tracer transport. Consequently, we fitted the non-partitioning tracer breakthrough curves to solutions of the conventional CDEct=D2cx2−vcxBecause dispersion coefficient and aqueous phase velocity are physically related by the notion of dispersivity (Bear, 1972), we checked the mathematical uniqueness of the sets of values obtained through breakthrough curve fitting. This was done by verifying that the set of parameters returned by the optimization scheme was insensitive to the values of the initial parameter guesses. Once values for v and D were obtained from the non-partitioning tracer breakthrough curve, they were used as fixed parameters during fitting of the partitioning tracer breakthrough curve with solutions of , . This last step resulted in estimates for the parameters R, β, and ω. Estimates for average NAPL contents were then calculated from Eq. (3), and the proportion of instantaneous sites F was obtained from , , asF=Rβ−1R−1The inverse technique was easily implemented by making use of the CXTFIT2 program (Parker and van Genuchten, 1984, Toride et al., 1995), which incorporates analytical solutions of , , , and also contains a Levenberg–Marquardt optimization algorithm.

Section snippets

Materials and methods

Non-partitioning and partitioning tracer breakthrough curves were obtained at 14 extraction ports and three outlets inside an extraction well in a nominally two-dimensional flow cell containing a 1-liter tetrachloroethene (PCE) spill. The rectangular porous medium (167 cm long, 62 cm high, 5 cm wide) consisted of coarse sand (F4.0 Flintshot Ottawa Sand; F&S Abrasives, Birmingham, AL) with embedded lenses of finer sands (Table 1; F2.8 and F75). The sands were packed under water. The porous medium

Sampling port data

Because the breakthrough curves collected at the extraction well were very much influenced by the porous medium and PCE distribution heterogeneity, the one-dimensional, non-equilibrium CDE could not correctly model the obtained results, and the inverse procedure was only used on port data sets. Two non-partitioning tracer data sets and four partitioning tracer data sets were obtained for each port, because we employed a step input from 0 to 1000 mg/l (noted left) followed by a step input from

Conclusion

A partitioning tracer test performed in a nominally two-dimensional, intermediate-scale aquifer model containing a tetrachloroethene (PCE) spill underestimated the amount of residual DNAPL and was insensitive to the presence of a pool comprising 30% of the contaminant. This was attributed to the low aqueous phase permeability within the DNAPL pool in combination with rate-limited partitioning of the tracers into the DNAPL. Our analysis indicate a general difficulty for the tracer technique to

Acknowledgements

This research was carried out as part of the US Environmental Protection Agency project R825409 “Investigation of the entrapment and surfactant enhanced recovery of NAPLs in heterogeneous sandy media”. We would like to thank Dr Mart Oostrom of PNNL, Richland, WA, for his valuable comments during the review process, and Dr Cor Hofstee (TNO, Utrecht, The Netherlands) for his contribution to the experimental part of this study.

The two junior authors would like to express their sorrow about the

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