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Non-aqueous phase liquid characterization via partitioning tracer tests: a modified Langmuir relation to describe partitioning nonlinearities
Journal of Contaminant Hydrology 36 Ž1999. 153–165
Non-aqueous phase liquid characterization via partitioning tracer tests: a modified Langmuir relation to describe partitioning nonlinearities William R. Wise a,) , Dongping Dai b, Elizabeth A. Fitzpatrick a , Lalenia W. Evans a , P. Suresh C. Rao b, Michael D. Annable a a
Department of EnÕironmental Engineering Sciences, UniÕersity of Florida, A.P. Black Hall, GainesÕille, FL 32611, USA b Department of Soil and Water Science, UniÕersity of Florida, GainesÕille, FL 32611, USA Received 28 May 1998; accepted 8 July 1998
Abstract The equilibrium interphase behaviors of alcohol partitioning tracers between NAPL and water are inherently nonlinear in nature. This nonlinearity may be described using an unfavorable form of the Langmuir partitioning relation with a good degree of agreement up to tracer mole fraction values of 0.3. The presence of co-tracers tends to move the equilibrium partitioning closer to Raoult’s law. It may be possible to manipulate tracer tests systems to minimize the effects of nonlinearities through the use of co-tracers. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Characterization; NAPL; Partitioning; Tracers
1. Introduction Partitioning tracers are emerging as tools for identifying and characterizing the presence of non-aqueous phase liquids ŽNAPLs. in the subsurface. When sweeping a candidate region of the subsurface with both nonreactive and partitioning tracers, the inferred presence of NAPL manifests as a retarded breakthrough for the partitioning tracer in comparison to the nonreactive tracer. The retardation is directly influenced by the amount of the NAPL present in the swept volume and the nature of the distribution )
Corresponding author. Fax: q1-3523923076; e-mail: [email protected]
0169-7722r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 7 7 2 2 Ž 9 8 . 0 0 1 0 8 - 9
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of the partitioning tracer between the aqueous and NAPL phases experienced during the tracer test. This distribution between phases is a function of both the equilibrium partitioning relationship and any kinetic limitations arising from subsurface heterogeneities andror spill geometry, as well as factors relating to the test design and operation. This communication focuses on the first consideration, the nature of the equilibrium partitioning of a tracer between phases. Specifically, it is the nonlinear nature of such partitioning that is addressed. Investigations that report the use of partitioning tracer tests include batch data ŽAnnable et al., 1994; Wang et al., 1998., laboratory column data ŽPope et al., 1994; Jin et al., 1995; Wilson and Mackay, 1995., field data ŽAnnable et al., 1994; Pope et al., 1994; Nelson and Brusseau, 1996; James et al., 1997; Rao et al., 1997; Annable et al., 1998. and modeling results ŽJin et al., 1995.. Common to all is the assumption that the partitioning tracers used distribute themselves in a linear manner between the aqueous and NAPL phases under equilibrium conditions. Practically, this is accomplished by specifying a partition coefficient for each partitioning tracer Žspecific to a particular NAPL. that is assumed to be independent of the tracer concentration. This brief communication examines the anticipated behavior of partitioning tracers in the presence of common NAPL components under equilibrium conditions. The chemicals that are considered herein for partitioning tracers are alcohols, as they have been used in laboratory and field studies to characterize NAPL distributions. The scenario considered is one in which the tracers are swept through the candidate region in the subsurface via the aqueous phase. As this work considers the nature of the equilibrium conditions only, no flow details are germane to the present discussion. Wise Ž1999. addresses the effects of the nature of the equilibrium discussed herein upon the interpretation of partitioning tracer test results.
2. Methodology The relative activity of a partitioning tracer with respect to a NAPL may be directly measured through the aqueous phase concentration of the tracer Žbecause the typical solubilities of such tracers are less than a mole fraction of 1% in the aqueous phase—see Mackay et al., 1991; Wise, 1998.. This is tantamount to saying that Henry’s law is followed for the partitioning tracer in the aqueous phase. As a result, the aqueous phase concentration of a partitioning tracer, divided by the solubility of that tracer yields the relative activity of the tracer in the NAPL. Basic thermodynamics requires the partitioning relation of the tracer to be linear at near-zero mole fractions in the NAPL, in accordance with Henry’s law Žnow specified in the NAPL.. As the mole fraction Žin the NAPL. of a tracer increases from this near-zero region, its activity coefficient decreases indicating that the partitioning is nonlinear in nature. ŽSee, for instance, Wise, 1998, for a detailed thermodynamic analysis of the partitioning behavior for binary NAPL mixtures.. Experimental data, along with results from the UNIFAC model ŽChen, 1992., are employed to evaluate the activities of tracers in NAPLs Žwhich are directly related to their concentrations in the aqueous phase..
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An ‘unfavorable’ form of the Langmuir relation is proposed to relate the equilibrium tracer mole fraction in the NAPL to the aqueous phase concentration: xs
yb c ya q c
,
Ž 1.
where x is the mole fraction in the NAPL, c is the dimensionless aqueous concentration Žthe actual aqueous concentration divided by the solubility of the tracer in water, representing the relative activity of the partitioning tracer in the NAPL., and a and b are both Ždimensionless. positive parameters. Mathematically, the domain of Eq. Ž1. is restricted to values of 0 F c - a . In practice, the domain should be restricted to the region in which the fit of Eq. Ž1. is deemed to be satisfactory. The relationship is considered to be unfavorable because Žgiven the restrictions on the parameters a and b . the tracer relatively abhors the NAPL at low concentrations. Eq. Ž1. agrees with Henry’s Law Žfor the NAPL. at near-zero tracer compositions. The fact that it seems to perform well for partitioning tracers at slightly higher mole fractions Žas demonstrated in Section 3. is serendipitous. This unfavorable form of the Langmuir relation does not have Žto the authors’ knowledge. a theoretical basis like that for the favorable form involved with the adsorption of nonelectrolytes from solution Žsee Adamson, 1976, pp. 386–388.. Herein, the relation is used based upon its empirical performance at fitting the lower regions of partitioning traces, which is demonstrated in Section 3.
3. Results This study includes results from experiments and ŽUNIFAC. modeling efforts. As the UNIFAC model is able to predict experimental behavior in the tracerrNAPL systems studied, as will be shown below, it may be used to supplement experimental results. Naturally, the motivation for modeling is the economy of effort involved in comparison to experimentation. The tracers considered are alcohols; the NAPLs include pure compounds such as decane and TCE, as well as multi-component mixtures. 3.1. Experimental results An alcohol partitioning tracer, 2,2-dimethyl-3-pentanol ŽDMP. ŽAldrich Chemical; 99 q % purity., was chosen for the experimental investigation. ŽSee Dai, 1997, for detailed experimental procedures.. Two NAPLs were used, pure decane and a synthetic, multi-component NAPL prepared by mixing reagent grade p-xylene Žmole fraction of 0.06., o-xylene Ž0.04., n-nonane Ž0.04., n-decane Ž0.10., n-undecane Ž0.20., n-dodecane Ž0.15., n-tridecane Ž0.10., 1,2-dichlorobenzene Ž0.10., 1,3,5-trimethylbenzene Ž0.10., 1,2,4,trichlorobenzene Ž0.02., and n-hexadecane Ž0.09.. Owing to the nature of the solubility of the tracer in water, two different regions Žof the tracer mole fraction in the NAPL. were considered when obtaining the partitioning isotherms—one below a tracer mole fraction of 0.10 and the other above that value.
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For tracer mole fractions below 0.10, the following procedure was followed. Saturated tracer solutions were made in HPLC water. Various dilutions were then made. To these dilutions, exact amounts of the NAPL Ždecane or the synthetic NAPL mixture. were added and capped immediately to avoid volatile losses. These solutions were then equilibrated on a rotator for 24 h. Next, the vials were centrifuged. The supernatant samples were immediately analyzed by gas chromatography and flame-ionization detection ŽGC-FID.. The amounts of tracer in the NAPLs were determined using the differences between the initial and equilibrium tracer concentrations in the aqueous phases, along with the measured amounts of NAPL. All measurements were made in triplicate. For tracer mole fractions above 0.10, two different procedures were followed. These are outlined below. In the first method, an aqueous solution at 80% of the tracer saturation was sequentially added then equilibrated and centrifuged Žas above. with the NAPLs. After each iteration, the supernatant samples were analyzed by GC-FID. In the second method, the tracer, DMP, was added directly to the NAPLs resulting in mole fractions ranging from 0.10 to 0.90. These mixtures were then equilibrated with HPLC water and then centrifuged. Supernatant samples were then analyzed by GC-FID in triplicate. The appropriate corrections for mass balance were made, the details of which are omitted here for the sake of tractability. ŽSee Dai, 1997, for details.. Presentation of the experimental data follows a brief outline of the UNIFAC modeling methodology. 3.2. UNIFAC modeling methodology The vapor–liquid equilibrium ŽVLE. version of UNIFAC is used to predict the activities of the tracers in the NAPL phases. Wang et al. Ž1998. found this version gives superior results Žin comparison to the liquid–liquid equilibrium version. for predicting the interphase distributions of typically-used partitioning tracers in common NAPLs, such as TCE, benzene, tetra-chloromethane, decane, and PCE. They, however, were determining partition coefficients for tracerrNAPL systems at infinite dilution Žof the tracer.; consequently they ignored nonlinearities in the partitioning relations for such systems. 3.3. Verification of the UNIFAC modeling methodology Figs. 1 and 2 illustrate both the experimental data and the UNIFAC modeling results for the DMPrdecane and DMPrsynthetic-NAPL-mixture systems, respectively. For both NAPLs, the UNIFAC model describes well the nature of the partitioning behavior for the tracer. 3.4. Mathematically describing the partitioning behaÕior Given the ability of the described UNIFAC modeling methodology to predict the behavior of waterrtracerrNAPL systems, UNIFAC simulations are used below to further explore the nature of tracer partitioning into NAPLs. As alluded to earlier, the
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Fig. 1. Comparison of experimental and UNIFAC simulation results for 2,2-dimethyl-3-pentanol partitioning into decane.
Fig. 2. Comparison of experimental and UNIFAC simulation results for 2,2-dimethyl-3-pentanol partitioning into synthetic NAPL mixture.
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primary motivation for using modeling rather than experimentation is the economy of effort involved. In addition, the UNIFAC model produces noise-free ‘data’ Ža one-to-one relationship between tracer mole fraction and aqueous concentration. from which to draw conclusions. For the present work, all fits are generated using the Solver routine in Microsoft Excel, fitting c s a xrŽ b q x ., which is equivalent to Eq. Ž1.. The exact values of the parameters sought, a and b , are somewhat sensitive to both the domain of tracer mole fractions used as well as the number and distribution of Ž x, c . pairs used in the fitting procedure. All of the UNIFAC simulations use a tracer mole fraction increment of D x s 0.01. For 5-methyl-2-hexanol partitioning into TCE, fits of the unfavorable Langmuir model to UNIFAC results are shown in Fig. 3 using different ranges of tracer mole fractions for the various fits. Fits to tracer mole fraction ranges of 0–0.1, 0–0.2, and 0–0.3 yield the following fits reported as Ž a , b , root-mean-square error.: Ž0.575, 0.111, 2.6 = 10y4 ., Ž0.589, 0.115, 1.2 = 10y3 ., and Ž0.625, 0.130, 3.7 = 10y3 ., respectively. As illustrated in Fig. 3, the three fits are in good agreement with the ‘data’ from the UNIFAC simulation. Fits for the 0–0.4 and 0–0.5 tracer mole fraction ranges Žnot shown. are less satisfying. This cut-off point Ž0–0.3 tracer mole fraction range. in model success was observed Žalbeit subjectively. for all of the tracerrNAPL systems studied. Because they are the most comprehensive Žcover the largest domain with an acceptable degree of accuracy., fits using the tracer mole fraction range of 0–0.3 will be used in the forthcoming analysis for all tracerrNAPL systems discussed.
Fig. 3. Fits of Eq. Ž1. to UNIFAC simulation results for 5-methyl-2-hexanol partitioning into TCE for tracer mole fraction ranges 0–0.1, 0–0.2, and 0–0.3.
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3.5. Performance of unfaÕorable form of Langmuir relation for different NAPL mixtures A series of UNIFAC runs was performed in order to test the robustness of Eq. Ž1. for describing interphase behavior for a given partitioning tracer, 5-methyl-2-hexanol, into a variety of NAPL mixtures comprised of TCE, toluene, decane, and naphthalene. ŽRemember, the UNIFAC model was shown to perform well for tracerrmulti-component-NAPL systems above.. These were followed by the simple fitting procedure to determine the appropriate values for a and b . The tracer mole fraction range used was 0–0.3 for all systems. Cases where each NAPL was taken individually were considered; all possible binary mixtures were considered for equal amounts of both constituents; the same held for ternary systems; and finally, for the quaternary NAPL mixture. The values of a and b determined for these cases are reported with their corresponding rms errors in Table 1. Note that the rms errors range from 1.0 = 10y3 to 8.6 = 10y3 , indicating that the performance of Eq. Ž1. for describing these systems is on par with that illustrated in Fig. 3. 3.6. Performance of unfaÕorable form of Langmuir relation for different tracers Five different alcohols were selected as possible partitioning tracers. They were selected to characterize a range representative of some that have been reported in the literature. Three are isomers of hexanol: 2-ethyl-1-butanol, 2-methyl-3-pentanol, and n-hexanol. As discussed above, one is 5-methyl-2-hexanol, an isomer of heptanol. The last is n-octanol. Fits for the UNIFAC simulations of these tracers into the four pure NAPL components are presented in Table 2. Again the fits are good, with rms errors
Table 1 Fits for 5-methyl-2-hexanol partitioning into various NAPL mixtures Ratio of NAPL TCE
Toluene
Decane
Naphthalene
1.00 1.00 1.00 1.00 0.50 0.50 0.50
0.50 0.50 0.50 0.50 0.50
0.3333 0.3333 0.3333 0.25
0.3333 0.3333 0.3333 0.25
0.50 0.50 0.3334 0.3333 0.3333 0.25
All fits use 0 F x tracer F 0.3 as the domain.
0.50 0.50 0.3334 0.3334 0.3334 0.25
a
b
rms error
0.629 0.692 0.710 0.824 0.764 0.655 0.766 0.650 0.738 0.722 0.664 0.707 0.752 0.697 0.700
0.130 0.173 0.053 0.077 0.207 0.090 0.140 0.095 0.113 0.100 0.114 0.114 0.152 0.112 0.123
0.0037 0.0036 0.0040 0.0086 0.0031 0.0024 0.0010 0.0028 0.0010 0.0011 0.0032 0.0017 0.0018 0.0017 0.0023
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Table 2 Fits for different tracers partitioning into different single component NAPLs Tracer
NAPL
a
b
rms error
2-ethyl-1-butanol 2-methyl-3-pentanol n-hexanol 5-methyl-2-hexanol n-octanol 2-ethyl-1-butanol 2-methyl-3-pentanol n-hexanol 5-methyl-2-hexanol n-octanol 2-ethyl-1-butanol 2-methyl-3-pentanol n-hexanol 5-methyl-2-hexanol n-octanol 2-ethyl-1-butanol 2-methyl-3-pentanol n-hexanol 5-methyl-2-hexanol n-octanol
TCE TCE TCE TCE TCE toluene toluene toluene toluene toluene decane decane decane decane decane naphthalene naphthalene naphthalene naphthalene naphthalene
0.653 0.653 0.653 0.629 0.618 0.699 0.699 0.699 0.692 0.696 0.761 0.761 0.761 0.710 0.669 0.882 0.881 0.883 0.824 0.776
0.110 0.110 0.110 0.130 0.156 0.146 0.146 0.145 0.173 0.204 0.049 0.049 0.049 0.053 0.058 0.077 0.077 0.077 0.077 0.075
0.0024 0.0024 0.0024 0.0037 0.0047 0.0030 0.0030 0.0030 0.0036 0.0040 0.0069 0.0069 0.0069 0.0040 0.0022 0.0100 0.0100 0.0100 0.0086 0.0072
All fits use 0 F x tracer F 0.3 as the domain.
ranging from 2.2 = 10y3 to 1.0 = 10y2 . Note that there are some readily identifiable trends in the results. The fits for the three isomers of hexanol are nearly identical for each NAPL studied, with a maximum deviation in a or b of two in the third significant digit for any NAPL. Values for a typically decrease with increasing tracer carbon count Žtoluene being the exception.; while values for b typically increase Žnaphthalene being the exception.. Table 3 presents the fits for these five tracers into a NAPL comprised of equal ratios of TCE, toluene, decane, and naphthalene. The same trends for a and b are exhibited in these results. Again, the fits are quite agreeable with the UNIFAC simulations; the rms error ranges from 1.2 = 10y3 to 3.2 = 10y3 for these five systems. Fig. 4 illustrates the
Table 3 Fits for different tracers partitioning into NAPL comprised of equal ratios of TCE, toluene, decane and naphthalene Tracer
a
b
rms error
2-ethyl-1-butanol 2-methyl-3-pentanol n-hexanol 5-methyl-2-hexanol n-octanol
0.729 0.728 0.729 0.700 0.682
0.108 0.109 0.108 0.123 0.141
0.0012 0.0012 0.0012 0.0023 0.0032
All fits use 0 F x tracer F 0.3 as the domain.
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Fig. 4. Fits of Eq. Ž1. to UNIFAC simulation results for 5-methyl-2-hexanol partitioning into NAPL mixture of equal parts TCE, toluene, decane, and naphthalene, for tracer mole fraction range 0–0.3.
fit for 5-methyl-2-hexanol and this NAPL mixture. Note that even with this fairly broad array of NAPL constituents, the partitioning is significantly nonlinear. Below, however, it will be demonstrated that when a significant portion of the NAPL chemically resembles the tracer, this nonlinearity is diminished. 3.7. Effect of co-tracers It is common practice to use a suite of partitioning tracers rather than just one in order to maximize the likelihood of obtaining agreeable retardation values Žpartitioning tracers arriving at the effluent well in a reasonable number of pore volumes.. By their very nature, partitioning tracers will Žtemporarily. change the composition of the original NAPL. Because the tracers are similar to one another in chemical structure, they may impact one another’s partitioning behavior. Fig. 5 presents experimental data for both the waterrDMPrNAPL mixture system discussed earlier and a system in which the NAPL mixture comprises 70% of the NAPL phase and octanol comprises the remaining 30%. ŽExperimental procedures were similar to those described earlier and are documented in detail in Dai, 1997.. Note that the addition of octanol tends to make the partitioning of DMP more linear Žcloser to Raoult’s law.. Again, Fig. 5 tends to support the UNIFAC modeling approach for such systems. To systematically investigate such potential interference, the partitioning of 5-methyl2-hexanol into TCE with varying amounts of n-hexanol was studied. The results are
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Fig. 5. Comparison of experimental and UNIFAC simulation results for 2,2-dimethyl-3-pentanol partitioning into synthetic NAPL mixture with and without a 30% mole fraction of octanol.
Fig. 6. UNIFAC simulation results for 5-methyl-2-hexanol partitioning into TCE with different mole fractions of n-hexanol for tracer mole fraction range 0–0.3.
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Table 4 Fits for 5-methyl-2-hexanol partitioning into NAPL comprised of TCE and varying amounts of n-hexanol % n-Hexanol
a
b
rms error
0 5 10 15 20 25 30
0.629 0.711 0.822 0.968 1.161 1.418 1.765
0.130 0.217 0.330 0.477 0.669 0.924 1.269
0.0037 0.0032 0.0025 0.0019 0.0014 0.0010 0.0007
All fits use 0 F x tracer F 0.3 as the domain.
illustrated in Fig. 6 and the corresponding fits to Eq. Ž1. are reported in Table 4. Note that the more ‘co-tracer’ Ž n-hexanol in this case. present, the more the partitioning of the tracer of interest Ž5-methyl-2-hexanol in this case. is affected. Because the co-tracer is chemically similar to the tracer of interest, the system becomes more ideal at higher co-tracer levels and the partitioning correspondingly becomes more linear in nature Žnearer to Raoult’s law.. It must be remembered that the co-tracer will also be partitioning into and out of the NAPL. Therefore, no individual curve in Fig. 6 represents what would be anticipated in the field, each curve is only marginal in nature, representing one degree of freedom Žfor the tracer of interest.. ŽA ternary diagram would be required to present the actual compositions that would be experienced during a tracer test for such a system.. Similar behavior results for 5-methyl-2-hexanol partitioning into various mixtures of TCE and n-octanol Žnot shown.. The qualitative nature of this sensitivity is in perfect concert with that observed for n-hexanol. In a partitioning tracer test employing n-hexanol, 5-methyl-2-hexanol, and n-octanol, the expected elution times would be in the order stated, with n-octanol experiencing the most retardation. Consequently, the interference effects suggested by Fig. 6 might be expected at the front of the 5-methyl2-hexanol migration; similar results for octanol at the back. The situation would be more dramatic nearer to the center of mass of 5-methyl-2-hexanol signal, as both co-tracers would have an impact. Therefore, when using a suite of tracers, there may not exist a unique one-to-one partitioning relation that may be defined for a given tracer throughout the swept volume of the partitioning tracer test—it evolves in response to the presence of co-tracers. This fact is not currently being considered when reducing data from partitioning tracer tests.
4. Discussion This communication documents the success of a simple function, interpreted as an unfavorable form of the Langmuir relation, at fitting the lower end of interphase partitioning behavior of systems of alcohol partitioning tracers and NAPLs. The function applicability is supported heuristically through its success at fitting the partitioning
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behavior of different types of systems. No theoretical basis is offered for its success Žaside from the fact that the function becomes linear in the region of the origin, in accordance with Henry’s law applied to the NAPL phase.. For the tracerrNAPL systems studied, the domains of applicability of Eq. Ž1. are taken to be tracer mole fraction ranges of 0–0.3. Wise Ž1999. uses the conclusion that Eq. Ž1. is a good predictor of the interphase distribution of partitioning tracers into NAPLs at equilibrium to deduce the ramifications of nonlinear partitioning behavior upon the interpretation of partitioning tracer tests, which are traditionally analyzed based upon the assumption of linear interphase partitioning. The effects of using multiple partitioning tracers may complicate the systems at hand, as now the partitioning relation might be a function of both space and time even for a uniformly distributed NAPL under equilibrium conditions. It is also, somewhat conversely, possible that they may be used to make the partitioning of a particular tracer more linear Žnear Raoult’s law. by preconditioning the NAPL. Further study of such effects is needed.
References Adamson, A.W., 1976. Physical Chemistry of Surfaces, 3rd edn. Wiley, New York, 698 pp. Annable, M.D., Rao, P.S.C., Hatfield, K., Graham, W.D., Wood, A.L., 1994. Use of partitioning tracers for measuring residual NAPL distribution in a contaminated aquifer: preliminary results from a field-scale test. Presented at the 2nd Tracer Workshop, The University of Texas at Austin, November 14 and 15, 1994, pp. 77–85. Annable, M.D., Rao, P.S.C., Hatfield, K., Graham, W.D., Wood, A.L., 1998. Use of partitioning tracers for measuring residual NAPL distribution in a contaminated aquifer: preliminary results from a field-scale test. J. Environmental Eng., in press. Chen, F., 1992. Manual for Program GAMMA: Calculation of Activity Coefficients by Means of UNIFAC. National Environmental Research Institute, Roskilde, Denmark, 36 pp. Dai, D., 1997. Solubility and partitioning behavior of organic compounds in complex NAPL mixtures. PhD dissertation. Soil and Water Sciences Department, University of Florida, 219 pp. James, A.I., Graham, W.D., Hatfield, K., Rao, P.S.C., Annable, M.D., 1997. Optimal estimation of residual non-aqueous phase liquid saturations using partitioning tracer concentration data. Water Resources Res. 33 Ž12., 2621–2636. Jin, M., Delshad, M., Dwarakanath, V., McKinney, D.C., Pope, G.A., Sepehrnoori, K., Tiburg, C.E., Jackson, R., 1995. Partitioning tracer test for detection, estimation and remediation performance assessment of subsurface non-aqueous phase liquids. Water Resources Res. 31 Ž5., 1201–1212. Mackay, D., Shiu, W.Y., Maijanen, A., Feenstra, S., 1991. Dissolution of non-aqueous phase liquids in groundwater. J. Contaminant Hydrology 8, 23–42. Nelson, N.T., Brusseau, M.L., 1996. Field study of the partitioning tracer method for detection of dense non-aqueous phase liquid in a trichlorothene contaminated aquifer. Environmental Sci. Technol. 30 Ž9., 2859–2863. Pope, G.A., Jin, M., Dwarakanath, V., Rouse, B., Sepehrnoori, K., 1994. Partitioning tracer tests to characterize organic contaminants. Presented at the 2nd Tracer Workshop, The University of Texas at Austin, November 14 and 15, 1994. Rao, P.S.C., Annable, M.D., Sillan, R.K., Dai, D., Hatfield, K., Graham, W.D., Wood, A.L., Enfield, C.G., 1997. Field-scale evaluation of in situ cosolvent flushing for enhanced aquifer remediation. Water Resources Res. 33 Ž12., 2673–2686.
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Wang, P., Dwarakanath, V., Rouse, B.A., Pope, G.A., Sepehrnoori, K., 1998. Partition coefficients for alcohol tracers between non-aqueous phase liquids and water from UNIFAC-solubility method. Adv. Water Resources 21 Ž2., 171–181. Wilson, R.D., Mackay, D.M., 1995. Direct detection of residual non-aqueous phase liquid in the saturated zone using SF6 as a partitioning tracer. Environmental Sci. Technol. 29 Ž5., 1255–1258. Wise, W.R., 1998. Thermodynamic evaluation of effluent tailing effects during dissolution of binary oil mixtures. J. Contam. Hydrol. 32 Ž1–2., 117–130. Wise, W.R., 1999. NAPL characterization through partitioning tracer tests: quantifying effects of partitioning nonlinearities. J. Contam. Hydrol. 36 Ž1–2., 167–183.
Non-aqueous phase liquid characterization via partitioning tracer tests: a modified Langmuir relation to describe partitioning nonlinearities William R. Wise a,) , Dongping Dai b, Elizabeth A. Fitzpatrick a , Lalenia W. Evans a , P. Suresh C. Rao b, Michael D. Annable a a
Department of EnÕironmental Engineering Sciences, UniÕersity of Florida, A.P. Black Hall, GainesÕille, FL 32611, USA b Department of Soil and Water Science, UniÕersity of Florida, GainesÕille, FL 32611, USA Received 28 May 1998; accepted 8 July 1998
Abstract The equilibrium interphase behaviors of alcohol partitioning tracers between NAPL and water are inherently nonlinear in nature. This nonlinearity may be described using an unfavorable form of the Langmuir partitioning relation with a good degree of agreement up to tracer mole fraction values of 0.3. The presence of co-tracers tends to move the equilibrium partitioning closer to Raoult’s law. It may be possible to manipulate tracer tests systems to minimize the effects of nonlinearities through the use of co-tracers. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Characterization; NAPL; Partitioning; Tracers
1. Introduction Partitioning tracers are emerging as tools for identifying and characterizing the presence of non-aqueous phase liquids ŽNAPLs. in the subsurface. When sweeping a candidate region of the subsurface with both nonreactive and partitioning tracers, the inferred presence of NAPL manifests as a retarded breakthrough for the partitioning tracer in comparison to the nonreactive tracer. The retardation is directly influenced by the amount of the NAPL present in the swept volume and the nature of the distribution )
Corresponding author. Fax: q1-3523923076; e-mail: [email protected]
0169-7722r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 7 7 2 2 Ž 9 8 . 0 0 1 0 8 - 9
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of the partitioning tracer between the aqueous and NAPL phases experienced during the tracer test. This distribution between phases is a function of both the equilibrium partitioning relationship and any kinetic limitations arising from subsurface heterogeneities andror spill geometry, as well as factors relating to the test design and operation. This communication focuses on the first consideration, the nature of the equilibrium partitioning of a tracer between phases. Specifically, it is the nonlinear nature of such partitioning that is addressed. Investigations that report the use of partitioning tracer tests include batch data ŽAnnable et al., 1994; Wang et al., 1998., laboratory column data ŽPope et al., 1994; Jin et al., 1995; Wilson and Mackay, 1995., field data ŽAnnable et al., 1994; Pope et al., 1994; Nelson and Brusseau, 1996; James et al., 1997; Rao et al., 1997; Annable et al., 1998. and modeling results ŽJin et al., 1995.. Common to all is the assumption that the partitioning tracers used distribute themselves in a linear manner between the aqueous and NAPL phases under equilibrium conditions. Practically, this is accomplished by specifying a partition coefficient for each partitioning tracer Žspecific to a particular NAPL. that is assumed to be independent of the tracer concentration. This brief communication examines the anticipated behavior of partitioning tracers in the presence of common NAPL components under equilibrium conditions. The chemicals that are considered herein for partitioning tracers are alcohols, as they have been used in laboratory and field studies to characterize NAPL distributions. The scenario considered is one in which the tracers are swept through the candidate region in the subsurface via the aqueous phase. As this work considers the nature of the equilibrium conditions only, no flow details are germane to the present discussion. Wise Ž1999. addresses the effects of the nature of the equilibrium discussed herein upon the interpretation of partitioning tracer test results.
2. Methodology The relative activity of a partitioning tracer with respect to a NAPL may be directly measured through the aqueous phase concentration of the tracer Žbecause the typical solubilities of such tracers are less than a mole fraction of 1% in the aqueous phase—see Mackay et al., 1991; Wise, 1998.. This is tantamount to saying that Henry’s law is followed for the partitioning tracer in the aqueous phase. As a result, the aqueous phase concentration of a partitioning tracer, divided by the solubility of that tracer yields the relative activity of the tracer in the NAPL. Basic thermodynamics requires the partitioning relation of the tracer to be linear at near-zero mole fractions in the NAPL, in accordance with Henry’s law Žnow specified in the NAPL.. As the mole fraction Žin the NAPL. of a tracer increases from this near-zero region, its activity coefficient decreases indicating that the partitioning is nonlinear in nature. ŽSee, for instance, Wise, 1998, for a detailed thermodynamic analysis of the partitioning behavior for binary NAPL mixtures.. Experimental data, along with results from the UNIFAC model ŽChen, 1992., are employed to evaluate the activities of tracers in NAPLs Žwhich are directly related to their concentrations in the aqueous phase..
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An ‘unfavorable’ form of the Langmuir relation is proposed to relate the equilibrium tracer mole fraction in the NAPL to the aqueous phase concentration: xs
yb c ya q c
,
Ž 1.
where x is the mole fraction in the NAPL, c is the dimensionless aqueous concentration Žthe actual aqueous concentration divided by the solubility of the tracer in water, representing the relative activity of the partitioning tracer in the NAPL., and a and b are both Ždimensionless. positive parameters. Mathematically, the domain of Eq. Ž1. is restricted to values of 0 F c - a . In practice, the domain should be restricted to the region in which the fit of Eq. Ž1. is deemed to be satisfactory. The relationship is considered to be unfavorable because Žgiven the restrictions on the parameters a and b . the tracer relatively abhors the NAPL at low concentrations. Eq. Ž1. agrees with Henry’s Law Žfor the NAPL. at near-zero tracer compositions. The fact that it seems to perform well for partitioning tracers at slightly higher mole fractions Žas demonstrated in Section 3. is serendipitous. This unfavorable form of the Langmuir relation does not have Žto the authors’ knowledge. a theoretical basis like that for the favorable form involved with the adsorption of nonelectrolytes from solution Žsee Adamson, 1976, pp. 386–388.. Herein, the relation is used based upon its empirical performance at fitting the lower regions of partitioning traces, which is demonstrated in Section 3.
3. Results This study includes results from experiments and ŽUNIFAC. modeling efforts. As the UNIFAC model is able to predict experimental behavior in the tracerrNAPL systems studied, as will be shown below, it may be used to supplement experimental results. Naturally, the motivation for modeling is the economy of effort involved in comparison to experimentation. The tracers considered are alcohols; the NAPLs include pure compounds such as decane and TCE, as well as multi-component mixtures. 3.1. Experimental results An alcohol partitioning tracer, 2,2-dimethyl-3-pentanol ŽDMP. ŽAldrich Chemical; 99 q % purity., was chosen for the experimental investigation. ŽSee Dai, 1997, for detailed experimental procedures.. Two NAPLs were used, pure decane and a synthetic, multi-component NAPL prepared by mixing reagent grade p-xylene Žmole fraction of 0.06., o-xylene Ž0.04., n-nonane Ž0.04., n-decane Ž0.10., n-undecane Ž0.20., n-dodecane Ž0.15., n-tridecane Ž0.10., 1,2-dichlorobenzene Ž0.10., 1,3,5-trimethylbenzene Ž0.10., 1,2,4,trichlorobenzene Ž0.02., and n-hexadecane Ž0.09.. Owing to the nature of the solubility of the tracer in water, two different regions Žof the tracer mole fraction in the NAPL. were considered when obtaining the partitioning isotherms—one below a tracer mole fraction of 0.10 and the other above that value.
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For tracer mole fractions below 0.10, the following procedure was followed. Saturated tracer solutions were made in HPLC water. Various dilutions were then made. To these dilutions, exact amounts of the NAPL Ždecane or the synthetic NAPL mixture. were added and capped immediately to avoid volatile losses. These solutions were then equilibrated on a rotator for 24 h. Next, the vials were centrifuged. The supernatant samples were immediately analyzed by gas chromatography and flame-ionization detection ŽGC-FID.. The amounts of tracer in the NAPLs were determined using the differences between the initial and equilibrium tracer concentrations in the aqueous phases, along with the measured amounts of NAPL. All measurements were made in triplicate. For tracer mole fractions above 0.10, two different procedures were followed. These are outlined below. In the first method, an aqueous solution at 80% of the tracer saturation was sequentially added then equilibrated and centrifuged Žas above. with the NAPLs. After each iteration, the supernatant samples were analyzed by GC-FID. In the second method, the tracer, DMP, was added directly to the NAPLs resulting in mole fractions ranging from 0.10 to 0.90. These mixtures were then equilibrated with HPLC water and then centrifuged. Supernatant samples were then analyzed by GC-FID in triplicate. The appropriate corrections for mass balance were made, the details of which are omitted here for the sake of tractability. ŽSee Dai, 1997, for details.. Presentation of the experimental data follows a brief outline of the UNIFAC modeling methodology. 3.2. UNIFAC modeling methodology The vapor–liquid equilibrium ŽVLE. version of UNIFAC is used to predict the activities of the tracers in the NAPL phases. Wang et al. Ž1998. found this version gives superior results Žin comparison to the liquid–liquid equilibrium version. for predicting the interphase distributions of typically-used partitioning tracers in common NAPLs, such as TCE, benzene, tetra-chloromethane, decane, and PCE. They, however, were determining partition coefficients for tracerrNAPL systems at infinite dilution Žof the tracer.; consequently they ignored nonlinearities in the partitioning relations for such systems. 3.3. Verification of the UNIFAC modeling methodology Figs. 1 and 2 illustrate both the experimental data and the UNIFAC modeling results for the DMPrdecane and DMPrsynthetic-NAPL-mixture systems, respectively. For both NAPLs, the UNIFAC model describes well the nature of the partitioning behavior for the tracer. 3.4. Mathematically describing the partitioning behaÕior Given the ability of the described UNIFAC modeling methodology to predict the behavior of waterrtracerrNAPL systems, UNIFAC simulations are used below to further explore the nature of tracer partitioning into NAPLs. As alluded to earlier, the
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Fig. 1. Comparison of experimental and UNIFAC simulation results for 2,2-dimethyl-3-pentanol partitioning into decane.
Fig. 2. Comparison of experimental and UNIFAC simulation results for 2,2-dimethyl-3-pentanol partitioning into synthetic NAPL mixture.
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primary motivation for using modeling rather than experimentation is the economy of effort involved. In addition, the UNIFAC model produces noise-free ‘data’ Ža one-to-one relationship between tracer mole fraction and aqueous concentration. from which to draw conclusions. For the present work, all fits are generated using the Solver routine in Microsoft Excel, fitting c s a xrŽ b q x ., which is equivalent to Eq. Ž1.. The exact values of the parameters sought, a and b , are somewhat sensitive to both the domain of tracer mole fractions used as well as the number and distribution of Ž x, c . pairs used in the fitting procedure. All of the UNIFAC simulations use a tracer mole fraction increment of D x s 0.01. For 5-methyl-2-hexanol partitioning into TCE, fits of the unfavorable Langmuir model to UNIFAC results are shown in Fig. 3 using different ranges of tracer mole fractions for the various fits. Fits to tracer mole fraction ranges of 0–0.1, 0–0.2, and 0–0.3 yield the following fits reported as Ž a , b , root-mean-square error.: Ž0.575, 0.111, 2.6 = 10y4 ., Ž0.589, 0.115, 1.2 = 10y3 ., and Ž0.625, 0.130, 3.7 = 10y3 ., respectively. As illustrated in Fig. 3, the three fits are in good agreement with the ‘data’ from the UNIFAC simulation. Fits for the 0–0.4 and 0–0.5 tracer mole fraction ranges Žnot shown. are less satisfying. This cut-off point Ž0–0.3 tracer mole fraction range. in model success was observed Žalbeit subjectively. for all of the tracerrNAPL systems studied. Because they are the most comprehensive Žcover the largest domain with an acceptable degree of accuracy., fits using the tracer mole fraction range of 0–0.3 will be used in the forthcoming analysis for all tracerrNAPL systems discussed.
Fig. 3. Fits of Eq. Ž1. to UNIFAC simulation results for 5-methyl-2-hexanol partitioning into TCE for tracer mole fraction ranges 0–0.1, 0–0.2, and 0–0.3.
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3.5. Performance of unfaÕorable form of Langmuir relation for different NAPL mixtures A series of UNIFAC runs was performed in order to test the robustness of Eq. Ž1. for describing interphase behavior for a given partitioning tracer, 5-methyl-2-hexanol, into a variety of NAPL mixtures comprised of TCE, toluene, decane, and naphthalene. ŽRemember, the UNIFAC model was shown to perform well for tracerrmulti-component-NAPL systems above.. These were followed by the simple fitting procedure to determine the appropriate values for a and b . The tracer mole fraction range used was 0–0.3 for all systems. Cases where each NAPL was taken individually were considered; all possible binary mixtures were considered for equal amounts of both constituents; the same held for ternary systems; and finally, for the quaternary NAPL mixture. The values of a and b determined for these cases are reported with their corresponding rms errors in Table 1. Note that the rms errors range from 1.0 = 10y3 to 8.6 = 10y3 , indicating that the performance of Eq. Ž1. for describing these systems is on par with that illustrated in Fig. 3. 3.6. Performance of unfaÕorable form of Langmuir relation for different tracers Five different alcohols were selected as possible partitioning tracers. They were selected to characterize a range representative of some that have been reported in the literature. Three are isomers of hexanol: 2-ethyl-1-butanol, 2-methyl-3-pentanol, and n-hexanol. As discussed above, one is 5-methyl-2-hexanol, an isomer of heptanol. The last is n-octanol. Fits for the UNIFAC simulations of these tracers into the four pure NAPL components are presented in Table 2. Again the fits are good, with rms errors
Table 1 Fits for 5-methyl-2-hexanol partitioning into various NAPL mixtures Ratio of NAPL TCE
Toluene
Decane
Naphthalene
1.00 1.00 1.00 1.00 0.50 0.50 0.50
0.50 0.50 0.50 0.50 0.50
0.3333 0.3333 0.3333 0.25
0.3333 0.3333 0.3333 0.25
0.50 0.50 0.3334 0.3333 0.3333 0.25
All fits use 0 F x tracer F 0.3 as the domain.
0.50 0.50 0.3334 0.3334 0.3334 0.25
a
b
rms error
0.629 0.692 0.710 0.824 0.764 0.655 0.766 0.650 0.738 0.722 0.664 0.707 0.752 0.697 0.700
0.130 0.173 0.053 0.077 0.207 0.090 0.140 0.095 0.113 0.100 0.114 0.114 0.152 0.112 0.123
0.0037 0.0036 0.0040 0.0086 0.0031 0.0024 0.0010 0.0028 0.0010 0.0011 0.0032 0.0017 0.0018 0.0017 0.0023
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Table 2 Fits for different tracers partitioning into different single component NAPLs Tracer
NAPL
a
b
rms error
2-ethyl-1-butanol 2-methyl-3-pentanol n-hexanol 5-methyl-2-hexanol n-octanol 2-ethyl-1-butanol 2-methyl-3-pentanol n-hexanol 5-methyl-2-hexanol n-octanol 2-ethyl-1-butanol 2-methyl-3-pentanol n-hexanol 5-methyl-2-hexanol n-octanol 2-ethyl-1-butanol 2-methyl-3-pentanol n-hexanol 5-methyl-2-hexanol n-octanol
TCE TCE TCE TCE TCE toluene toluene toluene toluene toluene decane decane decane decane decane naphthalene naphthalene naphthalene naphthalene naphthalene
0.653 0.653 0.653 0.629 0.618 0.699 0.699 0.699 0.692 0.696 0.761 0.761 0.761 0.710 0.669 0.882 0.881 0.883 0.824 0.776
0.110 0.110 0.110 0.130 0.156 0.146 0.146 0.145 0.173 0.204 0.049 0.049 0.049 0.053 0.058 0.077 0.077 0.077 0.077 0.075
0.0024 0.0024 0.0024 0.0037 0.0047 0.0030 0.0030 0.0030 0.0036 0.0040 0.0069 0.0069 0.0069 0.0040 0.0022 0.0100 0.0100 0.0100 0.0086 0.0072
All fits use 0 F x tracer F 0.3 as the domain.
ranging from 2.2 = 10y3 to 1.0 = 10y2 . Note that there are some readily identifiable trends in the results. The fits for the three isomers of hexanol are nearly identical for each NAPL studied, with a maximum deviation in a or b of two in the third significant digit for any NAPL. Values for a typically decrease with increasing tracer carbon count Žtoluene being the exception.; while values for b typically increase Žnaphthalene being the exception.. Table 3 presents the fits for these five tracers into a NAPL comprised of equal ratios of TCE, toluene, decane, and naphthalene. The same trends for a and b are exhibited in these results. Again, the fits are quite agreeable with the UNIFAC simulations; the rms error ranges from 1.2 = 10y3 to 3.2 = 10y3 for these five systems. Fig. 4 illustrates the
Table 3 Fits for different tracers partitioning into NAPL comprised of equal ratios of TCE, toluene, decane and naphthalene Tracer
a
b
rms error
2-ethyl-1-butanol 2-methyl-3-pentanol n-hexanol 5-methyl-2-hexanol n-octanol
0.729 0.728 0.729 0.700 0.682
0.108 0.109 0.108 0.123 0.141
0.0012 0.0012 0.0012 0.0023 0.0032
All fits use 0 F x tracer F 0.3 as the domain.
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Fig. 4. Fits of Eq. Ž1. to UNIFAC simulation results for 5-methyl-2-hexanol partitioning into NAPL mixture of equal parts TCE, toluene, decane, and naphthalene, for tracer mole fraction range 0–0.3.
fit for 5-methyl-2-hexanol and this NAPL mixture. Note that even with this fairly broad array of NAPL constituents, the partitioning is significantly nonlinear. Below, however, it will be demonstrated that when a significant portion of the NAPL chemically resembles the tracer, this nonlinearity is diminished. 3.7. Effect of co-tracers It is common practice to use a suite of partitioning tracers rather than just one in order to maximize the likelihood of obtaining agreeable retardation values Žpartitioning tracers arriving at the effluent well in a reasonable number of pore volumes.. By their very nature, partitioning tracers will Žtemporarily. change the composition of the original NAPL. Because the tracers are similar to one another in chemical structure, they may impact one another’s partitioning behavior. Fig. 5 presents experimental data for both the waterrDMPrNAPL mixture system discussed earlier and a system in which the NAPL mixture comprises 70% of the NAPL phase and octanol comprises the remaining 30%. ŽExperimental procedures were similar to those described earlier and are documented in detail in Dai, 1997.. Note that the addition of octanol tends to make the partitioning of DMP more linear Žcloser to Raoult’s law.. Again, Fig. 5 tends to support the UNIFAC modeling approach for such systems. To systematically investigate such potential interference, the partitioning of 5-methyl2-hexanol into TCE with varying amounts of n-hexanol was studied. The results are
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Fig. 5. Comparison of experimental and UNIFAC simulation results for 2,2-dimethyl-3-pentanol partitioning into synthetic NAPL mixture with and without a 30% mole fraction of octanol.
Fig. 6. UNIFAC simulation results for 5-methyl-2-hexanol partitioning into TCE with different mole fractions of n-hexanol for tracer mole fraction range 0–0.3.
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Table 4 Fits for 5-methyl-2-hexanol partitioning into NAPL comprised of TCE and varying amounts of n-hexanol % n-Hexanol
a
b
rms error
0 5 10 15 20 25 30
0.629 0.711 0.822 0.968 1.161 1.418 1.765
0.130 0.217 0.330 0.477 0.669 0.924 1.269
0.0037 0.0032 0.0025 0.0019 0.0014 0.0010 0.0007
All fits use 0 F x tracer F 0.3 as the domain.
illustrated in Fig. 6 and the corresponding fits to Eq. Ž1. are reported in Table 4. Note that the more ‘co-tracer’ Ž n-hexanol in this case. present, the more the partitioning of the tracer of interest Ž5-methyl-2-hexanol in this case. is affected. Because the co-tracer is chemically similar to the tracer of interest, the system becomes more ideal at higher co-tracer levels and the partitioning correspondingly becomes more linear in nature Žnearer to Raoult’s law.. It must be remembered that the co-tracer will also be partitioning into and out of the NAPL. Therefore, no individual curve in Fig. 6 represents what would be anticipated in the field, each curve is only marginal in nature, representing one degree of freedom Žfor the tracer of interest.. ŽA ternary diagram would be required to present the actual compositions that would be experienced during a tracer test for such a system.. Similar behavior results for 5-methyl-2-hexanol partitioning into various mixtures of TCE and n-octanol Žnot shown.. The qualitative nature of this sensitivity is in perfect concert with that observed for n-hexanol. In a partitioning tracer test employing n-hexanol, 5-methyl-2-hexanol, and n-octanol, the expected elution times would be in the order stated, with n-octanol experiencing the most retardation. Consequently, the interference effects suggested by Fig. 6 might be expected at the front of the 5-methyl2-hexanol migration; similar results for octanol at the back. The situation would be more dramatic nearer to the center of mass of 5-methyl-2-hexanol signal, as both co-tracers would have an impact. Therefore, when using a suite of tracers, there may not exist a unique one-to-one partitioning relation that may be defined for a given tracer throughout the swept volume of the partitioning tracer test—it evolves in response to the presence of co-tracers. This fact is not currently being considered when reducing data from partitioning tracer tests.
4. Discussion This communication documents the success of a simple function, interpreted as an unfavorable form of the Langmuir relation, at fitting the lower end of interphase partitioning behavior of systems of alcohol partitioning tracers and NAPLs. The function applicability is supported heuristically through its success at fitting the partitioning
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behavior of different types of systems. No theoretical basis is offered for its success Žaside from the fact that the function becomes linear in the region of the origin, in accordance with Henry’s law applied to the NAPL phase.. For the tracerrNAPL systems studied, the domains of applicability of Eq. Ž1. are taken to be tracer mole fraction ranges of 0–0.3. Wise Ž1999. uses the conclusion that Eq. Ž1. is a good predictor of the interphase distribution of partitioning tracers into NAPLs at equilibrium to deduce the ramifications of nonlinear partitioning behavior upon the interpretation of partitioning tracer tests, which are traditionally analyzed based upon the assumption of linear interphase partitioning. The effects of using multiple partitioning tracers may complicate the systems at hand, as now the partitioning relation might be a function of both space and time even for a uniformly distributed NAPL under equilibrium conditions. It is also, somewhat conversely, possible that they may be used to make the partitioning of a particular tracer more linear Žnear Raoult’s law. by preconditioning the NAPL. Further study of such effects is needed.
References Adamson, A.W., 1976. Physical Chemistry of Surfaces, 3rd edn. Wiley, New York, 698 pp. Annable, M.D., Rao, P.S.C., Hatfield, K., Graham, W.D., Wood, A.L., 1994. Use of partitioning tracers for measuring residual NAPL distribution in a contaminated aquifer: preliminary results from a field-scale test. Presented at the 2nd Tracer Workshop, The University of Texas at Austin, November 14 and 15, 1994, pp. 77–85. Annable, M.D., Rao, P.S.C., Hatfield, K., Graham, W.D., Wood, A.L., 1998. Use of partitioning tracers for measuring residual NAPL distribution in a contaminated aquifer: preliminary results from a field-scale test. J. Environmental Eng., in press. Chen, F., 1992. Manual for Program GAMMA: Calculation of Activity Coefficients by Means of UNIFAC. National Environmental Research Institute, Roskilde, Denmark, 36 pp. Dai, D., 1997. Solubility and partitioning behavior of organic compounds in complex NAPL mixtures. PhD dissertation. Soil and Water Sciences Department, University of Florida, 219 pp. James, A.I., Graham, W.D., Hatfield, K., Rao, P.S.C., Annable, M.D., 1997. Optimal estimation of residual non-aqueous phase liquid saturations using partitioning tracer concentration data. Water Resources Res. 33 Ž12., 2621–2636. Jin, M., Delshad, M., Dwarakanath, V., McKinney, D.C., Pope, G.A., Sepehrnoori, K., Tiburg, C.E., Jackson, R., 1995. Partitioning tracer test for detection, estimation and remediation performance assessment of subsurface non-aqueous phase liquids. Water Resources Res. 31 Ž5., 1201–1212. Mackay, D., Shiu, W.Y., Maijanen, A., Feenstra, S., 1991. Dissolution of non-aqueous phase liquids in groundwater. J. Contaminant Hydrology 8, 23–42. Nelson, N.T., Brusseau, M.L., 1996. Field study of the partitioning tracer method for detection of dense non-aqueous phase liquid in a trichlorothene contaminated aquifer. Environmental Sci. Technol. 30 Ž9., 2859–2863. Pope, G.A., Jin, M., Dwarakanath, V., Rouse, B., Sepehrnoori, K., 1994. Partitioning tracer tests to characterize organic contaminants. Presented at the 2nd Tracer Workshop, The University of Texas at Austin, November 14 and 15, 1994. Rao, P.S.C., Annable, M.D., Sillan, R.K., Dai, D., Hatfield, K., Graham, W.D., Wood, A.L., Enfield, C.G., 1997. Field-scale evaluation of in situ cosolvent flushing for enhanced aquifer remediation. Water Resources Res. 33 Ž12., 2673–2686.
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Wang, P., Dwarakanath, V., Rouse, B.A., Pope, G.A., Sepehrnoori, K., 1998. Partition coefficients for alcohol tracers between non-aqueous phase liquids and water from UNIFAC-solubility method. Adv. Water Resources 21 Ž2., 171–181. Wilson, R.D., Mackay, D.M., 1995. Direct detection of residual non-aqueous phase liquid in the saturated zone using SF6 as a partitioning tracer. Environmental Sci. Technol. 29 Ž5., 1255–1258. Wise, W.R., 1998. Thermodynamic evaluation of effluent tailing effects during dissolution of binary oil mixtures. J. Contam. Hydrol. 32 Ž1–2., 117–130. Wise, W.R., 1999. NAPL characterization through partitioning tracer tests: quantifying effects of partitioning nonlinearities. J. Contam. Hydrol. 36 Ž1–2., 167–183.