Using Partitioning Alcohol Tracers To Estimate Hydrophobicity of High

Partitioning alcohol tracers were evaluated for characterizing the hydrophobicity of high molecular weight light, nonaqueous phase liquids (LNAPLs). A...
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Environ. Sci. Technol. 2000, 34, 4701-4707

Using Partitioning Alcohol Tracers To Estimate Hydrophobicity of High Molecular Weight LNAPLs BIN WU AND DAVID A. SABATINI* School of Civil Engineering and Environmental Science, University of Oklahoma, 202 West Boyd Street, Room 334, Norman, Oklahoma 73019

substantially from crude oils (e.g., chlorinated solvents (5)). The EACN concept provides a simplified characteristic for otherwise complex subsurface contaminants, by quantifying their hydrophobicity. Formulation of middle phase microemulsion (MPM) systems for surfactant-enhanced subsurface remediation (SESR) can be greatly simplified by knowing the contaminant’s EACN (4). The following relationship, known as the Salager equation (7), correlates variables in a surfactant-oil system:

ln S* ) K*EACN + f(A) - σ

Partitioning alcohol tracers were evaluated for characterizing the hydrophobicity of high molecular weight light, nonaqueous phase liquids (LNAPLs). Alcohol partitioning coefficients were found to decrease with increasing n-alkane molecular size. It is hypothesized that this decrease in partitioning coefficient is due to a decreased entropy of mixing. A thermodynamic model and an empirical model were used for fitting alcohol partitioning coefficients for n-alkanes ranging from hexane to hexadecane. The resulting expressions were further evaluated for characterizing equally and more hydrophobic oils of unknown equivalent alkane carbon number (EACN), including squalane (expected EACN of 24-30), and lower EACN oils (3.0-20), including PCE (EACN ∼ 3.0). Good agreement was observed for all the high EACN oils and for PCE. The agreement becomes progressively poorer as the EACN decreases below 3.0, illustrating the danger of extrapolating well beyond the range of data used to develop an empirical relationship. Based on our results we propose that simultaneously using the thermodynamic and empirical models can further characterize a NAPL based on a single partitioning tracer test.

Introduction The hydrophobicity of subsurface contaminants is an important parameter for designing remediation systems. The more hydrophobic a contaminant is, the harder it will be to remediate the subsurface contamination by pump-and-treat methods. In chemical flooding techniques, such as surfactantand cosolvent-enhanced flushing, a contaminant’s solubility enhancement and thus system efficiency are inversely related to NAPL hydrophobicity. EACN is a parameter frequently used to represent a contaminant’s hydrophobicity. Analogous to the alkane carbon number (ACN), which is simply the number of carbons in an alkane (e.g., 8 for octane), the EACN is an equivalent ACN for more complex organic molecules. Wade, Schechter, and their co-workers used this concept to correlate the surfactant phase behavior of brine-oil systems as a function of system parameters (1, 2) in their enhanced oil recovery (EOR) research. More recently researchers have utilized this concept to study subsurface NAPL contamination (3-6). Not only has this concept been used successfully with light, nonaqueous phase liquids (LNAPLs), which are similar to the crude oils originally studied by Wade and Schechter (e.g., aviation fuels (4, 6)), it has also been extended to characterize dense, nonaqueous liquids (DNAPLs) that differ * Corresponding author phone: (405)325-4273; fax: (405)325-4217; e-mail: [email protected]. 10.1021/es991336f CCC: $19.00 Published on Web 09/26/2000

 2000 American Chemical Society

(1)

In this relationship, S* is the salinity (wt % of NaCl) needed to produce an optimal middle phase microemulsion system, K is a constant that is related to the surfactant’s headgroup (e.g., 0.10 for sulfates and 0.16 for sulfonates), EACN is the equivalent alkane carbon number of the oil, f(A) is a function of the alcohol that is considered as a cosolvent, and σ is a constant which is dependent on surfactant structure. Knowing the contaminant’s EACN, the contaminant’s optimal salinity can be estimated for a given surfactant system (i.e., knowing values for K, f(A), and σ) (3-6). Traditionally, contaminant EACN values have been experimentally determined from salinity scans using the Salager equation. For contaminant mixtures, if the fraction and EACN of each constituent are known, the EACN for the mixture can be calculated using ideal or nonideal mixing rules (1, 3, and 5). However most subsurface contaminants are complex mixtures, making it difficult to determine the individual constituents and their fractions in the mixture. EACN values for these contaminant mixtures can be determined by forming MPM systems with known surfactant systems and then back-calculating the EACN from the Salager equation. The irony here is that determining the EACN value requires formulation of MPM systems and is thus not useful in a-priori formulation of the surfactant system. Recently, Dwarakanath and Pope (8) presented a new approach for determining contaminant EACN values. In their studies of alcohol partitioning between water and oils, they found the following log-linear relationship

ln Kp ) - A*EACN(oil) + B1*EACN(alcohol) + B2

(2)

where Kp is the alcohol’s partitioning coefficient between water and an oil, EACN(alcohol) is an alcohol’s EACN value, and A, B1, and B2 are empirical constants. Similar to alkanes, the EACN of alcohol tracers can also be related to their hydrophobicity (8). The EACN of a linear alcohol is assumed to be the number of carbon atoms in the alcohol; this may be slightly in error because alcohols are more hydrophilic than alkanes. For a branched alcohol, its EACN is slightly different from number of its carbon atoms, just as in the case of a branched alkane. For a known EACN alcohol tracer, the following relationship is expected

ln Kp ) - A*EACN(oil) + B

(3)

Here, the constant B is the sum of B1*EACN(alcohol) and B2 in eq 2. Dwarakanath and Pope established eq 2 for oils with EACN’s values from -15 (chloroform) to +10 (decane), with most of their work focusing on chlorinated hydrocarbons. Using eq 2, they estimated EACN values for some common chlorinated contaminants (EACN of -15.13 to 2.27), and a jet fuel (EACN of 6.31), and compared the results with those values estimated from the salinity scans, demonstrating good agreement between the two methods. While their work VOL. 34, NO. 22, 2000 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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focused on low EACN oils (-15 to 10, with most less than 4), we extend their approach and focus on more hydrophobic (high EACN) oils (i.e., up to hexadecane) and compare results with unknown oils with EACNs in this same range. In addition, we develop a thermodynamically based model to estimate the contaminant’s molecular weight from the same experimental data, as described further below. The ultimate goal of this work is to provide guidance in formulating surfactant systems for remediating high-EACN LNAPL contamination.

Ca(o) Xa(o) )

Ca(o) Ca(w)

) Kp

(4)

Theoretical Development The chemical potential of a dilute alcohol solution can be expressed as follows

9

Ca(o)/Ca(w) ) mww/Fw*(Fo/mwo) exp((µa(w)° - µa(o)°)/RT) (10) Recalling the definition in eq 4 and further defining nd (mol/ mL), which is the molar density of the oil, as

nd ) Fo/mwo

(11)

we end up with the following relationship

Kp ) K*nd

(12)

where the constant K equals (mww /Fw)*exp((µa(w)° - µa(o)°)/ RT), mww )18 g/mol and Fw ) 1 g/mL for water. Equation 12 states that the oil-water partitioning coefficient of an alcohol is proportional to the oil’s molar density, at constant temperature and pressure. If the oil is an n-alkane, which can be expressed as CnH2n+2, then

Kp ) K*Fo/(14*ACN +2)

(13)

and if ACN is large enough

(6b)

where K′ ) K/14. This equation indicates that for a particular alcohol solute, its oil-water partitioning coefficient (Kp) is directly proportional to the Fo/EACN of the oil. Assuming a constant density for all alkanes, further simplification leads to

(7)

Since µa(w)° and µa(o)° are independent of composition, Xa(o)/ Xa(w) must also remain a constant, as first proposed by Nernst (16). If the alcohol solute concentration is expressed as Ca (mg/ L) instead of mole fraction, then in the oleic phase 4702

It should be pointed out that the physical properties of densities and molecular weights in eqs 8a, 8b, and 9 are not exactly the same as those for pure oil and water, since these are not neat phases (i.e., low concentrations of alcohol and other liquids are solubilized). However, the approximations of using pure oil and water values are valid if the solutions are dilute. Rearranging eq 9 gives

Kp ) K′*Fo/ACN

At equilibrium the aqueous and oil chemical potentials are equal and with rearranging we get

Xa(o)/Xa(w) ) exp((µa(w)° - µa(o)°)/RT)

Ca(o)Fwmwo/(Ca(w)Fomww) ) exp((µa(w)° - µa(o)°)/RT) (9)

(6a)

and

µa(w) ) µa(w)° + RT ln Xa(w)

(8b)

(5)

here µa is the chemical potential of the alcohol solute, µa° is the chemical potential of the alcohol solute at its standard state (its pure state)swhich is a function of temperature and pressure but not of composition, R is the ideal gas constant, T is temperature, and Xa is the mole fraction of the alcohol solute. When the alcohol solute is distributed between two immiscible liquids o and w, the following two chemical potential equations apply, one for the oleic and the second for the aqueous phase

µa(o) ) µa(o)° + RT ln Xa(o)

Ca(w) mwa Xa(w) ) Fw mww Substituting eqs 8a and 8b into eq 7 yields

where Ca(o) is the alcohol concentration in the first immiscible solvent (organic phase, here), Ca(w) is the alcohol concentration in the second solvent (water), and Kp is the partitioning coefficient of the alcohol between these two phases. Partitioning alcohols have been widely used for characterizing subsurface contaminants in the partitioning interwell tracer test (PITT) (8-13). In PITTs, a suite of partitioning and nonpartitioning alcohols is injected into the subsurface. In the presence of NAPL, alcohols will differentially partition into the NAPL and thus chromatographically separate. The NAPL residual saturation can be estimated by quantifying the relative alcohol separation and knowing the alcohol’s water-NAPL partitioning coefficients. A new application of the partitioning alcohol tracer technique is to estimate NAPL EACN values (8). This method is quick, economical, and effective. To our knowledge, the only published work on this subject is from Dwarakanath and Pope (8), as discussed above.

µa ) µa° + RT ln Xa

(8a)

In the above equation, mwa and mwo are molecular weights (g/mol) of the alcohol and the oil, respectively. Fo is density of the oil (g/mL). Similarly, in aqueous phase

Background An alcohol solute partitions between two immiscible phases as shown below

mwa F0 mwo

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Kp ) K′′/ACN

(14)

(15)

where K′′ ) K′Fo. For oils ranging from C8 to C16 this assumption would introduce an error of ∼17%, in the worst case (i.e., hexane to hexadecane), and much less in all others (see Table 2), which may well be acceptable. This deviation will likely be acceptable, given other uncertainties. However, much greater deviations and uncertainties will occur going

TABLE 1. Properties for Selected Tracers tracer

structure

molecular weight (g/mol)

density (g/mL)

n-pentanol 2-methyl-2-hexanol 2-methyl-3-hexanol 2,4-dimethyl-3-pentanol

CH3-(CH2)3-CH2(OH) CH3-C(CH3)(OH)-(CH2)3-CH3 CH3-(CH)CH3-(CH)(OH)-(CH2)2-CH3 CH3-(CH)CH3-(CH)(OH)-(CH)CH3-CH2-CH3

88.15 116.20 116.20 116.20

0.811 0.812 0.821 0.829

TABLE 2. Properties for Selected NAPLs NAPL

structure

molecular weight (g/mol)

density (g/mL)

molal density (mol/L)

n-hexane n-octane n-decane n-dodecane n-hexadecane squalane diesel Stony Lake LNAPL Tuebingen tetrachloroethylene (PCE)

CH3-(CH2)4-CH3 CH3-(CH2)6-CH3 CH3-(CH2)8-CH3 CH3-(CH2)10-CH3 CH3-(CH2)14-CH3 C30H62a NAb NAb NAb Cl2CdCCl2

88.2 114.2 142.3 170.3 226.5 422.8 NAb NAb NAb 165.8

0.659 0.703 0.730 0.750 0.773 0.810 0.77 0.84 0.85 1.623

7.65 6.15 5.13 4.40 3.41 1.92 NAb NAb NAb 9.79

a

[(CH3)2CH(CH2)3CH(CH3)(CH2)3CH(CH3)CH2CH2-]2.

b

NA - not available.

from alkanes to chlorinated solvents and this treatment should not be applied.

Research Objectives In this paper, we evaluate the use of partitioning tracers for characterizing high-EACN LNAPLs (versus the low EACN chlorinated solvents which were more the focus of Dwarakanath and Pope (8)), we develop a thermodynamically based model for determining additional contaminant properties (average molecular weight), and we evaluate these two methods for several unknown oils. We demonstrate the relative advantages and limitations of these two approaches for characterizing contaminant hydrophobicity (EACN and molecular weight). After developing the equations for nalkanes ranging from hexane to hexadecane, we subsequently use these methods for characterizing several differing compoundssone more hydrophobic (squalane) and a second more hydrophilic (PCE) than the n-alkanes used in developing the models. We also evaluate three unknown LNAPLs with EACN values in the range of 10-16. We also present additional results on chlorinated solvents in the Supporting Information. Our overall objective is to evaluate the use of partitioning tracers for characterizing high-EACN LNAPLs, thereby guiding surfactant system selection to be evaluated in laboratory studies for designing remediation systems.

Materials and Methods Chemicals. Partitioning alcohol tracers, as identified in Table 1, were purchased from Aldrich (Milwaukee WI), with purities of greater than 95%. Reagent grade alkanes and PCE were also purchased from Aldrich. They all have purity of 99% or higher (see Table 2 for their relevant properties). The diesel fuel was purchased from a gasoline station. Stony Lake LNAPL was collected at a remediation site in Stony Lake, Michigan by Surbec Environmental LLC, Norman, OK. Tuebingen LNAPL was collected at a remediation site in Germany by the Applied Hydrogeology group at the University of Tuebingen, Tuebingen, Germany. HPLC grade water was used in all studies. All chemicals were used as received. Batch Studies. Batch studies were used to determine the alcohols’ NAPL-water partitioning coefficient. The alcohol aqueous concentrations were varied between 80 and 800 mg/L. Equal volumes of oil and water (10 mL each) were placed in a 20-mL Techmar vial that was crimp-capped with a Teflon septum, leaving negligible headspace (i.e., volatilization losses were minimal). The vial was shaken on a wristaction shaker for 1 h and then equilibrated for another hour,

FIGURE 1. Partitioning of 2,4-dimethyl-3-pentanol between decane and water. which was determined adequate to achieve equilibrium. If an emulsion occurred during the mixing, the vial was sonicated and centrifuged to break the emulsion. Aqueous samples were taken through the septa by a 10-uL syringe and injected into a Varian 3300 GC for analysis of alcohol concentrations. Equilibrium alcohol concentrations in the oil phase were calculated by mass balance using the equation below.

Ca(o) ) (Cia(w) - Ca(w))*(Vw/Vo)

(16)

The variable Cia(w) is initial alcohol aqueous concentration before mixing, while Vw and Vo are volumes of aqueous phase and oleic phase, respectively. System blanks were conducted to verify that losses were negligible thus validating this approach. All batch studies were carried out at 23 °C. Gas Chromatography Analysis. A Supelco Cowax 60 m × 0.32 mm × 0.5 um column was used for GC analysis. The temperature was programmed at 70 °C for 2 min, followed by a 10 °C per min ramp to 180 °C. The injection volume was 1 uL. Varian Star 4.5 Chromatography Workstation software was used to record and integrate the chromatograms.

Results and Discussions Batch Results. For each partitioning tracer, equilibrium oilphase tracer concentrations were plotted against equilibrium aqueous tracer concentrations. Figure 1 shows partitioning of 2,4-dimethyl-3-pentanol between decane and water. Slopes of linear regression lines were taken as the partitioning coefficients of tracers in these water-oil systems. The resulting partitioning coefficients are listed in Table 3. VOL. 34, NO. 22, 2000 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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TABLE 3. Kp Measurements (with 95% Confidence Interval) from Batch Studies (at 23 °C) alcohol

hexane

octane

decane

dodecane

hexadecane

n-pentanol 2-methyl-2-hexanol 2-methyl-3-hexanol 2,4-dimethyl-3-pentanol

1.09 ( 0.08 11.22 ( 1.27 15.28 ( 0.43 23.43 ( 3.25

0.74 ( 0.03 8.88 ( 1.15 14.04 ( 0.73 18.10 ( 3.06

0.64 ( 0.16 7.47 ( 0.92 11.57 ( 0.56 16.41 ( 0.53

0.56 ( 0.02 6.67 ( 0.54 9.16 ( 0.22 15.25 ( 0.56

0.52 ( 0.02 5.37 ( 0.44 7.02 ( 0.56 11.45 ( 1.45

TABLE 4. Statistical Summary for Linear Regression Lines in Figures 2,a 4,b and 6c Ad and 95% confidence interval

tracer

0.0687 ( 0.0601 (0.0505)e 2-methyl-2-hexanol 0.0715 ( 0.0245 (0.0505)e 2-methyl-3-hexanol 0.0821 ( 0.0190 (0.0505)e 2,4-dimethyl-3-pentanol 0.0665 ( 0.0235 (0.0505)e

n-pentanol

4704

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R2

0.336 ( 0.659 (0.318)e 2.782 ( 0.269 (1.189)e 3.250 ( 0.209 (1.313)e 3.493 ( 0.157

0.815 0.966 0.984 0.964

b. Figure 4

FIGURE 2. Logarithm of Kp versus oil EACNsfitting data with eq 3. Four partitioning alcohol tracers (listed in Table 1) were studied in this research based on their medium hydrophobic characteristics. Alcohol tracers with higher or lower hydrophobicity would require higher or lower oil-water ratios to produce accurate partitioning coefficients. At first glance, the general trend is that, for a certain tracer, the oil-water partitioning coefficient decreases as the oil becomes more hydrophobic (i.e., higher EACN), as evaluated further below. Logarithm of Kp Versus EACN (Eq 3). When the logarithm of Kp values are plotted against corresponding EACN values, linear relationships are observed for all four alcohol tracers and all five oils as suggested by eq 3 (see Figure 2). Statistical analyses indicate the slopes of these plots are the same (within 95% confidence intervalss see Table 4a), which confirms the findings of Dwarakanath and Pope (8) who found A to be constant for all alcohol tracers (eq 2). These results validate and extend the use of the partitioning alcohol method to higher EACN LNAPLs (EACNs beween 10 and 16) and show that a similar relationship holds true in this higher EACN range. However, numerically the parameters A and B calculated in this work are different from those in ref 8 (see Table 4a for comparison). Presuming both sets of parameters are valid within their respective regression EACN ranges, extrapolating eq 3 with its parameters A and B calibrated in lower (higher) EACN range to higher (lower) EACN range could introduce significant errors, as discussed later in the section of EACN estimate for squalane. From Figure 2 and Table 4a, the intercepts of the regression lines increase in the order of pentanol, 2-methyl-2-hexanol, 2-methyl-3-hexanol, and 2,4-dimethyl-3-pentanol. This increasing order is consistent with the hydrophobicity of these alcohol tracers. Plotting the intercepts in Figure 2 against the corresponding alcohol tracers’ EACN values (as estimated by Dwarakanath and Pope’s (8)), a linear relationship is found, as displayed in Figure 3. This relationship can be predicted by eq 2 by setting EACN(oil) equal to zero. Kp Versus Oil Molar Density (nd) (Eq 12). Figure 4 displays the Kp values for the partitioning alcohol tracers as a function of oil molar density (nd values). Consistent with eq 12, the regression lines were all forced through the origin, even though including an intercept may have produced better fits. Generally, when the tracers are more hydrophobic the correlation improves. Recalling the physical meaning of this K value (see eq 12), we can predict that increasing alcohol hydrophobicity (i.e., increase the standard state chemical

B and 95% confidence interval

tracer

slope C (95% confidence)

R2

n-pentanol 2-methyl-2-hexanol 2-methyl-3-hexanol 2,4-dimethyl-3-pentanol

0.133 ( 0.015 1.473 ( 0.050 2.127 ( 0.174 3.129 ( 0.237

0.912 0.990 0.948 0.942

c. Figure 6 alcohol tracer

slope K′′

R2

n-pentanol 2-methyl-2-hexanol 2-methyl-3-hexanol 2,4-dimethyl-3-pentanol

6.50 71.9 103.7 152.4

0.911 0.905 0.845 0.787

a ln K ) -A*EACN + B, eq 3. b K ) K*n , eq 12. c K ) K′′/EACN, p p d p eq 15. d A(average) ) 0.0722, standard deviation ) 0.0069. e From ref 8.

FIGURE 3. Intercept in Figure 2 versus alcohol EACN. potential difference (µa(w)° - µa(o)°) of the alcohol) will increase the slope value in Figure 3. The more hydrophobic a tracer is the more sensitive it is to the changes in the oil EACN. The most hydrophobic tracer, 2,4-dimethyl-3-pentanol, has the greatest slope value among all the tracers shown in Figure 4, and the most hydrophilic tracer, n-pentanol, has the lowest slope value. If the logarithm of the slope values are plotted versus the corresponding alcohol EACN values, a linear relationship is observed (see Figure 5). An additional utility of this thermodynamically based model is that it can be used to empirically estimate the alcohols’ hydrophobicity. Kp Versus 1/EACN (Eq 15). Figure 6 shows results of fitting the partitioning data according to eq 15. By comparing the

FIGURE 4. Kp values versus oil molar densitiessfitting data with eq 12.

FIGURE 5. Logarithm of slope in Figure 4 versus alcohol EACN.

FIGURE 6. Kp versus reciprocal of oil EACN values fitting data with eq 15. R2 values, regression lines in Figure 6 are not as good as those in Figure 4. This is expected, since eq 15 is a simplified version of eq 12 by neglecting difference in the oil density. However, eq 15 is still quite valuable for providing a EACN estimate for an unknown oil, thereby helping to focus and guide surfactant formulation, reducing the trial and error effort common in this process. Estimate EACN and nd Values for Squalane. Since the two models (eqs 3 and 12) were developed for n-alkanes with EACN values of 6 to 16, it is interesting to see how well they work beyond this EACN. Squalane was chosen as a more hydrophobic oil with a different structure. Squalane has a total of 30 carbon atoms with 24 of those carbon atoms forming a linear chain. Thus, squalane’s structure suggests it would have an EACN between 24 and 30sthe uncertainty is caused by its branched carbon atoms. Three alcohol tracers, 2-methyl-2-hexanol, 2-methyl-3-hexanol, and 2,4-dimethyl3-pentanol, were selected for squalane studies. Partitioning coefficients of these alcohol tracers in water-squalane systems were measured (see Table 5). The estimated squalane EACN and nd values are listed in Table 5.

The squalane EACN values predicted by eqs 3 and 15 (ranging from 21.3 to 26.5, see Table 5) are consistent with the expected squalane EACN (a value between 24 and 30, see above). Conversely, the EACN estimated by ref 8 ranges from 13.1 to 15.9 (see Table 5), illustrating the danger of extrapolating from lower EACN data to much higher EACN compounds. Based on squalane’s molecular weight and density, the actual molar density for squalane is 1.92 mol/L. Values predicted from the three tracers and eq 12 range from 1.65 to 2.12 mol/L. The estimated values are all similar to and center around the actual value. If squalane density is considered as a known value, the estimated EACN values for squalane (from eq 15) are 29.8 with 2,2-dimethyl-2-pentanol, 27.3 with 2-methyl-3-hexanol, and 29.8 with 2,4-dimethyl3-pentanol, which are close to the expected maximum EACN of 30 for squalane. Estimate EACN and nd Values for PCE. The two models were also used to predict values for tetrachloroethylene (PCE). PCE was found to have a low EACN value (about 2.9 (5)) with the chlorine atoms making PCE even more different from the n-alkanes evaluated in this study. The same three partitioning tracers were used to evaluate PCE hydrophobicity as had been used for squalane. The measured partitioning coefficients and resulting EACN and nd values are summarized in Table 6. Compared with the literature EACN value of 2.9, eq 3 predicted the EACN values of PCE to be 2.6 ( 0.7. For practical purposes (i.e., guiding system formulation), these estimated EACN values are quite good for PCE. Compared with the true value of 9.79 mol/L, eq 10 predicted PCE molar density values of 8.88 ( 1.53 mol/L. Again, the estimated EACN and molar density values for PCE are very similar to and centered around the true value. While good agreement was observed between our predictions and actual PCE data, the agreement became poorer as the EACN further decreased (see the Supporting Information). This again illustrates the danger of extrapolating well beyond the data used to establish an empirical relationship. Comparisons of Models. Though empirical in nature, eq 3 has shown its success in relating a partitioning tracers’ Kp value with the oil’s EACN value as demonstrated in the previous study (8). The method is also robustsit can be used not only for n-alkanes but also for other “oils”, such as chlorinated solvents and branched alkanes. Nonetheless, extrapolating this relationship outside its calibration range might yield misleading information. In contrast to eqs 2 and 3, eq 12 was developed based on thermodynamic considerations of dilute solutions. It predicts that alcohols will have different partitioning coefficients in different oils due to entropy changes. When the oil molar density (nd) increases (i.e., more oil molecules per unit volume), the alcohol partitioning coefficient increases because of the increased number of mixing configurations of the solute in the oleic phase. This thermodynamic model can also be used to estimate EACN values for n-alkanes (e.g., eqs 14 and 15) as a preliminary screening model. However, for branched LNAPLs, EACN values predicted by this model were typically higher than actual values, at least for squalane. One needs to be cautious when applying this model to estimate EACN values of DNAPLs. Since eqs 12-15 and the relevant parameters were developed based on the assumptions of linear alkanes (eq 12), and since the density was assumed constant among the alkanes (eq 14), clearly highly chlorinated DNAPL (e.g., PCE) that is much denser than n-alkanes does not follow the assumptions. Equation 3 has two parameterssthe slope and intercept. Different alcohol tracers have identical slopes but different intercepts. Their intercepts can be related to their hydrophobicity (or EACN). However, the oil EACN estimated by VOL. 34, NO. 22, 2000 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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TABLE 5. Predicted EACN and Molar Density Values for Squalane estimated EACN

tracer

Kp

2-methyl-2-hexanol 2-methyl-3-hexanol 2,4-dimethyl-3-pentanol av (SD)

2.43 4.50 6.07

a

eq 3, A and B values from this work

eq 15

eq 2, A, B1, and B2 values from ref 8

26.5 21.3 25.4 24.4 ( 2.7

29.6 23.0 25.1 25.9 ( 3.4

15.9 13.1 NAa 14.5 ( 2.0

actual EACN 24-30 24-30 24-30

estimated molar density (mol/L, eq 12)

actual molar density

1.65 2.12 1.94 1.90 ( 0.24

1.92 1.92 1.92

NA - not available.

TABLE 6. Predicted EACN and Molar Density Values for PCE tracer

Kp

estimated lit. estimated actual EACN EACN molar density molar (eq 3) (8) (mol/L, eq 12) density

2-methyl-2-hexanol 12.88 3.2 2-methyl-3-hexnaol 22.23 1.8 2,4-dimethyl-327.50 2.7 pentanol av (SD) 2.6 ( 0.7

2.9 2.9 2.9

7.40 10.45 8.79

9.79 9.79 9.79

8.88 ( 1.53

this method could be zero or negative (e.g., EACN for TCE is -3.81 (5)), which is not structurally meaningful. On the contrary, the thermodynamic model of eq 12 is a simple model with one parametersthe slope. In this model, different alcohol tracers have different slopes. The magnitude of the slopes is related to the alcohols’ hydrophobicity (or EACN). The oil molar density and EACN estimated by this model are always positive since Kp is always greater than zero. In general, eq 3 can be used to estimate a NAPL EACN value with a satisfactory accuracy with minimum knowledge of the NAPL. Equation 12 can be used to accurately estimate a NAPL’s average molecular size. Combination Model of Eqs 3 and 12. We propose using the both models to obtain more information about the oil from a single partitioning alcohol test. Using PCE as an example, not only can we determine the EACN of PCE but also we can determine the degree of chlorination (i.e., number of chlorine atoms in one PCE molecule). This number can be estimated by combining results from both eqs 3 and 12 based on the inputs of partitioning coefficients and substituting results into the following equation

number of chlorine ) (nd*F - (14*EACN + 2))/35.5 (17) The nd value is estimated from eq 12. The term nd*F is the estimated molecular weight for PCE. The EACN value is estimated from eq 3. The above equation assumes that any deviation between the EACN values estimated by eqs 3 and 14 is caused by chlorine atoms replacing hydrogen atoms. The estimated chlorine numbers by eq 17 for PCE are listed in Table 6. This average number of 3.9 ( 0.3 is very close to the real chlorine number of 4. This example demonstrates the utility of combining these two models for more fully characterizing a NAPL. Using Kp-EACN Models To Guide Surfactant System Formulation for High-EACN LNAPL Contamination. A major motivation in developing these Kp-EACN models is to establish EACN values for uncharacterized NAPLs, thereby expediting the formulation of middle phase microemulsion with the NAPLs. Phase behavior studies of most LNAPLs are similar to those of n-alkanes. Thus, it is expected that EACN values predicted by the models for a LNAPL can be used with eq 1 to forecast the appropriate conditions (e.g., optimal salinity S*) to realize middle phase microemulsions with the LNAPL. 4706

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TABLE 7. Estimating Degree of Chlorination in PCE by the Combination Method

tracer

predicted EACN (eq 3)

estimated molecular wt (eq 12)

2-methyl-2-hexanol 2-methyl-3-hexnaol 2,4-dimethyl-3-pentanol av (SD)

3.2 1.8 2.7 2.6 ( 0.7

185.5 155.9 186.5 176.0 ( 17.4

estimated actual chlorine chlorine no. in PCE no. in (eq 17) PCE 4.0 3.6 4.1 3.9 ( 0.3

4 4 4

TABLE 8. Using 2-Methyl-2-hexanol Partitioning Data To Guide Laboratory Surfactant System Formulation for Three High-EACN LNAPLs

Kp

estimated EACN

predicted S*, wt %, using EACN in

eq 3

column 2a,b

column 3a,b

exptl S* (wt %)a

9.4 11.4 12.0

9.0 12.4 13.5

8.9 9.5 12.4

eq 14

diesel 6.30 13.2 12.7 Stony Lake LNAPL 5.47 15.1 16.0 Tuebingen LNAPL 5.27 15.7 16.8

a The surfactant system is 4% Alfotetra propoxylated alkyl sulfate, 16% 2-propanol, and sodium chloride. b S* is calculated from Salager equation: ln S ) K*EACN + f(A) - σ, where constants K, f(A), and σ are predetermined.

Three high-EACN LNAPLs (i.e., diesel, Stony Lake LNAPL, and Tuebingen LNAPL, Table 2) were selected to examine this hypothesis. The surfactant system used in the experiment was 4% Alfotetra propoxylated (4 PO) alkyl (C14) sulfate which is obtained from Condea Vista, 16% 2-propanol, and sodium chloride. This particular surfactant system was precalibrated with decane for its f(A) and σ values, leaving S* as the only variable in the formulation process (see eq 1). Procedures of conducting laboratory middle phase microemulsion studies can be found in refs 2-7. All three tracers (2-methyl-2-hexanol, 2-methyl-3-hexanol, and 2,4-dimethyl-3-pentanol) showed similar trends, but only 2-methyl-3-hexanol partitioning data were reported in Table 8. The predicted EACN values predicted for the LNAPLs, the predicted S*, and the experimental S* values are listed in Table 8. Equations 3 and 14 agree with each other very well in predicting EACN values. The predicted optimal salinities, based on the estimated EACN values, are generally in good agreement with the experimental values for both models. Results clearly indicate that using the partitioning tracer technique to characterize the NAPL hydrophobicity can successfully guide laboratory formulation of middle phase microemulsion for NAPLs of unknown composition (i.e., recall that the goal of these methods is to provide guidance to the laboratory formulation process, thereby greatly reducing laboratory efforts).

Supporting Information Available Additional chlorinated solvents studies and a table of 2-methyl-2-hexanol partitioning data to assess models performances with chlorinated solvents. This material is available free of charge via the Internet at http://pubs.acs.org.

Literature Cited (1) Salager, J. L.; Morgan, J. C.; Schetcher, R. S.; Wade, W. H. Soc. Pet. Eng. J. 1979, 107. (2) Bourell, M.; Schechter, R. S. Microemulsions and Related Systems; Marcel Dekker Inc.: New York, 1988; Vol. 30, Surfactant Science Series. (3) Shiau, B. J.; Rouse, J. D.; Sabatini, D. A.; Harwell, J. H.; Vu, D. Q. Environ. Sci. Technol. 1996, 30, 97-103. (4) Wu, B. Masters’ Thesis, University of Oklahoma, OK, 1996. (5) Baran, J. R., Jr.; Pope, G. A.; Wade, W. H.; Weerasooriya, V.; Yapa A. J. Colloid Interface Sci. 1994, 168, 67. (6) Baran, J. R., Jr.; Pope, G. A.; Wade, W. H.; Weersasooriya, V. J. Dispersion Sci. Technol. 1996, 17, 131-138. (7) Pope, G. A.; Wade, W. H. In Surfactant Enhanced Subsurface Remediation; Sabatini, D. A., Knox, R. C., Harwell, J. H., Eds.; ACS Symposium Series 594; American Chemical Society, Washington, DC, 1995; p 142.

(8) Dwarakanath, V.; Pope, G. A. Environ. Sci. Technol. 1998, 32, 1662-1665. (9) Tang, J. S.; Harker, B. J. Can. Pet. Technol. 1991, 30 (3), 76. (10) Tang, J. S.; Harker, B. J. Can. Pet. Technol. 1991, 30 (4), 34. (11) Jin, M.; Delshad, M.; Dwarakanath. V.; McKinney, D. C.; Pope, G. A.; Sepehrnoori, K.; Tilburg, C.; Jackson, R. E. Water Resour. Res. 1995, 31, 1201-1211. (12) Nelson, N.; Brusseau, M. Environ. Sci. Technol. 1996, 30, 28592863. (13) Rao, P. S.; Annable, M. D.; Sillan, R. K.; Dai, D.; Hatfield, K.; Graham, W. D.; Wood, A. L.; Enfield, C. Water Resour. Res. 1997, 33, 2673-86. (14) Brusseau, M. L. Water Resour. Res. 1992, 28, 33-45. (15) Jin, M.; Butler, G. W.; Jackson, R. E.; Mariner, P. E.; Pickens, J. F.; Pope, G. A.; Brown, C. L.; McKinney, D. C. Ground Water 1997, 35, 964-972. (16) Nernst, W. Z. Physik. Chem. 1891, 8, 110.

Received for review December 1, 1999. Revised manuscript received August 22, 2000. Accepted August 22, 2000. ES991336F

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