Microemulsion of Mixed Chlorinated Solvents Using Food Grade

Aldrich Chemical, and DCE was obtained from Eastman Kodak Company. Synthetic groundwater was prepared for all aqueous phase solutions having the f...
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Environ. Sci. Technol. 1996, 30, 97-103

Microemulsion of Mixed Chlorinated Solvents Using Food Grade (Edible) Surfactants B O R - J I E R S H I A U , * ,† DAVID A. SABATINI,† JEFFREY H. HARWELL,‡ AND DE QUANG VU‡ School of Civil Engineering and Environmental Science and School of Chemical Engineering and Materials Science, The Institute for Applied Surfactant Research, The University of Oklahoma, Norman, Oklahoma 73019

Ground water contamination frequently consists of mixed chlorinated solvents [e.g., tetrachloroethylene (PCE), trichloroethylene (TCE), and trans-1,2dichloroethylene (DCE)]. In this research, mixtures of the food grade (edible) surfactants bis(2ethylhexyl) sodium sulfosuccinate (AOT) and sodium mono- and dimethylnaphthalene sulfonate (SMDNS) were used in the formation of middle-phase microemulsions for mixed chlorinated solvents. Microemulsions of binary (e.g., PCE/TCE, PCE/DCE, DCE/ TCE) and ternary (PCE/TCE/DCE) chlorinated solvent systems were evaluated. Several empirical correlations were used for describing and/or predicting the phase behavior of the resulting middle-phase microemulsions (e.g., the ideal mixing rule or the nonideal regular mixing theory). The ideal mixing rule provided a good approximation for binary and ternary systems, but experimental deviations from the predictions were significant enough to affect the optimal surfactant system. Nonideal regular mixing theory demonstrated much better predictive capabilities than ideal mixing for the binary and ternary systems. The recognition of nonideal mixing behavior and the resulting predictive correlations will be valuable in the design of groundwater remediation scenarios when surfactants are used for remediation of mixed chlorinated solvents.

Introduction In a prior study (1), we demonstrated that mixtures of a food grade surfactant and hydrotrope produced classical Winsor type III (middle-phase) microemulsions for three chlorinated solvents [i.e., tetrachloroethylene (PCE), trichloroethylene (TCE), and trans-1,2-dichloroethylene (1,2-DCE or DCE)]. Utilization of middle-phase microemulsions has * Corresponding author telephone: (405) 325-4257; fax: (405) 3254217; e-mail address: [email protected]. † School of Civil Engineering and Environmental Science. ‡ School of Chemical Engineering and Materials Science.

0013-936X/96/0930-0097$12.00/0

 1995 American Chemical Society

the potential to significantly improve the efficiency of pumpand-treat remediation for residual/free phases of chlorinated solvents. Groundwater contamination commonly consists of two or more contaminants (2), and the surfactant formulation necessary for achieving a middle-phase microemulsion may be dramatically different for each component (3). In our prior research (1), pure (neat) chlorinated solvent systems were studied; this data is inadequate when addressing residual and/or free-phase systems comprised of mixed chlorinated solvents. For mixed chlorinated solvents, the solution behavior likely depends on the oil composition; that is, properties of the mixed chlorinated solvent system should be between that of the pure compounds. The screening process for obtaining middle-phase microemulsions for the myriad of possible solvent systems (even for binary and ternary systems) will be extremely time-consuming compared with that of single solvent systems. Thus, it will be virtually impossible to conduct the screening process for all possible contaminant compositions. Similar difficulties have been realized in enhanced oil recovery where crude oils typically have dozens of components. In order to reduce the screening efforts for obtaining middle-phase microemulsions with crude oils, empirical correlations capable of predicting the phase behavior of multicomponent systems have been developed (4-11). The applicability of these correlations for mixed chlorinated solvents is obviously of interest. If viable, these correlations can significantly reduce laboratory work and thus the costs associated with design of surfactant-enhanced subsurface remediation systems. The hypotheses for this study are as follows: (1) the molar compositions of mixed chlorinated solvents will affect formation of middle-phase microemulsions and (2) correlations can be derived from ideal mixing or nonideal mixing rules for predicting surfactant compositions necessary to achieve middle-phase microemulsion for mixed chlorinated solvents. The objectives of this study are to determine the optimal surfactant/cosurfactant concentrations for binary and ternary chlorinated solvent mixtures and to compare the experimental results with model predictions.

Theory Background. Previous research in surfactant-enhanced oil recovery demonstrated that optimal middle-phase microemulsions can solubilize large quantities of oil and produce ultralow interfacial tensions (IFTs) (ca. < 10-3 dyn/ cm between the excess phases and the surfactant rich middle phase). Reed and Healy (9) showed that the optimal surfactant formulation for maximizing oil recovery occurs when the IFTs between the excess oil and water phases and the surfactant-rich phase are equal. At this point in the three-phase region, equal amounts of oil and water are dissolved in the middle-phase system. Salager et al. (6) defined the optimal salinity as the midpoint of the salinity range for which the system exhibits three phases [comparable to the definition of Reed and Healy (9)]. These criteria are very useful because they permit the screening of microemulsion systems using simple laboratory tests. In our previous study (1), we define the optimal cosurfactant

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or hydrotrope concentration (comparable to optimal salinity) as the point where equal amounts of oil and water were dissolved in the middle-phase system [similar to Reed and Healy’s definition (9)]. Salager et al. (5) found that the optimal salinity can be expressed by the following empirical correlation:

ln S* ) K(ACN) + f(A) - σ

(1)

where S* is the optimal salinity; K is a constant (a function of the hydrophilic group of the surfactant); f(A) is a function that depends on the heavy alcohol (cosurfactant; e.g., pentanol or heavier) and its concentration (but independent of the surfactant); and σ is a parameter characteristic of the surfactant (or surfactant mixture). ACN denotes the alkane carbon number, which is strictly the number of carbons in the alkane chain of the hydrocarbon. The significance of eq 1 is that this correlation links the variables that produce an optimal formulation for systems containing anionic surfactants, sodium chloride, water, alkanes, and various alcohols. For example, increasing the ACN (longer chain alkane) will increase the value of ln S* of the optimal system [assuming the other parameters (i.e., f(A) and σ) are constant]. Cayias et al. (11) have shown that both crude oils and mixtures of pure hydrocarbons can be assigned an equivalent alkane carbon number (EACN). The implication is that the phase and IFT behavior of these complex hydrocarbon mixtures (potentially with dozens of components) can be modeled by a single alkane. Substituting EACN for ACN in eq 1 results in

ln S* ) K(EACN) + f(A) - σ

(2)

(SMDNS) scans to obtain middle-phase microemulsions for chlorinated solvents (1). Since we are scanning with a hydrotrope/cosurfactant instead of salinity, several assumptions are necessary before using eq 2 in our work. Three possible approaches can be used to derive the equations for binary chlorinated solvent systems and cosurfactant scans: (1) the effects of cosurfactant and surfactant (AOT) are analogous, (2) the effects of cosurfactant (SMDNS) and salinity are analogous, and (3) the effects of cosurfactant and the heavy alcohol (e.g., pentanol) are similar. Among these approaches, case 1 appears to be the most sound assumption while case 2 is the least. Based on a previous study (13), we have demonstrated that the cosurfactant SMDNS has properties similar to a surfactant (e.g., formation of micellar-type phase, precipitation, etc.). Although in actuality, the effect of cosurfactant may be a combination of its behavior as an electrolyte, alcohol, and/ or surfactant, the effect may be considered independently for practical engineering applications. In this initial analysis, it is assumed that for these three cases the mixed chlorinated solvent systems behave ideally. Case 1 will be expanded upon below (for cases 2 and 3 see ref 14). Assume that the effects of cosurfactant (SMDNS) and surfactant (AOT) are similar. In our study, AOT/SMDNS mixtures were used for achieving the middle-phase microemulsion for the chlorinated solvents. For this approach, the mixture of SMDNS and AOT can be considered as a binary surfactants mixture. Recalling that σ is the characteristic parameter of the surfactant used, various AOT/ SMDNS mixtures would thus have differing σ values. Equation 2 can be rewritten for individual chlorinated solvents as follows:

For mixtures having multiple components, researchers have found that

ln S* ) K(EACN)p - σp

(5a)

(EACN)M ) ∑Xi(EACN)i

(3)

ln S* ) K(EACN)t - σt

(5b)

where (EACN)M and (EACN)i are the equivalent alkyl carbon number for the oil mixture and component i, respectively (6, 8, 9). Xi is the mole fraction (on a oil-only basis) of the component i in the mixed oil phases; that is, ∑Xi ) 1. Thus, (EACN)M can be substituted into eq 2, resulting in

ln S* ) K(EACN)d - σd

(5c)

ln S*M ) K(EACN)M + f(A) - σ

(4)

Equation 4 has been very effective in predicting optimal salinity values for oil mixtures (6). For chlorinated solvent systems, no direct tests were conducted in our prior study (1) to evaluate the validation of eq 1. However, we have observed that the optimal cosurfactant (SMDNS) concentration is dependent linearly on temperature (between 15 and 25 °C) for various chlorinated solvent systems similar to the observations in alkane systems by others (5). Therefore, it is assumed that eq 1 is valid for single chlorinated solvent system in this study. A recent study also indicated that eq 1 is appropriate for single chlorinated solvent systems with different surfactants (12). Ideal Mixing Rule. Binary Chlorinated Solvent Mixtures. For groundwater remediation, scanning with salinity to achieve middle-phase microemulsions is not highly practical; the high salinities used in enhanced oil recovery would result in another difficult problemsremediating brine contamination. Thus, we previously used cosurfactant

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where σp, σt, and σd are the characteristic parameters of the surfactant mixtures (AOT/SMDNS) for PCE, TCE and DCE, respectively. f(A) is equal to 0 for this case (no alcohol added). For binary PCE/TCE mixtures, the following expression results:

ln S* ) K(EACN)pt - σpt

(6)

where σpt is the characteristic parameter of mixed surfactants for the PCE/TCE mixture. From eqs 5a, 5b, and 6, it can be shown that

σpt ) Xpσp + Xtσt

(7)

where Xp and Xt are the mole fraction (on solvent-only basis) of the PCE and TCE in the binary mixtures (i.e., Xp + Xt ) 1). Wade et al. (10) demonstrated that nmin, the alkane experiencing the minimum interfacial tension, varied linearly with the average equivalent weight of a mixture of sulfonated surfactants. In this study, both SMDNS and AOT contain a hydrophilic sulfonate group in the molecular structure. Therefore, by analogy it could be assumed that the optimum phase behavior can be assessed in a similar manner (minimum interfacial tension; n(i)min ) EACNi).

From eqs 5a-5c, we find that

n(p)min ) (1/K)[ln S* + σp] (t)

are expressed as follows:

(8a)

) (1/K)[ln S* + σt]

(8b)

n(d)min ) (1/K)[ln S* + σd]

(8c)

n

min

For PCE/TCE mixtures, from eq 7 and constant S* values in this study [note: originally, nmin was defined under S* ) 1 condition (10)], we get

n(pt)min ) Xpn(p)min + Xtn(t)min

(9)

which is similar to eq 7 above. A surfactant average equivalent weight was used instead of n(i)min by Wade et al. (10), as seen in the following equation

EW* )

WAOT + WSMDNS (WAOT/MWAOT) + (WSMDNS/MWSMDNS)

(10)

where EW* is the optimal average equivalent weight of the surfactant system achieving the optimal middle-phase microemulsion; WAOT and WSMDNS are the optimal AOT and SMDNS weight percent added, respectively; and MWAOT and MWSMDNS are the molecular weight of AOT and SMDNS, respectively. Since the molecular weight of AOT is greater than that of SMDNS, increases in SMDNS concentration in the optimal system will reduce the overall value of EW* and vice versa. The expression of average equivalent weight (eq 10) has proven to be applicable for both homologous and heterogeneous mixtures of surfactants (10). Since others observed that n(i)min is linearly dependent on the average equivalent weight of the surfactant mixture (10), it can be assumed that for individual PCE, TCE, and DCE systems

n(p)min ) K′EW*p

(11a)

n(t)min ) K′EW*t

(11b)

n(d)min ) K′EW*d

(11c)

where EW*p, EW*t, and EW*d are the optimal surfactant average equivalent weight for PCE, TCE, and DCE, respectively, and K′ is a constant for similar surfactant mixtures (e.g., both having sulfonated group). Similarly, for a binary PCE/TCE mixture, we get

n(pt)min ) K′EW*pt

(12)

where EW*pt is the optimal average equivalent weight for PCE/TCE mixtures. From eqs 9, 11a, 11b, and 12, the resulting equation for PCE/TCE mixtures is

EW*pt ) XpEW*p + XtEW*t

(13)

For case 1, EW*pt is observed to be linearly dependent on the mole fraction of PCE and TCE (analogous to case 3 and [SMDNS]*pt). Similar results can be obtained for other binary systems. For cases 2 and 3, the resulting equations

case 2 ln [SMDNS]*pt ) Xp ln [SMDNS]*p + Xt ln [SMDNS]*t (14) case 3 [SMDNS]*pt ) Xp[SMDNS]*p + Xt[SMDNS]*t (15) where [SMDNS]*p, [SMDNS]*t, and [SMDNS]*pt are the optimal SMDNS concentration for individual PCE, TCE, and PCE/TCE mixture phases, respectively. In summary, given the EW* (case 1), ln [SMDNS]* (case 2), and [SMDNS]* (case 3) parameters associated with individual chlorinated solvent systems (e.g., PCE, TCE, and DCE) and using the appropriate equation (eqs 13-15 plus the PCE/DCE and DCE/TCE corollaries), it will be possible to predict the optimal surfactant system for a mixed chlorinated solvent system (if the system exhibits ideal mixing behavior). Ternary Chlorinated Solvent Mixtures. Ternary chlorinated solvent mixtures were also evaluated in this study (i.e., PCE/TCE/DCE). The derivations for the ternary system are similar to that for the binary system (initially based on the same ideal mixing rule). Therefore, only the case 1 approach will be developed as an example prediction technique (i.e., assuming that cosurfactant and surfactant effects are similar). For ternary PCE/TCE/DCE mixtures and the case 1 assumption, eq 7 becomes

σptd ) Xpσp + Xtσt + Xdσd

(16)

where σptd is a characteristic parameter of the surfactant(s) for the PCE/TCE/DCE mixture, and Xp, Xt, and Xd are the mole fraction of PCE, TCE, and DCE in the mixed solvent, respectively. Similarly, eqs 9 and 13 can be written for the ternary system as follows:

n(ptd)min ) Xpn(p)min + Xtn(t)min + Xdn(d)min

(17)

EW*ptd ) XpEW*p + XtEW*t + XdEW*d

(18)

where n(ptd)min and EW*ptd are the equivalent alkane number corresponding to minimum interfacial tension and the optimal average equivalent weight for the ternary PCE/ TCE/DCE mixture, respectively. Other parameters are as previously defined. Ternary systems for other approaches (cases 2 and 3) can be developed and will have similar equations to the binary system except that three components will be involved. Nonideal Mixing Rule. Although ideal mixing has proven applicable in many cases, some researchers have observed nonideal behavior in certain systems (e.g., anionic and nonionic surfactant mixtures (5) and oil mixtures [e.g., n-alkane and alkylcyclohexane mixtures (4)]. Nonideal mixing behavior may be the result of the empirical nature of eq 1, or it may require utilization of different modeling approaches (4, 5). In considering the latter, we used the regular mixing theory in this research to explain the nonideality of the mixed oil phases; details about regular mixing theory can be found elsewhere (15, 16). Briefly, the regular mixing theory utilizes an interaction parameter, W, to account for the physical interactions between molecules in solution. In general, regular mixing theory is most

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TABLE 1

Selected Properties of the Chlorinated Organic Solvents Used in This Study solvent

mol wt

density (g/cm3)

mol vol (cm3/mol)

GW solubility mM (mg/L)a

solubility in middle-phase microemulsion mM (mg/L)a

tetrachloroethylene (PCE) trichloroethylene (TCE) trans-1,2-dichloroethylene (DCE)

165.83 131.39 96.94

1.62 1.46 1.26

102.36 89.99 76.94

0.486 (80.6) 7.54 (990) 55.1 (5340)

3,730 (619 000) 4,520 (594 000) 5,750 (557 000)

a

Data from Shiau et al. (1).

applicable for mixtures whose molecules are of a similar size, although they are chemically dissimilar (17). Also, regular mixing theory has been successfully used to describe nonideal mixing in mixed micelle formation (18-21). The proposed regular mixing theory is evaluated as one empirical correlation for explaining our resulting data; conducting fundamental studies to verify the assumptions in the regular mixing theory is beyond the scope of this study. Binary Chlorinated Solvent Mixtures. In this study, surfactant average equivalent weight (EW) was used for evaluating nonideal behavior of the system. For binary PCE/TCE mixtures and the regular mixing theory (16-19), we define the following equations:

EW*pt ) γpXpEW*p + γtXtEW*t

( ( )) ( ( ))

(19)

γp ) exp Xt2

Wpt RT

) exp(Xt2(βpt))

(20)

γt ) exp Xp2

Wpt RT

) exp(Xp2(βpt))

(21)

where EW*pt, EW*p, and EW*t are the optimal average equivalent weight for the PCE/TCE mixture, PCE, and TCE, respectively; γp and γt are solution activity coefficients of PCE and TCE, respectively; Wpt is the regular mixing theory interaction parameter for the binary PCE/TCE mixture; R is the ideal gas law constant; T is absolute temperature; and βpt ()Wpt/RT) is the net (pairwise) interaction parameter for the PCE/TCE system. Other parameters are as previously defined. Similar equations can be derived for the binary PCE/ DCE and TCE/DCE systems. Additional parameters, EW*pd, EW*td, βpd, and βtd will be used for the binary PCE/DCE and TCE/DCE systems. Although the interaction parameters (βij ) Wij/RT) can be obtained from independent experiments [e.g., enthalpy change for mixing solutions (17)], the βij’s are obtained in this research by analyzing EW* vs Xi data. Ternary Chlorinated Solvent Mixtures. For ternary PCE/TCE/DCE mixtures and using regular mixing theory (19, 21), we can define the following equations:

EW*ptd ) γpXpEW*p + γtXtEW*t + γdXdEW*d (22) γp ) exp[Xt2βpt + Xd2βpd + XtXd(βpt + βpd - βtd)] (23) γt ) exp[Xp2βpt + Xd2βtd + XpXd(βpt + βtd - βpd)] (24) γd ) exp[Xp2βpd + Xt2βtd + XpXt(βpd + βtd - βpt)] (25) where γp, γt, and γd are activity coefficients of PCE, TCE, and DCE, respectively; βpt, βpd, and βtd are the net (pairwise) interaction parameters for PCE/TCE, PCE/DCE, and TCE/ DCE mixtures, respectively. If values of βij are known from

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binary systems and Xi values are known for a ternary solvent system, we can predict the resulting EW*ptd for the ternary PCE/TCE/DCE mixtures using eqs 22-25.

Materials and Methods Food grade (edible) surfactants evaluated in this study were selected based on their use in our prior research (1). Mixtures of bis(2-ethylhexyl) sodium sulfosuccinate (aerosol OT, AOT) and sodium mono- and dimethylnaphthalene sulfonate (SMDNS, cosurfactant/hydrotrope) were used for producing classical Winsor type II-III-I transitions for the chlorinated solvent mixtures. AOT (cmc ) 1.12 mM, MW ) 445, obtained from American Cyanamid with purity >99%) and SMDNS (cmc ) 4.5 mM, MW ) 260, obtained from Witco) were used without further purification. Three chlorinated solvents [tetrachloroethylene (PCE), trichloroethylene (TCE), and trans-1,2-dichloroethylene (DCE)] were utilized in this study. Selective properties of these compounds are shown in Table 1. HPLC grade PCE and TCE were purchased from Aldrich Chemical, and DCE was obtained from Eastman Kodak Company. Synthetic groundwater was prepared for all aqueous phase solutions having the following composition: calcium, 16; sodium, 4.6; potassium, 23.5; bicarbonate, 48.8; chloride, 21.3; and sulfate, 9.6 (all on a mg/L basis). Batch studies were conducted in 10-mL pipets sealed to prevent volatilization losses. In each pipet, a 5 mL/5 mL oil/water ratio was used. Different mole ratios of chlorinated solvent mixtures were utilized, with a constant concentration of AOT (0.5 wt %) and variable SMDNS concentrations utilized. All pipets were well-shaken before equilibration (at least 1 week in a 15 °C refrigerator). The occurrence of middle-phase microemulsions was verified by visual observation and interfacial tension measurements (1, 22). Interfacial tension measurements were conducted using the spinning drop method (23). The optimal cosurfactant concentration ([SMDNS]*) was then determined by assessing the surfactant system having equal volumes of oil and water partitioning into the middle phase. Chlorinated solvent compositions in the middle phase were assessed for selected samples by using high-pressure liquid chromatography (Beckman Instrument) with a UV detector, as described elsewhere (22).

Results and Discussion Binary Chlorinated Solvent Mixtures. For each binary system of chlorinated solvents, a phase behavior diagram was developed. For example, Figure 1 shows the phase diagram for a 0.9:0.1 mixture of PCE/TCE (on a molar basis). An oil to water ratio of 1:1 and a constant concentration of AOT (0.5 wt % of a total weight basis) were used for all batch studies. At low SMDNS concentrations, a Winsor type II (water in oil) microemulsion was observed (resulting from the hydrophobicity of AOT and thus the surfactant

a

FIGURE 1. Phase behavior diagram for a PCE/TCE mixture (molar ratio ) 0.9/0.1) at 15 °C; AOT ) 0.5 wt %; volumetric oil to water ratio ) 1; [SMDNS]* ) optimal middle phase.

b

TABLE 2

Parameters from Single Solvent Systems Used To Predict Results for Binary Systems optimal concn of optimal surfactant SMDNS for middle ln [SMDNS]* av equiv weight, solvent phase ([SMDNS]*) (wt %) (wt %) EW*a (g/mol) PCE TCE DCE

1.442b 2.418 2.180

0.366 0.883 0.779

290.92 279.79 281.66

EW* was obtained from eq 10; WAOT ) 0.5 (wt %), WSMDNS ) [SMDNS]*, MWAOT ) 447, MWSMDNS ) 260 in this study. b [SMDNS]* ) 1.40 for PCE, 2.43 for TCE, and 2.19 for DCE from Shiau et al. (1). a

partitioning into the oil phase). Increasing SMDNS concentrations enhanced the surfactant balance and resulted in a Winsor type III (middle-phase) microemulsion. At yet higher SMDNS concentrations, the system was overoptimum, and the surfactants resided in the water phase forming a Winsor type I (oil in water) microemulsion. From each graph (for each oil composition), the optimal SMDNS concentration ([SMDNS]*) was determined. For example, for the 0.9:0.1 PCE/TCE mixture shown in Figure 1, [SMDNS]* is observed to be 1.57 wt % (equal oil and water in the middle-phase system, ultralow IFTssee ref 22). For each chlorinated solvent system (e.g., PCE/TCE), five to seven different mixtures (mole ratios) were evaluated. The parameters determined from single chlorinated solvent systems and used in estimating results for binary chlorocarbon systems are summarized in Table 2. [SMDNS]* values decrease in the following manner: TCE > DCE > PCE; EW* values decrease as follows: PCE > DCE > TCE. The value of [SMDNS]* for PCE in this study varies slightly from our previous result (1), likely due to PCE being obtained from a different source. Although commercially available SMDNS may also vary from batch to batch, SMDNS from the same batch was used throughout this study. The resulting plots of EW*, ln [SMDNS]*, and [SMDNS]* versus mole fraction (Xi) for binary mixtures of PCE/TCE are shown in Figure 2 (panels a-c). Similar results were observed for PCE/DCEs and TCE/DCEs (data not shown). The solid lines in the figures represent the ideal mixing rule predictions for each system (using single solvent parameters from Table 2 and eqs 13-15). In this study, all batch results evidenced deviations from ideal mixing (as observed by deviations in ideal mixing predictions and the experimental

c

FIGURE 2. (a) EW* vs PCE mole fraction (Xp) for PCE/TCE pair using case 1 analysis: (s) ideal mixing rule predicted, (9) experimental. (b) ln [SMDNS]* vs PCE mole fraction (Xp) for PCE/TCE pair using case 2 analysis: (s) ideal mixing rule predicted, (9) experimental. (c) [SMDNS]* vs PCE mole fraction (Xp) for PCE/TCE pair using case 3 analysis: (s) ideal mixing rule predicted, (9) experimental.

data). Deviations were such that experimental values of ln [SMDNS]* and [SMDNS]* were higher than and EW* were lower than the ideal mixing predictions (as observed in Figure 2 and Table 3). Interpretation of these data using nonideal mixing analysis is presented below. The experimental results in Figure 2 show that the greatest deviations between experimental and predicted results occurred when nearly equal mole fractions of solvents existed (i.e., Xi ) 0.5). Decreasing deviations were observed as one or the other of the components dominated. Similar results have been observed for different oil systems (4). Comparing predicted and observed results for case 3 (which is in units of cosurfactant concentration), the greatest net deviations between observed and predicted [SMDNS]* values were around 0.073 wt % for the PCE/TCE mixture, 0.097% for the PCE/DCE mixture, and 0.121% for the TCE/ DCE mixture (see Table 3). Considering that the average

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TABLE 3

Deviations of Experimental and Estimated Results for Binary Systems in This Study (Estimates Based on the Ideal Mixing Rule)

solvent mixture, i/ja

case 2 case 3 mol case 1 deviation deviation fraction of deviation (exp - cal), (exp - cal), component (exp - cal), ∆ ln [SMDNS]* ∆[SMDNS]* i, Xi ∆EW* (wt %) (wt %)

PCE/TCE

PCE/DCE

DCE/TCE

0.100 0.284 0.442 0.750 0.900 0.178 0.355 0.525 0.686 0.847 0.173 0.344 0.505 0.665 0.833

-0.457 -1.151 -1.889 -1.794 -1.176 -1.083 -1.697 -1.872 -1.971 -1.628 -0.846 -0.937 -0.721 -0.722 -0.679

0.015 0.039 0.069 0.064 0.041 0.044 0.068 0.075 0.073 0.061 0.048 0.052 0.039 0.040 0.036

0.011 0.029 0.073 0.063 0.043 0.068 0.097 0.097 0.093 0.078 0.114 0.121 0.088 0.088 0.081

FIGURE 3. Comparisons of EW* vs PCE mole fraction (Xp) for PCE/ TCE pair using ideal and nonideal mixing rules: (s) regular mixing theory predicted, (- - -) ideal mixing rule predicted, (*) experimental.

a i and j correspond to the first and second component of the binary mixture.

range of SMDNS concentrations over which a middle-phase microemulsion exists at all is only 0.15% for these systems, such deviations are not negligible. In evaluating these deviations, we first measured the compositions of selected middle-phase systems. The results did not indicate preferential partitioning of oils into the middle phase (i.e., the oil mixture in the middle phase was similar to that in the original solution). Nonideal behavior was suspected due to the interactions between the different oil molecules; subsequently, regular mixing theory was used to evaluate the data (as developed above and discussed below). The net (pairwise) interaction parameters (βij ) Wij/RT) for individual binary pairs (PCE/TCE, PCE/DCE, TCE/DCE) were obtained using a polynomial least squares fit program (Eureka: The Solver; Borland International); the resulting βij’s are -0.0277 for PCE/TCE, -0.029 for PCE/ DCE, and -0.0132 for DCE/TCE. The nonideal mixing predictions are depicted in Figure 3 (solid line) for PCE/ TCE. Obviously, the nonideal predictions are substantially better than the ideal mixing predictions. Among the three

binary pairs, PCE/DCE showed the largest value of βij (and thus the largest deviations from the ideal mixing rule) followed closely by PCE/TCE. The DCE/TCE pair showed the smallest βij and thus the least deviation from the ideal mixing rule. Although the βij values may be related to solvent properties [such as molar volume (Table 1) or hydrophobicity of the compounds (Table 2)], no conclusive correlations were possible based on these results; future research should further explore such correlations. Mixtures of surfactants with varying properties (e.g., anionic and nonionic surfactants) commonly demonstrate a nonideal mixing phenomenon (5, 18-20). If this were the source of nonideality in these results, we would expect that βij values would be similar for all three solvent pairs since the same AOT/SMDNS mixtures were used throughout this study. While the βij values for PCE/TCE and PCE/ DCE pairs are similar, different βij values are obvious for the DCE/TCE pair. Therefore, the nonideality observed is not due solely to the dissimilarity of AOT and SMDNS, as evidenced in other mixed surfactant systems. Ternary Chlorinated Solvent Mixtures. Since results from the binary systems were successfully described by predictions based on regular mixing theory, it seemed likely that regular mixing theory would better predict results for multiple component systems (i.e., ternary chlorinated solvent systems). In this study, data for ternary PCE/TCE/ DCE mixtures were compared with predictions from both models (ideal and nonideal mixing). DCE mole fractions

TABLE 4

Comparisons of Experimental and Calculated (Ideal and Nonideal Mixing) Results for Ternary Chlorinated Solvents System in This Study mol fraction of DCE, Xd

mole fraction of PCE, Xp

deviation of ideal mixing (exp - cal), ∆EW*

deviation of nonideal mixing (exp - cal), ∆EW*a

deviation of ideal mixing (exp - cal), ∆[SMDN]*b

deviation of nonideal mixing (exp - cal), ∆[SMDNS]*b

0.338

0.110 0.221 0.331 0.442 0.552 0.099 0.173 0.248 0.322 0.396

-0.978 -0.788 -1.606 -1.662 -1.752 -1.152 -1.390 -1.517 -1.769 -1.774

0.503 0.612 0.601 0.613 0.400 0.314 0.378 0.467 0.341 0.377

0.117 0.145 0.159 0.148 0.142 0.137 0.154 0.158 0.173 0.162

-0.064 -0.072 -0.065 -0.060 -0.035 -0.040 -0.046 -0.053 -0.037 -0.038

0.505

a From eqs 22-25; β ) -0.0277 for PCE/TCE pair, -0.029 for PCE/DCE pair, and -0.0132 for DCE/TCE pair. ij and eq 10.

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b

Calculated data obtained from EW*

Acknowledgments Although the research described in this article has been funded partially by the United State Environmental Protection Agency under Assistance Agreement 818553-01-0 to the University of Oklahoma, it has not been subjected to the Agency’s peer and administrative review and, therefore, may not necessarily reflect the views of the Agency, and no official endorsement should be inferred. Additional funding has been proved by supporting members of the Institute for Applied Surfactant Research (IASR). Gratitude is expressed to the EPA project officer, Dr. Candida Cook West, for her input and cooperation and is also extended to Clifton Page for technical assistance in the laboratory. FIGURE 4. Comparisons of EW* vs PCE mole fraction (Xp) for ternary PCE/TCE/DCE using ideal and nonideal mixing rules at Xd ) 0.5050: (s) regular mixing theory predicted, (- - -) ideal mixing rule predicted, (*) experimental.

were held constant at two different levels in ternary PCE/ TCE/DCE systems (Xd ) 0.3377 and 0.5050). Values of EW* for individual chlorinated solvents and eq 18 were used for ideal mixing predictions, while values for βij (as presented above) and eqs 22-25 were used for nonideal mixing predictions. Predictions based on ideal and nonideal mixing and experimental results for one DCE mole fraction (Xd ) 0.5050) are shown in Figure 4. While the ideal mixing rule tended to overestimate EW* values for a given mole fraction of PCE, nonideal mixing predictions underestimated EW* values (Figure 4); it should be noted that the deviations were smaller relative to nonideal mixing estimates (Table 4). Ternary PCE/TCE/DCE results thus showed nonideal mixing behavior, which was better described by regular mixing theory than ideal mixing. The net EW* deviations (∆EW*) ranged from -0.978 to -1.774 for ideal mixing rule and from 0.314 to 0.613 for nonideal mixing rule (regular mixing). Another advantage of the regular mixing theory is apparent if we compare the experimental [SMDNS]* and model predictions. Since the average range of SMDNS concentrations over which a middle phase existed in this research was 0.15 wt %, experimental deviations from ideal mixing predictions would likely result in a type II system (for ∆[SMDNS] > 0.08 wt %), while predictions from regular solution theory would still produce type III system (as absolute ∆[SMDNS] value < 0.08 wt %) (Table 4). Though the regular mixing theory gave better predictions for both binary and ternary chlorinated solvents mixtures in this study, additional nonideal solution theories exist. However, it can be argued that the regular mixing theory proved adequate for predicting the phase behavior of mixed chlorinated solvents in this study. These results imply that for realistic sites with complicated groundwater contamination (e.g., mixed petroleum hydrocarbons and/or chlorinated solvents) nonideal behavior may be anticipated. Future research should evaluate the relationships between interaction parameters and component properties, the feasibility of using regular mixing to predict properties of other hydrophobic contaminant systems, etc.

Literature Cited (1) Shiau, B. J.; Sabatini, D. A.; Harwell, J. H. Ground Water 1994, 32, 561. (2) Feenstra, S.; Cherry, J. A. Proceedings of the International Groundwater Symposium; International Association of Hydrogeologists: Halifax, Nova Scotia, 1988. (3) Baran, J. R., Jr.; Pope, G. A.; Wade, W. H.; Weerasooriya, V.; Yapa, A. Environ. Sci. Technol. 1994, 28, 1361. (4) Puerto, M. C.; Reed, R. L. SPEJ, Soc. Pet. Eng. J. 1983, 23, 669. (5) Salager, J. L.; Vasquez, E.; Morgan, J. C.; Schechter, R. S.; Wade, W. H. Soc. Pet. Eng. J. 1979, 19, 107. (6) Salager, J. L.; Bourrel, M.; Schechter, R. S.; Wade, W. H. Soc. Pet. Eng. J. 1979, 19, 271. (7) Cash, L.; Cayias, J. L.; Fournier, G.; McAllister, D.; Scharz, T.; Schechter, R. S.; Wade, W. H. J. Colloid Interface Sci. 1977, 59, 39. (8) Puertos, M. C.; Gale, W. W. Soc. Pet. Eng. J. 1977, 17, 193. (9) Reed, R. L.; Healy, R. N. In Improved Oil Recovery by Surfactant and Polymer Flooding; Shah, D. O., Schechter, R. S., Eds.; Academic Press Inc.: New York, 1977; p 383. (10) Wade, W. H.; Morgan, J. C.; Jacobson, J. K.; Schechter, R. S. Soc. Pet. Eng. J. 1977, 17, 122. (11) Cayias, J. L.; Schechter, R. S.; Wade, W. H. Soc. Pet. Eng. J. 1976, 16, 351. (12) Baran, J. R., Jr.; Pope, G. A.; Wade, W. H.; Weerasooriya, V.; Yapa, A. J. Colloid Interface Sci. 1994, 168, 67. (13) Shiau, B. J.; Sabatini, D. A.; Harwell, J. H. Properties of Food Grade (Edible) Surfactants Affecting Subsurface Remediation of Chlorinated Solvents. Environ. Sci. Technol. 1995, 29, 29292935. (14) Shiau, B. J. Ph.D. Dissertation, University of Oklahoma, 1995, Chapter 4. (15) Hildebrand, J. H.; Scott, R. L. Regular Solutions; Prentice-Hall, Inc.: Englewood Cliffs, NJ, 1962. (16) Guggenheim, E. A. Mixtures; Oxford University Press: New York, 1952; Chapter IV, p 29. (17) Balzhiser, R. E.; Samuels, M. R.; Eliassen, J. D. Chemical Engineering Thermodynamics; Prentice-Hall: Englewood Cliffs, NJ, 1972; p 403. (18) Rubingh, D. N. In Solution Chemistry of Surfactants; Mittal, K. L., Ed.; Plenum Press: New York, 1979; Vol. I, p 337. (19) Holland, P. M.; Rubingh, D. N. J. Phys. Chem. 1983, 87, 1984. (20) Rathman, J. F.; Scamehorn, J. F. Langmuir 1987, 3, 372. (21) Shaiu, B. J.; Harwell, J. H.; Scamehorn, J. F. J. Colloid Interface Sci. 1994, 167, 332. (22) Shiau, B. J.; Sabatini, D. A.; Harwell, J. H. Food Grade (Edible) Surfactants for Subsurface Remediation: Column Studies. J. Environ. Eng. Submitted for publication. (23) Cayias, J. L.; Schechter, R. S.; Wade, W. H. Adsorption at Interfaces; ACS Symposium Series 8; American Chemical Society: Washington, DC, 1970; p 234.

Received for review February 22, 1995. Revised manuscript received August 3, 1995. Accepted August 7, 1995.X ES9501169 X

Abstract published in Advance ACS Abstracts, November 1, 1995.

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