Energy & Fuels 2005, 19, 1977-1983
1977
Liquid-Liquid Equilibria for the Quaternary System Water + Methyl tert-Butyl Ether + Benzene + Cyclohexane and Its Constituent Partially Miscible Ternary Systems at 303.15 K Mo´nica B. Gramajo de Doz, Carlos M. Bonatti, and Horacio N. So´limo* Departamento de Fı´sica-Facultad de Ciencias Exactas y Tecnologı´a, Universidad Nacional de Tucuma´ n, Av. Independencia 1800, 4000 Tucuma´ n, Argentina Received November 4, 2004. Revised Manuscript Received May 12, 2005
Tie-line data for the water, methyl tert-butyl ether, and cyclohexane [w1H2O + w2C5H12O + (1 - w1 - w2)C6H12] and water, methyl tert-butyl ether, and benzene [w1H2O + w2C5H12O + (1 w1 - w2)C6H6] ternary systems (where w is the mass fraction) were investigated at a temperature of T ) 303.15 K. A quaternary system containing these four compounds [w1H2O + w2C5H12O + w3C6H6 + (1 - w1 - w2 - w3)C6H12] was also studied at the same temperature. Data for the other partially miscible ternary system [w1H2O + w3C6H6 + (1 - w1 - w3)C6H12] were taken from the literature, whereas the fourth ternary system [w2C5H12O + w3C6H6 + (1 - w2 - w3)C6H12] was completely miscible. The mutual hydrocarbon-water solubility with the addition of methyl tert-butyl ether was investigated. The equilibrium data of the three ternary systems (including that taken from the literature) were used to determine interaction parameters for the UNIQUAC and NRTL equations. The UNIQUAC parameters were then averaged to predict equilibrium data for the quaternary system using this model. The liquid-liquid equilibrium (LLE) were also predicted with the UNIFAC group contribution method. The UNIQUAC equation seems to be more accurate than the other methods both for the ternary systems and the quaternary system, as can be observed from the values of both residuals. However, its predicted distribution coefficients have high deviation percentages. On the other hand, the solubility curves are wellcorrelated by the UNIQUAC and NRTL equations for these ternary systems.
Introduction As a part of an ongoing research program, we have focused on the investigation of the phase equilibrium of quaternary systems containing two hydrocarbons (benzene + isooctane, toluene + isooctane, or benzene + cyclohexane), an alkan-1-ol (methanol or ethanol), and water,1-5 because this type of system has gained importance, given the increasing demands of oxygenated compounds used to produce lead-free gasoline. The U.S. Environmental Protection Agency (USEPA) recommends the use of alcohols (particularly ethanol) as gasoline additives to provide antiknock properties and to help reduce harmful combustion emissions.6,7 However, one of the oxygenated compounds that is presently * Author to whom correspondence should be addressed. E-mail address:
[email protected]. (1) Gramajo de Doz, M. B.; Bonatti, C. M.; Barnes, N.; So´limo, H. N. J. Chem. Thermodyn. 2001, 33, 1663-1677. (2) Gramajo de Doz, M. B.; Bonatti, C. M.; Barnes, N.; So´limo, H. N. Sep. Sci. Technol. 2002, 37, 245-260. (3) Gramajo de Doz, M. B.; Bonatti, C. M.; So´limo, H. N. Fluid Phase Equilib. 2003, 205, 53-67. (4) Gramajo de Doz, M. B.; Bonatti, C. M.; So´limo, H. N. J. Chem. Thermodyn. 2003, 35, 825-837. (5) Gramajo de Doz, M. B.; Bonatti, C. M.; So´limo, H. N. J. Chem. Thermodyn. 2003, 35, 2055-2065. (6) Oge, M. T., U. S. Environment Protection Agency. Presented before the Subcommittee on Energy and Environment of the Committee on Science U.S. House of Representatives, September 14, 1999. (Available via the Internet at http://www.epa.gov/oms/speeches/ mto99rfg.htm.)
used more often in reformulated gasoline is methyl tertbutyl ether (MTBE). Therefore, additional studies on the phase behavior of systems that contain hydrocarbons, water, and MTBE are necessary, to improve our knowledge of these types of systems. Experience shows that the commercial gasoline distribution system always contains water, because of air humidity or infiltration into storage tanks; therefore, water was included in this study. Consequently, phase diagram studies must be performed to show if phase separation occurs at room temperature and atmospheric pressure when water is present. In this work, we have used MTBE, a synthetic gasoline (represented by a mixture of an aromatic and a naphthenic hydrocarbon, i.e., benzene and cyclohexane, respectively), and water. Liquid-liquid equilibrium (LLE) measurements were performed for the ternary and quaternary systems at a temperature of T ) 303.15 ( 0.05 K and atmospheric pressure, although the data for the partially miscible ternary system (w1H2O + w2C6H6 + (1 - w1 - w2)C6H12) was taken from the literature.4,5 This particular temperature was selected because it is representative of tropical and subtropical climates. (7) Browner, C. M. Press Conference of the EPA Administrator. Remarks Available from the United States Environmental Protection Agency (USEPA), Office of Communications, Education and Public Affairs, Washington, DC, March 20, 2000.
10.1021/ef049717o CCC: $30.25 © 2005 American Chemical Society Published on Web 06/21/2005
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In addition, the experimental results were compared with those predicted by means of the UNIFAC group contribution method,8 using the LLE interaction parameters that were reported by Magnussen et al.9 for both ternary mixtures, and were correlated with the UNIQUAC10 and NRTL11 models that were fitted to the experimental results. As previously reported,3-5 all of the pairs of binary interaction parameters obtained from the three partially miscible ternary subsystems included in the quaternary system were averaged and then used to predict the quaternary LLE with the UNIQUAC model. The UNIFAC method was also used for this purpose.
Experimental Section Materials. Water (H2O, component 1) was doubly distilled in an all-glass apparatus. MTBE (C5H12O, component 2, which is considered as the solute throughout this work), benzene (C6H6, component 3), and cyclohexane (C6H12, component 4) (all of which have analytical-reagent purity) were supplied by Riedel de Hae¨n, Merck, and Raudo, respectively. The purity of the chemicals was verified chromatographically, showing that their mass fractions were >0.998. Therefore, they were used without further purification. The water content of these organic chemicals was periodically verified during the study, using a Mettler DL18 Karl Fischer Titrator with an accuracy of (0.3%, which never surpassed to 0.002 mass %. These chemicals were maintained over 0.3 nm molecular sieves, to prevent water absorption. Methods. Before obtaining the LLE results for the quaternary system, two of its partially miscible ternaries were studied while others were taken from the literature.4,5 Ternary or quaternary equilibrium data were obtained by weighing preparing mixtures of known overall composition within the heterogeneous region, using several 16-mL chromatographic vials as equilibrium cells. They were equipped with caps, septa, and Teflon-coated magnetic bars, to provide intense and continuous stirring for at least 7 days, using multipoint magnetic stirrers. After phase equilibrium was reached, the magnetic stirrers were turned off and both liquid phases were allowed to settle for 24 h before sampling, as previously reported.2 These chromatographic vials were filled up to ∼90% of their volumes, to maintain the vapor space at a minimum. At the end of each experiment, samples were taken from both phases with hypodermic syringes and analyzed by means of gas chromatography (GC). The internal standard method was applied to obtain quantitative results. Acetone (C3H6O) (Merck, chromatographic quality) with a purity of >0.999, in terms of mass fraction (as determined via GC), was the standard compound used for this purpose. First, the needle was introduced through the septum to take samples of the upper phases. They were immediately poured over constant amounts of the internal standard and placed in 2-mL chromatographic vials. Samples of the lower phases were then obtained by introducing the needle and blowing air through it while it went through the upper phase, to avoid its contamination. Before pouring the sample over the internal standard, the needle was dried with tissue paper and the mixture was analyzed in the same way as that for the upper phase. A Hewlett-Packard model 6890 gas chromatograph (8) Fredenslund, Aa.; Gmehling, J.; Rasmussen, P. Vapor-Liquid Equilibria Using UNIFAC; Elsevier: Amsterdam, 1977. (9) Magnussen, T.; Rasmussen, P.; Fredenslund, Aa. Ind. Eng. Chem. Process Des. Dev. 1981, 20, 331-339. (10) Abrams, D. S.; Prausnitz, J. M. AIChE J. 1975, 21, 116-128. (11) Renon, H.; Prausnitz, J. M. AIChE J. 1968, 14, 135-144.
Figure 1. Schematic representation of the w1H2O + w2C5H12O + w3C6H6 + (1 - w1 - w2 - w3)C6H12 quaternary system at T ) 303.15 K. P1, P2, P3, and P4 are sectional planes for the determination of the binodal surface. with an automatic injector (Agilent G2613A) directly connected to a ChemStation HP G2070AA system was used. Good separation of the four components was obtained on a 30 m long × 0.25 mm inner diameter (ID) × 0.5 µm film thickness capillary column (INNOWax, cross-linked poly(ethylene glycol), HP 19091N-233). The temperature program used was as follows: initial temperature of 343 K for 2 min, ramp of 50 K/min, and final temperature of 393 K for another 1.5 min. The nitrogen carrier gas flow rate was kept constant electronically, working with a split ratio of 20:1 and with the injector maintained at a temperature of 453 K. Detection was conducted by a thermal conductivity detector at 523 K. Three or four analyses were performed for each sample, to obtain a mean mass fraction value with better than 1% repeatability. A Mettler AG245 balance with an accuracy of (0.00001 g was used both for the calibration curves and for the analysis of the unknown samples. To validate the reported mass fraction values, three samples of different known overall compositions (determined by mass) were analyzed. These analyses show that the mass fraction values have an uncertainty of (0.0001, whereas the detection limit was below a mass fraction of 0.0010 for water, 0.0015 for MTBE, 0.0037 for benzene, and 0.0023 for cyclohexane. Table 1 shows the experimental masses of the components for several mixtures in the homogeneous region that were used to obtain chromatographic calibration curves for each component with the internal standard method, along with the fitting equations, residual standard deviations, and correlation coefficients for each component. To determine the quaternary binodal surface, the measurements were conducted at four different mixing ratios of benzene and cyclohexane, which characterize four quaternary planes (referenced as P1, P2, P3, and P4 in Figure 1). Figure 1 shows a schematic representation of the quaternary system w1H2O + w2C5H12O + w3C6H6 + (1 - w1 - w2 - w3)C6H12. The equilibrium data for this system were obtained with the same procedure used for the ternary systems. In this work, the initial mixtures (corresponding to the P1, P2, P3, and P4 planes) were selected to determine tie-lines within the entire heterogeneous region, assuming that gasoline is represented by a mixture of an aromatic and a naphthenic hydrocarbon.
LLE of Water-MTBE-Benzene-Cyclohexane Systems
Energy & Fuels, Vol. 19, No. 5, 2005 1979
Table 1. Experimental Masses of the Components (mi) in the Homogeneous Region Used To Construct the Calibration Curves, Using the Internal Standard Method, along with Correlation Coefficients and Residual Standard Deviations Resulting from the Fitting Experimental Mass of Components m1 m2 m3 m4
component
Values for the Fitting Equationa y ) ax3 + bx2 + cx + d b c
d
correlation coefficient, r2
standard deviation, SD
4.91 × 10-4 2.58 × 10-3 4.46 × 10-3
0.99967 0.99998 0.99998
0.00096 0.00335 0.00335
0.99886 0.99999
0.00176 0.00279
7.40 × 10-3
0.99998
0.00513
Water (1) + MTBE (2) + Benzene (3) + Cyclohexane (4) Quaternary System 0.26243 0.57763 0.14658 0.34278 0.49664 0.12603 0.41729 0.43241 0.10972 0.49225 0.36638 0.09297 0.56853 0.29674 0.07529 0.62967 0.24338 0.06176 0.64528 0.16777 0.04257 0.71628 0.10831 0.02748 549.29 -69.77 5.28 5.48 × 10-4 -9.84 × 10-2 1.25 × 10-1 9.53 × 10-1 2.94 × 10-3 6.40 × 10-2 -2.39 × 10-1 9.01 × 10-1 6.49 × 10-4 6.78 × 10-1 9.01 × 10-1 1.77 2.12 × 10-4
0.99963 0.99930 1.00000 1.00000
0.00092 0.01970 0.00110 0.00047
a
Water (1) + MTBE (2) + Benzene (3) Ternary System 0.00163 0.00224 0.00319 0.00397 0.00506 0.00489 0.00782 0.01080
0.12415 0.26299 0.35234 0.43507 0.51710 0.60106 0.75973 0.75502
0.89578 0.73708 0.63685 0.53316 0.43283 0.34536 0.14565 0.03663
(1) water (2) MTBE (3) benzene (4) cyclohexane
3812.78 4.02 × 10-2 3.25 × 10-2
0.00277 0.00388 0.00537 0.00644 0.00498 0.00826 0.00968 0.01116
0.20945 0.28955 0.37155 0.44578 0.51780 0.58990 0.67138 0.75538
(1) water (2) MTBE (3) benzene (4) cyclohexane
(1) water (2) MTBE (3) benzene (4) cyclohexane
6.50 1.14 8.59 × 10-1
Water (1) + MTBE (2) + Cyclohexane (4) Ternary System 0.64429 0.55364 0.47039 0.38922 0.30653 0.22856 0.14396 0.03586 3668.66 -165.00 5.84 -5.04 × 10-4 4.35 × 10-2 -2.21 × 10-1 1.14 2.89 × 10-3 6.73 × 10-2
0.00202 0.00286 0.00405 0.00438 0.00608 0.00671 0.00762 0.00812
-183.59 -2.13 × 10-1 -1.69 × 10-1
-3.45 × 10-1
1.61
a Provided by the ChemStation chromatographic software as the best fitting equation, where y and x denote the area ratio and the amount ratio, respectively. The average mass of the internal standard is 0.39388 g.
Table 2. Liquid-Liquid Equilibrium (LLE) Data for the w1H2O + w2C5H12O + (1 - w1 - w2)C6H12 Ternary System at T ) 303.15 Ka Global Composition
Aqueous Phase
w1H2O
w2C5H12O
(1 - w1 - w2)C6H12
w1H2O
w2C5H12O
0.5022 0.4688 0.4465 0.4340 0.4158 0.4124 0.4142 0.4242 0.4253 0.4508 0.4611 0.4976
0 0.0579 0.1136 0.1540 0.2020 0.2508 0.3000 0.3500 0.4064 0.4328 0.4797 0.5024
0.4978 0.4733 0.4399 0.4120 0.3822 0.3367 0.2858 0.2258 0.1683 0.1164 0.0592 0
1.0000 0.9962 0.9925 0.9902 0.9866 0.9850 0.9830 0.9784 0.9749 0.9714 0.9650 0.9620
0 0.0038 0.0075 0.0098 0.0134 0.0150 0.0170 0.0216 0.0251 0.0286 0.0350 0.0380
Organic Phase
(1 - w1 - w2)C6H12
0
w1H2O
w2C5H12O
(1 - w1 - w2)C6H12
0.0020 0.0029 0.0044 0.0064 0.0092 0.0137
0 0.1068 0.2009 0.2644 0.3401 0.4188 0.5000 0.5980 0.6985 0.7780 0.8727 0.9863
1.0000 0.8932 0.7991 0.7356 0.6599 0.5812 0.4980 0.3991 0.2971 0.2156 0.1181 0
a
The variable w denotes mass fraction. A blank space indicates that the component was not detectable, meaning that the chromatographic signal is below to the detection limit. A value of zero means that the component is absent.
Results and Discussion Tables 2 and 3 list the LLE data for the ternary systems w1H2O + w2C5H12O + (1 - w1 - w2)C6H12 and w1H2O + w2C5H12O + (1 - w1 - w2)C6H6 at T ) 303.15 ( 0.05 K, respectively, whereas Figures 2 and 3 show their corresponding LLE diagrams. Data predicted by the UNIFAC method and correlated by the UNIQUAC and NRTL equations are also shown. The LLE data were fitted with the UNIQUAC and NRTL equations, using an iterative computer program
developed by Sørensen12 that minimizes the values of the following objective functions: k
Fa ) k
Fx )
i
∑∑
[
]
(aIik - aII ik)
(aIik
i
j
+
aII ik)
2
n
+Q
∑P2n
(1)
n
∑min ∑∑(xijk - xˆ ijk)2 + Q∑P2n
(2)
Here, aI,II ik are the activities obtained from the experi-
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Table 3. (Liquid-Liquid) Equilibrium (LLE) Data for the w1H2O + w2C5H12O + (1 - w1 - w2)C6H6 Ternary System at T ) 303.15 Ka Global Composition
Aqueous Phase
w1H2O
w2C5H12O
(1 - w1 - w2)C6H6
w1H2O
0.5044 0.4813 0.4542 0.4417 0.4217 0.4038 0.4163 0.4175 0.4226 0.4498 0.4697 0.4989
0 0.0470 0.1085 0.1553 0.2071 0.2483 0.3043 0.3532 0.4068 0.4401 0.4871 0.5011
0.4956 0.4813 0.4374 0.4030 0.3712 0.3479 0.2794 0.2293 0.1706 0.1101 0.0432 0
1.0000 1.0000 0.9940 0.9913 0.9883 0.9864 0.9827 0.9796 0.9754 0.9720 0.9700 0.9620
w2C5H12O
Organic Phase
(1 - w1 - w2)C6H6
w1H2O
w2C5H12O
(1 - w1 - w2)C6H6
0.0016 0.0026 0.0029 0.0034 0.0044 0.0058 0.0072 0.0085 0.0115 0.0137
0 0.0924 0.1970 0.2721 0.3510 0.4089 0.5149 0.5984 0.6912 0.7886 0.9043 0.9863
1.0000 0.9076 0.8014 0.7253 0.6460 0.5878 0.4807 0.3958 0.3017 0.2029 0.0842 0
0 0.0060 0.0087 0.0117 0.0136 0.0173 0.0204 0.0246 0.0280 0.0300 0.0380
0
a
The variable w denotes mass fraction. A blank space indicates that the component was not detectable, meaning that the chromatographic signal is below to the detection limit. A value of zero means that the component is absent.
represents the components, j the phases, and k the tie lines), Pn is the parameter in the penalty term, and Q is the constant in the penalty term. This penalty term was designed to reduce the risk of multiple solutions associated with high parameter values. Table 4 shows the structural parameters for the pure components taken from the literature13 and the optimized binary interaction parameters of the UNIQUAC and NRTL models for the ternary systems. The nonrandomness parameter (Rij) for the NRTL equation is also shown. The goodness of fit, as measured by the root mean square (rms) deviation in mole fraction (F), is given by the following expression, for ternary systems: Figure 2. Liquid-liquid equilibrium (LLE) of the w1H2O + w2C5H12O + (1 - w1 - w2)C6H12 ternary system at T ) 303.15 K: (×) experimental, (b) UNIQUAC equation, (0) NRTL equation, (2) UNIFAC predictions, and (+) global compositions.
F ) 100
[∑∑∑ k
i
j
]
(xijk - xˆ ijk)2 6M
1/2
(3)
where M is the number of tie lines. For quaternary systems, this equation is divided by 8M instead of 6M. The rms relative error in the solute distribution ratio (∆m) is given by
∆m ) 100
∑k
{
}
[(mk - m ˆ k)/mk]2 M
1/2
(4)
mental concentrations, I and II are the phases, xijk and xˆ ijk are the experimental mole fraction values of the liquid phase and the calculated tie-line lying close to the considered experimental line, respectively (where i
These residuals are listed in Table 4 for all of the models used. Here, xijk is the experimental mole fraction of the ith component in the jth phase on the kth tie-line, xˆ ijk is the corresponding calculated value, and mk is the experimental solute distribution ratio, and m ˆ k is the calculated solute distribution ratio. The fit was poor, in terms of ∆m for all models, because of the large relative error associated with the very low concentrations of some compounds in both phases, whereas the goodness of fit, in terms of F, was satisfactory for the UNIQUAC and NRTL models. However, the UNIQUAC model presents the lowest ∆m values. Therefore, this last equation, when fitted to the experimental data, is more accurate than the other methods for the ternary systems, as can be observed through analysis of both residuals that are presented in Table 4.
(12) Sørensen, J. M. ESTM: Estimation of UNIQUAC and NRTL Parameters from Ternary LLE Data; ESTM. Phase Equilibria and Separation Processes, MAN 8106; Instituttet for Kemiteknik: Lyngby, Denmark, 1980.
(13) Sørensen, J. M.; Arlt, W. Liquid-Liquid Equilibrium Data Collection. Ternary and Quaternary Systems; Dechema Chemistry Data Series, Vol. 5, Part 3; Deutsche Gesellschaft fu¨r Chemisches Apparatewesen (DECHEMA): Frankfurt, Germany, 1980.
Figure 3. Liquid-liquid equilibrium (LLE) of the w1H2O + w2C5H12O + (1 - w1 - w2)C6H6 ternary system at T ) 303.15 K: (×) experimental, (b) UNIQUAC equation, (0) NRTL equation, (2) UNIFAC predictions, and (+) global compositions.
LLE of Water-MTBE-Benzene-Cyclohexane Systems
Energy & Fuels, Vol. 19, No. 5, 2005 1981
Table 4. Residuals F and ∆m for the UNIFAC Method, Optimized Parameters of the UNIQUAC and NRTL Equations, and Nonrandomness Parameters for the w1H2O + w2C5H12O + (1 - w1 - w2)C6H12 and w1H2O + w2C5H12O + (1 - w1 w2)C6H6 Ternary Systems at T ) 303.15 Ka aij
aji
nonrandomness parameter, Rij
system
F (%)
∆m (%)
i,j
H2O + C5H12O + C6H12 H2O + C5H12O + C6H12 H2O + C5H12O + C6H12
0.1 0.1 0.1
44.3 44.3 44.3
UNIQUAC 1,2 1,4 2,4
35.561 561.56 169.24
H2O + C5H12O + C6H6 H2O + C5H12O + C6H6 H2O + C5H12O + C6H6
0.1 0.1 0.1
7.6 7.6 7.6
1,2 1,3 2,3
63.545 367.29 -32.771
H2O + C5H12O + C6H12 H2O + C5H12O + C6H12 H2O + C5H12O + C6H12
0.2 0.2 0.2
94.9 94.9 94.9
NRTL 1,2 1,4 2,4
1070.8 1222.4 -304.35
456.03 1436.4 -288.55
0.2
H2O + C5H12O + C6H6 H2O + C5H12O + C6H6 H2O + C5H12O + C6H6
0.1 0.1 0.1
51.4 51.4 51.4
1,2 1,3 2,3
1131.2 1348.6 -190.89
513.02 1309.6 -190.79
0.25
H2O + C5H12O + C6H12
7.1
46.1
H2O + C5H12O + C6H6
10.3
615.65 1016.7 -211.16 594.99 848.19 24.415
UNIFAC 76.6
The following structural parameters were for H2O, r ) 0.9200 and q ) 1.400; for C5H12O, r ) 4.0678 and q ) 3.6320; for C6H6, r ) 3.1872 and q ) 2.400; and for C6H12, r ) 4.0464 and q ) 3.24. a
used:12
Table 5 lists LLE data, expressed in terms of mass fraction, for the w1H2O + w2C5H12O + w3C6H6 + (1 w1 - w2 - w3)C6H12 quaternary system, corresponding to the planes P1 ) 0.798C6H6 + 0.202C6H12, P2 ) 0.602C6H6 + 0.398C6H12, P3 ) 0.397C6H6 + 0.603C6H12, and P4 ) 0.194C6H6 + 0.816C6H12, which were used for the determination of the binodal surface. Because the concentrations of the four components were individually determined, the sums of the mass fractions for each phase in Table 5 may slightly differ from unity. The same consideration is applicable to Tables 2 and 3 for the ternary systems (within (0.0001, in terms of mass fraction). The water concentration in the organic phase represents the water tolerance for this quaternary system. These values are small, ranging from not detectable to 0.0142 (in terms of mass fraction) for P1, not detectable to 0.0128 for P2, not detectable to 0.0134 for P3, and not detectable to 0.0128 for P4, as can be observed in Table 5. Although the effect of temperature on this quaternary system was not studied, a decrease in temperature will certainly produce a decrease in solubility and a consequent decrease in water tolerance. Therefore, at lower temperatures, phase separation will occur at a smaller water content than that at T ) 303.15 K. The results also show that, when phase separation occurs, a small fraction of C5H12O is drawn into the aqueous phase, whereas neither C6H6 nor C6H12 could be detected in this phase. Table 5 also shows that the capacity for the oxygenated compound to keep water in the hydrocarbon-rich phase is increased as the MTBE concentration increases in the global composition. On the other hand, the solubility of the hydrocarbons in the water-rich phase is not affected when this happens, because the concentrations of both hydrocarbons were always below the detection limit for all the studied planes. Because storage tanks in gasoline stations must be purged periodically, this conclusion is very important, because it shows that no hydrocarbon contamination occurs. This contrasts with what occurs with MTBE, because of its
relatively high solubility in water. These purges and occasional spills produce serious groundwater14 and surface water15 contamination, which is the principal cause for the USEPA’s disagreement with the use of MTBE in reformulated gasoline.6,7 Only one similar quaternary system was found in the literature,16 which shows the same trend as that observed in this work. The averages of all the binary interaction parameter pairs, calculated from their respective ternary subsystems, were chosen as a unique set of binary parameters suitable for prediction of the quaternary equilibrium data for the UNIQUAC model. Although this procedure is not completely justified, because the values of these parameters are very different, the calculated results so obtained are surprisingly good, as can be observed by analyzing the residuals given by eqs 3 and 4 for the UNIQUAC model, which are presented in Table 6. For comparison, this table also lists the residuals for the UNIFAC model. On the other hand, Table 7 shows the interaction parameters for the UNIFAC equations used in this work, whereas Table 8 shows the UNIQUAC average interaction parameters used for the prediction of the quaternary system, along with all the binary interaction parameters used in their derivation. Conclusions Our experimental results show that the quaternary system w1H2O + w2C5H12O + w3C6H6 + (1 - w1 - w2 - w3)C6H12 presents a water tolerance as high as 1 mass % of water or greater (see Table 5) when the global composition is rich in methyl tert-butyl ether (MTBE). This water tolerance is greater than those obtained for (14) Squillace, P. J.; Zogorsky, J. S.; Wilber, W. G.; Price, C. V. Environ. Sci. Technol. 1996, 30, 1721-1730. (15) Reuter, J. E.; Allen, B. C.; Richards, R. C.; Pankow, J. F.; Goldman, C. R.; Scholl, R. L.; Seyfried, J. S. Environ. Sci. Technol. 1998, 32, 3666-3672. (16) Alkandary, J. A.; Aljimaz, A. S.; Fandary, M. S.; Fahim, M. A. Fluid Phase Equilib. 2001, 187-188, 131-138.
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Gramajo de Doz et al.
Table 5. Quaternary LLE Data for the w1H2O + w2C5H12O + w3C6H6 + (1 - w1 - w2 - w3)C6H12 System at T ) (303.15 ( 0.05) K, for Various Sectional Planesa Global Composition w1H2O w2C5H12O w3C6H6 0.5720 0.5104 0.5010 0.5020 0.4958 0.5013 0.4985 0.5021 0.5084 0.4997 0.4865 0.4890
0.0000 0.0346 0.0733 0.1286 0.1760 0.2169 0.2698 0.3202 0.3750 0.4189 0.4797 0.5110
Aqueous Phase
Organic Phase
(1 - w1 - w2 (1 - w1 - w2 (1 - w1 - w2 w3)C6H12 w3)C6H12 w3)C6H12 w1H2O w2C5H12O w3C6H6 w1H2O w2C5H12O w3C6H6
0.3414 0.3629 0.3395 0.2946 0.2618 0.2248 0.1848 0.1417 0.0930 0.0649 0.0269 0
0.0866 0.0921 0.0862 0.0748 0.0664 0.0570 0.0469 0.0360 0.0236 0.0165 0.0068 0
1.0000 1.0000 0.9963 0.9921 0.9887 0.9857 0.9801 0.9767 0.9739 0.9689 0.9631 0.9619
P1 ) 0.798C6H6 + 0.202C6H12 0 0.0037 0.0079 0.0113 0.0143 0.0199 0.0233 0.0263 0.0311 0.0369 0.0381
0
0
0.5002 0.5102 0.4828 0.5042 0.5093 0.5055 0.4992 0.5136 0.5063 0.5016 0.4754 0.5042
0.0000 0.0498 0.1022 0.1254 0.1684 0.2280 0.2763 0.3193 0.3765 0.4196 0.4862 0.4958
0.3006 0.2646 0.2497 0.2228 0.1939 0.1603 0.1350 0.1005 0.0705 0.0474 0.0231 0
0.1992 0.1753 0.1655 0.1476 0.1285 0.1062 0.0895 0.0666 0.0467 0.0314 0.0153 0
P2 ) 0.602C6H6 + 0.398C6H12 1.0000 0 1.0000 0.9943 0.0055 0.9922 0.0078 0.9887 0.0113 0.9841 0.0159 0.9808 0.0192 0.9772 0.0228 0.9723 0.0277 0.9676 0.0324 0.9640 0.0360 0.9620 0.0380 0 0
0.5158 0.4799 0.4998 0.5174 0.5021 0.5031 0.4948 0.4904 0.4989 0.4883 0.5026 0.5020
0 0.0424 0.0877 0.1147 0.1725 0.2212 0.2750 0.3205 0.3737 0.4325 0.4668 0.4980
0.1920 0.1894 0.1636 0.1459 0.1291 0.1093 0.0913 0.0750 0.0505 0.0314 0.0121 0
0.2922 0.2883 0.2489 0.2220 0.1963 0.1663 0.1389 0.1141 0.0769 0.0478 0.0184 0
1.0000 1.0000 0.9941 0.9923 0.9878 0.9843 0.9813 0.9765 0.9733 0.9687 0.9647 0.9620
0.3981 0.3871 0.3540 0.3569 0.2726 0.2241 0.1787 0.1444 0.0953 0.0632 0.0302 0
P4 ) 0.194C6H6 + 0.816C6H12 1.0000 0 1.0000 0.9946 0.0055 0.9890 0.0113 0.9871 0.0127 0.9839 0.0161 0.9799 0.0201 0.9775 0.0225 0.9730 0.0273 0.9678 0.0322 0.9650 0.0350 0.9618 0.0381 0 0
0.5059 0.4854 0.4827 0.4244 0.4781 0.4918 0.5053 0.5083 0.5164 0.5078 0.5010 0.5078
0 0.0342 0.0779 0.1326 0.1836 0.2301 0.2729 0.3124 0.3653 0.4137 0.4616 0.4922
0.0960 0.0933 0.0854 0.0861 0.0657 0.0540 0.0431 0.0348 0.0230 0.0153 0.0073 0
0.0024 0.0031 0.0044 0.0056 0.0070 0.0091 0.0113 0.0142
0 0.0715 0.1416 0.2486 0.3382 0.4133 0.5216 0.6260 0.7547 0.8253 0.9215 0.9858
0.7931 0.7387 0.6897 0.6014 0.5261 0.4658 0.3769 0.2927 0.1910 0.1320 0.0537 0
0.2069 0.1897 0.1687 0.1500 0.1333 0.1178 0.0970 0.0757 0.0474 0.0336 0.0134 0
0.0020 0.0030 0.0039 0.0059 0.0077 0.0091 0.0095 0.0136
0 0.0998 0.1897 0.2578 0.3418 0.4532 0.5369 0.6326 0.7431 0.8236 0.9127 0.9863
0.6246 0.5464 0.4905 0.4517 0.3951 0.3256 0.2751 0.2168 0.1498 0.1014 0.0467 0
0.3754 0.3538 0.3195 0.2906 0.2610 0.2183 0.1840 0.1447 0.0994 0.0659 0.0311 0
0.0023 0.0030 0.0037 0.0062 0.0079 0.0113 0.0137
0 0.0821 0.1676 0.2235 0.3527 0.4411 0.5316 0.6124 0.7286 0.8330 0.9239 0.9864
0.4357 0.3579 0.3336 0.3000 0.2648 0.2235 0.1860 0.1537 0.1059 0.0635 0.0261 0
0.5643 0.5600 0.4989 0.4499 0.3825 0.3332 0.2794 0.2303 0.1593 0.0959 0.0387 0
0.0020 0.0030 0.0038 0.0050 0.0077 0.0096 0.0136
0 0.0654 0.1457 0.2260 0.3494 0.4419 0.5445 0.6091 0.7403 0.8340 0.9241 0.9864
0.2513 0.1827 0.1658 0.1476 0.1310 0.1155 0.0922 0.0775 0.0497 0.0314 0.0130 0
0.7487 0.7520 0.6887 0.6262 0.5198 0.4405 0.3603 0.3095 0.2050 0.1269 0.0533 0
P3 ) 0.397C6H6 + 0.603C6H12 0 0.0052 0.0078 0.0122 0.0157 0.0187 0.0237 0.0267 0.0311 0.0353 0.0381
0
0
a The variable w denotes mass fraction. A blank space indicates that the component was not detectable, meaning that the chromatographic signal is below to the detection limit. A value of zero means that the component is absent.
Table 6. Residuals F and ∆m for the Quaternary System w1H2O + w2C5H12O + w3C6H6 + (1 - w1 - w2 - w3)C6H12 at T ) 303.15 K for Various Sectional Planesa UNIFAC
UNIQUAC
plane
F (%)
∆m (%)
F (%)
∆m (%)
P1 P2 P3 P4
0.6 6.0 12.1 18.2
101.9 74.6 53.3 47.5
0.3 5.9 12.1 18.2
12.6 14.0 12.0 3.5
a
The values of ∆m were calculated only for C5H12O. The distribution coefficient m for this compound is defined as the mass fraction of C5H12O in the organic phase divided by the mass fraction of C5H12O in the aqueous phase.
similar quaternary systems that have ethanol or methanol instead of MTBE.4,5 The results also show that, if phase separation occurs, a small fraction of MTBE is
Table 7. UNIFAC Interaction Parametersa main group
CH2
ACH
H2O
CH2O
1 CH2 3 ACH 8 H2O 15 CH2O
0 156.5 342.4 1571
-114.8 0 372.8 52.13
1300 859.4 0 212.8
662.1 32.14 64.42 0
a
Data taken from ref 9.
transferred to the aqueous phase. This behavior is contrary to that encountered when the oxygenated compound in reformulated gasoline is ethanol or methanol,2-5 because, for these last systems, small quantities of water from air humidity or from infiltration into storage tanks produce phase separation with a considerable loss of alcohol drawn into the aqueous phase.
LLE of Water-MTBE-Benzene-Cyclohexane Systems Table 8. UNIQUAC Average Interaction Parameters for the Prediction of the Quaternary System, along with the Binary Interaction Parameters Used in Their Derivation system
i,j
H2O + C2H12O + C6H6 H2O + C2H12O + C6H12 average parameter
1,2 1,2 1,2
H2O + C2H12O + C6H6 H2O + C6H6 + C6H12 average parameter
1,3 1,3 1,3
367.29a 426.09b 396.69
848.19a 1046.3b 947.24
H2O + C2H12O + C6H12 H2O + C6H6 + C6H12 average parameter
1,4 1,4 1,4
561.56a 19.565b 290.562
1016.7a 773.9b 895.3
H2O + C2H12O + C6H6
2,3
-32.771a
2,4
169.24a
3,4
-422.05b
H2O + C2H12O + C6H12 H2O + C6H6 + C6H12 a
aij
aji
63.545a 35.561a 49.553
594.99a 615.65a 605.32
Energy & Fuels, Vol. 19, No. 5, 2005 1983
Table 6 shows that residuals (F) are much higher than the experimental error, which means that these two models cannot adequately predict the LLE for this quaternary system, because, as shown in Table 6, the predicted distribution coefficients have a relatively high deviation. This is probably due to the presence of water and the lack of the second additional term in the objective function in eq 2, which ensures that the binary interaction parameters give a solute distribution ratio at infinite dilution that is similar to an optimal value previously defined by the user.
24.415a -211.16a 18.534b
Data taken from Table 4. b Data taken from ref 4.
An additional conclusion of this study is that the UNIQUAC model predicts the equilibrium data more accurately than the UNIFAC model. On the other hand,
Acknowledgment. Financial support from the Consejo de Investigaciones de la Universidad Nacional de Tucuma´n, Argentina (CIUNT, Grant 26/E236), is gratefully acknowledged. EF049717O
