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Ind. Eng. Chem. Res. 2003, 42, 3434-3440
Separation of Closely Boiling Compounds of 2-Methoxyphenol and 1,2-Dimethoxybenzene with Diphenylmethane as Entrainer Ming-Jer Lee, Yu-Hsing Chou, and Ho-mu Lin* Department of Chemical Engineering, National Taiwan University of Science and Technology, 43 Keelung Road, Section 4, Taipei 106-07, Taiwan
Solid-liquid equilibrium data were measured for binary and ternary mixtures composed of diphenylmethane with closely boiling compounds: 2-methoxyphenol (or guaiacol, CAS [90-051]) and 1,2-dimethoxybenzene (or veratrole, CAS [91-16-7]). Experimental results revealed that all the binaries behave as simple eutectic systems. The eutectic loci were also observed for the mixtures of diphenylmethane + 2-methoxyphenol + 1,2-dimethoxybenzene, from which a ternary solid-liquid equilibrium phase diagram was obtained. A feasible separation sequence, on the basis of the phase diagram, was then proposed to separate the mixture of 2-methoxyphenol and 1,2-dimethoxybenzene by means of extractive crystallization with diphenylmethane as an entrainer. The Wilson and the NRTL models were employed to correlate the equilibrium data of binary systems. These two models with the determined parameters predicted the soliddisappearance temperatures of the ternary system to grand average absolute deviations of better than 0.43%. Introduction Separation of a 2-methoxyphenol (Tb ) 478.15 K) and 1,2-dimethoxybenzene (Tb ) 479.15 K) mixture is needed in the process of manufacturing methoxyphenols. Conventional distillation appears to be economically unattractive to separate such closely boiling compounds. Lee et al.1 investigated the vapor-liquid equilibrium (VLE) behavior of these compounds with supercritical carbon dioxide over a temperature range 323.15-423.15 K and pressures up to 20 MPa in an attempt to separate the mixture by supercritical fluids. Instead of operating at elevated pressures with supercritical fluid technology, extractive crystallization, operating at near atmospheric pressure, could be another alternative method to separate these two compounds. Hwang et al.2 estimated the activity coefficient and the selectivity at infinite dilution for 2-methoxyphenol + 1,2-dimethoxybenzene with several solvents and found diphenylmethane to be a potential entrainer. Because the separation sequence is governed mainly by the phase equilibrium behavior of the related mixtures,3 measurements of phase equilibrium properties play an important role in development of the separation processes. Hwang et al.2 measured the VLE data of mixtures containing 2-methoxyphenol, 1,2-dimethoxybenzene, and diphenylmethane at temperatures from 433.15 to 463.15 K. No azeotropes were formed in these mixtures. It means that the entrainer, diphenylmethane, can be recovered from the mixtures by distillation. In the present study, the solid-liquid equilibrium (SLE) behavior was investigated for the same mixtures containing 2-methoxyphenol, 1,2-dimethoxybenzene, and diphenylmethane. The SLE data of these mixtures are not available in the literature at comparable conditions. A ternary phase diagram was also prepared from the results of SLE measurements, and subsequently, a feasible separation sequence was proposed on the basis of this phase diagram. * To whom correspondence should be addressed. Tel.: +8862-2737-6643. Fax: +886-2-2737-6644. E-mail:
[email protected]. edu.tw.
The Wilson4 and the NRTL5 models were adopted in the present study to correlate the binary SLE data. The parameters determined from the constituent binaries are utilized directly to predict the phase boundaries of the solid-liquid equilibrium and the eutectic loci for the ternary system. Good agreement was found between the predicted results and the experimental values. Experimental Method The purities of 2-methoxyphenol (Merck, Germany), 1,2-dimethoxyphenol (TCI, Japan), and diphenylmethane (Aldrich, USA) are higher than 99 mass %. Table 1 lists the properties of the chemicals. The molar enthalpies of fusion were measured with a differential scanning calorimeter (Du Pont, DSC-900; accuracy: (5%), and the liquid molar densities were measured with a vibrating U-tube densimeter (Anton Parr, DMA 4500; accuracy (1 × 10-4 g cm-3). All these substances were used without further purification. The SLE data were measured in the present study by a solid-disappearance method. This method has been widely used by a majority of research groups in the world, including Prof. McLaughlin,7 LSU, USA; Prof. Domanska,8 Warsaw Technical University, Poland; Prof. Chivate,9 University of Bombay, India; Prof. Makita,10 Kobe University, Japan; and our group.11,12 Typically, this method measures the SLE data to an accuracy of (0.2 K. Lee et al.12 compared the melting temperatures of dibenzofuran and fluorine determined from the solid disappearance method with those from DSC (Sediawan et al.13). The differences are found to within 0.4 K. Each mixture (about 3 g) was prepared by weighting pure compounds to (0.1 mg. The accuracy of sample composition was about (0.0002 in mole fraction. The homogenized sample was sealed in a tiny glass vial. The vial was immersed in a cold bath to crystallize the liquid sample. The solidified sample was then placed in a visual thermostated bath (Neslab, TV-4000, stability ) (0.03 K, operable from room temperature up to 503 K) and shaken vigorously for observation of solid disap-
10.1021/ie020592p CCC: $25.00 © 2003 American Chemical Society Published on Web 06/10/2003
Ind. Eng. Chem. Res., Vol. 42, No. 14, 2003 3435 Table 1. Properties of Pure Compounds ∆fusH VL at 298.15 K (kJ‚mol-1) (cm3‚mol-1)
Tm (K) substance
this work literature this work
this work
diphenylmethane 2-methoxyphenolc 1,2-dimethoxybenzened
298.39a
167.93b 110.00b 127.91
a Tsonopoulos (OCH3)C6H4OH.
298.2 301.2 295.7
d
et al.6 b At C6H4(OCH3)2.
14.7 12.0 12.6
subcooled
liquid
state. c 2-
Table 2. Solid-Liquid Equilibrium Data for Binary Systems x1
T (K)
x1
T (K)
2-Methoxyphenol (1) + 1,2-Dimethoxybenzene (2) 0.0 295.7 0.4697 266.4 0.1491 289.0 0.4797 265.8 0.2294 284.3 0.4896 264.6a 0.2998 279.7 0.4996 267.0 0.3200 278.5 0.4998 267.1 0.3400 277.5 0.5396 270.0 0.3596 275.2 0.5589 270.6 0.3700 274.6 0.5800 273.2 0.3999 272.6 0.5997 274.2 0.4397 269.2 0.7491 287.2 0.4500 268.0 0.8992 296.4 0.4600 267.5 1.0 301.2
Figure 1. Solid-liquid phase diagram for 2-methoxyphenol (1) + 1,2-dimethoxybenzene (2).
Diphenylmethane (1) + 2-Methoxyphenol (2) 0.0 301.2 0.4004 283.7 0.0997 296.7 0.4402 281.7 0.2000 292.1 0.4600 281.0 0.2403 290.9 0.4700 280.6a 0.2599 289.6 0.4807 281.1 0.2814 288.8 0.5003 281.8 0.2896 288.4 0.5501 283.7 0.3206 287.4 0.7003 288.8 0.3301 287.2 0.8490 293.9 0.3399 286.7 1.0 298.2 Diphenylmethane (1) + 1,2-Dimethoxybenzene (2) 0.0 295.7 0.4598 271.8 0.1019 291.5 0.4700 272.4 0.2506 284.1 0.5521 277.5 0.4002 275.2 0.7001 285.2 0.4402 272.1 0.8468 292.3 a 0.4498 271.4 1.0 298.2 a
Figure 2. Solid-liquid phase diagram for diphenylmethane (1) + 2-methoxyphenol (2).
Eutectic point.
pearance at a fixed temperature. The bath temperature was elevated by a tiny increment each time, if the solid in the vial still existed after about 30-min observation. The increment was as small as 0.1 K, when the temperature is near that of solid disappearance. To operate the bath at temperatures lower than room temperature, an external refrigeration circulator (Neslab, RTE-110, stability ) (0.01 K) was connected. The bath temperature was measured by a Hart Scientific Microtherm (model 1560) with a platimum RTD probe to an accuracy of (0.02 K. The uncertainty of the reported solid-disappearance temperatures was about (0.2 K under normal experimental conditions and (0.5 K around the vicinity of an eutectic point. It was estimated by repeatedly measuring the disapperance temperatures of the same sample.
Figure 3. Solid-liquid phase diagram for diphenylmethane (1) + 1,2-dimethoxybenzene (2).
Experimental Results and Discussion The experimental results are tabulated in Table 2 for 2-methoxyphenol + 1,2-dimethoxybenzene, diphenylmethane + 2-methoxyphenol, and diphenylmethane + 1,2-dimethoxybenzene. The eutectic point for each binary system is noted in the table. No solid solutions
were detected with DSC from several binary mixtures containing 2-methoxyphenol, 1,2-dimethoxybenzene, and diphenylmethane. Figures 1-3 present the experimental results for these three binaries, indicating that all the binaries behave as simple eutectic systems.
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Ind. Eng. Chem. Res., Vol. 42, No. 14, 2003
Table 3. Solid-Liquid Equilibrium Data for Ternary System of 2-Methoxyphenol, 1,2-Dimethoxybenzene, and Diphenylmethane x1
T (K)
x1
T (K)
x1
1,2-Dimethoxybenzene (1) + (Diphenymethane/ 2-Methoxyphenol ) 10:90) (2) 0.3504 276.2 0.4705 265.1 0.5102 0.4001 271.7 0.4798 264.5 0.5205 0.4505 266.5 0.4904 264.3 0.5399 0.4598 265.8 0.5002 263.0a 0.6499 1,2-Dimethoxybenzene (1) + (Diphenymethane/ 2-Methoxyphenol ) 20:80) (2) 0.3504 271.6 0.4599 260.8 0.5003 0.4116 265.7 0.4712 260.2a 0.5097 0.4199 265.2 0.4801 260.7 0.5205 0.4397 262.5 0.4896 261.7 0.5302 0.4497 261.6 0.4998 262.5
T (K)
264.0 265.8 266.4 276.2
263.0 263.9 265.8 266.5
1,2-Dimethoxybenzene (1) + (Diphenymethane/ 2-Methoxyphenol ) 30:70) (2) 0.4005 261.3 0.4503 257.1a 0.5004 262.9 0.4100 260.4 0.4605 258.2 0.5203 264.8 0.4198 259.3 0.4700 259.3 0.4403 257.9 0.4801 260.9
0.0499 0.2502 0.3217 0.3299
Diphenylmethane (1) + (2-Methoxyphenol/ 1,2-Dimethoxybenzene ) 20:80) (2) 283.4 0.3400 267.0 0.4526 272.7 0.3501 266.3a 0.5499 268.2 0.3600 267.3 0.6503 267.6 0.3701 268.2 0.7500
0.1504 0.1604 0.1700 0.1801 0.1898
Diphenylmethane (1) + (2-Methoxyphenol/ 1,2-Dimethoxybenzene ) 40:60) (2) 263.6 0.1904 261.6 0.2302 263.5 0.1999 260.8 0.2401 263.3 0.2029 260.1 0.2559 263.1 0.2098 259.4 0.2799 262.5 0.2200 259.2
0.1499 0.1598 0.1697 0.1807 0.1899
Diphenylmethane (1) + (2-Methoxyphenol/ 1,2-Dimethoxybenzene ) 50:50) (2) 261.8 0.1999 260.2 0.2499 261.4 0.2106 259.9a 0.2601 261.1 0.2199 260.6 0.2703 260.7 0.2299 261.5 0.2807 260.4 0.2397 262.5 0.3001
0.1498 0.2497 0.2601 0.2699
Diphenylmethane (1) + (2-Methoxyphenol/ 1,2-Dimethoxybenzene ) 60:40) (2) 270.0 0.2799 266.6 0.5499 266.6 0.2902 267.4 0.6519 265.7a 0.3504 271.7 265.9 0.4503 277.3
0.0485 0.1422 0.2381 0.3355 0.3500
Diphenylmethane (1) + (2-Methoxyphenol/ 1,2-Dimethoxybenzene ) 80:20) (2) 289.0 0.3606 276.2 0.4106 284.5 0.3706 276.0 0.4347 281.3 0.3798 275.4a 0.5341 277.3 0.3898 275.8 0.6361 276.5 0.4001 276.3
a
273.6 279.3 284.1 288.4
258.6a 260.2 261.9 263.8
263.3 264.1 264.9 266.0 267.0
281.6 285.6
276.7 278.0 282.2 285.7
Eutectic point.
Eight pseudobinary (ternary) systems were also investigated in this study. These pseudobinary samples were prepared with constant molar ratios of diphenylmethane/2-methoxyphenol ) 10:90, 20:80, and 30:70, and 2-methoxyphenol/1,2-dimethoxybenzene ) 20:80, 40:60, 50:50, 60:40, and 80:20. The experimental results are compiled in Table 3. Figure 4 shows the phase boundary of the pseudobinary system of diphenylmethane + (2-methoxyphenol/1,2-dimethoxybenzene ) 20:80). A eutectic point is exhibited on the liquidus line. Similar behavior was found in the other pseudobinary systems. The eutectic point for each pseudobinary system is indicated in Table 3.
Figure 4. Solid-liquid phase diagram for the pseudobinary system of diphenylmethane (1) + (2-methoxyphenol/1,2-dimethoxybenzene ) 20:80) (2).
Figure 5 is a projection of the SLE phase diagram onto the composition plane for the ternary system of 2-methoxyphenol + 1,2-dimethoxybenzene + diphenylmethane. The eutectic loci divide the phase diagram into three regions, marked respectively as A-C. Each region corresponds to a solid that will preferentially crystallize from the mother liquor, i.e., region A for 2-methoxyphenol, region B for 1,2-dimethoxybenzene, and region C for diphenylmethane. The ternary eutectic TE is located below the straight line connecting between the eutectic point of 2-methoxyphenol/1,2-dimethoxybenzene binary (E1) and the corner of diphenylmethane (S) as shown in Figure 5. As categorized by Rajagopal et al.,3 the separation can be achieved by the extractive crystallization with type-I sequence as presented in Figure 6. The corresponding separation path is also illustrated on the ternary SLE phase diagram of Figure 7. The conceptual separation procedure is as follows: (1)Add entrainer (diphenylmethane) into the mixture of 2-methoxyphenol and 1,2dimethoxybenzene (point 1) up to 0.16 in mole fraction (point 2). (2) Produce 2-methoxyphenol solid from the ternary solution in the first crystallizer at about 257 K, while the composition of the corresponding mother liquor (point 3) is located at nearby the ternary eutectic TE. (3) Recover diphenylmethane from the mother liquor of the first crystallizer by distillation, while the distillate (point 4) is about diphenylmethane-free. (4) Transfer the distillate into the second crystallizer to obtain 1,2dimethoxybenzene solid at about 264 K. The composition of the mother liquor (point 5) is about the eutectic mixture of 2-methoxyphenol + 1,2-dimethoxybenzene, which is recycled to combine with the feed stream (F). In comparison with the extractive distillation, the extractive crystallization may reduce the loading of the distillation column, due to part of 2-methoxyphenol being crystallized before distillation. It is also noted that the ternary eutectic point, TE, does not deviate far from the line of E1 to S, as shown in Figure 5, resulting that only a small amount of 1,2-dimethoxybenzene will crystallize out at crystallizer 2. Meanwile, the separation is infeasible if the feed compositions are positioned on the other side of the binary eutectic point, because the ternary eutectic TE is located below the straight line connecting between E1 and S. In this case, the extractive distillation method may be preferable.
Ind. Eng. Chem. Res., Vol. 42, No. 14, 2003 3437
Figure 5. Projection of SLE phase diagram for 2-methoxyphenol + 1,2-dimethoxybenzene + diphenylmethane.
perature (Tt,i) with the normal melting temperature (Tm,i) and canceling the last two terms of the right-hand side. Equation 1 thus becomes
ln ai ) ln(xiγi) )
Figure 6. Conceptual process for separation of 2-methoxyphenol + 1,2-dimethoxybenzene with diphenylmethane via extractive crystallization.
Correlation of Solid-Liquid Equilibrium Data
∆fusHi [(1/Tt,i) R ∆Cp,i ∆Cp,i T (1/T)] (1) (T - Tt,i) + ln RT R Tt,i
(2)
( (
) )
ln γ1 ) -ln(x1 + Λ12x2) + x2
Λ21 Λ12 x1 + Λ12x2 x2 + Λ21x1 (3)
ln γ2 ) -ln(x2 + Λ21x1) - x1
Λ21 Λ12 x1 + Λ12x2 x2 + Λ21x1 (4)
with
Λ12 ≡ where ai, γi, Tt,i, ∆fusHi, and ∆Cp,i are activity, activity coefficient, triple-point temperature, the molar enthalpy of fusion, and the difference between subcooled liquid and solid heat capacities for compound i, respectively. R is the gas constant and xi is the solid solubility of compound i at temperature T. The above equation is frequently simplified by replacing the triple-point tem-
)
As noted by Prausnitz et al.,14 this simplification usually introduces slight error. The solubility of compound i in an ideal solution (i.e., ideal solubility) is calculated from eq 2 by assuming that γi ) 1. However, the ideal solution assumption leads to underestimation of equilibrium temperatures as shown in Figures 1-3. The Wilson and the NRTL models were thus employed in the present study to calculate activity coefficient γi in the SLE calculation. The expressions of the Wilson model for a binary system is given as
The criterion of SLE is given by14
ln ai ) ln(xiγi) )
(
∆fusHi 1 1 R Tm,i T
VL2 VL1
[
exp -
]
(λ12 - λ11) RT
Λ21 ≡
VL1 VL2
[
exp -
]
(λ21 - λ22) (5) RT
where VLi is the molar liquid volume of pure component i.
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Figure 7. Separation path on the ternary SLE phase diagram. Table 4. Correlated Results for Binary Systems with the Wilson and the NRTL Models Wilson mixture 1 + 2
(λ12 - λ11)/R (K)
(λ21 - λ22)/R (K)
AADa (%)
diphenylmethane + 2-methoxyphenol diphenylmethane + 1,2-dimethoxybenzene 2-methoxyphenol + 1,2-dimethoxybenzene
143.62 35.55 150.93
364.46 175.48 -47.35
0.27 0.27 0.31
NRTL
a
mixture 1 + 2
(g12 - g22)/R (K)
(g21 - g11)/R (K)
R12
AADa (%)
diphenylmethane + 2-methoxyphenol diphenylmethane + 1,2-dimethoxybenzene 2-methoxyphenol + 1,2-dimethoxybenzene
203.68 95.35 -27.67
259.92 108.15 131.76
0.326 0.330 0.347
0.33 0.27 0.31
n AAD(%) ) (100/n)∑k)1 (|Tcalc - Texpt|/Texpt)k, where n is the number of data points.
composition range:
The NRTL model for a binary system is given by
[( [(
ln γ1 ) x22 τ21 ln γ2 ) x12 τ12
G21 x1 + x2G21 G12 x2 + x1G12
) )
2
2
+
+
τ12G12
] ]
(x2 + x1G12)2 τ21G21
(x1 + x2G21)2
(6)
(7)
with
G12 ) exp
[
]
-R(g12 - g22) RT
G21 ) exp
[
]
-R(g21 - g11) RT (8)
where R is the nonrandomness parameter. The model parameters are (λ12 - λ11) and (λ21 - λ22) in the Wilson and (g12 - g22), (g21 - g11), and R in the NRTL for each binary system. Upon specifying these parameters, the solid-disappearance temperature T at a given xi can be solved from eq 2 by an iterative procedure. The optimal values of the model parameters were obtained by minimizing the objective function π over the entire
π)
1
n
∑ (|Tcalc - Texpt|/Texpt)k
nk)1
(9)
where n is the number of data points. Table 4 lists the correlated results, indicating that both two models are equally good for data correlation. The calculated results from the Wilson model are compared with the ideal solubilities and the experimental values in Figures 1-3. In comparing with the ideal solubilities, substantial improvement has been obtained by using either the Wilson or the NRTL model to represent the nonideality of the solutions. SLE Calculation for Ternary System The solid-disappearance temperatures of ternary mixtures of 2-methoxyphenol + 1,2-dimethoxybenzene + diphenylmethane can be predicted from eq 2 with the aid of solution models by using the parameters determined from the binary SLE data as reported in Table 4. Table 5 presents the calculated results for the ternary
Ind. Eng. Chem. Res., Vol. 42, No. 14, 2003 3439 Table 5. Predicted Results for Ternary Systems AADa (%) mixture 10:90 20:80 30:70
n
Wilson
NRTL
Diphenylmethane/2-Methoxyphenol 12 0.30 14 0.41 10 0.60
2-Methoxyphenol/1,2-Dimethoxybenzene 20:80 12 0.44 40:60 14 0.25 50:50 15 0.46 60:40 10 0.44 80:20 14 0.35 grand AAD (%) 101 0.40
0.32 0.43 0.65 0.46 0.26 0.51 0.50 0.41 0.43
a AAD(%) ) (100/n)∑n (|T calc - Texpt|/Texpt)k, where n is the k)1 number of data points.
neously. The predicted ternary eutectic temperature is about 257.5 K by using either the Wilson or the NRTL model. Conclusions The SLE data were measured for the binary and ternary mixtures of 2-methoxyphenol, 1,2-dimethoxybenzene, and dimphenylmethane. All the investigated binary systems are simple eutectic. A ternary SLE phase diagram was obtained according to the experimental results. The phase diagram suggested that the separation of the closely boiling mixture of 2-methoxyphenol and 1,2-dimethoxybenzene is attainable by using diphenylmethane as an entrainer via the type I separation sequence of Rajagopal et al.3 The operating conditions of the separation process were also readily proposed by the SLE experimental results. The Wilson and the NRTL models are capable of correlating accurately the binary SLE data and predicting satisfactorily the phase boundaries of SLE and eutectic troughs for the ternary system. Acknowledgment Financial support from the National Science Council of ROC (NSC89-2214- E011-042) is gratefully acknowledged. Nomenclature
Figure 8. Comparison of predicted equilibrium temperatures from the Wilson model with experimental values.
system. It is shown that the Wilson and the NRTL models predict the equilibrium temperatures to the grand average absolute deviations (AADs) of 0.40% and 0.43%, respectively. The predicted equilibrium temperatures from the Wilson model are compared with experimental values in Figure 8. This model estimates accurately the equilibrium temperatures over a majority of composition range. Similarly, the eutectic troughs and the ternary eutectic can also be calculated if the binary parameters have already been determined. The following SLE criteria are needed to make the calculation:
(
)
(10)
(
)
(11)
(
)
(12)
∆fusH1 1 1 ln(x1γ1) ) R Tm,1 Teut ln(x2γ2) )
∆fusH2 1 1 R Tm,2 Teut
ln(x3γ3) )
∆fusH3 1 1 R Tm,3 Teut
The eutectic troughs are predicted by solving any two above equations simultaneously. The predicted results are shown in Figure 5, revealing that these two models are capable of predicting the eutectic troughs to within reasonable accuracy. Furthermore, the ternary eutectic can also be predicted by solving eqs 10-12, simulta-
a ) activity AAD ) average absolute deviation ∆Cp ) difference between subcooled liquid and solid heat capacity (kJ mol-1 K-1) gij - gjj ) parameters in the NRTL model (kJ mol-1) ∆fusH ) molar enthalpy change of fusion (kJ mol-1) n ) number of data points R ) gas constant (kJ mol-1 K-1) T ) temperature (K) TE ) ternary eutectic VL ) molar liquid volume (cm3 mol-1) x ) mole fraction Greek Symbols R ) nonrandomness parameter in the NRTL model γ ) activity coefficient λij - λii ) parameters in the Wilson model (kJ mol-1) π ) objective function Subscripts calc ) calculated value expt ) experimental value eut ) eutectic m ) melting i ) component i ij ) for i-j pair interaction t ) triple-point
Literature Cited (1) Lee, M. J.; Kou, C. F.; Cheng, J. W.; Lin, H. M. Vapor-Liquid Equilibria for Binary Mixtures of Carbon Dioxide with 1,2Dimethoxybenzene, 2-Methoxyphenol, or p-Cresol at Elevated Pressures. Fluid Phase Equilib. 1999, 162, 211. (2) Hwang, S. M.; Lee, M. J.; Lin, H. M. Isothermal VaporLiquid Equilibria for Mixtures of 1,2-Dimethoxybenzene, 2-Methoxyphenol, and Diphenylmethane. Fluid Phase Equilib. 2001, 178, 209.
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(3) Rajagopal, S.; Ng, K. M.; Douglas, J. M. Design and Economic Trade-Off of Extractive Crystallization Process. AIChE J. 1991, 37, 437. (4) Wilson, G. M. Vapor-Liquid Equilibrium. XI: A New Expression for the Excess Free Energy of Mixing. J. Am. Chem. Soc. 1964, 86, 127. (5) Renon, H.; Prausnitz, J. M. Local Compositions in Thermodynamic Excess Functions for Liquid Mixtures. AIChE J. 1968, 14, 135. (6) Tsonopoulos, C.; Heidman, J. L.; Hwang, S. C. Thermodynamic and Transport Properties of Coal Liquids; John Wiley: New York, 1986. (7) Gupta, A.; Gupta, S.; Groves, F. R., Jr.; McLaughlin, E. Correlation of Solid-Liquid Equilibrium for Polynuclear Aromatic Compounds. Fluid Phase Equilib. 1991, 64, 201. (8) Domanska, U. Solubility of Benzoyl-Substituted Naphthols in Mixtures of Hexane and 1-Butanol. Ind. Eng. Chem. Res. 1990, 29, 470. (9) Jadhav, V. K.; Chivate, M. R. Separation of Phenol from Its Mixture with o-Cresol by Adductive Crystallization. J. Chem. Eng. Data 1992, 37, 232.
(10) Nagaoka K.; Makita, T. Solid-Liquid Phase Equilibria of Benzene + Cyclohexane System Under High Pressures. Int. J. Thermophys. 1987, 8, 415. (11) Lee, M. J.; Chi, P. C. Solid-Liquid Equilibrium for Mixtures Containing Cresols, Piperazine, and Dibutyl Ether. J. Chem. Eng. Data 1993, 38, 292. (12) Lee, M. J.; Chen, C. H.; Lin, H. M. Solid-Liquid Equilibria for Binary Mixtures Composed of Acenaphthene, Dibenzofuran, Fluorene, Phenanthrene, and Diphenylmethane. J. Chem. Eng. Data 1999, 44, 1058. (13) Sediawan, W. B.; Gupta, S.; McLaughlin, E. Solid-Liquid Phase Diagrams of Binary Aromatic Hydrocarbon Mixtures from Calorimetric Studies. J. Chem. Eng. Data 1989, 34, 223. (14) Prausnitz, J. M.; Lichtenthaler, R. N.; de Azevedo, E. G. Molecular Thermodynamics of Fluid-Phase Equilibria, 2nd ed.; Prentice Hall: Englewood Cliffs, NJ, 1986.
Received for review August 1, 2002 Revised manuscript received April 4, 2003 Accepted April 18, 2003 IE020592P
