Liquid–Liquid Equilibria for Dipropylene Glycol–Hydrocarbon Binary

Article pubs.acs.org/jced

Liquid−Liquid Equilibria for Dipropylene Glycol−Hydrocarbon Binary Systems: Experimental Data and Regression Marilena Nicolae* and Florin Oprea Petroleum Processing and Environmental Engineering Department, Universitatea Petrol-Gaze din Ploieşti, Bd. Bucureşti, Nr. 39, Ploieşti, Romania ABSTRACT: Propylene glycols (mono- and di-) have an important potential as solvents in liquid−liquid extraction of aromatics and in azeotropic distillation. Literature and databases provide few accurate experimental data on liquid−liquid and vapor−liquid equilibria in systems consisting of propylene glycols and hydrocarbons (paraffinic, naphthenic, and aromatic hydrocarbons). However, an increasing interest in this field can be observed in recent years. This paper reports the results of an experimental study on the liquid−liquid equilibria in binary systems consisting of dipropylene glycol and paraffinic, naphthenic, and aromatic hydrocarbons with six, seven, and eight atoms of carbon. The experimental data were obtained in a high-precision thermostatic equilibrium cell. The first and most important result was that all normal paraffinic and naphthenic hydrocarbons are partially miscible with dipropylene glycol (4-oxa-2,6-heptanediol), whereas aromatics are completely dissolved. To obtain the binary interaction parameters of the NonRandom Two-Liquid (NRTL) activity coefficients, a regression procedure was applied to the experimental data (only for normal paraffinic and naphthenic hydrocarbon−dipropylene glycol systems) for each measured system. The NRTL parameters of the partially miscible binaries (complemented by the NRTL parameters for completely miscible binaries) can be subsequently used for simulations of liquid−liquid extraction, solvent recovery, and extractive-distillation processes.

E

of new solvents require good thermodynamic models, and the parameters of these models can only be obtained using accurate experimental data, to confirm their validity and range of applicability. There are very few binary LLE data concerning the hydrocarbon−DPG systems reported in the literature. The solvent considered in this work is in fact a mixture of dipropylene glycols. The DPGs are usually obtained as mixtures of three isomers: 2,2′-dihydroxydiisopropropylether (4-oxa-1,7heptanediol), 2,2′-dihydroxydipropylether (4-oxa-2,6-heptanediol), and 2-hydroxypropyl-2′-hydroxyisopropylether (1-propanol, 2−2-hydroxypropyl) and are typically 0.98 mass fraction glycols, with a boiling point ranging from 501.15 K to 509.15 K. Due to the difficult separation of these three isomers, we decided to use in our experimental measurements the mixture of the three isomers in the exact proportion resulting from their industrial fabrication process. The analysis showed that the preponderant isomer in this mixture is 4-oxa-2,6-heptanediol, and for this reason further we will use the nomenclature 4oxa-2,6-heptanediol or the abbreviation DPG for dipropylene glycol. In this work the reciprocal solubility between hydrocarbons and DPG is assessed using a special cloud-point cell by measuring the composition at which the phase separation occurs at a fixed temperature. The experimental data are regressed to

xtraction of aromatics is extensively used in refineries and petrochemical plants aiming to produce aromatic hydrocarbons and to obtain gasoline with low content of aromatics, as required by environmental regulations. Many studies concerning equilibrium data between aromatic hydrocarbons with six, seven, and eight atoms of carbon and different solvents such as: N-methylpyrrolidinone,1 sulfolane2−4 or ethylene glycols4−7 have been published. More recently, ionic liquids attracted the interest of researchers and were studied as solvents for extraction of aromatics.8,9 In 2003 our research group developed a program to study the possibility of using 1,2-propylene glycol (1,2-propanediol) in extractive distillation and liquid−liquid extraction based on its similarity to other glycols frequently used in such industrial processes.10,11 Our first experiments have shown remarkable performances in the extractive distillation of benzene from its mixture with hexane: an increase of the relative volatility to 2.3. This promising result has encouraged us to deeply investigate the liquid−liquid equilibria (LLE) of hydrocarbon−1,2-propylene glycol10,11 binary systems and, subsequently, to move on to the investigation of dipropylene glycols as solvents for such processes. A second strong motivation consisted of the similarity between dipropylene glycol (DPG) and diethylene glycol, a solvent widely used for many years for the liquid−liquid extraction of aromatics from gasoline. Our present contribution reports the results of the experimental study of liquid−liquid equilibria in binary systems consisting of DPG and paraffinic, naphthenic, and aromatic hydrocarbons with six up to eight atoms of carbon. The assessment © 2012 American Chemical Society

Received: August 15, 2012 Accepted: November 22, 2012 Published: December 4, 2012 3690

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Table 1. Specifications (Purity and Water Content) of the Chemicals Used in Experimental Determinations component

purity (mass fraction)

measured water content (mass fraction)

hexane cyclohexane heptane octane benzene 2,2,4-trimethylpentane

>0.997 >0.995 >0.997 >0.992 >0.998 >0.995

0.000057 0.000064 0.000066 0.000062 0.000087

component

purity (mass fraction)

measured water content (mass fraction)

toluene ethylbenzene o-xylene m-xylene p-xylene dipropylene glycol

>0.998 >0.998 >0.991 >0.991 >0.991 >0.998

0.000075 0.000082 0.000073 0.000069 0.000079 0.000605

Table 2. Binary Interaction Parameters of the NRTL Model for Five Binaries: Hexane−DPG, Cyclohexane−DPG, Heptane− DPG, Octane−DPG, and 2,2,4-Trimethylpentane−DPG NRTL binary interaction parameters

hexane−DPG

cyclohexane−DPG

heptane−DPG

octane−DPG

2,2,4-trimethylpentane−DPG

aij bij cij aji bji cji α′ij β′ij

−24.48683 9456.435 6122.689 16.04795 −5421.002 1679.672 −0.7056915 0.00247451

11.86737 −6634.515 991632.5 −2.247505 2030.599 −332001.6 −6.045208 0.01388661

−3.321812 2561.657 −110584.7 20.91567 −11614.13 1871952 0.3350848 0.00026514

−2.769601 1267.01 305748.9 16.26108 −10568.48 2111741 0.5283279 −0.00027226

20.32706 −13364.99 2595724 −19.91175 15575.49 −2565866 0.3776179 0.00013371

The procedure is repeated at least three times to minimize systematic errors. The cell was thermostatted using a Haake bath, and the temperature was measured with VWR International, LLC, NIST traceable digital thermometers (± 0.05 % accuracy and 0.001 K resolution). The experiments were carried out using the hydrocarbons presented in Table 1: hexane, cyclohexane, heptane, octane, 2,2,4-trimethylpentane, benzene, toluene, ethylbenzene, o-xylene, m-xylene, and p-xylene. The first five hydrocarbons are partially miscible with the solvent, while aromatics are completely soluble in DPG. The experimental data were correlated using the NRTL12 model. The NRTL parameters are presented in eqs 1 to 5 as they are available in PRO II reference manual.14

obtain binary parameters for activity coefficient models such as NRTL (Non-Random Two-Liquid) and UNIQUAC (UNIversal QUAsi Chemical).12,13

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METHODOLOGY Chemicals. The hydrocarbons used in our experiments were purified in our lab using a high efficiency column (DX Sulzer lab packing, 30 mm inner diameter and 1.2 m height) and then dried. The specifications of the chemicals used are presented in Table 1. The composition of the hydrocarbon samples was analyzed by gas chromatography per the ASTM D 6370 method, using a Clarus 500 instrument from Perkin− Elmer equipped with a split/splitless injector, and flame ionization detector, and using a capillary column coated with methyl silicon in liquid phase. Data were collected and processed using the DHA Software. The DPG solvent was also obtained in our lab from a commercial sample purified using the same Sulzer column and subsequently dried. The composition of the DPG sample was also analyzed with the Clarus 500 instrument using an Elite WAX (0.32 mm × 60 m × 0.25 mm) column. The distillation range (NBP) of the resulting solvent measured at 0.13332·105 N·m−2 was 441.25 K to 443.05 K, and the purity was 0.998 mass fraction (all isomers). The pressure was measured using a DPI 705 sensor with the measuring range between 0 N·m−2 and 0.46662·105 N·m−2. Experimental Procedure. The liquid−liquid equilibrium measurements for the DPG−hydrocarbon systems were carried out at atmospheric pressure or at small overpressure (to maintain the mixture in liquid phase), in a glass equilibrium cell (100 mL volume) for cloud-point determination. A measured amount of the major component is introduced in the cell before measurement, and after the temperature of the thermostatic bath reaches the desired value, the other component is added until the cloud point is observed (in this way each component becomes, alternately, the rich phase component). The liquid is stirred and maintained at the desired temperature for more than 1 h.

ln γi =

∑j τjiGjixji ∑k Gkixk

τij = aij +

τij = aij +

bij T

+

bij RT

+

+

∑ j

cij

∑ xτ G ⎞ xjGij ⎛ ⎜⎜τij − k k kj kj ⎟⎟ ∑k Gkjxk ⎠ ∑ Gkjxk ⎝ (unit is K)

T2

cij 2 2

RT

(unit is kcal or kJ)

(1)

(2)

(3)

Gij = exp( −αjiτij)

(4)

αji = αji′ + βji′T

(5)

The weighted Orthogonal Distance Regression algorithm, developed by the National Institute of Standards and Technology (NIST), as well as a nonlinear least-squares correlation,14,15 were employed for the regression of the experimental data using the Regress Thermo Data Manager module built in the PRO/II simulation software. The resulting NRTL parameters are presented in Table 2. We used the following procedure: - The first step was to calculate the partition ratio between the concentrations of the hydrocarbon in the glycol-rich 3691

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Table 3. Experimental (Liquid + Liquid) Equilibrium Data for the Hexane (1) + 4-Oxa-2,6-heptanediol (2) System for Mole Fractions x, Combined Uncertainty uc of Experimental Data, and Partition Ratios Calculated with Experimental Values of Mole Fractions, Kexp, and with Calculated Values of Mole Fractions with the NRTL Model, Kcalc, at Temperatures T between 298.15 K and 333.15 Ka experimental values T/K

uc(x)

xI1,exp

298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15

0.00020 0.00014 0.00164 0.00145 0.00100 0.00261 0.00063 0.00337

0.02960 0.05061 0.07347 0.08974 0.12024 0.13443 0.14028 0.15709

xII1,exp

K1 exp

calculated values with NRTL model K2 exp

0.99296 0.02981 137.8413 0.99145 0.05105 111.0396 0.98890 0.07429 83.4713 0.98631 0.09099 66.4908 0.98408 0.12218 55.2614 0.98059 0.13709 44.5943 0.97527 0.14383 34.7644 0.97122 0.16175 29.2880 average relative deviation (%)

K1 calc

K1, % deviation

K2 calc

K2, % deviation

0.03001 0.05034 0.07343 0.09469 0.11874 0.13552 0.14676 0.16058

0.6804 −1.3987 −1.1743 3.9055 −2.8963 −1.1581 1.9943 −0.7235 −0.0963

139.4687 107.8458 84.3419 67.3975 54.6667 44.3009 35.4969 28.9049

1.1668 −2.9615 1.0321 1.3452 −1.0873 −0.6622 2.0634 −1.3254 −0.0536

a Standard uncertainties are u(T) = 0.02 K, u(xI1) = 0.005, u(xII1 ) = 0.0003, and the combined expanded uncertainty Uc is Uc(x) = 0.01002 with a 0.95 level of confidence (k = 2).

Table 4. Experimental (Liquid + Liquid) Equilibrium Data for the Cyclohexane (1) + 4-Oxa-2,6-heptanediol (2) System for Mole Fractions x, Combined Uncertainty uc of Experimental Data, and Partition Ratios Calculated with Experimental Values of Mole Fractions, Kexp, and with Calculated Values of Mole Fractions with the NRTL Model, Kcalc, at Temperatures T between 298.15 K and 343.15 Ka experimental values T/K

uc(x)

xI1,exp

298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

0.0007 0.0015 0.0008 0.0006 0.0027 0.0053 0.0023 0.0028 0.0054 0.0031

0.0399 0.0527 0.1117 0.1252 0.1493 0.2059 0.2595 0.3183 0.3979 0.4361

xII1,exp

K1 exp

0.9869 0.0404 0.9846 0.0535 0.9823 0.1137 0.9784 0.1280 0.9735 0.1533 0.9642 0.2136 0.9521 0.2726 0.9412 0.3383 0.9173 0.4337 0.8836 0.4936 average relative deviation

calculated values with NRTL model K2 exp

K1 calc

K1, % deviation

K2 calc

K2, % deviation

73.5184 61.4339 50.0755 40.4251 32.1151 22.1630 15.4623 11.5830 7.2837 4.8428 (%)

0.0403 0.0537 0.1138 0.1276 0.1523 0.2144 0.2739 0.3394 0.4338 0.4916

−0.1972 0.4055 0.1016 −0.2899 −0.6925 0.4059 0.4762 0.3487 0.0270 −0.4088 0.0175

73.5184 61.4339 50.0755 40.4251 32.1151 22.1630 15.4623 11.5830 7.2837 4.8428

−0.5926 1.2209 −0.2783 −0.2267 −1.0976 0.7191 1.0730 −0.9953 −0.1099 0.3570 0.0069

a

Standard uncertainties are u(T) = 0.01 K, u(xI1) = 0.008, u(xII1 ) = 0.001, and the combined expanded uncertainty Uc is Uc(x) = 0.01612 with a 0.95 level of confidence (k = 2).

average error was −2.74 %, higher than for the NRTL model. Therefore we decided to abandon the UNIQUAC model and present only the NRTL binary interaction parameters.

phase and hydrocarbon-rich phase, K1, and the partition ratio between the concentrations of the glycol in the two phases mentioned above, K2 (see eqs 6 and 8); - The experimental data (as K1 and K2) were fitted either in the NRTL or the UNIQUAC model; - For the NRTL model we used successive models with three, five, six, and eight binary interaction parameters and selected the model with the highest accuracyin this case the model with eight binary interaction parameters; - For the UNIQUAC model we selected the model with four binary parameters; - The next step was to calculate the partition ratios, K1 and K2, for the glycol and hydrocarbon concentrations calculated with the NRTL model with eight binary interaction parameters (see eqs 7 and 9); - The final step was to calculate the differences (in percentage) for all points. The regression results for all binaries obtained using the UNIQUAC model were very poor. For example, for the hexane−4-oxa-2,6-heptanediol system the maximum error for the concentration of the first phase was 15.79 %, and the

K1,exp =

I x1,exp II x1,exp I x1,calc

K1,calc =

K 2,exp =

(6)

II x1,calc

(7)

I 1 − x1,exp II 1 − x1,exp

K 2,calc =

(8)

I 1 − x1,calc II 1 − x1,calc

(9)

xI1,exp

where is the experimental concentration of hydrocarbon in the glycol phase, expressed in molar fraction; xII1,exp is the experimental concentration of hydrocarbon in the hydrocarbon phase, expressed in molar fraction; xI1,calc is the 3692

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Table 5. Experimental (Liquid + Liquid) Equilibrium Data for the Heptane (1) + 4-Oxa-2,6-heptanediol (2) System for Mole Fractions x, Combined Uncertainty uc of Experimental Data, and Partition Ratios Calculated with Experimental Values of Mole Fractions, Kexp, and with Calculated Values of Mole Fractions with the NRTL Model, Kcalc, at Temperatures T between 298.15 K and 348.15 Ka experimental values T/K

uc(x)

xI1,exp

298.15 303.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15

0.0030 0.0016 0.0015 0.0008 0.0015 0.0015 0.0013 0.0017 0.0010 0.0015

0.0896 0.1101 0.1257 0.1298 0.1314 0.1320 0.1337 0.1447 0.1536 0.1569

xII1,exp 0.9888 0.9865 0.9831 0.9804 0.9781 0.9753 0.9708 0.9653 0.9598 0.9522

K1 exp

calculated values with NRTL model K2 exp

0.0906 81.1413 0.1116 66.0646 0.1279 51.8765 0.1324 44.3288 0.1343 39.7156 0.1353 35.1469 0.1377 29.7142 0.1499 24.6449 0.1601 21.0652 0.1648 17.6509 average relative deviation (%)

K1 calc

K1, % deviation

K2 calc

K2, % deviation

0.0905 0.1116 0.1283 0.1327 0.1344 0.1350 0.1371 0.1497 0.1604 0.1653

−0.1398 0.0353 0.3121 0.2113 0.0403 −0.2015 −0.4483 −0.1765 0.1898 0.3129 0.0136

80.1128 67.2464 51.7594 44.6441 39.5055 34.7337 29.6585 24.8002 21.0971 17.6744

−1.2799 1.7541 −0.2413 0.7000 −0.5330 −1.1792 −0.1722 0.6143 0.1533 0.1416 −0.0042

a

Standard uncertainties are u(T) = 0.01 K, u(xI1) = 0.005, u(xII1 ) = 0.0005, and the combined expanded uncertainty Uc is Uc(x) = 0.01005 with a 0.95 level of confidence (k = 2).

Table 6. Experimental (Liquid + Liquid) Equilibrium Data for the Octane (1) + 4-Oxa-2,6-heptanediol (2) System for Mole Fractions x, Combined Uncertainty uc of Experimental Data, and Partition Ratios Calculated with Experimental Values of Mole Fractions, Kexp, and with Calculated Values of Mole Fractions with the NRTL Model, Kcalc, at Temperatures T between 298.15 K and 363.15 Ka experimental values T/K

uc(x)

xI1,exp

298.15 308.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15

0.0001 0.0009 0.0003 0.0010 0.0003 0.0003 0.0008 0.0003 0.0009 0.0002 0.0008 0.0011

0.0143 0.0244 0.0378 0.0455 0.0488 0.0716 0.0753 0.0836 0.0979 0.1212 0.1299 0.1385

xII1,exp

K1 exp

calculated values with NRTL model K2 exp

0.9926 0.0144 133.1444 0.9901 0.0246 98.9764 0.9864 0.0383 70.7431 0.9827 0.0463 55.1503 0.9802 0.0498 48.1573 0.9747 0.0734 36.6834 0.9704 0.0776 31.2216 0.9668 0.0865 27.5720 0.9605 0.1020 22.8257 0.9543 0.1270 19.2210 0.9498 0.1368 17.3296 0.9334 0.1483 12.9421 average relative deviation (%)

K1 calc

K1, % deviation

K2 calc

K2, % deviation

0.0145 0.0245 0.0383 0.0464 0.0497 0.0744 0.0778 0.0862 0.1017 0.1281 0.1368 0.1470

0.2147 −0.3728 −0.0259 0.0773 −0.1967 1.2737 0.1428 −0.3852 −0.2807 0.8286 0.0344 −0.9147 0.0155

134.7778 97.2741 69.1500 55.4504 47.8872 37.3493 31.7025 27.6429 22.9058 19.1618 17.0440 12.9629

1.2119 −1.7500 −2.3038 0.5411 −0.5641 1.7829 1.5170 0.2563 0.3498 −0.3088 −1.6758 0.1609 −0.0138

a Standard uncertainties are u(T) = 0.07 K, u(xI1) = 0.005, u(xII1 ) = 0.001, and the combined expanded uncertainty Uc is Uc(x) = 0.0102 with a 0.95 level of confidence (k = 2).

square root of the estimated variance u2c (y).16 Its values were calculated with eq 10, taking into account as input variables the amounts (expressed as molar fraction) of hydrocarbon used for each experiment. In Tables 3 to 7 the combined standard uncertainties uc(x) calculated with eq 10 are displayed. In the footnotes of each table the standard uncertainty of temperature u(T), the standard uncertainty of molar fraction of hydrocarbon in the glycol phase u(xI1), the standard uncertainty of molar fraction of hydrocarbon in the hydrocarbon phase u(xII1 ), and the combined expanded uncertainty Uc(x) calculated taking into account the combined standard uncertainty uc(x) and a coverage factor k = 2 are also given.

concentration of hydrocarbon in the glycol phase, calculated with the NRTL model, expressed in molar fraction; xII1,calc is the concentration of hydrocarbon in the hydrocarbon phase, calculated with the NRTL model, expressed in molar fraction. The reciprocal solubility data for the systems formed by DPG with the first five hydrocarbons, as functions of temperature, are presented in Table 3 (for hexane), Table 4 (for cyclohexane), Table 5 (for heptane), Table 6 (for octane), and Table 7 (for 2,2,4-trimethylpentane). The partition ratios K1 and K2 of hydrocarbon, respectively, of DPG in both phases (see eqs 6 and 7) with the corresponding temperatures are presented in the same tables, along with the combined uncertainty for the experimental data. The differences between the experimental and the calculated values of K1 and K2 are also displayed, along with the average error. The combined standard uncertainty of the measurement represents the estimated standard deviation of the molar fraction of the hydrocarbon in both liquid phases, which is the positive

uc 2(y) = a12u 2(x1) + a 2 2u 2(x 2) + ... aN 2u 2(xN )

(10)

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DISCUSSION The data presented in Tables 3 to 7 allow the following observations: 3693

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Table 7. Experimental (Liquid + Liquid) Equilibrium Data for the 2,2,4-Trimethylpentane (1) + 4-Oxa-2,6-heptanediol (2) System for Mole Fractions x, Combined Uncertainty uc of Experimental Data, and Partition Ratios Calculated with Experimental Values of Mole Fractions, Kexp, and with Calculated Values of Mole Fractions with the NRTL Model, Kcalc, at Temperatures T between 298.15 K and 347.15 Ka experimental values T/K

uc(x)

xI1,exp

300.35 308.15 313.35 318.15 323.15 328.15 333.35 338.35 343.15 347.15

0.0005 0.0018 0.0021 0.0005 0.0002 0.0006 0.0005 0.0001 0.0016 0.0004

0.0682 0.0923 0.1039 0.1108 0.1112 0.1145 0.1160 0.1186 0.1249 0.1289

xII1,exp

K1 exp

calculated values with NRTL model K2 exp

0.9938 0.0686 149.5746 0.9896 0.0933 87.6197 0.9876 0.1052 72.1804 0.9852 0.1124 60.0870 0.9801 0.1134 44.7455 0.9775 0.1171 39.3190 0.9704 0.1195 29.8762 0.9678 0.1226 27.3708 0.9638 0.1296 24.1860 0.9576 0.1346 20.5409 average relative deviation (%)

K1 calc

K1, % deviation

K2 calc

K2, % deviation

0.0686 0.0930 0.1057 0.1135 0.1133 0.1170 0.1187 0.1217 0.1297 0.1351

−0.0309 −0.3803 0.5201 0.9291 −0.0880 −0.1421 −0.6945 −0.7093 0.0910 0.3566 −0.0148

147.4453 90.7497 71.7208 58.5201 45.3327 38.8105 30.4074 27.2397 23.9296 20.5524

−1.4442 3.4491 −0.6409 −2.6777 1.2952 −1.3102 1.7469 −0.4814 −1.0713 0.0560 −0.1078

a

Standard uncertainties are u(T) = 0.01 K, u(xI1) = 0.003, u(xII1 ) = 0.001, and the combined expanded uncertainty Uc is Uc(x) = 0.0063 with a 0.95 level of confidence (k = 2).

octane phase, whereas the average deviation is −0.013786 % for the DPG phase and 0.015542 % for the octane phase. - For the 2,2,4-trimethylpentane−DPG system the maximum deviation is 3.44911 % for the DPG phase and 0.929061 % for the 2,2,4-trimethylpentane phase, whereas the average deviation is −0.10784 % for the DPG phase and −0.014829 % for the 2,2,4-trimethylpentane phase. As it can be seen, the NRTL model with eight binary interaction parameters predicts the experimental data with a good accuracy.

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CONCLUSION The liquid−liquid equilibria for 11 binary systems formed by 4oxa-2,6-heptanediol with paraffinic, naphthenic, and aromatic hydrocarbons were measured in the temperature range from 298.15 K to 363.15 K. The experimental data were regressed to obtain temperature-dependent NRTL and UNIQUAC models. The NRTL models show good accuracy, whereas for the UNIQUAC models the accuracy is rather poor. The results of our studies encourage us to extend our work for other systems to obtain valuable thermodynamic models for liquid−liquid equilibria of hydrocarbon−DPG binaries in the domain of hydrocarbons with six up to eight atoms of carbon (paraffinic and naphthenic) and also vapor−liquid equilibria for aromatic−DPG binaries for which there are no data available in the literature.

Figure 1. Variation of the reciprocal solubility with the temperature for binary system hexane + 4-oxa-2,6-heptanediol. ■, this work, experimental values of molar fraction of hexane; , this work, calculated values of molar fraction of hexane using binary interaction parameters of the NRTL thermodynamic model.

- For the hexane−DPG system the maximum deviation is −2.9615 % for the DPG phase and 3.9055 % for the hexane phase, whereas the average deviation is −0.053616 % for the DPG phase and −0.096286 % for the hexane phase. The variation of the reciprocal solubility for this binary with the temperature is plotted in Figure 1. - For the cyclohexane−DPG system the maximum deviation is 1.0731 % for the DPG phase and −0.69169 % for the cyclohexane phase, whereas the average deviation is 0.00698 % for the DPG phase and 0.01751 % for the cyclohexane phase. - For the heptane−DPG system the maximum deviation is −1.75414 % for the DPG phase and −0.44831% for the heptane phase, whereas the average deviation is 0.004227 % for the DPG phase and 0.013558 % for the heptane phase. - For the octane−DPG system the maximum deviation is −2.30377 % for the DPG phase and 1.27369% for the

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected], fl[email protected] Tel.: +40-244573171. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors would like to thank Mr. Alexandru Pană, Head of Quality Control Department, S.C. Oltchim S. A. Râmnicu Vâlcea, Romania for assistance and fruitful discussions. 3694

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dx.doi.org/10.1021/je3009039 | J. Chem. Eng. Data 2012, 57, 3690−3695