Article pubs.acs.org/jced
Liquid−Liquid Equilibria at Three Temperatures (between 280.15 K and 333.15 K) of Binary, Ternary, and Quaternary Systems Involving Monoethylene Glycol, Water, Cyclohexane, para-Xylene, trans- and cis-Dimethylcyclohexane, and trans- and cis-Decahydronaphthalene Cécile Lindemann,† Pierre Duchet-Suchaux,‡ Ramy Abou Naccoul,† Ilham Mokbel,*,†,§ Vincent Malicet,† and Jose Jacques† †
Université Claude Bernard Lyon1, UMR 5615, 43 bd du 11 Novembre 1918, 69622 Villeurbanne, France TOTAL 2 place Jean Millier -La Défense 6, 92400 Courbevoie, France § Université de Saint Etienne, Jean Monnet, Saint Etienne−Université de Lyon, F-42023 Saint Etienne, France ‡
ABSTRACT: New solubility data for binary (ethylene glycol (or MEG) + cyclohexane or para-xylene), ternary (MEG/water + cyclohexane or paraxylene), and quaternary systems (MEG/water + trans- and cis-1,2dimethylcyclohexane or trans- and cis-decahydronaphthalene (decalin)) under atmospheric pressure at three temperatures between 280.15 K and 333.15 K are reported. No literature data was available to compare with the present study. The consistency of the experimental data was checked through an Othmer− Tobias plot. The nonrandom two-liquid (NRTL) and the Soave−Redlich− Kwong modified (SRKM) thermodynamic models were used to correlate the experimental liquid−liquid equilibrium (LLE) data for all of the studied systems.
1. INTRODUCTION Ethylene glycol (MEG), or ethane-1,2-diol, is widely used in industry. Among the various uses, we can quote heat transfer agent, precursor in the plastic industry, and gas hydrate inhibitor for the natural gas transportation. In the latter case, a reliable thermodynamic model is needed to predict with a reasonable accuracy the split of the MEG between the three phases (gas, condensate, and aqueous phase). The validation, and if needed the tuning of such model, requires experimental data such as mutual solubility of MEG (hydrate inhibitor), water, and hydrocarbons (representing the reservoir-fluid). At the present time, there are very few published data involving MEG−hydrocarbon mixtures. Main data are from the Technical University of Denmark.1−4 The scarcity of these data could be explained by the difficulty of measuring very low concentrations. For this reason we extended our previous study5 to ternary and quaternary systems. In this work, experimental data from liquid−liquid equilibrium (LLE) of two binary systems (MEG + cyclohexane or para-xylene), two ternary systems (MEG/water + cyclohexane or para-xylene), and two quaternary systems (MEG/water + trans- and cisdimethylcyclohexane or trans- and cis-decalin) are reported under atmospheric pressure and at three temperatures between 280.15 K and 333.15 K. This temperature range as well as the used aqueous phase composition (between 20 and 80 mass percent of MEG) have been chosen to be representative of the © 2014 American Chemical Society
conditions encountered in gas pipe-lines to prevent hydrates apparition. No data for comparison with the present work were found in the open literature.
2. EXPERIMENTAL SECTION 2.1. Materials. Monoethylene glycol (i.e., ethane-1,2-diol), cyclohexane, para-xylene (i.e., 1,4-dimethylbenzene), 1,2dimethylcyclohexane, and decahydronaphtalene (decalin) were obtained from Sigma-Aldrich. The two latter chemicals are supplied in the form of a mixture containing cis and trans isomer. The cis and trans composition in the commercial mixture was determined by gas chromatography. Specifications of chemicals used in this work are given in Table 1. Deionized water (conductivity = 18 MΩ.cm) from a Millipore Milli-Q system was used in this work. 2.2. Apparatus and Procedure. To establish liquid− liquid equilibrium, a glass cell of about 100 mL, described in detail in our previous paper, was used.5 The cell was equipped with a magnetic stirrer and a jacket for a circulating fluid to keep constant the temperature of the liquid mixture. The temperature was controlled to within 0.1 K. The mixtures Received: July 8, 2014 Accepted: October 23, 2014 Published: November 5, 2014 3749
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in the binary and ternary mixtures were determined by GC-2 and GC-3, respectively. Concerning the quaternary systems, prior to 1,2-dimethylcyclohexane and decalin GC analysis, a supplementary liquid−liquid extraction using dichloromethane (in the case of dimethylcyclohexane) and toluene (in case of decalin) was performed in order to concentrate the hydrocarbons present in the aqueous media. The used internal standard was n-decane and n-tetradecane, respectively, for 1,2dimethylcyclohexane and decalin determinations. Calibration curves were established by analyzing five different standard solutions containing known quantities of the component and the internal standard. The calibration curves covered the concentration range of the studied samples, with a good correlation coefficient (>0.999). The water content in the organic phase was determined using coulometric Karl Fischer (KF) titration. To ensure the homogeneity of the sample, the organic phase was dissolved in dry ethanol (maximum residual water not exceeding 30 ppm) before analysis. Prior to measurements, the KF determination of water was controlled by analyzing certified water standards “Hydranal-Water Standard 0.1” from Fluka. As the relative standard deviation (RSD) of the water analysis was 2.5%, the uncertainty on the molar fraction of water was estimated to be 5%. To obtain reliable data, each cell was subject to two or three samplings. Each sample was analyzed three times. The obtained reproducibility of the GC analysis was good, as the mean variation coefficient of the measurements was less than 2% for the different components analyzed. Uncertainty of the molar fraction of the MEG in the organic phase (except in decalin) and of para-xylene and cyclohexane in the polar phase was estimated to be twice the variation coefficient, namely, 4%. Uncertainty of the molar fraction of the MEG in decalin was estimated to be 5%, as the extraction/elution yield was found to be better than 99%. Because of their very low concentration in the polar phase, decalin and dimethylcyclohexane were subject to liquid−liquid extraction using dichloromethane (or toluene) prior to GC analysis. From the repeatability of three independent extractions followed by three GC analyses, the total uncertainty of their molar fraction was estimated to be equal to 10%.
Table 1. Mass Fraction Purity of the Used Compounds purity (mass fraction) compd
CAS number
SigmaAldrich
monoethylene glycol 1,2-dimethylcyclohexane
107−21−1 583−57−3
0.998 0.980
decahydronaphtalene
91−17−8
>0.99
cyclohexane para-xylene
110−82−7 106−42−3
>0.99 >0.99
GC analysis 0.995 cis: 0.826 cis: 0.4015 0.997 0.995
trans: 0.174 trans: 0.5985
contained in the glass cell were stirred during 8 h, and then the two phases were left to settle for 7 h. 2.3. Sampling and Analysis. The samples of the two phases were withdrawn from the equilibrium cell by means of two preheated sampling lines to avoid adsorption phenomena. They were collected in an auxiliary solvent (ethanol, dichloromethane, or toluene) in which they are miscible. In case the solute presented a molar fraction less than 10 −7 , a supplementary liquid−liquid extraction is applied. In both cases, an internal standard (for GC analysis) was added in the used solvent prior to the sampling. Only the minor compounds of each phase were analyzed, namely, the MEG and the water in the hydrocarbons rich phase and the hydrocarbons in the aqueous phase. With this aim, four gas chromatography (GC) apparatuses with different columns were used for the analysis of all compounds except water; see Table 2 for the descriptions of Table 2. Analytical GC Conditions for the Hydrocarbons and MEG Determination GC-1
GC-2
GC type
HP 6890
HP 6890 A
column type
Supelcowax 10
column length column i.d. film thickness injector type injection volume detector type He carrier gas
15 m
Restek Rtx-35 amine 30 m
0.53 mm 0.50 μm
GC-3
GC-4
HP 7890 A HP 7890 A Porabond HP-1 25 m
20 m
0.32 mm 1 μm
0.25 mm 3 μm
0.25 mm 1 μm
on-column
split
split
on-column
2 μL
1 μL
1 μL
2 μL
FID
FID
FID
FID
4.4 mL·min−1
70 kPa
70 kPa
70 kPa
3. RESULTS AND DISCUSSION In Table 3 are reported experimental LLE for the ternary systems MEG + water + para-xylene and MEG + water + cyclohexane. para-Xylene, due to its aromatic character, is twice more soluble in the polar phase than cyclohexane. In the same way, MEG and water are more soluble in para-xylene than in cyclohexane. For all the systems, as anticipated, the hydrocarbon solubility in the aqueous phase as well as the MEG and the water in the hydrocarbons phase increases with the temperature. MEG is much more soluble in the hydrocarbons than the water. The solubility of 1,2-dimethylcyclohexane in the polar phase is two times lower than its nonsubstituted homologue, namely, cyclohexane, Table 4. This phenomenon is due to the increase of 1,2-dimethylcyclohexane hydrophobicity compared to cyclohexane, which is confirmed by the increase of the carbon’s number. In the same way, because of hydrophobicity, decalin is less soluble in the polar phase (pure MEG or water and MEG/ water solvents) than 1,2-dimethylcyclohexane, Table 4. The ratio between cis and trans in the commercial dimethylcyclo-
the various GC conditions. Monoethylene glycol, MEG, in the hydrocarbon rich phase was determined by internal calibration using GC-1. In the cyclohexane and para-xylene-rich phase, the MEG was quantified using n-butylbenzene as internal standard, whereas in the 1,2-dimethylcyclohexane-rich phase, the internal standard is diethylene glycol. In the decalin-rich phase, the MEG was first extracted using a solid phase extraction supelclean LC−CN cartridge. This step is essential because it allows the extraction of the MEG from impurities originating in decalin. The sampled volume of the organic phase was 5 mL. The MEG is then eluted from the cartridge using 2 mL of ethanol containing n-tetradecane, used as internal standard. The hydrocarbons in the aqueous phase were analyzed by means of GC-2, GC-3, and GC-4. Cyclohexane and para-xylene 3750
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Table 3. Experimental Liquid−Liquid Equilibrium Data for the Ternary Systems Monoethylene Glycol (MEG) + Water + Cyclohexane or + para-Xylene Expressed in Molar Fractions (xi)a aqueous phase x1
a
x2
0.9962 0.5374 0.3034 0.0686
0 0.4621 0.6965 0.9313
0.9952 0.5373 0.3033 0.0686
0 0.4620 0.6965 0.9313
0.9923 0.5371 0.3032 0.0686
0 0.4617 0.6964 0.9313
0.9908 0.5367 0.3026 0.0678
0 0.4619 0.6971 0.9321
0.9899 0.5365 0.3025 0.0678
0 0.4618 0.6971 0.9321
0.9875 0.5361 0.3024 0.0678
0 0.4614 0.6969 0.9320
hydrocarbon-rich phase x3
x1
MEG (1) + Water (2) + Cyclohexane (3) 280.15 K (3.72 ± 0.15)·10−3 (2.61 ± (4.48 ± 0.18)·10−4 (1.80 ± (9.92 ± 0.40)·10−5 (7.77 ± (2.06 ± 0.08)·10−5 (3.17 ± 303.15 K (4.74 ± 0.19)·10−3 (1.34 ± (6.81 ± 0.27)·10−4 (8.73 ± (1.45 ± 0.06)·10−4 (3.35 ± (2.75 ± 0.11)·10−5 (6.37 ± 333.15 K (7.62 ± 0.30)·10−3 (5.23 ± (1.15 ± 0.05)·10−3 (3.52 ± (3.03 ± 0.12)·10−4 (1.61 ± (3.35 ± 0.13)·10−5 (2.63 ± MEG (1) + Water (2) + para-Xylene (3) 288.15 K (9.19 ± 0.37)·10−3 (1.08 ± (1.37 ± 0.05)·10−3 (5.44 ± (2.81 ± 0.11)·10−4 (2.83 ± (5.05 ± 0.20)·10−5 (5.71 ± 303.15 K (1.01 ± 0.04)·10−2 (1.86 ± (1.63 ± 0.07)·10−3 (8.62 ± (3.66 ± 0.15)·10−4 (4.87 ± (5.91 ± 0.24)·10−5 (8.08 ± 333.15 K (1.25 ± 0.05)·10−2 (4.80 ± (2.47 ± 0·10)·10−3 (2.34 ± (6.45 ± 0.26)·10−4 (1.14 ± (1.03 ± 0.04)·10−4 (2.30 ±
x2
0·10)·10−5 0.07)·10−5 0.31)·10−6 0.13)·10−6
0 (4.00 ± 0.20)·10−5 (6.91 ± 0.35)·10−5 (1.16 ± 0.06)·10−4
0.05)·10−4 0.35)·10−5 0.13)·10−5 0.25)·10−6
0 (1.97 ± 0·10)·10−4 (3.47 ± 0.17)·10−4 (4.42 ± 0.22)·10−4
0.21)·10−4 0.14)·10−4 0.06)·10−4 0.11)·10−5
0 (7.13 ± 0.36)·10−4 (8.73 ± 0.44)·10−4 (1.58 ± 0.08)·10−3
0.04)·10−3 0.22)·10−4 0.11)·10−4 0.23)·10−5
0 (7.34 ± 0.37)·10−4 (9.18 ± 0.46)·10−4 (1.16 ± 0.06)·10−3
0.07)·10−3 0.34)·10−4 0.19)·10−4 0.32)·10−5
0 (1.25 ± 0.06)·10−3 (1.81 ± 0.09)·10−3 (2.55 ± 0.13)·10−3
0.19)·10−3 0.09)·10−3 0.05)·10−3 0.09)·10−4
0 (2.14 ± 0.11)·10−3 (3.93 ± 0.20)·10−3 (5.69 ± 0.28)·10−3
Standard uncertainty u(T) = 0.1 K.
3.1. Data Correlation. Several empirical equations, such as Othmer−Tobias equation,6 the Bachman,7 and the Hand correlation,8 could be used to check the consistency of ternary and quaternary mixtures data especially when no literature data is available and assess the quality of the measurements. We correlated the obtained data using the Othmer−Tobias equation as shown in eq 1:
hexane and decalin is, respectively, R1cis/trans = 4.75 and R2cis/trans = 0.67, whereas in the MEG or water or MEG/water media, the ratios increase (5.6 ≤ R1cis/trans ≤ 6.3 and 0.70 ≤ R2cis/trans ≤ 1.26) letting conclude that the cis isomer is more soluble in the polar phase. No significant difference of solubility is observed for the MEG and water in the hydrocarbon rich phase for both systems, with decalin and with 1,2-dimethylcyclohexane, in the explored temperature range. As no literature data for comparison were found for all the mixtures studied in the present work, we plotted the molar fractions obtained in this study (cyclohexane, dimethylcyclohexane, and decalin) with those obtained from Derawi et al.,1 namely, methylcyclohexane, versus the number of carbons of these congeners (Figure 1). A straight line including the literature value is obtained both for the molar fraction of the hydrocarbons in the polar phase and the molar fraction of the MEG in the hydrocarbons. Folas et al.2 studied solubility of benzene and toluene in the MEG/water mixtures. In the same idea as previously, we plotted the mutual solubility of aromatic hydrocarbon and MEG versus the number of carbon of the hydrocarbons. The values of the present study are consistent with those of the authors (Figure 2).
o ⎞ aq ⎞ ⎛ 1 − wHC ⎛ 1 − wMEG ln⎜ ln = a + b ⎟ ⎟ ⎜ o aq ⎝ wHC ⎠ ⎝ wMEG ⎠
(1)
It is a linear two parameters correlation, where woHC stands for the mass fraction of the hydrocarbon in the organic phase and waq MEG is the mass fraction of MEG in the polar phase, both at equilibrium, and a and b are two adjustable parameters. The values of the latter along with the standard deviations σ (mean standard deviation between experimental points and calculated values) are summarized in Table 5. An example of a plot obtained in the case of para-xylene is given in Figure 3. In a second step, the experimental data were correlated using the NRTL and SRKM models. The latter was chosen because of its use in industrial simulations that have to be as predictive as possible. The adjustable binary parameters τij for NRTL model is 3751
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Table 4. Experimental Liquid−Liquid Equilibrium Data for the Systems Monoethylene Glycol (MEG) + Water + trans-1,2Dimethylcyclohexane + cis-1,2-Dimethylcyclohexane and Monoethylene Glycol (MEG) + Water + trans-Decalin + cis-Decalin Expressed in Molar Fractions (xi)a aqueous phase x1
x2
hydrocarbon-rich phase
x3
x4
x1
x2
MEG (1) + Water (2) + trans-1,2-Dimethylcyclohexane (3) + cis-1,2-Dimethylcyclohexane (4)
a
0 0.1105 0.2248 0.4035 0.9990
0.9999 0.8894 0.7751 0.5964 0
(1.36 (2.62 (7.43 (4.82 (1.37
± ± ± ± ±
0 0.1105 0.2248 0.4035 0.9985
0.9999 0.8894 0.7751 0.5964 0
(1.40 (3.72 (1.42 (8.04 (2.17
± ± ± ± ±
0 0.1105 0.2248 0.4035 0.9978
0.9999 0.8894 0.7751 0.5963 0
(2.12 (7.84 (3.13 (1.42 (3.18
± ± ± ± ±
0 0.1105 0.2248 0.4035 0.9996
0.9999 0.8894 0.7751 0.5964 0
(6.43 (1.68 (6.92 (4.90 (1.73
± ± ± ± ±
0 0.1105 0.2248 0.4035 0.9994
0.9999 0.8894 0.7751 0.5964 0
(6.86 (2.81 (1.40 (1.08 (3.46
± ± ± ± ±
0 0.1105 0.2248 0.4035 0.9989
0.9999 0.8894 0.7751 0.5964 0
(1.02 (5.70 (3.09 (2.43 (6.06
± ± ± ± ±
283.15 K (7.81 ± 0.78)·10−7 0 (1.53 ± 0.15)·10−6 (6.27 ± (4.63 ± 0.46)·10−6 (1.09 ± (2.91 ± 0.29)·10−5 (2.13 ± (7.82 ± 0.78)·10−4 (6.15 ± 303.15 K 0.14)·10−7 (8.23 ± 0.82)·10−7 0 0.37)·10−7 (2.19 ± 0.22)·10−6 (1.61 ± 0.14)·10−6 (8.65 ± 0.86)·10−6 (3.57 ± 0.80)·10−6 (4.83 ± 0.48)·10−5 (7.14 ± 0.22)·10−4 (1.22 ± 0.12)·10−3 (1.95 ± 333.15 K 0.22)·10−7 (1.27 ± 0.13)·10−6 0 −7 0.78)·10 (4.89 ± 0.49)·10−6 (8.29 ± 0.31)·10−6 (1.92 ± 0.19)·10−5 (1.61 ± 0.14)·10−5 (8.59 ± 0.86)·10−5 (3.00 ± 0.32)·10−4 (1.81 ± 0.18)·10−3 (8.04 ± MEG (1) + Water (2) + trans-Decalin (3) + cis-Decalin (4) 283.15 K 0.64)·10−8 (4.84 ± 0.48)·10−8 0 0.17)·10−7 (1.35 ± 0.13)·10−7 (3.43 ± 0.69)·10−7 (5.25 ± 0.52)·10−7 (1.30 ± 0.49)·10−6 (3.88 ± 0.39)·10−6 (1.59 ± 0.17)·10−4 (1.29 ± 0.13)·10−4 (5.15 ± 303.15 K 0.69)·10−8 (5.39 ± 0.54)·10−8 0 0.28)·10−7 (2.22 ± 0.22)·10−7 (1.39 ± 0.14)·10−6 (1.11 ± 0.11)·10−6 (3.36 ± 0.11)·10−5 (8.58 ± 0.86)·10−6 (6.53 ± 0.35)·10−4 (2.51 ± 0.25)·10−4 (1.76 ± 333.15 K 0·10)·10−7 (8.88 ± 0.89)·10−8 0 0.57)·10−7 (4.56 ± 0.46)·10−7 (6.71 ± 0.31)·10−6 (2.45 ± 0.25)·10−6 (1.46 ± 0.24)·10−5 (1.90 ± 0.19)·10−5 (2.52 ± 0.61)·10−4 (4.43 ± 0.44)·10−4 (7.13 ±
0.14)·10−7 0.26)·10−7 0.74)·10−7 0.48)·10−6 0.14)·10−4
0.25)·10 0.04)·10−5 0.09)·10−5 0.25)·10−5
(4.84 (3.09 (2.92 (2.57 0
± ± ± ±
0.24)·10−4 0.15)·10−4 0.15)·10−4 0.13)·10−4
0.06)·10−5 0.14)·10−5 0.29)·10−5 0.08)·10−4
(7.00 (6.05 (5.28 (4.55 0
± ± ± ±
0.35)·10−4 0.30)·10−4 0.26)·10−4 0.23)·10−4
(2.06 (1.60 (1.33 (1.07 0
± ± ± ±
0·10)·10−3 0.08)·10−3 0.07)·10−3 0.05)·10−3
0.17)·10 0.06)·10−5 0.08)·10−5 0.26)·10−5
(4.81 (3.73 (3.24 (3.00 0
± ± ± ±
0.24)·10−4 0.19)·10−4 0.16)·10−4 0.15)·10−4
0.07)·10−5 0.17)·10−5 0.33)·10−5 0.09)·10−4
(7.95 (6.81 (6.54 (5.16 0
± ± ± ±
0.40)·10−4 0.34)·10−4 0.33)·10−4 0.26)·10−4
0.34)·10−5 0.07)·10−4 0.13)·10−4 0.36)·10−4
(1.75 (1.56 (1.46 (1.21 0
± ± ± ±
0.09)·10−3 0.08)·10−3 0.07)·10−3 0.06)·10−3
−6
−5
0.33)·10 0.06)·10−4 0.12)·10−4 0.32)·10−4
−6
Standard uncertainty u(T) = 0.1 K.
τij =
Cij0 − CijT(T − 273.15)
The SRKM model in SimSci PRO/II developed by Invensys is a modification of the cubic equation of state of Soave10 proposed in 1986 by Panagiotopoulos and Reid11 consisting in an asymmetric mixing rule containing two parameters. The interaction parameter they proposed is given by
(2)
RT
The nonrandomness parameter (αij) of the NRTL equation was set to 0.2. Interaction parameters C0ij and CTij between MEG and water were obtained using vapor pressures data of the mixture.9 The remaining interaction parameters were obtained by minimizing the following objective function, OF: N
OF =
2
3−4
∑∑∑ k
j
i
exp calc xijk − xijk exp xijk
a=
∑ ∑ xixjaij i
(4)
j
aij = (aiaj)1/2 [(1 − kij) + (kij − kji)xi]
× 100 (3)
(5)
The two adjustable interaction parameters are kij and kji. The asymmetric definition of the binary interaction parameters (BIP) significantly improves the accuracy in correlating binary data for polar and nonpolar systems. This mixing rule has been improved by SimSci to prevent the advantage of this two BIP
where i, j, and k are, respectively, the component, the phase, and the tie line, Table 6. The quality of the fitting was determined by calculating the relative deviation between experimental and calculated data, Table 7. 3752
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Figure 1. Mutual solubility of the MEG + cycloalkane (cyclohexane, methylcyclohexane, dimethylcyclohexane, and decalin) systems: ●, cycloalkane in MEG at 333.15 K, this work; ○, MEG in cycloalkane at 333.15 K, this work; ×, methylcyclohexane in MEG at 332.35 K, from ref 1; *, MEG in methylcyclohexane at 332.35 K, from ref 1.
Figure 3. Othmer−Tobias correlation of liquid−liquid equilibrium data for the system MEG−water−para-xylene: ◆, at 288.15 K; ■, at 303.15 K; and ▲, at 333.15 K.
Table 6. Binary Interaction Parameters of the NRTL Model i
Figure 2. Mutual solubility of the MEG + aromatic hydrocarbon (benzene, toluene, and para-xylene) systems: ●, para-xylene in MEG at 303.15 K, this work; ○, MEG in para-xylene at 303.15 K, this work; ×, aromatic hydrocarbon (benzene and toluene) in MEG, from ref 2; *, MEG in aromatic hydrocarbon (benzene and toluene), from ref 2.
Table 5. Correlation of LLE Data Using the Othmer−Tobias Correlation a
b
C0ji
CTij
CTji
α0ij
MEG (1) + Water (2) + Cyclohexane (3) −1044.3 1528.8 2.8277 −4.3627 0.2 2844.1 4915.5 −6.3533 −17.679 7609.5 4794.2 −21.148 −23.253 MEG (1) + Water (2) + para-Xylene (3) 1 2 −1044.3 1528.8 2.8277 −4.3627 0.2 1 3 2072.1 3023.8 −0.8445 −5.9590 2 3 5045.7 2988.5 8.1108 −8.8085 MEG (1) + Water (2) + trans-1,2-Dimethylcyclohexane (3) + cis-1,2Dimethylcyclohexane (4) 1 2 −1044.3 1528.8 2.8277 −4.3627 0.2 1 3 4198.5 5273.3 −4.3937 246.40 1 4 4288.0 4476.9 −7.1214 −14.175 2 3 7567.5 4604.2 5.6491 −34.026 2 4 7020.3 3847.6 10.222 −1.3913 3 4 −341.13 329.98 −12.732 10.902 MEG (1) + Water (2) + trans-Decalin (3) + cis-Decalin (4) 1 2 −1044.3 1528.8 2.8277 −4.3627 0.2 1 3 4971.4 5311.4 −4.7580 −19.000 1 4 4715.3 4686.9 −1.3021 −27.794 2 3 8366.5 4320.2 11.215 −6.1339 2 4 7327.0 3668.4 34.030 −7.8207 3 4 −871.74 −147.45 −10.637 57.584 1 1 2
T/K
C0ij
j
σa
MEG + Water + Cyclohexane −10.66 0.087 0.0411 −9.205 −0.030 0.0125 −7.9450 −0.034 0.0757 MEG + Water + para-Xylene 288.15 −8.075 −0.231 0.0273 303.15 −7.452 −0.142 0.0579 333.15 −6.611 −0.157 0.0534 MEG + Water + (cis + trans)-1,2-Dimethylcyclohexane 283.15 −9.845 0.001 0.0011 303.15 −9.136 −0.035 0.0136 333.15 −8.076 −0.065 0.0176 MEG + Water + (cis + trans)-Decalin 283.15 −9.942 0.048 0.0004 303.15 −9.238 −0.009 0.0145 333.15 −8.283 −0.086 0.0057 280.15 303.15 333.15
2 3 3
The mixing rule adopted by SimSci is the following equation, identical to the previous one for binary systems if c12 = 1: ⎛ x ⎞Cij ⎤ i ⎟⎟ ⎥ (1 − kij) + (kij − kji)⎜⎜ ⎥ ⎢ x + x ⎝ i j⎠ ⎦ ⎣ ⎡
1/2 ⎢
aij = (aiaj)
(6)
The interaction parameters are given in Table 8. These parameters have been chosen to match more or less the experimental data but the target was to have a generic value for each family of hydrocarbons, not a perfect match for each component. The parameters kij are temperature dependent:
a
Mean standard deviation between experimental points and values calculated using Othmer−Tobias correlation.
kij = kija +
kijb
+
kijc
(7) T2 The NRTL model presents a satisfactory correlation of the experimental data for the MEG and water in the organic phase with a mean relative deviation between 5 and 19%. Considering
approach to vanish with the dilution of the polar component in a mixture with a large number of components. 3753
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Table 7. Mean Deviations between Experimental and Calculated Mole Fractions, in the Hydrocarbon (II) and Aqueous (I) Phases, with the NRTL Modela
a
Tmin
Tmax
Nx1
280.15
333.15
12
288.15
333.15
283.15
333.15
12 MEG (1) + 12
283.15
333.15
12
Nx2
Nx3
Nx4
ΔxII1 %
ΔxII2 %
MEG (1) + Water (2) + Cyclohexane (3) 12 19.1 14.1 MEG (1) + Water (2) + para-Xylene (3) 9 12 13.5 11.4 Water (2) + trans-1,2-Dimethylcyclohexane (3) + cis-1,2-Dimethylcyclohexane (4) 12 15 15 7.95 6.59 MEG (1) + Water (2) + trans-Decalin (3) + cis-Decalin (4) 12 15 15 14.6 5.48 9
ΔxI3 %
ΔxI4 %
29.7 20.6 26.6
34.6
39.9
39.6
Nxi: number of experimental data points for the compound i.
Table 8. Interaction Parameters of SRKM Model i
kija
j
1 1 2
2 3 3
1 1 2
2 3 3
1 1 1 2 2 3
2 3 4 3 4 4
1 1 1 2 2 3
2 3 4 3 4 4
kjia
kijb
kjib
kijc
kjic
MEG (1) + Water (2) + Cyclohexane (3) −0.1436 −0.0198 22.688 −10.601 0 0 0.35 0 0 0 0 0 0.9392 0.8769 −142.47 −498.18 0 57813 MEG (1) + Water (2) + para-Xylene (3) −0.1436 −0.0198 22.688 −10.601 0 0 0.2 0 0 0 0 0 0.3027 −0.2008 0 0 0 0 MEG (1) + Water (2) + trans-1,2-Dimethylcyclohexane (3) + cis-1,2-Dimethylcyclohexane (4) −0.1436 −0.0198 22.688 −10.601 0 0 0.35 0 0 0 0 0 0.35 0 0 0 0 0 0.445 −0.06 0 0 0 0 0.445 −0.06 0 0 0 0 0 0 0 0 0 0 MEG (1) + Water (2) + trans-Decalin (3) + cis-Decalin (4) −0.1436 −0.0198 22.688 −10.601 0 0 0.35 0 0 0 0 0 0.35 0 0 0 0 0 0.445 −0.06 0 0 0 0 0.445 −0.06 0 0 0 0 0 0 0 0 0 0
Cij
Cji
0.1224 1 1
4.5153 1 1
0.1224 1 1
4.5153 1 1
0.1224 1 1 1 1 1
4.5153 1 1 1 1 1
0.1224 1 1 1 1 1
4.5153 1 1 1 1 1
Table 9. Mean Deviations between Experimental and Calculated Mole Fractions, in the Aqueous (I) and Hydrocarbon (II) Phases, with the SRKM Model Tmin
Tmax
Nx1
280.15
333.15
12
288.15
333.15
283.15
333.15
283.15
333.15
12 MEG (1) + 12 12
Nx2
Nx3
Nx4
ΔxII1 %
ΔxII2 %
MEG (1) + Water (2) + Cyclohexane (3) 12 18.2 96.0 MEG (1) + Water (2) + para-Xylene (3) 9 12 14.9 29.1 Water (2) + trans-1,2-Dimethylcyclohexane (3) + cis-1,2-Dimethylcyclohexane (4) 12 15 15 30.7 34.5 MEG (1) + Water (2) + trans-Decalin (3) + cis-Decalin (4) 12 15 15 16.3 29.2 9
the low solubility of the hydrocarbons in the polar phase, the model still fits well the experimental data as the mean relative deviations range between 20 and 40%, Table 7. The solubility of polar compound in the organic phase is predicted by the SRKM model with a mean relative deviation between 15 and 35%. As for water in the cyclohexane−MEG− water system, the predictions in the aqueous phase are less satisfactory as the mean relative deviation reaches 96%. In the same way, the solubility of the hydrocarbon in the polar phase presents a mean relative deviation between 62 and 172%, Table 9. As mentioned previously, the interaction parameters of the
ΔxI3 %
ΔxI4 %
172.1 62.5 89.4
98.2
92.7
79.5
model were not optimized on the experimental data of each system, but for a family of hydrocarbons, the target having a generic predictive model, the main concern was the solubility of the MEG in the organic phase rather than that one of the hydrocarbons in the aqueous phase.
4. CONCLUSIONS In this work, experimental liquid−liquid equilibrium data for two binary systems (MEG + cyclohexane or para-xylene), two ternary systems, and two quaternary systems were measured at 3754
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three temperatures between 280.15 K and 333.15 K. All systems showed an increasing solubility of water and MEG in the organic phase with temperature. In the same way, the solubility of the hydrocarbons in the polar phase increases with temperature and with the quantity of monoethylene glycol. All data sets are satisfactorily represented by the Othmer−Tobias correlation. The measured data were successfully correlated with the NRTL model. The prediction with the SRKM model is less satisfactory, as the aim is to have a generic value of the interaction parameters for a family of hydrocarbons (and not for each hydrocarbon) and have a more predictive tendency of the model.
■
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
■ ■
ACKNOWLEDGMENTS Acknowledgement is made to Total for the financial support of this research. REFERENCES
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