LiquidâLiquid Equilibria of Binary, Ternary, and Quaternary Systems

Article pubs.acs.org/jced

Liquid−Liquid Equilibria of Binary, Ternary, and Quaternary Systems Involving Monoethylene Glycol, Water, Toluene, p‑Xylene, Hexane, and Octane Ilham Mokbel,*,†,‡ Cécile Lindemann,† Pierre Duchet-Suchaux,§ Freddy Garcia,§ and Jacques Jose† †

Laboratoire des Multimatériaux et Interfaces, UMR 5615, Université de Lyon, Université Claude Bernard Lyon, F-69622 Lyon, France ‡ Université de Lyon, Université Jean Monnet, F-42023 Saint-Etienne, France § TOTAL, 2 Place Jean Millier-La Défense 6, 92400 Courbevoie, France ABSTRACT: To prevent gas hydrate formation and the plugging of the pipe, monoethylene glycol, MEG, is injected into the wellhead. To develop the thermodynamic model for the optimization of MEG injection, liquid−liquid equilibrium, LLE, studies are necessary. In the present work, original data are presented of binary, ternary, and quaternary systems involving MEG, water, hexane, octane, toluene, and p-xylene under atmospheric pressure and in the temperature range between 278.15 and 333.15 K. The NRTL thermodynamic model was used for the solubility prediction of binary, ternary, and quaternary systems. The adjustable parameters of the model were determined through regression of binary mixtures data from literature. Experimental and predicted solubilities are in a quite good agreement, in view of the low solubility data involved in the different systems.

1. INTRODUCTION Several motivations encourage the researcher to study gas hydrates. Two main reasons could be quoted: the potential energy sources of gas hydrates situated in ocean sediments to anticipate the future depletion of gas reserves1,2 and the drawbacks their formation generates to oil and gas industries at the step of production and transportation.3,4 From the different authors who study the formation of gas hydrate, it appears that when water is in contact with oil and with natural gas component, a gas hydrate is formed in the pipeline.3,5−9 Gas hydrates are clathrates (molecular cage constituted of water molecules assembled by hydrogen bonds) less dense than the original crystalline water structure due to the gas molecule that water-ice imprisoned in their cage.10,11 Gas hydrate grows up until it causes the plugging of the pipe. The consequence is a pipe blast due to the pressure rise which can be hazardous for human life or cause severe damage at an economic level.12 To prevent gas hydrate formation, one effective solution is to inject inhibitor such as methanol or monoethylene glycol at the

Table 2. Analytical GC Conditions for the Hydrocarbons and MEG Determination in the hydrocarbonrich phase

compound

CAS No.

purity (mass fraction; Sigma-Aldrich)

107-21-1 110-54-3 111-65-9 108-88-3 106-42-3

0.998 >0.99 0.98 >0.997 >0.99

© XXXX American Chemical Society

analyzed solute

MEG

toluene, hexane

p-xylene, n-octane

internal standard column type column length column i.d. film thickness injector type injection volume detector type carrier gas

n-butylbenzene Supelcowax 10 15 m 0.53 mm 0.50 μm on-column 2 μL FID He, 4.4 mL·min−1

p-xylene FFAP WCOT 25 m 0.32 mm 0.3 μm splitless 1 μL FID He, 70 kPa

n-heptane Porabond 25 m 0.25 mm 3 μm splitless 1 μL FID He, 77 kPa

wellhead to shift the hydrate equilibrium curve toward higher pressure and lower temperature, so that the hydrate-phase stability region is outside the operating conditions of offshore flowlines.13,14 Nowadays, thermodynamic inhibitors are massively injected (10−50 wt %) to avoid plugging risk. The knowledge of MEG concentration and injection rate needs to be improved in order to decrease the prevention cost and due to environmental issues.15,16 Phase equilibrium study is necessary to model gas hydrate formation and dissociation.17

Table 1. Specifications of Chemicals monoethylene glycol n-hexane n-octane toluene p-xylene

in the polar phase

Received: December 19, 2016 Accepted: March 22, 2017

A

DOI: 10.1021/acs.jced.6b01048 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 3. Mutual Solubility Data at P = 101.3 kPa and T = 303.15 K for the Binary Systems Monoethylene Glycol (1) + Toluene or p-Xylene (2) and Water (1) + Toluene or p-Xylene (2) Expressed in Mole Fraction (xi) and Comparison with Literature Dataa x1 in the hydrocarbon-rich phase this work 2.29 × 10−3

1.84 × 10−3 3.48 × 10−3 3.25 × 10−3

+ p-xylene + octane} under atmospheric pressure and in the temperature range between 278.15 and 333.15 K. Literature LLE data of binary systems were correlated using NRTL activity coefficient models in order to determine the binary interaction parameters, Cij, which, in a second step, were used to predict the mutual solubility of the ternary and quaternary systems. Experimental and predicted solubilities are in quite good agreement.

x2 in the polar phase

lit. [ref]

this work

lit. [ref]

Monoethylene Glycol + Toluene 2.54 × 10−3 [21] 2.13 × 10−2 Monoethylene Glycol + p-Xylene 1.86 × 10−3 [18] 1.06 × 10−2 Water + Toluene 2.91 × 10−3 [23] 1.04 × 10−4 Water + p-Xylene 2.71 × 10−3 [24] 3.51 × 10−5 3.01 × 10−3 [25]

2.085 × 10−2 [21] 2.17 × 10−2 [22]

2. EXPERIMENTAL SECTION 2.1. Materials. Monoethylene glycol (i.e., ethane-1,2-diol), n-hexane, n-octane, toluene (i.e., methylbenzene), and p-xylene (i.e., 1,4-dimethylbenzene) were obtained from Sigma-Aldrich. Their purity and CAS number are given in Table 1. Deionized water (conductivity = 18 MΩ·cm) from a Millipore Milli-Q system was used. 2.2. Apparatus and Procedure. The details of the experimental equipment and equilibrium procedure have been presented in our previous works.18−20 Only the most salient information is reported in the present study. Experiments were carried out in a jacketed 300 mL glass cell equipped with a magnetic stirrer. The initial mixtures, prepared by weighting, are stirred for 8 h at the equilibrium temperature and left for 7 h to attain complete phase separation using a Julabo thermostat filled with glycol. Sampling of the two phases was carried out via two preheated lines into an auxiliary solvent: ethanol. An internal standard (for GC analysis) was added in the dilution solvent (ethanol) prior to the sampling. Only the minor compounds of each phase were analyzed.

1.01 × 10−2 [18] 1.17 × 10−4 [23] 2.86 × 10−5 [24] 3.28 × 10−5 [25]

Relative uncertainties: ur(xi) = 0.10 when 10−6 ≤ xi < 10−3; ur(xi) = 0.01 when 10−3 ≤ xi ≤ 10−2; ur(xi) = 0.001 when xi ≥ 0.1. u(T) = 0.1 K, and u(P) = 0.3 kPa.

a

As a continuation of our previous studies,18−20 the present work aims at generating new LLE data. Several mixtures were studied: four binary mixtures {(MEG + toluene), (MEG + p-xylene), (water + toluene), and (water + p-xylene)}; five ternary systems {(MEG + toluene + hexane), (MEG + p-xylene + octane), (MEG + water + toluene), (MEG + water + p-xylene), and (water + toluene + hexane); and two quaternary systems {MEG + water + toluene + hexane} and {MEG + water

Table 4. Experimental Liquid−Liquid Equilibrium Data at P = 101.3 kPa for the Ternary Systemsa polar phase T/K 278.15 303.15 303.15 303.15 333.15

1.02 5.62 1.08 1.56 1.27

× × × × ×

10−2 10−3 10−2 10−2 10−2

288.15 303.15 303.15 303.15 333.15

5.22 2.86 5.79 7.85 7.13

× × × × ×

10−3 10−3 10−3 10−3 10−3

303.15 303.15

3.11 × 10−5 5.74 × 10−5

T/K

hydrocarbon-rich phase x3

x2

x1

303.15 303.15 303.15

0.5352 0.3030 0.0676

303.15 303.15 303.15

0.5364 0.3032 0.0676

x1

Monoethylene Glycol (1) + Toluene (2) + Hexane (3) 8.88 × 10−4 2.30 × 10−4 −3 1.49 × 10 3.45 × 10−4 −3 1.18 × 10 6.65 × 10−4 7.68 × 10−4 1.29 × 10−3 1.71 × 10−3 1.81 × 10−3 Monoethylene Glycol (1) + p-Xylene (2) + Octane (3) 2.25 × 10−4 3.43 × 10−4 3.99 × 10−4 3.54 × 10−4 3.20 × 10−4 6.56 × 10−4 −4 1.75 × 10 1.10 × 10−3 −4 5.09 × 10 1.90 × 10−3 Water (1) + Toluene (2) + Hexane (3) 1.43 × 10−6 9.90 × 10−4 −7 9.88 × 10 1.52 × 10−3 polar phase x2

x3

Monoethylene Glycol (1) + Water (2) + Toluene (3) 0.4609 3.88 × 10−3 0.6960 9.66 × 10−4 0.9322 1.69 × 10−4 Monoethylene Glycol (1) + Water (2) + p-Xylene (3) 0.4619 1.68 × 10−3 0.6963 4.08 × 10−4 0.9323 7.87 × 10−5

x2

x3

0.4831 0.2376 0.4829 0.7363 0.4823

0.5166 0.7620 0.5164 0.2624 0.5158

0.5181 0.2639 0.5179 0.7626 0.5173

0.4815 0.7357 0.4814 0.2361 0.4808

0.2374 0.4825 hyrdocarbon-rich phase

0.7616 0.5159

x1

x2

1.17 × 10−3 5.83 × 10−4 1.27 × 10−4

1.58 × 10−3 2.40 × 10−3 3.27 × 10−3

8.76 × 10−4 4.36 × 10−4 9.24 × 10−5

1.45 × 10−3 2.23 × 10−3 2.89 × 10−3

Relative uncertainties: ur(xi) = 0.20 when 10−8 ≤ xi < 10−6; ur(xi) = 0.10 when 10−6 ≤ xi < 10−3; ur(xi) = 0.01 when 10−3 ≤ xi ≤ 10−2; ur(xi) = 0.001 when xi ≥ 0.1. u(T) = 0.1 K, and u(P) = 0.3 kPa.

a

B



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Table 5. Experimental Liquid−Liquid Equilibrium Data at P = 101.3 kPa for the Quaternary System Monoethylene Glycol (1) + Water (2) + Toluene (3) + Hexane (4) Expressed in Mole Fraction (xi)a polar phase x1

x2

hydrocarbon-rich phase

x3

x4

x1

x2

x3

x4

1.23 × 10−4 6.06 × 10−5 2.48 × 10−5

2.92 × 10−4 4.37 × 10−4 5.26 × 10−4

0.4830 0.4830 0.4830

0.5165 0.5165 0.5164

10−4 10−4 10−3 10−4 10−3 10−3 10−4 10−3 10−3

0.2375 0.4827 0.7359 0.2374 0.4826 0.7358 0.2374 0.4826 0.7356

0.7617 0.5160 0.2623 0.7617 0.5159 0.2622 0.7616 0.5160 0.2621

2.29 × 10−3 2.32 × 10−3 3.04 × 10−3

0.4818 0.4819 0.4818

0.5150 0.5152 0.5150

278.15 K 0.5363 0.3030 0.0677

0.4619 0.6966 0.9322

1.65 × 10−3 3.50 × 10−4 8.17 × 10−5

0.5366 0.5361 0.5357 0.3032 0.3032 0.3031 0.0677 0.0676 0.0676

0.4620 0.4617 0.4613 0.6964 0.6962 0.6961 0.9322 0.9322 0.9322

1.12 2.06 2.91 3.30 5.13 7.67 5.02 9.99 1.31

0.5355 0.3030 0.0676

0.4617 0.6960 0.9322

2.98 × 10−3 8.70 × 10−4 1.50 × 10−4

7.95 × 10−5 7.20 × 10−6 1.61 × 10−6 303.15 K

× × × × × × × × ×

10−3 10−3 10−3 10−4 10−4 10−4 10−5 10−5 10−4

1.83 1.27 8.60 3.79 2.26 1.50 2.64 2.06 1.15

× × × × × × × × ×

10−4 10−4 10−5 10−5 10−5 10−5 10−6 10−6 10−6

1.82 3.80 6.73 9.24 1.96 3.39 2.43 3.61 7.64

× × × × × × × × ×

10−4 10−4 10−4 10−5 10−4 10−4 10−5 10−5 10−5

5.30 8.85 1.05 7.62 1.22 1.65 9.68 1.36 2.21

× × × × × × × × ×

333.15 K 2.39 × 10−4 4.12 × 10−5 2.42 × 10−6

8.55 × 10−4 5.36 × 10−4 1.22 × 10−4

a Relative uncertainties: ur(xi) = 0.10 when 10−6 ≤ xi < 10−3; ur(xi) = 0.01 when 10−3 ≤ xi ≤ 10−2; ur(xi) = 0.001 when xi ≥ 0.1. u(T) = 0.1 K, and u(P) = 0.3 kPa.

Table 6. Experimental Liquid−Liquid Equilibrium Data at P = 101.3 kPa for the Quaternary System Monoethylene Glycol (1) + Water (2) + p-Xylene (3) + Octane (4) Expressed in Mole Fraction (xi)a polar phase

hydrocarbon-rich phase

x1

x2

x3

x4

0.5365 0.3031 0.0676

0.4625 0.6967 0.9323

8.94 × 10−4 1.42 × 10−4 3.15 × 10−5

1.81 × 10−5 1.43 × 10−6 9.25 × 10−8

0.5370 0.5367 0.5366 0.3033 0.3031 0.3032 0.0676 0.0676 0.0676

0.4624 0.4622 0.4621 0.6965 0.6967 0.6964 0.9323 0.9323 0.9323

5.15 1.01 1.28 1.38 1.84 3.40 2.18 3.96 6.83

0.5361 0.3030 0.0676

0.4621 0.6966 0.9323

1.66 × 10−3 3.13 × 10−4 8.46 × 10−5

x1

x2

x3

x4

1.77 × 10−4 9.46 × 10−5 1.55 × 10−5

3.94 × 10−4 5.59 × 10−4 6.73 × 10−4

0.5180 0.5180 0.5180

0.4814 0.4813 0.4813

10−4 10−4 10−3 10−4 10−3 10−3 10−3 10−3 10−3

0.2638 0.5177 0.7622 0.2637 0.5176 0.7620 0.2637 0.5175 0.7618

0.7354 0.4811 0.2361 0.7353 0.4811 0.2361 0.7352 0.4810 0.2360

1.76 × 10−3 2.78 × 10−3 2.94 × 10−3

0.5169 0.5166 0.5167

0.4803 0.4801 0.4802

288.15 K

303.15 K × × × × × × × × ×

10−4 10−3 10−3 10−4 10−4 10−4 10−5 10−5 10−5

3.26 2.76 1.36 4.63 2.30 1.99 3.48 1.35 -

× × × × × × × ×

10−5 10−5 10−5 10−6 10−6 10−6 10−7 10−7

1.83 3.40 5.51 9.40 1.84 2.65 2.94 4.70 6.54

× × × × × × × × ×

10−4 10−4 10−4 10−5 10−4 10−4 10−5 10−5 10−5

5.29 7.74 1.06 8.34 1.11 1.62 1.01 1.36 2.05

× × × × × × × × ×

333.15 K 5.49 × 10−5 5.60 × 10−6 3.46 × 10−7

1.03 × 10−3 5.00 × 10−4 1.06 × 10−4

Relative uncertainties: ur(xi) = 0.20 when 10−8 ≤ xi < 10−6; ur(xi) = 0.10 when 10−6 ≤ xi < 10−3; ur(xi) = 0.01 when 10−3 ≤ xi ≤ 10−2; ur(xi) = 0.001 when xi ≥ 0.1. u(T) = 0.1 K, and u(P) = 0.3 kPa.

a

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. The global uncertainty U was calculated as U2 = U2calibration + 2 U measurement. The interval of confidence of 95% leads to an expanded relative uncertainty, ur, twice the value of the global relative uncertainty: Ur = U/x (x = mole fraction of the hydrocarbon) and ur = 2Ur. The uncertainty on the mole fraction of water determined by Karl Fischer is estimated to be 5%.

With this aim, four analytical methodologies were developed using gas chromatography HP 7890 A, Table 2. The quantity of water in the hydrocarbon-rich phase was determined by Karl Fischer method. 2.3. Calibration, Analysis, and Uncertainties of the Measurements. The gas chromatography was calibrated by analyzing five different standard solutions in the composition range of the studied samples. Three analyzes were performed for each phase sampled three times. The experimental uncertainty of the gas chromatography was less than 3%. The water content in the organic phase was determined using coulometric C



Article

3. RESULTS: DATA CORRELATION AND PREDICTION BY NRTL Experimental data are reported in Tables 3−6. Binary mixtures values are compared with those from literature,18,21−25 Table 3. The agreement is good; mean relative deviation is between 10 and 16% which is tolerable in view of the low measured values (down to 10−5 in mole fraction). In the same way, the ternary system (MEG + water + p-xylene) shows good agreement with literature data,18 Figure 1. No literature data were found to compare with experimental quaternary systems.

polar phase. For both ternary systems, the values of KMEG are very close. In Figure 3, we plotted the solubility of aromatic compounds (benzene, toluene, p-xylene, and ethylbenzene) in the polar

Figure 3. Solubility of aromatic compounds (benzene, toluene, p-xylene, and ethylbenezene) in the polar phase versus the mole fraction of MEG in the polar phase for ternary systems MEG + water + aromatic compound: □, benzene at 298.15 K;21 ●, toluene from this work at 303.15 K; ○, toluene at 298.15 K;21 ▲, p-xylene from this work at 303.15 K; Δ, p-xylene at 303.15 K;18,25 ◊, ethylbenzene at 313.15 K.26 The dotted lines indicate the trend of the hydrocarbons solubility.

Figure 1. Comparison between experimental and literature solubilities18 of MEG + water + p-xylene mixtures at 303.15 K: ○, MEG in the organic phase; ×, water in the organic phase; ◆, p -xylene in the polar phase.

For the two ternary systems MEG + water + aromatic xiorg hydrocarbon, the partition coefficient K i = x aq is determined i and illustrated in Figure 2, where xi represents the mole fraction

Figure 4. Solubility of MEG in the organic phase versus the mole fraction of MEG in the polar phase for MEG + water + aromatic compound: □, benzene at 298.15 K;21 ●, toluene (this work) at 303.15 K ; ○, toluene at 298.15 K;21 ▲, p-xylene (this work) at 303.15 K; Δ, p-xylene at 303.15 K;18 ◇, ethylbenzene at 313.15 K.26 The dotted line indicates the trend of the hydrocarbons solubility. Figure 2. Experimental partition coefficient Ki (i, toluene or p-xylene or MEG) at 303.15 K versus the molar fraction of water in the polar phase for the ternary systems MEG + water + toluene or p-xylene: ●, Ktoluene; ○, Kp‑xylene; Δ, KMEG in toluene; □, KMEG in p-xylene. Plain lines represent the NRTL model for MEG + water + toluene and dotted lines for MEG + water + p-xylene.

phase (MEG + water solutions). Some data are from literature.18,21,25,26 In general terms the data, from literature and those from the present and previous studies carried out in our group,25 are very consistent: ethylbenzene from Riaz et al.26 and p-xylene (the present study) show very close solubility as they are isomers. On the other hand, the solubility of the aromatics in the polar phase reasonably increases from ethylbenzene to benzene through toluene, this trend of course expected due to the increase of the polarity of the aromatic

of toluene, or p-xylene, or MEG. The obtained experimental results for toluene and p-xylene are consistent: Ktoluene is lower than Kp‑xylene due to the lower solubility of the p-xylene in the D



Article

Table 8. Antoine Parametersa of Water, Monoethylene Glycol (MEG), and Their Mixtures, from Reference 29 compd water MEG X1 X1 X1 X1 X1 X1 a

= = = = = =

0.1673 0.2251 0.3246 0.5085 0.6955 0.8982

A

temp range 273.67 ≤ T/K ≤ 363.06 263.59 ≤ T/K ≤ 353.20 Water (1) + MEG 258.29 ≤ T/K ≤ 353.05 258.34 ≤ T/K ≤ 353.07 258.45 ≤ T/K ≤ 353.05 258.42 ≤ T/K ≤ 353.05 258.29 ≤ T/K ≤ 353.05 260.27 ≤ T/K ≤ 363.06

24.058 26.446 (2) 22.708 22.894 23.235 23.486 23.828 23.983

B

C

4319 6640

−28.2 −19.5

4431 4399 4431 4333 4333 4319

−30.4 −30.1 −27.0 −29.4 −30.1 −28.7

Antoine equation: ln(P/Pa) = A − B/((T/K) + C).

Figure 5. Solubilies at 303.15 K of n-alkane in the MEG phase versus mole fraction of toluene in the organic phase for the systems MEG + water + hexane, or heptane, or octane: ●, n-hexane (this work); □, n-heptane;27 Δ, n-octane.28 The dotted lines indicate the trend of the hydrocarbons solubility.

compound (or in other words, due to the decrease of the hydrophobicity of the hydrocarbons). In the same way, the solubility of MEG in the organic phase (MEG + water + benzene, or toluene, or p-xylene, or ethylbenzene) versus the mole fraction of MEG in the polar phase is reported in Figure 4. MEG solubilities do not substantially vary with each of the aromatic hydrocarbons except for ethylbenzene.26 A higher solubility of the MEG in the organic phase is observed which cannot be explained either by a measurement at higher temperature (313.15 K instead of 303.15 or 298.15 K for the rest of the hydrocarbons) or by its configuration very similar to p-xylene. We conclude that the solubility of MEG in ethylbenzene is not reliable. Figure 5 represents the solubility of the aliphatic hydrocarbon (hexane, heptane, and octane) in the ternary systems MEG + toluene + aliphatic hydrocabons versus the mole fraction of toluene. If Haghnazarloo et al.27 solubilities for heptane appear coherent because they are lower than those of hexane (from the present study), this is not the case for octane measured by Mohsen-Nia et al.28 where the solubilities increase and exceed those of hexane which is abnormal.

Figure 6. Comparison between experimental and NRTL predicted mole fraction of p-xylene in the polar phase involved in the binary, ternary, and quaternary systems: ○, at 288.15 K; ●, at 303.15 K; Δ, at 333.15 K.

NRTL model has proven to adequately correlate multicomponent LLE data. In the present work we see how the model predicts solubility data of binary, ternary, and quaternary systems using interaction parameters, BIPs, estimated from literature data of binary mixtures. By following this predictive approach, we can also check the good coherence between binary, ternary, and quaternary data as the same adjustable parameters

Table 7. Binary Interaction Parameters, BIPs, Obtained from NRTL Correlation of Literature Dataa VLE ref

binary

C120 (J·mol‑1)

C210 (J·mol‑1)

C12T (J·K‑1·mol‑1)

C21T (J·K‑1·mol‑1)

α120

Δy1 (%)

Δy2 (%)

29 30 30

MEG (1) + water (2) toluene (1) + hexane (2) p-xylene (1) + octane (2)

−4372.3 615.50 −1634.2

6400.8 1927.7 −243.56

11.839 54.110 12.533

−18.266 −57.790 7.7669

0.2 0.2 0.2

12 0.7 0.7

0.2 0.3 0.5

C120 (J·mol‑1)

C210 (J·mol‑1)

C12T (J·K‑1·mol‑1)

C21T (J·K‑1·mol‑1)

α120

ΔxII1 (%)

ΔxI2 (%)

5282.5 11838 6935.0 14803 17433 24891 20065 31289

12915 19603 13132 18808 12288 14538 11712 15042

8.8609 −5.0480 10.683 −3.8632 36.718 60.734 46.161 81.617

−43.731 −72.423 −41.829 −57.217 −51.584 −52.507 −27.533 −34.369

0.2 0.2 0.2 0.2 0.2 0.15 0.2 0.15

4.9 1.1 0.1 4.7 3.1 4.5 0.9 9.8

0.7 0.4 0.1 5.2 3.6 1.8 1.9 4.8

LLE ref 21 19 18 19 23 19 25 19 a

Δxi =

binary MEG MEG MEG MEG water water water water

(1) (1) (1) (1) (1) (1) (1) (1)

+ + + + + + + +

toluene (2) hexane (2) p-xylene (2) octane (2) toluene (2) hexane (2) p-xylene (2) octane (2)

exp calc 1 N |x − x | ∑ i i x exp i , N 1 i

Δyi =

calc exp 1 Ni |yi − yi | ∑ , exp 1 N yi

and N is the number of experimental data points for compound i. E



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Figure 9. Predicted (NRTL) mole fraction of water in the organic phase as a function of the experimental mole fraction for the MEG + water + p-xylene + octane system: ○, at 288.15 K; ●, at 303.15 K; Δ, at 333.15 K.

Figure 7. Predicted (NRTL) mole fraction of n-octane in the polar phase in function of the experimental mole fraction for the MEG + water + p-xylene + octane system: ○, at 288.15 K; ●, at 303.15 K; Δ, at 333.15 K.

Table 9. Comparison between Experimental and Predicted Mole Fraction, Δxi, in the Polar (I) and Hydrocarbon(II) Phasesa Tmin−Tmax

N

ΔxII1 (%)

ΔxII2 (%)

ΔxI3 (%)

MEG (1) + Toluene (3) 1 11 1.7 MEG (1) + p-Xylene (3) 303.15 K 1 1.0 4.8 Water (2) + Toluene (3) 303.15 K 1 20 1.2 Water (2) + p-Xylene (3) 303.15 K 1 7.4 6.6 MEG (1) + Toluene (3) + Hexane (4) 278.15−333.15 K 5 17 13 MEG (1) + p-Xylene (3) + Octane (4) 288.15−333.15 K 5 15 23 Water (2) + Toluene (3) + Hexane (4) 303.15 K 2 14 24 MEG (1) + Water (2) + Toluene (3) 303.15 K 3 29 19 63 MEG (1) + water (2) + p-Xylene (3) 303.15 K 3 29 4 63 MEG (1) + water (2) + toluene (3) + hexane (4) 278.15−333.15 K 15 27 21 79 MEG (1) + water (2) + p-Xylene (3) + Octane (4) 288.15−333.15 K 15 28 12 38

ΔxI4 (%)

303.15 K

Figure 8. Predicted (NRTL) mole fraction of MEG in the organic phase in function of the experimental mole fraction for the MEG + water + p-xylene + octane system: ○, at 288.15 K; ●, at 303.15 K; Δ, at 333.15 K.

are used in all cases. Below we explain how we got into the different steps. 3.1. Correlation of Literature Data Using NRTL. In Table 7, we listed the experimental data (LLE and VLE) of binary systems available in literature.18,19,21,23,25,29,30 Antoine parameters of {water + MEG} systems, obtained from our previous work,29 are reported in Table 8. All these data were correlated using the NRTL activity coefficient model with temperature-dependent parameter: τij =

a

Δxi =

CTij

N

2

2

∑∑∑ k

j

i

exp calc xijk − xijk exp xijk

39

40 25

and N is the number of experimental data

where i, j, and k are respectively the component, the phase, and the tie line. Estimated BIP from correlation are reported in Table 7. 3.2. Solubility Prediction Using NRTL. As explained previously, the adjustable parameters of the NRTL model (BIP) were determined through regression of binary mixtures data from literature. In a second step, the BIPs were used to predict solubility data in order to compare with those determined experimentally. The model provides results that are consistent with the entire experimental data (binary, ternary, and quaternary systems), Figures 6−9 and Table 9. The NRTL

Cij0 + CijT(T − 273.15)

OF =

19

points for compound i.

(1) RT and are the binary parameters of NRTL model. The nonrandomness parameter αij is assumed to be constant and set at 0.2 or 0.15. BIPs were calculated from minimizing the objective function (OF):

C0ij

exp calc Ni |xi − xi | 1 ∑ exp 1 N xi

10

× 100 (2) F



Article

(12) Sloan, E. D., Jr. Hydrate Engineering, Digital Edition.; Society of Petroleum Engineers: Richardson, TX, USA, 2000. (13) Lee, J. W.; Kang, S. E. Phase Equilibria of Natural Gas Hydrates in the Presence of Methanol, Ethylene Glycol, and NaCl Aqueous Solutions. Ind. Eng. Chem. Res. 2011, 50, 8750−8755. (14) Cha, M.; Shin, K.; Kim, J.; Chang, D.; Seo, Y.; Lee, H.; Kang, S. P. Thermodynamic and kinetic hydrate inhibition performance of aqueous ethylene glycol solutions for natural gas. Chem. Eng. Sci. 2013, 99, 184−190. (15) Sloan, E. D. A changing hydrate paradigm−from apprehension to avoidance to risk management. Fluid Phase Equilib. 2005, 228-229, 67−74. (16) Li, X. S.; Xu, C. G.; Zhang, Y.; Ruan, X. K.; Li, G.; Wang, Y. Investigation into gas production from natural gas hydrate: A review. Appl. Energy 2016, 172, 286−322. (17) Anderson, F. E.; Prausnitz, J. M. Inhibition of gas hydrate by methanol. AIChE J. 1986, 32, 1321−1333. (18) Lindemann, C.; Duchet-Suchaux, P.; Abou Naccoul, R.; Mokbel, I.; Malicet, V.; Jose, J. Liquid-Liquid Equilibria at Three Temperatures (between 280.15 and 333.15 K) of Binary, Ternary and Quaternary Systems Involving Monoethylene Glycol, Water, Cyclohexane, paraXylene, trans- and cis-Dimethylcyclohexane, and trans- and cis-Decahydronaphthalene. J. Chem. Eng. Data 2014, 59, 3749−3755. (19) Mokbel, I.; Lindemann, C.; Duchet-Suchaux, P.; Jose, J. Liquid− liquid equilibria of binary and ternary systems involving monoethyleneglycol, water, n-alkanes at three temperatures: 283.15, 303.15 and 333.15 K. Fuel 2016, 163, 17−24. (20) Razzouk, A.; Naccoul, R. A.; Mokbel, I.; Duchet-Suchaux, P.; Jose, J.; Rauzy, E.; Berro, C. Liquid-Liquid Equilibria for Monoethyleneglycol + Hexane and 2,2,4-Trimethylpentane, Water + Hexane and 2,2,4-Trimethylpentane, Monoethyleneglycol + Water + Hexane, and Monoethyleneglycol + Water + 2,2,4-Trimethylpentane in the Temperature Range between T = 283.15 K and T = 323.15 K. J. Chem. Eng. Data 2010, 55, 1468−1472. (21) Folas, G. K.; Kontogeorgis, G. M.; Michelsen, M. L.; Stenby, E. H.; Solbraa, E. Liquid-Liquid Equilibria for Binary and Ternary Systems Containing Glycols, Aromatic Hydrocarbons, and Water: Experimental Measurements and Modeling with the CPA EoS. J. Chem. Eng. Data 2006, 51, 977−983. (22) Rehák, K.; Dreiseitlová, J. Binary liquid-liquid equilibrium in systems containing monofunctional benzene derivates and 1,2ethanediol. Fluid Phase Equilib. 2006, 249, 104−108. (23) Chen, H.; Wagner, J. An Efficient and Reliable Gas Chromatographic Method for Measuring Liquid-Liquid Mutual Solubilities in Alkylbenzene + Water Mixtures: Toluene + Water from 303 to 373 K. J. Chem. Eng. Data 1994, 39, 475−479. (24) Chen, H.; Wagner, J. Mutual Solubilities of Alkylbenzene + Water Systems at Temperatures from 303 to 373 K: Ethylbenzene, p-Xylene, 1,3,5-Trimethylbenzene, and Butylbenzene. J. Chem. Eng. Data 1994, 39, 679−684. (25) Bassil, G.; Mokbel, I.; Abou Naccoul, R.; Stephan, J.; Jose, J.; Goutaudier, C. Tar removal from biosyngas in the biomass gasification process. (Liquid + liquid) equilibrium {water + solvent (paraxylene and methyl hexadecanoate) + model molecules of tar (benzene, toluene, phenol)}, J. Chem. J. Chem. Thermodyn. 2012, 48, 123−128. (26) Riaz, M.; Yussuf, M. A.; Kontogeorgis, G. M.; Stenby, E. H.; Yan, W.; Solbraa, E. Distribution of MEG and methanol in welldefined hydrocarbon and water systems: Experimental measurement and modeling using the CPA EoS. Fluid Phase Equilib. 2013, 337, 298−310. (27) Haghnazarloo, H.; Lotfollahi, M. N.; Mahmoudi, J.; Asl, A. H. Liquid−liquid equilibria for ternary systems of (ethylene glycol + toluene + heptane) at temperatures (303.15, 308.15, and 313.15) K and atmospheric pressure: Experimental results and correlation with UNIQUAC and NRTL models. J. Chem. Thermodyn. 2013, 60, 126− 131. (28) Mohsen-Nia, M.; Mohammad Doulabi, F. S.; Manousiouthakis, V. I. (Liquid + liquid) equilibria for ternary mixtures of (ethylene

model satisfactorily restitutes the experimental Ki of the two ternary systems, Figure 2.

4. CONCLUSION We reported original solubility data (between 10−2 and 10−7 in mole fraction) of several hydrocarbons (toluene, p-xylene, hexane, and octane) systems in monoethylene glycol/water media. The prediction of ternary and quaternary LLE using BIP from literature data is known to be difficult but the results provided by NRTL are quite good considering the low solubility values to be determined. Obviously the predicted values for the binary systems are in very good agreement with the experimental points. The LLE data presented in this work can be used to study hydrate thermodynamic inhibition thanks to process simulation software.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Ilham Mokbel: 0000-0003-2384-900X Notes

The authors declare no competing financial interest. Funding

Acknowledgement is made to Total SA for the financial support of this research.

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REFERENCES

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Article

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