LiquidâLiquid Equilibria in Ternary and Quaternary Systems Present

Article pubs.acs.org/jced

Liquid−Liquid Equilibria in Ternary and Quaternary Systems Present in Biodiesel Production from Soybean Oil at (298.2 and 333.2) K Alex Barreto Machado,† Yurany Camacho Ardila, Leonardo Hadlich de Oliveira, Martín Aznar, and Maria Regina Wolf Maciel* School of Chemical Engineering, University of Campinas, Av. Albert Einstein 500, CEP 13083-852, Campinas-SP, Brazil ABSTRACT: Liquid−liquid equilibrium (LLE) data for soybean oil biodiesel (BIO-SO) + ethanol + glycerol and BIO-SO + ethanol + glycerol + sodium hydroxide systems at (298.2 and 333.2) K and atmospheric pressure (≈ 95 kPa) were determined by gas chromatography and potentiometric titration. These systems occur in the biodiesel production process and present a biodiesel-rich (upper layer) and a glycerolrich phase (bottom layer). The influence of temperature and NaOH in ethanol partition coefficient (K) and biodiesel selectivity (S) was studied. Results show that ethanol distributes preferably to the glycerol-rich phase and that biodiesel solubilizes more ethanol than glycerol. Increasing the temperature by 35 K causes an increase in K and S. Adding 1 wt % of NaOH in the system does not affect K but enhances S at 298.2 K and diminishes it at 333.2 K. The nonrandom two-liquid (NRTL) model was used for correlation LLE experimental data, presenting a root-mean-square deviation equal to 1.6 % for both ternary and quaternary systems. Data were submitted to the Ishida test, giving R2 > 0.96 for all systems. In a previous paper,19 the authors have studied the solubility curves systems of soybean oil or castor oil biodiesel + ethanol + glycerol at different temperatures, but without determining tie lines or LLE data. This work is part of a more ample study in that LLE data for ternary and quaternary systems are studied using the products/ reagents of soybean and castor oil transesterification reaction: biodiesel, ethanol, glycerol, water, and NaOH. Here, ternary LLE data for soybean oil biodiesel (BIO-SO) + ethanol + glycerol and quaternary LLE data for BIO-SO + ethanol + glycerol + NaOH systems at T = 298.2 K and T = 333.2 K and atmospheric pressure (≈ 95 kPa) were obtained. This data can complement the work of Liu et al.12 The distribution of ethanol and the biodiesel selectivity were calculated, to investigate their behavior in real industrial biodiesel purification processes. The LLE data were correlated with the nonrandom two-liquid (NRTL) local composition model.

1. INTRODUCTION It is well-known that biodiesel represents a complement and a future alternative for petroleum diesel fuel. In consequence of that, the environmental emission of pollutants such as SOx, CO, and CO2 can be reduced.1 Biodiesel consists of a mixture of alkyl esters of fatty acids, which can be obtained from biomass sources, such as oleaginous seeds and animal fats. Regarding the oleaginous seeds, soybean oil is the raw material most used for biodiesel production in Brazil and United States.2−4 Other oils obtained from oleaginous seeds are also used, such as castor, rapeseed, canola, sunflower, and palm oil.4 In biodiesel manufacturing, the transesterification of triacylglycerol by an alcohol produces a mixture of alkyl esters of straight chain fatty acids and glycerol and water as byproducts. At the end, the system separates into two phases. Methanol has been the most commonly used alcohol to perform transesterification reactions,5,6 but ethanol has received much attention in the last decade, because it is obtained from biomass7 and provides a totally renewable alternative for biodiesel production. In the end of biodiesel production reaction, a heterogeneous liquid mixture is formed. So, the knowledge of liquid−liquid equilibrium (LLE) data is useful for understanding the steps of purification and separation of biodiesel-rich phases from glycerol-rich phases. In literature, LLE data for biodiesel or fatty acid esters + alcohol + glycerol systems have been reported by Komers et al.,8 Zhou et al.,9 Negi et al.,10 Andreatta et al.,11 Liu et al.,12 Tizvar et al.,13 França et al.,14 Barreau et al.,15 and Follegatti-Romero et al.16 LLE data with ethanolysis reagents were determined by Lanza et al.17 The distribution of alcohol in biodiesel systems was reported by Felice et al.18 © 2012 American Chemical Society

2. EXPERIMENTAL SECTION 2.1. Chemicals. Soybean oil biodiesel was produced, separated, and purified according to a previous work,19 which also presents its properties and characteristics. Ethanol (purity 0.995), glycerol (purity 0.995), and NaOH (purity 0.97) were purchased from Synth. 2.2. Procedure. Liquid−liquid equilibrium experiments were performed as in our previous work.20 Received: November 28, 2011 Accepted: March 22, 2012 Published: April 17, 2012 1417

dx.doi.org/10.1021/je201243u | J. Chem. Eng. Data 2012, 57, 1417−1422

Journal of Chemical & Engineering Data

Article

The agitation and separation times were used according to that reported by some works,10,21,22 and preliminary experiments showed that they are enough to ensure equilibrium. The mass fractions of biodiesel and glycerol were determined using calibration curves presented in Table 1. Biodiesel Table 1. Mass Fraction (w) versus Peak Area (A) Calibration Curves component

R2 a

calibration curve

glycerol (glycerol-rich phase) glycerol (biodiesel-rich phase) ethyl palmitate ethyl oleate ethyl linoleate ethyl linolenate ethyl ricinolenate

w w w w w w w

= = = = = = =

−8

4.2078·10 2.9191·10−8 9.9949·10−8 9.4972·10−9 9.2430·10−9 9.5324·10−9 1.0000·10−8

A A A A A A A

+ + + + + + +

−4

6.7606·10 6.8734·10−3 4.2000·10−8 4.8000·10−5 1.7200·10−4 4.1400·10−5 6.0000·10−5

0.9991 0.9997 0.9986 0.9997 0.9991 0.9997 0.9995

a 2

R : linear correlation coefficient.

considered here is a pseudocomponent formed mainly by four ethyl esters: ethyl linoleate (mass fraction = 0.5555), ethyl oleate (0.2595), ethyl palmitate (0.1233), and ethyl linolenate (0.0617).19 The mass fraction of NaOH was measured by potentiometric titration using a Metrohm, model 809 Titrando, potentiometric titrator coupled with Tiamo software. The ethanol mass fractio n was obtained by the difference.

Figure 1. Experimental and calculated LLE data for BIO-SO + ethanol + glycerol system at T = 298.2 K: ■, cloud points of previous work;19 ●, feed points; ▲, experimental tie lines; ○- - -, NRTL calculated tie lines; ···, NRTL calculated binodal curve; *, NRTL calculated plait point.

3. THERMODYNAMIC CORRELATION The NRTL22 was used to correlate the experimental data. The authors choose this model because of its mathematical simplicity concerning the physical character of the solution. As example, the biodiesel or NaOH can be treated as one component. The authors expect that NRTL to be useful only for correlation. NRTL is given by eqs 1 to 3. ⎡ ⎤ ∑k xk τkjGki ⎥ ⎢ +∑ τij − ln γi = ∑k Gkixk ∑k Gkjxk ⎢⎢ ∑k Gkjxk ⎥⎥ j ⎣ ⎦ ∑j τjiGjixj

xjGij

(1)

τij =

Δgij RT

= A ij +

Gij = exp( −αijτij)

Bij T

(τij ≠ τji) (αij = αji)

(2) Figure 2. Experimental and calculated LLE data for the BIO-SO + ethanol + glycerol system at T = 333.2 K: ●, feed points; ▲, experimental tie lines; ○···, NRTL calculated tie lines.

(3)

where i, j, and k refer to each component; γ is the activity coefficient; τij and τji are related to the characteristic energy of interaction between the molecules of type i and j; Gij is a Boltzmann-type expression for the local composition energy interactions between i and j; x is the mole fraction; Aij and Bij are the binary interaction parameters, and αij is the nonrandomness parameter. The energy interaction parameters were estimated using the same procedure and equations of our previous work.20

ethanol, and glycerol mass fraction were found to be less than 10−4; for NaOH mass fractions, less than 5.7·10−3 for glycerolrich phase and 8.8·10−5 for biodiesel-rich phase. In Figures 2 and 4 the LLE data for quaternary systems are shown in free basis of NaOH, where each component mass fraction was calculated by eq 4.

4. RESULTS AND DISCUSSION 4.1. LLE Data. LLE data obtained for ternary BIO-SO (1) + ethanol (2) + glycerol (3) and quaternary BIO-SO (1) + ethanol (2) + glycerol (3) + NaOH (4) at (298.2 and 333.2) K and atmospheric pressure (≈ 95 kPa) are shown in Figures 1 to 4 and reported in Tables 2 and 3. The uncertainties for BIO-SO,

w′ j =

wi 1 − w4

(4)

In eq 4, i refers to components 1, 2, 3, and 4; j refers to components 1, 2, and 3; w′i is the ternary system mass fraction in free basis of NaOH (w4); wi is the quaternary system mass fraction. 1418



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The superscripts bio and gly refer to the biodiesel-rich phase and glycerol-rich phase, respectively. Figure 5 shows the ethanol distribution coefficient as a function of ethanol mass fraction in the glycerol-rich phase. It can be verified that a temperature increase by 35 K causes an increase of 0.1 in ethanol distribution for both ternary and quaternary systems studied. Also, the K profile is changed: at 298.2 K, K increases with ethanol composition, but at T = 333.2 K, it remains practically constant (approximately equal to 0.46). The presence of 0.01 of NaOH in the feed composition does not affect significantly the K profile for both temperatures. For all systems the K values are below 0.48, which means that ethanol solubilizes preferably in the glycerol-rich phase. Also, this behavior can be explained by the predominance of long chain ester linolenate molecules in biodiesel, which probably has a low affinity for ethanol. The selectivity of biodiesel gives its preference to solubilize ethanol (the solute) or glycerol (the diluent). Here all systems presented S values greater than 6, as shown in Figure 6. For ternary systems, increasing the temperature from (298.2 to 333.2) K gives an increase of S greater than 4 units; for quaternary systems, S increases by 5 units, as verified for an ethanol mass fraction lower than 0.25. The addition of NaOH enhances the selectivity of biodiesel at 298.2 K, which means that it solubilizes less glycerol by the presence of NaOH. However at 333.2 K, an opposite trend is observed, giving lower values of selectivity by the presence of NaOH. All systems present a similar S profile: increasing the ethanol mass fraction in glycerol-rich phase gives a decrease in selectivity of biodiesel. This probably occurs because the presence of ethanol in glycerol-rich phase enhances the solubility of this phase in biodiesel-rich phase, which solubilizes an amount of glycerol together with ethanol (acting as a glycerol carrier), diminishing the S value. LLE data reported here were tested by two methods: (a) the agreement of tie lines with the feed composition, indicating low experimental error by loss of mass or analysis; and (b) submitting LLE data to Ishida23 correlation, eq 7, once there is no thermodynamic consistency equation to submit LLE data.

Figure 3. Experimental and calculated LLE data for the BIO-SO + ethanol + glycerol system at T = 298.2 K in free basis of NaOH catalyst: ●, feed points; ▲, experimental tie lines; ○···, NRTL calculated tie lines.

⎛ gly bio ⎞ ⎛ gly bio ⎞ w · w2 ⎟ w ·w3 ⎟ log⎜ 1 = a log⎜ 1 +b ⎜ bio gly ⎟ ⎜ bio gly ⎟ ⎝ w1 ·w2 ⎠ ⎝ w1 ·w3 ⎠

Figure 4. Experimental and calculated LLE data for BIO-SO + ethanol + glycerol system at T = 333.2 K in free basis of NaOH catalyst: ●, feed points; ▲, experimental tie lines; ○···, NRTL calculated tie lines.

In eq 7 a is the angular coefficient, while b is the linear coefficient. The standard deviations for the correlation were calculated with eq 8.

The study of ethanol phase distribution was made by the solute partition coefficient (K) given by eq 5. K=

w2bio

σ=

gly

w2

(5)

gly

gly

∑

d−p

(8)

where d is the number of data points and p the number of parameters. R2 > 0.96 and σ < 0.0453 were achieved for all systems, as presented in Table 4 and Figure 7. 4.2. NRTL Parameters. The NTRL model was used considering biodiesel as a pseudocomponent, and its molecular mass was estimated through the weighted arithmetic mean of the constituent esters molecular masses. The same value of biodiesel

w2bio/w2 w3bio/w3

d (F − F )2 exp calc i i

The relationship of ethanol/glycerol solubility in biodieselrich phase was made by solvent selectivity (S), given by eq 6. S=

(7)

(6) 1419



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Table 2. LLE Data in Mass Fraction (w), Ethanol Partition Coefficients (K), and Biodiesel Selectivities (S) for BIO-SO (1) + Ethanol (2) + Glycerol (3)a at T = 298.2 K and T = 333.2 K LLE feed

glycerol-rich phase

T/K

w1

w2

w1

w2

w1

w2

K

S

298.2

0.1617 0.3542 0.3899 0.5191 0.3996 0.3005 0.5331 0.4863 0.4416

0.1532 0.2207 0.2745 0.2717 0.2008 0.3017 0.2688 0.3144 0.3654

0.9269 0.8818 0.8423 0.8165 0.8531 0.8058 0.787 0.7510 0.7196

0.0514 0.0926 0.1324 0.1614 0.1283 0.1753 0.1934 0.2281 0.2566

0.0025 0.0039 0.0084 0.0140 0.0066 0.0056 0.0077 0.0128 0.0207

0.1726 0.2966 0.3915 0.4428 0.2682 0.3902 0.4334 0.4817 0.5329

0.30 0.31 0.34 0.36 0.48 0.45 0.45 0.47 0.48

11.32 8.53 8.02 8.96 18.65 14.36 12.72 11.45 9.03

333.2

a

biodiesel-rich phase

w3 = 1 − w1 − w2.

Table 3. LLE Data in Mass Fraction (w), Ethanol Partition Coefficients (K), and Biodiesel Selectivities (S) for BIO-SO (1) + Ethanol (2) + Glycerol (3) + NaOH (4)a at T = 298.2 K and T = 333.2 K LLE data feed

glycerol-rich phase

w1

w2

w3

w1

w2

w3

w1

w2

w3

K

S

298.2

0.3156 0.3316 0.3571 0.4677 0.4203 0.3509 0.2901 0.5385 0.1798

0.1332 0.1977 0.2386 0.2974 0.1692 0.2678 0.2998 0.2521 0.4686

0.5512 0.4599 0.3940 0.2235 0.4004 0.3713 0.4001 0.1994 0.3416

0.9271 0.9029 0.8807 0.7916 0.8819 0.8283 0.8144 0.7819 0.7182

0.0517 0.0789 0.1018 0.1837 0.1012 0.1519 0.1644 0.1908 0.2483

0.0206 0.0177 0.0172 0.0231 0.0169 0.0196 0.0210 0.0271 0.0330

0.0057 0.0038 0.0103 0.0145 0.0047 0.0046 0.0046 0.0055 0.0337

0.1705 0.2612 0.3329 0.4503 0.2314 0.3450 0.3650 0.4055 0.5220

0.8083 0.7143 0.6393 0.5139 0.7475 0.6248 0.6095 0.5649 0.4314

0.30 0.30 0.31 0.41 0.44 0.44 0.45 0.47 0.48

11.90 12.19 11.37 9.08 19.34 14.04 13.07 9.81 6.22

333.2

a

biodiesel-rich phase

T/K

w4 = 1 − w1 − w2 − w3.

Figure 5. Ethanol partition coefficient, K, as a function of ethanol mass fraction in the glycerol-rich phase, w2gly: ■, ternary system at T = 298.2 K; □···, ternary system at T = 333.2 K; ●, quaternary system at T = 298.2 K; ○···, quaternary system at T = 333.2 K.

Figure 6. Biodiesel selectivity, S, as a function of ethanol mass fraction in glycerol-rich phase, w2gly: ■, ternary system at T = 298.2 K; □···, ternary system at T = 333.2 K; ●, quaternary system at T = 298.2 K; ○···, quaternary system at T = 333.2 K.

weighted molecular mass fraction was detected experimentally in both phases, indicating that the constituent esters present an equal distribution. Table 5 presents 12 parameters to correlate the total of 33 tie lines: 18 tie lines presented in Tables 2 and 3 and 15 tie

lines presented in the work of Liu et al.12 The calculated tie lines are shown in Figures 1 to 4. The model does not correlate the experimental data well, presenting a percent root-mean-square deviation equal to 0.016 for all systems studied here. 1420



■

Table 4. Ishida Equation Coefficients (a, b), Linear Correlation Coefficient (R2), and Standard Deviations (σ) for Systems Studied in This Work T/K 298.2 333.2 298.2 333.2

a

*Tel.: +55 19 3521 3957. E-mail: [email protected]. Funding

BIO-SO (1) + Ethanol (2) + Glycerol (3) 0.8939 1.3277 0.9801 0.1288 0.7084 0.2992 0.9686 0.1095 BIO-SO (1) + Ethanol (2) + Glycerol (3) + NaOH (4) 0.8578 1.2283 0.9957 0.0507 0.7031 0.0909 0.9722 0.1609

The financial support from Brazilian agency FAPESP is gratefully acknowledged. Notes

The authors declare no competing financial interest. † E-mail: [email protected].

■

Table 5. Estimated Binary NRTL Parameters (A, B) for Systems Studied Here: BIO-SO (1), Ethanol (2), Glycerol (3), and NaOH (4)a i

j

Aij

Aji

2 3 4 3 4 4

−359.14 721.41 4999.8 1225.3 −1.9428 −1994.0

1195.9 3522.1 −420.85 −413.43 4999.6 1108.4

REFERENCES

(1) Conceiçaõ , M. M.; Fernandes, V. J. Jr.; Araújo, A. S.; Farias, M. F.; Santos, I. M. G.; Souza, A. G. Thermal and Oxidative Degradation of Castor Oil Biodiesel. Energy Fuels 2007, 21, 1522− 1527. (2) Nogueira, C. A.; Feitosa, F. X.; Fernandes, F. A. N.; Santiago, R. S.; de Sant'Ana, H. B. Densities and Viscosities of Binary Mixtures of Babassu Biodiesel + Cotton Seed or Soybean Biodiesel at Different Temperatures. J. Chem. Eng. Data 2010, 55, 5305−5310. (3) Jung, H.; Kittelson, D. B.; Zachariah, M. R. Characteristics of SME Biodiesel-Fueled Diesel Particle Emissions and the Kinetics of Oxidation. Environ. Sci. Technol. 2006, 40, 4949−4955. (4) Lin, L.; Cunshan, Z.; Vittayapadung, S.; Xiangqian, S.; Mingdong, D. Opportunities and challenges for biodiesel fuel. Appl. Energy 2010, 88, 1020−1031. (5) Fukuda, H.; Kondo, A.; Noda, H. J. Biodiesel fuel production by transesterification of oils. J. Biosci. Bioeng. 2001, 92, 405−416. (6) Berchmans, H. J.; Hirata, S. Biodiesel production from crude Jatropha curcas L. seed oil with a high content of free fatty acids. Bioresour. Technol. 2008, 99, 1716−1721. (7) Zhang, S.; Maréchal, F.; Gassner, M.; Périn-Levasseur, Z.; Qi, W.; Ren, Z.; Yan, Y.; Favrat, D. Process Modeling and Integration of Fuel Ethanol Production from Lignocellulosic Biomass Based on Double Acid Hydrolysis. Energy Fuels 2009, 23, 1759−1765. (8) Komers, K.; Tichý, J.; Skopal, F. Ternäres Phasendiagramm Biodiesel-Methanol-Glyzerin. J. Prakt. Chem. 1995, 337, 328−331. (9) Zhou, H.; Lu, H.; Liang, B. Solubility of Multicomponent Systems in the Biodiesel Production by Transesterification of Jatropha curcas L. Oil with Methanol. J. Chem. Eng. Data 2006, 51, 1130−1135. (10) Negi, D. S.; Sobotka, F.; Kimmel, T.; Wozny, G.; Schomäcker, R. Liquid−Liquid Phase Equilibrium in Glycerol−Methanol−Methyl Oleate and Glycerol−Monoolein−Methyl Oleate Ternary Systems. Ind. Eng. Chem. Res. 2006, 45, 3693−3696. (11) Andreatta, A. E.; Casás, L. M.; Hegel, P.; Bottini, S. B.; Brignole, E. A. Phase Equilibria in Ternary Mixtures of Methyl Oleate, Glycerol, and Methanol. Ind. Eng. Chem. Res. 2008, 47, 5157−5164. (12) Liu, X.; Piao, X.; Wang, Y.; Zhu, S. Liquid−Liquid Equilibrium for Systems of (Fatty Acid Ethyl Esters + Ethanol + Soybean Oil and Fatty Acid Ethyl Esters + Ethanol + Glycerol). J. Chem. Eng. Data 2008, 53, 359−362. (13) Tizvar, R.; McLean, D. D.; Kates, M.; Dubé, M. A. Optimal Separation of Glycerol and Methyl Oleate via Liquid−Liquid Extraction. J. Chem. Eng. Data 2009, 54, 1541−1550. (14) França, B. B.; Pinto, F. M.; Pessoa, F. L. P.; Uller, A. M. C. Liquid−Liquid Equilibria for Castor Oil Biodiesel + Glycerol + Alcohol. J. Chem. Eng. Data 2009, 54, 2359−2364. (15) Barreau, A.; Brunella, I.; Hemptinne, J.-C.; Coupard, V.; Canet, X.; Rivollet, F. Measurements of Liquid−Liquid Equilibria for a Methanol + Glycerol + Methyl Oleate System and Prediction Using Group Contribution Statistical Associating Fluid Theory. Ind. Eng. Chem. Res. 2010, 49, 5800−5807. (16) Follegatti-Romero, L. A.; Lanza, M.; Batista, F. R. M.; Batista, E. A. C.; Oliveira, M. B.; Coutinho, J. A. P.; Meirelles, A. J. A. Liquid− Liquid Equilibrium for Ternary Systems Containing Ethyl Esters, Anhydrous Ethanol and Water at 298.15, 313.15, and 333.15 K. J. Chem. Eng. Data 2010, 49, 12613−12619.

Figure 7. Ishida plot for LLE data determined in this work: ■, ternary system at T = 298.2 K; □- - -, ternary system at T = 333.2 K; ●···, quaternary system at T = 298.2 K; ○-·-·, quaternary system at T = 333.2 K.

1 1 1 2 2 3

AUTHOR INFORMATION

Corresponding Author

σ

R2

b

Article

a The percent rms deviation (δx) was equal to 0.016. A total of 12 parameters was used for the correlation of 33 tie lines: 18 tie lines presented in Tables 2 and 3, and 15 tie lines presented in the work of Liu et al.12

5. CONCLUSION LLE data for the ternary soybean oil biodiesel + ethanol + glycerol and quaternary soybean oil biodiesel + ethanol + glycerol + NaOH (0.01 overall mass fraction) systems at (298.2 and 333.2) K and atmospheric pressure (≈ 95 kPa) were obtained. These systems present higher values of ethanol distribution at 333.2 K; however, all K values are below 0.48. This indicates that ethanol solubilized preferably in glycerolrich phase. For selectivity, the greater values were obtained for the system without the presence of NaOH, at 333.2 K. The NRTL model does not correlate the experimental data well. The model presents a root-mean-square deviation equal to 0.016 for all systems. The experimental tie lines were submitted to the Ishida test, giving R2 > 0.96 for all systems. 1421



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(17) Lanza, M.; Borges Neto, W.; Batista, E.; Poppi, R. J.; Meirelles, A. J. A. Liquid−Liquid Equilibrium Data for Reactional Systems of Ethanolysis at 298.3 K. J. Chem. Eng. Data 2008, 53, 5−15. (18) Felice, R. D.; Faveri, R. D.; Andreis, P. D.; Ottonello, P. Component Distribution between Light and Heavy Phases in Biodiesel Processes. Ind. Eng. Chem. Res. 2008, 47, 7862−7867. (19) Ardila, Y. C.; Pinto, G. M. F.; Machado, A. B.; Wolf Maciel, M. R. Experimental Determination of Binodal Curves and Study of the Temperature in Systems Involved in the Production of Biodiesel with Ethanol. J. Chem. Eng. Data 2010, 55, 4592−4596. (20) Machado, A. B.; Ardila, Y. C.; de Oliveira, L. H.; Aznar, M.; Wolf Maciel, M. R. Liquid -Liquid Equilibrium Study in Ternary Castor Oil Biodiesel + Ethanol + Glycerol and Quaternary Castor Oil Biodiesel + Ethanol + Glycerol + NaOH Systems at (298.2 and 333.2) K. J. Chem. Eng. Data 2011, 56, 2196−2201. (21) Gao, H.; Luo, M.; Xing, J.; Wu, Y.; Li, Y.; Li, W.; Liu, Q.; Liu, H. Desulfurization of Fuel by Extraction with Pyridinium-Based Ionic Liquids. Ind. Eng. Chem. Res. 2008, 47, 8384−8388. (22) Renon, H.; Prausnitz, J. M. Local compositions in thermodynamic excess functions for liquid mixtures. AIChE J. 1968, 14, 135−144. (23) Ishida, K. Ternary Liquid Equilibria in System n-HeptaneThiophene-Liquid Ammonia. New Tie Line Correlation. Bull. Chem. Soc. Jpn. 1960, 33, 693−697.

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