Isobutyl Acetate

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J. Torre - One of the best experts on this subject based on the ideXlab platform.

M.c. Burguet - One of the best experts on this subject based on the ideXlab platform.

  • study of liquid liquid equilibrium of the systems Isobutyl Acetate acetic acid water and Isobutyl alcohol acetic acid water at different temperatures
    Fluid Phase Equilibria, 2008
    Co-Authors: Amparo Cháfer, Estela Lladosa, J. Torre, M.c. Burguet
    Abstract:

    Abstract In this work, experimental liquid–liquid equilibria (LLE) data of the systems Isobutyl Acetate + acetic acid + water and Isobutyl alcohol + acetic acid + water are presented. The liquid–liquid equilibria of both systems have been measured at 283.15 and 323.15 K. The NRTL and UNIQUAC models were applied to fit the data for both ternary systems. The interaction parameters obtained from both models successfully correlated the equilibrium compositions. The experimental tie lines were compared to the values predicted by the UNIFAC method. Moreover, the solvent capabilities of Isobutyl Acetate and Isobutyl alcohol were compared.

  • Study of liquid-liquid equilibrium of the systems Isobutyl Acetate + acetic acid + water and Isobutyl alcohol + acetic acid + water at different temperatures
    Fluid Phase Equilibria, 2008
    Co-Authors: Amparo Cháfer, Estela Lladosa, J. Torre, M.c. Burguet
    Abstract:

    Abstract In this work, experimental liquid–liquid equilibria (LLE) data of the systems Isobutyl Acetate + acetic acid + water and Isobutyl alcohol + acetic acid + water are presented. The liquid–liquid equilibria of both systems have been measured at 283.15 and 323.15 K. The NRTL and UNIQUAC models were applied to fit the data for both ternary systems. The interaction parameters obtained from both models successfully correlated the equilibrium compositions. The experimental tie lines were compared to the values predicted by the UNIFAC method. Moreover, the solvent capabilities of Isobutyl Acetate and Isobutyl alcohol were compared.

  • Study of liquid–liquid equilibrium of the systems Isobutyl Acetate + acetic acid + water and Isobutyl alcohol + acetic acid + water at different temperatures
    Fluid Phase Equilibria, 2008
    Co-Authors: Amparo Cháfer, Estela Lladosa, J. Torre, M.c. Burguet
    Abstract:

    Abstract In this work, experimental liquid–liquid equilibria (LLE) data of the systems Isobutyl Acetate + acetic acid + water and Isobutyl alcohol + acetic acid + water are presented. The liquid–liquid equilibria of both systems have been measured at 283.15 and 323.15 K. The NRTL and UNIQUAC models were applied to fit the data for both ternary systems. The interaction parameters obtained from both models successfully correlated the equilibrium compositions. The experimental tie lines were compared to the values predicted by the UNIFAC method. Moreover, the solvent capabilities of Isobutyl Acetate and Isobutyl alcohol were compared.

  • separation of Isobutyl alcohol and Isobutyl Acetate by extractive distillation and pressure swing distillation simulation and optimization
    Separation and Purification Technology, 2006
    Co-Authors: Rosa Munoz, Juan B. Montón, M.c. Burguet, J. Torre
    Abstract:

    Abstract We have studied, simulated and evaluated economically two separation alternatives of a mixture made up of 52 mole% of Isobutyl alcohol and 48 mole% of Isobutyl Acetate by means of a practical case of a plant to treat 12,000 Tm/year of the original mixture. The simulation has been carried out satisfactorily by means of a package of commercial software (Aspen HYSYS ® ) using the thermodynamic model UNIQUAC with binary parameters obtained experimentally by us. The two processes evaluated (extractive distillation using n -butyl propionate as a solvent and pressure-swing distillation) have been optimized independently from each other and the best configurations have been evaluated economically. The simulation and economic evaluation of the two separation alternatives that we have considered allow us to conclude that, for a 12,000 Tm/year plant, the pressure-swing distillation is more attractive than the extractive distillation using n -butyl propionate as an entrainer.

  • vapor liquid equilibria in the ternary system Isobutyl alcohol Isobutyl Acetate butyl propionate and the binary systems Isobutyl alcohol butyl propionate Isobutyl Acetate butyl propionate at 101 3 kpa
    Fluid Phase Equilibria, 2005
    Co-Authors: Rosa Munoz, Juan B. Montón, M.c. Burguet, J. Torre
    Abstract:

    Abstract Consistent vapor–liquid equilibrium (VLE) data at 101.3 kPa have been determined for the ternary system Isobutyl alcohol (IBA) + Isobutyl Acetate (IBAc) + butyl propionate (BUP) and two constituent binary systems: IBA + BUP and IBAc + BUP. The IBA + BUP system show lightly positive deviation from Raoult's law and IBAc + BUP system exhibits no deviation from ideal behaviour. The activity coefficients of the solutions were correlated with its composition by the Wilson, NRTL, UNIQUAC models. The ternary system is very well predicted from binary interaction parameters. BUP eliminates the IBA–IBAc binary azeotrope. The change of phase equilibria behaviour is significant therefore this solvent seems to be an effective agent for that azeotrope mixture separation. In fact, the mean relative volatility on a solvent free basis is 1.8. The binary VLE data measured in the present study passed the thermodynamic consistency test of Fredenslund et al. [A. Fredenslund, J. Gmehling, P. Rasmussen, Vapor–Liquid Equilibria Using UNIFAC, A Group Contribution Method, Elsevier, Amsterdam, 1977], and were correlated by the Wilson, NRTL and UNIQUAC models to relate activity coefficients with mole fractions. The VLE data obtained for the ternary system passed both the Wisniak L–W [J. Wisniak, Ind. Eng. Chem. Res. 32 (1993) 1531–1533] and McDermott–Ellis [C. McDermott, S.R. Ellis, Chem. Eng. Sci. 20 (1965) 293–296] consistency test. The parameters obtained from binary data were utilized directly to predict the phase behaviour of the ternary system. The results showed an excellent agreement with experimental values.

Juan B. Montón - One of the best experts on this subject based on the ideXlab platform.

  • liquid liquid equilibria of the systems Isobutyl Acetate Isobutyl alcohol water and Isobutyl Acetate Isobutyl alcohol glycerol at different temperatures
    Fluid Phase Equilibria, 2008
    Co-Authors: Amparo Cháfer, Juan B. Montón, J. Torre, Estela Lladosa
    Abstract:

    Abstract In this work, experimental liquid–liquid equilibria (LLE) data of the Isobutyl Acetate + Isobutyl alcohol + water and Isobutyl Acetate + Isobutyl alcohol + glycerol systems are presented. The LLE of both systems have been measured at 283.15 and 323.15 K. The NRTL and UNIQUAC models were applied to both ternary systems. The interaction parameters obtained from both models successfully correlated the equilibrium compositions. The experimental tie lines were compared to the values predicted by the UNIFAC method. Moreover, the solvent capabilities of water and glycerol were compared.

  • Liquid–liquid equilibria of the systems Isobutyl Acetate + Isobutyl alcohol + water and Isobutyl Acetate + Isobutyl alcohol + glycerol at different temperatures
    Fluid Phase Equilibria, 2008
    Co-Authors: Amparo Cháfer, Juan B. Montón, J. Torre, Estela Lladosa
    Abstract:

    Abstract In this work, experimental liquid–liquid equilibria (LLE) data of the Isobutyl Acetate + Isobutyl alcohol + water and Isobutyl Acetate + Isobutyl alcohol + glycerol systems are presented. The LLE of both systems have been measured at 283.15 and 323.15 K. The NRTL and UNIQUAC models were applied to both ternary systems. The interaction parameters obtained from both models successfully correlated the equilibrium compositions. The experimental tie lines were compared to the values predicted by the UNIFAC method. Moreover, the solvent capabilities of water and glycerol were compared.

  • separation of Isobutyl alcohol and Isobutyl Acetate by extractive distillation and pressure swing distillation simulation and optimization
    Separation and Purification Technology, 2006
    Co-Authors: Rosa Munoz, Juan B. Montón, M.c. Burguet, J. Torre
    Abstract:

    Abstract We have studied, simulated and evaluated economically two separation alternatives of a mixture made up of 52 mole% of Isobutyl alcohol and 48 mole% of Isobutyl Acetate by means of a practical case of a plant to treat 12,000 Tm/year of the original mixture. The simulation has been carried out satisfactorily by means of a package of commercial software (Aspen HYSYS ® ) using the thermodynamic model UNIQUAC with binary parameters obtained experimentally by us. The two processes evaluated (extractive distillation using n -butyl propionate as a solvent and pressure-swing distillation) have been optimized independently from each other and the best configurations have been evaluated economically. The simulation and economic evaluation of the two separation alternatives that we have considered allow us to conclude that, for a 12,000 Tm/year plant, the pressure-swing distillation is more attractive than the extractive distillation using n -butyl propionate as an entrainer.

  • vapor liquid equilibria in the ternary system Isobutyl alcohol Isobutyl Acetate butyl propionate and the binary systems Isobutyl alcohol butyl propionate Isobutyl Acetate butyl propionate at 101 3 kpa
    Fluid Phase Equilibria, 2005
    Co-Authors: Rosa Munoz, Juan B. Montón, M.c. Burguet, J. Torre
    Abstract:

    Abstract Consistent vapor–liquid equilibrium (VLE) data at 101.3 kPa have been determined for the ternary system Isobutyl alcohol (IBA) + Isobutyl Acetate (IBAc) + butyl propionate (BUP) and two constituent binary systems: IBA + BUP and IBAc + BUP. The IBA + BUP system show lightly positive deviation from Raoult's law and IBAc + BUP system exhibits no deviation from ideal behaviour. The activity coefficients of the solutions were correlated with its composition by the Wilson, NRTL, UNIQUAC models. The ternary system is very well predicted from binary interaction parameters. BUP eliminates the IBA–IBAc binary azeotrope. The change of phase equilibria behaviour is significant therefore this solvent seems to be an effective agent for that azeotrope mixture separation. In fact, the mean relative volatility on a solvent free basis is 1.8. The binary VLE data measured in the present study passed the thermodynamic consistency test of Fredenslund et al. [A. Fredenslund, J. Gmehling, P. Rasmussen, Vapor–Liquid Equilibria Using UNIFAC, A Group Contribution Method, Elsevier, Amsterdam, 1977], and were correlated by the Wilson, NRTL and UNIQUAC models to relate activity coefficients with mole fractions. The VLE data obtained for the ternary system passed both the Wisniak L–W [J. Wisniak, Ind. Eng. Chem. Res. 32 (1993) 1531–1533] and McDermott–Ellis [C. McDermott, S.R. Ellis, Chem. Eng. Sci. 20 (1965) 293–296] consistency test. The parameters obtained from binary data were utilized directly to predict the phase behaviour of the ternary system. The results showed an excellent agreement with experimental values.

  • Phase equilibria in the ternary system Isobutyl alcohol + Isobutyl Acetate + 1-hexanol and the binary systems Isobutyl alcohol + 1-hexanol, Isobutyl Acetate + 1-hexanol at 101.3 kPa
    Fluid Phase Equilibria, 2005
    Co-Authors: Rosa Munoz, Juan B. Montón, M.c. Burguet, J. Torre
    Abstract:

    Abstract Consistent vapor–liquid equilibrium (VLE) data at 101.3 kPa have been determined for the ternary system Isobutyl alcohol (IBA) + Isobutyl Acetate (IBAc) + 1-hexanol and two constituent binary systems: IBA + 1-hexanol and IBAc + 1-hexanol. The IBA + 1-hexanol system exhibits no deviation from ideal behaviour and IBAc + 1-hexanol system show lightly positive deviation from Raoult's law. The activity coefficients of the solutions were correlated with its composition by the Wilson, NRTL, UNIQUAC models. The ternary system is well predicted from binary interaction parameters. 1-Hexanol eliminates the IBA–IBAc binary azeotrope. However, the change of phase equilibria behaviour is small therefore this solvent is not an effective agent for that azeotrope mixture separation. In fact, the mean relative volatility on a solvent free basis is 1.28 (close to unity).

Rosa Munoz - One of the best experts on this subject based on the ideXlab platform.

  • separation of Isobutyl alcohol and Isobutyl Acetate by extractive distillation and pressure swing distillation simulation and optimization
    Separation and Purification Technology, 2006
    Co-Authors: Rosa Munoz, Juan B. Montón, M.c. Burguet, J. Torre
    Abstract:

    Abstract We have studied, simulated and evaluated economically two separation alternatives of a mixture made up of 52 mole% of Isobutyl alcohol and 48 mole% of Isobutyl Acetate by means of a practical case of a plant to treat 12,000 Tm/year of the original mixture. The simulation has been carried out satisfactorily by means of a package of commercial software (Aspen HYSYS ® ) using the thermodynamic model UNIQUAC with binary parameters obtained experimentally by us. The two processes evaluated (extractive distillation using n -butyl propionate as a solvent and pressure-swing distillation) have been optimized independently from each other and the best configurations have been evaluated economically. The simulation and economic evaluation of the two separation alternatives that we have considered allow us to conclude that, for a 12,000 Tm/year plant, the pressure-swing distillation is more attractive than the extractive distillation using n -butyl propionate as an entrainer.

  • vapor liquid equilibria in the ternary system Isobutyl alcohol Isobutyl Acetate butyl propionate and the binary systems Isobutyl alcohol butyl propionate Isobutyl Acetate butyl propionate at 101 3 kpa
    Fluid Phase Equilibria, 2005
    Co-Authors: Rosa Munoz, Juan B. Montón, M.c. Burguet, J. Torre
    Abstract:

    Abstract Consistent vapor–liquid equilibrium (VLE) data at 101.3 kPa have been determined for the ternary system Isobutyl alcohol (IBA) + Isobutyl Acetate (IBAc) + butyl propionate (BUP) and two constituent binary systems: IBA + BUP and IBAc + BUP. The IBA + BUP system show lightly positive deviation from Raoult's law and IBAc + BUP system exhibits no deviation from ideal behaviour. The activity coefficients of the solutions were correlated with its composition by the Wilson, NRTL, UNIQUAC models. The ternary system is very well predicted from binary interaction parameters. BUP eliminates the IBA–IBAc binary azeotrope. The change of phase equilibria behaviour is significant therefore this solvent seems to be an effective agent for that azeotrope mixture separation. In fact, the mean relative volatility on a solvent free basis is 1.8. The binary VLE data measured in the present study passed the thermodynamic consistency test of Fredenslund et al. [A. Fredenslund, J. Gmehling, P. Rasmussen, Vapor–Liquid Equilibria Using UNIFAC, A Group Contribution Method, Elsevier, Amsterdam, 1977], and were correlated by the Wilson, NRTL and UNIQUAC models to relate activity coefficients with mole fractions. The VLE data obtained for the ternary system passed both the Wisniak L–W [J. Wisniak, Ind. Eng. Chem. Res. 32 (1993) 1531–1533] and McDermott–Ellis [C. McDermott, S.R. Ellis, Chem. Eng. Sci. 20 (1965) 293–296] consistency test. The parameters obtained from binary data were utilized directly to predict the phase behaviour of the ternary system. The results showed an excellent agreement with experimental values.

  • Phase equilibria in the ternary system Isobutyl alcohol + Isobutyl Acetate + 1-hexanol and the binary systems Isobutyl alcohol + 1-hexanol, Isobutyl Acetate + 1-hexanol at 101.3 kPa
    Fluid Phase Equilibria, 2005
    Co-Authors: Rosa Munoz, Juan B. Montón, M.c. Burguet, J. Torre
    Abstract:

    Abstract Consistent vapor–liquid equilibrium (VLE) data at 101.3 kPa have been determined for the ternary system Isobutyl alcohol (IBA) + Isobutyl Acetate (IBAc) + 1-hexanol and two constituent binary systems: IBA + 1-hexanol and IBAc + 1-hexanol. The IBA + 1-hexanol system exhibits no deviation from ideal behaviour and IBAc + 1-hexanol system show lightly positive deviation from Raoult's law. The activity coefficients of the solutions were correlated with its composition by the Wilson, NRTL, UNIQUAC models. The ternary system is well predicted from binary interaction parameters. 1-Hexanol eliminates the IBA–IBAc binary azeotrope. However, the change of phase equilibria behaviour is small therefore this solvent is not an effective agent for that azeotrope mixture separation. In fact, the mean relative volatility on a solvent free basis is 1.28 (close to unity).

  • phase equilibria in the ternary system Isobutyl alcohol Isobutyl Acetate 1 hexanol and the binary systems Isobutyl alcohol 1 hexanol Isobutyl Acetate 1 hexanol at 101 3 kpa
    Fluid Phase Equilibria, 2005
    Co-Authors: Rosa Munoz, Juan B. Montón, M.c. Burguet, J. Torre
    Abstract:

    Abstract Consistent vapor–liquid equilibrium (VLE) data at 101.3 kPa have been determined for the ternary system Isobutyl alcohol (IBA) + Isobutyl Acetate (IBAc) + 1-hexanol and two constituent binary systems: IBA + 1-hexanol and IBAc + 1-hexanol. The IBA + 1-hexanol system exhibits no deviation from ideal behaviour and IBAc + 1-hexanol system show lightly positive deviation from Raoult's law. The activity coefficients of the solutions were correlated with its composition by the Wilson, NRTL, UNIQUAC models. The ternary system is well predicted from binary interaction parameters. 1-Hexanol eliminates the IBA–IBAc binary azeotrope. However, the change of phase equilibria behaviour is small therefore this solvent is not an effective agent for that azeotrope mixture separation. In fact, the mean relative volatility on a solvent free basis is 1.28 (close to unity).

  • phase equilibria in the systems Isobutyl alcohol n n dimethylformamide Isobutyl Acetate n n dimethylformamide and Isobutyl alcohol Isobutyl Acetate n n dimethylformamide at 101 3kpa
    Fluid Phase Equilibria, 2005
    Co-Authors: Rosa Munoz, Juan B. Montón, M.c. Burguet, J. Torre
    Abstract:

    Abstract Consistent vapor–liquid equilibria (VLE) were determined for the ternary system Isobutyl alcohol (IBA) + Isobutyl Acetate (IBAc) + N,N-dimethylformamide (DMF) and two constituent binary systems at 101.3 kPa. The IBA + DMF system exhibits negative deviation from ideal behaviour and IBAc + DMF system deviates positively from ideal behaviour. The activity coefficients of the solutions were correlated with its composition by the Wilson, NRTL and UNIQUAC models. The ternary system is well predicted from binary interaction parameters.

Jun Gao - One of the best experts on this subject based on the ideXlab platform.

  • liquid liquid equilibrium measurements and interaction exploration for separation of Isobutyl alcohol Isobutyl Acetate by imidazolium based ionic liquids with different anions
    The Journal of Chemical Thermodynamics, 2020
    Co-Authors: Xianglin Meng, Jun Gao, Lianzheng Zhang, Xiaobin Bing, Yinglong Wang
    Abstract:

    Abstract For separation of the azeotropic mixture Isobutyl alcohol and Isobutyl Acetate, liquid-liquid extraction was adopted in this work and three imidazolium-based ionic liquids with different anions 1-butyl-3-methylimidazolium dihydrogen phosphate ([Bmim][H2PO4]), 1-butyl-3-methylimidazolium hydrogen sulfate ([Bmim][HSO4]) and 1-butyl-3-methylimidazolium methyl sulfate ([Bmim][MeSO4]) were chosen as extractants. The liquid – liquid equilibrium data (LLE) for Isobutyl alcohol + Isobutyl Acetate + ([Bmim][H2PO4]/[Bmim][HSO4]/[Bmim][MeSO4]) were determined at 298.15 K and 101.3 kPa. The distribution coefficient and selectivity were calculated to evaluate extraction capability of the selected extractants. Furthermore, the σ-profiles and interaction energies based on conductor-like screening segment activity coefficient model (COSMO-SAC) were calculated to provide theoretical insight to interactions among the components. Also, the measured LLE data was correlated by the NRTL model and binary interaction parameters were regressed which is helpful for the separation process design and optimization.

  • Liquid-liquid equilibrium measurements and interaction exploration for separation of Isobutyl alcohol + Isobutyl Acetate by imidazolium-based ionic liquids with different anions
    The Journal of Chemical Thermodynamics, 2020
    Co-Authors: Xianglin Meng, Jun Gao, Lianzheng Zhang, Xiaobin Bing, Yinglong Wang
    Abstract:

    Abstract For separation of the azeotropic mixture Isobutyl alcohol and Isobutyl Acetate, liquid-liquid extraction was adopted in this work and three imidazolium-based ionic liquids with different anions 1-butyl-3-methylimidazolium dihydrogen phosphate ([Bmim][H2PO4]), 1-butyl-3-methylimidazolium hydrogen sulfate ([Bmim][HSO4]) and 1-butyl-3-methylimidazolium methyl sulfate ([Bmim][MeSO4]) were chosen as extractants. The liquid – liquid equilibrium data (LLE) for Isobutyl alcohol + Isobutyl Acetate + ([Bmim][H2PO4]/[Bmim][HSO4]/[Bmim][MeSO4]) were determined at 298.15 K and 101.3 kPa. The distribution coefficient and selectivity were calculated to evaluate extraction capability of the selected extractants. Furthermore, the σ-profiles and interaction energies based on conductor-like screening segment activity coefficient model (COSMO-SAC) were calculated to provide theoretical insight to interactions among the components. Also, the measured LLE data was correlated by the NRTL model and binary interaction parameters were regressed which is helpful for the separation process design and optimization.

  • Liquid–Liquid Equilibrium of Isobutyl Acetate+ Isobutyl Alcohol + Imidazolium-Based Ionic Liquids at 298.15 and308.15 K
    Journal of Chemical & Engineering Data, 2019
    Co-Authors: Xianglin Meng, Jun Gao, Lianzheng Zhang, Xiaowei Liu, Yinglong Wang
    Abstract:

    For separation of the azeotrope Isobutyl Acetate and Isobutyl alcohol, imidazolium-based ionic liquids 1-hexyl-3-methylimidazolium hexafluorophosphate [Hmim][PF6] and 1-octyl-3-methylimidazolium hexafluorophosphate [Omim][PF6] were applied as the extractants in the extraction process. The liquid–liquid equilibrium (LLE) data for the ternary systems Isobutyl Acetate + Isobutyl alcohol + ([Hmim][PF6]/[Omim][PF6]) were determined at temperature of 298.15 and 308.15 K. To evaluate extraction performance of the ILs, the selectivity and distribution coefficient were calculated from the experimental data. The effect of the alkyl chain length of the cations and the temperature on the LLE for the systems were explored. In addition, the experimental LLE data were correlated by the NRTL model, and the binary interaction parameters of the NRTL model were optimized.

  • liquid liquid equilibrium of Isobutyl Acetate Isobutyl alcohol imidazolium based ionic liquids at 298 15 and308 15 k
    Journal of Chemical & Engineering Data, 2019
    Co-Authors: Xianglin Meng, Jun Gao, Lianzheng Zhang, Xiaowei Liu, Yinglong Wang
    Abstract:

    For separation of the azeotrope Isobutyl Acetate and Isobutyl alcohol, imidazolium-based ionic liquids 1-hexyl-3-methylimidazolium hexafluorophosphate [Hmim][PF6] and 1-octyl-3-methylimidazolium hexafluorophosphate [Omim][PF6] were applied as the extractants in the extraction process. The liquid–liquid equilibrium (LLE) data for the ternary systems Isobutyl Acetate + Isobutyl alcohol + ([Hmim][PF6]/[Omim][PF6]) were determined at temperature of 298.15 and 308.15 K. To evaluate extraction performance of the ILs, the selectivity and distribution coefficient were calculated from the experimental data. The effect of the alkyl chain length of the cations and the temperature on the LLE for the systems were explored. In addition, the experimental LLE data were correlated by the NRTL model, and the binary interaction parameters of the NRTL model were optimized.

  • Isobaric Vapor–Liquid Equilibrium Measurements for Separation of Azeotrope (Methanol + Methyl Acetate)
    Journal of Chemical & Engineering Data, 2018
    Co-Authors: Shiliang Jiang, Jun Gao, Lianzheng Zhang, Yinglong Wang
    Abstract:

    For separation of the azeotrope (methanol + methyl Acetate), extractive distillation is applied and Isobutyl Acetate, isopentyl Acetate, and p-xylene are chosen as the entrainers. To obtain the binary interaction parameters of thermodynamic models for design of the extractive distillation process, the isobaric vapor–liquid equilibrium (VLE) data for the three binary systems of (methyl Acetate + Isobutyl Acetate), (methyl Acetate + isopentyl Acetate), and (methyl Acetate + p-xylene) were determined at the pressure of 101.3 kPa. The thermodynamic consistency for the VLE experimental data of the three mixtures were tested by the Herington and van Ness methods. The NRTL, UNIQUAC, and Wilson thermodynamic models were adopted to correlate the VLE experimental data, and the binary interaction parameters of the three models were regressed.