Modified UNIQUAC Model Research Articles

Solubility Measurement of Cholesterol in Several Solvents from 283.2 to 323.2 K

The solubilities of cholesterol in methanol, anisole, acetic acid, ethyl acetate, heptane, methyl isobutyl ketone (MIBK), and mixed solvent (ethanol–MIBK) are determined in the temperature range of 283.2 to 318.2 K. The experimental solubilities of cholesterol in pure solvents and binary mixed solvents are found to increase with increasing temperature. In the binary mixed solvent (ethanol–MIBK), the cholesterol solubilities with increasing mass fraction of ethanol first increase and then decrease. The maximum cholesterol solubility can be obtained when the mass fraction of ethanol is approximately 10%. The solubilities of cholesterol in MIBK, ethyl acetate, and anisole are larger than those in methanol, heptane, and acetic acid. The experimental solubilities are correlated with the van′t Hoff, modified Apelblat, Yaws, van’t Hoff–Jouyban–Acree, and modified UNIQUAC models. The modified UNIQUAC model shows a better fitting result. The modified UNIQUAC model shows an average relative error (ARD) of less than 9%. The ARD values for the other models are all less than 12%.

Measurement and modeling of the solubility of [formula omitted]-lactose in water-ethanol electrolyte solutions at 298.15 K

The present work reports experimental data of the solubility of α-lactose in solutions of water-ethanol-NaCl and water-ethanol-CaCl2 at 298.15 K. For low ethanol contents, the salts decrease the solubility of α-lactose, whereas for high ethanol contents the salts increase the solubility of α-lactose. The experimental solubility data are successfully modeled using two approaches, both of which are based on the UNIQUAC model. A modified UNIQUAC model extended by a Debye-Hückel term as well as a UNIQUAC model extended by a general perturbation scheme are used.

A modified UNIQUAC model for calculating phase-equilibrium of ionic liquid containing systems

Since ionic liquids are increasingly employed as separation media in separation technologies, the development of thermodynamic model for design and optimization of the corresponding separation operations is very urgent. At present, the widely used thermodynamic models treat ionic liquid as a non-electrolyte or strong electrolyte. Although the calculation results are close to the experimental results, the treatment of ionic liquid does not consistent with the physical fact that ionic liquids ionize in solution, even in pure ionic liquid. In this work, we proposed a modified model for the calculation of the phase behavior of ionic liquid containing systems. The model combines a term of the modified Debye-Hückel type with a UNIQUAC equation and treats ionic liquid as a weak electrolyte, using an empirical expression to describe the ionization of ionic liquid. The new model has been utilized to correlate the vapor-liquid equilibrium, liquid-liquid equilibrium, solid-liquid equilibrium data as well as infinite dilution activity coefficient for ionic liquid containing systems with high accuracy. Besides, the model can be used to quantitatively describe the ionization behavior of ionic liquid.

Identification of UNIQUAC binary interaction parameters in liquid-liquid equilibrium

An algorithm is presented for the estimation of the UNIQUAC interaction parameters for liquid-liquid equilibrium of ternary systems. The algorithm is based on two optimization levels. In the inner level the algorithm performs the minimization of an objective function based on the isoactivity conditions. The outer level aims to minimize the error between calculated and experimental compositions. The Common Tangent Plane condition is checked at the end to guarantee a thermodynamically consistent representation of the phase behavior of ternary liquid systems.The algorithm is challenged with a historical Type 1 ternary liquid-liquid equilibrium system from the seminal study of Anderson and Prausnitz in which the authors showed the limitations of the original UNIQUAC model and justified its amendment in the modified UNIQUAC model. The present algorithm makes available single temperature and temperature-dependent interaction parameters enabling accurate and thermodynamically correct description of the experimental data with the original UNIQUAC model, therefore without the need of any model modification. This outcome does not change when the interaction parameters from the binary partially miscible constituent pair are first regressed and kept constant during the estimation of the remaining parameters on ternary equilibrium data. This investigation confirms that a model cannot be judged if the correctness of the model parameters has not been proved first.

Paraffin solubility curves of diesel fuels from thermodynamic model adjusted through experimental DSC thermograms

DSC and wax solubility curves were measured for two diesel fuel samples. Compositional profiles were also measured for the solubility curve points. The paraffin distributions of the samples were determined and the non-paraffinic components were lumped into pseudocomponents. The liquid phase was modeled using the Peng-Robinson equation of state with the classical van der Waals mixing rule. For the solid phase, the modified UNIQUAC model was employed. The models were fitted to the DSC data by tuning only four multipliers acting on the molecular weights, boiling and critical temperatures of the pseudocomponents as well as on the paraffins’ pair interaction energies from the UNIQUAC model. Then the model is used to predict wax appearance temperature, amount and composition of solid deposit as a function of temperature during cooling. Excellent results were obtained for the two samples analyzed. This way, the methodology developed is able to predict adequately the formation of solid paraffin from diesel fuels.

Liquid–Liquid Equilibrium of Water + 1-Propanol or 1-Butanol + Dibutyl Ether Ternary Systems: Measurements and Correlation at Three Temperatures

Liquid–liquid equilibrium (LLE) date for the ternary systems of {water + 1-propanol + dibutyl ether (DBE)} and (water + 1-butanol + DBE) were determined at T = (293.15, 303.15, 308.15) K under atmospheric pressure. Distribution coefficients and separation factors of 1-propanol in the mixtures were calculated and are discussed. The influence of temperature on the liquid phase regions was analyzed. In addition, the experimental values were correlated well with the modified and extended UNIQUAC models; the modified UNIQUAC model represents the data better than the extended UNIQUAC model.

(Liquid + liquid) equilibria for (water + 1-propanol or acetone + β-citronellol) at different temperatures

On this paper, experimental (liquid+liquid) equilibrium (LLE) results are presented for systems composed of β-citronellol and aqueous 1-propanol or acetone. To evaluate the phase separation properties of β-citronellol in aqueous mixtures, LLE values for the ternary systems (water+1-propanol+β-citronellol) and (water+acetone+β-citronellol) were determined with a tie-line method at T=(283.15, 298.15, and 313.15±0.02)K and atmospheric pressure. The reliability of the experimental tie-lines was verified by the Hand and Bachman equations. Ternary phase diagrams, distribution ratios of 1-propanol and acetone in the mixtures are shown. The effect of the temperature on the ternary (liquid+liquid) equilibria was examined and discussed. The experimental LLE values were satisfactorily correlated by extended UNIQUAC and modified UNIQUAC models.

Isobaric Vapor-Liquid-Liquid Equilibria for 1-Butanol + Water + 2,3-Butanediol at 101.3 kPa

Vapor-liquid-liquid equilibria (VLLE) data were determined for the ternary system 1-butanol + water + 2,3-butanediol at 101.3 kPa. A binary heterogeneous minimum boiling azeotrope was found at 365.95 K with mass fractions of 0.526 and 0.474 for 1-butanol and water, respectively. A modified UNIQUAC model was used to predict VLLE by using experimental data, including VLE of 1-butanol + 2,3-butanediol, VLE of water + 2,3-butanediol, LLE of 1-butanol + water, and one LLE tie-line of 1-butanol + water + 2,3-butanediol. The experimental data were compared with the calculated values. The absolute average relative deviations (AARD) are 1.65%, 1.72%, and 2.22% for organic liquid phase, aqueous liquid phase, and vapor phase, respectively. It demonstrates an appropriate fit of the modified UNIQUAC model.

Solubility Determination and Correlation of (2R,3S,4S,5S)-6-(Hydroxymethyl)-tetrahydro-2H-pyran-2,3,4, 5-tetraol in Fatty Alcohol

(2R,3S,4S,5S)-6-(Hydroxymethyl)-tetrahydro-2H-pyran-2,3,4,5-tetraol (d-glucose) solubility in 1-dodecanol, 1-decanol, and 1-octanol from 343.15 K to 393.15 K was determined, respectively. The solubility of d-glucose increased with an increase in temperature and decreased with the increase of fatty alcohol chain length. The modified UNIQUAC model, S-UNIFAC model, and mS-UNIFAC model were applied to predict the solubility data; the interaction parameters were determined. Of the three models, the modified UNIQUAC model showed better prediction accuracy.

Solubility of Xylose, Mannose, Maltose Monohydrate, and Trehalose Dihydrate in Ethanol–Water Solutions

The solubilities of (2R,3S,4R)-2,3,4,5-tetrahydroxypentanal (xylose), (2R,3R,4R,5R)-2,3,5,6-tetrahydroxy-4-[(2R,3R,4S,5S,6R)-3,4,5-trihydroxy-6-(hydroxymethyl)oxan-2-yl]oxyhexanal hydrate (maltose monohydrate), (2R,3S,4S,5R,6R)-2-(hydroxymethyl)-6-[(2R,3R,4S,5S,6R)-3,4,5-trihydroxy-6-(hydroxymethyl)oxan-2-yl]oxyoxane-3,4,5-triol dihydrate (trehalose dihydrate), and (3S,4S,5S,6R)-6-(hydroxymethyl)oxane-2,3,4,5-tetrol (mannose) in the mixtures of ethanol and water from (278.2 to 298.2) K were determined. The solubilities of all the four saccharides in ethanol–water mixtures increased as equilibrium temperature increased. The solubilities of trehalose dihydrate, xylose, and mannose decreased as ethanol mass fraction in the mixed solvent increased. Maltose monohydrate solubility decreased when ethanol mass fraction in the mixed solvent was less than 0.9. The solubilities of xylose and mannose were predicted with A-UNIFAC, and the average relative deviations (ARD) values were less than 22 %. The solubilities of maltose monohydrate and trehalose dihydrate were calculated with the modified UNIQUAC model. New interaction parameters were calibrated. The ARD values for trehalose dihydrate solubility and maltose monohydrate solubility are 28.6 % and 17.9 %, respectively.

Ternary (liquid + liquid) equilibria for β-citronellol in aqueous alcohol at different temperatures

(Liquid+liquid) equilibrium (LLE) data for {water (1)+methanol (2)+β-citronellol (3)} and {water (1)+ethanol (2)+β-citronellol (3)} ternary systems at T=(283.15, 298.15, and 313.15)K are reported. The immiscible region of (water+methanol+β-citronellol) system was found to be larger than that for the ethanol system at the same temperature. The effect of the temperature on the ternary (liquid+liquid) equilibria was examined and discussed. The experimental (liquid+liquid) equilibrium data have been satisfactorily represented by using extended UNIQUAC and modified UNIQUAC models.

Ternary (liquid + liquid) equilibria for (water + 2-propanol + α-pinene, or β-pinene) mixtures at four temperatures

Ternary (liquid+liquid) equilibria date for the (water+2-propanol+α-pinene, or β-pinene) systems were measured at T=(293.15, 298.15, 303.15, and 308.15)K under atmospheric pressure. The experimental results were correlated using the extended and modified UNIQUAC models. The calculated results obtained from the modified UNIQUAC model successfully represent the experimental tie-line data. The temperature influence on liquid-phase equilibria was studied.

Liquid–Liquid Phase Behaviors of Geraniol in Aqueous Alcohol Mixtures

Liquid–liquid equilibrium (LLE) data of the binodal curves and tie-line compositions were examined for ternary mixtures of (water + methanol + geraniol) and (water + ethanol + geraniol) at T = (283.15, 298.15, and 313.15) K. The immiscible area of the (water + methanol + geraniol) system is wider than that for the ethanol system at the same temperature. The experimental liquid–liquid equilibrium data have been represented by using the original UNIQUAC, extended UNIQUAC, and modified UNIQUAC models.

Isobaric vapor–liquid–liquid equilibrium for isopropenyl acetate + water + acetic acid at 101 kPa

Isobaric vapor–liquid–liquid equilibria (VLLE) were measured for the ternary system isopropenyl acetate + water + acetic acid at 101 kPa. The apparatus for determination of the VLLE was an all-glass dynamic recirculating still. The experimental data demonstrated the existence of a binary heterogeneous azeotrope at 353.05 K with a composition of 0.5269, 0.4731 mole fractions of isopropenyl acetate and water. The prediction of VLLE used the modified UNIQUAC model which was based on the experimental data includes binary VLE of isopropenyl acetate + acetic acid, binary VLE of water + acetic acid, binary LLE of isopropenyl acetate + water and a single tie-line of ternary LLE of isopropenyl acetate + water + acetic acid. Comparison of the experimental data and the calculated results was made, which shows a satisfactory fit of the thermodynamic model.

Mutual solubility measurements and correlations of imidazolium-based ionic liquid mixtures with alcohols

The mutual solubility of ionic liquids (ILs), 1-butyl-3-ethylimidazolium tetrafluoroborate, 1-butyl-3-propylimidazolium tetrafluoroborate, and 1,3-dibutylimidazolium tetrafluoroborate with alcohols, 1-propanol, 1-butanol, 1-pentanol, and 1-hexanol were measured at atmospheric pressure. Upper critical solution temperatures (UCSTs) were estimated from experimental results using a polynomial equation. The UCSTs increased as increasing the chain length of alcohol. On other hand, the decreasing UCSTs occurred when the alkyl chain length on the cation of ionic liquids increased. The (liquid + liquid) equilibrium data were correlated by the original UNIQUAC, extended UNIQUAC, and modified UNIQUAC models. The temperature dependence of the solubility of ILs in alcohols and alcohols in ILs is represented successfully using the UNIQUAC, extended UNIQUAC, and modified UNIQUAC models with a quadratic function of temperature for binary energy parameters.

Liquid–Liquid Equilibrium for Fuel Oxygenate Systems Containing Dialkyl Carbonate in Aqueous Solution

Experimental tie-line data were investigated for two quaternary systems of water + n-hexane + diethyl carbonate + dimethyl carbonate and water + toluene + isooctane + dimethyl carbonate, and two related ternary systems of water + n-hexane + diethyl carbonate and water + n-hexane + dimethyl carbonate at 298.15 K and ambient pressure. The experimental tie-line data have been correlated using a modified UNIQUAC model and an extended UNIQUAC model, both with multicomponent interaction parameters in addition to the binary ones.

Solid-Liquid Equilibria of D-Glucose, D-Fructose and Sucrose in the Mixture of Ethanol and Water from 273.2 K to 293.2 K

Experimental data on the solubility of D-glucose, D-fructose and sucrose in the mixed solvents composed of water and ethanol from 273.2 to 293.2 K were determined. The solubility of D-glucose, D-fructose and sucrose decreased as the ethanol content increased in the mixed solvent. The solubility of D-glucose, D-fructose and sucrose decreased with decreasing equilibrium temperature. The modified UNIQUAC model, S-UNIFAC model and mS-UNIFAC model were applied to predict the solid-liquid equilibria. The prediction results were compared and discussed. Better prediction accuracy was generated using the modified UNIQUAC model.

Liquid−Liquid Equilibria of Water + Pentan-1-ol + 2,6,6-Trimethylbicyclo[3.1.1]hep-2-ene or 6,6-Dimethyl-2-methylenebicyclo[3.1.1]heptane at (293.15, 303.15, 313.15, and 323.15) K

Mutual solubility data of water + pentan-1-ol and liquid−liquid equilibrium of water + pentan-1-ol +2,6,6-trimethylbicyclo[3.1.1]hep-2-ene (α-pinene) and water + pentan-1-ol + 6,6-dimethyl-2-methylenebicyclo[3.1.1]heptane (β-pinene) have been measured experimentally at (293.15, 303.15, 313.15, and 323.15) K under atmospheric pressure. The estimated uncertainty of phase composition and temperature were about (0.0005 and 0.05) K, respectively. The experimental ternary liquid−liquid equilibrium data have been simultaneously predicted and correlated by the extended and modified UNIQUAC models.

(Ternary liquid + liquid) equilibria for (water + acetone + α-pinene, or β-pinene, or limonene) mixtures

(Ternary liquid + liquid) equilibria (tie-lines) of (water + acetone + α-pinene) at T = (288.15, 298.15, and 308.15) K and (water + acetone + β-pinene, or limonene) at T = 298.15 K have been measured. The experimental (ternary liquid + liquid) equilibrium data have been correlated successfully by the original UNIQUAC and modified UNIQUAC models. The modified UNIQUAC model reproduced accurately the experimental results for the (water + acetone + α-pinene) system at all the temperatures but fairly agreed with the experimental data for the (water + acetone + β-pinene, or limonene) systems.

Quaternary Liquid–Liquid Equilibria for Fuel Additive Systems Containing Diethyl Carbonate or 1,1-Dimethylethyl Methyl Ether at 298.15 K and Atmospheric Pressure

Liquid–liquid equilibrium tie line data were determined for three quaternary systems water + ethanol + diethyl carbonate+n-heptane, water + ethanol + 1,1-dimethylethyl methyl ether + diethyl carbonate, and water + 1,1-dimethylethyl methyl ether + diethyl carbonate+n-heptane at 298.15 K and atmospheric pressure. The experimental liquid–liquid equilibria results have been correlated using a modified UNIQUAC model and an extended UNIQUAC model, both with multicomponent interaction parameters in addition to the binary ones.