Modification of the NRTL model for ternary and quaternary liquid-liquid equilibrium calculations

The original NRTL model is modified for the correlation of ternary liquid-liquid equilibria. The ternary expression of the modified NRTL model includes three additional ternary parameters and the ternary terms vanish when a ternary system degenerates to a binary. The ability of the modified NRTL model has been evaluated in the calculations of ternary vapor-liquid-liquid equilibria and quaternary liquid-liquid equilibria.     

Quaternary Liquid–Liquid Equilibria for Aqueous Systems Containing Dimethyl Carbonate at 298.15 K

Experimental tie-line data for two ternary systems, water + dimethyl carbonate + methanol or ethanol, and two quaternary systems, water + dimethyl carbonate + toluene + methanol or ethanol were investigated at 298.15 K and atmospheric pressure. The experimental liquid–liquid equilibrium data were correlated using a modified UNIQUAC activity coefficient model with binary and ternary as well as quaternary parameters. The calculated results were further compared with those obtained from an extended UNIQUAC model.     

Liquid–Liquid Equilibria of Oxygenate Fuel Additives with Water at 298.15 K: Ternary and Quaternary Aqueous Systems of Diisopropyl Ether and Hydrocarbons with 2-Propanol

Experimental tie-line data were determined for one ternary system, water + diisopropyl ether + n-heptane and two quaternary systems, water + diisopropyl ether + 2-propanol + n-heptane or toluene at 298.15 K and ambient pressure. The experimental liquid–liquid equilibrium data were successfully correlated using a modified UNIQUAC model with ternary and quaternary mixture parameters, in addition to the binary ones. The calculated results were also compared with those obtained from an extended UNIQUAC model of Nagata [Fluid Phase Equilib. 54, 191 (1990)].     

Liquid-liquid equilibria of (cyclohexane + acetonitrile + methylcyclohexane + toluene) and of {(acetonitrile + methylcyclohexane) + benzene or + toluene or + cyclohexane or + chlorobenzene} at 298.15 K

Tie-line results at 298.15 K and atmospheric pressure are reported for (cyclohexane + acetonitrile + methylcyclohexane + toluene) and for {(acetonitrile + methylcyclohexane) + benzene or + toluene or + cyclohexane or + chlorobenzene). The extended UNIQUAC and UNIQUAC equations are used to correlate binary vapour-liquid equilibria and mutual solubilities for 10 mixtures constituting the ternary mixtures and to predict the ternary and quaternary liquid-liquid equilibria by use of only binary parameters.     

Liquid–Liquid Equilibria of Oxygenate Fuel Additives with Water: Two Quaternary Aqueous Systems of Diisopropyl Ether + 2,2,4-Trimethylpentane with Methyl <Emphasis Type="Italic">tert</Emphasis>-Butyl Ether or Toluene

Experimental tie-line data for two quaternary systems, water + diisopropyl ether + 2,2,4-trimethylpentane + methyl tert-butyl ether or toluene, were investigated at 298.15 K and atmospheric pressure. The experimental liquid–liquid equilibrium data were correlated using a modified UNIQUAC activity coefficient model with ternary and quaternary parameters, in addition to the binary ones. The calculated results were further compared with those obtained with an extended UNIQUAC model from Nagata [Fluid Phase Equilib. 54, 191–206 (1990)].     

Correlation of liquid-liquid equilibria in aqueous and organic systems using a modified Wilson model

A modified Wilson model is extended to involve three ternary parameters per ternary to allow the model to represent ternary liquid-liquid equilibria accurately. The calculated results for 19 ternary systems obtained from the present modification are compared with the previous results obtained from other modified Wilson models. The model is further extended to treat quaternary liquid-liquid equilibria for six aqueous systems and one nonaqueous system using binary, ternary, and quaternary parameters. Mutual solubilities for 19 systems over a wide temperature range are represented with the model having temperature-dependent energy parameters.     

Ternary Liquid-Liquid Equilibria Of (Acetonitrile + n-Octane + Propanols or Butanols)

Abstract

The liquid-liquid equilibria of (acetonitrile + n-octane + 1-propanol or 2-propanol or 1-butanol or 2-butanol, or iso-butanol or tert-butanol) at 298.15 K have been measured. The ternary experimental results agree well with those predicted from the UNIQUAC associated-solution model with binary parameters alone.     

Solubility of pyrene in simple and mixed solvent systems

The solubility of pyrene was experimentally determined in simple and complex solvent systems (single, binary, ternary, quaternary and pentinary solvent systems) composed of benzene, ethylbenzene, hexane, hexanol and methylcyclohexane over a temperature range from 293 to 318 K. In addition, six models were used in this study to represent pyrene solubility in the different solvent systems. The interaction parameters for modified Wilson, NIBS/Redlich-Kister, UNIQUAC and NRTL models were estimated using the solubility data generated for pyrene in single, binary and ternary solvent systems. By re-adjusting the interaction parameters reported for Dortmund UNIFAC and ASOG models, a better representation of the solubility of pyrene was obtained compared to using reported values. Furthermore, a correction term is introduced for the ASOG model in this study to better improve pyrene solubility prediction in simple and mixed solvent systems. These estimated or re-adjusted interaction parameters for the different models, along with the reported parameters for Dortmund UNIFAC and ASOG models, were tested on complex solvent systems (quaternary and pentinary solvent mixtures), in order to check their validity and accuracy for such predictions.     

Interaction parameters for multi-component aromatic extraction with sulfolane

Aromatic extraction is an important operation in petrochemical processing. Design of an aromatic extractor requires the knowledge of multi-component liquid–liquid equilibrium (LLE) data. Such experimental LLE data are usually not available and therefore can be predicted using various activity coefficient models. These models require proper binary interaction parameters, which are not yet available for all aromatic extraction systems. Furthermore, the parameters available for most of the ternary systems are specific to that system only and cannot be used for other ternary or multi-component systems. An attempt has been made to obtain these parameters that are globally applicable. For this purpose, the parameter estimation procedure has been modified to estimate the parameters simultaneously for different systems involving common pairs. UINQUAC and UNIFAC models have been used for parameter estimation. The regressed parameters are shown to be applicable for the ternary as well as for the multi-component systems. It is observed that UNIQUAC parameters provide a better fit for ternary LLE data, whereas, as one moves towards the higher component systems (quaternary and quinary) the UNIFAC parameters, which are a measure of the group contributions, predict the LLE better. Effect of temperature on UNIQUAC binary interaction parameters has been studied and a linear dependence has been observed.     

Isobaric vapor–liquid equilibria for the quaternary reactive system: Ethanol + water + ethyl lactate + lactic acid at 101.33 kPa

Isobaric vapor–liquid equilibrium (VLE) data of the reactive quaternary system ethanol (1) + water (2) + ethyl lactate (3) + lactic acid (4) have been determined experimentally. Additionally, the reaction equilibrium constant was calculated for each VLE experimental data. The experimental VLE data were correlated using the UNIQUAC equation to describe the chemical and phase equilibria simultaneously. For some of the non-reactive binary systems, UNIQUAC binary interaction parameters were obtained from the literature. The rest of the binary UNIQUAC parameters were obtained by correlating the experimental quaternary VLE data obtained in this work. A maximum pressure azeotrope at high water concentration for the binary reactive system ethyl lactate + water has been calculated.     

Liquid–Liquid Equilibria of Oxygenate Fuel Additives with Water at 25°C: Ternary and Quaternary Aqueous Systems of Methyl tert-Butyl Ether and tert-Amyl Methyl Ether with Methanol or Ethanol

Experimental tie-line data have been determined for the ternary system water + methyl tert-butyl ether + tert-amyl methyl ether and the quaternary systems water + methanol + methyl tert-butyl ether + tert-amyl methyl ether, and water + ethanol + methyl tert-butyl ether + tert-amyl methyl ether at 25°C and ambient pressure. The experimental results have been satisfactorily correlated using the modified UNIQUAC and extended UNIQUAC models with ternary and quaternary, in addition to binary parameters.     

Binary,ternary and quaternary liquid–liquid equilibria in 1-butanol,oleic acid,water and n-heptane mixtures

This work reports on liquid–liquid equilibria in the system 1-butanol, oleic acid, water and n-heptane used for biphasic, lipase catalysed esterifications. The literature was studied on the mutual solubility in binary systems of water and each of the organic components. Experimental results were obtained on the composition of the coexisting phases of a series of ternary and quaternary mixtures of the components at 301, 308 and 313 K. The data were correlated successfully with the UNIQUAC model that was extended with ternary interaction parameters.     

Ternary liquid–liquid equilibria for (water + terpene + 1-propanol or 1-butanol) systems at the temperature 298.15 K

Liquid–liquid equilibria and tie-lines for the ternary (water + 1-propanol + α-pinene, β-pinene or limonene) and (water + 1-butanol + α-pinene, β-pinene or limonene) mixtures have been measured at T = 298.15 K. The experimental ternary liquid–liquid equilibrium data have been successfully represented using the additional ternary parameters as well as the binary parameters in terms of the extended and modified UNIQUAC models.     

Prediction of ternary phase equilibria from binary data

The two-parameter UNIQUAC equation is modified to give better results of vapor—liquid and liquid—liquid equilibria for a variety of binary systems. The proposed equation is easily extended to a multicomponent system without including any ternary (or multicomponent) parameters. The good capability of the equation in data reduction is shown by many illustrative examples for various kinds of strongly nonideal binary and ternary mixtures.     

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.     

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.     

Liquid–liquid equilibria for the quaternary system methyl isobutyl ketone–water–phenol–hydroquinone

Liquid–liquid equilibria data of the quaternary system methyl isobutyl ketone (MIBK)–water–phenol–hydroquinone were measured at 25 °C under atmosphere pressure. The experimental data were correlated with the UNIQUAC and NRTL activity coefficient models on the base of the fixed binary interaction parameters that were obtained from two sub-ternary systems MIBK–water–phenol and MIBK–water–hydroquinone. The root mean square deviations (RMSD) show that the regressed results for the quaternary system were in good agreement with the experimental data for both UNIQUAC and NRTL models. The comparison between experimental and calculated distribution coefficient values of phenol and hydroquinone shows that a relative deviation of less than 5% is obtained.     

Combined chemical and phase equilibrium for the hydration of ethylene to ethanol calculated by means of the Peng-Robinson-Stryjek-Vera equation of state and the Wong-Sandler mixing rules

Due to the economics of the ethylene market and the subsidized production of fermentation-based ethanol in some countries, use of the ethylene hydration process to make ethanol has been steadily declining. The economics of this process might improve by combining the reaction and separation in a reactive distillation column, whose conceptual design requires a study of the combined chemical and phase equilibrium (CPE) of the reacting system. In this work, the Peng-Robinson-Stryjek-Vera equation of state was combined with the UNIQUAC activity coefficient model through the Wong-Sandler (WS) mixing rules in order to correlate the available experimental data for the vapor-liquid equilibria (VLE) of the ethylene-water, ethylene-ethanol, and ethanol-water binary systems at 200 °C. The interaction energies of the UNIQUAC model and the binary interaction coefficient of the WS mixing rules were used as the fitting parameters. From the optimum values of these parameters, both the VLE and the combined CPE of the ethylene-water-ethanol ternary system were predicted at 200 °C and various pressures. At this temperature, the catalytic activity of a H-pentasil zeolite has already been reported to exhibit a maximum for ethylene hydration, and also the experimentally measured two-phase region of the ternary system is sufficiently wide. By means of the reactive flash method, the chemical equilibrium compositions of the liquid and vapor phases were determined for several pressures, and the equilibrium conversion and the vapor fraction were calculated as functions of the ethylene to water feed mole ratio. It turns out that the vapor-liquid mixed-phase hydration of ethylene achieves equilibrium conversions much higher than those computed for a vapor-phase reaction that would hypothetically occur at the same conditions of pressure and feed mole ratio. It was found that the reactive phase diagram of the ternary system exhibits a critical point at 200 °C and 155 atm.     

A new modification of the UNIQUAC equation including temperature dependent parameters

The UNIQUAC equation was modified by introduction of a linear temperature dependence of the volume and surface area parameters, r_i and q_i. The slope of r_i and q_i functions were found to be the same for hydrocarbons and pyridine. The modified equation was used for prediction of vapor–liquid equilibria (VLE) in binary mixtures of hydrocarbons and pyridine with hydrocarbons as well as for the prediction of the excess enthalpy (H^E) in binary mixtures formed by pyridine with aliphatic alkanes. The results obtained were compared with predictions by UNIFAC and further with UNIQUAC equation and its modification involving temperature dependant coordination number z. The proposed temperature dependence of the r_i and q_i parameters enables prediction of the VLE at various temperatures and leads to reasonable values of H^E. The necessary input reduces to one set of isothermal VLE data. One set of UNIQUAC interaction parameters u_ij is sufficient for representation of VLE in a wide range of temperature and to obtain a reasonable prediction of H^E.     

Vapor-liquid and liquid-liquid equilibria of water, 2-methoxyethanol and cyclohexanone: Experiment and correlation

Vapor-liquid equilibria and liquid-liquid equilibria of a ternary mixture consisting of water, 2-methoxyethanol and cyclohexanone and in addition of all binary subsystems were studied experimentally at several temperatures. A ternary corrective term in the expression for the Gibbs free energy based on the NRTL model improves simultaneous representation of binary and ternary phase equilibria.