Ternary liquid—liquid equilibria and their representation by modified NRTL equations

Experimental liquid—liquid equilibrium data are reported for the systems acetonitrile—acetone—cyclohexane at 318.15 K and acetonitrile—methyl acetate—cyclohexane at 313.15 K. Two modified forms of the NRTL equation proposed by Renon are presented by substituting local surface fractions for local mole fractions and further by including Guggenheim's combinatorial entropy for athermal mixtures whose molecules differ in size and shape. The resultant equations involve three adjustable parameters and are extended to multicomponent systems without adding ternary (or higher) parameters. Calculated results of vapor—liquid and liquid—liquid equilibria for typical binary and ternary mixtures are presented.     

The prediction of isobaric phase equilibria for non-ideal multicomponent mixtures from heat of mixing data

A method for predicting isobaric binary and ternary vapor—liquid equilibrium data using only isothermal binary heat of mixing data and pure component vapor pressure data is presented. Three binary and two ternary hydrocarbon liquid mixtures were studied. The method consists of evaluating the parameters of the NRTL equation from isothermal heat of mixing data for the constituent binary pairs. These parameters are then used in the multicomponent NRTL equation to compute isobaric vapor—liquid equilibrium data for the ternary mixture. No ternary or higher order interaction terms are needed in the ternary calculations because of the nature of the NRTL equation. NRTL parameters derived from heat of mixing data at one temperature can be used to predict vapor—liquid equilibrium data at other temperatures up to the boiling temperature of the liquid mixture.For the systems studied this method predicted the composition of the vapor phase with a standard deviation ranging from 1–8% for the binary systems and from 4–12% for the ternary systems.     

A perturbed hard-sphere-chain equation of state for mixtures: Prediction from critical point constants

A modified perturbed hard-sphere-chain equation of state by Eslami [H. Eslami, Fluid Phase Equilibr. 216 (2004) 21-26], is extended to mixtures. The resulting equation of state for mixtures consists of two temperature-dependent parameters as well as an additional parameter, reflecting the segment size for pure components. The temperature-dependent parameters of the equation of state are correlated as universal functions of the reduced temperature. It is shown that knowing just the critical constants of pure components is sufficient to calculate the temperature-dependent parameters. The equation of state for mixtures is checked against the experimental pressure-volume-temperature data for a large number of mixtures, having varieties of molecular sizes and shapes. It is shown that no interaction parameter is needed to describe the behavior of fluid mixtures. Among about 3500 data points for mixtures, the average absolute deviation, compared to the experimental data, is about 0.93%.     

Vapour–liquid equilibrium measurements and modelling for the ternary system (water + 2-propanol + 1-butyl-3-methylimidazolium acetate)

Vapour–liquid equilibrium (VLE) data were measured for the ternary mixtures of water (1)?+?2-propanol (2)?+?1-butyl-3-methylimidazolium acetate ([bmim][OAc]) (3). Complete T, x and y data were obtained in a relatively wide range of ionic liquid (IL) mass fractions up to 0.8. The data were correlated by means of NRTL and eNRTL equations with satisfactory results. Using the eNRTL equation, the ternary VLE behaviour was also modelled through correlation of two data sets, in which the mole fraction of 2-propanol on IL-free basis is respectively at 0.1 and 0.98. In this way, the six data sets were reproduced satisfactorily, with root mean square deviations of 1.06?K for temperature and 0.0098 for vapour-phase mole fractions. Owing to the regular distribution of the experimental data, good agreement between experiment and calculation was graphically presented. Effect of the IL on the VLE behaviour of the volatile components was also illustrated.     

Liquid—liquid equilibrium data: Their retrieval,correlation and prediction Part II: Correlation

The correlation of liquid—liquid equilibrium data using models for the liquid phase activity coefficients — for example NRTL and UNIQUAC — is reviewed. Different numerical procedures used in the computation of liquid—liquid equilibrium compositions on the basis of these models are evaluated. Methods for obtaining parameters from liquid—liquid equilibrium data are described, and a method leading to improved representation of tie lines using relatively few parameters is recommended. The NRTL and UNIQUAC equations are compared with respect to their ability of representing binary and ternary liquid—liquid equilibrium data. The UNIQUAC equation appears to be more convenient to use and to correlate the data slightly better than does NRTL with the same number of parameters.     

The prediction of isothermal phase equilibria for non-ideal multicomponent mixtures from heats of mixing

A method is presented for predicting both vapor—liquid and liquid—liquid equilibria for multicomponent mixtures using heat of mixing data for the constituent binary pairs together with pure component vapor pressures. Its application to two highly non-ideal hydrocarbon ternary systems is discussed. The parameters of the hybrid local composition model of Renon and Prausnitz, known as the NRTL equation, were evaluated from heat of mixing data for the three binary pairs in each of the two ternary systems. The parameters thus obtained were used in the multicomponent form of the NRTL equation to predict the ternary vapor—liquid equilibrium data for the completely miscible system cyclohexane(1)—n-heptane(2)—touluene(3) and for the partially miscible system acetonitrile(1)—benzene(2)—n-heptane(3) without the need for any ternary or higher order parameters.This method predicted compositions of the single phase region of the partially miscible ternary system with a standard deviation of 10%. It also predicted compositions for the fully miscible system with a standard deviation of 4.6%. Total pressure curves for the partially miscible and miscible ternaries were predicted with standard deviations of 6.6% and 4.5% respectively. Poor predictions of the binodal curve for the partially miscible region were obtained. The method offers a means of predicting the whole range of ternary phase equilibria for miscible systems.     

Kirkwood correlation factors in liquid mixtures from an extended Onsager-Kirkwood-Fröhlich equation

Two approaches for applying the Onsager-Kirkwood-Fr?hlich equation to liquid mixtures are revisited at the light of recent developments leading to the estimation of relative permittivities and refractive indices of thermodynamically ideal liquid mixtures. From the one-liquid approach, the squared permanent dipole moment of the mixture molecular-equivalent species M is demonstrated to be a mole-fraction average of squared permanent dipole moments of the components. An expression is obtained for calculating the ideal Kirkwood correlation factor of M at any composition by using only pure-constituent properties. From the two-liquid approach (B?ttcher's equation), equations are obtained to describe the dependence on composition of the Kirkwood correlation factor of both components in the ideal mixture, even in mixtures of Onsager liquids. This dependency is tentatively ascribed to London dispersion forces acting between unlike molecules. It is demonstrated that B?ttcher's equation can only be applied to mixtures where the relative permittivity of each component is larger than the squared refractive index of the other component. From the interplay of one- and two-liquid approaches, the ideal Kirkwood correlation factor of M and of both constituents are inter-related. Thermodynamic expressions are given for the calculation of excess Kirkwood correlation factors. In the case where permanent dipole moments are unknown, the ratio excess/ideal, termed the relative excess Kirkwood correlation factor for components and species M can still be evaluated. These ratios are related to more conventional excess properties. Density, relative permittivity and refractive index data are reported for binary mixtures of 2,2,2-trifluoroethanol with mono-, di-, tri- or tetra-glyme over the whole composition range at 288 K and 298 K. For these systems, ideal, excess and relative excess and Kirkwood correlation factors are calculated and discussed. In particular, by regarding Kirkwood correlation factors as a measure of order/molecular organisation in liquid mixtures, it is found that the formation of ideal mixtures entails a decrease of order which, for the present binary systems, is almost cancelled out upon passage to the corresponding real mixtures. It is concluded that the present formulation permits to estimate Kirkwood correlation factors of each constituent of liquid mixtures and thereby to draw information on their molecular organisation.     

Vapor pressure measurement for water,methanol, ethanol,and their binary mixtures in the presence of an ionic liquid 1-ethyl-3-methylimidazolium dimethylphosphate

Vapor pressure data were measured for water, methanol and ethanol as well as their binary mixtures with an ionic liquid (IL) 1-ethyl-3-methylimidazolium dimethylphosphate ([EMIM][DMP]) at varying temperature and IL-content ranging from mass fraction of 0.10–0.70 by a quasi-static method. The vapor pressure data for the IL-containing binary systems were correlated using NRTL equation with average absolute relative deviation (ARD) within 0.0076, and the binary NRTL parameters was used for predicting the vapor pressure of the IL-containing ternary systems with reasonable accuracy. In addition, the infinite activity coefficients of solvents in [EMIM][DMP] and isobaric vapor–liquid equilibrium for IL-containing ternary systems at 101.325 kPa and mass fraction of IL being 0.5 were predicted with the regressed NRTL parameters. The results indicate that ionic liquid [EMIM][DMP] can depress the volatility of the solvents of water, methanol and ethanol but to a varying degree, leading to the variation of relative volatility of a solvent and even removal of azeotrope for water–ethanol mixture.     

Vapor–liquid equilibria and density measurement for binary mixtures of o-xylene + NMF, m-xylene + NMF and p-xylene + NMF at 333.15 K, 343.15 K and 353.15 K from 0 kPa to 101.3 kPa

Isothermal vapor–liquid equilibria at 333.15 K, 343.15 K and 353.15 K for three binary mixtures of o-xylene, m-xylene and p-xylene individually mixed with N-methylformamide (NMF), have been obtained at pressures ranged from 0 kPa to 101.3 kPa over the whole composition range. The Wilson, NRTL and UNIQUAC activity coefficient models have been employed to correlate experimental pressures and liquid mole fractions. The non-ideal behavior of the vapor phase has been considered by using the Peng–Robinson equation of state in calculating the vapor mole fraction. Liquid and vapor densities were measured by using two vibrating tube densitometers. The excess molar volumes of the liquid phase were also determined. Three systems of o-xylene + NMF, m-xylene + NMF and p-xylene + NMF mixtures present large positive deviations from the ideal solution and belong to endothermic mixings because their excess Gibbs energies are positive. Temperature dependent intermolecular parameters in the NRTL model correlation were finally obtained in this study.     

Liquid–liquid equilibria of water/1-propanol/methyl ethyl ketone/potassium chloride

The liquid–liquid equilibrium of water/1-propanol/methyl ethyl ketone (MEK) at 25°C was significantly modified by the presence of dissolved potassium chloride. Water is salted out of the organic phase while MEK is more preferentially salted out of the aqueous phase than 1-propanol. These results in considerable enlargement of the two-phase region and enhancement of the extractive efficiency of MEK for the separation of 1-propanol from its aqueous mixture. Good correlation of the liquid–liquid equilibria (LLE) of the system in the presence of potassium chloride up to saturation was obtained with Tan’s modified NRTL phase model for multicomponent solute–solvent mixtures with the solute–solvent interaction parameters expressed as a third-order polynomial function in salt concentration. Similar to the observation reported for vapour–liquid equilibrium (VLE) of solvent–solute mixtures, salting-in and salting-out of the solvent components from the respective phases can be predicted according to the relative solute–solvent interaction parameters of the solvent components in the two phases.     

Ternary liquid–liquid equilibria for mixtures of (ethanol + toluene + n -decane)

The data on the liquid–liquid equilibrium in (ethanol?+?toluene?+?n-decane) have been measured at three temperatures 298.15, 303.15 and 313.15?K and ambient pressure. Gas liquid chromatography has been employed, to determine the composition of the substances in liquid phases. The measured tie-line data are presented. The experimental ternary liquid–liquid equilibrium data have been correlated, using the universal quasi chemical (UNIQUAC) and non-random tow-liquid (NRTL) activity coefficient models to obtain the binary interaction parameters of these components. Both the UNIQUAC and NRTL models, satisfactorily predict the equilibrium compositions. The partition coefficients and the selectivity factor of the toluene extraction from n-decane mixtures were calculated and presented.     

Liquid–liquid equilibria of water/acetic acid/1-butanol system — effects of sodium (potassium) chloride and correlations

Sodium and potassium chloride were experimentally shown to be effective in modifying the liquid–liquid equilibrium (LLE) of water/acetic acid/1-butanol system in favour of the solvent extraction of acetic acid from an aqueous solution with 1-butanol, particularly at high salt concentrations. Both the salts enlarged the area of the two-phase region; decreased the mutual solubilities of water and marginally decreased the concentrations of 1-butanol and acetic acid in the aqueous phase while significantly increased the concentrations of the same components in the organic phase. These effects essentially increased the heterogeneity of the system, which is an important consideration in designing a solvent extraction process. The equilibrium data were well correlated by Eisen–Joffe equation with respect to the overall molar ratio of salt to water in the liquid phases. By expressing the salt–solvent interaction parameters as a third order polynomial of salt concentration in the liquid phase, Tan's modified NRTL model [T.C. Tan, Trans. Inst. Chem. Eng., Part A 68 (1990) 93–103.] for solvent mixtures containing salts or dissolved non-volatile solutes was able to provide good correlation of the present LLE data. Using the regressed salt concentration coefficients for the salt–solvent interaction parameters and the solvent–solvent interaction parameters obtained from the same system without salt, the calculated phase equilibria compared satisfactorily well with the experimental data.     

Isobaric vapor–liquid phase equilibria for the binary systems of tert-butanol + 2-ethyl-1-hexanol and n-butanol + 2-ethyl-1-hexanol

Isobaric vapor–liquid equilibria for the binary mixtures of tert-butanol (TBA) + 2-ethyl-1-hexanol and n-butanol (NBA) + 2-ethyl-1-hexanol were experimentally investigated at atmospheric pressure in the temperature range of 353.2–458.2 K. The raw experimental data were correlated using the UNIQUAC and NRTL models and used to estimate the interaction parameters between each pair of components in the systems. The experimental activity coefficients were obtained using the gas chromatographic method and compared with the calculated data obtained from these equilibrium models. The results show that UNIQUAC model gives better correlation than NRTL for these binary systems. The liquid–liquid extraction of TBA from aqueous solution using 2-ethyl-1-hexanol was demonstrated by simulation and the variation of separation factor of TBA at several temperatures was reported.     

Perfect wetting along a three-phase line: theory and molecular dynamics simulations

Wetting behavior along a three-phase equilibrium has been obtained by density gradient theory (DGT) and molecular dynamics simulations for a type-II equal size Lennard-Jones mixture. In order to perform a consistent comparison between both methodologies, the molecular parameters of this type of mixture were defined from the global phase diagram of equal size Lennard-Jones mixtures. We have found excellent agreement between predictions from the DGT (coupled to a Lennard-Jones equation for the bulk phases) and simulations results for both the phase and interface behavior, in the whole temperature, pressure, and concentration ranges. For all conditions explored in this work, this type-II mixture shows a three-phase equilibrium composed by a bulk immiscible liquid phase (L1) and a bulk gas phase (G) separated by a second immiscible liquid phase (L2). A similar phase distribution is obtained from the interfacial concentration profile in the whole range of conditions used in this work. This type of structure is a clear evidence that L2 completely wets the GL1 interface. The wetting behavior is also confirmed by the values and evolution of the interfacial tensions. In summary, this kind of type-II mixture does not show wetting transitions and exhibits a permanent perfect wetting in all the thermodynamic conditions explored here.     

Phase equilibria of (water + levulinic acid + dibasic esters) ternary systems

Liquid–liquid equilibrium (LLE) data of the solubility (binodal) curves and tie-line end compositions were examined for mixtures of {(water (1) + levulinic acid (2) + dimethyl succinate or dimethyl glutarate or dimethyl adipate (3)} at 298.15 K and 101.3 ± 0.7 kPa. The reliability of the experimental tie-line data was confirmed by using the Othmer–Tobias correlation. The LLE data of the ternary systems were predicted by UNIFAC method. The LLE data were correlated fairly well with UNIQUAC and NRTL models, indicating the reliability of the UNIQUAC and NRTL equations for these ternary systems. The best results were achieved with the NRTL equation, using non-randomness parameter (α = 0.3) for the correlation. Distribution coefficients and separation factors were measured to evaluate the extracting capability of the solvents.     

The excess characteristics of binary Lennard-Jones systems calculated by integral equation theory for partial distribution functions

The excess properties of Lennard-Jones systems were studied using the Ornstein-Zernike equation and integral equation theory for partial distribution functions. The calculation results are presented and the behavior of excess functions (internal energy, enthalpy, and isochoric heat capacity) is analyzed. The calculations were performed for liquid mixtures in the sub-and supercritical states whose components differed in the size of molecules, σ₁/σ₂ = 1–4, and attraction energy, ?₁/?₂ = 1–4.     

Estimation of the Activity Coefficients in Liquid Mixtures by Using Volumetric Data

We present an equation that relates the partial molar volume of binary liquid mixtures with the natural logarithms of the activity coefficients of solute and solvent. This equation, in combination with one of the activity coefficient models such as those of Margules, Wilson, Van Laar or NRTL, can be used to estimate the activity coefficients of binary liquid mixtures, knowing only the densities of the mixtures over the full range of concentration. In addition, we show a comparison of the estimated activities and activity coefficients at infinite dilution with experimental values for aqueous solutions of 1,2-butanediol, 2,3-butanediol, 1,3-butanediol, and 1,4-butanediol at 298.15?K. This method for the estimation of activity coefficients can be applied to aqueous binary mixtures, because the equation presented is deduced from physicochemical principles.     

Liquid–liquid equilibria of copolymer mixtures based on an equation of state

Liquid–liquid equilibria of copolymer mixtures were studied by an equation of state (EoS) for chain-like fluids. The equation consists of a reference term for hetero-nuclear hard-sphere chain fluids developed by Hu et al. where the next-to-nearest-neighbor correlations have been taken into account; and a perturbation term from Alder et al.’s square-well attractive potential. The segment parameters, including number of segments, segment diameter and interaction energy between segments, are obtained by fitting pVT data of pure homopolymer. For the case of different species in the same copolymer, the interaction parameters for unlike segment pairs are obtained by fitting pVT data of pure copolymer. For the interaction between segment of homopolymer and different species in copolymer, the parameters are treated as adjustable by fitting liquid–liquid equilibria data. In the latter case, the difference between different species in a copolymer is simply neglected as an approximation. Therefore, in general, only one pair of adjustable interaction parameter is determined from LLE data. To model miscibility maps of copolymer mixtures having two or three kinds of species, the interaction parameters are obtained from the boundary between miscible and immiscible regions. The EoS used in this work can correlate phase behavior including coexistence curves, miscibility windows and miscibility maps.     

Isobaric vapor–liquid equilibria of three aromatic hydrocarbon-tetraethylene glycol binary systems

Isobaric vapor–liquid equilibrium data have been determined at 101.33 kPa for the binary mixtures of benzene-tetraethylene glycol (TeEG), toluene-TeEG and o-xylene-TeEG. The vapor-phase fugacity coefficients were calculated from the virial equation. The thermodynamic consistency of the data has been tested via Herington analysis. The binary parameters for four activity coefficient models (van Laar, Wilson, NRTL and UNIQUAC) have been fitted with the experimental data. A comparison of model performances has been made by using the criterion of root mean square deviations in boiling point and vapor-phase composition.