Evaluation of thermodynamic consistency of isobaric and isothermal binary vapor–liquid equilibrium data using the PAI test II,alcohol + n-alkane, +aromatic, +cycloalkane systems

The thermodynamic consistency of binary vapor–liquid equilibrium data has been examined for 46 binary alcohol + hydrocarbon systems with 310 data sets in total (145 isobaric and 165 isothermal sets) using the PAI test proposed in our previous study. The PAI test permits an overall check of the data by combining three tests: a point test, an area test, and an infinite dilution test. In this work, the PAI test was incorporated with the NRTL equation for fitting data. The results of the PAI test for the vapor–liquid equilibrium data showed that the PAI test was able to strictly select reliable data.     

Phase behavior of the system hyperbranched polyglycerol + methanol + carbon dioxide

Phase equilibrium data have been measured for the ternary system hyperbranched polyglycerol + methanol + carbon dioxide at temperatures of 313–450 K and pressures up to 13.5 MPa. Phase changes were determined according to a synthetic method using the Cailletet setup. At elevated temperatures the system shows a liquid–liquid–vapor region with lower solution temperatures. Besides the vapor–liquid and liquid–liquid equilibria, the vapor–liquid to vapor–liquid–liquid and vapor–liquid–liquid to liquid–liquid phase boundaries are reported at different polymer molar masses and can serve as test sets for thermodynamic models. A distinct influence of the polymer molar mass on the vapor–liquid equilibrium can be noticed and indicates the existence of structural effects due to the polymer branching. Modeling the systems with the PCP-SAFT equation of state confirms these findings.     

High pressure vapor–liquid equilibria for carbon dioxide + tetrahydrofuran mixtures

Vapor–liquid equilibria and saturated density for carbon dioxide + tetrahydrofuran mixtures at high pressures were measured by the analytical method at the temperatures 298.15 and 313.15 K. The experimental apparatus equipped with three Anton Paar DMA 512S vibrating tube density meters was previously developed for measuring vapor–liquid–liquid equilibrium at high pressures. The equilibrium composition and saturated density of each phase were determined by gas chromatograph and vibrating tube density meters, respectively. The bubble point pressure at the temperature 313.15 K was further measured by the synthetic method. The experimental data were correlated with Soave–Redlich–Kwong (SRK) equation of state and the pseudocubic equation of state.     

Equation of state for square-well chain molecules with variable range II. Extension to mixtures

An equation of state (EOS) developed in our previous work for square-well chain molecules with variable range is further extended to the mixtures of non-associating fluids. The volumetric properties of binary mixtures for small molecules as well as polymer blends can well be predicted without using adjustable parameter. With one temperature-independent binary interaction parameter, satisfactory correlations for experimental vapor–liquid equilibria (VLE) data of binary normal fluid mixtures at low and elevated pressures are obtained. In addition, VLE of n-alkane mixtures and nitrogen + n-alkane mixtures at high pressures are well predicted using this EOS. The phase behavior calculations on polymer mixture solutions are also investigated using one-fluid mixing rule. The equilibrium pressure and solubility of gas in polymer are evaluated with a single adjustable parameter and good results are obtained. The calculated results for gas + polymer systems are compared with those from other equations of state.     

A thermodynamic consistency test for the binary constant-temperature VLE data using numerically optimized binary parameters

A thermodynamic consistency (TC) test for the constant-temperature VLE data was investigated by numerically optimizing the binary parameters of the activity coefficient equations to satisfy the Gibbs–Duhem (GD) equation. It was shown that the one parameter Margules equation can best satisfy the GD equation, even if significant experimental errors are involved. A thermodynamic consistency (TC) criterion was defined using the one parameter Margules equation. The TC criterion showed that, of the 37 alkane–alkane, 18 methanol–water and 44 ethanol–water binaries, 36, 16 and 1 binaries are reliable, respectively. Simple liquid mixtures meet the TC criterion.     

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.     

Vapor–liquid equilibrium for binary system of tetrahydrothiophene + 2,2,4-trimethylpentane and tetrahydrothiophene + 2,4,4-trimethyl-1-pentene at 358.15 and 368.15 K

Isothermal vapor–liquid equilibrium (VLE) for tetrahydrothiophene + 2,2,4-trimethylpentane and tetrahydrothiophene + 2,4,4-trimethyl-1-pentene at 358.15 and 368.15 K were measured with a circulation still. All systems studied exhibit positive deviation from Raoult's law. No azeotropic behavior was found in all systems at the measured temperatures. The experimental results were correlated with the Wilson model and compared to COSMO-SAC predictive model. Analyses of liquid and vapor phase composition were determined with gas chromatography. All VLE measurements passed the three thermodynamic consistency tests used. The activity coefficients at infinite dilution are also presented.     

Isobaric vapor–liquid and vapor–liquid–liquid equilibrium data for the water–ethanol–hexane system

Isobaric vapor–liquid and vapor–liquid–liquid equilibria were measured for the water–ethanol–hexane system at normal atmospheric pressure. The apparatus used for the determination of vapor–liquid–liquid equilibrium data was an all-glass dynamic recirculating still with an ultrasonic homogenizer coupled to the boiling flask.     

Thermodynamic properties of new heat pump working pairs: 1,3-Dimethylimidazolium dimethylphosphate and water,ethanol and methanol

Ionic liquid 1,3-dimethylimidazolium dimethylphosphate ([MMIM][DMP]) + water/ethanol/methanol mixtures exhibit properties which render them suitable as candidates for working pairs in industrial applications of absorption heat pumps or chillers. In this paper, the thermodynamic properties including vapor pressure, density, viscosity, heat capacity as well as excess enthalpy of these binary systems were measured at various temperatures with different ionic liquid concentrations. The thermodynamic properties were correlated by different equations, respectively. The correlated values were significantly consistent with the experimental ones. In conclusion, the vapor–liquid equilibrium (VLE) data indicated that the vapor pressures of the three solvents in [MMIM][DMP] displayed a considerable negative deviation from Raoult's law, and the excess enthalpies of the three binary systems are negative. These characteristics are necessary and important for an absorption working pair.     

Prediction of ternary vapor–liquid equilibria for 33 systems by molecular simulation

A set of molecular models for 78 pure substances from prior work is taken as a basis for systematically studying vapor–liquid equilibria (VLE) of ternary systems. All 33 ternary mixtures of these 78 components for which experimental VLE data are available are studied by molecular simulation. The mixture models are based on the modified Lorentz–Berthelot combining rule that contains one binary interaction parameter which was adjusted to a single experimental binary vapor pressure of each binary subsystem in prior work. No adjustment to ternary data is carried out. The predictions from the molecular models of the 33 ternary mixtures are compared to the available experimental data. In almost all cases, the molecular models give excellent predictions of the ternary mixture properties.     

Monte Carlo simulations of vapor–liquid–liquid equilibrium of some ternary petrochemical mixtures

The aim of this study was to determine the capability and accuracy of Monte Carlo simulations to predict ternary vapor–liquid–liquid equilibrium (VLLE) for some industrial systems. Hence, Gibbs ensemble Monte Carlo simulations in the isobaric–isothermal (NpT) and isochoric–isothermal (NVT) ensembles were performed to determine vapor–liquid–liquid equilibrium state points for three ternary petrochemical mixtures: methane/n-heptane/water (1), n-butane/1-butene/water (2) and n-hexane/ethanol/water (3). Since mixture (1) exhibits a high degree of mutual insolubility amongst its components, and hence has a large three-phase composition region, simulations in the NpT ensemble were successful in yielding three distinct and stable phases at equilibrium. The results were in very good agreement with experimental data at 120 kPa, but minor deviations were observed at 2000 kPa. Obtaining three phases for mixture (2) with the NpT ensemble is very difficult since it has an extremely narrow three-phase region at equilibrium, and hence the NVT ensemble was used to simulate this mixture. The simulated results were, once again, in excellent agreement with experimental data. We succeeded in obtaining three-phase equilibrium in the NpT ensemble only after knowing, a priori, the correct three-phase pressure (corresponding to the force fields that were implemented) from NVT simulations. The success of the NVT simulation, compared to NpT, is due to the fact that the total volume can spontaneously partition itself favorably amongst the three boxes and only one intensive variable (T) is fixed, whereas the pressure and the temperature are fixed in an NpT simulation. NpT simulations yielded three distinct phases for mixture (3), but quantitative agreement with experimental data was obtained at very low ethanol concentrations only.     

Phase equilibria on four binary systems containing 3-methylthiophene

Isothermal vapor–liquid equilibrium (VLE) for 3-methylthiophene + 2,2,4-trimethylpentane at 368.15 K, 3-methylthiophene + 2,4,4-trimethyl-1-pentene at 368.15 K, 3-methylthiophene  + cyclohexane at 348.15 K, and 3-methylthiophene + 1-hexene at 333.15 K were measured with a recirculation still. All systems exhibit positive deviation from ideality. No azeotropic behavior was found in all systems. The experimental results were correlated with the Wilson model and also compared with the original UNIFAC and UNIFAC-Dortmund predictive models. Analyses of liquid and vapor-phase composition were determined with gas chromatography (GC). All VLE measurements passed the used thermodynamic consistency tests (integral, infinite dilution and point test). The activity coefficients at infinite dilution are also presented.     

Liquid–liquid equilibrium data for binary perfluoroalkane (C6 and C8) + n-alkane systems

This study aims to make detailed measurements of the solubility data for perfluoroalkane + n-alkane systems. Using a laser-scattering technique developed in our laboratory, we determined the liquid–liquid equilibria (LLE) for three binary mixtures: perfluorohexane + n-hexane, perfluorohexane + n-octane, and perfluorooctane + n-octane. The experimental LLE data were represented by the NRTL equation. In addition, the activity coefficients obtained from the experimental LLE data were compared with those obtained from the vapor–liquid equilibrium (VLE) data.     

High pressure vapor–liquid equilibrium measurements of carbon dioxide with naphthalene and benzoic acid

High pressure vapor–liquid equilibrium data for binary systems of carbon dioxide with naphthalene and benzoic acid were measured at three different temperatures for each system. Experimental temperatures and pressures ranged from 373 to 458 K and 0 to 22 MPa, respectively. Dew points were also measured for naphthalene in the CO₂ rich region. The data measured provides valuable solubility information and is used to derive gas–solvent group interaction parameters for the predictive Soave–Redlich–Kwong equation of state.     

New analytic apparatus for experimental determination of vapor–liquid equilibria and saturation densities

A new experimental apparatus for performing simultaneous determination of high-pressure vapor–liquid equilibria (VLE) and saturated densities was developed in this work. The experimental methodology was verified by measuring these properties for the carbon dioxide + 1-propanol and carbon dioxide + 2-propanol systems from 313 to 363 K. The apparatus is based on the static-analytic method for VLE determinations and was slightly modified by coupling a vibrating U-tube densitometer to obtain saturated densities for both vapor and liquid phases. VLE measurements agreed with previous literature data and were correlated with the Peng–Robinson equation of state coupled to the Wong–Sandler mixing rules. Saturation densities at temperatures above 313 K have not been published up to now.     

Isothermal vapor–liquid equilibrium data for the binary mixture ethyl fluoride (HFC-161) + 1,1,1,2,3,3,3-heptafluoroproane (HFC-227ea) over a temperature range from 253.15 K to 313.15 K

Vapor–liquid equilibrium (VLE) data for the refrigerant mixture ethyl fluoride (HFC-161) + 1,1,1,2,3,3,3-heptafluoroproane (HFC-227ea) are reported in the temperature range from 253.15 K to 313.15 K with a single-phase circulation vapor–liquid equilibrium still. The results of the correlation for the vapor–liquid equilibrium data with Peng–Robinson (PR) equation of state (EOS), combined with the first Modified Huron-Vidal (MHV1) mixing rule and Wilson model, are presented. These results are in a good agreement with experimental data. The average and maximum derivations of vapor molar composition are within 0.0130 and 0.0295 respectively, and the average and maximum relative derivations of pressure are within 1.04% and 2.96%, respectively. The model parameters, determined from these binary data, are given to predict the phase behavior for a later ternary system. The binary system HFC-161 + HFC-227ea is a non-azeotropic mixture and exhibits a negative deviation from Raoult's law.     

Equation of state for square-well chain molecules with variable range. I: Application for pure substances

An equation of state (EOS) for square-well chain molecules with variable range developed on the basis of statistical mechanics for chemical association in our previous work is employed for the calculations of pVT properties and vapor–liquid equilibria (VLE) of pure non-associating fluids. The molecular parameters for 73 normal substances and 46 polymers are obtained from saturated vapor pressure and liquid molar volume data for normal fluids or pVT data for polymers. Linear relations are found for the molecular parameters of normal fluids with their molecular weight of homologous compounds. This indicates that the model parameters of homologous series, subsequently pVT and VLE, can be predicted when experimental data are not available. The predicted saturated vapor pressures and/or liquid volumes are satisfactory through the generalized model parameters. The calculated VLE and pVT for normal fluids and polymers by this EOS are compared with those from other engineering models, respectively.     

Molecular models for 267 binary mixtures validated by vapor–liquid equilibria: A systematic approach

By assessing a large number of binary systems, it is shown that molecular modeling is a reliable and robust route to vapor–liquid equilibria (VLE) of mixtures. A set of simple molecular models for 78 pure substances from prior work is taken to systematically describe all 267 binary mixtures of these components for which relevant experimental VLE data is available. The mixture models are based on the modified Lorentz–Berthelot combining rule. Per binary system, one state independent binary interaction parameter in the energy term is adjusted to a single experimental vapor pressure. The unlike energy parameter is altered usually by less than 5% from the Berthelot rule. The mixture models are validated regarding the vapor pressure at other state points and also regarding the dew point composition, which is a fully predictive property in this work. In almost all cases, the molecular models give excellent predictions of the mixture properties.     

Vapor–liquid equilibria and phase densities at saturation of carbon dioxide + 1-butanol and carbon dioxide + 2-butanol from 313 to 363 K

Experimental vapor–liquid equilibria for the systems carbon dioxide + 1-butanol and carbon dioxide + 2-butanol were obtained from 313 to 363 K via a static-analytic set-up. A vibrating U-tube densitometer was coupled to this apparatus to perform simultaneous measurements of both saturated densities of the vapor and liquid phases. The suitability of this apparatus was checked by comparing the experimental vapor–liquid equilibrium and saturated density results with the literature data. The experimental vapor–liquid equilibrium data were correlated using the Peng–Robinson equation of state coupled to the Wong–Sandler mixing rules with good agreement; however densities using the same model were not satisfactorily represented.