Vapor–liquid equilibria for systems of diethyl carbonate and ketones and determination of group interaction parameters for the UNIFAC and ASOG methods

Densities and speeds of sound for the binary mixtures acetone, 2-butanone and 2-pentanone + diethyl carbonate, over the whole composition range, at T = 298.15 K and atmospheric pressure have been measured. Excess molar volumes and deviations in isentropic compressibility for the binary systems were fitted to the Redlich–Kister polynomial. Isobaric vapor–liquid equilibria for the binary systems acetone + diethyl carbonate, 2-butanone + diethyl carbonate and 2-pentanone + diethyl carbonate at P = 101.3 kPa have been determined. The activity coefficients were calculated to be thermodynamically consistent and they were correlated with the Wilson, NRTL, UNIQUAC and Redlich–Kister equations. Interaction parameters related to the carbonate (OCOO) and ketone (CO) groups, in ASOG and UNIFAC methods, have been determined using our experimental VLE data.     

Predicting vapor–liquid equilibria of fatty systems

In the present work, a group contribution method is proposed for the estimation of the vapor pressure of fatty compounds. For the major components involved in the vegetable oil industry, such as fatty acids, esters and alcohols, triacylglycerols (TAGs) and partial acylglycerols, the optimized parameters are reported. The method is shown to be accurate when it is used together with the UNIFAC model for estimating vapor–liquid equilibria (VLE) of binary and multicomponent fatty mixtures comprised in industrial processes such as stripping of hexane, deodorization and physical refining. The results achieved show that the group contribution approach is a valuable tool for the design of distillation and stripping units since it permits to take into account all the complexity of the mixtures involved. This is particularly important for the evaluation of the loss of distillative neutral oil that occurs during the processing of edible oils.The combination of the vapor pressure model suggested in the present work with the UNIFAC equation gives results similar to those already reported in the literature for fatty acid mixtures and oil–hexane mixtures. However, it is a better tool for predicting vapor–liquid equilibria of a large range of fatty systems, also involving unsaturated compounds, fatty esters and acylglycerols, not contemplated by other methodologies. The approach suggested in this work generates more realistic results concerning vapor–liquid equilibria of systems encountered in the edible oil industry.     

Vapor–liquid equilibria of asymmetrical systems using UNIFAC-NRF group contribution activity coefficient model

The UNIFAC-NRF group contribution activity coefficient model is used for the calculation of vapor–liquid equilibria of binary systems of the heavy alkanes and light gases such as CH₄, C₂H₆, CO₂ and N₂. The linear combination mixing rule, LCVM, of the Huron–Vidal and Michelsen, Chen et al. modification of PSRK and Universal Group Contribution Equation of State of Ahlers and Gmehling are combined with the UNIFAC-NRF group activity coefficient model to correlation of the vapor–liquid equilibrium of both light and heavy hydrocarbons. The results show that the LCVM mixing rule combing with UNIFAC-NRF group contribution model correlate the asymmetric systems better than the LCVM-UNIFAC and the other EOS/G^E models. Also the group contribution model is used for the prediction of the phase envelope of the synthetic fluid with accurate results.     

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.     

Vapour–liquid equilibria of dimethyl carbonate with linear alcohols and estimation of interaction parameters for the UNIFAC and ASOG method

Isobaric vapour–liquid equilibria have been experimentally determined for the binary systems methanol+dimethyl carbonate, ethanol+dimethyl carbonate, dimethyl carbonate+1-propanol, dimethyl carbonate+1-butanol and dimethyl carbonate+1-pentanol at 101.3 kPa. The activity coefficients were calculated to be thermodynamically consistent and were correlated with the Wilson and UNIQUAC equations. Interaction parameters related to the carbonate group (OCOO) and alcohols, in ASOG and UNIFAC methods, have been determined using our experimental VLE data. The experimental results, as well as those by other authors, agree with the calculated VLE using the new ASOG and UNIFAC parameters.     

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.     

Liquid–liquid equilibria of polydisperse polymer systems: applicability of continuous thermodynamics

Continuous thermodynamics is a suitable tool for describing the thermodynamic properties of solutions of polydisperse polymers. To represent liquid–liquid equilibria of polydisperse polymer/solvent systems, a continuous distribution function to represent the composition of polydisperse polymers has to be considered. In this study, we calculate the molar mass distributions of both principal phases and conjugate phases, using the extended Flory–Huggins model. The results for various polydisperse polymer systems are compared with experimental data.     

A non-recycle flow still for the experimental determination of vapor–liquid equilibria in reactive systems

Experiments for the determination of vapor–liquid equilibrium (VLE) data with a Non-Recycle Flow Still (NFS) are described. Due to short residence times, the NFS is especially suited for systems with thermally unstable components and for reactive mixtures. VLE data of the latter are necessary for modeling reactive distillation processes. With the NFS isobaric data both at atmospheric and at reduced pressure can be gained. The potential of this technique is demonstrated and validated with the well-known, non-reactive systems methanol–ethanol and ethanol–water. The other (mainly reactive) binary mixtures investigated stem from two esterification systems (methyl formate and ethyl acetate production) and one etherification system (tert-amyl methyl ether production). The NRTL equation is used for modeling of the VLE data. The data acquired with the NFS are compared with literature data (whenever possible) or with results of group contribution methods.     

Liquid—liquid equilibria for ternary systems of water—phenol and solvents: new UNIFAC parameters for interactions between the groups ACOH/COOH and prediction

The UNIFAC group-contribution method is used to predict ternary liquid—liquid equilibrium data presented in a recent paper (Alvarez Gonzalez et al.) for the systems water/phenol/benzene, water/phenol/ethylbenzene, water/phenol/nonanoic acid, water/phenol/ethyl acetate, water/phenol/isopropyl acetate, water/phenol/n-butyl acetate, water/phenol/isoamyl acetate and water/phenol/cyclohexyl acetate at 25°C and water/phenol/n-hexyl acetate at 25, 35 and 45°C. New UNIFAC interaction parameters between the groups ACOH/COOH have been obtained.A comparison between the experimental and predicted values is presented.     

Prediction of solubilities of salts,osmotic coefficients and vapor–liquid equilibria for single and mixed solvent electrolyte systems using the LIQUAC model

The electrolyte model LIQUAC has been used up till now to predict osmotic coefficients, mean ion activity coefficients, the vapor–liquid equilibrium (VLE) behavior, the solubility of gases in single and mixed solvent electrolyte systems, and solubilities of salts in aqueous solutions. In this paper, the required expressions for the calculation of salt solubilities not only in aqueous systems, but also in organic solvents and water–solvent electrolyte systems were deduced in detail based on the LIQUAC model with a fixed reference state and thermodynamic relations. Four salts (NaCl, KCl, NH₄Cl and NaF) and two solvent (water and methanol) were selected to test the derived expressions. The results show that the LIQUAC model with a fixed reference state can be used to predict osmotic coefficients, solubilities of salts in aqueous solutions, vapor–liquid equilibria, and the solubilities of salts in water–organic solvent systems with strong electrolytes.     

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.     

Calculation of pVT and vapor–liquid equilibria of copolymer systems based on an equation of state

A molecular thermodynamic model for copolymers and their mixtures has been established by adopting the hard-sphere-chain fluid as a reference and a square-well (SW) term as well as an association term as a perturbation. The latter is introduced to consider various associating functions in a chain-like molecule based on the shield-sticky model of chemical association. The model adopts five molecular parameters, i.e. r_i, σ_ii ε_ii/k, δε_ii/k and ω_ii, for a polymer species i, where the last two are responsible for association. These parameters can be obtained from the pVT data of the corresponding molten homopolymer i. The model can be used to correlate pVT data for molten copolymers with an adjustable parameter describing the interaction between different polymer species. The model can also be used to calculate vapor–liquid equilibria (VLE) for copolymer solutions with three adjustable interaction parameters.     

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.     

Correlation and prediction of salt effects on vapor–liquid equilibrium in alcohol–water–salt systems

A modification of the solvation model of Ohe is proposed for the calculation of vapor–liquid equilibria (VLE) in alcohol–water–salt systems. The modified method employs the Bromley equation to calculate the activity of water in salt solutions, and a one-parameter empirical expression to calculate the activity of the alcohol. The single parameter is obtained by fitting ternary alcohol–water–salt data. The method is simple to use and does not require data on the vapor-pressures of alcohol–salt mixtures that are seldom available in the literature. Experimental data for 17 salts in 36 alcohol–water–salt systems, covering a temperature range from 298 to 375 K, and salt concentrations up to about 8 m, were correlated using the new approach. In all, 69 data sets and 1045 data points were correlated satisfactorily. The method was also used to predict VLE in four ternary alcohol–alcohol–salt systems and one quaternary alcohol–alcohol–water–salt system with satisfactory results.     

Liquid–liquid equilibrium in ternary ionic liquid systems by UNIFAC: New volume,surface area and interaction parameters. Part I

Ternary liquid–liquid equilibria (LLE) data in systems involving ionic liquids has been investigated by several years, mainly due to the innovative role of ionic liquids as extraction solvents. The thermodynamic modeling of these systems has been performed almost invariably with the well-known NRTL model. In recent years, the UNIQUAC model has also been used, with structural parameters for ionic liquids determined either by empirical correlations or, more recently, through quantum mechanics calculations. In this work, the structural group volume and area parameters for the group-contribution UNIFAC method have been calculated for six ionic liquids following the quantum mechanics approach. The Density Functional Theory (DFT) was used to optimize the molecular geometry and the Polarizable Continuum Method (PCM) was used to calculate the area and volume. The obtained parameters were used to correlate LLE data for twenty-four ternary systems, totalizing 169 tie-lines. New interaction parameters were also estimated between the solvent and ionic liquid functional groups. The results are very satisfactory, with root mean square deviations between experimental and calculated compositions about 1.6%.     

A new three-parameter cubic equation of state for calculation physical properties and vapor–liquid equilibria

A new three-parameter cubic equation of state is presented by combination of a modified attractive term and van der Waals repulsive expression. Also a new alpha function for the attractive parameter of the new EOS is proposed. The new coefficients of alpha function and the other parameters of the attractive term are adjusted using the data of the saturated vapor pressure and liquid density of almost 60 pure compounds including heavy hydrocarbons. The new EOS is adopted for prediction of the various thermophysical properties of pure compounds such as saturated and supercritical volume, enthalpy of vaporization, compressibility factor, heat capacity and sound velocity. Following successful application of the new EOS for the pure components, using vdW one-fluid mixing rules, the new EOSs are applied to prediction of the bubble pressure and vapor mole fraction of the several binary and ternary mixtures. The accuracy of the new EOS for phase equilibrium calculation is demonstrated by comparison of the results of the present EOSs with the PT, PR, GPR and SRK cubic EOSs.