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.     

Phase and extraction equilibria in water–polyethyleneglycol ethers of monoethanolamides of synthetic fatty acid–ammonium chloride systems

Phase equilibria in layering systems of water, polyethyleneglycol ethers of monoethanolamides of synthetic fatty acids (SFAs) (synthamide-5), and ammonium chloride are studied. The possibility of using such systems for the liquid extraction of metal ions is evaluated. The effect the nature of salting-out agents has on the processes of segregation of the systems has been considered.     

Liquid—liquid equilibria in water—aliphatic alcohol systems in the presence of sodium chloride

Liquid—liquid equilibria in mixtures of water, propyl or butyl alcohol isomers and sodium chloride have been studied experimentally at 25 °C The solvent behaviour of the various alcohols is discussed. Setschenow constants, calculated from the measured data, are compared with the results of the scaled particle theory.     

Solid–liquid equilibria for systems containing 1-butyl-3-methylimidazolium chloride

The solubility of 1-butyl-3-methylimidazolium chloride [C₄mim][Cl] in alcohols {ethanol, 1-butanol, 1-hexanol, 1-octanol, 1-decanol, 1-dodecanol, 2-butanol, 2-methyl-2-propanol (tert-butanol)} has been measured by a dynamic method from 270 K to the melting point of the ionic liquid or to the boiling point of the solvent. The melting point, enthalpy of fusion, and the temperature of the glass phase transition were determined by differential scanning calorimetry.The solubility data were correlated by means of the Wilson, UNIQUAC ASM and modified NRTL1 equations utilizing parameters derived from the solid–liquid equilibrium data. The root-mean-square deviations of the solubility temperatures for all calculated data were higher than 0.9 K and depended on the particular equation used.     

Modelling of high-pressure phase equilibria using the Sako–Wu–Prausnitz equation of state: II. Vapour–liquid equilibria and liquid–liquid equilibria in polyolefin systems

Phase equilibria in binary and ternary polyolefin systems are calculated using the cubic equation of state proposed by Sako–Wu–Prausnitz (SWP). Calculations were done for high-pressure phase equilibria in ethylene/polyethylene (LDPE) systems and for liquid–liquid equilibria (LLE) in systems containing either high-density polyethylene or poly(ethylene-co-propylene). The calculations for the copolymer/solvent systems are compared with those using the SAFT EOS. The two equations of state can describe UCST, LCST as well as U-LCST behaviour with similar accuracy. Whereas, the binary interaction parameter is temperature-independent for SAFT, it is found to be a function of temperature for the SWP model. Moreover, the influence of an inert gas on the LCST of the polyethylene/hexane system is investigated using the SWP EOS. The polydispersity of the different polyethylenes is considered in the phase equilibrium calculations using pseudocomponents chosen by the moments of the experimental molecular weight distributions.     

Salt effects on liquid–liquid equilibria in the partially miscible systems water+2-butanone and water+ethyl acetate

Liquid–liquid equilibrium data for the partially miscible systems of water+2-butanone+salt and water+ethyl acetate+salt were measured at 298.15 K. The salts used were potassium iodide, sodium bromide and lithium chloride. The systems were compared in terms of salting effect. The three-contribution electrolyte NRTL model is used to perform the data regression of the experimental data. New binary parameters are obtained. The calculated results are compared with the experimental data.     

Liquid–liquid equilibria in ternary systems of linear and cross-linked water-soluble polymers

In this study, ternary liquid–liquid equilibrium data of structurally similar linear and cross-linked polymers have been measured in order to elucidate the significance of mixing and elastic effects in sorption of binary liquid mixtures by cross-linked polymers. Dextran, sodium poly(styrene sulfonate), and sodium poly(acrylate) were used as the linear analogues for Sephadex gels and for strong and weak cation exchange resins. Cloud-point and co-existence curves were measured in water/ethanol and water/2-propanol mixtures at 283–343 K and the results were correlated by using a generalized Flory–Huggins model. The mixing parameters of the linear polymers were used to simulate the sorption data in the cross-linked materials and the effect of cross-links was accounted for by a non-ideal elastic model. Good agreement between the simulated and experimental values is obtained, when the chemical heterogeneity and the incomplete functionalization of the cross-linked materials are taken into account. The influence of temperature on the sorption equilibria in cross-linked polymers is also discussed on the basis of the temperature dependence of the cloud-point data.     

Temperatures of liquid–liquid separation and excess molar volumes of {N-methylpiperidine–water} and {2-methylpiperidine–water} systems

Partial miscibility in binary systems {N-methylpiperidine–water} and {2-methylpiperidine–water} was studied. The temperatures of liquid–liquid separation were determined as function of composition using both calorimetric technique and phase equilibrium cell. The densities of {amine–water} mixtures were determined in the domain of total miscibility at temperatures between 288 K and 338 K. Excess molar volumes were derived from experimental density data and fit to a Redlich–Kister polynomial.     

Liquid–liquid equilibrium behavior of tetrabutylammonium bromide,benzene, and water mixture

Tetrabutylammonium bromide (QBr) is a weak organic salt and used as a phase-transfer catalyst in phase-transfer catalytic reaction producing the desired product of benzyl bromide in the organic phase. The distribution of QBr between the organic phase (benzene is the organic phase solvent) and the aqueous phase is the important factor influencing benzyl bromide yield. In this study, the liquid–liquid equilibrium of benzene, water, and QBr ternary mixture were measured at 318.15, 328.15, and 338.15 K, respectively. The experimental results exhibited that the solubility of QBr is very large in this heterogeneous liquid mixture and the amount of aqueous phase increases whenever more QBr was added at constant temperature. The concentration of QBr in aqueous phase decreased with the increasing temperature. The organic phase composition did not vary obviously since the solubilities of water and QBr in benzene are very low. An empirical parameter was introduced to represent the degree of dissociation of QBr in solvent while the experimental data were correlated since it is very difficult to measure the degree of dissociation of QBr attributed to the partial dissociation of a weak organic salt. Finally, the experimental data were correlated with the NRTL model of Renon and Prausnitz taking account ion–molecule and molecule–molecule interactions.     

High-pressure phase equilibria of some carbon dioxide–organic–water systems

Homogeneous catalysts offer better activity and selectivity than heterogeneous catalysts, but their use is limited by the need to separate them from product and reuse them. Preferential dissolution of gaseous carbon dioxide has been shown to alter phase boundaries and facilitate recovery of such homogenous catalysts. The addition of a polar organic co-solvent to a water/organic biphasic system, coupled with subsequent phase splitting induced by the dissolution of gaseous carbon dioxide creates the opportunity to run homogeneous reactions in an organic/aqueous mixture with a water-soluble catalyst. In homogeneous catalyzed reactions, the catalyst can be tuned to be soluble or insoluble with carbon dioxide present, thus allowing for high catalyst recovery.High-pressure phase equilibria for the systems containing carbon dioxide, an organic (tetrahydrofuran, acetonitrile, or 1,4-dioxane), and water were measured using a variable-volume view cell, by a method capable of rapid and facile measurement of compositions and density in both phases with no sampling or calibration. These systems are well predicted with the Peng–Robinson Equation of State with Huron–Vidal type mixing rules from correlations of the binary systems, with the modified Huron–Vidal 1 (MHV1) and Huron–Vidal–Orbey–Sandler (HVOS) model with UNIQUAC excess energy model performing the best. Applications of the phase behavior on reaction conditions and separations are addressed.     

Isobaric vapour–liquid equilibria of methyl cellosolve–aliphatic alcohol systems

Isobaric vapour–liquid equilibrium data are determined at 40 and 95 kPa for six binary mixtures consisting of methyl cellosolve (2-methoxyethanol) as a common component and aliphatic alcohols as non-common components. The non-common components include ethanol, 1-propanol, 1-butanol, 2-methyl 1-propanol, 2-methyl 2-propanol and 1-pentanol. The experimental T–x data are correlated using Wilson and NRTL equations for the liquid phase activity coefficients using a non-linear regression approach based on maximum likelihood principle. Excess free energy of mixing, computed from the activity coefficients, is positive in all the systems over the entire range of composition.     

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.     

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.     

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 aqueous two-phase systems containing polyethylene glycol and ammonium dihydrogen phosphate or diammonium hydrogen phosphate. Experiment and correlation

Phase diagrams and liquid–liquid equilibrium (LLE) data of the aqueous systems polyethylene glycol 6000 (PEG₆₀₀₀)–ammonium dihydrogen phosphate and aqueous PEG₆₀₀₀–diammonium hydrogen phosphate have been determined experimentally at 298.15, 308.15 and 318.15 K. Furthermore, the osmotic virial equation was used to correlate the phase behavior of these systems. Good agreement was obtained with the experimental data. Finally, the effect of temperature and the type of salt on the LLE are discussed.     

Isobaric vapor–liquid equilibria for 1-propanol + water + lithium chloride at 100 kPa

Isobaric vapor–liquid equilibria for the ternary system 1-propanol+water+lithium chloride has been measured at 100 kPa using a recirculating still. The addition of lithium chloride to the solvent mixture produced an important salting-out effect over the alcohol and the azeotrope tended to be eliminated when the salt content increased, and two immiscible liquid phases were observed in a broad range of salt concentration. The experimental data sets were fitted with the electrolyte NRTL model and the parameters of Mock et al.’s model were estimated. This model has proved to be suitable to represent experimental data in the entire range of compositions. The effect of lithium chloride on the vapor–liquid equilibrium of the propanol+water system has been compared with that produced by other salts.     

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.     

Characteristics of sodium alginate membranes for the pervaporation dehydration of ethanol–water and isopropanol–water mixtures

Alginate membranes for the pervaporation dehydration of ethanol–water and isopropanol–water mixtures were prepared and tested. The sodium alginate membrane was water soluble and mechanically weak but it showed promising performance for the pervaporation dehydration. To control the water solubility the sodium alginate membrane was crosslinked ionically using various divalent and trivalent ions. Among them the alginate membrane crosslinked with Ca²⁺ ion showed the highest pervaporation performance in terms of the flux and separation factors.     

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.