A Modified Local Composition-Based Model for Correlating the Vapor-Liquid and Liquid-Liquid Phase Equilibria of Aqueous Polymer-Salt Systems

In this research, a new local composition model has been proposed to study the vapor-liquid and liquid-liquid phase equilibria of polyelectrolyte solutions. The proposed model has been used in order to obtain the activity of water in polyethylene glycol (PEG) and polypropylene glycol (PPG) solutions. The interaction parameters introduced into the proposed model have been reported. The interaction parameters between the salt and water molecule have been estimated using the experimental mean ionic activity coefficients of aqueous electrolytes studied in this work. Also, the interaction parameters between the polymer and salt molecule, and the polymer and water molecule have been computed using the experimental activity of water data in aqueous polymer solutions. The results showed that the proposed model, segment-based Wilson and segment-based NRTL models have good accuracy in correlating the vapor-liquid phase equilibria of the water-polymer and water-polymer-salt systems. Also, the liquid-liquid phase behavior of the polymer-salt aqueous two-phase systems has been correlated using the proposed model. The results show that the proposed model can more accurately correlate the phase behavior of aqueous two-phase systems than the UNIQUAC and the modified Wilson models.     

Study of phase behaviour for the aqueous two-phase polymer–polymer systems using the modified UNIQUAC-NRF model

A modified form of the UNIQUAC-NRF activity coefficient model was used to study the phase behaviour of the aqueous two-phase systems (ATPSs) of polyethylene glycol (PEG) and dextran (DEX) with different molecular weights at various temperatures. In the proposed model, a ternary interaction parameter was added to the expression for the excess Gibbs free energy and, in turn, to the corresponding activity coefficient rendered by the UNIQUAC-NRF model. The combinatorial part of the new model takes the same form as that of the original UNIQUAC model and the residual part considers the nonrandomness and also the binary and the ternary interactions among the molecules in mixtures of PEG, DEX, and water. The results show that the new model can more accurately correlate the experimental data for the systems studied in this work than those obtained from the original UNIQUAC and the UNIQUAC-NRF activity coefficient models. In order to favourably compare the results the same minimisation procedure and the same experimental data were used for the models studied in this work. The results for the Root Mean Square Deviations (RMSD) produced by the three UNIQUAC-based models are also reported.     

Representation of Multicomponent Liquid-Liquid Equilibria for Aqueous and Organic Solutions Using a Modified UNIQUAC Model

A modified form of the UNIQUAC model is presented to accurately reproducebinary phase equilibria and ternary and quaternary liquid-liquid equilibria ofaqueous and organic solutions. The model gives a good representation in thereproduction of binary coexistence curves over a wide temperature range usingtemperature-dependent parameters and of binary vapor-liquid equilibria usingtwo binary energy parameters, and in the correlation of ternary and quaternaryliquid-liquid equilibria using ternary and quaternary parameters, in addition tobinary parameters. The quaternary calculated results are compared with thoseobtained from the modified Wilson and extended UNIQUAC models.     

Experimental measurement and thermodynamic modeling of liquid-liquid equilibrium for 1-pentanol + water + NaNO3 at 298.15 and 308.15 K

Experimental measurements have been performed for liquid-liquid equilibria in aqueous systems containing 1-pentanol and sodium nitrate at temperatures of 298.15 and 308.15 K and at atmospheric pressure. The results have been modeled using the extended UNIQUAC model and also a modified version of this model. Relevant model parameters have been adjusted using the experimental data. Both models are capable of correlating the experimental data with an average deviation of less than 0.8 weight percent, with the modified model producing slightly better results. The predictive nature of the models has also been verified.     

Liquid-liquid equilibria for the acetonitrile + methanol + saturated hydrocarbon and acetonitrile + 1-butanol + saturated hydrocarbon systems

Tie-line results at 25°C and atmospheric pressure are presented for {(acetonitrile + methanol) + cyclohexane, or + n-hexane, or + n-heptane or + n-octane} and for {(acetonitrile + 1-butanol) + cyclohexane, or + n-hexane or + n-heptane}. Vapor-liquid equilibria for acetonitrile + methanol at 25° C are reported. The UNIQUAC associated-solution model is used to correlate binary vapor-liquid equilibria and mutual solubilities for the 13 systems constituting the ternary systems and to predict the ternary liquid-liquid equilibria by using binary parameters alone.     

Local-composition models and prediction of binary liquid-liquid binodal curves from heats of mixing

The temperature dependence of several local-composition models has been studied in conjunction with the Gibbs-Helmholtz identity. Binary heat-of-mixing data at temperatures near but above the critical solution temperature have been used to fit parameters obtained from excess-free-energy models in conjunction with the Gibbs-Helmholtz equation. These models, if the temperature dependence is adequate, should allow prediction of liquid-liquid equilibria (LLE) from the fitted parameters. The NRTL, UNIQUAC, and modified NRTL and UNIQUAC models (modified by inclusion of temperature-dependent parameters) seldom provide even qualitatively correct LLE predictions. A new local-composition model due to Wang and Chao (1983) yields reasonably good predictions for some systems but incorrect results for others. Reasons for these model inadequacies are discussed in terms of a local-composition model for the excess enthalpy which can be used to predict binodal curves accurately, including reasonably accurate values for the critical solution temperature, if reference excess-free-energy data at higher temperatures are available from VLE maesurements.     

Phase Equilibria in the Ternary System Methyl 1,1-Dimethylethyl Ether + Benzene + Toluene

Abstract

Consistent vapor-liquid equilibrium data at 94kPa have been determined for the ternary system methyl 1,1-dimethylethyl ether (MTBE) + benzene + toluene. The results indicate that the system deviates positively from ideality and that no azeotrope is present. The ternary activity coefficients of the system have been correlated with the composition using the Redlich-Kister, Wilson, NRTL, UNIQUAC, and UNIFAC, models. It is shown that most of the models allow a very good prediction of the phase equilibrium of the ternary system using the pertinent parameters of the binary systems. In addition, the Wisniak-Tamir relations were used for correlating bubble-point temperatures.     

Development and extension of PSRK/UNIQUAC model to methane and nitrogen gases

Two successful procedures for matching the equation of state (EOS) and the excess Gibbs energy model at zero pressure belong to Michelsen [M.L. Michelsen, Fluid Phase Equilibria, 60 (1990) 213] and Holderbaum-Gmehling [T. Holderbaum, J. Gmehling, Fluid Phase Equilibria, 70 (1991) 251]. These procedures lead to volume independent mixing rules for the mixture parameter a. Michelsen proposed the MHV1 and MHV2 mixing rules and Holderbaum-Gmehling proposed the PSRK mixing rule. Keshtkar et al. [A. Keshtkar, F. Jalali, M. Moshfegian, Fluid Phase Equilibria, 140 (1997) 107] demonstrated the utility of these mixing rules together with UNIFAC and UNIQUAC models for the prediction of high-pressure vapor-liquid equilibrium (VLE) of CO₂-binary systems. Also, they showed that the PSRK/UNIQUAC model gives better VLE results than other models. In this paper, we develop and extend the above model to methane and nitrogen gases. For this purpose, it is required that the missing interaction parameters of model are fitted with experimental VLE data. The VLE calculations show that good agreement between calculated results and experimental data can be produced by using the obtained parameters.     

The new experimental data and a new thermodynamic model based on group contribution for correlation liquid–liquid equilibria in aqueous two-phase systems of PEG and (K2HPO4 or Na2SO4)

The new experimental data of liquid–liquid equilibria for aqueous two-phase systems PEG–K₂HPO₄–water and PEG–Na₂SO₄–water are presented. The effects of pH and molecular weight of polyethylene glycol were investigated and the tie lines with binodal curves for both systems are shown. A new thermodynamic model based on group contribution has been proposed for studying the phase behavior of aqueous two-phase polymer–salt systems. The assumptions of NRTL-NRF model and the activity coefficient equation of UNIQUAC-NRF model have been used for the groups. In this new model, UNIFAC-NRF, the nonrandom state of groups were selected as a reference state. The binary interaction parameters were adjusted using the data of binary salt–water systems and the ternary systems were correlated with only six binary adjustable parameters. The Debye–Huckel equation based on Fowller–Guggenheim equation was used to calculate the long range electrostatic interaction of the ions. The UNIFAC-NRF model was applied to correlate the experimental data of aqueous two-phase systems: PEG–K₂HPO₄–water and PEG–Na₂SO₄–water for two different molecular weight of PEG at different pH. The results of the new model showed that it can be used to correlate the LLE in aqueous solution of polymer–salt very well.     

pePC-SAFT: Modeling of polyelectrolyte systems 2. Aqueous two-phase systems

This work considers aqueous two-phase systems (ATPS) containing one polymer-polyelectrolyte as well as one salt. To model the liquid-liquid equilibria (LLE) of these systems, the recently presented model pePC-SAFT has been employed. ATPS containing poly(acrylic acid) of different degrees of neutralization or poly(vinyl pyrrolidone), respectively, were considered. The binary interaction parameters used between water-poly(acrylic acid) and water-poly(vinyl pyrrolidone) were adjusted to vapor-liquid equilibrium (VLE) data of these systems. ATPS consisting of poly(vinyl pyrrolidone)-water-sodium sulfate were predicted as function of temperature as well as of molar mass of the polymer. For poly(acrylic acid) systems, ATPS were predicted as function of charge density (degree of neutralization) for different types of salt. For these calculations, the polyelectrolyte model parameters were determined from the non-charged polymer whereas the effect of increasing charge density has been purely predicted by the model. Using this approach, it is possible to predict the shrinking of the liquid-liquid equilibrium region with increasing charging of the polyelectrolyte.     

Phase diagrams of liquid-liquid equilibria for the systems water-phosphoric acid-solvent entrainer at 313.15 and 333.15 K

Liquid-liquid equilibria data have been determined for the ternary system of water + phosphoric acid + solvent entrainer (1,4-dimethylbenzene, 1,2-dichloroethane, and n-hexane) at 313.15 and 333.15 K. Experiments were carried out at atmospheric pressure using stirred and thermo-regulated cells. The ternary phase diagrams were obtained by the experimental solubility and tie-line data. The Othmer-Tobias equation was used to correlate the tie-line compositions. The measured liquid-liquid equilibrium data were compared with the non-random two liquid activity coefficient model. Root mean square deviations between experimental and calculated compositions were considered satisfactory. It was showed that the non-random two liquid model of all ternary systems presented very good satisfactory results with root mean square deviations so that this model was highly appropriate to calculate thermodynamic properties of the ternary solutions. The liquid-liquid equilibrium thermodynamic properties of water + phosphoric acid + solvent entrainer can be used in research on the nature of mixing behavior of the ternary system for molecular models and industrial applications in concentration the phosphoric acid aqueous solution.     

Electroextraction

Since both phases of aqueous two-phase systems are electrically conductive, application of electric fields in these systems gives rise to electrokinetic mass transfer of charged species. We have shown that an aqueous two-phase system can be used as a medium for electrophoretic separation with the liquid-liquid interface providing stability against convection and facilitating product recovery. Proteins have been directed into either the top or bottom phases of polyethylene glycol/dextran aqueous two-phase systems using 20–50 V/cm electric fields perpendicular to the phase interfaces. Binary protein mixtures have been separated in both batch and continuous modes by operating between isoelectric points and directing oppositely charged proteins into separate phases. Preliminary results on focusingE. coli cells into one phase while directing a proteinaceous product into the other phase indicate that two-phase electrophoresis may prove useful for commercial-scale recovery of proteins from fermentation broth. Recent studies in our laboratory indicate that the electrostatic potential profile near the interface of conducting liquid-liquid systems can influence electrophoretic migration of charged species across the interface. We have observed that phase systems with high Donnan potentials hinder electrophoretic mass transfer across liquid-liquid interfaces, whereas phase systems with low Donnan potentials do not.     

Thermodynamic phase equilibria of wax precipitation in crude oils

Economic loss due to wax precipitation in oil exploitation and transportation has reached several billion dollars a year recently. Development of a model for better understanding of the process of wax precipitation is therefore very important to reduce the loss. In this paper, a new thermodynamic model for predicting phase equilibriums of crude oils is proposed. The modified SRK EOS and the UNIQUAC equations are used to describe the vapor, liquid phase and the wax, respectively. New correlations have been introduced to calculate the volume parameter, c, in SRK EOS and the heat of vaporization in UNIQUAC equation. The model can be used to describe the systems which contain paraffin, naphthene and aromatic fractions. New correlations for the enthalpies, temperatures of solid–solid transitions and fusion enthalpies of paraffins are established in this paper based on data obtained from open literature. By using the proposed modified model, the wax precipitation in hydrocarbon fluids has been predicted for three crude oil systems. The calculation results have been compared with experimental observations and those results obtained using regular solution models. It is found that wax precipitation in complex systems can be better predicted by using this new model.     

Isobaric Phase Equilibria in the Binary Systems Ethyl 1,1-Dimethylethyl Ether + 1-hexene and + Cyclohexene at 94.00 kPa

Abstract

Consistent vapor-liquid equilibrium has been determined for the binary systems 1-hexene + ethyl 1,1-dimethylethyl ether (ETBE) and ethyl 1,1-dimethylethyl ether + cyclohexene at 94.00 kPa. The two systems present slight positive deviations from ideal behavior, can be considered to behave like regular solutions and do not present azeotropic behavior. Pure component vapor pressures are also reported for 1-hexene and cyclohexene. The phase equilibrium of the systems was correlated well by the Wilson, UNIQUAC, and NRTL models and reasonably predicted by the UNIFAC group contribution method. The boiling points of the binary systems were correlated with the Wisniak-Tamir equation.     

LLE for the extraction of alcohol from aqueous solutions with diethyl ether and dichloromethane at 293.15 K, parameter estimation using a hybrid genetic based approach

Experimental liquid-liquid equilibrium (LLE) data for the extraction of methanol, ethanol and 1-propanol from water by diethyl ether and dichloromethane at 293.15 K and at ambient pressure were investigated. Data for the binodal curves have been determined by cloud-point titration method and conjugate points on tie-line were obtained by correlating the refractive index of the binodal curves as a function of composition. The experimental ternary (liquid + liquid) equilibrium data have been estimated using the NRTL and UNIQUAC activity coefficient models to obtain the binary interaction parameters of these components by a combination of Levenberg-Marquardt method and the genetic algorithm based method. The distribution coefficients and the selectivity factor of the solvent used were calculated and presented. From our experimental and calculated results, we conclude that for the extraction of alcohol from aqueous solutions with dichloromethane solvent has a higher selectivity factor than the diethyl ether solvent.     

Correlation and prediction the activity coefficients and solubility of amino acids and simple peptide in aqueous solution using the modified local composition model

In this work, the modified Wilson model was used to obtain the activity coefficients of amino acids and simple peptides in non-electrolyte aqueous solutions. The Wilson model was modified using the new local mole fraction proposed by Zhao et al. and non-random case for the reference state. The binary interaction parameters (BIP) of the modified Wilson model for amino acid–water pairs were obtained using the experimental data of the activity coefficients for amino acids available in the literature. The modified Wilson model was also used to correlate the solubility of amino acids in water and the values of Δh/R, Δs/R, and Δg/R of the solutions studied were reported. The results obtained showed that the modified Wilson model can accurately correlate the activity coefficients as well as the solubility of amino acids and simple peptides in aqueous solutions. Also the modified Wilson model was coupled with the Pazuki–Rohani model to correlate the mean ionic activity coefficients of electrolytes in aqueous amino acid solutions. The results showed that the proposed model can accurately correlate the activity coefficients of the electrolytes in aqueous amino acid solution.     

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

Ionic liquids are potential solvents for liquid extraction processes; thermodynamic modeling of liquid-liquid equilibrium (LLE) data is essential for the optimization and operation of these processes. Therefore, ternary LLE data in systems involving ionic liquids have been investigated by several years. In most of the cases, the thermodynamic modeling of these systems has been made using the NRTL model; in some cases, the UNIQUAC model has also been used. The structural parameters of UNIQUAC for ionic liquids have been determined either by empirical correlations or, more recently, through quantum mechanics calculation. This work is a continuation of a recent paper, in which the structural group volume and area parameters for the group-contribution UNIFAC method have been calculated for five ionic liquids following the quantum mechanics approach. In order to optimize the molecular geometry and to calculate the area and volume, the Density Functional Theory (DFT) and the Polarizable Continuum Method (PCM) were used, respectively. The obtained parameters were used to correlate LLE data for fifteen ternary systems, totalizing 155 tie-lines. New interaction parameters were also estimated between the solvent and the ionic liquid functional groups. The results are very satisfactory, with root mean square deviations 0.0037 between experimental and calculated equilibrium mole fractions.     

聚合物溶液热力学模型的评述

预测聚合物溶液体系的气液平衡数据是热力学模型的一个重要内容.热力学模型大体可分3类,以过量吉布斯自由GF能表示的最为常用.本文选取基于GF的Flory-Huggins(FH)、UNIQUAC、UNIFAC和ENSIC 4种常用模型进行评述,认为FH模型出现较早,形式最简单;UNIQUAC模型发展较完善,应用范围较广,UNIFAC模型弥补了UNIQUAC模型参数缺乏的不足,应用最为;ENSIC模型具有较好的预测效果,但参数难以获得.