UNIQUAC Interaction Parameters Research Articles

Identification of UNIQUAC binary interaction parameters in liquid-liquid equilibrium

An algorithm is presented for the estimation of the UNIQUAC interaction parameters for liquid-liquid equilibrium of ternary systems. The algorithm is based on two optimization levels. In the inner level the algorithm performs the minimization of an objective function based on the isoactivity conditions. The outer level aims to minimize the error between calculated and experimental compositions. The Common Tangent Plane condition is checked at the end to guarantee a thermodynamically consistent representation of the phase behavior of ternary liquid systems.The algorithm is challenged with a historical Type 1 ternary liquid-liquid equilibrium system from the seminal study of Anderson and Prausnitz in which the authors showed the limitations of the original UNIQUAC model and justified its amendment in the modified UNIQUAC model. The present algorithm makes available single temperature and temperature-dependent interaction parameters enabling accurate and thermodynamically correct description of the experimental data with the original UNIQUAC model, therefore without the need of any model modification. This outcome does not change when the interaction parameters from the binary partially miscible constituent pair are first regressed and kept constant during the estimation of the remaining parameters on ternary equilibrium data. This investigation confirms that a model cannot be judged if the correctness of the model parameters has not been proved first.

Investigation into the use of gas hydrate technology for the treatment of vinasse

One of the challenges associated with vinasse, the by-product of bioethanol production, is the high concentration of dissolved solids, largely in the form of K+, SO42−, Mg2+, Ca2+, and Cl−. While traditional desalination technologies such as evaporation and distillation are employed in the concentration of salts to recover purified or potable water, these methods are energy intensive. The application of a novel technology known as gas hydrate technology can make the process of desalination less energy intensive, since the latent heat of fusion is much less compared to the heat of vaporisation for water. Reliable gas hydrate equilibrium experimental data plays a crucial role in the design of a hydrate-based process to treat vinasse. The systems measured in this study were based on the results of an extensive literature review conducted on the characterisation of vinasse. The isochoric pressure search method was used to measure the dissociation points for carbon dioxide hydrate in the presence of mixed salt solutions and synthesized vinasse mixtures containing (5 wt % KCl + 1 wt % Na2SO4 + 0.5 wt % MgCl2 + 0.5 wt % CaCl2 + 2.2 wt % ethanol + 0.5 wt % propionic acid + 0.3 wt % acetic acid). A thermodynamic model based on the solid solution theory of van der Waals and Platteeuw, UNIQUAC model along with Debye-Hückel term were used to calculate the hydrate dissociation conditions in the presence of mixed salts and synthetic vinasse mixtures. New UNIQUAC interaction parameters were optimized. Good agreement between the experimental data and model results were achieved.

Solid–Liquid Equilibria for the Glycine–Alcohol–NaCl–H2O System

An investigation of the solubility of glycine–alcohol (ethanol/1-propanol)–NaCl–H2O system was carried out by dynamic method over the temperature range from 283.15 to 333.15 K. The studied systems were glycine–alcohol (ethanol/1-propanol)–H2O, glycine–ethanol–NaCl (0.5, 1.0, 2.0 mol·kg–1 water)–H2O, glycine–1-propanol–NaCl (0.5 mol·kg–1 water)–H2O, and NaCl–alcohol (ethanol/1-propanol)–glycine (0.25 mol·kg–1 water )–H2O. The solubilities of glycine and NaCl were found to increase with increasing temperature and decrease with increasing concentration of alcohols. A chemical model was successfully developed based on the mixed solvent electrolyte (MSE) model by regressing experimental and literature solubilities data of glycine in the glycine–ethanol–NaCl–H2O and glycine–1-propanol–H2O systems. New sets of middle range and UNIQUAC interaction parameters were obtained. The average absolute deviation between regressed and experimental values was found to be less than 7%.

Phase stability conditions of carbon dioxide and methane clathrate hydrates in the presence of KBr, CaBr2, MgCl2, HCOONa, and HCOOK aqueous solutions: Experimental measurements and thermodynamic modelling

Experimental data on dissociation conditions of carbon dioxide clathrate hydrate in the presence of KBr, CaBr2, MgCl2, HCOONa, and HCOOK aqueous solutions, as well as methane clathrate hydrate in the presence of HCOONa and HCOOK aqueous solutions have been measured and are reported in this study. Measurements were conducted in the temperature and pressure ranges of (266.9–285.8)K and (1.47–9.68)MPa, respectively, using an isochoric pressure-search method. Results reveal that at varying concentrations, the aqueous salt solutions have a satisfactory inhibition effects on both carbon dioxide and methane hydrate formation, causing a shift in the P-T (pressure–temperature) equilibrium cruves to higher pressures and lower temperatures. A thermodynamic model based on the solid solution theory of van der Waals and Platteeuw (vdW-P) was used for estimation of hydrate dissociation conditions in the presence of the salt aqueous solutions. The gas phase was modeled using the Valderrama modification of the Patel-Teja equation of state (VPT EoS). The UNIQUAC approach, along with the Debeye-Huckel method, was applied to calculate the activity coefficient of water in the presence of salt. The UNIQUAC interaction parameters between water and anions and cations were optimized using the measured hydrate dissociation data. The model results provide a reasonable agreement with the experimental data, with an average absolute deviation (ARD%) below 0.3%.

Experimental measurement and prediction of (liquid + liquid + liquid) equilibrium for the system (n-hexadecane + water + triacetin)

The phase diagram for the ternary system containing (n-hexadecane+water+triacetin) was obtained experimentally at T=296.15K and ambient pressure. Results show that this system is of Type 3 according to the Treybal classification of ternary system. NRTL and UNIQUAC interaction parameters were calculated from binary phase equilibrium values and were used to predict the (liquid+liquid+liquid) equilibrium (LLLE) region. Results indicated that both NRTL and UNIQUAC could predict the LLLE region of the system with similar precision as indicated by the comparable standard deviations. This indicates that the enthalpic contribution to the activity coefficient is predominant and entropic contributions can be neglected.

Thermodynamic modeling of gas hydrate formation conditions in the presence of organic inhibitors, salts and their mixtures using UNIQUAC model

Gas hydrate formation conditions of CH4, C2H6, C3H8, CO2 and H2S in the presence of inhibitors are modeled in this study by applying a combination of Chen-Guo model, SRK-HV EoS and UNIQUAC model in conjunction with Henry’s law. Methanol, ethanol, monoethylene glycol, diethylene glycol, triethylene glycol, glycerol, NaCl, KCl, CaCl2 and MgCl2 are considered as hydrate inhibitors. The predictions are performed in the presence of single inhibitors, mixed salts and mixture of alcohol and salts. All the possible interactions between components in the aqueous phase including water, salts, alcohol and gases are incorporated in the UNIQUAC model. The UNIQUAC interaction parameters are optimized directly through the hydrate data so that any dependence on various VLE data is eliminated. Also the parameters of both supercritical and condensable components are calculated. The strong salts are treated as molecular species in the aqueous phase so that no electrostatic model is used for long-range interaction. Based on this assumption, the original UNIQUAC model is easily extendable for electrolyte and mixture of electrolyte and non-electrolyte solutions. For the first time, the original UNIQUAC model is employed here to calculate the hydrate formation conditions in the presence of electrolytes. Despite the simplicity of the proposed approach, the results of this study are in good consistency with the experimental data, particularly for hydrate systems containing mixture of salts and alcohol.

Distribution of cyclohexanol and cyclohexanone between water and cyclohexane

Liquid–liquid equilibrium (LLE) data for ternary systems water+cyclohexane+cyclohexanol and water+cyclohexane+cyclohexanone were measured at (303.2–333.2)K and under atmospheric pressure. The reliability of the experimental tie-line data was checked by the empirical Othmer–Tobias correlation. The distribution coefficient and separation factor were used to investigate the distribution of cyclohexanol and cyclohexanone between water and cyclohexane. The results show that the distribution coefficient of cyclohexanol or cyclohexanone between organic and aqueous phases increases with the increasing content of cyclohexanol or cyclohexanone in water, and so does it with the increasing of temperature. By using the NRTL and UNIQUAC activity coefficient models, the experimentally determined LLE data, along with the LLE data for another ternary system water+cyclohexanol+cyclohexanone [G. Xing, W. Qinbo, L. Fuqiong, S. Binwei, J. Chem. Eng. Data 59 (2013) 1651–1655], were correlated simultaneously. Good agreements were obtained between the correlated and experimentally determined tie-line data. The binary NRTL and UNIQUAC interaction parameters were obtained. Furthermore, four sets of quaternary LLE data for water+cyclohexane+cyclohexanol+cyclohexanone were experimentally determined at 318.2K. The experimentally determined quaternary LLE data were compared with the NRTL model predicted LLE data, and generally agreements were obtained. It further verifies the reliability of the obtained binary model parameters, and indicates the obtained parameters could be used for prediction, as well as design and optimization of the related separation process.

An algorithm for the regression of the UNIQUAC interaction parameters in liquid–liquid equilibrium for single- and multi-temperature experimental data

This paper describes an algorithm for the computation of the UNIQUAC interaction parameters from liquid–liquid experimental data. The algorithm comprises two separate levels. The inner level is devoted to the calculation of the interaction parameters, minimizing an objective function which is function of the activities. The outer level uses the parameters by the inner level and aims to minimize the error between experimental and calculated molar fractions through an adjustment of the experimental molar fractions, provided that the condition of common tangent to the change of the Gibbs free energy of mixing is matched.The algorithm is applied to seven binary systems for the evaluation of single temperature parameters and to the tetrahydrofuran/water system for the evaluation of the temperature dependent parameters. In both cases, the calculated parameters provide results with lower error than the previously published parameters. In all cases thermodynamically consistent and precise results are obtained in terms of common tangent of the Gibbs free energy of mixing and molar faction errors.

Liquid–liquid equilibria for the binary systems of propylene glycol ether + water measured by the phase volume method

Liquid–liquid phase equilibrium for two binary systems: 1-propoxy-2-propanol+water and 1-(1-methyl-2-propoxyethoxy)2-propanol+water ranging from their lower critical solution temperatures to 328.15K under atmospheric pressure were performed by using the phase volume method. The experimental data were further correlated with the UNIQUAC model by fitting the UNIQUAC interaction parameters as a function of temperature. The critical mass fraction and the lower critical solution temperature were determined by fitting the experimental data to the critical scaling law.

Isothermal vapor – liquid and vapor–liquid–liquid equilibrium for the ternary system ethanol + water + diethyl carbonate and constituent binary systems at different temperatures

Isothermal vapor–liquid–liquid equilibrium data were measured for the ethanol+water+diethyl carbonate (DEC) ternary system and the constituent binaries using static headspace gas chromatography (HSGC) at 353.15 and 363.15K. Multiple headspace extraction was used to calibrate the gas chromatograph. The activity coefficients were calculated using the Gibbs–Duhem equation and thermodynamic correlations. The thermodynamic consistency of the experimental vapor–liquid and vapor–liquid–liquid equilibrium data was verified. The experimental data were correlated using NRTL and UNIQUAC models, obtaining new UNIQUAC and NRTL interaction parameters for the VLE and VLLE.

Liquid–Liquid Equilibrium for the Water + Diethyl Carbonate + Ethanol System at Different Temperatures

Liquid–liquid equilibrium (LLE) and tie lines were measured for the ternary system water + diethyl carbonate + ethanol between 296.15 and 338.15 K and at atmospheric pressure. Thermodynamic consistencies of the experimental data were verified by Othmer and Tobias correlation. The liquid–liquid equilibrium results were correlated with the NRTL and UNIQUAC coefficient models and the reliability of these models was tested by comparison with experimental results. New UNIQUAC and NRTL binary interaction parameters are reported.

Vapor−Liquid Equilibrium Data, Excess Enthalpy Data, and Azeotropic Data for the Binary System Dibutyl Ether + o-Xylene

For the binary system dibutyl ether + o-xylene, isothermal and isobaric vapor−liquid equilibrium (VLE) data were measured with the static synthetic and the dynamic method. Additionally, excess enthalpy (HE) data were determined by means of an isothermal flow calorimeter, and azeotropic data were investigated using a spinning band column. The experimental data from this work were correlated using linear temperature-dependent UNIQUAC interaction parameters.

Equilibrium data for systems composed by cottonseed oil + commercial linoleic acid + ethanol + water + tocopherols at 298.2 K

The present paper reports liquid–liquid equilibrium data for the system refined cottonseed oil + commercial linoleic acid + ethanol + water at 298.2 K. The experimental data were used for adjusting parameters of the NRTL and UNIQUAC models. The global deviations between calculated and experimental concentrations were 0.80% for the NRTL model and 1.44% for the UNIQUAC equation. The influence of the solvent on the distribution coefficient of tocopherols was also studied. UNIQUAC and NRTL interaction parameters between tocopherols and the other pseudocomponents were determined assuming that the nutraceutical compound is present at infinite dilution in the liquid–liquid equilibrium system. The obtained parameter set enables the simulation of liquid–liquid extractors.

Volume, surface and UNIQUAC interaction parameters for imidazolium based ionic liquids via Polarizable Continuum Model

Ionic liquids (ILs) have shown great potential as solvent/media for reactions and separations. However, the physico-chemical characteristics of ILs are scarce and the limitless different combinations of cations and anions further complicate the matter. The ternary tie line data along with the binodal curve gives a fair indication regarding the feasibility of the ILs as solvents. Most of the ternary (with ILs) liquid–liquid equilibrium data available in literature has been correlated through the NRTL model as r and q are not available. The absence of the volume and surface parameters poses a hindrance in calculation of the binary interaction parameters for UNIQUAC and UNIFAC models. A novel method has been developed for deriving these volume and surface parameters from the Polarizable Continuum Model (PCM). PCM is widely used for studying solvation effects. Here, the solute is represented by a charge distribution in a molecular shaped cavity embedded in an infinite polarizable dielectric medium. GEnerating POLyhedra (GEPOL), which is based on the concept of solvent excluding surface, is used for calculating this cavity. This novel approach for volume and surface parameters has been verified initially for 71 compounds belonging to several homologous series (paraffins, isoparaffins, olefins, naphthenes, aromatics, alkynes, alcohols, ketones, aldehydes, acids, esters and amines) and 24 solvents. The predicted values of r and q for alcohols, ethers and oxygen containing systems showed significant deviations (2.5–20% for r and 5–25% for q) from the literature values. The values of r and q obtained by PCM method have been applied to 17 ternary systems and 1 quaternary system belonging to these deviant components. The PCM method gives a significantly better fit (average of 60% improvement in rmsd) for all the systems studied. This approach has been used to estimate the structural parameters for 25 dialkylimidazolium based ILs. Subsequently, these values have been used to estimate the UNIQUAC interaction parameters for seven IL based ternary systems, giving a 40% improvement in rmsd over NRTL.

Modeling of the phase equilibria of polystyrene in methylcyclohexane with semi-empirical quantum mechanical methods I

A method for calculating interaction parameters traditionally used in phase-equilibrium computations in low-molecular systems has been extended for the prediction of solvent activities of aromatic polymer solutions (polystyrene+methylcyclohexane). Using ethyl-benzene as a model compound for the repeating unit of the polymer, the intermolecular interaction energies between the solvent molecule and the polymer were simulated. The semiempirical quantum mechanical method AMI, and a method for sampling relevant internal orientations for a pair of molecules developed previously were used. Interaction energies are determined for three molecular pairs, the solvent and the model molecule, two solvent molecules and two model mole-cules, and used to calculated UNIQUAC interaction parameters, a ij and a ji. Using these parameters, the solvent activities of the polystyrene 90,000 amu+methylcyclohexane system, and the total vapor pressures of the methyl-cyclohexane+ethylbenzene system were calculated. The latter system was compared to experimental data, giving qualitative agreement.

Liquid−Liquid Equilibria of Water + 1-Butanol + 2-Ethyl-1-hexanol System

Liquid−liquid equilibria (LLE) for the ternary system water + 1-butanol + 2-ethyl-1-hexanol at (298.2, 303.2, 308.2, and 313.2) K are reported. A type-2 liquid−liquid phase diagram was obtained for this ternary system. The UNIQUAC model was used to correlate the LLE data with a root-mean-square deviation value of 1.08%. The UNIQUAC interaction parameters between each pair of components in the system were obtained using the experimental results. The effect of 1-butanol addition on mutual solubility of 2-ethyl-1-hexanol and water was also investigated at different temperatures.

Phase equilibrium for the system rice bran [formula omitted

This work reports experimental equilibrium data for fatty systems containing rice bran oil, free fatty acids, ethanol, water, γ-oryzanol and tocols, at 298.2 K. Model fatty systems composed by refined rice bran oil, commercial oleic acid, γ-oryzanol, ethanol and water were used for adjusting NRTL and UNIQUAC interaction parameters between γ-oryzanol and the other pseudocompounds. UNIQUAC interaction parameters between tocols and the other pseudocomponents were determined assuming that the tocols are present at infinite dilution in the liquid–liquid equilibrium system. Despite the complexity of the systems studied, the interaction parameters obtained were capable of correctly predicting the equilibrium for systems containing Brazilian and Thai crude rice bran oils and aqueous ethanol.

Liquid–liquid equilibria for the ternary system water + tetradecane + 2-butyloxyethanol

Liquid–liquid equilibria of the ternary system water + tetradecane + 2-butyloxyethanol in the temperature range from 298.15 to 338.15 K were investigated at atmospheric pressure. The experimental data correlated well with the UNIQUAC model. For the system with a three-liquid-phase-coexisting region, all the six UNIQUAC interaction parameters can be determined numerically by minimizing the deviation of the compositions of three coexisting liquid phases only.

Vapor−Liquid Equilibrium and Excess Enthalpy Data for the Binary Systems Propane + Dimethyl Ether and Propene + Dimethyl Ether at Temperatures from (298 to 323) K

Isothermal vapor−liquid equilibrium (VLE) data for the binary systems propane + dimethyl ether and propene + dimethyl ether were determined experimentally with the static synthetic and the static analytic methods. Additionally, excess enthalpy (HE) data were determined by means of an isothermal flow calorimeter. For the system propane + dimethyl ether, the azeotropic compositions were derived graphically from the VLE data. The experimental data from this work were correlated by using a linear temperature dependence for the UNIQUAC interaction parameters and by treating the real vapor phase behavior with the Soave−Redlich−Kwong equation of state. On the basis of this correlation, the new data were compared to values taken from the literature.

Transesterification processes by combination of reactive distillation and pervaporation

The development of a reactive distillation process for the production of n-butyl acetate by transesterification of methyl acetate with n-butanol is presented. Thermodynamic aspects of the quaternary system n-butyl acetate– n-butanol–methyl acetate–methanol are discussed and UNIQUAC interaction parameters derived using the Dortmund Data Bank (DDB) are given. The reaction kinetics of the heterogeneously by a strongly acidic ion-exchange resin (Amberlyst 15) catalyzed reaction has been investigated and the kinetic constants for a pseudohomogeneous kinetic model are presented. Pervaporation experiments using Pervap 2255 membranes have been conducted for the separation of the methanol–methyl acetate binary mixture which forms the distillate stream of the reactive distillation column. Reactive distillation experiments have been performed using the structured catalytic packings Katapak-S (Sulzer Chemtech) and Katapak-SP (type SP 11, Sulzer Chemtech). Important operating conditions (reflux ratio, total feed rate) have been varied experimentally. The experimental results are presented in comparison with simulation results. An equilibrium stage model for the modeling of the distillation is capable of describing the composition profiles quantitatively. Finally, a new process, combining reactive distillation with pervaporation, has been developed and investigated by means of simulation studies. It has been shown that the combination of reactive distillation with pervaporation is favorable since conversions close to 100% can be obtained with a reasonable size of the reactive section.