Liquid-liquid Equilibrium Calculations Research Articles

Crossover models for near-critical and subcritical liquid-liquid equilibrium calculations of ionic liquids + alcohols

Crossover models for near-critical and subcritical liquid-liquid equilibrium calculations of ionic liquids + alcohols

Problems and limitations in the calculation of liquid-liquid equilibrium

Problems and limitations in the calculation of liquid-liquid equilibrium

Systematic method of screening deep eutectic solvents as extractive solvents for m-cresol/cumene separation

Deep eutectic solvents (DESs) have been widely applied as extractive solvents for the separation of phenolic compounds from low-temperature coal tar (LTCT). However, systematic study of screening suitable DESs from numerous candidates for this separation process is still scarce. In this work, a systematic method of screening promising DESs as extractive solvents is proposed for the separation of m-cresol/cumene, as a representative phenolic compound/neutral oil mixture in LTCT. Experimental data of DES-involved systems are collected from literature to validate the reliability of conductor-like screening model for real solvents (COSMO-RS), which serves as the foundation for thermodynamic calculation and process simulation. Then, the crucial influencing factors for DESs screening (i.e., salt and solvent, and the molar ratio) on the thermodynamic properties are investigated by COSMO-RS. After that, a systematic DESs screening method combining the calculation of infinite dilution thermodynamic properties, the estimation of melting point and viscosity, the calculation of liquid-liquid equilibria, and the evaluation of process performance is proposed. The results indicate that chlorocholine chloride (CChC): acetic acid (AA) (1:2) and choline chloride (ChCl): ethylene glycol (EG) (1:3) are identified as the optimum DESs for m-cresol/cumene separation. Finally, the high separation performances of CChC:AA (1:2) and ChCl:EG (1:3) are confirmed by extraction experiments.

Acetone + 1-ethyl-3-methylimidazolium acetate phase diagram: A correlation challenge

Several physical properties and the isobaric vapour-liquid equilibria at 101.32, 50, and 30 kPa were measured for the binary system consisting of acetone and the ionic liquid 1-ethyl-3-methyl-imidazolium acetate. Liquid-liquid equilibrium data were also measured at temperatures from 298.15 up to 328.35 K and atmospheric pressure. An hourglass-shaped miscibility gap was found. The simultaneous correlation of both VLE and LLE regions at 101.32 kPa was addressed. The NRTL model, considering different options to formulate the temperature dependence of the parameters, was tested and found unable to correlate the whole set of equilibrium data. A detailed analysis of the excess Gibbs energy demonstrated the limitations of the classical equation and allowed the definition of a new model with a correction term. A unique set of parameters were used to simultaneously correlate both sets of equilibrium data with very low deviations from experimental data. Moreover, the corrected NRTL function overcomes some uncertainty problems that may occur in liquid-liquid equilibrium calculations.

Vapor-liquid and liquid-liquid equilibria in the water + poly(propylene glycol) system

The aim of this study was to investigate phase equilibria in a water + poly(propylene glycol) [Mn = 425 g mol−1] system. Vapor-liquid equilibria (VLE) were determined ebulliometrically in the completely miscible region with higher water concentrations at isotherms 323.15, 333.15, 343.15, and 353.15 K. These data were correlated with the UNIQUAC free-volume (FV) model to be consistent with our previous studies. Liquid-liquid equilibrium (LLE) was determined using the cloud-point method at 320–350 K, and lower critical solution temperature was found at 320.2 K. LLE was correlated with the entropic FV-UNIQUAC segmental interaction model developed earlier, which is suited for correlation and calculation of LLE of polymer solutions. We estimated new binary segmental interaction parameters for interactions between propylene glycol and water segments.

Aerosol Optical Tweezers Constrain the Morphology Evolution of Liquid-Liquid Phase-Separated Atmospheric Particles

Summary Chemical models of atmospheric particles are vital in understanding the role of aerosol particles in atmospheric chemistry, air pollution, human health, and climate change. Advancing these models requires new frameworks that can realistically predict how critical particle properties evolve. We present such a framework for predicting particle phase separation and which morphology will prevail; this controls how each particle interacts with and affects the atmosphere. We studied the mixing behavior of α-pinene secondary organic aerosol (SOA) with different organic phases, as relative humidity was varied to determine the interplay between polarity, miscibility, interfacial tension, and the resulting morphology. Using measurements from aerosol optical tweezers experiments and literature data, a general trend in morphology with increasing atmospheric oxidation was observed, from biphasic partially engulfed (where both phases are immediately accessible to the gas phase) to biphasic core shell (where the organic shell conceals the core) and finally to a single-phase, homogeneous morphology.

Calculation of thermodynamic equilibria with the predictive electrolyte model COSMO-RS-ES: Improvements for low permittivity systems

The predictive electrolyte model COSMO-RS-ES is refined to improve the description of systems at 25 °C in which strong ion pairing is expected due to a low static permittivity of the liquid phase. Furthermore, the short-range ion energy interaction equations have been modified to better describe the interactions between ions and solvent molecules. In addition, the salt solubility database is extended with additional non-aqueous systems containing solvents that have a low (εs<15) dielectric constant and promote near to full ion association. Throughout this work it is demonstrated that liquid-liquid equilibrium calculations and solid-liquid equilibrium predictions for electrolyte systems can be markedly improved with the inclusion of Bjerrum treatment based phenomenological considerations while introducing only one general additional parameter. Our modified approach reinforces the capabilities of COSMO-RS-ES as a powerful predictive tool for the calculation of phase equilibria in systems with scarce experimental data.

A new approach to model asphaltene induced permeability damage with emphasis on pore blocking mechanism

Asphaltene deposition in porous media could reduce permeability up to 90%. Nonetheless, this would occur often for a slight reduction in porosity. This, in turn, indicates that while the volume of deposition is not noticeable it can block pore throats and consequently, it affects conductivity of porous media. This phenomenon is strongly dependent on the pore structure, initial porosity and permeability and also precipitated asphaltene particle size which is a function of oil composition and the condition of asphaltene precipitation. Often, regardless of these facts, permeability reduction is simulated by a power law porosity-permeability relationship. This study highlights the necessity of a new permeability model based on previous studies and experiments. A new permeability reduction model based on Gruesbeck and Collins' parallel plugging/non-plugging pathways model is proposed. The model considers two different mechanisms including surface deposition and throat plugging based on pore size distribution, and is implemented into an IMPEC (Implicit Pressure and Explicit Composition) compositional cylindrical simulator. Precipitated asphaltenes, considered as moving phase during simulation, are characterized by LLE (Liquid/Liquid equilibrium) calculations using PR-EoS. It is observed that permeability damage due to throat blocking is severe and abrupt while surface deposition is a gradual mechanism. Furthermore, convexity and concavity of permeability reduction curves are obtained for plugging and non-plugging pathways, respectively.

Vapor-liquid (azeotropic systems) and liquid-liquid equilibrium calculations using UNIFAC and NRTL-SAC activity coefficient models

The aim of present study was to investigate some of the most important maximum and minimum azeotrope boiling temperature systems using UNIFAC and NRTL-SAC models as the predictive models. Also, the predictive power of UNIFAC, UNIFAC-LLE and NRTL-SAC models were compared in liquid-liquid equilibrium calculations. For maximum azeotrope temperature systems, except for formic acid-water, the UNIFAC model had higher degree of accuracy than the NRTL-SAC model. The NRTL-SAC model could not appropriately predict the maximum azeotrope temperature systems, in particular for acetone-chloroform, chloroform-methyl acetate, and chloroform-diethyl amine systems. For these systems, the NRTL-SAC model gave a minimum azeotrope temperature. For the examined minimum azeotrope boiling temperature systems, the results of both models were in consistent with the experimental data, but in most cases, the results of the UNIFAC model were in good agreement with the experimental data. On the other hand, as the pressure deviated from 101.3 kPa, the deviation of both models increased. In the case of ternary VLE systems under study, UNIFAC model indicated better results than NRTL-SAC model. Totally, in most VLE systems, UNIFAC was much better than NRTL-SAC and we preferred UNIFAC model as a good candidate for VLE calculations of the studied systems. Based on the overall deviation of models for LLE calculations at all temperatures, the best representation of the system was in the following order: UNIFAC-LLE > UNIFAC > NRTL-SAC. There would appear to be a major difficulty in selecting one thermodynamic model as the best, as the choice might be system-dependent.

Liquid-liquid equilibrium of hydrogen bonding polymer solutions

The liquid-liquid equilibrium (LLE) calculation for polymer solutions is essential for processes design of polymerization. The hydrogen bonding in polymer solutions leads to deviate remarkably from normal solutions behaviors. The perturbed hard-sphere-chain-association (PHSC-AS) equation of state (EoS) is applied to calculate the liquid-liquid equilibrium (LLE) of polymer mixtures with hydrogen bonding association such as self- and cross-association with various phase behaviors such as UCST, LCST and closed-loop of polymer solutions. In addition, the calculation results are compared with those obtained by the PC-SAFT EoS, which is known to be useful for calculating phase equilibria of polymer systems. PHSC-AS EoS shows a satisfactory performance for LLE calculation with similar accuracy compared to that with PC-SAFT EoS.

Modified quadrupole Cubic Plus Association Equation of State (mqCPA EoS) for thermodynamic modeling of polymer-supercritical CO2 systems

In this work, a modified quadrupole Cubic Plus Association Equation of State (mqCPA EoS) is used to model the cloud point pressure of polymers-supercritical carbon dioxide (scCO2) systems. The residual Helmholtz free energy is expressed as sum of SRK and Quadrupole terms. We used the experimental data of the cloud point pressure for the different copolymer-scCO2 systems to investigate the capability of the present model through liquid-liquid equilibrium calculations. Using mqCPA EoS, the cloud point pressures of the polymer-scCO2 systems for the three types of poly(lactic acid) (PLA), the three types of poly(1-O-(vinyloxy) ethyl-2,3,4,6-tetra-O-acetyl-β-d-glucopyranoside) (P(AcGlcVE) and seven types of poly(vinyl acetate-alt-dibutyl maleate) (PVAc-alt-PDBM) were calculated. These copolymers have different molecular structures, end groups and molar masses. Moreover, we applied both PC-SAFT and PCP-SAFT equations of state for the same polymer-scCO2 systems and their results were compared to those obtained by mqCPA EoS that showed in overall the both PCP-SAFT and mqCPA EoSs give better results with very good accuracy.

Correlation and prediction of liquid–liquid equilibria for alcohol/hydrocarbon mixtures using PC-SAFT equation of state at high pressure up to 150 MPa

In this paper, we present a systematic study of the ability of the PC-SAFT equation of state to predict of liquid–liquid equilibria (LLE) for alcohol/hydrocarbon mixtures at high pressure on the basis of LLE data at 0.1 MPa. The adjustable temperature-independent binary interaction parameters, kij, in the PC-SAFT model were determined from LLE data at 0.1 MPa. The new proposed parameters set for methanol and ethanol with the two-site association scheme reproduce vapor pressures and liquid density with the same accuracy of PC-SAFT original parameters but show a better representation of the LLE data. In addition to using pure component PC-SAFT parameters derived from the standard method of fitting to liquid density and saturated vapor pressure, the new PC-SAFT parameters set for methanol and ethanol are determined from experimental association energy. The new association energy parameter of methanol and ethanol shows better agreement with the experimental results at approximately 298 K compared to all previously published PC-SAFT parameters.Different binary methanol + hydrocarbon and ethanol + hydrocarbon systems at high pressure up to 150 Mpa were tested using the PC-SAFT. LLE calculations and prediction show good agreement with experimental data for almost considered systems.

Liquid–Liquid Equilibrium for Ternary Systems Water + Acetic Acid + m-Xylene and Water + Acetic Acid + o-Xylene at (303.2 to 343.2) K

Liquid–liquid equilibrium (LLE) for ternary systems water + acetic acid + m-xylene and water + acetic acid + o-xylene were measured at (303.2 to 343.2) K and under atmospheric pressure. The consistency of the experimental tie-line data was checked by both the Othmer–Tobias and the Hand equations as well as verified by comparison with the literature data. Both the nonrandom two-liquid (NRTL) and universal quasichemical activity coefficient (UNIQUAC) models were adopted to correlate the measured LLE data, and the binary interaction parameters were obtained by data-fitting. The predicted LLE data by using the obtained model parameters show good consistency with the literature data. It indicates the obtained binary NRTL and UNIQUAC model interaction parameters could be used in the calculation of LLE for the ternary systems water + acetic acid + m-xylene and water + acetic acid + o-xylene as well as for the design, simulation, and optimization of the related separation process.

A crossover‐UNIQUAC model for critical and noncritical LLE calculations

A new model, named the crossover‐UNIQUAC model, has been proposed based on the crossover procedure for predicting constant‐pressure liquid–liquid equilibria (LLE). In this manner, critical fluctuations were incorporated into the classical UNIQUAC equation. Coexistence curves were estimated for systems having a diverse range of asymmetries. These systems included the LLE of five different mixtures, composed of nitrobenzene with one of the members of the alkane homologous family (either pentane, octane, decane, dodecane, or tetradecane), as well as an extra system having a different chemical nature, namely the mixture of n‐perfluorohexane and hexane, to further check the validity of the proposed approach. Using these nonideal mixtures, the validity of the new model was investigated within wide ranges, covering near‐critical to regions falling far away from the critical point. The graphical trends, as well as the quantitative comparison with experimental data indicated the good agreement of the proposed model results with the experimental data. A maximum AARD% value of 3.97% was obtained in calculating molar compositions by the proposed model for such challenging systems covering noncritical, as well as critical regions. In addition, to show the strength of the proposed crossover approach to describe properties other than LLE, molar heat capacities were investigated for the system of nitrobenzene + dodecane. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3094–3103, 2015

Liquid–liquid equilibria for ternary system water + toluene + benzaldehyde at (303.2–343.2) K

Liquid–liquid equilibrium (LLE) data for the ternary system of water+benzaldehyde+toluene have been determined at (303.2–343.2)K under atmospheric pressure. The Othmer–Tobias and the Hand correlations were used to check the reliability of the experimental data. The obtained LLE data were correlated by both the NRTL and UNIQUAC activity coefficient models. The relevant interaction parameters were extracted by the regression of the experimental data. The calculated values by these two models show good consistency with the measured data. The relative-mean-standard deviations obtained is 0.82% by the NRTL model and 0.12% by the UNIQUAC model. The obtained interaction parameters might be used in the calculation of LLE for the ternary system water+benzaldehyde+toluene as well as for the design and optimization of the related separation process.

Liquid–liquid equilibria for ternary system water + acetic acid + cyclohexanone at (293.2–323.2) K

Liquid–liquid equilibria (LLE) for the ternary system water+acetic acid+cyclohexanone was studied at (293.2–323.2)K and at atmospheric pressure. The immiscibility region was found to be relatively small and not sensitive to the change of temperature. The Othmer–Tobias equation and the Bachman equation were both used to check the reliability of the obtained experimental tie-line data. The experimental results were correlated with both the NRTL and the UNIQUAC activity coefficient models. The calculated results showed good agreement with the experimentally determined ternary LLE data. The root mean square deviations (RMSD) obtained by comparing the calculated and experimental two-phase compositions are 0.72% for the UNIQUAC model and 0.40% for the NRTL model. The obtained interaction parameters can be used in the calculation of LLE for the ternary system water+acetic acid+cyclohexanone as well as for the design and optimization of the related separation process.

Liquid–Liquid Equilibria for the Ternary System Water + Benzyl Alcohol + Methylbenzene at (303.2 to 343.2) K

Liquid–liquid equilibrium (LLE) data for the ternary system water + benzyl alcohol + methylbenzene were measured at (303.2 to 343.2) K under atmospheric pressure. The Othmer–Tobias and the Hand correlations were used to check the reliability of the experimental LLE data. The distribution coefficient and separation factor were used to investigate the ability of water to extract benzyl alcohol from methylbenzene. The results show that the distribution coefficient of benzyl alcohol increases with the increasing mass fraction of water in the aqueous phase. The experimental data were correlated by both the nonrandom two-liquid (NRTL) and the universal quasichemical (UNIQUAC) activity coefficient models. The relevant model interaction parameters were regressed by data fitting. The model calculated results show good agreement with the measured data. The obtained interaction parameters can be used in the calculation of LLE for the ternary system water + benzyl alcohol + methylbenzene as well as for the design and...

Measurements and Correlation of Liquid–Liquid Equilibria for the Ternary System Water + Cyclohexanol + Cyclohexanone

Liquid–liquid equilibrium (LLE) data of the ternary system water + cyclohexanol + cyclohexanone was measured from (303.2 to 333.2) K. The reliability of the experimental tie-line data was confirmed by applying the Othmer–Tobias and the Bachman equations. The equilibrium data were correlated with the nonrandom two-liquid (NRTL) and universal quasichemical activity coefficient (UNIQUAC) models. The calculated LLE data for the ternary system agreed well with the experimental data. The root-mean-square deviations (rmsd’s) obtained comparing calculated and experimental two-phase compositions are 0.46 % for the NRTL model and 0.44 % for the UNIQUAC model. The obtained interaction parameters can be used in the calculation of LLE for the ternary system water + cyclohexanol + cyclohexanone as well as for the design, simulation, and optimization of the related separation process.

Using genetic algorithm (GA) and particle swarm optimization (PSO) methods for determination of interaction parameters in multicomponent systems of liquid–liquid equilibria

For the prediction of liquid–liquid equilibria (LLE), Wilson, universal quasi chemical (UNIQUAC) and non-random two liquid (NRTL) models were used. Evolutionary algorithms such as genetic algorithm (GA) and particle swarm optimization (PSO) were used for estimation of binary interaction parameters of these models. These two optimization methods are rarely used in LLE calculations; as far as we know the PSO algorithm has never been used and it is reported for the first time. For ternary, quaternary and quinary systems, the calculation done and the obtained results are compared to experimental data. The reliability of GA and PSO in LLE applications was successfully approved.

Liquid–Liquid Equilibrium for Ternary System Water + Cyclohexane + Acetic Acid at (303.2 to 333.2) K

Liquid–liquid equilibrium (LLE) data for the ternary system water + cyclohexane + acetic acid have been measured at (303.2 to 333.2) K under atmospheric pressure. The Othmer–Tobias and Bachman equations were used to check the reliability of the obtained tie-line data. The experimental data were correlated by NRTL (nonrandom two-liquid) activity coefficient model, and the relevant interaction parameters were regressed with the experimental data. The predicted values by NRTL method show good consistency with the measured data. The obtained interaction parameters can be used in the calculation of LLE for the ternary system water + cyclohexane + acetic acid as well as for the design and optimization of the related separation process.