Correlation Of Phase Equilibria Research Articles

A Geometric Approach for the Calculation of the Nonrandomness Factor Using Computational Chemistry.

The nonrandomness factor (α) is a parameter related to the polarity (and consequent randomness of spatial orientation) of the molecules and is generally fixed between 0.20 and 0.47 since no technique has been developed so far for its accurate estimation. However, the consideration of a constant nonrandomness factor for mixtures is known to harden azeotrope description and to cause convergence issues in both the Nonrandom Two-Liquid (NRTL) and Universal Quasi-chemical (UNIQUAC) models, which have been widely applied in the correlation of phase equilibria. In this work, a novel geometric methodology, named Porto's approach, was applied in the calculation of the nonrandomness factors for 50 pure components (mainly alkanes, alcohols, and ketones) at 298.15 K and 0.1 MPa. This methodology relied on computational chemistry (Density Functional Theory, DFT) to minimize the energy of molecules in a cavity within a solvent composed of molecules of their own (applying the Polarizable Continuum Model, PCM), and thereafter define the most stable chemical configuration in the pure liquid state. Then, the nonrandomness factor of each component was determined based on its molecular dipole moment, which was calculated after a population analysis of the optimized partial electrical charges with the Natural Bond Orbital (NBO) function. This innovative approach was applied in the correlation of liquid-liquid equilibria (LLE) data for 15 ternary systems comprising only neutral molecules with NRTL and UNIQUAC. The classical methods (α = 0.2 or 0.3 for NRTL and α = 0.2 for UNIQUAC) were compared against the usage of a component-specific nonrandomness factor, and similar standard deviations were obtained. Hence, this work is considered a strong advance in the application of these excess free Gibbs energy models to phase equilibria estimation and opens the door to more accurate thermodynamic modeling of nonideal mixtures (such as the ones containing electrolytes) by providing enhanced physical meaning to the nonrandomness factors.

Measurement and correlation of phase equilibria in aqueous two-phase systems containing ionic liquid ([EOMiM]Br) and potassium citrate/ammonium citrate/potassium tartrate at different temperatures

An aqueous two-phase system (ATPS) containing an ionic liquid (1-(2-methoxyethyl)-3-methylimidazolium bromide) and three organic salts (K3C6H5O7, (NH4)3C6H5O7, and K2C4H4O6) at different temperatures was designed. Binodal data were correlated using two empirical equations, and tie-line data were fit with the utilization of Bancroft and Othmer-Tobias equations. In the systems investigated, three conclusions were drawn from the study of the phase-forming ability of salt through effective excluded volume, Gibbs free energy of ions, and the phase diagram. First, if the same cations of salt were present, the ability of salt to form phases increased with increasing valence of the anion. Second, the larger the effective excluded volume, the stronger the aforementioned ability of salt in forming phases. Third, salt had more ability to form phases if cations (or anions) contained in the salt possessed higher negative Gibbs free energy when the cation (anion) of the salt was the same. The effect of temperature on ATPSs was also investigated. It was found that it was easier to form ATPSs at lower temperature, and the tie-line slope showed growing absolute values as the temperature was decreased.

110th Anniversary: A Case Study on Developing Accurate and Reliable Excess Gibbs Energy Correlations for Industrial Application

Excess Gibbs energy (GE) or activity-coefficient models have a strong niche in applied thermodynamics since they provide an effective method to correlate and estimate phase equilibrium for nonideal systems. The history of their development is well represented by many papers in the technical literature, and notably in the five score and ten years of publications in Industrial & Engineering Chemistry. The science and technology has moved from formulating and establishing ideas and concepts to the automation of modern software, where phase-equilibrium correlations are often developed by algorithms with little or no expert human intervention. In addition, there is belief among practitioners that increasingly theoretical models, based upon molecular thermodynamics, will lead to more accurate correlations and with wider applicability. In this paper we use an apparently complex, but actually simple system (the lower alcohols), to study the development of GE correlations for industrial application. The subjects focused on are (1) use of multiproperty data, (2) property trends within the family of compounds, and (3) the need for advanced models.

Correlation of phase equilibria by new activity coefficient model

Iwai et al. proposed a new model for activity coefficients in the previous work [Y. Iwai, Fluid Phase Equilib. 465 (2018) 24–33]. In this work, the number of interactions for Lennard-Jones fluids in liquid phase was calculated by molecular dynamics simulation to check the validity of the assumptions in the new model. The calculated results show that the number of interactions per molecule depends on partner molecules and concentrations, and the assumptions are reasonable. The new model was applied to correlate the activity coefficients for the real systems in which the activity coefficients exceptionally increase or decrease in the dilute regions. The vapor-liquid equilibria for hydrocarbon + alcohol systems were calculated by combining an equation of state with excess Gibbs free energy (GE) mixing rules. It is observed that the calculated results of vapor-liquid equilibria are improved by using the new model for GE.

Measurement and correlation of phase equilibria in aqueous two-phase systems containing functionalized magnetic ionic liquids and potassium phosphate at different temperatures

Functionalized magnetic ionic liquids ([C2TMG][TEMPO-OSO3], [C3TMG] [TEMPO-OSO3], [C4TMG][TEMPO-OSO3]) and K3PO4 were used as phase forming compounds of aqueous two-phase system at three temperatures (278.15 K, 298.15 K and 318.15 K). The effects of temperature and magnetic ionic liquid (MIL) species on the binodal curves were investigated. Three classical empirical equations were used for the correlations of the binodal curves. They have shown satisfactory performances in data fitting. An increase of the two-phase separation ability was observed when the temperature decreased. Additionally, all these three MILs have preferable phase forming ability as well as wide range of two-phase area in the binodal curve for our systems. This is strongly expected in practical applications. Furthermore, tie line data were experimentally acquired for the three MILs at 298.15 K. Three empirical formulas including Othmer–Tobias, Bancroft equations as well as an equation derived from binodal theory were used to fit the tie-line data with successful correlation. These aqueous two-phase equilibrium data should be useful in the areas of separation, purification and analysis.

Measurement and Correlation of Phase Equilibria in Aqueous Two-Phase Systems Containing Polyoxyethylene Cetyl Ether and Three Organic Salts at Different Temperatures

Measurement and Correlation of Phase Equilibria in Aqueous Two-Phase Systems Containing Polyoxyethylene Cetyl Ether and Three Organic Salts at Different Temperatures

Measurement and correlation of phase equilibria in aqueous two-phase systems containing polyethyleneglycol (2 000, 4 000, and 6 000) and sulfate salts (manganese sulfate and copper sulfate) at different temperatures (298.15, 318.15, and 338.15 K)

Liquid–liquid equilibrium (LLE) data were obtained for polyethylene glycol (PEG)-salt aqueous two-phase system (ATPS) at 298.15, 318.15 and 338.15 K. Two salts, copper sulfate and manganese sulfate, and PEG with different molecular weights, 2 000, 4000 (manganese sulfate only), and 6 000, were used. The effects of the molecular weight of PEG and temperature on phase separation and the salting-out effect were studied. For all aqueous two-phase systems, the increase in the polymer molecular weight provides a larger biphasic region. The temperature promoted an increase in the biphasic region, and the slope of tie-lines tended to decrease with increasing temperature. The Setschenow-type equation was used to evaluate the salting-out effect of MnSO4 and CuSO4, as well as the temperature and molecular weight of the PEG influence on the phase formation. The rank order of salting-out coefficients is Mn2+ > Cu+2 since the cation Mn2+ is more kosmotropic than Cu2+. NRTL and UNIQUAC models have been used to fit the 18 experimental LLE data. The interaction parameters of the models were estimated. The results show that the quality of fitting is better with the UNIQUAC model.

Measurement and correlation of phase equilibrium of the aqueous two-phase system formed by Fe2(SO4)3 + PEG 4000 + H2O at different temperatures

Liquid-liquid equilibrium (LLE) data for the Fe2(SO4)3+polyethylene glycol 4000 (PEG 4000)+H2O system were determined experimentally at T=(323.15, 333.15 and 343.15) K. The effect of temperature on the binodal curves and tie-lines were studied and it was found that an increasing in temperature caused the expansion of two-phase region.Additionally, experimental density, sound velocity, refractive index and viscosity data were also reported at T=(323.15, 333.15 and 343.15) K.The Chen-NRTL, modified Wilson and extended UNIQUAC models and the Othmer-Tobias and Bancroft equations were used to correlate the experimental tie-line data obtaining a good representation of the equilibrium. Furthermore, the Merchuk equation was used to correlate the binodal curves.

Measurement and correlation of phase equilibria in aqueous two-phase systems containing functionalized magnetic ionic liquids and K2HPO4/K2CO3/Na2CO3 at 298.15 K

Abstract Functionalized magnetic ionic liquids (MILs)([C2TMG][TEMPO-OSO3], [C3TMG][TEMPO-OSO3], [C4TMG][TEMPO-OSO3]) and three inorganic salts (K2HPO4/K2CO3/Na2CO3) were used to form aqueous two-phase system at 298.15 K. Three classical experienced equations were applied for the correlations of the binodal curves. All of them demonstrated satisfactory performance in data association. The binodal curves were investigated in detail. Both K2HPO4 and K2CO3 was excellent phase forming salts for all the three MILs. Both of them can meet the need of practical applications. There is a narrow biphasic region for the MIL + Na2CO3 + water system because of a relatively low solubility of salt in water. Additionally, tie-line data were experimentally obtained for the three MILs with K2HPO4 or K2CO3 at 298.15 K. Three empirical formulas including Othmer-Tobias equation, Bancroft equation together with another equation derived from binodal theory were used to fit the tie-line data. Consequently, Othmer-Tobias has shown ideal correlation performance and the reliability of our experimental tie-line data can be ensured. Hopefully, these aqueous two-phase equilibrium data should be useful in the areas of chemical separation, purification and analysis.

Measurement and Correlation of Phase Equilibria in Aqueous Two-Phase Systems Containing Polyoxyethylene Cetyl Ether and Potassium Salt at Different Temperatures

The aqueous two-phase system (ATPS) containing the polyoxyethylene(20) cetyl ether (C56H114O21, POELE20) and three potassium salts (KOH, K2CO3, and K3PO4) at the three temperatures (288.15, 298.15, and 308.15) K were designed. The binodal data of the studied systems were determined and correlated with three experience equations, and a satisfactory correlation effect was gained. The effect of the type of salt on the phase-forming ability of the system was discussed in the study of effective excluded volume (EEV), phase diagram, and Gibbs free energy of ionic hydration. It was found that the phase-forming ability of the system was enhanced with the increase in system EEV and anion valence, and it also increased with an increase in the absolute value of Gibbs free energy of ionic hydration. The binodal curves are influenced by the system temperature, and it was found that, with the increase in temperature, the binodal curves moved to the left and the two-phase areas expanded. Moreover, the effect of temperature on the slope of the tie line was studied, and we have drawn a conclusion that the value of the slope of the tie line increased with rising temperature.

Measurement and Correlation of Phase Equilibria in Aqueous Two-Phase Systems Containing Polyoxyethylene Lauryl Ether and Sulfate Salt at Different Temperatures

The aqueous two-phase system (ATPS) containing the polyoxyethylene(20) cetyl ether (C56H114O21, POELE20) and three potassium salts (KOH, K2CO3, and K3PO4) at the three temperatures (288.15, 298.15, and 308.15) K were designed. The binodal data of the studied systems were determined and correlated with three experience equations, and a satisfactory correlation effect was gained. The effect of the type of salt on the phase-forming ability of the system was discussed in the study of effective excluded volume (EEV), phase diagram, and Gibbs free energy of ionic hydration. It was found that the phase-forming ability of the system was enhanced with the increase in system EEV and anion valence, and it also increased with an increase in the absolute value of Gibbs free energy of ionic hydration. The binodal curves are influenced by the system temperature, and it was found that, with the increase in temperature, the binodal curves moved to the left and the two-phase areas expanded. Moreover, the effect of temperat...

Measurement and Correlation of Phase Equilibria in Aqueous Two-Phase Systems Containing Polyoxyethylene Lauryl Ether and Tartrate Salt at Different Temperatures

Measurement and Correlation of Phase Equilibria in Aqueous Two-Phase Systems Containing Polyoxyethylene Lauryl Ether and Tartrate Salt at Different Temperatures

High-pressure phase equilibrium measurements and thermodynamic modeling for the systems involving CO2, ethyl esters (oleate, stearate, palmitate) and acetone

The aim of this work was to study the phase behavior of systems involving carbon dioxide (CO2), fatty acid ethyl esters (ethyl oleate, ethyl stearate and ethyl palmitate) and acetone at high pressures. The phase behavior involving these components is an important step regarding the design and optimization of industrial processes based on supercritical conditions, such as biodiesel production and fatty esters fractionation involving supercritical and/or pressurized solvents. In addition, supercritical CO2 can offer an interesting alternative for glycerol separation in water-free biodiesel purification processes. The binary systems investigated in this work were CO2+ethyl oleate, and CO2+ethyl stearate and these were compared with the CO2+ethyl palmitate system. The ternary CO2+ethyl palmitate+acetone was also investigated at two different ethyl palmitate to acetone molar ratios of (1:1) and (1:3). The static synthetic method using a variable-volume view cell was employed to obtain the experimental data in the temperature range of 303.15–353.15K. Vapor–liquid (VL), liquid–liquid (LL) and vapor–liquid–liquid (VLL) phase transitions were observed in these systems. In the binary systems, the solubility increased with the presence of unsaturation and decreased with the number of carbon atoms in the fatty ester chain. Addition of acetone as well as ethanol eliminated the liquid–liquid immiscibility and reduced the pressure transitions, therefore increasing the solubility of the ester in supercritical CO2. The experimental data sets for the binary and ternary systems were successfully modeled using the Peng–Robinson equation of state with the classical van der Waals quadratic mixing rule (PR-vdW2) and Wong-Sandler (PR-WS) mixing rule. Both models showed good performance in the phase equilibrium correlations and in predictions for the binary and ternary systems.

Experimental investigation and modeling of liquid–liquid equilibria in two systems of concern in biodiesel production

The binary systems of water+biodiesel and ternary systems of methanol+glycerol+biodiesel, which are involved in the biodiesel production process, were investigated in order to find the corresponding equilibrium data. In the case of binary systems, water solubilities in two biodiesels from either corn or frying oil were determined within a temperature range of 297.2–333.2K. For the ternary mixtures of methanol+glycerol+either corn or frying oil biodiesel, the binodal curves and tie lines were determined at the three temperatures of 293.2, 303.2, and 313.2K. Results showed that the solubilities in both binary and ternary systems increased with increasing temperature. The Othmer–Tobias correlation was applied to each ternary system to ascertain the reliability of the experimental tie line data obtained, and to provide phase equilibrium correlations at conditions where data are not available. All of the investigated systems were also modeled using the UNIQUAC model. The satisfactory results obtained indicate the suitability of this model for such systems.

Measurement and Correlation of Phase Equilibria in Aqueous Two-Phase Systems Containing Polyoxyethylene Lauryl Ether and Three Kinds of Potassium Salts at Different Temperatures

The binodal curves of the aqueous two-phase system (ATPS) containing the polyoxyethylene (10) lauryl ether (POELE10, C32H66O11) and three potassium salts (KOH/K2CO3/K3PO4) were determined at the temperatures (288.15, 293.15, 303.15, and 308.15) K. The three experience equations were used to fit the binodal data for the studied systems, and a satisfactory correlation effect was obtained. The effect of salts on the binodal curves for the investigated systems was discussed by the effective excluded volume (EEV), and we found that the salting-out effect is mainly influenced by valence of anion of salts. The salt containing the higher valence of anion has a stronger phase-forming ability than that with a lower charge of anion. The liquid–liquid equilibrium (LLE) data for the investigated systems were determined and correlated by the Othmer–Tobias and Bancroft equations. The effect of the change of temperature on the binodal curves and tie-lines was also studied through the analysis of the EEV values and cloud point (CP) figure. The increase in temperature leads to the strengthening hydrophobicity of POELE10 that drive more water transferring from the top phase to the bottom phase, which means the phase-forming ability of the whole systems was strengthened. Thus, the critical concentration of POELE10 and salts for forming ATPS decreases with the rising temperature.

Measurement and Correlation of Phase Equilibria in Aqueous Two-Phase Systems Containing Polyoxyethylene Lauryl Ether and Diammonium Hydrogen Phosphate or Dipotassium Hydrogen Phosphate at Different Temperatures

The phase diagrams for the systems containing polyoxyethylene lauryl ether (Brij35) and K2HPO4/(NH4)2HPO4 have been determined experimentally at three temperatures, (288.15, 298.15, and 308.15) K. Three experiential equations were used to correlate the binodal data. The liquid–liquid equilibrium (LLE) data of these systems obtained by the experimental method were fitted by using Othmer–Tobias and Bancroft along with simple Setschenow-type equations. Furthermore, the effect of temperature on the binodal curve for the disquisitive systems has been discussed, and it was found that two-phase region expands with the increase in temperature, which is corresponded to the value of the effective excluded volume (EEV) calculated according to the binodal model. In the investigated systems, the free energy (ΔG), enthalpy change (ΔH), and entropy change (ΔS) were calculated, and it indicated that the phase separation processes are endothermic and driven by the entropy increase. That the slope of tie-line increases wit...

Correlation of phase equilibria and liquid densities for gases with ionic liquids

We describe a method for correlating and estimating gas solubilities and liquid densities of ionic liquids based on a corresponding-states form for direct correlation function integrals (DCFIs) from fluctuation solution theory, as previously applied to nonionic systems. A quantitative description is obtained for the volumetric behavior of pure liquids at elevated pressures. Solubilities and partial molar volumes are given over wide ranges of conditions using only pure component information and a binary parameter for hydrogen, carbon monoxide, oxygen and methane in the ionic liquids 1-butyl-3-methyl-imidazolium hexafluorophosphate, [bmim][PF 6], and 1-hexyl-3-methyl-imidazolium bis(trifluoromethylsulfonyl)imide, [hmim][Tf 2N]. Comparisons are made with other literature treatments and a predictive approach is described.

Measurement and correlation of phase equilibria in aqueous two-phase systems containing polyvinylpyrrolidone and di-potassium tartrate or di-potassium oxalate at different temperatures

Experimental (liquid + liquid) equilibrium (LLE) measurements and the phase diagram have been determined for aqueous two-phase systems containing polyvinylpyrrolidone (PVP) and di-potassium oxalate or di-potassium tartrate at T = (298.15, 308.15, and 318.15) K. Also, the effects of temperature on the binodal curve and tie-lines have been studied. The Merchuk equation was used to correlate the binodal curves of these systems. Furthermore, several suitable equations were used to fit the tie-line data points. The results show that at each temperature, the agreement between the correlated and the experimental values is good with all of these equations. Also, the effects of the type of salt on LLE are discussed.

An evaluation of the performance of the Cubic-Plus-Association equation of state in mixtures of non-polar, polar and associating compounds: Towards a single model for non-polymeric systems

The aim of this work is to investigate the possibility of identifying a single model that will be able to accurately describe the phase equilibrium in non-polymeric systems, which involve non-polar, polar and hydrogen bonding compounds. To this purpose the Cubic-Plus-Association (CPA) EoS, developed in this laboratory about 10 years ago, is examined in the correlation of phase equilibrium in binary systems and prediction of multicomponent phase equilibrium from binary data. When possible the results of the CPA EoS are compared with those obtained from the PC-SAFT EoS. To account for dipolar or quadrupolar interactions, present when molecules such as acetone or carbon dioxide are involved, these molecules are treated using the concept of “pseudo-association”, i.e. as being able to act as associating compounds. This approach renders CPA applicable to systems that involve polar compounds without the need of extra terms to account for polar and/or quadrupolar interactions. It is concluded that CPA, coupled with the “pseudo-association” approach for polar molecules, represents a model that is able to accurately describe the phase equilibrium in a variety of binary systems involving non-polar, polar and hydrogen bonding compounds and provide satisfactory prediction of multicomponent phase equilibrium from binary data.

Phase Equilibrium of Asymmetric Systems by Predictive Equations of State Models

In this study the modified Wong−Sandler (WS), the modified Huron−Vidal second-order (MHV2), and the Orbey−Sandler (HVOS) mixing rules were used for phase equilibrium correlation of carbon dioxide i...