Improper matching of solvation energy components in G-based mixing rules

The physical significance of terms in two excess Gibbs free energy (G^ex)-based mixing rules, the modified Huron–Vidal (MHV1) and Wong–Sandler (WS) mixing rule, are examined through the use of solvation free energy. It is found that these mixing rules are in fact matching the charging contributions of solvation in an equation of state (EOS) to the complete solvation free energy in a liquid activity coefficient model (LM). The cavity contributions in the EOS are canceled as a result of the constant liquid molar volume to molecular volume ratio. The underlying idea of G^ex-based mixing rules that the EOS should behave like a LM at some limiting condition breaks down due to such an improper matching of solvation free energy components.     

Experimental measurement and modeling of the vapor–liquid equilibrium of carbon dioxide + chloroform

Isothermal bubble and dew points, saturated molar volumes, and mixture critical points for binary mixtures of carbon dioxide+chloroform (trichloromethane) (CO₂/CHCl₃) have been measured in the temperature region 303.15–333.15 K and at pressures up to 100 bar. Mixture critical points are reported at 313.15, 323.15, and 333.15 K. The data were modeled with the Peng–Robinson equation of state using both the van der Waals-1 (vdW-1) mixing rule and the Wong–Sandler (WS) mixing rule incorporating the UNIQUAC excess free energy model. The WS mixing rule provided a better representation of the data than did the vdW-1 mixing rule, though with three adjustable parameters instead of one. The extrapolating ability of both of the mixing rules was investigated. Using the parameters regressed at 323.15 K, the WS mixing rule yielded better extrapolations for the composition dependence at 303.15, 313.15, and 333.15 K than the vdW-1 mixing rule.     

Thermodynamic consistency of experimental VLE data for asymmetric binary mixtures at high pressures

A thermodynamic consistency of isothermal vapor–liquid equilibrium data for 9 non-polar and 8 polar binary asymmetric mixtures at high pressures has been evaluated. A method based on the isothermal Gibbs–Duhem equation was used for the test of thermodynamic consistency using a Φ–Φ approach. The Peng–Robinson equation of state coupled with the Wong–Sandler mixing rules were used for modeling the vapor–liquid equilibrium (VLE) within the thermodynamic consistency test. The VLE parameters calculations for asymmetric mixtures at high pressures were highly dependent on bubble pressure calculation, making more convenient to eliminate the data points yielding the highest deviations in pressure. However the results of the thermodynamic consistencies test of experimental data for many cases were found not fully consistent. As a result, the strategies for solving these problems were discussed in detailed.     

Isothermal vapor–liquid equilibria for binary mixtures of benzene, toluene, m-xylene, and N-methylformamide at 333.15 K and 353.15 K

Isothermal vapor–liquid equilibrium (VLE) at 333.15 K and 353.15 K for four binary mixtures of benzene + toluene, benzene + N-methylformamide, toluene + m-xylene and toluene + N-methylformamide have been obtained at pressures ranged from 0 kPa to 101.3 kPa. The NRTL, UNIQUAC and Wilson activity coefficient models have been employed to correlate experimental pressures and liquid mole fractions. The non-ideal behavior of the vapor phase has been considered by using the Soave–Redlich–Kwong equation of state in calculating the vapor mole fraction. Liquid and vapor densities were also measured by using two vibrating tube densitometers. The P–x–y diagram and the activity coefficient indicate that two mixtures of benzene + toluene and toluene + m-xylene were close to the ideal solution. However, two mixtures containing N-methylformamide present a large positive deviation from the ideal solution. The excess Gibbs energy in the benzene + toluene mixture is negative indicates that it is an exothermic system.     

Parameters estimation and VLE calculation in asymmetric binary mixtures containing carbon dioxide + n-alkanols

In the present work, the estimation of the parameters for asymmetric binary mixtures of carbon dioxide + n-alkanols has been developed. The binary interaction parameter k₁₂ of the second virial coefficient and non-random two liquid model parameters τ₁₂ and τ₂₁ were obtained using Peng–Robinson equation of state coupled with the Wong–Sandler mixing rules. In all cases, Levenberg–Marquardt minimization algorithm was used for the parameters optimization employing an objective function based on the calculation of the distribution coefficients for each component. Vapor–liquid equilibrium for binary asymmetric mixtures (CO₂ + n-alkanol, from methanol to 1-decanol) was calculated using the obtained values of the mentioned parameters. The agreement between calculated and experimental values was satisfactory.     

An equation-of-state-based viscosity model for non-ideal liquid mixtures

A viscosity model based on the Eyring’s theory and a cubic equation of state (Peng–Robinson–Stryjek–Vera) has been applied to the correlation and prediction of experimental liquid viscosities of binary mixtures containing polar fluids within a wide range of temperature, pressure and composition (encompassing low-pressure and compressed liquid conditions). Highly non-idealities of the binary mixtures considered in this study were conveniently handled via the application of the Wong–Sandler approach for the mixing rules used in the cubic equation of state. The results obtained were highly satisfactory for various non-ideal binary mixtures over the whole composition range at a low pressure. The predictive capabilities of the present approach were also verified in the representation of liquid viscosities at elevated pressures preserving the same model parameters previously obtained at low pressure.     

An equation of state for hydrogen fluoride

Using a similar approach as Lencka and Anderko [AIChE J. 39 (1993) 533], we developed an equation of state for hydrogen fluoride (HF), which can correlate the vapor pressure, the saturated liquid and vapor densities of it from the triple point to critical point with good accuracy. We used an equilibrium model to account for hydrogen bonding that assumes the formation of dimer, hexamer, and octamer species as suggested by Schotte [Ind. Eng. Chem. Process Des. Dev. 19 (1980) 432]. The physical and chemical parameters are obtained directly from the regression of pure component properties by applying the critical constraints to the equation of state for hydrogen fluoride. This equation of state together with the Wong–Sandler mixing rule as well as the van der Waals one-fluid mixing rule are used to correlate the phase equilibria of binary hydrogen fluoride mixtures with HCl, HCFC-124, HFC-134a, HFC-152a, HCFC-22, and HFC-32. For these systems, new equation of state with the Wong–Sandler mixing rule gives good results.     

Modelling the Vapor–Liquid Equilibrium of Polymer Solutions Using a Cubic Equation of State

This work presents the vapor–liquid equilibrium calculations in an isothermal flash, applied to polymer solutions, using the Peng–Robinson cubic equation of state modified by Stryjek–Vera, and the mixing rule introduced by Wong–Sandler. This rule allows combining the rigid lattice thermodynamic model of Flory–Huggins to the Peng–Robinson–Stryjek–Vera equation of state. As the Gibbs free energy must be minimum in the equilibrium state, a stochastic optimization method, the simulated annealing algorithm, was used to find out the extreme of this thermodynamic potential.     

Thermodynamic modeling of saturated liquid compositions and densities for asymmetric binary systems composed of carbon dioxide,alkanes and alkanols

The present study mainly focuses on the phase behavior modeling of asymmetric binary mixtures. Capability of different mixing rules and volume shift in the prediction of solubility and saturated liquid density has been investigated. Different binary systems of (alkane + alkanol), (alkane + alkane), (carbon dioxide + alkanol), and (carbon dioxide + alkane) are considered. The composition and the density of saturated liquid phase at equilibrium condition are the properties of interest. Considering composition and saturated liquid density of different binary systems, three main objectives are investigated. First, three different mixing rules (one-parameter, two parameters and Wong–Sandler) coupled with Peng–Robinson equation of state were used to predict the equilibrium properties. The Wong–Sandler mixing rule was utilized with the non-random two-liquid (NRTL) model. Binary interaction coefficients and NRTL model parameters were optimized using the Levenberg–Marquardt algorithm. Second, to improve the density prediction, the volume translation technique was applied. Finally, Two different approaches were considered to tune the equation of state; regression of experimental equilibrium compositions and densities separately and spontaneously. The modeling results show that there is no superior mixing rule which can predict the equilibrium properties for different systems. Two-parameter and Wong–Sandler mixing rule show promoting results compared to one-parameter mixing rule. Wong–Sandler mixing rule in spite of its improvement in the prediction of saturated liquid compositions is unable to predict the liquid densities with sufficient accuracy.     

(Vapour + liquid) equilibria of the {trifluoromethane (HFC-23) + propane} and {trifluoromethane (HFC-23) + n-butane} systems

Isothermal (vapour + liquid) equilibrium data were measured for the two systems, {trifluoromethane (HFC-23) + propane} and {trifluoromethane (HFC-23) + n-butane}, at temperatures ranging from 283.15 K to 313.15 K at 10 K intervals. These experiments were performed with a circulating-type apparatus and on-line gas chromatography. Experimental data were well correlated by the Peng–Robinson equation of state using the Wong–Sandler mixing rules and the NRTL model.     

Vapor–liquid equilibria and interfacial tensions for the ternary system acetone + 2,2′-oxybis[propane] + cyclohexane and its constituent binary systems

Isobaric vapor–liquid equilibrium data have been measured for the ternary system acetone + 2,2′-oxybis[propane] + cyclohexane, and its constituent binaries at 94 kPa and in the temperature range 324–350 K in a vapor–liquid equilibrium still with circulation of both phases. The dependence of the interfacial tensions of these mixtures on concentration was also determined at atmospheric pressure and 303.15 K, using the maximum bubble pressure technique.From the experimental results, it follows that both the ternary and binary mixtures exhibit positive deviations from ideal behavior and, additionally, azeotropy is present for the binaries that contain acetone. The application of a model-free approach allows conclusions about the reliability of the present vapor–liquid equilibrium data for all the indicated mixtures. Furthermore, the determined interfacial tensions exhibit negative deviation from linear behavior for all the analyzed mixtures, and aneotropy is observed for the acetone + cyclohexane mixture.The vapor–liquid equilibrium data of the binary mixtures were well correlated using the NRTL, Wilson and UNIQUAC equations. In a similar manner, the interfacial tensions of the binary mixtures were smoothed using the Redlich–Kister equation. Scaling of these models to the ternary mixture allows concluding that both the vapor–liquid equilibrium data and the interfacial tensions can be reasonably predicted from binary contributions.     

Experimental measurements of vapor–liquid equilibria at low pressure: Systems containing alcohols,esters and organic acids

In this work the vapor–liquid equilibria for nine binary mixtures (methanol + acetic acid, methanol + methyl acetate, methanol + water, methyl acetate + acetic acid, water + acetic acid, ethyl acetate + acetic acid, ethanol + acetic acid, ethanol + ethyl acetate and ethanol + water) at subatmospherical pressure (580 mmHg) is presented. Peng–Robinson Stryjek–Vera equation of state coupled with the Wong–Sandler mixing rules were used for predicting phase equilibria of these mixtures. The measurements were developed using an apparatus with recirculation that can also be employed for liquid–vapor equilibrium with chemical reaction.     

Thermodynamic excess quantities of ternary Au–Co–Pd melts by computer-aided Knudsen cell mass spectrometry

Computer-aided Knudsen cell mass spectrometry is used for the thermodynamic investigations on ternary Au–Co–Pd melts over the entire range of composition. The “digital intensity-ratio” (DIR)-method has been applied for the determination of the thermodynamic excess quantities, and the ternary thermodynamically adapted power (TAP) series concept is used for algebraic representation of the thermodynamic mixing behavior. The corresponding TAP parameters as well as the values of the molar excess Gibbs energies G^E, of the molar heats of mixing H^E, of the molar excess entropies S^E, and of the thermodynamic activities at 1800 K are presented.     

A new model and extension of Wong–Sandler mixing rule for prediction of (vapour + liquid) equilibrium of polymer solutions using EOS/GE

The cubic equation of state (CEOS) is a powerful method for calculation of (vapour + liquid) equilibrium (VLE) in polymer solutions. Using CEOS for both the vapour and liquid phases allows one to calculate the non-ideality of polymer solutions based on a single EOS approach. However, the traditional mixing rules are not appropriate to extend the CEOS to non-ideal mixtures such as polymer solutions. Several authors have applied the EOS/G^E approach to predict (vapour + liquid) equilibria in polymer solutions, however, incorporating an appropriate excess Gibbs free energy for the new mixing rule is a major step. In this research, the NRTL-NRF model was extended in terms of volume fraction of polymer and solvent (instead of mole fraction), then equilibrium calculations were carried out using PRSV EOS and Wong–Sandler mixing rules. Using the adjustable parameters as a function of solution temperature, the NRTL-NRF model can be used as a predictive model. In comparison with NRTL model, the results of the new NRTL-NRF model show better accuracy.     

Excess Gibbs Energy of Mixing for Organic Carbonates from Fitting of Their Binary Phase Diagrams with Nonideal Solution Models

The excess Gibbs energies of mixing in the liquid state were evaluated for all the ten binary combinations of these five organic carbonates: ethylene carbonate (EC), propylene carbonate, dimethyl carbonate (DMC), ethyl methyl carbonate, and diethyl carbonate by fitting their measured binary phase diagrams with thermodynamic nonideal solution models based on the regular solution model. Using the results of these model fits, activity coefficients of the components in the solvent mixtures were calculated for the binary series containing EC and DMC as the common component, and the composition-averaged excess Gibbs energies of mixing were calculated by integrating the energy in the whole composition range for all the binaries. The results showed the excess Gibbs energy of mixing, and therefore the intermolecular forces, to be responsible for the changes in the phase diagrams, in the activity coefficients, and in the composition-averaged excess energy for the different binary solution combinations.     

(Vapor + liquid) equilibria for the {water + poly(ethylene glycol diacetyl ether) (PEGDAE) and methanol + PEGDAE} systems

We measured binary (vapor + liquid) equilibrium data for the {water + poly(ethylene glycol diacetyl ether) (PEGDAE) and methanol + PEGDAE} systems at pressures up to 400 kPa and temperatures from 333 K to 393 K. A static apparatus was used in this study. The measured data were correlated by the Peng–Robinson equation of state using the Wong–Sandler mixing rules with NRTL as the excess Gibbs free energy model.     

Vapor–liquid equilibria of the carbon dioxide (CO2) + 2,2-dichloro-1,1,1-trifluoroethane (R123) system and carbon dioxide (CO2) + 1-chloro-1,2,2,2-tetrafluoroethane (R124) system

Binary vapor–liquid equilibrium data were measured for the carbon dioxide (CO₂) + 2,2-dichloro-1,1,1-trifluoroethane (R123) system and the carbon dioxide (CO₂) + 1-chloro-1,2,2,2-tetrafluoroethane (R124) system at temperature from 313.15 to 333.15 K. These experiments were carried out with a circulating-type apparatus with on-line gas chromatography. The experimental data were correlated well by Peng–Robinson equation of state using the Wong–Sandler mixing rules.     

Modeling of high-pressure vapor–liquid equilibrium in ionic liquids + gas systems using the PRSV equation of state

Ionic liquids are environmentally friendly solvents composed of large organic cations and relatively small inorganic anions, whose melting point is below T = 373.15 K. This is an arbitrary limit defined in order to organize the dramatically increasing number of possible applications in chemical processes. These compounds are regarded as potentially environmentally benign solvents due to their almost negligible vapor pressure, which essentially eliminates emission to the atmosphere; besides, they present a wide range of liquid existence. Ionic liquids are applicable in separation processes, such as recovery of valuable products and remotion of polluting agents in effluents 1, 2, 3 and 4 and are a new and exciting class of compounds that have the potential to overcome many of the problems associated with current CO₂-capture techniques. In this work, high-pressure vapor–liquid equilibrium (VLE) of 17 binary mixtures ionic liquid + gas has been modeled with the Peng–Robinson/Stryjek–Vera (PRSV) 5 and 6 equation of state (EoS) applying the Wong–Sandler (WS) [7] mixing rules, including the van Laar (VL) model for the excess Gibbs free energy [8] for the gamma–phi approach and the one-fluid van der Waals (VDW) mixing rules for the phi–phi approach. Critical properties and acentric factor of ionic liquids [pmim][Tf₂N] and [hmmim][Tf₂N] were determined using the extended group contribution method by Lydersen–Joback–Reid [9], while, for the other ionic liquids, these properties are available in the literature 10 and 11. Experimental data were obtained from literature 12, 13, 14, 15, 16, 17 and 18 and the adjustable parameters were fitted by minimizing the errors between predicted and experimental bubble pressure. van Laar and binary interaction parameters were regarded as temperature-dependent. The results, in terms of main deviations between experimental and calculated pressures for the 17 binary systems, are reasonably satisfactory (3.62% and 2.59% for the gamma–phi and phi–phi approaches, respectively).     

Thermophysical properties of binary mixtures of {ionic liquid 2-hydroxy ethylammonium acetate + (water,methanol, or ethanol)}

In this work, density and speed of sound data of binary mixtures of an ionic liquid consisting of {2-hydroxy ethylammonium acetate (2-HEAA) + (water, methanol, or ethanol)} have been measured throughout the entire concentration range, from the temperature of (288.15 to 323.15) K at atmospheric pressure. The excess molar volumes, variations of the isentropic compressibility, the apparent molar volume, isentropic apparent molar compressibility, and thermal expansion coefficient were calculated from the experimental data. The excess molar volumes were negative throughout the whole composition range. Compressibility data in combination with low angle X-ray scattering and NMR measurements proved that the presence of micelles formed due to ion pair interaction above a critical concentration of the ionic liquid in the mixtures. The Peng–Robinson equation of state coupled with the Wong–Sandler mixing rule and COSMO–SAC model was used to predict densities and the calculated deviations were lower than 3%, for binary mixtures in all composition range.     

Vapor–liquid equilibrium in the n-butane + methanol system,measurement and modeling from 323.2 to 443.2 K

New experimental vapor–liquid equilibrium (VLE) data for the n-butane + methanol binary system are reported over a wide temperature range from 323.2 to 443.2 K and pressures up to 5.4 MPa. A static–analytic apparatus, taking advantage of two pneumatic capillary samplers, was used. The phase equilibrium data generated in this work are in relatively good agreement with previous data reported in the literature. Three different thermodynamic models have been used to represent the new experimental data. The first model is the cubic-based Peng–Robinson equation of state (EoS) combined with the Wong–Sandler mixing rules. The two other models are the non-cubic SAFT-VR and PC-SAFT equations of state. Temperature-dependent binary interaction parameters have been adjusted to the new data. The three models accurately represent the new experimental data, but deviations are seen to increase at low temperature. A similar evolution of the binary parameters with respect to temperature is observed for the three models. In particular a discontinuity is observed for the k_ij values at temperatures close to the critical point of butane, indicating the effects of fluctuations on the phase equilibria close to critical points.