Search

The present study compares the ability of three semipredictive approaches, namely, the global phase diagram based semipredictive approach (GPDA), predictive Soave−Redlich−Kwong (PSRK), and linear combination of the Vidal and Michelsen mixing rules (LCVM), to describe the experimental data in the binary homologue series of ethane−n-alkanes. The applicability of GPDA has been extended by attachment of an additional empirical functionality. Now it can predict not only the data of a homologues series to which the reference system belongs but also other series that include solvents from the same chemical group. Yet, both GPDA and PSRK appear as entirely predictive models. However, LCVM has a correlative character rather than predictive. Although the models under consideration yield rather similar results for the light homologues of the series, starting from ethane−n-decane, GPDA shows a clear superiority over PSRK and LCVM. Moreover, it is demonstrated that the G^E mixing rules of both PSRK and LCVM generate the nonphysical behavior of liquid−liquid equilibrium. This result strongly affects the reliability of these models in predicting the data of heavy homologues. In contrast, GPDA predicts robust results even for very asymmetric systems. These facts confirm the clear advantage of an approach based on consideration of the complete phase diagram and not of its separate parts.

This study tests the ability of the best presently available semipredictive models, namely, predictive Soave−Redlich−Kwong (PSRK), linear combination of Vidal mixing rules (LCVM), and the novel global phase diagram approach (GPDA), to estimate the three-phase liquid−liquid−vapor equilibrium (LLVE) in the homologous series methane−n-alkanes, ethane−n-alkanes, propane−n-alkanes, and n-butane−n-alkanes. It is demonstrated that at high pressures G^E mixing rules predict the wrong shape of the liquid−liquid critical curves, which involves fictitious closed loops of liquid−liquid equilibrium. Such a behavior is responsible for predicting nonrealistic three-phase LLVE behavior along the homologous series under consideration. In addition, both PSRK and LCVM fail in estimating the lower critical end-point curve. The results presented here for the G^E-based models under consideration are probably characteristic for them. In contrast, GPDA is consistent in the entire thermodynamic phase space and does not predict nonphysical results. Although GPDA tends to underestimate the temperatures of the end points and to overestimate the double critical end points, its results are at least qualitatively accurate.

Empirical thermal cohesion functions, α(Tr), are frequently used in conventional equations of state (EOS) for fitting the vapor pressures of pure fluids. Accurate vapor pressure predictions are required for correlating and/or predicting the phase equilibrium and interfacial tension of multicomponent mixtures. This is the case for the Redlich−Kwong−Soave and Peng−Robinson models, two well-established models for engineering applications. In this work, we demonstrate that, in the case of pure fluids, the α(Tr) function can potentially predict multiple mechanically stable critical points, thus affecting the global topology of phase equilibrium predictions. A detailed analysis, based on the consistency of the prediction of the Joule−Thomson inversion curve, reveals that these predictions are not reliable from a physical point of view. In fact, conventional cubic EOS are able to predict multiple Joule−Thomson inversion curves, a behavior symptomatic of the prediction of multiple stable critical points for pure fluids. Similar pitfalls have been detected in theoretically based EOS such as SAFT and the model proposed by Johnson et al. (Johnson, J. K.; Zollweg, J. A.; Gubbins, K. E. Mol. Phys. 1993, 78, 591−615) for Lennard-Jones fluids, although beyond the range in which such models are usually employed. In the case of conventional cubic EOS with quadratic mixing rules, another pitfall related to conventional α(Tr) functions is the prediction of nondifferentiable critical lines and equilibrium envelopes for mixtures. Such a physical inconsistency might generate a mechanism that predicts closed loops of immiscibility in van der Waals-type EOS that contain a temperature-dependent parameter.

This study looks for the first time at the possibility of predicting liquid−liquid−vapor equilibria without preliminary resource to experimental data. For this purpose, the two most successful G^E-based semipredictive models (PSRK and LCVM) and the global phase diagram (klGPD)-based semi-predictive approach (GPDA) have been implemented and compared. Although G^E-based models require a significant amount of experimental data for evaluation of their parameters and prediction of the equilibrium, GPDA needs no more that 2−3 key experimental points. The superiority of GPDA, which considers the entire thermodynamic phase space, over the G^E-based models, which are based on the fit of VLE data, is clearly demonstrated. Although the G^E-based models fail to predict global phase behavior and to describe three-phase data accurately, GPDA yields exact predictions of the global phase behavior and accurate estimations of the composition and density of the vapor and the CO2-rich phases. In addition, it is accurate in describing the P−T projection of three-phase lines. All of the models considered are unable to predict the hydrocarbon-rich phase accurately. Presently, this problem cannot be solved without violating the predictive character of the model.

Vapor−liquid equilibrium data at 35 kPa have been determined for the ternary system 1,1,1,2,3,4,4,5,5,5-decafluoropentane (HFC-4310mee) + 2-methylfuran + oxolane, and for their constituent binaries HFC-4310mee + 2-methylfuran and 2-methylfuran + oxolane, in the temperature range 297 to 310 K. Vapor pressures of 2-methylfuran have also been measured in the range of boiling temperatures of the mixture. Depending on the concentration range, the ternary system exhibits positive to negative deviations from ideal behavior and no ternary azeotrope has been detected. The binary system HFC-4310mee (1) + 2-methylfuran (2) exhibits positive deviations form ideal behavior and a minimum temperature azeotrope at a composition rich in HFC-4310mee (x1 ≅ 0.561, T ≅ 297.55 K). The binary system 2-methylfuran (2) + oxolane (3) exhibits negative deviations form ideal behavior and a maximum temperature azeotrope at a composition rich in oxolane (x2 ≅ 0.310, T ≅ 309.95 K). The vapor−liquid equilibrium data of the binary mixtures were correlated with the Redlich−Kister model and were used to predict the equilibrium properties of the ternary mixture. In addition, a model-free approach that is applicable to ternary mixtures has been used to analyze the properties of the ternary mixture.

It is demonstrated that empirical temperature functionalities for the cohesive parameter in van der Waals-like equations can be responsible for prediction of nonphysical results such as fictitious critical points of pure compounds, that can result in prediction of unrealistic phase behavior in the entire thermodynamic phase space. Simple numerical tests for detecting this pitfall are proposed, and the roles played by the empirical and the theoretically based parts in semiempirical engineering equations are investigated. In particular, it is demonstrated that improvement of the accuracy with which equations of state approximate the hard sphere virial coefficients makes the theoretical part more self-sufficient for an accurate description of data. This significantly reduces the contribution of the corresponding empirical part and has a positive effect on the overall robustness and reliability of the model. In addition, an improved theoretical base contributes to the ability of the model so simultaneously and accurately predict both liquid and vapor densities.

Vapor−liquid equilibrium data at (26.68, 35, and 55) kPa over the whole concentration range and vapor−liquid equilibria at (23 and 45) kPa over a partial concentration range have been determined for the binary system 1,1,1,2,3,4,4,5,5,5-decafluoropentane (HFC-4310mee) + oxolane (THF), in the temperature range (294 to 322) K. Pure component vapor pressures of each constituent have also been measured in the range of boiling temperatures of the mixture. Depending on the concentration range, the system exhibits positive and negative deviations from ideal behavior. Two azeotropes, rich in oxolane and with opposite deviations, have been found both at (23, 26.68, and 35) kPa, while no azeotrope appears at (45 and 55) kPa. According to these results, polyazeotropic behavior ends in a tangent azeotrope as the pressure increases. The vapor−liquid equilibrium data of the solutions were correlated with the mole fraction by the Redlich−Kister equation.

Consistent vapor−liquid equilibria data at 94.00 kPa have been determined for the ternary system 1-hexene + ethyl 1,1-dimethylethyl ether + benzene and for its constituent binary 1-hexene + benzene, in the temperature range 334−351 K. According to the experimental results, the systems exhibit slight positive deviations from ideal behavior and no azeotrope is present. The VLE data have been correlated with the mole fraction using the Redlich−Kister, Wilson, NRTL, UNIQUAC, and Tamir relations. These models, in addition to UNIFAC, allow good prediction of the VLE properties of the ternary system from those of the pertinent binary systems.

Isobaric vapor−liquid equilibrium (VLE) data at 94.00 kPa have been determined for the ternary system 1-hexene + ethyl 1,1-dimethylethyl ether + benzene and for its constituent binary system 1-hexene + 2,2,4-trimethylpentane (isooctane), in the temperature range 335 to 360 K. According to the experimental results, the system 1-hexene + 2,2,4-trimethylpentane exhibits ideal behavior. The ternary system exhibits slight positive deviations from ideal behavior, and no azeotrope is present. The VLE data have been correlated with the mole fraction using the Redlich−Kister, Wilson, NRTL, UNIQUAC, and Wisniak−Tamir relations. These models, in addition to UNIFAC, allow good prediction of the VLE properties of the ternary system from those of the pertinent binary systems.

In the first part of this work, a model-free technique for treating ternary systems was presented. The procedure avoids the use of empirical activity coefficient models by generating numerically vapor-phase concentrations, activity coefficients, and excess Gibbs energy values directly from [T, P, x] data. Here we illustrate the use of the method as a complementary tool for modeling and assessing multicomponent vapor−liquid equilibrium data. Guidelines are given for fitting bubble surfaces and for treating azeotropic systems. In addition, reasonable approximations are outlined for handling ternary systems for which excess volume or enthalpy data are not available. Examples are presented for experimental isothermal and isobaric systems.

A new data treatment approach for ternary systems is presented. The method is a model-free technique based on Barker's equation and integration of the Gibbs−Duhem relation. It yields numerical information for the excess Gibbs energy and activity coefficients of a ternary system and its constituent binaries. Depending on the availability of data, the method is applicable to completely miscible isothermal or isobaric systems in vapor−liquid equilibrium, at low pressures, and is useful for selecting a G^E model able to correlate accurately the data. Physical constraints for the curvature of the bubble surface in the vicinity of multicomponent azeotropic concentrations are deduced from the displacement theory. The relation of these constraints with the model-free approach is discussed.

Vapor−liquid equilibrium at 94 kPa has been determined for the binary systems methyl acetate + 2,2‘-oxybis[propane], 2,2‘-oxybis[propane] + toluene, and methanol + 2-methyl-2-butanol. The system methyl acetate + 2,2‘-oxybis[propane] deviates positively from ideal behavior and presents a minimum boiling azeotrope at 327.29 K with 78 mol % methyl acetate. The system 2,2‘-oxybis[propane] + toluene exhibits slight positive deviations from ideal behavior. The system methanol + 2-methyl-2-butanol shows negative deviations from ideal behavior, and this experimental result is explained in terms of the competitive self- and cross-association of the constituent alcohols. The vapor−liquid equilibrium data of the measured systems were compared to predictions of the UNIFAC group contribution method and correlated by the Wohl, NRTL, Wilson, and UNIQUAC models. The boiling points of all the binary systems were correlated with mole fractions by the Wisniak−Tamir and Wisniak−Segura equations.

Consistent vapor−liquid equilibria data at 94 kPa have been determined for the ternary system ethyl 1,1-dimethylethyl ether + cyclohexane + 2,2,4-trimethylpentane and for its constituent binary cyclohexane + 2,2,4-trimethylpentane, in the temperature range 343 to 369 K. According to the experimental results, the systems exhibit slight positive deviations from ideal behavior and no azeotrope is present. The VLE data have been correlated with the mole fraction using the Redlich−Kister, Wilson, NRTL, UNIQUAC, and Wisniak−Tamir relations. These models, in addition to UNIFAC, allow good prediction of the VLE properties of the ternary system from those of the pertinent binary systems.

Consistent vapor−liquid equilibria (VLE) at 94.00 kPa has been determined for the ternary system ethyl 1,1-dimethylethyl ether + 2,2,4-trimethylpentane + methylcyclohexane and the two constituent binaries ethyl 1,1-dimethylethyl ether + methylcyclohexane and 2,2,4-trimethylpentane + methylcyclohexane in the temperature range from 343 to 371 K. In addition, vapor pressures have been measured for methylcyclohexane from 331 to 374 K. According to the experimental results, the systems exhibit slight positive deviations from ideal behavior and no azeotrope is present. The VLE data have been correlated with the composition using the Redlich−Kister, Wilson, NRTL, UNIQUAC, and Wisniak−Tamir relations. These models, in addition to UNIFAC, allow good prediction of the VLE properties of the ternary system from those of the pertinent binary systems.

New consistent vapor−liquid equilibrium data for the binary systems 3-methylpentane + ethyl 1,1-dimethylethyl ether, + diisopropyl ether, and + tetrahydrofuran are reported at 101.3 kPa. The measured systems, which deviate from ideal behavior, can be described as symmetric solutions, and only the system 3-methylpentane + tetrahydrofuran presents an azeotrope. The activity coefficients and boiling points of the solutions were correlated with composition by Wilson, UNIQUAC, NRTL, and Wisniak−Tamir equations.

Vapor−liquid equilibrium for the binary system methanol + methyl 1,1-dimethylethyl ether has been measured at 50, 78.4, and 94 kPa. The system presents a minimum boiling point azeotrope that is enriched in the ether when the pressure decreases. The activity coefficients and boiling points of the solutions were correlated with its composition by the Wohl, Wilson, UNIQUAC, NRTL, and Wisniak−Tamir equations.

Vapor-liquid equilibrium at 101.3 kPa has been determined for the ternary system 2-chlorobutane + 1-chlorobutane + cyclohexane and its binaries 2-chlorobutane + cyclohexane and 1-chlorobutane + cyclohexane. The binary system 1-chlorobutane + cyclohexane presents an azeotropic point at 76.86°C that contains 57.5% mol 1-chlorobutane. No ternary azeotrope is present. The data were correlated by the Redlich-Kister, Van Laar, Wilson and Wisniak-Tamir equations and the appropriate parameters are reported. The activity coefficients of the ternary system can be predicted from those of the pertinent binary systems.