Equations for describing liquid-vapor phase equilibria in binary mixtures

Three forms of equations for describing experimental data on liquid and vapor pressures, depending on temperature and composition at phase equilibria in binary mixtures, are proposed and evaluated. It is determined that the form of equation depends on the relationship between the temperature of a mixture and the critical temperatures of the components of the mixture. Exact data on the phase equilibria in nitrogenoxygen, nitrogen-argon, and oxygen-argon mixtures [1] are approximated to assess the effectiveness of the equations’ forms. It is found that the equations also allow us to determine the phase composition at a given temperature and pressure and temperatures of phases at a given pressure and composition.     

Molecular simulation of the high-pressure phase equilibria of binary atomic fluid mixtures using the exponential-6 intermolecular potential

Molecular simulation results using the exponential-6 intermolecular potential are reported for the phase behaviour of the atomic binary mixtures of neon+xenon, helium+neon, helium+argon and helium+xenon. These binary mixtures exhibit both vapour–liquid and liquid–liquid phase equilibria up to very high pressures. Comparison with experiment indicates good overall agreement. The results indicate that the exponential-6 intermolecular potential is a useful generic potential for molecular simulation.     

Solid-liquid phase equilibria of binary salt hydrate mixtures involving ammonium alum

Summary The solid-liquid phase diagrams of binary mixtures of ammonium alum with ammonium iron(III) alum, with aluminum nitrate nonahydrate and with ammonium nitrate and of aluminum sulfate hexadecahydrate with aluminum nitrate nonahydrate are presented. The alum rich branches of the former three-phase diagrams were fitted by the Ott equation. The specific enthalpy of fusion/freezing of some compositions of the former three mixtures was determined by differential drop calorimetry.     

Isothermal vapor-liquid equilibria for binary and ternary mixtures formed by 1-butanol,acetonitrile and benzene

Isothermal vapor-liquid equilibrium data are presented for the binary acetonitrile-1-butanol and ternary 1-butanol-acetonitrile-benzene systems at 60 °C. The experimental results are well correlated with the UNIQUAC associated-solution model.     

Influence of bond flexibility on the vapor-liquid phase equilibria of water

The authors performed Gibbs ensemble simulations on the vapor-liquid equilibrium of water to investigate the influence of incorporating intramolecular degrees of freedom in the simple point charge (SPC) water model. Results for vapor pressures, saturation densities, heats of vaporization, and the critical point for two different flexible models are compared with data for the corresponding rigid SPC and SPC/E models. They found that the introduction of internal vibrations, and also their parametrization, has an observable effect on the prediction of the vapor-liquid coexistence curve. The flexible SPC/Fw model, although optimized to describe bulk diffusion and dielectric constants at ambient conditions, gives the best prediction of saturation densities and the critical point of the examined models.     

On the fluid phase behaviour of fluid binary mixtures using the Yukawa fluid molecular model

By expanding Ginoza’s mean spherical approximation (MSA) results in an inverse-temperature expansion, Henderson et al. obtained explicit results for the thermodynamic functions of a pure Yukawa fluid. We have recently published explicit results for the coefficients in an inverse-temperature expansion of the thermodynamic functions for the MSA for mixtures of Yukawa fluids. Attention is drawn to the fact that the MSA in the Ginoza formulation, does not always yield a convergent solution. The expansion used in this paper will always yield a result. In this work we present our investigations of the fluid phase diagram of Yukawa binary mixtures by considering an expansion of the MSA Helmholtz free energy up to the fifth order of the inverse-temperature expansion. The calculated fluid phase diagrams for Yukawa binary mixtures are similar to those of real mixtures.     

Liquid-liquid-vapor phase equilibria behavior of certain binary carbon dioxide + n-alkylbenzene mixtures

The liquid-liquid-vapor loci for the binary mixtures CO₂ + n-hexylbenzene, n-heptylbenzene, and n-octylbenzene were experimentally studied. The compositions and molar volumes of the liquid phases are reported along with the pressure and temperature. For these three alkylbenzenes, the nature of the liquid-liquid-vapor loci experiences a transition, with the CO₂ + n-heptylbenzene mixture exhibiting two separate liquid-liquid-vapor branches.     

Isothermal measurements of vapor-liquid equilibria for three n-alkane-chloroalkane mixtures

Results of isothermal vapor-liquid equilibrium (VLE) measurements for 1-chlorobutane with n-hexane and n-heptane at three temperatures and for 1,2-dichloroethane with n-heptane at two temperatures are reported.New constants of the Antoine vapor pressure equation for 1,2-dichloroethane are presented. The consistency of the new vapor-pressure data with published experimental data of heat of vaporization is checked.The VLE data are used for the determination of group interaction parameters of UNIFAC and of the quasichemical group surface interaction model (QUAGSIM).     

Effect of deuterium substitution on the surface interactions in binary polymer mixtures

We have examined the effect of deuterium labeling on surface interactions in mixtures of random olefinic copolymers [C₄H₈]_1−x[C₂H₃(C₂H₅)]_x. Based on surface segregation data we have determined a surface energy difference χ_s between pure blend constituents. In each binary mixture components have different fractions x₁, x₂ of the group C₂H₃(C₂H₅), and one component is labeled by deuterium (dx) while the other is hydrogenous (hx). The mixtures are grouped in four pairs of structurally identical blends with swapped labeled constituent (dx₁/hx₂, hx₁/dx₂). For each pair the surface energy parameter χ_s increases when the component with higher fraction x is deuterated, i.e., χ_s(dx₁/hx₂) > χ_s(hx₁/dx₂) for x₁ > x₂. A similar pattern has been found previously for the bulk interaction parameter χ. This is explained by the solubility parameter formalism aided by the lattice theory relating the surface excess to missing-neighbor effect. χ_s has also an additional contribution, insensitive to deuterium swapping effect, and related to entropically driven surface enrichment in a more stiff blend component with a lower fraction x. Both enthalpic and entropic contributions to χ_s seem to depend on the extent of chemical mismatch between blend components. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 2691–2702, 1998     

Adsorption equilibria of binary gas mixtures on graphitized carbon black

Adsorption equilibria for binary gas mixtures (methane-carbon dioxide, methane-ethane, and carbon dioxide-ethane) on the graphitized carbon black STH-2 were measured by the open flow method at 293.2 K. The experimental pressure range was (0 to 1.6) MPa. The extended Langmuir (EL) model and the ideal adsorption solution theory (IAST) have been adopted to predict the equilibria of binary gas mixtures. The results indicate that gas mixtures adsorbed on the homogeneous surface of STH-2 exhibit the nonideal behavior, which is mainly induced by adsorbate-adsorbate interactions. The real adsorption solution theory (RAST) has been used to analyze the property of the adsorbed mixtures. The activity coefficients have been correlated with the Wilson equation. The investigation demonstrates that the nonideality of adsorbed phase is completely dissimilar with the bulk liquid phase. The adsorption of the heavier component would benefit the adsorption of the lighter component.     

Analytical applications of liquid-liquid phase equilibria: analysis of binary mixtures of chemically similar components

A new, simple and rapid method based on the principle of liquid-liquid phase equilibria has been developed for the analysis of binary mixtures of chemically similar organic compounds. The method does not require elaborate instrumentation and can be used to analyse mixtures of members of homologous series. The application of the method has been illustrated by analysing binary mixtures of n-hexane and n-octane; the maximum uncertainty in this analysis is ~2%.     

Phase equilibria in binary mixtures with monoethyl succinate

Monoethyl succinate was produced by partial esterification of succinic anhydride with ethanol using Amberlyst 15^® as catalyst. After separation and purification, the purity of monoethyl succinate was confirmed by nuclear magnetic resonance (NMR). Vapor pressure of monoethyl succinate was measured and correlated with Antoine equation. Vapor-liquid equilibria at constant temperature were measured for the binary systems ethyl acetate + monoethyl succinate, acetic acid + monoethyl succinate, and water + monoethyl succinate at 323.15 K, and ethanol + monoethyl succinate at 313.15 K. Binary parameters for the NRTL equations were obtained by fitting experimental data using the regression tool in ASPEN Plus^® using the Hayden-O’Connell method for vapor phase fugacities. The model agrees reasonably well with the experimental data.     

Solid and liquid phase equilibria and solid-hydrate formation in binary mixtures of water with amines

Solid and liquid phase diagrams have been constructed for {water+triethylamine,or+N,N-dimethylformamide(DMF) or+N,N-dimethlacetamide (DMA)} Solid-hydrates form with the empirical formulae N(C2H5)3 3H2O,DMF 3H2O,DMF 2H2O,DMA 3H2O and (DMA)2 3H2O.All are congruently melting except the first which melts incongruently.The solid-hydrate formation is attributed to hydrogen bond.The results are compared with the references     

An extension of cubic equations of state to vapor-liquid equilibria in polymer-solvent mixtures

Cubic equations of state (EOS) are extended to describe polymer-solvent vapor-liquid equilibria (VLE). The solvents are described the conventional way using critical parameters. To describe the pure polymers, only the weight-average molecular weight is necessary, though number-average molecular weight, polydispersity and melt density can be incorporated if desired. To extend the model to mixtures, a mixing rule that combines EOS with excess energy models is used. In this formulation, the excess Gibbs energy term is considered in two parts: the classical Flory term for the entropic contributions and a residual term that takes care of specific interactions between the solvent and the polymer. For athermal mixtures that exhibit no such interactions, the residual term drops out and the model becomes completely predictive. Otherwise, for residual contributions, depending upon the complexity of specific molecular interactions anticipated in the mixture, either a single parameter Flory expression or a two-parameter NRTL equation can be used. We conclude that the simple cubic EOS approach presented here is easy to use, yet competes successfully with more sophisticated EOS models developed particularly for polymer solutions. Moreover, it offers more flexibility if one or more parameters are to be tuned to the process data.     

Global fluid phase equilibria and critical phenomena of selected mixtures using the crossover soft-SAFT equation

We present here the extension of the crossover soft-statistical associating fluid theory (soft-SAFT) equation of state to mixtures, as well as some illustrative applications of the methodology to mixtures of particular scientific and technological interest. The procedure is based on White's work (White, J. A. Fluid Phase Equilib. 1992, 75, 53) from the renormalization group theory, as for the pure fluids, with the isomorphism assumption applied to the mixtures. The equation is applied to three groups of mixtures: selected mixtures of n-alkanes, the CO2/n-alkane homologous series, and the CO2/1-alkanol homologous series. The crossover equation is first applied to the pure components of the mixtures, CO2 and the 1-alkanol family, while an available correlation is used for the molecular parameters of the n-alkane series (Llovell et al. J. Chem. Phys 2004, 121, 10715). A set of transferable molecular parameters is provided for the 1-alkanols series; these are accurate for the whole range of thermodynamic conditions. The crossover soft-SAFT equation is able to accurately describe these compounds near to and far from the critical point. The theory is then used to represent the phase behavior and the critical phenomena of the selected mixtures. We use binary interaction parameters xi and eta for dissimilar mixtures. These parameters are fitted at some particular conditions (one subcritical temperature or binary critical data) and used to predict the behavior of the mixture at different conditions (other subcritical conditions and/or critical conditions). The equation is able to capture the continuous change in the critical behavior of the CO2/n-alkane and the CO2/1-alkanol homologous series as the chain length of the second compound increases. Excellent agreement with experimental data is obtained, even in the most nonideal cases. The new equation is proved to be a powerful tool to study the global phase behavior of complex systems, as well as other thermodynamic properties of very challenging mixtures.     

Phase equilibria in binary mixtures of ethane and hexadecane

This paper reports experimental results of a study of the phase behaviour of binary mixtures of ethane + hexadecane. In the near-critical region of ethane liquid + vapour and solid hexadecane + liquid two-phase boundaries have been measured. Also the three-phase equilibrium solid hexadecane + liquid + vapour has been determined experimentally. The experimental data cover the complete mole fraction range. Pressures up to 18 MPa were applied and the investigation was performed in a temperature region from about 260 K up to 450 K.     

Phase equilibria in binary mixtures of propane + acenaphthene

In the near-critical region of propane, phase equilibria of binary mixtures of propane + acenaphthene have been investigated experimentally. Apart from the three-phase equilibrium solid acenaphthene + liquid + vapour, two-phase boundaries liquid + vapour and solid acenaphthene + liquid have been investigated over the entire mole fraction range. The measurements were performed in the temperature region 350–420 K with pressures up to 10 MPa.     

Phase equilibria in chemical reactive fluid mixtures

Downstream processing is a major part of nearly all processes in the chemical industries. Most separation processes in the chemical (and related) industries for fluid mixtures are based on phase equilibrium phenomena. The majority of separation processes can be modelled assuming that chemical reactions are of no (or very minor) importance, i.e., assuming that the overall speciation remains unchanged during a separation process. However, there are also a large number of industrially important processes where the thermodynamic properties are influenced by chemical reactions. The phase equilibrium of chemical reactive mixtures has been a major research area of the author’s group over nearly 40 years. In this contribution, three examples from that research are discussed. The first example deals with the vapour phase dimerisation of carboxylic acids and its consequences on phase equilibrium phenomena and phase equilibrium predictions. The second example deals with the solubility of sour gases (e.g., carbon dioxide and sulfur dioxide) in aqueous solutions of ammonia. That topic has been of interest for many years, e.g., in relation with the gasification and liquefaction of coal and, more recently, with the removal of carbon dioxide from flue gas in the “chilled ammonia process”. The third example deals with phase equilibrium phenomena in aqueous solutions of polyelectrolytes. It deals with the phenomenon of “counter ion condensation” and methods to model the Gibbs free energy of such solutions.