Effect of nonvolatile solute on vapor–liquid equilibrium at fixed liquid composition

The influence of some nonvolatile solutes on boiling points of two azeotropic mixtures (1-propanol–water and methanol–tetrahydrofuran systems) was determined by means of isobaric vapor–liquid equilibrium experiments. A basic thermodynamic equation of nonvolatile solute effect on vapor–liquid equilibrium at fixed liquid composition was derived. Based on the theoretical analysis about the equation, two criterions of universal significance were obtained: (1) when a little nonvolatile solute dissolves in a binary liquid mixture with constant composition, if the vapor composition of less volatile component is increased the boiling point must be elevated at given pressure or the vapor pressure must be depressed at given temperature; (2) when a little nonvolatile solute dissolves in an azeotropic mixture, any kind of nonvolatile solute always causes the elevation of boiling point at given pressure or the depression of vapor pressure at given temperature irrespective of the variation of vapor composition. Verifying through the experiments of this paper and lot of the relevant experimental data in the literature, all of the experimental results were in agreement with both criterions without exception.     

Critical parameters of liquid–vapor equilibrium and its geometric interpretation

Expressions are derived for the Gibbs and free energies of a liquid–vapor system. The critical parameters of the liquid are determined, and the character of the relationship between them is found. The temperature dependence of the vaporization heat is found. The analytical expression of the empirical Tait rule is substantiated. General patterns of subcritical and critical equilibria were revealed. A geometric definition of a critical state is proposed, and the existence of two critical states is proven.     

Molecular dynamics simulation of the equilibrium liquid–vapor interphase with solidification

The equilibrium structure of the finite, interphase interfacial region that exists between a liquid film and a bulk vapor is resolved by molecular dynamics simulation. Argon systems are considered for a temperature range that extends below the melting point. Physically consistent procedures are developed to define the boundaries between the interphase and the liquid and vapor phases. The procedures involve counting of neighboring molecules and comparing the results with boundary criteria that permit the boundaries to be precisely established. Two-dimensional radial distribution functions at the liquid and vapor boundaries and within the interphase region demonstrate the physical consistency of the boundary criteria and the state of transition within the region. The method developed for interphase boundary definitions can be extended to nonequilibrium systems. Spatial profiles of macroscopic properties across the interphase region are presented. A number of interfacial thermodynamic properties and profile curve-fit parameters are tabulated, including evaporation/condensation coefficients determined from molecular flux statistics. The evaporation/condensation coefficients away from the melting point compare more favorably with transition state theory than those of previous simulations. Near the melting point, transition theory approximations are less valid and the present results differ from the theory. The effects of film substrate wetting on evaporation/condensation coefficients are also presented.     

Thermodynamics of the multicomponent vapor–liquid equilibrium under capillary pressure difference

We discuss the two-phase multicomponent equilibrium, provided that the phase pressures are different due to the action of capillary forces. We prove the two general properties of such an equilibrium, which have previously been known for a single-component case, however, to the best of our knowledge, not for the multicomponent mixtures. The importance is emphasized on the space of the intensive variables P, T and μⁱ, where the laws of capillary equilibrium have a simple geometrical interpretation. We formulate thermodynamic problems specific to such an equilibrium, and outline changes to be introduced to common algorithms of flash calculations in order to solve these problems. Sample calculations show large variation of the capillary properties of the mixture in the very neighborhood of the phase envelope and the restrictive role of the spinodal surface as a boundary for possible equilibrium states with different pressures.     

Evaluation of stochastic global optimization methods for modeling vapor–liquid equilibrium data

Parameter estimation for vapor–liquid equilibrium (VLE) data modeling plays an important role in design, optimization and control of separation units. This optimization problem is very challenging due to the high non-linearity of thermodynamic models. Recently, several stochastic optimization methods such as Differential Evolution with Tabu List (DETL) and Particle Swarm Optimization (PSO) have evolved as alternative and reliable strategies for solving global optimization problems including parameter estimation in thermodynamic models. However, these methods have not been applied and compared with respect to other stochastic strategies such as Simulated Annealing (SA), Differential Evolution (DE) and Genetic Algorithm (GA) in the context of parameter estimation for VLE data modeling. Therefore, in this study several stochastic optimization methods are applied to solve parameter estimation problems for VLE modeling using both the classical least squares and maximum likelihood approaches. Specifically, we have tested and compared the reliability and efficiency of SA, GA, DE, DETL and PSO for modeling several binary VLE data using local composition models. These methods were also tested on benchmark problems for global optimization. Our results show that the effectiveness of these stochastic methods varies significantly between the different tested problems and also depends on the stopping criterion especially for SA, GA and PSO. Overall, DE and DETL have better performance for solving the parameter estimation problems in VLE data modeling.     

Molecular thermodynamics of salt effect in vapor–liquid equilibrium of ethanol–water systems

Scaled particle theory was used to derive a general expression for the salt effect parameter, K, of isobaric vapor–liquid equilibrium for ethanol–water-1-1 type electrolytic systems, which appears in the Furter equation. This expression was essentially a sum of two terms: 1, the hard sphere interaction term calculated by Masterton–Lee's equation, 2, the soft sphere interaction term calculated by Y. Hu's molecular thermodynamical model, in which the diameters of nacked ions were replaced by that of solvated ions, the solvation coefficients (i.e., in the radio of the latter to the former) were taken to be adjustable parameters, their magnitude implies the ionic solvation rules. A correlation equation for the local dielectrical constant around central ions with liquid concentration was obtained by mapping out experimental points. The calculated salt effect parameters of 9 ethanol–water-1–1 type electrolytic systems were in good agreement with the literature values within the wide range of liquid concentration.     

Isobaric vapor–liquid equilibrium of systems containing triethyl orthoformate at 101.3 kPa

Isobaric vapor–liquid equilibrium data of ethanol(1)-triethyl orthoformate(2), benzene(1)-triethyl orthoformate(2) and ethanol(1)-benzene(2)-triethyl orthoformate(3) were measured at 101.3 kPa and under a wide range of temperatures (349–420 K), using the Rose–Williams still modified by the authors. The experimental data of binary systems were tested for thermodynamic consistency with the method of Fredenslund and coworkers and correlated satisfactorily with SRK equation and PR equation of state. The VLE data of ethanol(1)-benzene(2)-triethyl orthoformate(3) ternary system were tested with the method of McDermont–Ellis and were predicted with the parameters of SRK and PR equation of state obtained from binary systems.     

Correlation and prediction of salt effects on vapor–liquid equilibrium in alcohol–water–salt systems

A modification of the solvation model of Ohe is proposed for the calculation of vapor–liquid equilibria (VLE) in alcohol–water–salt systems. The modified method employs the Bromley equation to calculate the activity of water in salt solutions, and a one-parameter empirical expression to calculate the activity of the alcohol. The single parameter is obtained by fitting ternary alcohol–water–salt data. The method is simple to use and does not require data on the vapor-pressures of alcohol–salt mixtures that are seldom available in the literature. Experimental data for 17 salts in 36 alcohol–water–salt systems, covering a temperature range from 298 to 375 K, and salt concentrations up to about 8 m, were correlated using the new approach. In all, 69 data sets and 1045 data points were correlated satisfactorily. The method was also used to predict VLE in four ternary alcohol–alcohol–salt systems and one quaternary alcohol–alcohol–water–salt system with satisfactory results.     

Predicting vapor–liquid equilibria of fatty systems

In the present work, a group contribution method is proposed for the estimation of the vapor pressure of fatty compounds. For the major components involved in the vegetable oil industry, such as fatty acids, esters and alcohols, triacylglycerols (TAGs) and partial acylglycerols, the optimized parameters are reported. The method is shown to be accurate when it is used together with the UNIFAC model for estimating vapor–liquid equilibria (VLE) of binary and multicomponent fatty mixtures comprised in industrial processes such as stripping of hexane, deodorization and physical refining. The results achieved show that the group contribution approach is a valuable tool for the design of distillation and stripping units since it permits to take into account all the complexity of the mixtures involved. This is particularly important for the evaluation of the loss of distillative neutral oil that occurs during the processing of edible oils.The combination of the vapor pressure model suggested in the present work with the UNIFAC equation gives results similar to those already reported in the literature for fatty acid mixtures and oil–hexane mixtures. However, it is a better tool for predicting vapor–liquid equilibria of a large range of fatty systems, also involving unsaturated compounds, fatty esters and acylglycerols, not contemplated by other methodologies. The approach suggested in this work generates more realistic results concerning vapor–liquid equilibria of systems encountered in the edible oil industry.     

Modification of the Furter equation and correlation of the vapor–liquid equilibrium for mixed-solvent electrolyte systems

Isobaric vapor–liquid equilibrium values at 1 atm pressure were measured for the systems 1-propanol–water–potassium acetate and 2-propanol–water–potassium acetate under fixed salt mole fractions using a modified Othmer recirculation still. A modified Furter equation, ln(α_s/α)=k₁z+k₂z², was proposed for correlating the effect of dissolved salts on vapor–liquid equilibrium (VLE). The modified equation contains two parameters that are applicable to the entire salt/solvent composition range. Correlation of VLE for 15 mixed-solvent electrolyte systems was made by means of the proposed modified equation with better results than those obtained from the original equation.     

Molecular simulation of vapor–liquid equilibria of toxic gases

In this paper, we derived the potential parameters for three toxic gases, hydrogen sulfide, phosgene and nitrous oxide, modeled by the effective Stockmayer potential model proposed by Gao et al. [Fluid Phase Equilib. 137 (1997) 87]. The vapor–liquid equilibria (VLE) of these substances have been extensively investigated over a wide range of temperatures by the Gibbs ensemble Monte Carlo (GEMC) technique. The simulated saturated densities and pressures are in good agreement with experimental data. The critical properties obtained by regression of the simulated data also agree well with the experimental values. The present work demonstrates that the effective Stockmayer potential can describe well the toxic gases concerned.     

Liquid–liquid phase equilibrium in ternary immiscible Al–Bi–Sn melts

In this paper, the liquid-phase separation of ternary immiscible Al–Bi–Sn melts was studied with resistivity and thermal analysis methods at different temperatures. The resistivity–temperature curves appear anomalous and abrupt change as rising temperature, corresponding to the distinctive and low peak of melting process in the differential scanning calorimetry (DSC) curves, indicative of the occurrence of the liquid-phase separation. The anomalous behaviour of the resistivity temperature dependence is attributable to concentration–concentration fluctuations. The microheterogeneity–microhomogeneity transformation causes large fluctuations in concentration, which make the randomness and chaos of the atoms larger, leading to the greater impediment to electron movement and the sharp rise of resistivity. The addition of tin to the Al–Bi immiscible alloys decreases the monotectic reaction. It is concluded that concentration–concentration fluctuations are responsible for the anomalous behaviour of resistivity and DSC methods.     

A corresponding states treatment of the liquid–vapor saturation line

In this work we analyze correlations for the maxima of products of some liquid–vapor saturation properties. These points define new characteristic properties of each fluid that are shown to exhibit linear correlations with the critical properties. We also demonstrate that some of these properties are well correlated with the acentric factor. An application is made to predict the properties of two new low global warming potential (GWP) refrigerants.     

Liquid–liquid equilibrium calculations for methanol–gasoline blends using continuous thermodynamics

This work presents the application of continuous thermodynamics to investigate the limited miscibility of methanol–gasoline blends. To predict the liquid–liquid equilibrium of these systems, the Gaussian distribution function was used to represent the composition of paraffins in the gasoline. The naphthenes and aromatics were represented by model compounds. A model has been developed using three different continuous versions of the UNIFAC model. Methanol is an associating component, and association affects phase equilibria. Therefore, the CONTAS (continuous thermodynamics of associating systems) model based on the Flory–Huggins equation, for multicomponent methanol–gasoline blends has also been investigated. The predicted results including the cloud point curve, shadow curve and phase separation data have been compared with experimental data and good agreement was found for the two UNIFAC and CONTAS models.     

Thermodynamic study of the vapor–liquid equilibrium (VLE) data of the mixture formed by diethylenimide oxide with benzene

The thermodynamic evaluation of the experimental vapor?Cliquid equilibrium (VLE) data obtained at 760?mmHg in a recirculatory still, is presented for the binary system formed by diethylenimide oxide with benzene. The experimental VLE data were checked for thermodynamic consistency and reduced to the binary parameters calculated from three activity coefficients models.     

The influence of the temperature on the liquid–liquid equilibrium of the ternary system 1-pentanol–ethanol–water

Liquid–liquid equilibrium data for the ternary system 1-pentanol–ethanol–water have been determined experimentally at 25, 50, 85 and 95°C. These results have been correlated simultaneously by the uniquac method obtaining two sets of interaction parameters: one of them independent of the temperature and the other with a linear dependence. Both sets of parameters fit the experimental results well.     

Soft-SAFT modeling of vapor–liquid equilibria of nitriles and their mixtures

Nitriles are strong polar compounds showing a highly non-ideal behavior, which makes them challenging systems from a modeling point of view; in spite of this, accurate predictions for the vapor–liquid equilibria of these systems are needed, as some of them, like acetonitrile (CH₃CN) and propionitrile (C₂H₅CN), play an important role as organic solvents in several industrial processes. This work deals with the calculation of the vapor–liquid equilibria (VLE) of nitriles and their mixtures by using the crossover soft-SAFT Equation of State (EoS). Both polar and associating interactions are taken into account in a single association term in the crossover soft-SAFT equation, while the crossover term allows for accurate calculations both far from and close to the critical point. Molecular parameters for acetonitrile, propionitrile and n-butyronitrile (C₃H₇CN) are regressed from experimental data. Their transferability is tested by the calculation of the VLE of heavier linear nitriles, namely, valeronitrile (C₄H₉CN) and hexanonitrile (C₅H₁₁CN), not included in the fitting procedure. Crossover soft-SAFT results are in excellent agreement with experimental data for the whole range of thermodynamic conditions investigated, proving the robustness of the approach. Parameters transferability has also been used to describe the isomers n-butyronitrile and i-butyronitrile. Finally, the nitriles soft-SAFT model is further tested in VLE calculation of mixtures with benzene, carbon tetrachloride and carbon dioxide, which proved to be satisfactory as well.     

Isobaric vapor–liquid equilibria of three aromatic hydrocarbon-tetraethylene glycol binary systems

Isobaric vapor–liquid equilibrium data have been determined at 101.33 kPa for the binary mixtures of benzene-tetraethylene glycol (TeEG), toluene-TeEG and o-xylene-TeEG. The vapor-phase fugacity coefficients were calculated from the virial equation. The thermodynamic consistency of the data has been tested via Herington analysis. The binary parameters for four activity coefficient models (van Laar, Wilson, NRTL and UNIQUAC) have been fitted with the experimental data. A comparison of model performances has been made by using the criterion of root mean square deviations in boiling point and vapor-phase composition.