# Fluid Phase Equilibria (v.259, #1)

VII Iberoamerican conference on phase equilibria and fluid properties for process design by Luis A. Galicia-Luna; Dominique Richon; Theo W. de Loos

*(1-2)*.**Keywords:**Thermodynamics; Phase Equilibria; Process design; Simulation;

Nanoporous carbon membranes for separation of nitrogen and oxygen: Insight from molecular simulations by Gaurav Arora; Stanley I. Sandler

*(3-8)*. Here we summarize some of our recent work on using molecular simulations to understand the key mechanism that result in large differences in the reported permeation rates of O

_{2}and N_{2}in nanoporous carbon membranes. Two different representation of the amorphous nanoporous membrane structure are used; the hypothetical C_{168}Schwarzite and a single wall carbon nanotube with a constriction. By comparing the results obtained from empirical planar graphite potential and an ab initio-based potential, the effect of carbon curvature and the presence of non-hexagonal carbon rings in C_{168}Schwarzite is also investigated. It is found using either force field, that the energetic effect alone cannot explain the experimental observations. However, simulations performed using carbon nanotube with a constriction show that the size or entropic effect can be dominant. In particular, it is shown that an appropriate size constriction can result in large transport resistance to nitrogen while letting oxygen to pass through at a much higher rate, even though these gases have very similar molecular sizes and interaction energetics.**Keywords:**Nanoporous carbon sieves; Membrane; Adsorption; Diffusion; Molecular dynamics; Monte Carlo; Nanotubes; Nitrogen; Oxygen; Ideal selectivity;

Effective intermolecular potentials in theoretical thermodynamics of pure substances and solutions by Fernando del Río; Orlando Guzmán; J. Eloy Ramos; Benjamín Ibarra-Tandi

*(9-22)*. Effective potentials have been used extensively as model molecular interactions to account for the thermodynamic properties of pure fluids and solutions. Here we develop the concept of effective potential and apply it to a variety of properties in the dilute- and dense-fluid states. We show how a simple kind of potential, named Approximate Non-Conformal (ANC), can be used effectively to calculate accurately a variety of thermodynamic properties of fluid substances. We present evidence for properties in the gaseous state (second and third virial coefficients), for the liquid–vapour coexistence and critical properties (

*T*_{c},*V*_{c}and*P*_{c}). Most gaseous-phase properties are obtained within estimated experimental errors. The molecular features whose effects have been incorporated into the ANC effective potentials are overlap, dispersion, electrostatic (dipolar and quadrupolar) and many-body interactions, and steric features such as elongation Applications to a selection of non-polar substances noble gas molecules, diatomics and light alkanes highlight the main features of the theory. New results include Gibbs ensemble Monte Carlo simulations of ANC fluids, an effective potential to account for many-body forces, prediction of critical temperatures and volumes, and we also prove a general relation satisfied by the critical temperatures of many substances.**Keywords:**Effective interactions; Real fluids; Critical properties; Many-body forces; Molecular models;

High-pressure vapor–liquid equilibria for CO

_{2}+ alkanol systems and densities of*n*-dodecane and*n*-tridecane by Octavio Elizalde-Solis; Luis A. Galicia-Luna; Luis E. Camacho-Camacho*(23-32)*. An apparatus based on the static-analytic method was used to measure the vapor–liquid equilibria (VLE) for CO

_{2}+ alkanol systems. Equilibrium measurements for the CO_{2}+ 1-propanol system were performed from 344 to 426 K. For the case of the CO_{2}+ 2-propanol system, measurements were made from 334 to 443 K, and for the CO_{2}+ 1-butanol were obtained from 354 to 430 K. VLE data were correlated with the Peng–Robinson equation of state using the classical and the Wong–Sandler mixing rules. Moreover, compressed liquid densities for the*n*-dodecane and*n*-tridecane were obtained via a vibrating tube densitometer at temperatures from 313 to 363 K and pressures up to 25 MPa. The Starling and Han (BWRS), and The five-parameter Modified Toscani-Swarcz (MTS) equations were used to correlate them. The experimental density data were compared with those from literature, and with the calculated values obtained from available equations for these*n*-alkanes.**Keywords:**Vapor–liquid equilibria; Density; Alkanes; Alkanols; Carbon dioxide;

Volumetric properties of the boldine + alcohol mixtures at atmospheric pressure from 283.15 to 333.15 K by Christophe Coquelet; Alain Valtz; Dominique Richon; Juan C. de la Fuente

*(33-38)*. Densities of boldine + alcohol binary mixtures were measured over the whole accessible range of boldine compositions at temperatures from 283.15 to 333.15 K using an Anton-Paar digital vibrating glass tube densimeter. The binary systems studied include, as a solvent, seven normal alcohols from

*n*-C_{1}to*n*-C_{6},*n*-C_{8}, and isopropanol. The density of these systems has been found an increasing function of the boldine composition. A new methodology based on density data of solutions of solid solutes with normal alcohols is described in order to determine solid molar volume of pure solutes. This methodology was validated with pure solid naphthalene molar volumes data at 298.15 K, with an average uncertainty of 6%.**Keywords:**Binary system; Boldine;

*n*-Alcohols; Isopropanol; Density; Partial molar volume; Estimation of solid density; New method;

Thermodynamics of mixtures containing amines by M. Fernández Regúlez; I. Mozo; J.A. González; I. García de la Fuente; J.C. Cobos

*(39-44)*. The binodal curves of the liquid–liquid equilibria (LLE) for systems of

*o*-toluidine with heptane, octane, nonane, decane or dodecane have been determined visually. All the curves show an upper critical solution temperature (UCST), which increases with the chain length of the alkane. The bimodal curves have a rather flat horizontal top and their symmetry depends on the chain length of the alkane. For the studied systems, interaction parameters in the framework of the DISQUAC model are reported. DISQUAC represents the coordinates of the critical points in the correct range of temperature and composition.**Keywords:**

*o*-Toluidine; Alkanes; LLE; Upper critical solution temperatures; DISQUAC;

New isothermal vapor–liquid equilibria for the CO

_{2}+*n*-nonane, and CO_{2}+*n*-undecane systems by Luis E. Camacho-Camacho; Luis A. Galicia-Luna; Octavio Elizalde-Solis; Zenaido Martínez-Ramírez*(45-50)*. Experimental vapor–liquid equilibria (VLE) for the CO

_{2}+*n*-nonane and CO_{2}+*n*-undecane systems were obtained by using a 100-cm^{3}high-pressure titanium cell up to 20 MPa at four temperatures (315, 344, 373, and 418 K). The apparatus is based on the static-analytic method; which allows fast determination of the coexistence curve. For the CO_{2}+*n*-nonane system, good agreement was found between the experimental data and those reported in literature. No literature data were available for the CO_{2}+*n*-undecane system at high temperature and pressure. Experimental data were correlated with the Peng–Robinson equation of state using the classical and the Wong–Sandler mixing rules.**Keywords:**Vapor–liquid equilibria; Equation of state; Static-analytic method;

Study of the behaviour of the azeotropic mixture ethanol–water with imidazolium-based ionic liquids by Noelia Calvar; Begoña González; Elena Gómez; A. Domínguez

*(51-56)*. In this work, experimental data of isobaric vapour–liquid equilibria for the ternary system ethanol + water + 1-hexyl-3-methylimidazolium chloride ([C

_{6}mim][Cl]) and for the corresponding binary systems containing the ionic liquid (ethanol + [C_{6}mim][Cl], water + [C_{6}mim][Cl]) were carried out at 101.300 kPa. VLE experimental data of binary and ternary systems were correlated using the NRTL equation. In a previous work [N. Calvar, B. González, E. Gómez, A. Domínguez, J. Chem. Eng. Data 51 (2006) 2178–2181], the VLE of the ternary system ethanol + water + [C_{4}mim][Cl] was determined and correlated, so we can study the influence of different ionic liquids in the behaviour of the azeotropic mixture ethanol–water.**Keywords:**Ethanol; Water; Ionic liquid; Binary; NRTL;

Isobaric vapor–liquid equilibria of 1,1-dimethylethoxy-butane + methanol or ethanol + water at 101.32 kPa by Alberto Arce; Alberto Arce; José Manuel Martínez-Ageitos; Ana Soto

*(57-65)*. Isobaric vapor–liquid equilibrium data (VLE) at 101.325 kPa have been determined in the miscible region for 1,1-dimethylethoxy-butane (BTBE) + methanol + water and 1,1-dimethylethoxy-butane (BTBE) + ethanol + water ternary systems, and for their constituent binary systems, methanol + BTBE and ethanol + BTBE. Both binary systems show an azeotrope at the minimum boiling point. In the ternary system BTBE + methanol + water no azeotrope has been found, however, the system BTBE + ethanol + water might form a ternary azeotrope near the top of the binodal. Thermodynamically consistent VLE data have been satisfactorily correlated using the UNIQUAC, NRTL and Wilson equations for the activity coefficient of the liquid phase. Temperature and vapor phase compositions have been compared with those calculated by the group-contribution methods of prediction ASOG, and the original and modified UNIFAC. Predicted values are not in good agreement with experimental values.

**Keywords:**VLE; BTBE; Alcohols; Water;

Isobaric vapor–liquid and vapor–liquid–liquid equilibrium data for the water–ethanol–hexane system by V. Gomis; A. Font; R. Pedraza; M.D. Saquete

*(66-70)*. Isobaric vapor–liquid and vapor–liquid–liquid equilibria were measured for the water–ethanol–hexane system at normal atmospheric pressure. The apparatus used for the determination of vapor–liquid–liquid equilibrium data was an all-glass dynamic recirculating still with an ultrasonic homogenizer coupled to the boiling flask.The experimental data demonstrated the existence of a ternary heterogeneous azeotrope at 329.2 K with a composition of 0.105, 0.236 and 0.658 mol fraction of water, ethanol and hexane, respectively. The experimental vapor–liquid and vapor–liquid–liquid equilibria data were found to be thermodynamically consistent. The correlation of these data was carried out using NRTL and UNIQUAC models and predicted with UNIFAC.The equilibrium data of the system were compared with other hydrocarbon systems previously analyzed and commonly used as entrainers in the dehydration of the ethanol by azeotropic distillation such as benzene and cyclohexane.

**Keywords:**Vapor–liquid equilibria; Vapor–liquid–liquid equilibria; Ethanol; Hexane;

Quinary liquid–liquid equilibria for mixtures of nonane + undecane + two pairs of aromatics (benzene/toluene/

*m*-xylene) + sulfolane at 298.15 and 313.15 K by Rílvia S. Santiago; Martín Aznar*(71-76)*. In this work, liquid–liquid equilibrium data were measured for three quinary mixtures (nonane + undecane + benzene + toluene + sulfolane), (nonane + undecane + benzene +

*m*-xylene + sulfolane) and (nonane + undecane + toluene +*m*-xylene + sulfolane) at 298.15 and 313.15 K and ambient pressure. The experimental LLE data were determined by using a jacketed glass cell with temperature controlled. The quantitative analysis was performed by using a Varian gas chromatograph equipped with a flame ionization detector and a SPB™-1 column. The experimental quinary liquid–liquid equilibrium data have been satisfactorily correlated by using NRTL and UNIFAC-LLE models. The calculated values based on the NRTL model were found to be in a better agreement with the experiment than those based on the UNIFAC-LLE model.**Keywords:**Quinary mixtures; Liquid–liquid equilibria; Sulfolane; Activity coefficient models;

Bubble-point measurements for the system CO

_{2}+ aqueous ethanol solutions of boldo leaf antioxidant components (boldine and catechin) at high pressures by Juan C. de la Fuente; Gonzalo Núñez; José M. del Valle*(77-82)*. The bubble-points pressures of solute(s) + ethanol + water + CO

_{2}mixtures were determined visually using a synthetic method in an experimental apparatus that included a variable-volume equilibrium cell. Tested solutes included boldo leaf tincture, a boldine + catechin mixture, pure boldine, and pure catechin. Uncertainties in bubble-point pressures were estimated to be <5%, based on comparisons with literature values and replicate measurements. The largest effect we observed was an average increase of 205% in the bubble-point pressure when decreasing the ethanol-to-water ratio from 63:37 to 37:63 (w/w). The bubble-point pressure increased 11% when increasing the temperature from 313 to 343 K, and decreased 8.2% when increasing the concentration of solids from 400 to 1500 ppm. The bubble-point pressure was higher for boldo leaf tincture than for a boldine + catechin mixture having the same boldine-to-catechin weight ratio, but this was partially due to a lower content of solids in the tincture. On the other hand, bubble-point pressures of the boldine + catechin mixture were marginally (0.33%) higher than the weighed average of the bubble-point pressures for pure boldine and pure catechin.**Keywords:**Antisolvent precipitation; Aqueous ethanol extract; Boldine; Boldo leaf antioxidants; Bubble-point pressure; Catechin; Supercritical CO

_{2};

Liquid–liquid equilibrium of ternary systems containing nicotine by Raquel M. Maduro; Martín Aznar

*(83-88)*. Liquid–liquid equilibrium data for the ternary systems nicotine + water + cyclohexane and nicotine + water + 1-butanol were measured at 298.15, 303.15 and 313.15 K. The results show that cyclohexane is better than 1-butanol as a solvent for nicotine extraction. The experimental data were correlated through the well-known NRTL and UNIQUAC models for the activity coefficient, with estimation of new interaction energy parameters, using the simplex minimization method and a composition-based objective function. The results, analyzed in terms of root mean square deviations between experimental and calculated compositions, were considered satisfactory, with NRTL yielding a better representation of the equilibrium data for the studied systems.

**Keywords:**Liquid–liquid equilibrium; Experimental; Nicotine; Modeling; NRTL; UNIQUAC;

Modeling high-pressure densities at wide temperature range with volume scaling: Cyclohexane +

*n*-hexadecane mixtures by Josinira A. Amorim; Osvaldo Chiavone-Filho; Márcio L.L. Paredes; Krishnaswamy Rajagopal*(89-98)*. High-pressure density data for cyclohexane +

*n*-hexadecane mixtures at a wide temperature range was modeled with several classical equations of state (EOS) and correlative models. A modification for softening the co-volume and another for a volume scaling of the Peng–Robinson EOS (VS-PR) were proposed. The VS-PR model is able to correlate the pure component experimental data employing only five adjustable parameters, with root-mean-square deviation (RMSD) between calculated and experimental densities essentially within the experimental error. This result is superior to widely used approaches, i.e., a six parameter Tait model and six parameter volume translations (temperature and pressure dependent) for Peng–Robinson and Patel–Teja EOS. The VS-PR model also represents well the isobaric thermal expansion and the isothermal compressibility coefficients of the pure cyclohexane, a small naphthenic substance as well as a long chain*n*-alkane hydrocarbon,*n*-hexadecane. When modeling the mixture data, the use of VS-PR model of pure components along with the Redlich–Kister expansion, truncated at the first term, the density was correlated within a RMSD only 60% greater than the experimental error. The proposed model is able to accurately represent all the tested mixture data with a relatively small number of parameters.**Keywords:**High-pressure density; Equation of state modeling; Thermal expansion coefficient; Isothermal compressibility; Volume scaling;

New volume translation for cubic equations of state by S. Laugier; F. Rivollet; D. Richon

*(99-104)*. Peneloux's volume translation is found of not equal benefit depending on pressure and temperature ranges for which volumetric properties are represented (some ranges being unfortunately worse described after correction than before).Other expressions for volume translations have been proposed up to now. They are slightly better than original Peneloux's one. However, the main default of most of these published modifications contain translation parameters that are not pressure dependent or, if they are, lead to time consuming non-cubic equations of state. It is clearly demonstrated herein that parameters must be pressure dependent. It is also clearly demonstrated that pressure dependence can be conveniently, easily and accurately represented using neural networks.Through volume translations using temperature and pressure dependent parameters, we show it is possible to represent simultaneously VLE and volumetric properties with accuracy degree similar to that obtained using Lee–Kessler–Plöcker equation.The new model (cubic equation of state + neural network based volume translation) is very competitive in terms of accuracy with respect to more complex equations of state based on virial developments for VLE and volumetric properties. It is easier to use with mixtures, as mixing rules are quite straightforward. Simplicity use of cubic equations of state is strictly maintained using neural networks. Furthermore, we show that weights for mixtures comes from weights adjusted on pure compound

*PVT*data, no new adjustment is required to treat mixtures provided pure component weights are available.Pure component weights related to neural networks are conveniently adjusted on*PVT*data obtained through the vibrating tube experimental method.**Keywords:**Volume translation; Cubic equation of state; Neural networks; Accurate

*PVT*representation; Derived properties calculation;

*PVT*measurements; Vibrating tube densimetry;

Generalized parameters of the Stryjek–Vera and Gibbons–Laughton cohesion functions for use with cubic EOS of the van der Waals type by Freddy L. Figueira; Leonor Lugo; Claudio Olivera-Fuentes

*(105-115)*. In this work, the parameters of the Stryjek–Vera and Gibbons–Laughton cohesion functions were determined for over 800 fluids by fitting vapor pressure data generated from the DIPPR database from the triple to the critical point. Parameter sets were obtained for use with the van der Waals, Redlich–Kwong and Peng–Robinson equations of state. The average vapor pressure deviations did not exceed 2.6%, with the Gibbons–Laughton function performing slightly better. Contrary to assertions in the literature, we showed that a generalized correlation of these parameters is possible. We developed this in the framework of a four-parameter corresponding states principle for non-polar and polar compounds, which allows the estimation of Stryjek–Vera and Gibbons–Laughton parameters from the acentric and critical compressibility factors of any given fluid.

**Keywords:**Cubic equation of state; Cohesion function; Vapor pressure; Corresponding states principle; Correlation;

A simplified approach to vapor–liquid equilibria calculations with the group-contribution lattice-fluid equation of state by Adam T. Jones; Samer Derawi; Ronald P. Danner; J. Larry Duda

*(116-122)*. Equations of state that are based on the lattice-statistics approach use Guggenheim's quasi-chemical approximation to describe the non-randomness in the mixture due to the energetic interactions between the molecules. For ternary and higher-component systems the non-randomness expression is complex and requires an iterative calculation procedure. We have shown that the non-randomness parameters play a negligible role in the application of the GCLF-EoS model (based on the Panayiotou–Vera EoS) for predicting vapor–liquid equilibria. Omission of the non-randomness parameters from such calculations can significantly improve the computation efficiency. Binary, ternary, and quaternary vapor–liquid equilibria predictions were made including polystyrene, polyvinyl acetate, polyethylene, and polypropylene in polar and non-polar solvents to test the theory.

**Keywords:**Equation of state; Polymer–solvent systems; Fugacity coefficient;

Evaluation of mixing and combining rules for asymmetric Lennard–Jones chain mixtures: Effect of segment diameter, energy interaction, and chain length by Rodrigo A. Reis; Márcio L.L. Paredes; Marcelo Castier; Frederico W. Tavares

*(123-134)*. Equations of state (EOS) capable of accurately representing the thermodynamic properties of chain molecules are of academic and industrial interest. In many cases, the systems of interest are composed by highly asymmetrical molecules, i.e., of different chain length, segment diameter, and segment interaction energy. The aim of this work is to evaluate mixing and combining rules (M&CR) for a SAFT-type equation of state. In the first part of this work, M&CR from literature are used together with the Wertheim Thermodynamic Polymerization Theory, in its dimer version, to calculate thermodynamic properties and then compare to those from molecular simulations. A data bank of compressibility factor and residual internal energy of Lennard–Jones chain asymmetrical mixtures was prepared for this purpose. In order to perform a systematic evaluation of M&CR, the one-fluid mixing rule (1FMR) and van der Waals one-fluid approximation (vdW1F) were coupled with the Berthelot combining rule (CR) and different CR for segment diameter, including Lorentz, Chen et al. [J. Chen, J. Lu, Y. Li, Fluid Phase Equilib. 140 (1997) 37], and a CR with one adjustable parameter. Results from comparisons with simulated data show that the 1FMR along with the Lorentz–Berthelot CR fails to represent thermodynamic properties of binary mixtures with simultaneous asymmetry in chain length and segment diameter. On the other hand, the density-dependent Chen et al. CR and vdW1F, only tested for Lennard–Jones sphere and hard-sphere chain asymmetrical mixtures, shows good performance in calculating compressibility factor and residual internal energy of asymmetrical mixtures of Lennard–Jones chains. The CR proposed in this work, with one optimized parameter, presented even better results than the Chen et al. CR, allowing a better description of simulated data employing a simpler rule.

**Keywords:**Combining rules; Mixing rules; Mixtures; Lennard–Jones chains; Equations of state;