Study on vapor-liquid equilibria and surface tensions for nonpolar fluids by renormalization group theory and density gradient theory

An equation of state (EOS) applicable for both the uniform and nonuniform fluids is established by using the density-gradient theory (DGT). In the bulk phases, the EOS reduces to statistical associating fluid theory (SAFT). By combining the EOS with the renormalization group theory (RGT), the vapor-liquid-phase equilibria and surface tensions for 10 nonpolar chainlike fluids are investigated from low temperature up to the critical point. The obtained results agree well with the experimental data.     

The uniquac associated-solution theory: vapor-liquid equilibria of binary systems containing one associating and one inert or active component

Brandani, V. and Evangelista, F., 1984. The UNIQUAC associated-solution theory: vapor-liquid equilibria of binary systems containing one associating and one inert or active component. Fluid Phase Equilibria, 17: 281–302.This article critically reconsiders UNIQUAC associated-solution theory, clearly identifying the physical approximations of the model. Data for binary vapor-liquid equilibria are correlated with this theory using pure-liquid association parameters determined by the method described in a preceding paper. For alcoholic systems, fitting of only two (inert component) or three parameters (active component) to the experimental data gives good improvement over the results from the original UNIQUAC equation. However, in the case of amine systems with inert components, such as saturated hydrocarbons, the UNIQUAC associated-solution theory fails unless a solvation effect is considered empirically.     

An improved renormalization group theory for real fluids

On the basis of White's theory, an improved renormalization group (RG) theory is developed for chain bonding fluids inside the critical region. Outside the critical region, the statistical associating fluid theory based on the first-order mean sphere approximation [Fluid Phase Equilibria 171, 27 (2000)] is adopted and all the microscopic parameters are taken directly from its earlier application of real fluids. Inside the critical region, the RG transformation for long-range density fluctuation is derived in the k space, which illustrates explicitly the contributions from the mean-field term, the local density fluctuation, and the nonlocal density fluctuation. The RG theory is applied to describe physical behavior of ten n alkanes (C1-C10) both near to and far from the critical point. With no additional parameters for chain bonding fluids, good results are obtained for critical specific heat and phase coexistence curves and the resulting critical exponents are in good agreement with the reported nonclassic values.     

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).     

Modelling of phase equilibria for associating mixtures using an equation of state

In the present work, the group contribution with association equation of state (GCA-EoS) is extended to represent phase equilibria in mixtures containing acids, esters, and ketones, with water, alcohols, and any number of inert components. Association effects are represented by a group-contribution approach. Self- and cross-association between the associating groups present in these mixtures are considered. The GCA-EoS model is compared to the group-contribution method MHV2, which does not take into account explicitly association effects. The results obtained with the GCA-EoS model are, in general, more accurate when compared to the ones achieved by the MHV2 equation with less number of parameters. Model predictions are presented for binary self- and cross-associating mixtures.     

GCA-EoS: A SAFT group contribution model—Extension to mixtures containing aromatic hydrocarbons and associating compounds

GCA-EoS is the first equation of state that takes into account association using a SAFT-like group contribution term. It has been recently upgraded to deal simultaneously with multiple associating and solvating groups. In this work a review of applications and parameters revisions are presented and the GCA-EoS extension to aromatic hydrocarbons is discussed. These compounds are important in different industrial fields (textile, fine chemicals, pharmaceutical, petrochemicals, materials, etc.). Moreover, compounds like phenol play a major role not only in several polymers syntheses but also in biomass processing mixtures. Specifically, the extension to systems containing aromatic hydrocarbons (BETX and alkylbenzenes), water and alkanols is discussed.     

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.     

Thermodynamics of liquid mixtures containing n-alkanes and strongly polar components: VE and C P E of mixtures with either pyridine or piperidine

Excess molar volumes V _E and excess molar heat capacities C _P ^/E at constant pressure have been obtained, as a function of mole fraction x₁, for several binary liquid mixtures belonging either to series I: pyridine+n-alkane (C_lH_2l+2), with l=7, 10, 14, 16, or series II: piperidine+n-alkane, with l=7, 8, 10, 12, 14. The instruments used were a vibrating-tube densimeter and a Picker flow microcalorimeter, respectively. V ^E of pyridine+n-heptane shows a S-shaped composition dependence with a small negative part in the region rich in pyridine (x₁>0.90). All the other systems show positive V ^E only. The excess volumes increase with increasing chain length l of the n-alkane. The excess molar heat capacities of the mixtures belonging to series II are all negative, except for a small positive part for piperidine+n-heptane in the region rich in piperidine (x₁>0.87). The C _P ^/E at the respective minima, C _P ^/E (x_1,min ), become more negative with increasing l, and the x_1,min values range from about 0.26 (l=7) to 0.39 (l=14). Most interestingly, mixtures of series I exhibit curves of C _P ^/E against x₁ with two minima and one maximum, the so-called W-shape curves.Dedicated to Professor A. Néckel on the occasion of his 65^th birthday. Communicated in part at the XVII^èmes Journées de Calorimétrie, d'Analyse Thermique et de Thermodynamique Chimique, Ferrara, Italy, 27–30 October, 1986.     

Phase equilibria for the binary mixtures containing hydrogen fluoride and non-polar compound

Isothermal vapor–liquid equilibria for propane+hydrogen fluoride have been measured. The experimental data are correlated with the association model proposed by Lencka and Anderko for the mixtures containing hydrogen fluoride and the relevant parameters are presented. The recalculated parameters of the association model for pure hydrogen fluoride are presented. The problems occurred in the applications of the association model for the mixtures containing hydrogen fluoride are discussed. The correlation was found to be in good agreement with the experimental data. However, the calculated equilibrium pressures at very diluted compositions of hydrogen fluoride below about 0.01 were shown rather higher than the experimental values.     

Phase equilibria for mixtures containing nonionic surfactant systems: Modeling and experiments

Surfactants are important materials with numerous applications in the cosmetic, pharmaceutical, and food industries due to inter-associating and intra-associating bond. We present a lattice fluid equation-of-state that combines the quasi-chemical nonrandom lattice fluid model with Veytsman statistics for (intra + inter) molecular association to calculate phase behavior for mixtures containing nonionic surfactants. We also measured binary (vapor + liquid) equilibrium data for {2-butoxyethanol (C₄E₁) + n-hexane} and {2-butoxyethanol (C₄E₁) + n-heptane} systems at temperatures ranging from (303.15 to 323.15) K. A static apparatus was used in this study. The presented equation-of-state correlated well with the measured and published data for mixtures containing nonionic surfactant systems.     

Density of methanol-carbon dioxide mixtures at three temperatures: Comparison with vapor-liquid equilibria measurements and results obtained from chromatography

The density of methanol-carbon dioxide mixtures has been measured at 40, 50, and 60°C and the data presented as constant density curves in plots of pressure against composition. Mixtures containing from 1 to 23.5% methanol were covered. The density information was compared with liquid-vapor equilibria data from the literature and with results from chromatographic separations using both sub- and supercritical conditions. The results indicate that phase transitions do not usually occur when the concentration of the modifier is increased while holding temperature and pressure constant. Similarly, no phase transition occurs when the temperature is increased from 28 to 80°C, at a constant (high) pressure and modifier concentration. Binary fluids with many desirable compositions cannot be prepared at low densities: densities below 0.4–0.5 g/cm³ cannot be obtained from methanol-carbon dioxide mixtures because the fluids separate into two phases. This means that density programming with many binary fluid combinations will be of secondary importance compared with composition programming.     

Isothermal vapor-liquid equilibria of bromochloroalkanes with heptane or cyclohexane: Measurement and analysis in terms of group contributions

Isothermal vapor-liquid equilibria (VLE) have been measured for liquid bromochloromethane + heptane or cyclohexane at 25‡C and 40‡C, and for 1-bromo-chloroethane + heptane or cyclohexane at 40‡C. These experimental results, along with our previous ones on excess enthalpies, as well as literature data on activity coefficients at infinite dilution, are interpreted in terms of the DISQUAC group contribution model, and are compared with UNIFAC predictions.     

Improving vapour-liquid-equilibria predictions for mixtures with non-associating polar components using sPC-SAFT extended with two dipolar terms

A considerable improvement in VLE predictions is obtained for mixture with non-associating polar components when the sPC-SAFT equation of state (EOS) is extended with the dipolar terms of Jog and Chapman (JC) and Gross and Vrabec (GV). These extended models are termed sPC-SAFT-JC and sPC-SAFT-GV, respectively. New model parameters for selected ketones, aldehydes, esters and ethers are presented for these two EOSs, as determined by the inclusion of pure component data and binary vapour-liquid-equilibria (VLE) data in the objective function of the regression procedure. Predictions of the VLE of polar/alkane and polar/polar systems show that most of these systems can be represented accurately by both models without using any binary interaction parameters (BIPs). Little difference in the performance of the two models is observed. In sPC-SAFT-GV, n_p (number of polar segments) is included in the regression routine as an adjustable pure component parameter instead of using a default value of 1. This enables the model to capture the contribution of the polar term more correctly, resulting in more accurate VLE predictions.     

Prediction of vapor-liquid equilibrium from excess enthalpy data for binary ether +n-alkane or cyclohexane mixtures

Vapor liquid equilibrium (VLE) is successfully predicted from excess enthalpy H^E data for binary ether + n-alkane or cyclohexane mixtures. Parameters for the continuous linear association model (CLAM) and for the UNIQUAC Model for the excess Gibbs energy G^E were determined from H^E data measured at a low temperature (ambient temperature). These parameters are used to predict VLE data at low and high temperatures. The dependence of the accuracy of predictions on the set of H^E data chosen to evaluate the parameters and on the model for G^E are discussed.     

Extension of the exp-6 model to the simulation of vapor-liquid equilibria of primary alcohols and their mixtures

Configurational-biased Gibbs ensemble Monte Carlo simulations were performed to obtain the phase behavior of the homologous series of primary alcohols from ethanol to 1-heptanol. Molecular interactions in these systems are modeled by a newly developed exp-6 potential in combination with a Coulombic intermolecular potential. Some of exp-6 potential parameters required to describe these alcohols were taken from the previous literature data reported for methanol and n-alkanes. The oxygen's potential parameters were optimized to fit the coexistence curve of these alcohols to the experimental data. Simulated values of saturated liquid and vapor densities, vapor pressures and critical constants of the alcohols are in good agreement with experimental data. The efficiency of the new model in the prediction of binary phase diagram of water/ethanol and n-hexane/1-propanol mixtures is also evaluated. The calculated mole fractions in the vapor and liquid phases of these binary mixtures also show satisfactory agreement with the experimental data.     

Extension of the associated perturbed anisotropic chain theory to mixtures with more than one associating component

The Associated Perturbed Anisotropic Chain Theory (APACT), a theory useful for calculation of equilibrium thermodynamic properties for fluid mixtures presented recently by Ikonomou and Donohue has been extended to treat multicomponent mixtures in which two or more components associate. Mixtures containing non-associating components (diluents) also can be treated. Association equilibria for each component hydrogen bonding to itself as well as for cross-association between associating components are considered. Following an approach similar to that used previously in the derivation of APACT, a closed-form equation of state has been derived. Preliminary results show that APACT does well in fitting phase equilibrium data for binary mixtures involving alcohols and water with small values of k_ij. The fits are not as good, however, for systems containing small molecules (water and methanol) and the reasons for this shortcoming are discussed.     

Excess properties of mixtures of polar components and hydrocarbons of varying local polarisability

The inhomogeneous electric field of a neighbouring polar molecule exerts a special induction in an unsaturated hydrocarbon, giving rise to more negative excess properties. This effect has been investigated for the excess Gibbs energy g^E and the excess volume v^E for mixtures of the polar components 1-chlorobutane, 2-butanone, and ethanenitrile with the four hydrocarbons cyclohexane, cyclohexene, 1,4-cyclohexadiene, and benzene at 293.15 K and 313.15 K. The measurements of g^E were done by VLE (static vapour pressures by a continuous dilution apparatus) and checked by LLE for the systems with phase separation. Excess volumes were determined via a vibratim tube densimeter. Equation of state calculations enabled the evaluation of the interaction virial coefficient B₁₂. The special induction effect, which shows up strongly in g_E and v_E of the liquid mixtures, is only weakly reflected in B₁₂.     

Multiphase equilibria for mixtures containing water, isopropanol, propionic acid, and isopropyl propionate

Vapor pressures of isopropyl propionate and isobaric vapor-liquid equilibrium (VLE) properties of isopropyl propionate + isopropanol and propionic acid + isopropyl propionate were measured. Isothermal vapor-liquid-liquid equilibrium (VLLE) data were also determined experimentally for water + isopropyl propionate and water + isopropyl propionate + isopropanol at temperatures from 323.24 K to 373.15 K. The binary VLE and VLLE data can be correlated well with the NRTL-HOC and the UNIQUAC-HOC models. The ternary VLLE data were used to test the validity of two versions of the UNIFAC model and the NRTL-HOC and the UNIQUAC-HOC models with the parameters determined from the phase equilibrium data of the constituent binaries. The ternary VLLE data were also correlated with the NRTL-HOC and the UNIQUAC-HOC models and the Soave-Redlich-Kwong equation of state with the Wong-Sandler mixing rule.     

Investigation of the surface tension of methane and n-alkane mixtures by perturbed-chain statistical associating fluid theory combined with density-gradient theory

The perturbed-chain statistical associating fluid theory (PC-SAFT) and density-gradient theory are used to construct an equation of state to describe the phase behavior of binary methane–n-alkane mixtures. With the molecular parameters and influence parameters regressed from bulk properties and surface tensions of pure fluids, respectively as input, both the bulk and interfacial properties are investigated. The surface tension of the binary systems methane–propane, methane–pentane, methane–heptane and methane–decane are predicted, and the results are satisfactory compared with the experimental data. Our results show that PC-SAFT combined with density-gradient theory is able to describe the interfacial properties of binary methane–n-alkane mixtures in wide temperature and pressure ranges, and illustrate the influence of the equilibrium bulk properties and chain length of n-alkane molecule on the interfacial properties.