Fluid phase equilibria in the binary system trifluoromethane + 1-phenyloctane

Vapour–liquid, liquid–liquid and liquid–liquid–vapour equilibria in the binary system consisting of trifluoromethane (refrigerant R23) and 1-phenyloctane were determined in the temperature range T = 250–400 K and at pressures up to 15 MPa. The experiments were carried using a Cailletet apparatus according to the synthetic method. The investigated system exhibits type III phase behaviour according to the classification of van Konynenburg and Scott. Modelling of the equilibrium data was done with the Peng–Robinson (PR) and Soave–Redlich–Kwong (SRK) equations of state coupled with classical van der Waals mixing rules. In order to predict the global phase behaviour of the system, one single set of binary parameters was used. The topology of the phase behaviour was correctly reproduced.     

Modeling the high-pressure phase equilibria of carbon dioxide–triglyceride systems: A parameterization strategy

The group contribution equation of state (GC-EOS) has been used in several published works to correlate or predict the high-pressure phase equilibria of a variety of systems of practical interest. Nevertheless, quantitative and even qualitative disagreement among predictions and experimental data has been detected in mixtures of CO₂ with heavy compounds, such as triglycerides, when operating at high pressure. For instance, phase split up to indefinitely high pressures has been computed, when the observed experimental behavior shows full miscibility at sufficiently high pressure. In the present work, we study the influence on calculated critical lines and solubilities (Pxy diagrams) of the group-based interaction parameters k_ij, for the interactions of CO₂ with both, the triglyceride (TG) group and the paraffinic groups. Based on such study, we propose a parameterization procedure that improves upon the conventional parameter regression practice. The distinguishing feature of such procedure is the repeated observation of the global phase equilibrium behavior, studying in particular the effect of the group–group interaction parameters on critical lines, on the composition of the phases at equilibrium along liquid–liquid–vapor lines, and on selected isothermal or isobaric phase equilibrium diagrams. For the case of the non-randomness parameter, we use a universal positive value, more consistent with its physical meaning.     

Fluid phase stability and equilibrium calculations in binary mixtures: Part II: Application to single-point calculations and the construction of phase diagrams

The methodology presented in Part I of this work is applied to a large number of pressure–temperature flash calculations, and to the automated construction of constant temperature pressure–composition phase diagrams, and constant pressure temperature–composition phase diagrams for binary mixtures modeled with an augmented van der Waals equation of state. An automated prototype implementation of the algorithm is developed for this purpose. We follow the classification of Scott and van Konynenburg [R.L. Scott, P.H. van Konynenburg, Discuss. Faraday Soc. 49 (1970) 87] and present phase diagrams corresponding to non-azeotropic mixtures of the five main types of fluid phase behavior (I–V), studying in detail representative diagrams at constant pressure and constant temperature. Special attention is given to the solution of numerically problematic equilibrium regions, such as those close to three-phase equilibria where metastable and unstable critical points can also be found. Of the order of 10⁴ flash calculations at varying temperatures and pressures, and for different intermolecular parameters of the components in the mixture, have been carried out. The algorithm provides the correct stable equilibrium state for all of the points considered. Despite the fact that our implementation is not optimised for performance, we find that the algorithm identifies the stable solution in difficult regions of the phase space without any penalty in terms of computational time, when compared to simpler regions.     

Vapour-liquid equilibrium and critical locus curve calculations with the soave equation for hydrocarbon systems with carbon dioxide and hydrogen sulphide

Huron, M.-J., Dufour, G.-N. and Vidal, J., 1978. Vapour-liquid equilibrium and critical locus curve calculations with the Soave equation for hydrocarbon systems with carbon dioxide and hydrogen sulphide. Fluid Phase Equilibria, 1: 247–265The aim of this work is to test the value of the Soave-Redlich-Kwong equation of state for predicting phase behaviour of mixtures. Special attention is paid to systems containing hydrogen sulphide or carbon dioxide with hydrocarbons. The properties analysed are critical loci and liquid vapour equilibria, with calculations of standard deviations for pressures and compositions. Optimum values of binary interaction parameters are proposed for these mixtures. Calculation methods to avoid trivial solutions in phase equilibria calculations and for finding critical loci with temperature extrema are described.     

The phase envelopes of alternative solvents (ionic liquid,CO2) and building blocks of biomass origin (lactic acid,propionic acid)

Solid–liquid, liquid–liquid and vapour–liquid equilibrium measurements for binary and ternary systems containing building blocks of biomass origin such as propionic acid, lactic acid and alternative solvents like carbon dioxide and 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ionic liquid have been carried out at 313.15 K. The binary solid–liquid and liquid–liquid equilibrium measurements were performed at ambient pressure. The vapour–liquid equilibrium was studied in the range of pressure from 3.54 to 12 MPa while ternary systems were examined at 9, 10 and 12 MPa. The samples from the coexisting phases were taken and the compositions of both liquid and vapour phases were determined experimentally. The three-phase system was observed for lactic acid + ionic liquid + CO₂ as well. The achieved results were correlated using the Peng–Robinson equation of state with the Mathias–Klotz–Prausnitz mixing rule. The set of interaction parameters for the employed equations of state and the mixing rule for the investigated systems were obtained.     

Separation of systems based on uranium hexafluoride and some of halogen fluorides

The purpose of this paper is to present the results of the comprehensive study of the phase equilibriums liquid-solid and liquid-vapour in binary and ternary systems, formed by uranium hexafluoride, bromine trifluoride and iodine pentafluoride.Investigation of the phase equilibriums in condensed systems is done by methods of differential thermoanalysis and visual polythermal analysis. All systems belong to simple eutectics; formation of the compounds is not detected. For all systems under investigation diagrams of the phase equilibrium liquid-solid are plotted.Phase equilibriums liquid-vapour in studied systems were studied by statistical method. All systems are non-aseotropic. The article presents diagrams of the phase equilibrium liquid-vapour in binary systems, pressure of the saturated vapour dependences on liquid composition, surface of the boiling liquid and lines of the constant content of uranium hexafluoride and iodine pentafluoride in vapour phase of the ternary system UF₆-BrF₃-IF₅.     

A comparative study of particle swarm optimization and its variants for phase stability and equilibrium calculations in multicomponent reactive and non-reactive systems

Particle swarm optimization is a novel evolutionary stochastic global optimization method that has gained popularity in the chemical engineering community. This optimization strategy has been successfully used for several applications including thermodynamic calculations. To the best of our knowledge, the performance of PSO in phase stability and equilibrium calculations for both multicomponent reactive and non-reactive mixtures has not yet been reported. This study introduces the application of particle swarm optimization and several of its variants for solving phase stability and equilibrium problems in multicomponent systems with or without chemical equilibrium. The reliability and efficiency of a number of particle swarm optimization algorithms are tested and compared using multicomponent systems with vapor–liquid and liquid–liquid equilibrium. Our results indicate that the classical particle swarm optimization with constant cognitive and social parameters is a reliable method and offers the best performance for global minimization of the tangent plane distance function and the Gibbs energy function in both reactive and non-reactive systems.     

Modeling of three-phase vapor–liquid–liquid equilibria for a natural-gas system rich in nitrogen with the SRK and PC-SAFT EoS

In this work, we present the modeling of three-phase vapor–liquid–liquid equilibria for a mixture of natural gas (Hogback gas) containing high concentrations in nitrogen (51.8 mol%) with the SRK and PC-SAFT equations of state. The interest of studying this mixture is due to the experimental evidence of the occurrence of multiple equilibrium liquid phases for this mixture over certain ranges of temperature and pressure. The calculation of the multiphase equilibria was carried out by using an efficient numerical procedure based on the minimization of the system Gibbs energy and thermodynamic stability tests to find the most stable state of the system. The results of the calculated vapor–liquid–liquid equilibria (VLLE) show that the PC-SAFT equation of state predicts satisfactorily the phase behavior that experimentally exhibits this mixture, whereas the SRK equation of state predicts a three-phase region wider than the experimentally observed. The two-phase boundary for this mixture was also calculated through flash calculations, and the results showed that this mixture does not present any gas-liquid critical point.     

Phase equilibria and phase separation dynamics in a polymer composite containing a main-chain liquid crystalline polymer

Various topological phase diagrams of blends of main-chain liquid crystalline polymer (MCLCP) and flexible polymer have been established theoretically in the framework of Matsuyama–Kato theory by combining Flory–Huggins (FH) free energy for isotropic mixing, Maier–Saupe (MS) free energy for nematic ordering in the constituent MCLCP, and free energy pertaining to polymer chain-rigidity. As a scouting study, various phase diagrams of binary flexible polymer blends have been solved self-consistently that reveal a combined lower critical solution temperature (LCST) and upper critical solution temperature (UCST), including an hourglass phase diagram. The calculated phase diagrams exhibit liquidus and solidus lines along with a nematic–isotropic (NI) transition of the constituent MCLCP. Depending on the strengths of the FH interaction parameters and the anisotropic (nematic–nematic) interaction parameters, the self-consistent solution reveals an hourglass type phase diagram overlapping with the NI transition of the constituent MCLCP. Subsequently, thermodynamic parameters estimated from the phase diagrams hitherto established have been employed in the numerical computation to elucidate phase separation dynamics and morphology evolution accompanying thermal-quench induced phase separation of the MCLCP/polymer mixture. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3621-3630, 2006     

Application of stochastic algorithms for parameter estimation in the liquid–liquid phase equilibrium modeling

In this work the Simulated Annealing (SA) and Particle Swarm Optimization (PSO) algorithms were employed to modeling liquid–liquid phase equilibrium data. For this purpose, some strategies for stochastic algorithms were investigated from common test functions and used in LLE parameter estimation procedure. The strategy used for the flash calculation was based on the isoactivity criteria associated with phase stability test and interpolation function for the initial estimate to improve reliability of phase equilibria calculations. It is shown that both algorithms SA and PSO were capable of estimating the parameters in models describing liquid–liquid phase behavior of binary and multicomponent systems with a good representation of the experimental data.     

Development and extension of PSRK/UNIQUAC model to methane and nitrogen gases

Two successful procedures for matching the equation of state (EOS) and the excess Gibbs energy model at zero pressure belong to Michelsen [M.L. Michelsen, Fluid Phase Equilibria, 60 (1990) 213] and Holderbaum-Gmehling [T. Holderbaum, J. Gmehling, Fluid Phase Equilibria, 70 (1991) 251]. These procedures lead to volume independent mixing rules for the mixture parameter a. Michelsen proposed the MHV1 and MHV2 mixing rules and Holderbaum-Gmehling proposed the PSRK mixing rule. Keshtkar et al. [A. Keshtkar, F. Jalali, M. Moshfegian, Fluid Phase Equilibria, 140 (1997) 107] demonstrated the utility of these mixing rules together with UNIFAC and UNIQUAC models for the prediction of high-pressure vapor-liquid equilibrium (VLE) of CO₂-binary systems. Also, they showed that the PSRK/UNIQUAC model gives better VLE results than other models. In this paper, we develop and extend the above model to methane and nitrogen gases. For this purpose, it is required that the missing interaction parameters of model are fitted with experimental VLE data. The VLE calculations show that good agreement between calculated results and experimental data can be produced by using the obtained parameters.     

Phase equilibria of imidazolium ionic liquids and the refrigerant gas, 1,1,1,2-tetrafluoroethane (R-134a)

A number of applications with ionic liquids (ILs) and hydrofluorocarbon gases have recently been proposed. Detailed phase equilibria and modeling are needed for their further development. In this work, vapor–liquid equilibrium, vapor–liquid–liquid equilibrium, and mixture critical points of imidazolium ionic liquids with the hydrofluorocarbon refrigerant gas, 1,1,1,2-tetrafluoroethane (R-134a) was measured at temperatures of 25 °C, 50 °C, 75 °C and pressure up to 143 bar. The ionic liquids include 1-hexyl-3-methyl-imidazolium bis(trifluoromethylsulfonyl)amide ([HMIm][Tf₂N]), 1-hexyl-3-methyl-imidazolium hexafluorophosphate ([HMIm][PF₆]), and 1-hexyl-3-methyl-imidazolium tetrafluoroborate ([HMIm][BF₄]). The effects of the anion and cation on the solubility were investigated with the anion having greatest impact. [HMIm][Tf₂N] demonstrated the highest solubility of R-134a. The volume expansion and molar volume were also measured for the ILs and R-134a. The Peng–Robinson Equation of State with van der Waals 2-parameter mixing rule with estimated IL critical points were employed to model and correlate the experimental data. The models predict the vapor–liquid equilibrium and vapor–liquid–liquid equilibrium pressure very well. However, the mixture critical points predictions are consistently lower than experimental values.     

Vapor–liquid equilibria of asymmetrical systems using UNIFAC-NRF group contribution activity coefficient model

The UNIFAC-NRF group contribution activity coefficient model is used for the calculation of vapor–liquid equilibria of binary systems of the heavy alkanes and light gases such as CH₄, C₂H₆, CO₂ and N₂. The linear combination mixing rule, LCVM, of the Huron–Vidal and Michelsen, Chen et al. modification of PSRK and Universal Group Contribution Equation of State of Ahlers and Gmehling are combined with the UNIFAC-NRF group activity coefficient model to correlation of the vapor–liquid equilibrium of both light and heavy hydrocarbons. The results show that the LCVM mixing rule combing with UNIFAC-NRF group contribution model correlate the asymmetric systems better than the LCVM-UNIFAC and the other EOS/G^E models. Also the group contribution model is used for the prediction of the phase envelope of the synthetic fluid with accurate results.     

Prediction of critical transitions of ternary mixtures containing ammonia and n-alkanes

The analysis of the critical transitions that occur in ternary mixtures is important to describe their physical behavior. It also enables the phase behavior of multi-component mixtures at high temperatures to be inferred. The objective of this work was to identify the critical transitions that occur in ternary mixtures containing ammonia and n  -alkane. The mixture’s critical loci were obtained and tested for stability using thermodynamic criteria expressed in terms of the Helmholtz free energy. Two equations of state were used to represent the Helmholtz free energy: the Carnahan–Starling–Redlich–Kwong (CSRK) and the Simplified Perturbed Hard Chain Theory (SPHCT). In order to identify the existing critical transitions, profiles of the critical loci were calculated along constant compositional ratios χ=x₁/x₂$\chi =x_1/x_2$. Some of the curves depict higher order critical transitions between liquid–liquid and gas–liquid critical point regions, or two different liquid–liquid critical regions. One of the critical transitions found could be considered as a new sub-class within existing classifications for ternary mixtures proposed by Sadus [R.J. Sadus, J. Phys. Chem. 96 (1992) 5197–5202].     

Temperatures of liquid–liquid separation and excess molar volumes of {N-methylpiperidine–water} and {2-methylpiperidine–water} systems

Partial miscibility in binary systems {N-methylpiperidine–water} and {2-methylpiperidine–water} was studied. The temperatures of liquid–liquid separation were determined as function of composition using both calorimetric technique and phase equilibrium cell. The densities of {amine–water} mixtures were determined in the domain of total miscibility at temperatures between 288 K and 338 K. Excess molar volumes were derived from experimental density data and fit to a Redlich–Kister polynomial.     

Interfacial properties of water + alcohol mixtures

Mixtures of water with alcohol are important in numerous engineering applications. Caused by the polarity of water and alcohol self-association of water and alcohol as well cross-association between water and alcohol appear in such complex mixtures. These features show significant impact on physical and chemical properties, especially phase equilibrium behaviour and hence interfacial properties. The Cahn–Hilliard theory was combined with original statistical associated fluid theory equation of states (SAFT EOS) in order to describe both the phase behaviour and interfacial properties with respect of association. The paper focuses on theoretical investigations of surface tension, density profiles, surface thickness in vapour–liquid or vapour–liquid–liquid equilibrium of mixtures of water with ethanol or 1-butanol. Results of vapour–liquid equilibrium surface tension calculations were compared with experimental data taken from the literature.