Phase Equilibria Of Binary Systems Research Articles

Development of the PhDi software package for the calculation of phase diagrams of binary systems using parameters of state equations and thermodynamic models for solutions

The PhDi software package developed earlier for calculations of phase equilibria by the convex hull method was modified by incorporating two additional modules: “State equations” and “Local composition thermodynamic models.” The possibility of the application of the convex hull method with cubic state equations to construct phase diagrams of binary systems was shown. A new database containing parameters of the corresponding thermodynamic models has been added to the initial version of the PhDi package. The efficiency of the performance of the package in solving the problem of choosing an appropriate state equation to predict conditions of phase equilibria in binary systems was demonstrated.

Phase Equilibria of Ester + Alcohol Systems and Their Description with the Cubic-Plus-Association Equation of State

The knowledge and the capability to describe the phase equilibria of binary systems formed by a fatty acid ester and an alcohol are of great interest in biodiesel production, where these mixtures can be found after the transesterification unit and where they must be separated to purify the biodiesel stream and to recover the unreacted alcohol. Despite this interest, little information is available on the vapor-liquid equilibria (VLE) of fatty acid ester + alcohol systems. To overcome this lack of data, new VLE measurements of six ester + methanol/ethanol systems were carried at atmospheric pressure. This new experimental data was successfully modeled with the Cubic-Plus-Association equation of state (CPA EoS), with global average deviations of 0.5% for the bubble-point temperatures. In all cases small and temperature independent parameters were enough to adequately describe the measured data. Furthermore a constant value for the cross-association energy parameter was proposed for each alcohol system, as well as a linear correlation for the binary interaction parameter with the ester chain length, making the CPA EoS a powerful predictive model for these systems.

MODELLING OF HIGH‐PRESSURE PHASE EQUILIBRIUM IN SYSTEMS OF INTEREST IN THE FOOD ENGINEERING FIELD USING THE PENG‐ROBINSON EQUATION OF STATE WITH TWO DIFFERENT MIXING RULES

ABSTRACT In this work, thermodynamic models for fitting the phase equilibrium of binary systems were applied, aiming to predict the high pressure phase equilibrium of multicomponent systems of interest in the food engineering field, comparing the results generated by the models with new experimental data and with those from the literature. Two mixing rules were used with the Peng‐Robinson equation of state, one with the mixing rule of van der Waals and the other with the composition‐dependent mixing rule of Mathias et al. The systems chosen are of fundamental importance in food industries, such as the binary systems CO2‐limonene, CO2‐citral and CO2‐linalool, and the ternary systems CO2‐Limonene‐Citral and CO2‐Limonene‐Linalool, where high pressure phase equilibrium knowledge is important to extract and fractionate citrus fruit essential oils. For the CO2‐limonene system, some experimental data were also measured in this work. The results showed the high capability of the model using the composition‐dependent mixing rule to model the phase equilibrium behavior of these systems.PRACTICAL APPLICATIONSThe use of the Peng–Robinson equation of state (PR‐EOS) in description of phase equilibrium of systems at high pressure has been largely reported in the scientific literature. On the other hand, the low prediction capability of the PR‐EOS to thermodynamic properties of polar multicomponent systems has been provided with the development and application of new mixing rules. The main purpose of the present work was to study a thermodynamic model to correlate systems of interest in the food engineering field, applying the PR‐EOS to a composition‐dependent mixing rule, by comparing the results with those represented by the classical mixing rule of van Der Waals (PR‐EOS). In spite of the large interest in applying supercritical technology in obtaining highly purified extracts from food, available data from systems at high pressure related to food process, and passable to be modeled, are scarce in the literature. Therefore, the investigation of simple and effective models on the description of these systems is of great importance and is a valuable tool in the study of the high‐pressure systems behavior in the food processing field.

Thermodynamics of organic mixtures containing amines. X. Phase equilibria for binary systems formed by imidazoles and hydrocarbons: Experimental data and modelling using DISQUAC

(Solid + liquid) equilibrium (SLE) temperatures have been determined using a dynamic method for the systems (1 H -imidazole, + benzene, + toluene, + hexane, or + cyclohexane; 1 -methylimidazole + benzene, or + toluene, 2-methyl-1 H -imidazole + benzene, + toluene, or + cyclohexane, and benzimidazole + benzene). In addition (liquid + liquid) equilibrium (LLE) temperatures have been obtained using a cloud point method for (1 H -imidazole, + hexane, or + cyclohexane; 1 -methylimidazole + toluene, and 2-methyl-1 H -imidazole + cyclohexane). The measured systems show positive deviations from the Raoult’s law, due to strong dipolar interactions between amine molecules related to the high dipole moment of imidazoles. On the other hand, DISQUAC interaction parameters for the contacts present in these solutions and for the amine/hydroxyl contacts in (1 H -imidazole + 1-alkanol) mixtures have been determined. The model correctly represents the available data for the examined systems. Deviations between experimental and calculated SLE temperatures are similar to those obtained using the Wilson or NRTL equations, or the UNIQUAC association solution model. The quasichemical interaction parameters are the same for mixtures containing 1 H-imidazole, 1-methylimidazole, or 2-methyl-1 H-imidazole and hydrocarbons. This may be interpreted assuming that they are members of a homologous series. Benzimidazole behaves differently.

Phase equilibria of binary systems of 3-methylthiophene with four different hydrocarbons

Isothermal vapor–liquid equilibrium (VLE) for systems 3-methylthiophene + 2-methylpentane at 333.15 K, 3-methylthiophene + n-hexane at 333.15 K, 3-methylthiophene + methylcyclopentane at 343.15 K, and 3-methylthiophene + methylcyclohexane at 373.15 K were measured with a recirculation still. All systems exhibit positive deviation from Raoult's law. No azeotropic behavior was found in any of the systems at the measured temperatures. The experimental results were correlated with the Wilson model and also compared with the original UNIFAC and UNIFAC-Dortmund predictive models. Liquid and vapor-phase composition were determined with gas chromatography. All VLE measurements passed the used thermodynamic consistency tests (integral, infinite dilution and point test). The activity coefficients at infinite dilution are also presented.

Correlation Dependences of the Thermodynamic Properties of Liquid Haloarenes and Their Binary Solutions

Liquid-vapor phase equilibria in binary systems formed by haloarenes were studied. The contributions of intermolecular interactions to the thermodynamic functions of liquid haloarenes and their binary solutions were calculated. The contributions of intermolecular interactions to the Helmholtz energy of binary solutions of constant molar concentrations formed by fluoroarene and haloarenes were found to depend linearly on the molecular weight of haloarenes. The corresponding correlation equations were suggested.

An evaluation of the performance of the Cubic-Plus-Association equation of state in mixtures of non-polar, polar and associating compounds: Towards a single model for non-polymeric systems

The aim of this work is to investigate the possibility of identifying a single model that will be able to accurately describe the phase equilibrium in non-polymeric systems, which involve non-polar, polar and hydrogen bonding compounds. To this purpose the Cubic-Plus-Association (CPA) EoS, developed in this laboratory about 10 years ago, is examined in the correlation of phase equilibrium in binary systems and prediction of multicomponent phase equilibrium from binary data. When possible the results of the CPA EoS are compared with those obtained from the PC-SAFT EoS. To account for dipolar or quadrupolar interactions, present when molecules such as acetone or carbon dioxide are involved, these molecules are treated using the concept of “pseudo-association”, i.e. as being able to act as associating compounds. This approach renders CPA applicable to systems that involve polar compounds without the need of extra terms to account for polar and/or quadrupolar interactions. It is concluded that CPA, coupled with the “pseudo-association” approach for polar molecules, represents a model that is able to accurately describe the phase equilibrium in a variety of binary systems involving non-polar, polar and hydrogen bonding compounds and provide satisfactory prediction of multicomponent phase equilibrium from binary data.

Phase behavior of olive and soybean oils in compressed propane and n-butane

The aim of this work is to report the experimental data and thermodynamic modeling of phase equilibrium of binary systems containing soybean and olive oils with propane and n-butane. Phase equilibrium experiments were carried out using the static synthetic method in a high-pressure variable-volume view cell in the temperature range from 30 to 70ºC and varying the solvent overall composition from 5 to 98 wt%. Vapor-liquid, liquid-liquid and vapor-liquid-liquid phase transitions were observed at relatively low pressures. The Peng-Robinson and the SAFT equations of state without any binary interaction parameters were employed in an attempt at representing the phase behavior of the systems. Results show the satisfactory performance of SAFT-EoS in predicting qualitatively all phase transitions reported in this work.

Phase equilibria for binary systems of octane boosters with 2,2,4-trimethylpentane

Isobaric vapor–liquid equilibrium data at 95.96 kPa for the three binary systems of 2,2,4-trimethylpentane with methyl tert-butyl ether, di-isopropyl ether and dimethoxymethane are determined. A Swietoslawski type ebulliometer is used for the measurements. The experimental T– x data are used to estimate Wilson parameters and the parameters, in turn, are used to calculate vapor phase compositions and activity coefficients. All the systems studied here do not exhibit azeotropes and behave like non-ideal solutions.

The Solvent-Solute Interaction in Supercritical Solution at Equilibrium: Modeling and Related Industrial Applications

Supercritical solutions are studied from the thermodynamic point of view by giving a comprehensive review of phase equilibrium of binary systems. The numerical modeling of the phase behavior is an approach used by several authors to describe and analyze supercritical applications. The thermodynamic equilibrium models are employed to determine the interaction coefficient between the solvent and the solute. Depending on the nature of the compound and the operating conditions three different experimental methods are used. Understanding the phase equilibrium of supercritical solutions and deeper knowledge of the supercritical fluids are needed for industrial applications such as powder elaboration by rapid expansion of supercritical solution and essential oil extraction processes.

Phase equilibria for binary systems of methyl oleate–supercritical CO 2 and α-tocopherol–supercritical CO 2

In order to study the possibility of using supercritical CO 2 to concentrate tocopherols from soybean oil de-odorizer distillate (DOD), the binary phase equilibrium data for methyl oleate–CO 2 and α-tocopherol–CO 2 were measured at 313.15–353.15 K in the pressure ranges of 5–23 MPa for methyl oleate and 5–30 MPa for α-tocopherol, respectively. The measured data were well correlated using the Soave–Redlich–Kwong (SRK) equation of state (EOS) with the Adachi–Sugie (AS) mixing rule. The solubilities and distribution coefficients of methyl oleate and α-tocopherol in CO 2 were investigated. Finally, on the basis of these results, a conclusion was preliminarily drawn, supercritical CO 2 can be used to concentrate natural tocopherols from the esterified DOD in the experimental range investigated. In addition, the critical points of methyl oleate–CO 2 at three temperatures were estimated.

An atomistic study of solid/liquid interfaces and phase equilibrium in binary systems

A semiempirical Lennard-Jones/Embedded Atom Method model is used to capture real materials’ behavior through the introduction of many-body forces. By means of molecular dynamics (MD) calculations, the model is used to study the dependence of the solid/liquid interface velocity on temperature and composition. Based on the MD results, the free energies and the chemical potentials in the solid and liquid phases are calculated to produce the phase diagrams. These calculations illustrate the consequences of differences in energy and size between the components on the phase diagrams. An asymmetry in velocity between solidification and melting is found. Slowing of the interface velocity by solutes during solidification is demonstrated.

Thermodynamic Analysis of Solid−Solid and Solid−Liquid Equilibria in Binary Systems Composed of n-Alkanes: Application to the System Tricosane (C23H48) + Pentacosane (C25H52)

This paper presents the elements needed to carry out thermodynamic assessments of phase equilibria in binary systems of normal alkanes in the range from hexadecane (C16H34) to octacosane (C28H58) a...

Prediction of phase equilibria for binary systems of hydrogen chloride with ethane, propane and n-dodecane

In many industrially important processes hydrogen chloride occurs as one of the major constituents. Due to its corrosive nature, hydrogen chloride is not an easy substance to handle in industrial or experimental facilities and, as a consequence, accurate basic data of its mixtures is scarce. In this study, we examine the ability of two theoretical approaches, PACT (perturbed anisotropic chain theory), and SAFT (statistical associating fluid theory), to predict the phase behaviour of three binary mixtures of hydrogen chloride with n-alkanes. In the PACT approach, the molecules are modelled with Lennard–Jones spherical segments with a contribution to describe the dipole of the hydrogen chloride molecule. The non-sphericity of the n-alkane molecules is accounted for via Prigogine's approximation for the external degrees of freedom. In the SAFT approach, the molecules are represented by chains of spherical repulsive segments with attractive short-range sites. Hydrogen chloride is represented by a single sphere, with two attractive sites to model the dipole of the molecule. Chain molecules, such as the n-alkanes, are modelled fusing together a number of spherical segments. No attractive sites are included as these molecules are non-polar. We treat the long-range dispersion forces via variable-range square-well potentials; with the SAFT-VR approach. We find that both approaches accurately reproduce the experimental phase behaviour of the three mixtures for wide ranges of temperature and pressure. In the case of the SAFT-VR approach, both the critical region and the low temperature region are well represented with one set of parameters. However, the PACT approach requires two different sets of parameters: one for the critical region and one for lower temperature regions.

Experimental liquid–liquid phase equilibria for binary systems: ethanenitrile with several hydrocarbon isomers

Liquid–liquid miscibility temperatures, as a function of composition, for the nine binary systems formed by ethanenitrile (acetonitrile), as common component, with 2-methylpentane, 3-methylpentane, 2,2-dimethylbutane, 2,3-dimethylbutane, cyclopentane, methylcyclopentane, cyclohexane, methylcyclohexane and cyclooctane, have been determined by the sealed-tube technique. All the studied systems show an upper critical solution temperature (UCST). We have used the Weimer–Prausnitz modification for polar components of Hildebrand's regular solution theory (RST) to calculate UCSTs and the results compare very well with those obtained experimentally for the systems studied. We have established that the value for the induction energy density parameter included in the modified RST, which arises from induction forces between the polar component and the nonpolar component, originally proposed only for linear and cyclic saturated hydrocarbons in polar solvents, is also valid for binary systems of the type polar component+branched paraffin. The RST with the Flory–Huggins entropy gives values of the critical composition which are systematically higher than the experimental values.

Phase Equilibria of Binary Systems Formed by Hydrocarbons from Petroleum Fractions and the Solvents N-Methylpyrrolidone and N,N-Dimethylformamide. 1. Isobaric Vapor−Liquid Equilibria

Isobaric vapor−liquid equilibrium data at 101.33 kPa are reported for binary systems formed by N-methylpyrrolidone (NMP) and N,N-dimethylformamide (DMF) with benzene, heptane, hexane, or cyclohexane. Data reduction based on the Van Laar, Wilson, NRTL, and UNIQUAC models provides a correlation for the liquid-phase activity coefficients. All the systems, except for the ones formed with benzene, are strongly nonideal, yielding two phases at low temperatures.

Topology of P-T-X phase diagrams of binary systems. Polymorphism, metastable states and high-pressure equilibria

Abstract A step-by-step geometrical approach is presented to the P-T-X phase equilibrium in binary systems with different types of polymorphism and metastable states, and the relationship between these two phenomena. Mutual solubility of the components in all the states of aggregation is taken into account, as well as formation of crystalline non-stoichiometric compounds. Special attention is given to equilibria at high pressures because until now, these types of phase diagrams have not been adequately discussed. At first, P-T relations in onecomponent systems are analysed and afterwards the third co-ordinate (composition X) is introduced for binary systems. The phase states of the systems are examined by means of P-T and T-X projections of the corresponding equilibria along with isobaric T-X sections of the representative and most complicated regions. All possible types of phase diagrams of binary systems with both parallel and non-parallel polymorphism of the components are discussed. Complete and limited solid state solubility is considered. Metastable states of the binary systems as well as different crystallization routes of non-stoichiometric compounds ( stable and metastable) are examined in connection with the polymorphism of the components. Certain general trends of metastable crystallization characteristic of all types of the phase diagrams are discussed

Phase equilibria in binary systems containing N-monosubstituted amides and hydrocarbons

The binary vapour-liquid equilibrium of seven systems of ε-caprolactam + octane, + decane, + dodecane, octane, + decane, + dodecane, of N-methylacetamide + octane, of N-ethylacetamide of N-methylpropionamide + octane and of N-methylpropionamid + ε-caprolactam was measured in the temperature range from 363 to 423 K and in the low pressure region. A static equilibrium apparatus for the measurements was constructed. In the system N-methylpropionamide + octane measurements of liquid-liquid equilibrium were carried out in the temperature range from 310 K up to the critical solution temperature. The experimental results were correlated applying activity coefficients models such as NRTL. The data obtained from our measurements were used to estimate UNIFAC interaction parameters for the groups CH 2 CONHCH 2 , CH 2 C 5H 10CONH and CONHCH 2 C 5H 10CONH .

High-pressure binary phase equilibria of aromatic hydrocarbons with carbon dioxide and ethane

The authors describe high-pressure vapor-liquid equilibria of several binary systems containing aromatic hydrocarbons as one component and supercritical carbon dioxide or ethane as the other component measured by using a dynamic system in which both vapor and liquid phases were circulated. The aromatic hydrocarbons that were used in this study are anisole, benzaldehyde, tetralin, and 1-methylnaphthalene. The phase equilibria of binary systems containing carbon dioxide were measured at two different temperatures, 343 and 373 K, and pressures up to 22 MPa. For ethane binary systems, equilibrium measurements were made at 373 K and pressures up to 12 MPa. In addition to measuring temperature, pressure, and phase compositions, the vapor- and liquid-phase densities also were determined for both carbon dioxide and ethane binary systems.

Vapor-liquid equilibria in binary systems containing ethanol with hexamethyldisiloxane and dimethyl sulfoxide

Results of the experimental determination of isobaric vapor-liquid equilibrium data for the binary systems hexamethylidisiloxane (HMDS) with ethanol and ethanol with dimethyl sulfoxide (DMSO) are reported. This work is a continuation of studies on phase equilibria in binary systems.