Phase Equilibria Of Binary Systems Research Articles

Vapor–liquid phase equilibrium prediction for mixtures of binary systems using graph neural networks

AbstractVapor–liquid phase equilibrium (VLE) plays a crucial role in chemical process design, process equipment control, and experimental process simulation. However, experimental acquisition of VLE data is a challenging and complex task. As an alternative to experimentation, VLE data prediction offers great convenience and utility. In this article, an artificial intelligence network is proposed to predict the temperature and the vapor phase composition of binary mixtures. We constructed a graph neural network (GNN) and designed an uncertainty‐aware learning and inference mechanism (UALF) in the prediction process. The model was tested on both a self‐constructed dataset and a publicly available dataset. The results demonstrate that the proposed method effectively reveals the phase equilibrium properties of the target data. This work presents a novel approach for predicting vapor–liquid phase equilibrium in binary systems and proposes innovative ideas for investigating phase equilibrium mechanisms and principles.

Interfacial tension and phase equilibria for binary systems containing (CH4-CO2)+(n-dodecane; n-butanol; water)

This study aims to investigate and predict the interfacial tension at elevated pressure for binary systems, that are essential for the ongoing energy transition. A comprehensive review is carried out on saturated mixture densities as well as interfacial tension in binary, ternary and quaternary systems comprising nonpolar and polar compounds at elevated pressures. In view of the research gap especially with regard to quaternary model systems that contain H2O, a hydrocarbon, a gas and a surface-active compound, new experimental and theoretical data on binary systems are presented that are required for systematically approaching the respective quaternary system. Mixture densities are determined for the nonpolar systems CO2+n-dodecane and CH4+n-dodecane, as well as systems comprising n-butanol with CO2 or CH4 at pressures up to 30 MPa in a range of temperatures between 313.15-353.15 K as well as its interfacial tension plus the systems CO2+H2O and CO2+CH4. In order to theoretically determine these properties, the Perturbed Chain Polar Statistical Associating Fluid Theory is applied for describing the bulk phase equilibrium, subsequently being combined with the Density Gradient Theory for calculating the concentrations across the interface from which the interfacial tension is derived. Experimental results are in very good agreement with the simulation as well as previously available data ranging from an absolute average deviation of 0.44 mN/m for CO2+n-butanol to 2.58 mN/m for CO2+water. Furthermore, the simulation is able to reflect the characteristic crossover with respect to pressure and temperature.

Solid–liquid phase equilibria in binary systems with paracetamol

Solid–liquid phase equilibria in binary systems with paracetamol

MESOPHASE AND GLASS FORMATION IN BINARY SYSTEMS CEASIUM AND BARIUM ALKANOATESMESOPHASE AND GLASS FORMATION IN BINARY SYSTEMS CEASIUM AND BARIUM ALKANOATES

Phase equilibria in binary systems of individually non-mesomorphic components: propionates, isobutyrates, butyrates and valerates of cesium and barium at temperatures from 20 to 400 °C have been investigated by the me­thods of differential thermal analysis and polarization polythermal microscopy. In all systems, the formation of intermediate li­quid-crystalline solutions of smectic modification (type A) was established. The tempe­rature-concentration regions of the formation of ionic liquid crystals and glasses are determined. The studies carried out show that in binary systems of cesium and barium alkanoates interme­diate liquid-crystal solutions are generated due to the latent mesomorphism of the correspon­ding cesium alkanoate and due to the eutectic decrease in liquidus temperatures in the binary systems. The thermal stability of the induced mesophase in the case of systems of the consi­dered type is influenced by the following factors: the degree of ordering of the melt, which correlates with the length of the alkyl chain of the alkanoate anion, and a decrease in the temperatures of the liquidus line relative to the latent clearing temperature. The possible influence of compounds melting congruently or incongruently, formed in binary systems, should also be taken into account. Experimental data indicate the largest temperature-concentration range of the mesophase in the butyrate system, where there are the most favorable conditions for the implementation of intermediate li­quid crystal solutions. Such conditions are the lar­gest decrease in liquidus temperatures in a series of systems relative to the latent clearing point, as well as an additional increase in thermal stability due to the formation of a congruently melting compound of anisometric structure. In the case of the valerate system, a certain increase in anisotropy in comparison with the butyrate system is leveled by high liquidus temperatures; here is the narrowest region of existence of the intermediate mesophase due to its thermal destabilization.

Experimental analysis of vapour-liquid phase equilibria for binary systems of diethyl carbonate with methyl, ethyl, isopropyl, n-butyl and isoamyl acetates at 95 kPa

Experimental analysis of vapour-liquid phase equilibrium (VLE) for five binary pairs of diethyl carbonate (DEC) with methyl acetate, ethyl acetate, isopropyl acetate, n-butyl acetate and isoamyl acetate was carried out in this study. VLE data were generated experimentally at local atmospheric pressure of 95 kPa in a glass dynamic recirculation still. Reliability of data was checked with the thermodynamic consistency tests by Van Ness, infinite dilution, pure component and mean absolute deviation test. Experimental data was found to be thermodynamically consistent with all tests and data was regressed with Wilson, NRTL and UNIQUAC activity coefficient models to determine binary interaction parameters. Binary pair of DEC with n-butyl acetate has shown azeotropic behaviour with minimum boiling azeotrope and a close-boiling behaviour through-out the composition range. No azeotropic behaviour was observed for the rest of the binary pairs.

Анализ фазовых равновесий в тройной системе Ge–P–Sn

На основании анализа характера фазовых равновесий в двойных системах, ограняющих диаграмму состояний тройной системы Ge – P – Sn, предложены теоретически возможные схемы ее фазового субсолидусного разграничения. Исследование методом рентгенофазового анализа образцов, принадлежащих политермическим сечениям Sn4P3-Ge, Sn4P3-GeP, показало, что разделение трехкомпонентной диаграммы состояния ниже солидуса осуществляется с помощью сечений Sn4P3-Ge, Sn4P3 -GeP и SnP3-GeP. Построенная по данным дифференциального термического анализа фазовая диаграмма сечения Sn4P3-Ge представляет диаграмму эвтектического типа с координатами эвтектической точки 800 К, 15 mol % Ge.
 
 
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Experimental Data of Fluid Phase Equilibria- Correlation and Prediction Models: A Review

The examples of phase equilibria in binary systems, solid/liquid (SLE), liquid/liquid (LLE), vapor/liquid (VLE), as well as liquid/liquid equilibria in ternary systems mainly containing ionic liquids (ILs), or the infragrance materials, or pharmaceuticals with molecular organic solvents, such as an alcohol, or water, or hydrocarbons, are presented. The most popular correlation methods of the experimental phase equilibrium data are presented, related to the excess Gibbs free energy models such as Wilson, universal-quasichemical, UNIQUAC and non-random two-liquid model, NRTL as well as several popular theories for the modeling of the phase equilibria and excess molar enthalpy, HE in binary or ternary mixtures are presented: the group contribution method (Mod. UNIFAC) and modified UNIFAC model for pharmaceuticals and lattice theory based on non-random hydrogen bonding (NRHB). The SLE, LLE, or VLE and HE of these systems may be described by the Perturbed-Chain Polar Statistical Associating Fluid Theory (PC-SAFT), or a Conductor-like Screening Model for Real Solvents (COSMO-RS). The examples of the application of ILs as extractants for the separation of aromatic hydrocarbons from alkanes, sulfur compounds from alkanes, alkenes from alkanes, ethylbenzene from styrene, butan-1-ol from water phase, or 2-phenylethanol (PEA) from water are discussed on the basis of previously published data. The first information about the selectivity of extrahent for separation can be obtained from the measurements of the limiting activity coefficient measurements by the gas–liquid chromatography technique. This review outlines the main research work carried out over the last few years on direct measurements of phase equilibria, or HE and limiting activity coefficients, the possibility of thermodynamic modeling with emphasis on recent research achievements and potential for future research.

Extraction of 2-Phenylethanol (PEA) from Aqueous Solution Using Ionic Liquids: Synthesis, Phase Equilibrium Investigation, Selectivity in Separation, and Thermodynamic Models.

This study assessed the effect of ionic liquids (ILs) on extraction of 2-phenylethanol (PEA) from aqueous phase. It consists the synthesis of four new ILs, their physicochemical properties, and experimental solubility measurements in water as well as liquid-liquid phase equilibrium in ternary systems. ILs are an important new media for imaging and sensing applications because of their solvation property, thermal stability, and negligible vapor pressure. However, complex procedures and nonmiscibility with water are often required in PEA extraction. Herein, a facile and general strategy using four ILs as extraction media including the synthesis of new bis(fluorosulfonyl)imide-based ILs, 1-hexyl-methylmorpholinium bis(fluorosulfonyl)imide, [HMMOR][FSI], N-octylisoquinolinium bis(fluorosulfonyl)imide, [OiQuin][FSI], 1-butyl-1-methylpyrrolidinium bis(fluorosulfonyl)imide, [BMPYR][FSI], and N-triethyl-N-octylammonium bis(fluorosulfonyl)imide, [N2228][FSI], were investigated. The thermal properties, density, viscosity, and surface tension of new ILs were measured. Calorimetric measurements (DSC) were used to determine the melting point and the enthalpy of melting as well as the glass transition temperature and heat capacity at glass transition of the ILs. The phase equilibrium in binary systems (IL + PEA, or water) and in ternary systems {IL (1) + PEA (2) + water (3)} at temperature T = 308.15 K and ambient pressure are reported. All systems present liquid-liquid equilibrium with the upper critical solution temperature (UCST). All ILs revealed complete miscibility with PEA. In all ternary systems immiscibility gap was observed, which classified measured systems as Treybal's type II. The two partially miscible binaries (IL + water) and (PEA + water) exist in these systems. The discussion contains the specific selectivity and the solute distribution ratio of separation for the used ILs. The commonly used NRTL model was used for the correlation of the experimental binary and ternary systems with acceptable root-mean-square deviation. The prediction of binary and ternary compositions was provided with acceptable deviations using COSMO RS. The data of ternary LLE show the possible use of [HMMOR][FSI] as a good entrainer for the separation of PEA from water using solvent extraction.

Growth Mechanism and Luminescent Properties of Amorphous SiOx Structures via Phase Equilibrium in Binary System.

Balloon whisk-like and flower-like SiOx tubes with well-dispersed Sn and joining countless SiOx loops together induce intense luminescence characteristics in substrate materials. Our synthetic technique called “direct substrate growth” is based on pre-contamination of the surroundings without the intended catalyst and source powders. The kind of supporting material and pressure of the inlet gases determine a series of differently functionalized tube loops, i.e., the number, length, thickness, and cylindrical profile. SiOx tube loops commonly twist and split to best suppress the total energy. Photoluminescence and confocal laser measurements based on quantum confinement effect of the embedded Sn nanoparticles in the SiOx tube found substantially intense emissions throughout the visible range. These new concepts related to the synthetic approach, pre-pollution, transitional morphology, and permeable nanoparticles should facilitate progress in nanoscience with regard to tuning the dimensions of micro-/nanostructure preparations and the functionalization of customized applications.

Phase equilibria in binary systems formed by a hyperbranched aliphatic polyester and alcohols

Hyperbranched polymers (HBPs) possess unique properties that make them interesting for use in a wide variety of applications. Examples are their potential use in separation processes such as distillation and solvent extraction. The design of the separation process demands a thorough knowledge of the phase behaviour in systems composed of HBPs and common organic solvents. This contribution reports on the phase behaviour in binary systems formed by the hyperbranched polyester H3200 and alcohols. Both liquid–liquid and solid–liquid equilibria were investigated. It was shown that a small amount of water present in these systems has a significant impact on the extent of the liquid–liquid phase split. At temperatures below 325 K alcohol solutions of H3200 form gels over a wide concentration range of the polymer. It seems that in these systems gelation results from arrested phase instability.

Phase equilibrium in binary systems of ionic liquids, or deep eutectic solvents with 2-phenylethanol (PEA), or water

The production of 2-phenylethanol (PEA), an important flavor and fragrance compound, with a rose-like odor has been significantly increased last decade. The aim of this study was to propose a new ionic liquids (ILs) and Deep Eutectic Solvents (DES) as an entrainers in a biphasic systems in possible bioproduction of PEA. ILs and DESs reveal many unique properties which make them very interesting for applications in modern ‘green’ technologies. In present contribution we have reported new experimental results on (solid, or liquid + liquid) phase equilibrium (SLE/LLE) measurements of eight binary systems composed of pyrrolidinium-based, imidazolium-based and phosphonium-based ILs (namely: 1-butyl-1-methylpyrrolidinium tricyanomethanide, [BMPYR][TCM], 1-butyl-1-methylpyrrolidinium tetracyanoborate, [BMPYR][TCB], 1-butyl-1-methylpyrrolidinium trifluoromethanesulfonate (triflate), [BMPYR][CF3SO3], 1-butyl-1-methylpyrrolidinium tris(pentafluoroethyl)trifluorophosphate, [BMPYR][FAP], and 1-butyl-1-methylpyrrolidinium dicyanamid, [BMPYR][DCA], 1-butyl-1-methylimidazolium tricyanomethanide, [BMIM][TCM] and trihexyl-tetradecyl-phosphonium tricyanomethanide, [P6,6,6,14][TCM] with PEA and water. The complete miscibility with PEA was observed for [BMPYR][FAP], [BMPYR][DCA] and [BMIM][TCM]. The best solubility of solid IL in PEA was found for [BMPYR][TCM]. Complete miscibility with water was observed for [BMPYR][CF3SO3] and [BMPYR][DCA]. Moreover, new results on SLE/LLE of six binary systems of DES: {choline chloride + resorcinol (1:4), or phenylacetic acid (1:1), or phenylacetic acid (1:2), or oxalic acid (1:1), or malonic acid (1:1)} and {acetylocholine chloride + 1,10-decanediol} are shown. The initial information of the eutectic temperature and composition was found for {acetylocholine chloride + 1,10-decanediol}. Complete miscibility with PEA was observed only for {choline chloride + malonic acid (1:1)}. Simple eutectic systems of phase behavior with complete miscibility in the liquid phase for all the later mixtures were observed. The solubility of DES in water reveals SLE/LLE phase equilibrium. The best solvent was {choline chloride + malonic acid (1:1)}. The modeling of liquidus curves of ILs in PEA was proposed with excess Gibbs energy model, NRTL. It correlates the solubility with the average root mean square deviation, σT = 0.78 K. To our best knowledge this is the very first paper when the SLE/LLE of PEA and water have been tested for systems with ILs and DESs.

Solubility of pharmaceuticals in water and alcohols

The aim of this study was to examine the phase equilibria in binary systems: {pharmaceutical, Ph (1)+water, or alcohol (2)}. This work was carried out for four pharmaceuticals, Phs: aminophylline and (−) lobeline hydrochloride, perphenazine and indomethacin. Solubility of tested Phs was determined in three solvents. Water, the main component of any living organism. Ethanol, substance corresponding to the transport of the Ph in the body, and 1-octanol, a model compound of human cell and skin membrane. All studied Phs have aromatic structure and functional groups typical for drugs.The differential scanning microcalorimetry technique, DSC was used to measure basic thermal properties of pure drugs, i.e., temperatures of fusion, enthalpy of fusion, glass-transition temperatures and heat capacity change at the glass-transition temperature. Molar volumes have been calculated with Barton group contribution method. The Bates–Schwarzenbach method enabled us to determinate the pKa of used Phs. These values are important because it may designate the Phs dosage and the activity at the certain pH. The pKa experimental values are slightly different than the literature data which was already published as a results of different experimental methods. In this work, altogether 12 binary systems {Ph (1)+solvent (2)} were studied with the use of dynamic and spectrophotometric method. Three GEx thermodynamic models were used to correlate the experimental data: Wilson equation, NRTL equation and UNIQUAC equation.

Experimental Measurement and Modeling of Phase Diagrams of Binary Systems Encountered in the Gasoline Desulfurization Process Using Ionic Liquids

The aim of this work is to investigate phase equilibrium of binary systems encountered in the extractive desulfurization of gasoline and diesel using ionic liquids. This work is focused on two ionic liquids: 1,3-dimethylimidazolium methylphosponate [DMIM][Ph] and 1-ethyl-3-methylimidazolium thiocynate [EMIM][SCN]. Vapor–liquid equilibrium (VLE) measurements on binary systems of ionic liquids with various solutes including thiophene, pyridine, toluene, and water at pressures close to the atmospheric pressure were performed and correlated by the PC-SAFT equation of state. The molecular parameters of pure ILs were determined from experimental density data, whereas binary interaction parameters kij were optimized on experimental VLE data. The eight binary mixtures: {thiophene+ILs}, {pyridine+ILs}, {toluene+ILs}, and {water+ILs} studied in this paper were accurately described by the PC-SAFT equation of state.

Classification of global fluid-phase equilibrium behaviors in binary systems

The study of phase equilibria is one of the most important sources of information about the nature of intermolecular forces in liquids and their mixtures and is of the highest importance for designing and optimizing processes. Many of the main features of vapor–liquid and liquid–liquid phase behavior were well characterized experimentally during the early part of the 20th century, and many equations of state were developed to reproduce the many types of phase diagrams observed for binary systems. In spite of the quasi-infinite number of possible configurations and rearrangements of fluid–fluid equilibrium phase diagrams, this paper presents a near-exhaustive classification scheme of fluid phase equilibria in binary systems. It starts from the one proposed by Van Konynenburg and Scott and brings it up-to-date by detailing the progress carried out on this topic since their classification scheme was first proposed. The second part of this paper is devoted to describing the transitions between the various types of systems.

Thermodynamic modeling based on particle swarm optimization to predict phase equilibrium of binary systems containing ionic liquids

Vapor–liquid equilibrium data of binary mixtures containing imidazolium ionic liquids were correlated using the UNIQUAC activity coefficient model optimized with a particle swarm algorithm. Twenty eight binary systems taken from literature were selected for this study, and the new optimization algorithm was used to determine the binary interaction parameters of each system. The results given by the model have been compared with experimental data, and show that the optimized UNIQUAC model is a good model to correlate and predict the vapor–liquid equilibrium for this type of systems. • PSO was used for the thermodynamic modeling of the vapor–liquid phase of 28 mixtures containing ionic liquids. • Binary interaction parameters of the UNIQUAC activity coefficient model were optimized. • The proposed model is reliable enough to estimate the vapor–liquid phase equilibrium with an average deviation of 3%.

A simple and unified algorithm to solve fluid phase equilibria using either the gamma–phi or the phi–phi approach for binary and ternary mixtures

A new algorithm is proposed for calculating phase equilibria in binary systems at a fixed temperature and pressure. This algorithm is then extended to ternary systems (in which case, the mole fraction of one constituent in a given phase must be fixed in order to satisfy the Gibbs’ phase rule). The algorithm has the advantage of being very simple to implement and insensitive to the procedure used to initialize the unknowns. Most significantly, the algorithm allows the same solution procedure to be used regardless of the thermodynamic approach considered (γ–φ or φ–φ), the type of phase equilibrium (VLE, LLE, etc.) and the existence of singularities (azeotropy, criticality and so on).

Vapor–Liquid Equilibria, Excess Enthalpy, and Excess Volume of Binary Mixtures Containing an Alcohol (1-Butanol, 2-Butanol, or 2-Methyl-2-butanol) and 2-Ethoxy-2-methylbutane

Pure component vapor pressure between (324 and 374) K, isothermal vapor–liquid equilibria at 358 K, excess enthalpy, excess volume, and density at 298 K were determined for three binary systems consisting of 2-ethoxy-2-methylbutane + 1-butanol, + 2-butanol, or + 2-methyl-2-butanol. Excess enthalpy was measured with a microflow calorimeter and excess volume with a vibrating-tube densimeter. A recirculation still was used to measure both the pure component vapor pressures and the phase equilibria of binary systems. The measured data were well-represented with local composition models. A maximum pressure azeotrope was observed for all measured systems.

Phase Equilibria of CO2 + n-Alkane Binary Systems in Wide Ranges of Conditions: Development of Predictive Correlations Based on Cubic Mixing Rules

The phase equilibria of binary CO2 + n-alkane mixtures have been studied by an important number of authors, both experimentally and using different types of thermodynamic models. Modeling studies of the phase behavior of such highly nonideal systems have generally achieved only partially accurate results in the correlation of phase equilibrium data when considering wide ranges of temperature, pressure, and n-alkane molecular weight. In this study, a predictive correlation for the phase behavior of CO2 + n-alkane systems, based on a three-parameter cubic equation of state (EOS), that is, the RK-PR EOS, coupled to cubic mixing rules (CMRs), is developed and tested. CMRs have been shown to be capable of an accurate correlation of the phase equilibria asymmetric CO2 + n-alkane binary systems, in wide ranges of temperature and pressure, when using system-specific interaction parameters. For developing the predictive correlation a critical review of published experimental data for the series was carried out, covering a total of about 100 references. An important degree of inaccuracy or scatter is often found when comparing data sets from different laboratories, specially for the more asymmetric systems (CO2 + a long chain n-alkane). Tables of references covering CO2 + n-alkane systems from C1 to C36 are presented for different types of experimental data, including critical end points (CEPs), critical points, liquid–liquid–vapor (LLV) equilibrium, and isobaric (Txy), isothermal (Pxy), and isoplethic (PT) two-phase equilibrium data sets. Examples of disagreement between different sets of data are presented and discussed. In some cases, a decision concerning the identification of the set that should be regarded as the most reliable, can be based on the experimental method employed, on the purity of the n-alkane, and on the observation of other data for conditions, and/or systems in the series, which are close to those of the data set under scrutiny. Nevertheless, the availability of such information is not enough, in other cases, to assess the quality of a given data set, where we have either different data sets in disagreement or a unique set, for which we are in doubt about its accuracy. In such situation, a predictive correlation for the whole series of binary systems is helpful to make a decision on the possible level of reliability of a given phase equilibrium data set. The present study is useful both to make decisions on conflicts between contradictory phase equilibrium data sets and to predict the phase equilibria of binary systems that have no experimental information available in the literature.

Thermodynamic prediction of vapor–liquid equilibrium of supercritical CO2 or CHF3+ionic liquids

A new approach for the development of a method to predict the vapor–liquid equilibria of binary systems of supercritical CO2 or CHF3 + ionic liquids is presented. Quantitative Structure–Property Relations (QSPR) based on the Conductor-like Screening Model-Segment Activity Coefficient (COSMO-SAC) and the artificial neural network (ANN) were implemented to predict the infinite dilution activity coefficient using a database of 1567 points. The infinite dilution activity coefficients were used to determine the binary interaction parameters of the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) equation of state. This thermodynamic model was applied to the whole interval of concentrations of binary mixtures, and the results were compared to experimental data reported in the literature. The applicability of the predictive method is demonstrated for binary systems, involving supercritical CO2 or CHF3 + ionic liquids. Furthermore, the parameterization allows extrapolations in temperature. This study shows that the neural network model predicts well, with a mean square error value of 0.056, while the PC-SAFT model predicts the phase equilibria of binary systems with deviations ranging from 5 up to 70%. The prediction was more reliable at pressures lower than 150 bar.

Particle swarm modeling of vapor-liquid equilibrium data of binary systems containing CO2 + imidazolium ionic liquids based on bis[(trifluoromethyl)sulfonyl]imide anion

Based on particle swarm optimization (PSO), a thermodynamic modeling for the vapor-liquid equilibrium of binary mixtures of carbon dioxide with ionic liquids is presented. The Peng-Robinson equation of state with the Wong-Sandler mixing rules is used to evaluate the fugacity coefficient of the systems. Simulations are carried out in five systems containing 1-alkyl-3-methylimidazolium ionic liquids based on bis[(trifluoromethyl)sulfonyl]imide anion. Then, PSO algorithm was used to minimize the difference between calculated and experimental bubble pressure, and calculate the interaction parameters and the excess Gibbs free energy for all systems used. The results show that the bubble pressures were correlated with low deviations between experimental and calculated values. These deviations show that the PSO algorithm is the preferable method to optimize the interaction parameters of the phase equilibria of binary systems of supercritical carbon dioxide with ionic liquids, and can be used for other similar systems.