Phase Equilibria Of Binary Mixtures Research Articles

Efficient Approximation with Space Filling Quadtrees: Application to Phase Equilibria in Binary Mixtures.

A relatively succinct set of property calculations can be used to construct efficient (in memory and speed) numerical approximations of that function in a rectangular domain. Through the use of adaptive subdivision with quadtrees and bi-Chebyshev expansions in each leaf, the function can be practically represented to the order of the noise in the function to be approximated. A further benefit is that evaluation of the approximation is noniterative and thus cannot fail to converge (a relatively common problem in thermophysical property libraries, especially for mixtures). Evaluation of the approximation function requires only a few bisection steps to identify the leaf of interest such that evaluation of the approximation data structure takes less than a microsecond. The technique is demonstrated by application to the vapor-liquid-equilibria evaluated with two different models (COSMO-SAC activity coefficient model and multifluid model). For the more expensive COSMO-SAC case, the approximation function is more than 2000 times faster to evaluate, and deviations in pressure are less than a part in 108 which is practically equal to the iteration convergence criterion.

Phase Equilibria of Binary Mixtures of 3-Chloro-2-Hydroxypropyl Methacrylate and 2-N-Morpholinoethyl Methacrylate in Supercritical Carbon Dioxide

Phase Equilibria of Binary Mixtures of 3-Chloro-2-Hydroxypropyl Methacrylate and 2-N-Morpholinoethyl Methacrylate in Supercritical Carbon Dioxide

Predicting the phase equilibria of binary mixtures containing carbon dioxide + n-alkanols from a quadrupolar SAFT-VR approach

The vapor–liquid equilibria of binary mixtures containing carbon dioxide + n-alkanols is studied in the framework of the statistical associating fluid theory for potentials of variable range (SAFT-VR). The effect of the quadrupole moment of carbon dioxide on the phase equilibria is considered into the original SAFT-VR approach by incorporating an additional contribution to the Helmholtz free energy due to quadrupole–quadrupole interactions. The carbon dioxide is modeled as two spherical segments tangentially bonded with an axial quadrupolar moment. The n-alkanol molecules are represented as chains of spherical monomer segments with three associating sites to describe the hydrogen bonding interactions between the molecules. The association effects are taken into consideration by using the first-order thermodynamic perturbation theory of Wertheim. The attractive interactions between monomer segments and site-site associative interactions have been accounted for by using a square-well intermolecular potential. The pure component parameters for carbon dioxide and n-alkanols (from methanol to 1-decanol) are obtained by fitting the SAFT-VR approach to experimental saturated liquid density and vapor pressure. These optimized parameters are used to determine the vapor–liquid equilibria of the mixtures. The pressure-composition and density-composition projections predicted by SAFT-VR for the carbon dioxide + n-alkanols are in good agreement with the experimental data. A significant improvement in the description of the vapor–liquid equilibria of binary mixtures containing carbon dioxide + n-alkanols is obtained with the quadrupolar contribution compared with the results obtained from the original SAFT-VR. The optimized molecular parameters are rescaled in order to determine critical lines and the types of phase behavior. The critical lines and critical points are predicted by the original SAFT-VR approach and the quadrupolar version of the SAFT-VR in good agreement with experimental data. The inclusion of the quadrupolar interactions, present in the carbon dioxide, avoids the treatment of these interactions in an effective way via the square-well potential of variable range. The results of the present work are useful for further exploration of adsorption-extraction of n-alkanols in supercritical fluids.

Accounting for quadrupolar interactions in the CPA equation of state: A modelling approach for binary mixtures of CO2 or benzene with n-alkanes and 1-alkanols

The Cubic Plus Association (CPA) equation of state (EoS) is extended with the theory for quadrupolar molecules of Gross, yielding the CPA-G model. CPA-G is compared to the recently developed qCPA, which uses the polar theory of Larsen and coworkers. Each model requires an additional adjustable parameter for quadrupolar molecules.The models are evaluated by means of their ability to model the phase equilibria of binary mixtures of CO2 or benzene with n-alkanes and 1-alkanols, as well as binary mixtures of quadrupolar molecules. A refined technique of accounting for cross-association in the CO2 + 1-alkanol systems is proposed, allowing an improved description of these systems without the use of a binary interaction parameter. Accounting for cross-association in the benzene + 1-alkanol systems investigated in this work did not lead to improved results. Both CPA-G and qCPA provide significant improvements over nonpolar CPA in both n-alkane and 1-alkanol mixtures, with excellent results obtained in the subcritical region without the use of binary interaction parameters. qCPA continues to provide excellent predictions in the supercritical region, while CPA-G overestimates the solubility pressures in the supercritical region. Both quadrupolar models can qualitatively predict the existence of three-phase equilibrium in the CO2 + n-alkane and CO2 + 1-alkanol systems. The simple combining rules used for cross-quadrupolar interactions in both CPA-G and qCPA do not take molecular orientation into account and are unable to truly capture the phase behaviour in the CO2 + benzene system.

Phase Equilibria in Binary Mixtures of Water with Triglyme and Tetraglyme: Experimental Determination and Thermodynamic Modeling

Because of their many favorable properties and specifically balanced amphiphilic nature, glymes (oligomeric ethylene glycol diethers) are of great technological and theoretical interest. This study...

Phase equilibria modeling of polar systems with Cubic-Plus-Polar (CPP) equation of state

In this study, an equation of state (EoS), Cubic-Plus-Polar (CPP), has been constructed to model phase equilibria of polar and practical systems in a wide range of temperatures and pressures. In the proposed model, Soave-Redlich-Kwong (SRK) EoS takes into account dispersive forces while a set of polar terms was employed to account for dipolar and quadrupolar interactions. By applying these terms, dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole interactions were directly taken into consideration. The CPP EoS with four pure-compound parameters could accurately correlate both vapor pressure and saturated liquid molar volume of studied pure compounds (water, methanol, ethanol, propanol, 2-propanol, 2-butanol, acetone, N-methyl-2-pyrrolidone (NMP), CO2, and H2S). By utilizing two temperature-dependent binary interaction parameters (BIPs), the phase equilibria of binary mixtures including water-CO2, water-H2S, CO2–H2S, methanol-CO2, ethanol-CO2, propanol-CO2, acetone-CO2, water-acetone, ethanol-acetone, water-NMP, 2-propanol-NMP, and 2-butanol-NMP were satisfactorily calculated by the model. Moreover, the proposed model is sufficiently efficient which is capable of representing minimum water mole fraction in the nonaqueous phase of water-CO2 and water-H2S mixtures. Additionally, the CPP EoS accurately predicted the saturated and single phase mixtures densities of water-CO2 mixture. Finally, the solubility values of CO2 and H2S mixtures in water were reasonably predicted by the model.

Comparison between a soft computing model and thermodynamic models for prediction of phase equilibria in binary mixtures containing 1-alkanol, n-alkane, and CO2

In the present work, vapor-liquid equilibrium (VLE) for binary systems containing 1-alkanols, n-alkanes and CO2 were examined to compare the predictions of a soft computing model namely least square support vector machine optimized by coupled simulated annealing (CSA-LSSVM) with the predictions of two thermodynamic models namely perturbed chain statistical fluid association (PC-SAFT) and the Peng Robinson model coupled with Wong-Sandler mixing rule and non-random two liquid model (PR-WS-NRTL). Results revealed that all of the three models provide acceptable predictions for calculation of the vapor-liquid equilibrium data. However, it was found that the CSA-LSSVM model provides better predictions in comparison with the PC-SAFT and PR-WS-NRTL models in the studied systems.

Phase equilibria of binary mixtures with alkanes, ketones, and esters based on the Transferable Anisotropic Mie force field

The transferable anisotropic Mie potential (TAMie) force field is extended to acetates and formates. Intramolecular bending and torsion potentials were obtained from quantum chemical calculations. The parameters defining the Mie pair potential, representing the van der Waals interactions, as well as point charges were optimized. These force field parameters were optimized based on an objective function that considers vapor pressure and liquid density data of several members of one chemical group simultaneously. Like in earlier work, the parameterization is conducted using an analytic equation of state to locally approximate the objective function, ensuring swift convergence of the optimization problem. Acetates, from ethyl ester to n-pentyl ester, have average errors (AAD) of 0.9–6.9% in vapor pressure and of 0.4–0.7% in liquid densities. Formates, from ethyl formate to n-butyl formate have average errors of 2.0–4.2% in vapor pressure and 0.8–1.1% for liquid densities for reduced temperature ranges of T/Tc=0.56 to 0.96, where Tc is the critical temperature of the considered substance. For a binary mixture of ethyl acetate with n-hexane results of the TAMie force field are found in good agreement to experimental data. Because phase equilibrium data for esters with alkanes is scarce, we also investigate mixtures of ketones with alkanes. For mixtures of butanone with n-hexane and butanone with n-heptane, molecular simulations are in satisfying agreement to experimental data when Berthelot-Lorentz combining rules are employed. After adjusting corrections to the Berthelot combining rules the agreement of molecular simulations to experimental data is very good. Additionally to phase equilibria, we calculated excess properties for the mixture of hexane and butanone, which also show very promising results compared to experimental data.

Phase equilibria for binary mixtures of hexane with orthoxylene, metaxylene, and nonane with hexane at 101.3 kPa

Experimental measurements of isobaric vapour, liquid equilibrium boiling point temperature were determined at 101.3 kPa as function of concentration for the two mixtures of hexane with orthoxylene, metaxylene and nonane with hexane by using a continuous recirculation type apparatus. The measured temperature, vapour and liquid concentration (T-x-y) results were correlated with the NRTL and the UNIQUAC models. Each binary mixture system has passed the thermodynamic consistency test of Herington. The activity coefficient values (ᵧ) are greater than unity in three systems for all measurements. The systems studied in the present investigation are hexane with orthoxylene, metaxylene and nonane with hexane show relatively larger deviations from Results' law. All the systems studied here behave like non-ideal solutions. All binary systems investigated were found to be nonazeotropic in nature.

Distinctive Features of the Phase Equilibrium of Mixtures of C1-C3 Hydrocarbons and Nitrogen

Study of the phase equilibrium of natural gas components plays an important role in the designing of LNG plants. Since the problems of equilibrium in two-phase vapor-liquid systems of natural gas hydrocarbons have been extensively studied, investigations are currently focused on multiphase systems of hydrocarbons in mixtures with inorganic substances such as water, carbon dioxide, hydrogen sulfide, hydrogen, and nitrogen. This article dwells on the phase equilibrium of binary mixtures of methane, ethane, and propane with nitrogen. Depending on the ratio of the components and the thermobaric parameters, mixtures of these hydrocarbons with nitrogen may exist as mixtures of mutually soluble components or mixtures of only partially soluble components. The areas of existence of three-phase liquid-liquid-gas system were determined by calculation. The results obtained hold great importance for LNG process design and modernization.

Individualized force fields for alkanes, olefins, ethers and ketones based on the transferable anisotropic Mie potential

Transferable force fields allow the prediction of physical properties for substances with scarce or absent experimental data. For substances with a comprehensive experimental database, however, transferable force fields produce results with higher errors than desired, because the transferable force fields are designed to represent a compromise in correlating the properties of many substances. For applications in chemical engineering, where requirements for accurate vapor pressure correlations and predictions exist, the results from transferable force fields are sometimes insufficient. We individualize the transferable anisotropic Mie force field (TAMie) for 38 substances of various chemical families, by introducing a correction parameter that scales all van der Waals energy parameters εi of the considered substance. We find markedly reduced deviations, mainly in the description of vapor pressures while the errors in liquid density do not change significantly. For polar species, the improvement in vapor pressure is typically a factor four in absolute average deviation to experimental data, when compared to the original TAMie force field. The improved description of pure substances enables more reliable predictions of phase equilibria in binary mixtures. The concept of individualizing substances that are well-characterized by experimental data within a transferable force field is appealing, because the ability to predict mixtures with substances that are not covered by experimental data is preserved.

High pressure phase equilibria for binary mixtures of CO2 + 2-pentanol, vinyl butyrate, 2-pentyl butyrate or butyric acid systems

High pressure phase equilibrium for four binary systems, (CO2 + 2-pentanol, CO2 + vinyl butyrate, CO2 + 2-pentyl butyrate and CO2 + butyric acid), were measured at three temperatures of (313.15, 323.15 and 333.15) K and pressures up to 11 MPa. These four organic compounds are those involved in the kinetic resolution of rac-2-pentanol and their phase equilibria play a significant role in the separation processes of the reaction compounds. Phase behaviour measurements were taken using a synthetic method in a variable volume high-pressure cell. It was checked that the solubility of CO2 in the four systems decreases with increases in temperature at a constant pressure and all systems present type-I phase behaviour within scope of this work. Modifications of Henry's Law and Peng-Robinson and Soave-Redlich-Kwong equations of state combined with the Quadratic mixing rule were used to correlate experimental equilibrium data to determine the phase behaviour of these systems.

Phase Behavior of Binary Mixtures Containing Succinic Acid or Its Esters

This work provides experimental data and thermodynamic modeling on phase equilibria of binary mixtures that are relevant for esterification reactions. The components under investigation include water, succinic acid (SA), ethanol (EtOH), 1-butanol (1-BuOH), and the diesters of SA, namely, diethyl succinate (DES) and dibutyl succinate (DBS), respectively, as well as the organic solvents acetonitrile (ACN) and tetrahydrofuran (THF). Liquid–liquid equilibria (LLE) of water/DBS were measured at ambient pressure for temperatures between 313 and 353 K. Isobaric vapor–liquid equilibria (VLE) were measured for the binary systems ACN/DES, ACN/DBS, 1-BuOH/DBS, and THF/DBS at pressures of 10 or 20 or 30 kPa. Temperature ranges for the isobaric VLE varied between 300 and 500 K. The measured data and phase equilibria reported in literature were accurately modeled using perturbed-chain statistical associating fluid theory (PC-SAFT). For this purpose, pure-component PC-SAFT parameters, which were not already reported in ...

РАВНОВЕСИЕ ЖИДКОСТЬ–ПАР В БИНАРНЫХ СМЕСЯХ ГЕЛИЯ С ОСНОВНЫМИ КОМПОНЕНТАМИ ВОЗДУХА

Compiled equations describing the experimental data of the liquid-vapor phase equilibrium in binary mixtures of helium with nitrogen, oxygen and argon. Equations represents the dependence of liquid or vapor pressure from temperature and composition. At their compiling selected automaticaly most significant coefficients of equation. Standard deviations of the experimental values of the pressure from calculated are equal from 3,5 to 4,5 %. Equations permits to determine the composition or temperature of phases at known values of other parameters of the phase equilibrium.

A comprehensive study of phase equilibria in binary mixtures of carbon dioxide + alcohols: Application of a hybrid intelligent model (CSA-LSSVM)

The phase equilibria of binary mixtures of CO2+alcohols are crucial for the design and optimization of supercritical fluid applications with recently growing reliance on CO2 as the primary solvent at its supercritical conditions. Essentially, alcohols, as cosolvent, contribute to the solvating characteristic of supercritical CO2, which is de facto required for (polar) compound extraction in different industries. However, the proposed, less time-consuming alternatives to experimentally measuring the vapor-liquid equilibrium (VLE) data have been successful in such non-ideal mixtures only to a certain extent. In particular, the observed high deviation in existing models from the experimental values in correlating VLE data necessitates developing an intelligent, self-learning, unique model with more accuracy as well as applicability to a notably broader range of conditions. To this end, we have employed a novel Least-Squares Support Vector Machine (LSSVM) approach as a problem-independent, general-purpose tool. In this research, the LSSVM model is optimized with a Coupled Simulated Annealing (CSA) optimization algorithm. The hybrid model is based on a comprehensive databank of 531 reliable experimental VLE data that cover binary systems of CO2+13 types of short to medium chained alcohols at temperature and pressure overall ranges of 293.15–432.45K and 5.2–213.91bar, respectively. The statistical and graphical error analyses vividly demonstrate the supremacy and robustness of the developed CSA-LSSVM model, particularly compared to the conventional SRK and PR equations of state. However, minor deviations in mixtures containing Pentanol and Hexanol are observed, despite the overall model accuracy that strongly satisfies engineering purposes. We hypothesize that uncertainty in the corresponding experimental data could be the cause; we prove this by applying a Leverage approach, while studying the validity and applicability domain of the model. Furthermore, detailed sensitivity analysis is conducted through a relevancy factor, which suggests that the CO2 mole fraction is the most influential parameter on the studied binary mixture bubble/dew point pressures.

Modeling of vapor–liquid–liquid equilibria in binary mixtures

Vapor compression and Joule–Thomson (JT) cycles provide cooling power at the boiling temperatures of the refrigerants. Maintaining a fixed pressure in the evaporator allows for a stable cooling temperature at the boiling point of a pure refrigerant. In these coolers enhanced cooling power can be achieved by using mixed refrigerants. However, gas mixtures usually do not change their phase at a constant temperature, therefore, the cooling temperature has to be actively controlled. An exception to this rule holds for binary mixtures that can form a vapor–liquid–liquid equilibrium (VLLE).Phase equilibria in binary mixtures are usually modeled based on experimental results only. In the present study only the vapor pressures of the pure mixture components are required. The calculated results of nitrogen–ethane, nitrogen–ethylene, and nitrogen–propane mixtures are compared with experimental data presented in literature showing deviations of less than 1%.

РАВНОВЕСИЕ ЖИДКОСТЬ–ПАР В СМЕСЯХ НЕОНА С АЗОТОМ ЛИБО КИСЛОРОДОМ

Compiled equations describing the experimental data of the liquid-vapor phase equilibrium in binary mixtures of neon with nitrogen and oxygen. Equations represents the dependence of liquid or vapor pressure from temperature and composition. At their compiling the program selected most significant coefficients of equation. Standard deviations of the experimental values of the pressure from calculated are equal from 4,5 to 5,0 %. Equations permits to determine the composition or temperature of phases at known values of other parameters of the phase equilibrium.

Solid–liquid phase equilibria in binary mixtures of functionalized ionic liquids with sugar alcohols: New experimental data and modelling

Solid–liquid equilibrium (SLE) phase diagrams of binary systems composed of dicyanamide ionic liquid and sugar alcohols (meso-erythritol, xylitol and D-sorbitol) are presented. The studied ionic liquids are based on imidazolium cations having in their structure functionalized side chains: allyl, 2-hydroxyethyl, 3-cyanopropyl, 2-chloroethyl. An impact of the terminal group is discussed in terms of molecular interactions (polarity, hydrogen bonding) between ionic liquids and sugar alcohol. Apparent thermodynamic functions of dissolution of sugar alcohols in ionic liquids were calculated with the Van’t Hoff equation. Thermodynamic modelling of the studied SLE phase diagrams with perturbed-chain statistical associating fluid theory (PC-SAFT) is presented. It is proven that accurate correlations of the considered cross-associating systems can be obtained by using relatively simple molecular schemes applied for both ionic liquids and sugar alcohols.

Equations for describing liquid-vapor phase equilibria in binary mixtures

Three forms of equations for describing experimental data on liquid and vapor pressures, depending on temperature and composition at phase equilibria in binary mixtures, are proposed and evaluated. It is determined that the form of equation depends on the relationship between the temperature of a mixture and the critical temperatures of the components of the mixture. Exact data on the phase equilibria in nitrogenoxygen, nitrogen-argon, and oxygen-argon mixtures [1] are approximated to assess the effectiveness of the equations’ forms. It is found that the equations also allow us to determine the phase composition at a given temperature and pressure and temperatures of phases at a given pressure and composition.

Phase Equilibrium of Binary Mixtures ofn-Hexane + Branched Chlorobutanes: Experimental Results and Group Contribution Predictions

In this work the study of the phase equilibrium (experimental and modeled) of three binary mixtures formed by n-hexane and a branched chlorobutane (2-chlorobutane, 1-chloro-2-methylpropane, or 2-chloro-2-methylpropane) is presented. New and consistent experimental vapor–liquid equilibrium data at isothermal conditions T = (288.15, 298.15, and 308.15) K have been obtained and correlated using the Wilson equation. In addition, two group contribution models, modified-UNIFAC (universal functional activity coefficient) and VTPR (volume-translated Peng–Robinson), have been used to predict the vapor–liquid equilibrium of the mixtures. The agreement between experimental results and predicted ones is not satisfactory.