Vapor-liquid Equilibria Of Binary Systems Research Articles

Vapor-liquid equilibrium for binary systems containing n-alkanes and cycloalkanes

In this study, VLE data for five binary systems comprising n-octane, n-nonane, methylcyclopentane, and methylcyclohexane were measured using the total pressure method at 393.15 K, 433.15 K, and 473.15 K. The NRTL-HOC and the UNIQUAC-HOC models were used to successfully correlate all VLE data and determine binary interaction parameters. No azeotropic behavior was observed in any of the binary systems under the operating conditions. The predictive UNIFAC-DMD and COSMO-SAC models were implemented to predict binary VLE phase diagram and unveiled the mechanism of the separation efficiency of alkanes–cycloalkanes. Through the examination of the COSMO-SAC based molecular surface charge profile (σ-profile), the variance in non-hydrogen bonding segments within the σ-profiles of the analyzed alkanes determines both the strength of electrostatic interactions and the temperature-dependent VLE separation behaviors. The results indicate that σ-profile could be suggested as a good indicator to assess operating conditions of the alkanes VLE separation.

High-pressure vapor-liquid equilibrium of hydrogen and diesel components: Maximum likelihood implicit estimation of equation-of-state binary parameters

Due to increasing environmental requirements and efforts to improve fuel quality, hydro-processing has attained worldwide importance as a critical oil refining operation. Hydro-processing involve hydrogenation of oil fractions and subsequent separations at high-temperature, high-pressure and high hydrogen fugacity. Thus, effective thermodynamic modeling of hydro-processing systems allows accurate vapor and liquid property calculation to solve mass-energy hydro-processing balances. In this work, experimental data of high-pressure vapor-liquid equilibrium of binary systems consisting of hydrogen and Diesel hydrocarbons were compiled and used to statistically calibrate classical cubic equations-of-state and variants with different alpha functions. To accomplish this, the Maximum Likelihood Principle was used to conduct the implicit estimation of binary interaction parameters of hydrogen and each one of 22 hydrocarbons (paraffin, naphthenic and aromatic hydrocarbons) typical of Diesel fractions. Several statistical estimators were used to evaluate the estimated parameters as well as to test the insertion of a second binary interaction parameter or temperature dependence. In general, the FT Equation-of-State – i.e., the Peng-Robinson Equation-of-State using Fu & Tan alpha function for hydrogen – attained the best adherence to data and this adherence is improved by using two binary interaction parameters per pair or imposing temperature-dependence on the binary interaction parameter.

Molecular Modeling of Double Retrograde Vaporization Using Monte Carlo Simulations and Equations of State.

Vapor-liquid equilibria of binary systems consisting of a low-boiling (i.e., more volatile) and a high-boiling compound may exhibit unexpected behavior near the critical point of the low-boiling compound. Near the critical temperature of the low-boiling compound and for compositions rich in the low-boiling compound, increasing the pressure may result in multiple crossings of the dew- and bubble-point curves. This phenomenon is often called double retrograde vaporization (or condensation) and may play a role in oil field operations and gas transport through pipelines, but the microscopic driving forces for the unusual shape of the dew-point curve are not well understood. Monte Carlo simulations in the constant-pressure, constant-temperature Gibbs ensemble using the united-atom version of the TraPPE force field were carried out for the methane/n-butane mixture at temperatures ranging from 0.95 to 1.05 of the reduced (T/Tc) temperature of methane. The simulations predict a wealth of additional thermodynamic data (densities and free energies of transfer) and structural data that are used to provide much needed molecular-level insights into the fluid properties associated with double retrograde vaporization. Simulated thermodynamic data are also compared with calculations using the Peng-Robinson and PC-SAFT equations of state.

Isobaric Vapor-Liquid Equilibria for Binary System of Ethanol (1) + Eugenol (2) at 400 and 760 mmHg

Eugenol is the main component of clove oil, while the main impuritis of it is β-caryophyllene. Eugenol with a purity higher than 98% has a higher price than low purity eugenol. Thus, further eugenol purification process is needed. Common purification processes are extraction and distillation. In the design and simulation of the distillation process it requires a knowledge of Vapor-Liquid Equilibrium (VLE) data from a mixture of components to be separated (eugenol and ethanol) as the result of extraction process. In this work, the experimental VLE data were measured for binary mixtures of ethanol(1) + eugenol(2) at 400 and 760 mmHg. The apparatus used for this experiment is an othmer still equipped with a vacuum pump and a manometer. The experiments were performed to obtain equilibrium data (T), component concentrations in liquid phase (x), and in vapor phase (y). The binary VLE data were correlated with the Wilson, NRTL and UNIQUAC models to obtain the binary parameters. The reliability of these models were tested by comparing with experimental results using Root Mean Square Deviation (RMSD). For the system and the operation condition studied, the Wilson, NRTL and UNIQUAC models suited well and give satisfactory results based on the RMSD values .

Isobaric Vapor-Liquid Equilibria for Binary System of Ethanol (1) + Eugenol (2) at 400 and 760 mmHg

Eugenol is the main component of clove oil, while the main impuritis of it is β-caryophyllene. Eugenol with a purity higher than 98% has a higher price than low purity eugenol. Thus, further eugenol purification process is needed. Common purification processes are extraction and distillation. In the design and simulation of the distillation process it requires a knowledge of Vapor-Liquid Equilibrium (VLE) data from a mixture of components to be separated (eugenol and ethanol) as the result of extraction process. In this work, the experimental VLE data were measured for binary mixtures of ethanol(1) + eugenol(2) at 400 and 760 mmHg. The apparatus used for this experiment is an othmer still equipped with a vacuum pump and a manometer. The experiments were performed to obtain equilibrium data (T), component concentrations in liquid phase (x), and in vapor phase (y). The binary VLE data were correlated with the Wilson, NRTL and UNIQUAC models to obtain the binary parameters. The reliability of these models were tested by comparing with experimental results using Root Mean Square Deviation (RMSD). For the system and the operation condition studied, the Wilson, NRTL and UNIQUAC models suited well and give satisfactory results based on the RMSD values .

Vapor-liquid equilibrium of binary systems containing low GWP refrigerants with cubic equations of state

Different Cubic Equations of State (CESs) were used to represent Vapor-Liquid Equilibrium (VLE) of binary systems containing low Global Warming Potential (GWP) refrigerants. The calculated VLE data from some of the widely used CESs were compared with the experimental data collected from the literature. To extend CESs to binary systems, van der Waals one-fluid mixing rules with a single binary interaction parameter were used. Although the deviations between the experimental and calculated values are generally low, a comparison of the results was performed to find the most accurate CES for VLE of the studied binary systems.

Vapor-liquid equilibrium of binary systems with EoS/GE models at low pressure: Revisiting the Heidemann-Kokal Mixing Rule

In this work, a ϕ-ϕ approach is tested in the description of vapor-liquid equilibrium of 18 different binary systems by means of EoS/GE type models. These models combine the potentialities of the Peng-Robinson cubic equation of state and the UNIQUAC local composition model. The focus is on the Heidemann-Kokal Mixing Rule, whose derivation is presented. Systems including nonpolar - nonpolar, weakly polar - weakly polar, water - weakly polar, nonpolar - weakly polar, weakly polar - strongly polar and strongly polar - strongly polar compounds, besides systems involving immiscible components and carboxylic acids, were evaluated. Binary interaction parameters of the UNIQUAC model were estimated using a stochastic particle swarm algorithm, coupled to a Quasi-Newton deterministic algorithm. As a result, average deviations of less than 2% and 1% were obtained for vapor phase composition and bubble temperature or pressure correlation, respectively. The proposed modeling was efficient in the treatment of all evaluated systems and appears as a good alternative for the development of new models.

Isobaric vapor-liquid equilibrium for binary system of methyl caprate + methyl laurate at 2, 4 and 6 kPa

In this work, we measured the isobaric vapor-liquid equilibrium (VLE) data for the binary system of methyl caprate (1)+methyl laurate (2) at 2,4 and 6kPa with a modified Othmer still. The point consistency test of Van Ness test method was applied to check the thermodynamic consistency of all the experimental values, which guaranteed the reliability of our measurements. Afterwards, the experimental data were regressed by two activity coefficient models (Wilson, NRTL). Furthermore, we made the data prediction with the group contribution method (UNIFAC) and the COSMO-SAC model. The results of all the regressions and predictions are satisfying and reasonable, while the results provided by the NRTL model are relatively better than the other three models, with the root mean square deviations of temperature and vapor-phase mole fraction less than 0.33K and 0.0069, respectively.

Isobaric vapor-liquid equilibrium for binary system of methyl caprylate + methyl caprate at 2, 6 and 10 kPa

The isobaric vapor-liquid equilibrium data for the binary system methyl caprylate (1)+methyl caprate (2) at 2, 6 and 10kPa were measured with a modified Othmer still. All the experimental data were verified to be thermodynamically consistent according to the Van Ness test method. Two activity coefficient models (Wilson and NRTL) were applied to regress the experimental values. Furthermore, the group contribution method (UNIFAC) and the COSMO-SAC model were also employed to predict vapor-liquid equilibrium data. The four models reproduced the experimental values very well, while the NRTL model provided a slightly better result than the other three models, with the root mean square deviations of temperature and vapor-phase mole fraction less than 0.36K and 0.0042, respectively.

Isobaric Vapor-Liquid Equilibrium of Binary Systems: p-Xylene + (Acetic Acid, Methyl Acetate and n-Propyl Acetate) and Methyl Acetate +n-Propyl Acetate in an Acetic Acid Dehydration Process

The vapor-liquid equilibrium data of four binary systems (acetic acid +p-xylene, methyl acetate +n-propyl acetate, n-propyl acetate +p-xylene and methyl acetate +p-xylene) are measured at 101.33 kPa with Ellis equilibrium still, and then both the NRTL and UNIQUAC models are used in combination with the HOC model for correlating and estimating the vapor-liquid equilibrium of these four binary systems. The estimated binary VLE results using correlated parameters agree well with the measured data except the methyl acetate +p-xylene system which easily causes bumping and liquid rushing out of the sampling tap due to their dramatically different boiling points. The correlation results by NRTL and UNIQUAC models have little difference on the average absolute deviations of temperature and composition of vapor phase, and the results by NRTL model are slightly better than those by UNIQUAC model except for the methyl acetate +n-propyl acetate system, for which the latter gives more accurate correlations.

Vapor-Liquid Equilibrium for Binary Systems of Methyl Ethyl Ketone and Methyl Isobutyl Ketone

Atmospheric vapor-liquid equilibrium data of methyl ethyl ketone (MEK) - methyl isobutyl ketone (MIBK) were measured using an improved Rose still and were used to recover the parameters of NRTL and UNIQUAC models. The results show that the simulated results agree well with the experimental data. The mean temperature variation is 0.14 °C and the mean mole fraction variation is 0.0023 using UNIQUAC model while the mean temperature variation is 0.17 °C and the mean mole fraction variation is 0.0025 using NRTL model. Both models can be used to calculate the atmospheric vapor-liquid equilibrium data of MEK - MIBK.

Activity coefficient models to describe isothermal vapor-liquid equilibrium of binary systems containing ionic liquids

Isothermal vapor-liquid equilibrium data of binary mixtures containing ionic liquids are correlated using three activity coefficient models: UNIQUAC, Wilson, and NRTL. Twenty binary systems taken from the literature were selected for this study. A genetic algorithm is used to determine the interaction parameters for the three models. The results given by the three models have been compared with experimental data, and show that the UNIQUAC model is the best method to correlate and predict the vapor-liquid equilibrium of this type of systems.

Phase Equilibrium Calculations in Mixtures Containing Caprolactam with a UNIFAC Model

An extended liquid-liquid equilibrium (LLE) UNIFAC model is proposed to describe phase equilibria of mixtures containing caprolactam. In this model, caprolactam is introduced as a new group. New group interaction parameters are calibrated from 156 sets of liquid-liquid equilibrium data. The present model gives satisfactory correlation and prediction in liquid-liquid equilibrium, including quaternary systems containing the mixed solvent of an alcohol and an alkane. The model can be applied to predict caprolactam solubility in water and benzene accurately. Freezing point and vapor-liquid equilibrium of binary systems containing caprolactam are also predicted with the extended LLE UNIFAC model. Satisfactory prediction results are obtained.

Measurements of Vapor-liquid Equilibria for Binary Systems Including Tetrahydropyran

分離溶媒，反応溶媒などへの応用が期待されているテトラヒドロピラン（THP）を含む系の気液平衡データは重要であるにもかかわらず，ほとんど報告されていない。三つの2成分系（THP＋n-ヘプタン，THP＋トルエン，THP＋水）に対して40.00～98.66 kPa間の6圧力における沸点をホールドアップ補償型エブリオメーターによって測定した。THP＋トルエンが非共沸系であるのに対し，THP＋n-ヘプタンとTHP＋水は共沸系であること，およびTHP＋水は不均一系であることが分かった。測定した沸点データに基づきNRTL（Non Random Two-Liquid）式を用いて気液平衡の決定を行った。決定したNRTLパラメーターによる沸点の計算値と実測値との絶対算術平均偏差はTHP＋n-ヘプタン，THP＋トルエン，THP＋水系でおのおの0.08，0.09，1.75 Kであった。また，CH2，ArCH，H2O，pyranグループのASOG（Analytical Solution of Groups）グループ対パラメーターを決定した。さらに，THPと溶媒に対して無限希釈過剰部分モルエントロピーとエンタルピーを求めた。

Prediction of vapor-liquid equilibria of binary systems using PRSV equation of state and Wong-Sandier mixing rules

The Peng-Robinson equation of state modified by Stryjek and Vera (1986) has been used with Wong-Sandier mixing rules (1992) to predict vapor-liquid equilibria of forty-three binary mixtures involving organic alcohols, esters, ketones, amines, etc. The Wong-Sandier mixing rules are theoretically correct in the sense that they reproduce quadratic composition dependence of the second virial coefficient. However, recent studies indicate that the basic premises of these rules break down for highly asymmetric systems and at high pressures. The systems studied have low to moderate asymmetry. It has been observed that the non random two liquid (NRTL) model provides a good representation of G E models and the results obtained from optimization compare well with those reported in DECHEMA data series in spite of the asymmetry inherent to these systems. The results obtained from this study can be used directly to predict vapor-liquid equilibria involving such systems.

Thermodynamic properties of water + normal alcohols and vapor-liquid equilibria for binary systems of methanol or 2-propanol with water

Experiments have been carried out to determine densities and refractive indices of binary and ternary mixtures of water with normal alcohols (methanol and n-butanol) at 293.15 K. Also, vapor-liquid equilibrium data have been measured for binary systems of methanol-water and 2-propanol-water at atmospheric pressure, from which the excess Gibbs free energy was computed for both systems. The experimental vapor-liquid equilibrium (VLE) data have been compared with those predicted by the Wilson, NRTL and UNIQUAC equations. Agreement has been found to be very satisfactory.

A group-contribution equation of state for predicting vapor-liquid equilibria and volumetric properties of carbon dioxide-hydrocarbons systems

In order to predict the solubility of carbon dioxide in heavy solvents the model excess function-equation of state is applied. It combines an accurate equation of state for carbon dioxide, a Peng-Robinson-type one for hydrocarbons and a Van Laar-like excess function defined at constant packing fraction in which interaction parameters are estimated from contribution-group method. It is shown that the model proposed leads to a good correlation and prediction of vapour-liquid equilibria of binary systems composed of carbon dioxide and hydrocarbons. Its ability for estimating volumetric properties is also analyzed.

Calculation of vapor-liquid equilibria from infinite-dilution excess enthalpy data using the Wilson or NRTL equation

A study was undertaken to determine the potential for using infinite-dilution excess enthalpy data with activity coefficient models to predict vapor-liquid equilibria for binary systems. Expressions for the infinite-dilution reduced excess enthalpies in a binary liquid mixture derived from the Wilson or NRTL equation with temperature-independent parameters are solved for two unknown model parameters given limiting values of reduced excess enthalpy (partial molar excess enthalpy) H E /x 1 x 2 . The Wilson equation is modified using the van der Waals covolume b in place of the pure-liquid molar volume, and an average value of the nonrandomness factor is chosen to obtain a two-parameter NRTL equation. Vapor-liquid equilibria were predicted for 19 isothermal and 8 isobaric binary systems. Good results are generally obtained for nearly ideal systems using either model; however, the Wilson equation is superior for moderately nonideal systems. The temperature-independent Wilson model fails to accurately describe vapor-liquid equilibria for strongly nonideal mixtures with highly unsymmetric excess enthalpy profiles. The proposed method appears to be particularly well suited for estimating phase behavior of environmentally safe refrigerant mixtures

Evaluation of wohl parameters in binary systems

Wisniak, J. and Apelblat, A., 1993. Evaluation of Wohl parameters in binary systems. Fluid Phase Equilibria 90: 1-13. Efficient graphical and numerical methods have been developed to calculate the adjustable parameters in the Wohl equation for vapor-liquid equilibrium in binary systems. The Wohl parameters for about 70 binary systems which represent different types of thermodynamic behavior are presented for the first time.

Application of a generalized Bender equation of state to the description of vapour-liquid equilibria in binary systems

Abstract Platzer, B. and Maurer, G., 1993. Application of a generalized Bender equation of state to the description of vapour-liquid equilibria in binary systems. Fluid Phase Equilibria , 84: 79-110. A recently published four-parameter corresponding state generalization of the Bender equation of state is extended to describe fluid mixtures. Interactions between species of different kinds are considered by introducing three temperature-independent binary parameters which were fitted to experimental vapour-liquid equilibrium data. Altogether 71 binary mixtures are treated. Data correlated by the generalized Bender equation are compared with experimental results and with data correlated by the Lee-Kesler-Plocker (LKP) procedure. The generalized Bender equation needs less computing time than the LKP method and gives a better representation of the experimental data, especially when the components differ considerably in molecular size and/or structure, while there is no or only a minor improvement for simple systems such as argon/methane.