Estimation of VLE of binary systems (tert-butanol + 2-ethyl-1-hexanol) and (n-butanol + 2-ethyl-1-hexanol) using GMDH-type neural network

The group method of data handling (GMDH) method was used to estimate (vapour + liquid) equilibrium (VLE) for the binary systems of (tert-butanol + 2-ethy1-1-hexanol) and (n-butanol + 2-ethy1-1-hexanol). Using this method, a new model was proposed, which is suitable for predicting the VLE data. In this publication, the proposed model was ‘trained’ before requested predictions. The data set was divided into two parts: 70% were used as data for ‘training’ (either 10 or 12), and 30% were used as a test set, which were randomly extracted from the database (either 14 or 16). After the training on the input–output process, the predicted values were compared with those of experimental values in order to evaluate the performance of the GMDH neural network method. The model values showed a very good regression with the experimental results.     

Isobaric vapor–liquid phase equilibria for the binary systems of tert-butanol + 2-ethyl-1-hexanol and n-butanol + 2-ethyl-1-hexanol

Isobaric vapor–liquid equilibria for the binary mixtures of tert-butanol (TBA) + 2-ethyl-1-hexanol and n-butanol (NBA) + 2-ethyl-1-hexanol were experimentally investigated at atmospheric pressure in the temperature range of 353.2–458.2 K. The raw experimental data were correlated using the UNIQUAC and NRTL models and used to estimate the interaction parameters between each pair of components in the systems. The experimental activity coefficients were obtained using the gas chromatographic method and compared with the calculated data obtained from these equilibrium models. The results show that UNIQUAC model gives better correlation than NRTL for these binary systems. The liquid–liquid extraction of TBA from aqueous solution using 2-ethyl-1-hexanol was demonstrated by simulation and the variation of separation factor of TBA at several temperatures was reported.     

Measurement and modeling of high-pressure (vapour + liquid) equilibria of (CO2 + alcohol) binary systems

An apparatus based on a static-analytic method assembled in this work was utilized to perform high pressure (vapour + liquid) equilibria measurements with uncertainties estimated at <5%. Complementary isothermal (vapour + liquid) equilibria results are reported for the (CO₂ + 1-propanol), (CO₂ + 2-methyl-1-propanol), (CO₂ + 3-methyl-1-butanol), and (CO₂ + 1-pentanol) binary systems at temperatures of (313, 323, and 333) K, and at pressure range of (2 to 12) MPa. For all the (CO₂ + alcohol) systems, it was visually monitored to insure that there was no liquid immiscibility at the temperatures and pressures studied. The experimental results were correlated with the Peng–Robinson equation of state using the quadratic mixing rules of van der Waals with two adjustable parameters. The calculated (vapour + liquid) equilibria compositions were found to be in good agreement with the experimental values with deviations for the mol fractions <0.12 and <0.05 for the liquid and vapour phase, respectively.     

The precise measurement of the (vapour + liquid) equilibrium properties for (CO2 + isobutane) binary mixtures

Recently, it has been suggested that natural working fluids, such as CO₂, hydrocarbons, and their mixtures, could provide a long-term alternative to fluorocarbon refrigerants. (Vapour + liquid) equilibrium (VLE) data for these fluids are essential for the development of equations of state, and for industrial process such as separation and refinement. However, there are large inconsistencies among the available literature data for (CO₂ + isobutane) binary mixtures, and therefore provision of reliable and new measurements with expanded uncertainties is required. In this study, we determined precise VLE data using a new re-circulating type apparatus, which was mainly designed by Akico Co., Japan. An equilibrium cell with an inner volume of about 380 cm³ and two optical windows was used to observe the phase behaviour. The cell had re-circulating loops and expansion loops that were immersed in a thermostatted liquid bath and air bath, respectively. After establishment of a steady state in these loops, the compositions of the samples were measured by a gas chromatograph (GL Science, GC-3200). The VLE data were measured for CO₂/propane and CO₂/isobutane binary mixtures within the temperature range from 300 K to 330 K and at pressures up to 7 MPa. These data were compared with the available literature data and with values predicted by thermodynamic property models.     

Isothermal (vapour + liquid) equilibrium and thermophysical properties for (1-butyl-3-methylimidazolium iodide + 1-butanol) binary system

Experimental isothermal (vapour + liquid) equilibrium (VLE) data are reported for the binary mixture containing 1-butyl-3-methylimidazolium iodide ([bmim]I) + 1-butanol at three temperatures: (353.15, 363.15, and 373.15) K, in the range of 0 to 0.22 liquid mole fraction of [bmim]I. Additionally, refractive index measurements have been performed at three temperatures: (293.15, 298.15 and 308.15) K in the whole composition range. Densities, excess molar volumes, surface tensions and surface tension deviations of the binary mixture were predicted by Lorenz–Lorentz (n_D-ρ) mixing rule. Dielectric permittivities and their deviations were evaluated by known equations. (Vapour + liquid) equilibrium data were correlated with Wilson thermodynamic model while refractive index data with the 3-parameters Redlich–Kister equation by means of maximum likelihood method. For the VLE data, the real vapour phase behaviour by virial equation of state was considered. The studied mixture presents S-shaped abatement from the ideality. Refractive index deviations, surface tension deviations and dielectric permittivity deviations are positive, while excess molar volumes are negative at all temperatures and on whole composition range. The VLE data may be used in separation processes design, and the thermophysical properties as key parameters in specific applications.     

(Liquid + liquid) equilibria of (water + propionic acid + 2-ethyl-1-hexanol): Experimental data and correlation

(Liquid + liquid) equilibrium (LLE) data for (water + propionic acid + 2-ethyl-1-hexanol) were determined at atmospheric pressure over the temperature range of (298.15 to 308.15) K. A type-1 LLE phase diagram was obtained for this ternary system. The LLE data were correlated fairly well with UNIQUAC model, indicating the reliability of the UNIQUAC equation for this ternary system. The average root mean square deviation between the observed and calculated mole fractions was 1.57%. Distribution coefficients and separation factors were measured to evaluate the extracting capability of the solvent.     

(Liquid + liquid) equilibria for (water + acetic acid + 2-ethyl-1-hexanol): experimental data and prediction

(Liquid + liquid) equilibrium (LLE) data for (water + acetic acid + 2-ethyl-1-hexanol) were measured at atmospheric pressure in the temperature range of (298.2 to 313.2) K. The UNIFAC model was used to predict the observed LLE data with a root-mean-square deviation value of 2.03%. A high degree of consistency of experimental data was obtained using the Othmer–Tobias correlation. The solubility of water in 2-ethyl-1-hexanol was measured at different temperatures.     

Volumetric and viscometric behaviour of binary systems: (1-hexanol + hydrocarbons)

Densities and viscosities of binary liquid mixtures of (1-hexanol  + n -hexane, or cyclohexane, or benzene) have been measured at a number of mole fractions at T =  (303, 313, and 323) K. The excess molar volume V_m^Eand apparent molar volume V_φhave been calculated from the density data. TheV_m^E anddV_m^E / dT for the system, (1-hexanol  + n -hexane) have been found negative, while those for the systems, (1-hexanol  +  cyclohexane) and (1-hexanol  +  benzene), were found to be positive. Excess viscosities η^Ecalculated from viscosity data, have been found to be negative over the whole composition range at the temperatures studied for all the three systems. Volumetric and viscometric behaviours indicate that dispersion is the major force of interaction between the components in (1-hexanol  +  cyclohexane, or benzene), while inclusion of hydrocarbon chains into the interstices of polymolecular ring structures of alcohol formed by hydrogen bonding has been assumed to play a significant role apart from dispersion in the system (1-hexanol  + n -hexane). Thermodynamic parameters of activation for viscous flow have been calculated from the viscosity data at different temperatures and a possible explanation suggested.     

Isothermal (vapour + liquid) equilibrium for binary mixtures of (tetrahydrofuran + 1,1,2,2-tetrachloroethane or tetrachloroethene) at nine temperatures

Vapour pressures of (tetrahydrofuran + 1,1,2,2-tetrachloroethane, or tetrachloroethene) at nine temperatures between T = 283.15 K and T = 323.15 K were measured by a static method. The reduction of the vapour pressures data to obtain activity coefficients and excess molar Gibbs energies was carried out by fitting the vapour pressure data to the Redlich–Kister polynomial according to Barker’s method. Excess molar volumes were also measured at T = 298.15 K. A comparative analysis about the thermodynamic behaviour of both systems is performed, in terms of hydrogen bonding and electron-donor–acceptor interactions, as well as the resonance effect in tetrachloroethene.     

Salt effect on (liquid + liquid) equilibrium of (water + tert-butanol + 1-butanol) system: Experimental data and correlation

(Liquid + liquid) equilibrium data for the quaternary systems (water + tert-butanol + 1-butanol + KBr) and (water + tert-butanol + 1-butanol + MgCl₂) were experimentally determined at T = 293.15 K and T = 313.15 K. For mixtures with KBr, the overall salt concentrations were 5 and 10 mass percent; for mixtures with MgCl₂, the overall salt concentrations were 2 and 5 mass percent. The experimental results were used to estimate molecular interaction parameters for the NRTL activity coefficient model, using the Simplex minimization method and a concentration-based objective function. The correlation results are extremely satisfactory, with deviations in phase compositions below 1.7%.     

Isobaric (vapour + liquid) equilibrium for N-methyl-2-pyrrolidone with branched alcohols

The (vapour + liquid) equilibrium (VLE) and boiling temperature measurements have been determined at 95.3 kPa as a function of composition for the binary liquid mixtures of N-methyl-2-pyrrolidone (NMP) with branched alcohols using a Swietoslawski-ebulliometer. The branched alcohols include 2-propanol, 2-butanol, 2-methyl-l- propanol, 2-methyl-2-propanol, and 3-methyl-l-butanol. The experimental temperature-composition (T–x) results were used to estimate Wilson parameters and then used to calculate the equilibrium vapour compositions and the excess Gibbs free energy at T = 298.15 K. The experimental temperature-composition (T, x) results were correlated with the Wilson, the NRTL and the UNIQUAC models. The experimental results are interpreted in terms of intermolecular interactions between constituent molecules.     

Isobaric (vapour + liquid) equilibria data for the binary systems {1,2-dichloroethane (1) + toluene (2)} and {1,2-dichloroethane (1) + acetic acid (2)} at atmospheric pressure

In this study for two binary systems {1,2-dichloroethane (1) + toluene (2)} and {1,2- dichloroethane (1) + acetic acid (2)}, the isobaric (vapour + liquid) equilibrium (VLE) data have been measured at atmospheric pressure. An all-glass Fischer–Labodest type capable of handling pressures from (0.25 to 400) kPa and temperatures up to 523.15 K was used. Experimental uncertainties for pressure, temperature, and composition have been calculated for each binary system. The data were correlated by means of the NRTL, UNIQUAC, UNIFAC, and Wilson models with satisfactory results.     

Isobaric (vapour + liquid) equilibria for the (1-propanol + 1-butanol) binary mixture at (53.3 and 91.3) kPa

In this work, isobaric (vapour + liquid) equilibrium data have been determined at (53.3 and 91.3) kPa for the binary mixtures of (1-propanol + 1-butanol). The thermodynamic consistency of the experimental values was checked by means the traditional area test and the direct test methods. According to the criteria for the test methods, the (vapour + liquid) equilibrium results were found to be thermodynamically consistent. The experimental values obtained were correlated by using the van Laar, Margules, Wilson, NRTL, and UNIQUAC activity-coefficient models. The binary interaction parameters of the activity-coefficient models have been determined and reported. They have been compared with those calculated by the activity-coefficient models. The average absolute deviation in boiling point and vapour-phase composition were determined. The calculated maximum average absolute deviations were 0.86 K and 0.0151 for the boiling point and vapour-phase composition, respectively. Therefore, it was shown that the activity-coefficient models used satisfactorily correlate the (vapour + liquid) equilibrium results of the mixture studied. However, the performance of the UNIQUAC model was superior to all other models mentioned.     

Experimental (vapour + liquid) equilibrium data of (methanol + water), (water + glycerol) and (methanol + glycerol) systems at atmospheric and sub-atmospheric pressures

Experimental (vapour + liquid) equilibrium results for the binary systems, (methanol + water) at the local atmospheric pressure of 95.3 kPa and at sub-atmospheric pressures of (15.19, 29.38, 42.66, 56.03, and 67.38) kPa, (water + glycerol) system at pressures (14.19, 29.38, 41.54, 54.72, 63.84, and 95.3) kPa and the (methanol + glycerol) system at pressures (32.02 and 45.3) kPa were obtained over the entire composition range using a Sweitoslwasky-type ebulliometer. The relationship of the liquid composition (x₁) as a function of temperature (T) was found to be well represented by the Wilson model. Computed vapour phase mole fractions, activity coefficients and the measured values along with optimum Wilson parameters are presented.     

Phase equilibria in the ternary system isobutyl alcohol + isobutyl acetate + 1-hexanol and the binary systems isobutyl alcohol + 1-hexanol,isobutyl acetate + 1-hexanol at 101.3 kPa

Consistent vapor–liquid equilibrium (VLE) data at 101.3 kPa have been determined for the ternary system isobutyl alcohol (IBA) + isobutyl acetate (IBAc) + 1-hexanol and two constituent binary systems: IBA + 1-hexanol and IBAc + 1-hexanol. The IBA + 1-hexanol system exhibits no deviation from ideal behaviour and IBAc + 1-hexanol system show lightly positive deviation from Raoult's law. The activity coefficients of the solutions were correlated with its composition by the Wilson, NRTL, UNIQUAC models. The ternary system is well predicted from binary interaction parameters. 1-Hexanol eliminates the IBA–IBAc binary azeotrope. However, the change of phase equilibria behaviour is small therefore this solvent is not an effective agent for that azeotrope mixture separation. In fact, the mean relative volatility on a solvent free basis is 1.28 (close to unity).     

Solvation model for estimating the properties of (vapour + liquid) equilibrium

A solvation energy relation (SERAS) has been developed for correlating the properties and (vapour + liquid) equilibrium (VLE) of associated systems capable of hydrogen bonding or dipole–dipole interaction. The model clarifies the simultaneous impact of hydrogen bonding, solubility and thermodynamic factors of activity coefficients derived from the UNIFAC-original model. The consistency test has been processed against binary VLE data for six isobaric systems of hydrogen bonding (I to III) and dipole–dipole interaction (IV to VI) types, and two isothermal systems of both types (VII and VIII). Systems II, III, and VIII show negative non-ideal deviations. The reliability analysis has been conducted on the performance of the SERAS model with 5- and 10-parameters. The model matches relatively well with the observed performance, yielding mean error of 9.7% for all the systems and properties considered.     

Compressed liquid density measurements for {methylbenzoate + (cyclohexane or 1-hexanol)} binary systems

Densities of the binary systems {methyl benzoate + (1-hexanol or cyclohexane)} were measured over the full composition range from (278.15 to 358.15) K and pressures up to 60 MPa, as a part of a study on the interactions between MB and organic solvents provided with six atoms of carbon but different functional groups and structures. Experimental data were correlated with temperature and pressure using the TRIDEN-10 parameter equation. From these parameters, isobaric expansivity, isothermal compressibility, and internal pressure were calculated. The complex behavior of the derived excess properties was interpreted in terms of intermolecular interactions and structural effects between the system components.     

Isobaric (vapour + liquid) equilibria for the (1-pentanol + propionic acid) binary mixture at (53.3 and 91.3) kPa

Isobaric (vapour + liquid) equilibrium measurements have been reported for the binary mixture of (1-pentanol + propionic acid) at (53.3 and 91.3) kPa. Liquid phase activity coefficients were calculated from the equilibrium data. The thermodynamic consistency of the experimental results was checked using the area test and direct test methods. According to these criteria, the measured (vapour + liquid) equilibrium results were found to be consistent thermodynamically. The obtained results showed a maximum boiling temperature azeotrope at both pressures studied. The measured equilibrium results were satisfactorily correlated by the models of Wilson, UNIQUAC, and NRTL activity coefficients. The results obtained indicate that the performance of the NRTL model is superior to the Wilson and UNIQUAC models for correlating the measured isobaric (vapour + liquid) equilibrium data.     

(Liquid + liquid) equilibria in (water + ethanol + 2-ethyl-1-hexanol) at T=(298.2, 303.2, 308.2, and 313.2) K

(Liquid + liquid) equilibrium data for (water + ethanol + 2-ethyl-1-hexanol) were measured at atmospheric pressure in the temperature range (298.2 to 313.2) K. A type 1 (liquid + liquid) phase diagram was obtained for this ternary system. The experimental tie-line data for this system were correlated with the UNIQUAC solution model. The values of the interaction parameters between each pair of components in the system were obtained for the UNIQUAC model with the experimental results. The root mean square deviation between the observed and calculated mole per cent was 1.70%. The mutual solubility of 2-ethyl-1-hexanol and water was also investigated by the addition of ethanol at different temperatures.     

Isobaric (vapour + liquid + liquid) equilibrium data for (di-n-propyl ether + n-propyl alcohol + water) and (diisopropyl ether + isopropyl alcohol + water) systems at 100 kPa

Isobaric (vapour + liquid + liquid) equilibria were measured for the (di-n-propyl ether + n-propyl alcohol + water) and (diisopropyl ether + isopropyl alcohol + water) system at 100 kPa.The apparatus used for the determination of (vapour + liquid + liquid) equilibrium data was an all-glass dynamic recirculating still with an ultrasonic homogenizer couple to the boiling flask.The experimental data demonstrated the existence of a heterogeneous ternary azeotrope for both ternary systems. The (vapour + liquid + liquid) equilibria data were found to be thermodynamically consistent for both systems.The experimental data were compared with the estimation using UNIQUAC and NRTL models and the prediction of UNIFAC model.