Vapor-liquid Equilibrium Results Research Articles

Vapor-liquid equilibrium of light hydrocarbon multicomponent systems by solving the Rachford-Rice equation

Mixed-refrigerants are required for cryogenic cooling systems, as well as for refrigeration systems, in order to provide enhanced cooling performances and to comply with new global environmental protection regulations. Thus, the vapor–liquid equilibrium (VLE) of light hydrocarbon (LHC) multicomponent systems is studied numerically by solving the Rachford-Rice flash equations using the Peng-Robinson equation of state and the van der Waals mixing rules. Among many other methods for calculating VLE of mixtures, the presented method does not involve numerical iterations, there aren’t any convergence problems, and it is a fast responding method, which allows extensive investigations of many compositions at various conditions. VLE results are presented for binary systems of nitrogen, methane, ethane, propane, n-butane, and carbon dioxide at temperatures between 240 K and 330 K; and ternary systems of nitrogen, methane, ethane, propane, n-butane, and carbon dioxide at temperatures between 220 K and 330 K and pressures between 5 bar and 40 bar. All the computational results are validated against experimental results, which are taken from literature, and the maximum obtained deviation between calculated and experimental results is 4.03 %, while most of the deviations are less than 2.0 %. As the number of components in the system increases, the deviations between calculated and experimental results increase, although the liquid and the vapor line trends are maintained. In the current research, seven different alpha functions are examined, and the results show that they all provide similar accuracies. The presented numerical method may be used by any equation of state, it is numerically stable, and successfully validated against reported experimental results; consequently, it is recommended for the development of future mixed-refrigerants.

Isobaric vapor–liquid equilibria and distillation process design for separating ketones in biomass pyrolysis oil

Biomass pyrolysis oil is a renewable resource and some of compounds (such as ketones, phenols and furans) in biomass pyrolysis oil are very useful compounds that can be used as raw materials for production of fine chemicals. Vapor-liquid equilibrium (VLE) data are critical and fundamental for designing distillation separation process. The VLE experiment and calculation of ketone-related binary systems (2-butanone + cyclopentanone, 2,3-butanedione + cyclopentanone) at atmospheric pressure are studied in this work. Binary interaction parameters of activity coefficient models (NRTL, Wilson and UNIQUAC) are obtained by correlating VLE experimental data. The new group CH2COCH2 is defined and the new group interaction parameters are presented and used to predict VLE data by UNIFAC-DMD model. The distillation separation process of ketones is designed and simulated based on VLE results. This work will provide theoretical basis and technical guidance for industrial separation process of biomass pyrolysis oil.

Vapour-liquid equilibria of systems containing deep eutectic solvent based on choline chloride and glycerol

Deep eutectic solvents (DES) have been recently proposed as potential entrainers for extractive distillation to obtain anhydrous ethanol. However, the lack of thermodynamic data of mixtures containing DESs still hampers studies of their application in separation processes. In this work, the DES based on choline chloride and glycerol (ChCl:G) at the molar ratio of 1:2 was proposed as extracting solvent for ethanol dehydration. Therefore, the vapour-liquid equilibrium (VLE) of the pseudo-binary systems {water - ChCl:G(1:2.000) & ethanol - ChCl:G(1:2.000)} were measured at 11.3 kPa. The pseudo-ternary VLE data of {ethanol–water-ChCl:G(1:2.000)} were also obtained, keeping the concentration of ChCl:G(1:2.000) nearly constant (x3 = 0.50). The experimental VLE data were correlated to non-random two-liquid (NRTL) and universal quasichemical (UNIQUAC) models aiming to calculate the interaction binary parameters. Through the overall average errors, it was concluded that the UNIQUAC model describes better the binary systems {ethanol - ChCl:G(1:2.000)} (0.465%) while NRTL is more suitable to describe the system {water - ChCl:G(1:2.000)} (0.113%). However, the pseudo-ternary system {ethanol – water – ChCl:G (1:2.000)} could not be successfully represented by the coefficients obtained from the binary data. In addition, the VLE results of the pseudo-ternary system demonstrated that ChCl:G(1:2.000) increased the relative volatility of ethanol–water, indicating the potential use of ChCl:G(1:2.000) in the production of anhydrous ethanol through extractive distillation.

The investigation on the vapour liquid phase equilibrium of (ammonia + 1,1,1,2-tetrafluoroethane) system over the temperatures ranging from (243.150 to 283.150) K

To blend ammonia with some hydrofluorocarbons may give these mixed refrigerants lower flammability and global warming potential. In this paper, the isothermal vapour liquid equilibrium (VLE) of (ammonia+1,1,1,2-tetrafluoroethane) system at temperatures ranging from (243.150 to 283.150) K are presented. Two models were employed to regress the experimental VLE results, namely the Peng–Robinson (PR) equation of state with the simple van der waals (VDW) mixing rule; the Peng–Robinson equation of state combined non-random two-liquid (NRTL) activity coefficient model with the modified Huron-Vidal one-order (MHV1) mixing rule. The maximum average absolute relative deviation of pressure (AARDp) and average absolute deviation of the vapour phase mole fraction (AADy) for PR-VDW are 0.56% and 0.010, respectively, while the maximum AARDp and AADy for PR-MHV1-NRTL are 0.27% and 0.014, respectively. Positive azeotropic behaviour was exhibited at each temperature investigated.

Recent advances in modeling the vapor-liquid equilibrium of mixed working fluids

Vapor-liquid equilibrium (VLE) properties of mixed working fluids are essential for the study of organic fluids for thermodynamic cycles such as heat pumps or organic Rankine cycles. Thus, the typical and recent models for the VLE calculation of mixed working fluids are reviewed in this paper. The most popular cubic equations of state (EOSs) and two mixing rules, namely the Van der Waals and the excess free energy, are summarized, respectively. VLE data of 13 alternative working fluids at different temperatures are employed to exhibit the capacities and limitations of three predictive models. The calculated VLE results show that the model with Van der Waals mixing rules is only valid for some types of mixture, while the accuracy of the model with excess free energy mixing rules is greatly influenced by the UNIFAC group parameters, which are usually fitted from the VLE data instead of the activity coefficient data. Thus, a generalized model for mixed working fluids should be derived from the molecular theory or the group contribution method, in which the group parameters are fitted from the large VLE data.

Isothermal (vapour + liquid) equilibrium (VLE) for binary mixtures containing diethyl carbonate, phenyl acetate, diphenyl carbonate, or ethyl acetate

The isothermal (vapour+liquid) equilibrium (VLE) (P–T–xi–yi) was determined the binary systems of (ethyl acetate+diethyl carbonate) from T=(373.2 to 453.2)K, (ethyl acetate+phenyl acetate) at T=373.2K, and (diethyl carbonate+phenyl acetate) at T=373.2K, while the VLE (P–T–xi) of three diphenyl carbonate-containing binary systems was also determined experimentally at temperatures from (373.2 to 453.2)K. The experimental results show no azeotrope formation and near ideal solution behaviour for each binary system. These new VLE (P–T–xi–yi) data have been passed by the point, area, and infinite dilution thermodynamic consistency tests. The Wilson-HOC, the NRTL-HOC, and the UNIQUAC-HOC models were applied to correlate the VLE results and the optimal values of the model parameters have been determined through data reduction. Comparable results were obtained from these three models.

Phase Equilibrium, Excess Enthalpies, and Densities of Binary Mixtures of Trimethylbutylammonium Bis(trifluoromethylsulfonyl)imide with Ethanol, 1-Propanol, and Dimethylformamide

The molecular interactions between the ionic liquid trimethylbutylammomium bis(trifluoromethylsulfonyl)imide, [N1114][Tf2N], and three common solvents, including short chain alcohols (ethanol and 1-propanol) and an aprotic solvent (N,N-dimethylformamide or DMF) were investigated through experimental properties. The excess enthalpies were measured by calorimetry at temperatures from 308.15 K to 323.15 K over the whole composition range and excess volumes were calculated from density measurements. The vapor–liquid equilibrium (VLE) measurements of the [N1114][Tf2N] + DMF mixture were obtained using a headspace gas chromatography instrument. It was determined that hydrogen bonds between the alcohol molecules contribute to the positive excess enthalpies, while the favorable interactions between DMF and [N1114][Tf2N] might be explained by electrostatic interactions between the ionic liquid and the zwitterionic resonance structure of DMF. The nonrandom two liquid (NRTL) equation was successfully used to correlate the excess enthalpy and VLE results.

Vapor–Liquid Equilibrium and Liquid–Liquid Equilibrium of Ethyl Acetate + Ethanol + 1-Ethyl-3-methylimidazolium Acetate

The vapor–liquid equilibrium (VLE) and liquid–liquid equilibrium (LLE) of the ternary system of ethyl acetate + ethanol + 1-ethyl-3-methylimidazolium acetate ([EMIM][Ac]), together with the vapor–liquid–liquid equilibrium (VLLE) for the binary system of ethyl acetate + [EMIM][Ac], were measured. The experimental VLE, LLE, and VLLE data were correlated by the nonrandom two-liquid (NRTL) equation, and the calculated results agreed well with the experimental results. The VLE and VLLE results show that [EMIM][Ac] can enhance the relative volatility of ethyl acetate to ethanol, and the azeotrope of ethyl acetate + ethanol can be eliminated. The LLE data indicate that [EMIM][Ac] is a potential solvent for the separation of ethyl acetate + ethanol via liquid–liquid extraction.

Finding a suitable thermodynamic model and phase equilibria for hydrodeoxygenation reactions of methyl heptanoate

Replacement of fossil fuels with biomass-based components is of increasing public and scientific interest. Unfortunately, most biomass-based compounds contain oxygen and oxygen content must be diminished before use of the compounds as fuel. Removal is usually done catalytically, with hydrogen supplied to convert the oxygen to water. Hydrodeoxygenation (HDO) of biomass-based compounds is often studied with model compounds, and the system investigated here was methyl heptanoate+m-xylene. Modeling of the reaction kinetics requires that behavior of the reaction mixture as a function of reaction time must be described. A suitable thermodynamic model for non-ideal system at high pressure and temperature is needed, and this demands correct modeling of the solubility of hydrogen and the water of reaction. For validation of the thermodynamic models isothermal vapor–liquid equilibrium (VLE) for the methyl heptanoate+m-xylene system was measured at 398.15K and 408.15K with a circulation still. The experimental VLE exhibited slight negative deviation from Raoult’s law. No azeotropic behavior was found. The experimental VLE results were correlated with the Wilson model with temperature-dependent parameters and used in testing of the SRK, original UNIFAC, UNIFAC-Dortmund, and PSRK predictive models. PSRK was preferred for further estimations. All VLE measurements passed the point consistency tests. Simulated reaction conditions for HDO of methyl heptanoate at the initial and final points were calculated to determine the effect of vapor–liquid equilibrium on the composition of reaction mixtures.

Modification of Peng Robinson EOS for modelling (vapour+liquid) equilibria with electrolyte solutions

► Extended PR-EOS was presented for VLE of H 2 O/Salt/CO 2 systems at high pressure. ► The proposed EPR-EOS is based upon contributions to the Helmholtz energy. ► Born, Margules, and Debye–Huckel or mean spherical approximation terms were used. ► Two different mixing rules Panagiotopoulos and Reid and Kwak and Mansoori (KM) were used. ► A combination of KM mixing rule with DH term results more accurate VLE results. A modification of the extended Peng–Robinson equation of state (PR-EOS) is presented to describe the (vapour + liquid) equilibria of systems containing water and salts. The modification employs three additional terms including a Born term, a Margules term and two terms separately used for estimation of the long-range electrostatic interactions (the Debye–Huckel (DH) or the mean spherical approximation (MSA) terms). Effects of two mixing rules, first, the Panagiotopoulos and Reid mixing rule (PR) and, second, the Kwak and Mansoori mixing rule (KM), on the final values of VLE calculations are also investigated. The results show that the KM mixing rule is more appropriate than the PR mixing rule. The proposed equation of state is used to calculate the (vapour + liquid) equilibrium (VLE) of the systems containing (water + sodium sulphate + carbon dioxide) and (water + sodium chloride + carbon dioxide) at high pressure. The comparison of calculated results with the experimental data shows that a combination of KM mixing rule with the DH term results a more accurate VLE values.

Vapor−Liquid Equilibrium and Liquid−Liquid Equilibrium of Methyl Acetate + Methanol + 1-Ethyl-3-methylimidazolium Acetate

The vapor–liquid equilibrium (VLE) and liquid–liquid equilibrium (LLE) of the ternary system of ethyl acetate + ethanol + 1-ethyl-3-methylimidazolium acetate ([EMIM][Ac]), together with the vapor–liquid–liquid equilibrium (VLLE) for the binary system of ethyl acetate + [EMIM][Ac], were measured. The experimental VLE, LLE, and VLLE data were correlated by the nonrandom two-liquid (NRTL) equation, and the calculated results agreed well with the experimental results. The VLE and VLLE results show that [EMIM][Ac] can enhance the relative volatility of ethyl acetate to ethanol, and the azeotrope of ethyl acetate + ethanol can be eliminated. The LLE data indicate that [EMIM][Ac] is a potential solvent for the separation of ethyl acetate + ethanol via liquid–liquid extraction.

PρT and VLE for Ethane + Hydrogen Sulfide from (254.05 to 363.21) K at Pressures up to 20 MPa

Pressure, density, and temperature (PρT) data are presented for ethane (1) + hydrogen sulfide (2) at z2 = (0.0380, 0.0563, 0.0977, and 0.1430) and various temperatures in the (254.05 to 363.21) K range. A vibrating tube densimeter, with the forced path mechanical calibration model, was used to determine both PρT data and vapor−liquid equilibrium (VLE) even when the mixture is close to its critical temperature. PρT and VLE results were correlated with the Benedict−Webb−Rubin−Starling's equation of state (BWRS EoS), the re-evaluated pure component parameters, and the mixing parameters derived using Starling's generalized mixing rules. Finally, we have compared, in VLE conditions, the BWRS EoS to a Peng−Robinson EoS using quadratic mixing rules.

Prediction of Vapor-Liquid Equilibrium inside Capillary Porous Plates

Capillary distillation is a relatively new separation process which uses capillary porous media for the separation of mixtures. It utilizes the solid-liquid interfacial forces to alter the vapor-liquid equilibrium (VLE) of mixtures inside the capillary porous plates. Previous studies have shown that capillary porous plates could significantly alter the VLE of binary mixtures. It was shown that the main factors affecting the alteration of VLE of binary mixtures are the polarization of the liquids and the porous plates as well as the polarization difference between the mixture components. In this study, the VLE data for the mixtures inside capillary porous plates have been predicted using the Wilson model and the theory of Abu Al-Rub and Datta on VLE inside capillary porous media. The validity of the developed model has been assessed by comparing predicted VLE results of some binary mixtures inside capillary porous plates with experimental VLE data. The comparison showed that the model developed could predict the VLE of the studied systems accurately.

A new simulation method for the determination of phase equilibria in mixtures in the grand canonical ensemble

A grand canonical Monte Carlo (GCMC) simulation method is presented for the determination of the phase equilibria of mixtures. The coexistence is derived by expanding the pressure into a Taylor series as a function of the temperature and the chemical potentials that are the independent intensive variables of the grand canonical ensemble. The coefficients of the Taylor series can be calculated from ensemble averages and fluctuation formulae that are obtained from GCMC simulations in both phases. The method is able to produce the equilibrium data in a certain domain of the (T, p) plane from two GCMC simulations. The vapour-liquid equilibrium results obtained for a Lennard-Jones mixture agree well with the corresponding Gibbs ensemble Monte Carlo data.

Isobaric Vapour - Liquid Equilibrium for the Binary Systems Cycloalkane and Benzene with 1,3-Dioxolane

Isobaric vapour-liquid equilibrium (VLE) is reported for the binary systems cyclopentane, cyclohexane, benzene with 1,3-dioxolane. All the systems show a minimum temperature azeotrope. The VLE results were thermodynamically consistent and correlated with six previously proposed equations.

Development and extension of PSRK/UNIQUAC model to methane and nitrogen gases

Two successful procedures for matching the equation of state (EOS) and the excess Gibbs energy model at zero pressure belong to Michelsen [M.L. Michelsen, Fluid Phase Equilibria, 60 (1990) 213] and Holderbaum-Gmehling [T. Holderbaum, J. Gmehling, Fluid Phase Equilibria, 70 (1991) 251]. These procedures lead to volume independent mixing rules for the mixture parameter a. Michelsen proposed the MHV1 and MHV2 mixing rules and Holderbaum-Gmehling proposed the PSRK mixing rule. Keshtkar et al. [A. Keshtkar, F. Jalali, M. Moshfegian, Fluid Phase Equilibria, 140 (1997) 107] demonstrated the utility of these mixing rules together with UNIFAC and UNIQUAC models for the prediction of high-pressure vapor-liquid equilibrium (VLE) of CO 2-binary systems. Also, they showed that the PSRK/UNIQUAC model gives better VLE results than other models. In this paper, we develop and extend the above model to methane and nitrogen gases. For this purpose, it is required that the missing interaction parameters of model are fitted with experimental VLE data. The VLE calculations show that good agreement between calculated results and experimental data can be produced by using the obtained parameters.

Evaluation of vapor—liquid equilibrium of CO 2 binary systems using UNIQUAC-based Huron—Vidal mixing rules

Since Huron and Vidal [M.J. Huron, J. Vidal, Fluid Phase Equilib. 3 (1979) 255] developed the basic idea of the so-called G E mixing rules, similar models have been proposed by different authors. In most of them, a group-contribution method like the UNIFAC model is used with the equation of state to enable the description of vapor-liquid equilibrium (VLE) at high temperatures and pressures including supercritical compounds. In this work we intended to use the UNIQUAC instead of the UNIFAC method as G E model in SRK equation of state. For comparison between Huron-Vidal-type mixing rules, we selected the modified Huron-Vidal first-order (MHV1) and second-order (MHV2) mixing rules proposed by Michelsen [M.L. Michelsen, Fluid Phase Equilib. 60 (1990a) 213; M.L. Michelsen, Fluid Phase Equilib. 60 (1990b) 42.] and PSRK mixing rule proposed by Holderbaum and Gmehling [T. Holderbaum, J. Gmehling, Fluid Phase Equilib. 70 (1991) 251.]. In other words, this paper investigates the ability of several mixing rules to predict and correlate the high-pressure vapor-liquid equilibrium used in combination with the UNIFAC and UNIQUAC models. For comparison of these mixing rules, the carbon dioxide binary mixtures have been chosen because carbon dioxide has numerous applications in supercritical fluid processes. The missing interaction parameters of UNIFAC and UNIQUAC were estimated through the regression of experimental vapor-liquid equilibrium data. For comparison of UNIQUAC-based mixing rules with each other, the interaction parameters of 51 carbon dioxide binary systems have been determined. Furthermore, a comparison between UNIFAC- and UNIQUAC-based SRK equation of state is presented. The results show that all of the UNIFAC- and UNIQUAC-based mixing rules, with parameters derived from VLE, can be used for reliable calculations of phase equilibrium. It is shown that the PSRK/UNIQUAC mixing rule can correlate the data for the best VLE results. Also, it is shown that the use of the second-order mixing rule in UNIQUAC-based SRK equation of state does not necessarily improve the results of VLE calculations.

97/03641 Thermal transformations of sulfur compounds during secondary pyrolysis of the products of oil shale retorting

Since Huron and Vidal [M.J. Huron, J. Vidal, Fluid Phase Equilib. 3 (1979) 255] developed the basic idea of the so-called GE mixing rules, similar models have been proposed by different authors. In most of them, a group-contribution method like the UNIFAC model is used with the equation of state to enable the description of vapor-liquid equilibrium (VLE) at high temperatures and pressures including supercritical compounds. In this work we intended to use the UNIQUAC instead of the UNIFAC method as GE model in SRK equation of state. For comparison between Huron-Vidal-type mixing rules, we selected the modified Huron-Vidal first-order (MHV1) and second-order (MHV2) mixing rules proposed by Michelsen [M.L. Michelsen, Fluid Phase Equilib. 60 (1990a) 213; M.L. Michelsen, Fluid Phase Equilib. 60 (1990b) 42.] and PSRK mixing rule proposed by Holderbaum and Gmehling [T. Holderbaum, J. Gmehling, Fluid Phase Equilib. 70 (1991) 251.]. In other words, this paper investigates the ability of several mixing rules to predict and correlate the high-pressure vapor-liquid equilibrium used in combination with the UNIFAC and UNIQUAC models. For comparison of these mixing rules, the carbon dioxide binary mixtures have been chosen because carbon dioxide has numerous applications in supercritical fluid processes. The missing interaction parameters of UNIFAC and UNIQUAC were estimated through the regression of experimental vapor-liquid equilibrium data. For comparison of UNIQUAC-based mixing rules with each other, the interaction parameters of 51 carbon dioxide binary systems have been determined. Furthermore, a comparison between UNIFAC- and UNIQUAC-based SRK equation of state is presented. The results show that all of the UNIFAC- and UNIQUAC-based mixing rules, with parameters derived from VLE, can be used for reliable calculations of phase equilibrium. It is shown that the PSRK/UNIQUAC mixing rule can correlate the data for the best VLE results. Also, it is shown that the use of the second-order mixing rule in UNIQUAC-based SRK equation of state does not necessarily improve the results of VLE calculations.

The surface thermodynamics of alkane+ perfluoroalkane and dimethylsiloxane+ perfluoroalkane liquid mixtures

The surface thermodynamics of alkane + perfluorolkane liquid mixtures reflects the bulk thermodynamics of the same class of mixture. In particular, the dominating feature in both is the influence of the as-yet-unexplained anomalous weakness of the unlike interaction energy compared to that predicted by the Berthelot combining rule. The chief outcome in the bulk thermodynamics is the prevalence of large positive deviations from Raoult's law, most characteristically manifest by liquid-liquid immisciblity in almost every mixture and an abundance of positive azeotropy. In the surface thermodynamics the corresponding characteristic feature is the occurrence of large negative deviations from a simple mole-fraction weighted average surface tension which serves in the absence of a superior definition as an operational statement of surface ideality. In a number of mixtures the deviation is sufficiently extreme as to give rise to negative aneotropy or a minimum in the surface tension.The thermodynamics of dimethylsiloxane + perfluoroalkane mixtures bears many similarities to that of alkane + perfluoroalkane mixtures. With a less full set of results we highlight the similarities and differences of the behaviour of the two series of mixtures.We report here the surface tensions as a function of composition of a number of alkane + perfluoroalkane mixtures ranging from methane + tetrafluoromethane at 100 K to octane + octadecafluorooctane at 303 K. In the interpretation of the results we employ with varying degrees of success a variety of theories, chiefly based on the principle of corresponding states.For those mixtures for which appropriate vapour-liquid equilibrium results have been reported we discuss the relative adsorption both in terms of intermolecular forces and the proximity of the consolute point.