Thermodynamic Consistency Test Research Articles

Isobaric vapor–liquid equilibrium for binary system of N, N-dimethyl formamide + N, N-dimethyl acetamide and quaternary system of sec-butyl alcohol + sec-butyl acetate + N, N-dimethyl formamide + N, N-dimethyl acetamide at 101.3 kPa

Isobaric vapor–liquid equilibrium (VLE) for the binary system N, N-dimethyl formamide (DMF) + N, N-dimethyl acetamide (DMAC) and the quaternary system sec-butyl alcohol (SBA) + sec-butyl acetate (SBAC) + DMF + DMAC were determined at 101.3 kPa using a vapor–liquid equilibrium still. The thermodynamic consistency test for the experimental data was checked by Van Ness point test. The binary VLE data were correlated with the NRTL, UNIQUAC and Wilson activity coefficient models respectively. And the VLE data of the quaternary system predicted by the correlated binary interaction parameters agree well with the experimental data. And the mixture of DMF (3) and DMAC (4) can eliminate the pseudo-azeotrope of sec-butyl alcohol (1) + sec-butyl acetate (2). Thus, the mixture of DMF and DMAC is appropriate for separation of the pseudo-azotrope of SBA and SBAC by extractive distillation.

Isothermal vapor–liquid equilibria measurements for binary systems of 2,3,3,3-tetrafluoropropene (HFO-1234yf) + 2-chloro-3,3,3-trifluoropropene (HCFO-1233xf) and 2-chloro-3,3,3-trifluoropropene (HCFO-1233xf) + 2-chloro-1,1,1,2-tetrafluoropropane (HCFC-244bb)

This paper presents the measurements of isothermal vapor-Liquid equilibria (VLE) data for two binary systems of 2,3,3,3-tetrafluoropropene (HFO-1234yf) + 2-chloro-3,3,3-trifluoropropene (HCFO-1233xf) and 2-chloro-3,3,3-trifluoropropene (HCFO-1233xf) + 2-chloro-1,1,1,2-tetrafluoropropane (HCFC-244bb). The measurements were performed with an apparatus based on the static-analysis method. The HFO-1234yf + HCFO-1233xf system was measured at three temperatures from (293.15 to 313.15) K, and the HCFO-1233xf + HCFC-244bb system was measured at three temperatures from (303.15 to 323.15) K. The system of HFO-1234yf + HCFO-1233xf shows a small deviation from Raoult's law and dose not exhibit azeotropic behavior, while the system of HCFO-1233xf + HCFC-244bb exhibits near azeotropic behavior within the complete range of composition. All of the experimental data were correlated with the Peng–Robinson equations of state with the van der Waals mixing rules. Good consistency was obtained between the experimental data and correlated values for the both systems in the experimental temperature range. Thermodynamic consistency testing was also performed by the data-reduction method for the observed experimental data.

Isobaric Vapor–Liquid Equilibrium for the Binary Systems of sec-Butyl Acetate + Methyl Ethyl Ketone, 2-Methoxyethanol, or 1,2-Dimethoxyethane at 101.3 kPa

The isobaric vapor–liquid equilibrium (VLE) data of methyl ethyl ketone (MEK) + sec-butyl acetate (SBAC), 2-methoxyethanol + SBAC, and 1, 2-dimethoxyethane (DME) + SBAC were determined at 101.3 kPa by using an Ellis vapor–liquid equilibrium still. The experimental data passed the thermodynamic consistency test by Herington method and Wisniak test. The VLE values were correlated by the nonrandom two-liquid (NRTL), universal quasichemical activity coefficience (UNIQUAC), and Wilson activity-coefficient models. The results indicated that the three models had good agreement with the experimental data. The 2-methoxyethanol + SBAC system forms a minimum temperature binary azeotrope at 101.3 kPa. The azeotropic temperature is 383.86 K, and the composition of SBAC is 85.1 mol %.

Vapor–Liquid Equilibrium of Binary Mixtures Containing Isopropyl Acetate and Alkanols at 101.32 kPa

Isobaric vapor–liquid equilibria of binary mixtures of isopropyl acetate plus an alkanol (1-propanol, 2-propanol, 1-butanol, or 2-butanol) were measured at 101.32 kPa, using a dynamic recirculating still. An azeotropic behavior was observed only in the mixtures of isopropyl acetate + 2-propanol and isopropyl acetate + 1-propanol. The application of four thermodynamic consistency tests (the Herington test, the Van Ness test, the infinite dilution test, and the pure component test) showed the high quality of the experimental data. Finally, both NRTL and UNIQUAC activity coefficient models were successfully applied in the correlation of the measured data, with the average absolute deviations in vapor phase composition and temperature of 0.01 and 0.16 K, respectively.

Thermodynamic consistency testing of PTx-data via the Gibbs-Helmholtz equation 2.: Methodology and limitations

Measurement of mixture vapor-pressure data, Px or Tx (PTx) data, is a fast, efficient, and often more accurate method to determine low-pressure binary vapor–liquid equilibrium (VLE) data compared with measurement of PTxy data in re-circulating equilibrium stills. PTx data are the minimum necessary to specify VLE according to the phase rule so that Gibbs–Duhem slope and area thermodynamic consistency tests are not possible. However, GE/RT data derived from PTx data measured at several temperatures can be compared to measured HE data with the Gibbs–Helmholtz (GH) equation, GE/RT=HE/RT–SE/R. This comparison can be used as a thermodynamic consistency test for PTx data. Previous work (Fluid Phase Equilibria, 14 (1983) 383–392) showed that random errors in pressure measurement large enough to give GH inconsistency usually are not large enough to cause unacceptable errors in the vapor compositions calculated by Barker's method. This present work demonstrates that using a Redlich–Kister GE expansion at each temperature rather than using a Local Composition GE model, e.g., NRTL, fitted to all of the Px data over the entire temperature range is an effective methodology for GH testing; this methodology is demonstrated by analysis of high-precision ethanol + water Px data. In addition, the special GH testing problems presented by nearly-ideal systems are illustrated by analysis of recent high-precision ethanol + n-propanol Px data. Other limitations of and recommendations for Gibbs–Helmholtz testing of VLE data are discussed.

Experimental isobaric vapor–liquid equilibrium for the binary and ternary systems with methanol, methyl acetate and dimethyl sulfoxide at 101.3 kPa

Isobaric vapor–liquid equilibrium (VLE) data for the systems of methyl acetate+dimethyl sulfoxide (DMSO), methanol+DMSO and methyl acetate+methanol+DMSO were determined with a modified Othmer still at 101.3kPa. And all experimental VLE data have passed the Herington and Van Ness thermodynamic consistency tests. The experimental binary VLE data were correlated by NRTL, Wilson and UNIQUAC models and the binary interaction parameters were obtained. And the VLE data predicted by the obtained parameters agree well with the experimental data. The binary azeotrope of methyl acetate and methanol is eliminated when the mole ratio of DMSO to the binary azeotrope is approximately 1.5:1. Therefore, DMSO is a promising extractive agent for the separation of the binary azeotrope of methanol and methyl acetate in extractive distillation.

Vapour liquid equilibria of monocaprylin plus palmitic acid or methyl stearate at P = (1.20 and 2.50) kPa by using DSC technique

The Differential Scanning Calorimetry (DSC) technique is used for measuring isobaric (vapour+liquid) equilibria for two binary mixtures: {monocaprylin+palmitic acid (system 1) or methyl stearate (system 2)} at two different pressures P=(1.20 and 2.50)kPa. The obtained PTx data are correlated by Wilson, NRTL and UNIQUAC models. The original UNIFAC group contribution method is also considered and new binary interaction parameters for the main groups CH2, CCOO, OH and COOH are regressed, to account for the non-idealities found in these lipid systems. Established thermodynamic consistency tests are applied and attest the quality of the measured data. In terms of relevance of the selected components, system 1 can be found in the purification and deodorization steps during the production of edible oils, while, system 2 can be found in the purification steps of biodiesel. It should be noted that no such data could be found in the open literature, not only for the specific components selected but also for the combination of the classes of components considered; that is, acylglycerol plus fatty acid or fatty ester.

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.

Experimental isobaric vapor liquid equilibrium for the ternary system of sec-butyl alcohol + sec-butyl acetate + dimethyl sulfoxide at 101.3 kPa

Isobaric vapor–liquid equilibrium (VLE) data were measured for the binary systems sec-butyl alcohol+dimethyl sulfoxide (DMSO), sec-butyl acetate+DMSO and the ternary system sec-butyl alcohol+sec-butyl acetate+DMSO at 101.3kPa using a vapor–liquid equilibrium still. The thermodynamic consistency test for the binary experimental data was made by Herington method, Wisniak's L–W method and a point to point method of Van Ness test described by Fredenslund et al. And the thermodynamic consistency of the ternary system was checked by Van Ness test. The VLE data for the binary systems were correlated with the NRTL, Wilson and UNIQUAC activity coefficient models. And the binary and ternary VLE data predicted by the obtained binary interaction parameters agree well with the experimental data. The experimental results show that the relative volatility between sec-butyl alcohol and sec-butyl acetate is changed obviously when the mass ratio of DMSO to the pseudo-azeotrope mixture is 6:5. And DMSO is a promising extractive agent for the separation of the mixture of sec-butyl alcohol and sec-butyl acetate in extractive distillation.

The Kwak–Mansoori approach to the Peng–Robinson equation for determining the thermodynamic consistency of VLE in ethanol + congener mixtures

The modified Peng–Robinson equation of state proposed by Kwak and Mansoori (PR/KM) is used in a thermodynamic consistency test of phase equilibrium data for binary ethanol + congener mixtures found in alcoholic distillation processes. Congener substances are those components in a must that are present at very low concentration, but their presence is necessary to give the distilled liquor their particular aromatic and tasting characteristics. The congener substances considered in this study are: acetic acid, ethyl acetate, furfural, methanol, 2-methyl-1-propanol, 1-pentanol, 1-propanol and methyl acetate. A flexible area test method is applied to analyse 25 isothermal P – x – y data of ethanol + congener mixtures available in the open literature. The consistency method determines the value of three integral expressions derived from the Gibbs–Duhem equation; one integral is calculated using experimental data only and the other two by using values calculated with the PR/KM model. For all cases, the method gives a clear answer about consistency or inconsistency of a set of isothermal P – x – y data.

Constant-pH MD Simulations of an Oleic Acid Bilayer.

Oleic acid is a simple molecule with an aliphatic chain and a carboxylic group whose ionization and, consequently, intermolecular interactions are strongly dependent on the solution pH. The titration curve of these molecules was already obtained using different experimental methods, which have shown the lipid bilayer assemblies to be stable between pH 7.0 and 9.0. In this work, we take advantage of our recent implementations of periodic boundary conditions in Poisson-Boltzmann calculations and ionic strength treatment in simulations of charged lipid bilayers, and we studied the ionization dependent behavior of an oleic acid bilayer using a new extension of the stochastic titration constant-pH MD method. With this new approach, we obtained titration curves that are in good agreement with the experimental data. Also, we were able to estimate the slope of the titration curve from charge fluctuations, which is an important test of thermodynamic consistency for the sampling in a constant-pH MD method. The simulations were performed for ionizations up to 50%, because an experimentally observed macroscopic transition to micelles occurs above this value. As previously seen for a binary mixture of a zwitterionic and an anionic lipid, we were able to reproduce experimental results with simulation boxes usually far from neutrality. This observation further supports the idea that a charged membrane strongly influences the ion distribution in its vicinity and that neutrality is achieved significantly far from the bilayer surface. The good results obtained with this extension of the stochastic titration constant-pH MD method strongly supports its usefulness to sample the coupling between configuration and protonation in these types of biophysical systems. This method stands now as a powerful tool to study more realistic lipid bilayers where pH can influence both the lipids and the solutes interacting with them.

Measurements of isothermal (vapor + liquid) phase equilibrium for {trifluoroiodomethane (R13I1) + 1,1-difluoroethane (R152a)} from T = (258.150 to 283.150) K

In this paper, isothermal (vapor+liquid) equilibrium (VLE) values for {trifluoroiodomethane (R13I1)+1,1-difluoroethane (R152a)} at T=(258.150 to 283.150)K are presented. The experimental apparatus was based on a vapor-recirculation method. The VLE measurements were regressed by the Peng–Robinson equation of state with two models, the Van der Waals mixing rules and the Huron–Vidal mixing rules using the NRTL activity coefficient model. The newly measured VLE values satisfied the thermodynamic consistency test. The results have led to that the two models selected are both suitable for the description of the binary system. Azeotropic behavior can be found for the system measured.

Isobaric vapor–liquid equilibrium for ternary system of sec-butyl alcohol + sec-butyl acetate + N,N-dimethyl acetamide at 101.3 kPa

Isobaric vapor–liquid equilibrium (VLE) data were measured for the binary systems sec-butyl alcohol+N,N-dimethyl acetamide (DMAC), sec-butyl acetate+DMAC and the ternary system sec-butyl alcohol+sec-butyl acetate+DMAC at 101.3kPa using a vapor–liquid equilibrium still. The thermodynamic consistency test for the binary experimental data was made by Herington method and McDermott–Ellis method. And the thermodynamic consistency test for the ternary experimental data was made by McDermott–Ellis method. The binary VLE data were correlated with the NRTL, Wilson and UNIQUAC activity coefficient models. The obtained binary interaction parameters were used to predict the binary and ternary VLE data. The results indicate that the calculated values of vapor phase mole fraction and boiling temperature by the NRTL, Wilson and UNIQUAC models agree well with the experimental data. And the binary pseudo-azeotrope of sec-butyl alcohol and sec-butyl acetate was eliminated when the mass ratio of DMAC to the pseudo-azeotrope mixture is 6:5. Thus, DMAC is an appropriate solvent for separation of the mixture of sec-butyl alcohol and sec-butyl acetate in extractive distillation.

Isobaric Vapor–Liquid Equilibrium for Two Binary Systems{Propane-1,2-diol + Ethane-1,2-diol and Propane-1,2-diol + Butane-1,2-diol} at p = (10.0, 20.0, and 40.0) kPa

Isobaric vapor–liquid equilibrium (VLE) data for the two binary systems of {propane-1,2-diol + ethane-1,2-diol and propane-1,2-diol + butane-1,2-diol} at p = (10.0, 20.0, and 40.0) kPa have been determined using a modified Rose–Williams still with continuous circulation of both vapor and liquid phases in this work. The thermodynamic consistency tests of the experimental VLE data were performed according to the methods of the Herington area test and Van Ness point test. The experimental isobaric VLE data were then correlated using the universal quasichemical (UNIQUAC), nonrandom two-liquid (NRTL), Margules, and Wilson activity coefficient models. Consequently, the calculation values showed good agreements with the experimental data measured in this study.

Experimental Investigation and Thermodynamic Modeling of CH4/N2 Adsorption on Zeolite 13X

To implement an experimental study of CH4/N2 adsorption on Zeochem Co. zeolite 13X, a volumetric apparatus was utilized. In this regard, pure adsorption isotherms were measured at different temperatures [(273, 283, 303, 323, and 343) K] and pressures up to 10 bar, while binary data were collected at (303 and 323) K and different pressures and bulk gas phase molar fractions. Integral and differential thermodynamic consistency tests (TCT) were performed to validate the collected data and certify accuracy of the measurements. To have a thermodynamic view over the investigated system, thermodynamic functions such as enthalpy, entropy, surface potential, and Gibbs free energy were estimated numerically. Besides, the measured pure isotherms were regressed using different isotherm equations and the regressed parameters were applied to different models based on the thermodynamic theory of solutions, i.e., ideal adsorbed solution theory (IAST), vacancy solution models (VSM), and Peng–Robinson two-dimensional equat...

A thermodynamic consistency test for experimental isobaric data of wax solubility in gaseous systems

The ever-increasing demand for natural gas as an energy source has led to a great deal of interest and numerous studies being undertaken by researchers in the field. The efficient production of natural gas from deep well reservoirs has always been an area of intense research in the gas production industry, with immense efforts to understand and mitigate issues which can affect this efficiency. The solubility of the waxy compounds in some natural gases can be regarded as one of these issues that may affect production efficiency. In order to fully understand the phenomenon of wax solubility in natural gas, reliable experimental data are required. This study aims to investigate the reliability of such data using a thermodynamic model. For this purpose, the wax solubility in supercritical constituents of natural gas, such as carbon dioxide and ethane, has been estimated using the Peng–Robinson equation of state and two-fluid van der Waals (vdW2) mixing rules. The residual enthalpies were evaluated using the results obtained. The Gibbs–Duhem equation at constant pressure was applied for evaluation of the consistency of the experimental data. From the analysis, the data were classified as thermodynamically consistent (TC), not fully consistent (NFC), and thermodynamically inconsistent (TI).

Isobaric vapor–liquid equilibrium data for methylcyclohexane + 2-methoxyethanol and methylcyclohexane + 2-ethoxyethanol at 50.00 and 101.33 kPa

Isobaric vapor–liquid equilibrium (VLE) for methylcyclohexane+2-methoxyethanol and methylcyclohexane+2-ethoxyethanol systems were investigated to provide a basis for the design of the separation process of both systems by distillation. The measurements were carried out at 50.00 and 101.33kPa using an all-glass dynamic recirculating still (Fischer VLE 602). The results showed that both systems form the minimum boiling azeotropes at 50.00 and 101.33kPa. All the VLE data passed the thermodynamic consistency test by Herington method and showed positive deviations from ideal behavior. The correlations of the experimental data were completed using the Wilson-HOC, NRTL-HOC and UNIQUAC-HOC models. The results showed all three models had good agreement with the experimental data, especially the NRTL-HOC and UNIQUAC-HOC models. The azeotropic temperatures and compositions at 50.00 and 101.33kPa were determined with the UNIQUAC-HOC model, respectively, which showed that the concentration of methylcyclohexane of both azeotropic systems tended to increase with the descent of the system pressure.

Isobaric vapor–liquid equilibrium for binary system of 2-ethylthiophene + n-octane at 101.33 kPa

Isobaric vapor–liquid equilibrium (VLE) data of 2-ethylthiophene and n-octane binary system were measured at 101.33kPa with a modified Rose-Williams still. Gas chromatography was used to analyze compositions of the samples from the vapor–liquid equilibrium system. The VLE measurement passed the thermodynamic consistency test proposed by Herington and no azeotropic behavior was found. The experimental data were correlated by Wilson, the non-random two-liquid (NRTL) and universal quasi-chemical activity coefficient (UNIQUAC) models, respectively. The corresponding parameters for the three models were obtained. Results showed that the Wilson model gave better predictions than NRTL and UNIQUAC models.

Equilibrium Adsorption Isotherms of Pure N2 and O2 and Their Binary Mixtures on LiLSX Zeolite: Experimental Data and Thermodynamic Analysis

An isothermal–isobaric column dynamic test apparatus was built to measure equilibrium adsorption isotherms of pure N2 and O2 and their binary mixtures at 0, 30, and 65 °C in the pressure range of 0–6 atm on LiLSX zeolite. The data successfully passed an integral and a differential thermodynamic consistency test between pure and binary gas isotherms. The binary selectivities of N2 over O2 were functions of the gas-phase mole fraction and pressure, and the pure gas isosteric heats of adsorption decreased with increased loadings. Thus, the adsorbent was energetically heterogeneous for both gases. The degree of heterogeneity for N2 was larger than that for O2.

Vapor–Liquid Equilibrium Data for 1-Methyl-2-Pyrrolidone + (1-Butanol or 1-Hexene or Water) Binary Mixtures

The unusual properties of 1-methyl-2-pyrrolidone or N-methyl-2-pyrrolidone (NMP) make it a solvent of interest in industrial extractive distillation processes. To augment available data, vapor–liquid equilibrium (VLE) measurements were made for NMP + 1-hexene at (313.15, 335.15, and 363.15) K, for NMP + water at (343.15, 363.15, and 380.15) K, and for NMP + 1-butanol at (10, 25, and 50) kPa using a dynamic recirculating apparatus. Limiting activity coefficients are reported for water and n-hexene as solutes in NMP. Activity coefficient minima were found for 1-butanol as solvent in NMP in the very dilute regions at (10 and 25) kPa. All systems were modeled satisfactorily with the nonrandom two-liquid (NRTL) equation for the Gibbs excess energy with a variable alpha parameter. Thermodynamic consistency testing of the isothermal data with the Van Ness (Van Ness, H. C. Pure Appl. Chem. 1995, 67, 859–872) direct test is discussed.