Vapor–liquid Equilibrium Data Sets Research Articles

A generalized neural network model for the VLE of supercritical carbon dioxide fluid extraction of fatty oils

In the present work, a neural network (NN) model was developed for the precise prediction of the phase behavior of supercritical carbon dioxide (SC-CO2) and fatty oils. A total of 678 SC-CO2 + fatty oils vapor–liquid equilibrium datasets for fatty acids, methyl and ethyl esters plus 120 data points for further accuracy examinations were used. The Cascade-Forward scheme was used as the basic architecture for the NN model calculations and predictions. Comparison between the values of the average absolute deviation of the NN model and the most important existing models showed that the NN model outperforms the other alternatives. The overall AAD for CO2 mole fractions in liquid and vapor phases were obtained to be 1.516 and 0.312%, respectively.

Thermophysical Properties of the Lennard-Jones Fluid: Database and Data Assessment.

Literature data on the thermophysical properties of the Lennard-Jones fluid, which were sampled with molecular dynamics and Monte Carlo simulations, were reviewed and assessed. The literature data were complemented by simulation data from the present work that were taken in regions in which previously only sparse data were available. Data on homogeneous state points (for given temperature T and density ρ: pressure p, thermal expansion coefficient α, isothermal compressibility β, thermal pressure coefficient γ, internal energy u, isochoric heat capacity cv, isobaric heat capacity cp, Grüneisen parameter Γ, Joule-Thomson coefficient μJT, speed of sound w, Helmholtz energy a, and chemical potential) were considered, as well as data on the vapor-liquid equilibrium (for given T: vapor pressure ps, saturated liquid and vapor densities ρ' and ρ″, respectively, enthalpy of vaporization Δhv, and as well as surface tension γ). The entire set of available data, which contains about 35 000 data points, was digitalized and included in a database, which is made available in the Supporting Information of this paper. Different consistency tests were applied to assess the accuracy and precision of the data. The data on homogeneous states were evaluated pointwise using data from their respective vicinity and equations of state. Approximately 10% of all homogeneous bulk data were discarded as outliers. The vapor-liquid equilibrium data were assessed by tests based on the compressibility factor, the Clausius-Clapeyron equation, and by an outlier test. Seven particularly reliable vapor-liquid equilibrium data sets were identified. The mutual agreement of these data sets is approximately ±1% for the vapor pressure, ±0.2% for the saturated liquid density, ±1% for the saturated vapor density, and ±0.75% for the enthalpy of vaporization-excluding the region close to the critical point.

The unavoidable necessity of considering temperature dependence of the liquid Gibbs energy of mixing for certain VLE data correlations

Running vapor-liquid equilibrium (VLE) data correlation with interaction parameters independent of temperature is a common practice that may lead to incongruous situations, which may remain unnoticed. A non-negligible number of VLE data sets for binary systems appear very poorly correlated in literature by using any of the existing models with constant parameters and without any apparent explanation. This paper illustrates the unavoidable necessity of considering the temperature dependence for the parameters of the models used to formulate the activity coefficients of the liquid mixtures (such as NRTL, UNIQUAC, Wilson, among others) in order to adequately represent certain experimental data. For these systems, such an approach is mandatory and not a choice. Moreover, there are certain cases where even considering such temperature dependence of the parameters of the liquid phase is not enough and other alternatives must be used in order to enable a coherent correlation of the VLE data.In addition, a strategy has been suggested that allows knowing in advance when the parameters should be considered temperature dependent. The attractive feature of this proposal is that the answer to the question of whether a T-dependence is necessary is obtained just from the experimental VLE data, without using any particular model for the Gibbs energy of mixing for the liquid phase. New results of VLE data correlation showing markedly improved fittings are presented for some of the systems poorly correlated in literature, showing the potential of the procedure.

Isothermal Vapor–Liquid Equilibrium Data for Binary Mixtures of Hexafluoroethane (R116) + n-Pentane or n-Hexane at Two Temperatures, 288 and 296 K

The isothermal vapor–liquid equilibrium (VLE) data for two hexafluoroethane (R-116)/n-alkane systems were each measured at two temperatures of 288 and 296 K. The two n-alkanes of interest are n-pentane and n-hexane. The pressures which were measured ranged from 0.017 to 7.040 MPa. A “static-analytic” VLE apparatus, equipped with pneumatic Rapid Online Sampler-Injector (ROLSI) capillary samplers, was used to perform the measurements. The ROLSI gives this apparatus the capability of sampling both the liquid and the vapor phases, without significant equilibrium perturbation with respect to the estimated analytical uncertainties. Vapor–liquid–liquid equilibria and liquid–liquid equilibria were experienced at R-116 compositions close to unity for the R-116 and n-hexane system. Each of the four P–x–y VLE data sets was correlated with the Peng–Robinson equation of state, modified by the inclusion of the Mathias-Copeman alpha function in preference to the original Peng-Robinson configuration. The Wong-Sandler mix...

Thermodynamic and statistical consistency of vapor–liquid equilibrium data

The validation of vapor–liquid equilibrium (VLE) data sets using point to point or area tests is not a sufficient condition for their consistency. It is also necessary to analyze the statistical consistency of the activity coefficient model that represents the VLE data. In this work it is shown how to test both consistencies applying statistical tests to the residuals (differences between experimental and calculated values) of the variables related with the VLE data fit. Results from the application to four different VLE data sets shows that thermodynamic consistency and statistical consistency are not necessarily related, making necessary to apply both the area test and the analysis of residuals, for all variables.

Vapor–liquid equilibria for ethyl acetate + methanol and ethyl acetate + ethanol mixtures: Experimental verification and prediction

This work aims of the determination of a series of vapor–liquid equilibrium (VLE) experimental data at low pressure (70kPa) for binary mixtures of ethyl acetate with methanol and ethanol. The Fischer's ebulliometer was used for the measurements of VLE data. A complete series of equilibrium data was obtained such as pressure, temperature and compositions of the liquid and vapor phases (PTxy). The two VLE data sets were submitted to a thermodynamic consistence test, where the deviations were evaluated in all variables, using the UNIQUAC activity coefficient equation. The magnitude of the average deviations was within the experimental uncertainty satisfying the Gibbs–Duhen equation. The data sets were also used to test the prediction of the UNIFAC model in its original and modified editions and the results were also within experimental uncertainties. Then a series of binary systems containing alcohols (methanol and ethanol) and esters (methyl and ethyl acetate) were collected from the literature for testing systematically the capability of the UNIFAC contribution method for this type of mixtures.

Development and analysis of the Original UNIFAC-CI model for prediction of vapor–liquid and solid–liquid equilibria

In this work, we present a further development and analysis of the Original UNIFAC-CI models for the prediction of vapor–liquid equilibrium (VLE) and solid–liquid equilibrium (SLE) for a wide range of mixtures. Three sets of atom interaction parameters (AIPs) have been regressed. For the first two sets, only VLE experimental data were used in parameter estimation. In the first set, no weighting factors were used for each of the VLE data in the objective function when regressing the AIPs. However, for the second set, the AIPs have been regressed using the so-called QVLE quality factors obtained for each of the VLE data from a quality assessment algorithm (consistency tests) as weighting factors in the objective functions. For the third set of parameters, SLE and VLE data were used in the regression of AIPs. The result of the correlations in terms of deviations errors and predictions using these three sets of regressed parameters are presented, compared and discussed. The significance of adding the QVLE values and SLE systems in the regression of the AIPs are also highlighted. UNIFAC is a model that can be in principle used for both VLE and SLE (as well as other types of phase behavior) calculations. The range of applicability of the predictive UNIFAC-CI is investigated and it is shown to what extent the Original UNIFAC-CI model can successfully predict SLE especially when the needed parameters are missing.

Quality Assessment Algorithm for Vapor−Liquid Equilibrium Data

A quality assessment algorithm for vapor−liquid equilibrium (VLE) data has been developed. The proposed algorithm combines four widely used tests of VLE consistency based on the requirements of the Gibbs−Duhem equation, with a check of consistency between the VLE binary data and the pure compound vapor pressures. A VLE data-quality criterion is proposed based on the developed algorithm, and it has been implemented in a software application in support of dynamic data evaluation. VLE predictions (NRTL and UNIFAC) were deployed to detect possible anomalies in the data sets. The proposed algorithm can be applied to VLE data sets with at least three state variables reported (pressure, temperature, plus liquid and/or vapor composition) and is applicable to all nonreacting chemical systems at subcritical conditions. Application of the developed algorithms to identification of erroneous published VLE data sets is demonstrated.

Isothermal Vapor−Liquid Equilibrium Data for the Hexafluoropropylene (R1216) + Propylene System at Temperatures from (263.17 to 353.14) K

Isothermal vapor−liquid equilibrium (VLE) data are presented for the system hexafluoropropylene (R1216) + propylene (R1270). Measurements were performed for six isotherms ranging from (263.17 to 353.14) K, at pressures from (0.224 to 4) MPa. The measurements were undertaken using a “static−analytic” type apparatus, with sampling of the equilibrium phases via pneumatic capillary samplers (Rolsi, Armine’s patent). The apparatus and the samplers were developed in the CEP/TEP laboratory. The uncertainties in the measurements are within ± 0.02 K, ± 0.0005 MPa, and less than ± 4.0 % for temperature, pressure, and mole fractions, respectively. The full set of isothermal VLE data is correlated with the Peng−Robinson equation of state (PR EoS), incorporating the original Soave α function, with the Wong−Sandler mixing rule utilizing the nonrandom two-liquid (NRTL) activity coefficient model.

Vapor−Liquid Equilibrium for Binary System of 1-Propanethiol, Thiophene, and Diethyl Sulfide with Toluene at 90.03 kPa

Isobaric vapor−liquid equilibrium (VLE) for three systems with different organic sulfur compounds (1-propanethiol + toluene, thiophene + toluene, and diethyl sulfide + toluene) were measured at 90.03 kPa with a circulation still. The experimental results were compared with original UNIFAC, UNIFAC-Dortmund, and COSMO-RS predictive models. All systems showed nearly ideal behavior. VLE data sets measured passed the point consistency test.

Prediction of VLE data using radial basis function network

Artificial neural network with radial basis function (RBF) was explored for prediction of the vapor liquid equilibrium (VLE) data. Four typical binary systems, representing different deviations from ideality (in mixing) were considered. For each type of binary system, a set of experimental VLE data from Dechema series was used to train the network. The rest of the available experimental data was used for testing the predictive capability of the network. VLE data for two ternary systems were predicted utilizing a similar network. Three sets of binary data include all the binary combinations possible with three components of the ternary system. These three sets were used to train the network for each ternary system. UNIQUAC model stores the VLE data through regression of the model parameters. The same set of VLE data can be reproduced utilizing thermodynamic models. The accuracy of such reproduction (as reported in Dechema series) is compared with the accuracy of prediction of the same set of data by RBF network. The comparison is presented here for all the four binary systems and the ternary system. The computational (storage) requirements for the networks were also evaluated.

Aqueous Ammonia Vapor-Liquid Equilibria: Entropy and Temperature Dependence of Wilson Coefficients

This study extends a model for nonideal solution behavior by considering the temperature dependence of the coefficients in the Wilson equation for the aqueous ammonia system. Twenty-seven isothermal sets of experimental PXY data up to 2 MPa (20 atm) pressure (284 points) were analyzed using an objective function based on the excess Gibbs free energy to determine the pair of Wilson coefficients for each data set. Evaluation of these results supports the interpretation of the interaction parameters in Wilson's equation as temperature-dependent entropy functions. Comparison of computed results is made with four categories of vapor–liquid equilibrium (VLE) data: (1) primary PTXY, (2) refined PTXY, (3) secondary PTXY or PTM, and (4) partial. Excellent agreement is found with computed results for all but two of these VLE data sets in the region of rapidly changing vapor composition up to 90 mole % of ammonia. A comparison is also made to the only three previously published single-temperature (isothermal) pairs of Wilson coefficients with better agreement in Y, for all three cases, and in P, for two cases. A straightforward procedure is outlined to estimate any set of PTXY values (in the range P < 2 MPa, Y < 0.9) for the aqueous ammonia system.

Reliable nonlinear parameter estimation in VLE modeling

The reliable solution of nonlinear parameter estimation problems is an important computational problem in the modeling of vapor–liquid equilibrium (VLE). Conventional solution methods may not be reliable since they do not guarantee convergence to the global optimum sought in the parameter estimation problem. We demonstrate here a technique that is based on interval analysis, which can solve the nonlinear parameter estimation problem with complete reliability, and provides a mathematical and computational guarantee that the global optimum is found. As an example, we consider the estimation of parameters in the Wilson equation, using VLE data sets from a variety of binary systems. Results indicate that several sets of parameter values published in the DECHEMA VLE Data Collection correspond to local optima only, with new globally optimal parameter values found by using the interval approach. When applied to VLE modeling, the globally optimal parameters can provide significant improvements in predictive capability. For example, in one case, when the previously published locally optimal parameters are used, the Wilson equation does not predict experimentally observed homogeneous azeotropes, but, when the globally optimal parameters are used, the azeotropes are predicted.

Vapor-liquid equilibrium measurements and data analysis of tert-butanolisobutanol and tert-butanolwater binaries at 94.9 kPa

Isobaric vapor-liquid equilibrium (VLE) data were measured for the systems tert-butanol-isobutanol and tert-butanolwater at 94.9 kPa using a modified Malanowski equilibrium still. While the experimental data of the former binary showed a slight deviation from ideality, the latter binary showed a significant deviation. The experimental data of this work, in addition to two isobaric VLE data sets from the literature, have been analyzed using Wilson, NRTL, UNIQUAC, ASOG, and the modified UNIFAC models. Optimum interaction parameters, together with their correlation coefficients, for the first three models were generated using the maximum likelihood principles. As to the group contribution models (ASOG and UNIFAC), interaction parameters from the literature were utilized in the data analysis. A comparable correlation of the experimental data was obtained for the first three models; the maximum values of Root-Mean-Square-Deviation (RMSD) of bubble point temperatures and vapor mole fractions were 0.24 K and 0.044, respectively (using NRTL). ASOG and the modified UNIFAC gave similar predictions; the maximum RMSD of bubble point temperatures was found to be 0.7 K whereas that of vapor mole fractions was 0.022.

On the temperature dependence of the UNIQUAC/UNIFAC models

Local composition models for the description of the properties of liquid mixtures do not in general give an accurate representation of excess Gibbs energy and excess enthalpy simultaneously. The introduction of temperature dependent interaction parameters leads to considerable improvements of the simultaneous correlation. The temperature dependent parameters have, however, little physical meaning and very odd results are frequently obtained when the interaction parameters obtained from excess enthalpy information alone are used for the prediction of vapor-liquid equilibria. The UNIQUAC/UNIFAC models are modified in this work by the introduction of a general temperature dependence of the coordination number. The modified UNIQUAC/UNIFAC models are especially suited for the representation of mixtures containing non-associating components. The modified models contain the same number of interaction parameters as the original ones, namely two per binary pair of molecules/groups. The resulting simultaneous representation of excess Gibbs energy and excess enthalpy by means of one unique set of parameters is remarkably successful. One may with very good results predict excess Gibbs energy information from UNIQUAC parameters based on excess enthalpy data, and the prediction of excess enthalpy information from only one isothermal set of vapor-liquid equilibrium data is qualitatively acceptable. A parameter table for the modified UNIFAC model is given for the five main groups: CH 2, C  C, ACH, ACCH 2 and CH 2O.