Editorial pubs.acs.org/jced
Guidelines for the Analysis of Vapor−Liquid Equilibrium Data ABSTRACT: It is current practice to represent and analyze vapor−liquid equilibrium data through the use of state conditions (temperature and pressure) and phase compositions. However, these representations do not reveal and identify the accuracy of the data for important purposes, such as separation by distillationand this is particularly a problem for the important lowconcentration regions. The intent of this editorial is to present the guidelines of the Journal of Chemical & Engineering Data that vapor−liquid equilibrium data should be evaluated through the use of charts and related analyses that bring to light the lowconcentration regions, for example, K-values and relative volatilities.
Figures are essential to communicating the content and accuracy of measured and estimated data in the Journal of Chemical & Engineering Data (JCED). Ambrose1 captured the crux of the idea when he wrote: “The eye can see at a glance what may not be easy to deduce from columns of numbers and a few statistical parameters.” Diky2 recently demonstrated that modifying the mole fraction x1 to log10(x1/x2) = log10(x1/(1 − x1)) for liquid− liquid and solid−liquid equilibria of binary mixtures enables “stretching” of both ends of the mole fraction, and hence “is probably the most efficient way to communicate such information to a human.” It is sufficient to visualize and analyze just the low mole fraction in liquid−liquid and solid− liquid equilibria because the other phase usually has the analogous concentration at a relatively high value, and, in fact, the value of Diky’s proposed figure is that it highlights both low mole fractions in a single chart. Vapor−liquid equilibrium (VLE) data are inherently different because both the vapor and liquid concentrations are simultaneously at low values, and it is the ratio of the concentrations that is relevant to industrial separation processes such as distillation, and especially distillations that produce ultrapure products. Mathias3 investigated the benzene + chloroform + acetone system and showed the improved effectiveness of K-value and relative-volatility charts over the customary Txy diagram to quantitatively estimate the data accuracy, and to establish uncertainty estimates for engineering design and analysis. Representative ideas and results from this paper are reproduced here to highlight the key views. Figure 1 compares calculations from the NRTL-RK property option (nonrandom two liquid (NRTL) activity-coefficient model and Redlich−Kwong equation of state for the vapor phase) with the data of Kojima et al.4 for the acetone + chloroform binary mixture at 101.3 kPa using a Txy diagram. The figure indicates that the agreement between model and data is good, and that both the model and data clearly depict the maximum-boiling azeotrope, but charts such as Figure 1 are unable to provide quantitative uncertainty estimates, and are particularly weak in this respect at the two pure ends. Figure 2 compares calculated relative volatilities for the same acetone + chloroform binary at 101.3 kPa with data from Kudryavtseva and Kusarev,5 Kogan and Deizenrot,6 Kojima et al.,4 and Segura et al.7 The data from all four sources agree well (except for two outliers from Kogan and Diezenrot, which are readily identified), and the chart clearly demonstrates that the relative standard uncertainty of the model for the relative volatility is better than 0.05; note that 51 out of 62 points or 82% are within the 5% corridor, and the © 2017 American Chemical Society
Figure 1. Txy diagram of the acetone−chloroform binary mixture at 101.3 kPa. Comparison of model calculations to the data of Kojima et al.4 Figure reprinted with permission from ref 3. Copyright 2016 Elsevier.
standard uncertainty corresponds to 68%. Figure 1 is effective in showing the existence of the azeotrope, but Figure 2 is far superior since it also identifies the azeotrope (relative volatility equal to unity), and, in addition, enables quantification of model and data uncertainties “at a glance,” and is an effective way to “communicate such information to a human.” Figure 3 shows a comparable way to visualize information analogous to Figure 2 for ternary and higher mixtures; it presents percentage differences between acetone K-values from model and data plotted against the mole fraction of acetone; note that Mathias3 also presented analogous charts to Figure 3 for benzene and chloroform as the chosen component. We expect the most interesting and relevant comparisons at low concentrations. Indeed, review of Figure 3 shows that the model K-values agree with the data of Kojima et al.4 to within ±5%, but the deviations from the data of Reinders and de Minjer8 are much larger, suggesting greater uncertainty of the latter data set. The relatively high uncertainty of the Reinders and de Minjer8 data is likely a consequence of their indirect analytical approach in which the compositions were deduced through measurements of the mixture density and refractive index rather than by direct composition measurements. Kojima et al.4 did not seem to recognize the large uncertainty of the Reinders and de Minjer8 K-values since their paper simply stated: “The predicted vapor compositions of our parameters agree with Reinders’ data in the Published: August 10, 2017 2231
DOI: 10.1021/acs.jced.7b00582 J. Chem. Eng. Data 2017, 62, 2231−2233
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Editorial
Figure 4. Percentage errors of model K-values of ethanol in comparison to the ternary VLE data of Kurihara, Nakamichi, and Kojima,9 and Resa et al.10 for the water + methanol + ethanol ternary mixture at 101.3 kPa. It is noted that the y-axis range has been restricted to ±40% in order to clearly reveal the data accuracy. There are six points from Resa et al. for which the percentage error exceeds 40%.
Figure 2. Relative volatilities of the acetone + chloroform system at 101.3 kPa. Comparison of model results to the data of Kudryavtseva and Susarev,5 Kogan and Diezenrot,6 Kojima et al.,4 and Segura et al.7 The chart also shows (dashed lines) ± 5% deviations from the calculated relative volatility. Figure reprinted with permission from ref 3. Copyright 2016 Elsevier.
is further evidence that indirect concentration measurements have poorer accuracy at low concentrations. It is noted here that Resa et al. did report activity coefficients, and comparison of calculated to experimental activity coefficients will give a chart equivalent to Figure 4 since vapor-phase nonideality is not important at the low pressure of 101.3 kPa. The editors of JCED do not stipulate that any particular model should be used, but the analysis in this editorial clearly demonstrates the value of using a phase-equilibrium model as an aid to data analysis. The editors of JCED also do not wish to prejudge particular experimental and estimation procedures as these constantly evolve and improve over time due to the skill and creativity of researchers. However, the editors of JCED emphasize the following guidelines for the analysis of measured and estimated VLE data: 1. Data should be analyzed through the use of an appropriate model. 2. Data analysis should be performed such that the sensitivity remains valid even when the measured concentrations are low. 3. Data analysis should include distribution coefficients such as K-values and relative volatilities, similar to those in Figure 2, Figure 3, and Figure 4 of this Editorial. 4. Charts should be designed such that the key results can be “seen at a glance by a human.”
Figure 3. Percentage errors of model K-values of acetone in comparison to the ternary VLE data of Reinders and de Minjer8 and Kojima et al.4 for the acetone + chloroform + benzene ternary mixture at 101.3 kPa. Figure reprinted with permission from ref 3. Copyright 2016 Elsevier.
accuracy of 0.003 mole fraction on the average;” however, a chart such as Figure 3 renders the conclusion obvious “at a glance.” The use of Txy and analogous charts is, unfortunately, the norm in VLE data evaluation. Figure 4 presents another example where the calculated ethanol K-values for the water + methanol + ethanol ternary mixture at 101.3 kPa are compared to two sets of experimental data, from Kurihara, Nakamichi, and Kojima,9 and Resa et al.10 The model used is the NRTLRK property option in Aspen Plus V8.811 with out-of-the-box parameters. Figure 4 is similar to Figure 3 in that the data of Kurihara, Nakamichi, and Kojima9 obviously have relatively low scatter and agree with the model to about ±5%, while the data of Resa et al.10 have larger uncertainty, particularly at low ethanol mole fractions. The experimental procedure used by Resa et al. is similar to that of Reinders and de Minjer,8 and this
Paul M. Mathias*
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Fluor Corporation, 3 Polaris Way, Aliso Viejo, California 92698, United States
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Paul M. Mathias: 0000-0001-5781-9525 Notes
Views expressed in this editorial are those of the author and not necessarily the views of the ACS. 2232
DOI: 10.1021/acs.jced.7b00582 J. Chem. Eng. Data 2017, 62, 2231−2233
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REFERENCES
(1) Ambrose, D. The Evaluation of Vapor Pressure Data, unpublished manuscript, 1985. (2) Diky, V. An Efficient Way of Visualization of Mutual Solubility Data in the Whole Range of Compositions. J. Chem. Eng. Data 2017, DOI: 10.1021/acs.jced.7b00174. (3) Mathias, P. M. Effect of VLE Uncertainties on the Design of Separation Sequences by Distillation - Study of the BenzeneChloroform-Acetone System. Fluid Phase Equilib. 2016, 408, 265−272. (4) Kojima, K.; Tochigi, K.; Kurihara, K.; Nakamichi, M. Isobaric Vapor- Liquid Equilibria for Acetone + Chloroform + Benzene and the Three Constituent Binary Systems. J. Chem. Eng. Data 1991, 36, 343− 345. (5) Kudryavtseva, L. S.; Susarev, M. P. Liquid-Vapor Equilibrium in Chloroform-Hexane and Acetone-Chloroform Systems. Zh. Prikl. Khim. (Leningrad) 1963, 36, 1231−1237. (6) Kogan, L. V.; Deizenrot, I. V. Apparatus for Determination of Liquid-Vapor Equilibrium in Systems with Nonideal Vapor Phases. Zh. Prikl. Khim. (Leningrad) 1975, 48, 2757−2759. (7) Segura, H.; Mejia, A.; Reich, R.; Wisniak, J.; Loras, S. Isobaric Vapor-Liquid Equilibria and Densities for the Binary Systems Oxolane + Ethyl 1,1-Dimethylethyl Ether, Oxolane + 2-Propanol and Propan-2One + Trichloromethane. Phys. Chem. Liq. 2003, 41, 283−301. (8) Reinders, W.; de Minjer, C. H. Vapour-Liquid Equilibria in Ternary Systems. II. The System Acetone-Chloroform-Benzene. Rec. Trav. Chim. 1940, 49, 369−391. (9) Kurihara, K.; Nakamichi, M.; Kojima, K. Isobaric Vapor-Liquid Equilibria for Methanol + Ethanol + Water and the Three Constituent Binary Systems. J. Chem. Eng. Data 1993, 38, 446−449. (10) Resa, J. M.; Goenaga, J. M.; Gonzalez-Olmos, R.; Iglesias, M. Measurement and Modeling of Phase Equilibria for Ethanol + Water + Methanol at Isobaric Condition. J. Chem. Eng. Data 2006, 51, 2114− 2120. (11) For further details on Aspen Plus property options, refer to documentation available from Aspen Technology, Inc.
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