Comment/Reply Cite This: J. Chem. Eng. Data XXXX, XXX, XXX-XXX
pubs.acs.org/jced
Reply to “Comment on ‘Reliable Correlation for Liquid−Liquid Equilibria outside the Critical Region’” Łukasz Ruszczyński,† Alexandr Zubov,† John P. O’Connell,‡ and Jens Abildskov*,† †
PROSYS, Department of Chemical and Biochemical Engineering, Technical University of Denmark, Building 229, 2800 Kongens Lyngby, Denmark ‡ Department of Chemical Engineering, University of Virginia, 102 Engineers’ Way, Charlottesville, Virginia 22904-4741, United States ABSTRACT: We respond to the comments by Glass and Mitsos regarding our approach to validation of binary liquid−liquid equilibrium data.
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he essence of the comments by Glass and Mitsos1 appears to be that we2 did not include limits on the ranges of the parameters cα and cβ for meeting stability criteria. They also claim that all of the parameters should be regressed simultaneously rather than piecewise. Our paper2 presented an alternative approach for validating binary liquid−liquid equilibrium (LLE) data. We reported some initial comparisons with other models, including attention to meaningful parameter identification. Glass and Mitsos acknowledge that identifiability is not a question of choosing an appropriate regression technique. Nevertheless, the focus of their comment is only to recommend selection of a different regression technique. Such a selection is usually made because an alternative would be simpler to implement or would give more accurate and/or reliable results. We first note that their suggestion of parameter constraints could limit application of the model, and prevent the most meaningful outcome. Then we explore the consequences of the results provided in their Supporting Information. In response to the first point of Glass and Mitsos, there are statements in our paper following eqs 16 and eq 24 that the values of cα and cβ are expected to be negative, consistent with normal negative derivatives of the activity coefficients of the dilute components in each phase. Table 1 contains a similar statement. We did not emphasize the quantitative aspects of stability because the phase boundaries of the systems of our initial interest are well outside the bounds of instability. Thus, while the limit of cα,β > −2T from Glass and Mitsos could be appropriate for systems where the mole fractions cover the range 0 ≤ xα,β ≤ 1, for the LLE systems of our interest, the mole fractions are mostly close to pure-component limits. In fact, since the factor with mole fractions in the numerator of their eq 1 is much less than 0.25 for most systems investigated, cα,β could be much more negative without instability appearing. Property variations with composition in dilute solutions can be different from those at midrange. Therefore, constraining the cα,β values as Glass and Mitsos propose could prevent finding values of physical significance in certain situations. We explore this below but note here that all of the regressed cα,β values listed in our Table 7 are far less negative than the −2T from stability. © XXXX American Chemical Society
Second, we did regress all of the parameters simultaneously, but we found that the great differences in parameter sensitivity gave unreliable results, especially in cases where the miscibilities were very dilute, so that the calculated phase boundary compositions were quite insensitive to the cα,β values. We wanted to make explicit the uncertainties in the cα,β values and concluded that the outputs from simultaneous regression were not as informative as when regression was done in two stages. Figures 3 and 7 attempt to demonstrate these uncertainties, and the issue is discussed following eq 24; the uncertainties are listed in Table 7. The concern of Glass and Mitsos about not finding a global optimal fit is not relevant here because we examined very large ranges of these parameters and found that the objective function showed simple behavior. In their Supporting Information, Glass and Mitsos1 present a GAMS code to regress LLE data with our2 equations. They examined the octanol/water system. That system shows extremely low concentrations of octanol in the aqueous phase. In contrast, the mole fractions of water in the organic phase are significant, though they change little over the temperature range of the data. The input to the GAMS regression sets negative lower bounds associated with stability and small negative upper bounds on the cα,β. In the end, agreement with the data was not fully within the reported significant figures of the data, and the final cα,β values were at the upper bounds. No parameter uncertainties were tabulated. Our interpretation of these parameter values is that both phases are said to have negligible nonideality relative to infinite dilution. This is unexpected for an organic phase with significant amounts of water. It seems that the small temperature variation of the organic phase composition caused the organic phase to be considered dilute in water. Unfortunately, it is not clear from the material if other cα,β values, within uncertainty, would be at least equally successful in matching the data. Manually exploring a greater parameter range could have revealed whether other parameters would also Received: August 10, 2017 Accepted: September 28, 2017
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DOI: 10.1021/acs.jced.7b00724 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Comment/Reply
fit the data. It seems from the code that this possibility was not explored during regression. Thus, it is not apparent that the approach of Glass and Mitsos produces better regression results. In any case, this issue is not the principal focus of our work. We appreciate the Editor’s patience through the several iterations of this communication.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
John P. O’Connell: 0000-0003-0817-5887 Jens Abildskov: 0000-0003-1187-8778 Notes
The authors declare no competing financial interest.
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REFERENCES
(1) Glass, M.; Mitsos, A. J. Chem. Eng. Data 2017, DOI: 10.1021/ acs.jced.7b00642. (2) Ruszczyński, Ł.; Zubov, A.; O’Connell, J. P.; Abildskov, J. J. Chem. Eng. Data 2017, 62, 2842.
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DOI: 10.1021/acs.jced.7b00724 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
