A thermodynamic consistency test for the binary constant-temperature VLE data using numerically optimized binary parameters

Kato, Satoru

doi:10.1016/j.fluid.2010.06.002

Cited by 9 publications

(10 citation statements)

References 15 publications

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“…(12). In a previous investigation [10], the D value was approximated using a finite difference method as follows:…”

Section: Thermodynamic Consistency (Tc) Linesmentioning

confidence: 99%

“…(15) clearly demonstrates that the GD equation, D = 0, is satisfied, if A = B holds in spite of the notable experimental error represented by x 1 / = 0. Based on this fact, an intrinsic TC test was proposed [10] using the A = B relationship, i.e., a one-binary parameter Margules equation. It was shown that non-polar binaries mainly satisfy the intrinsic test [10].…”

Section: Thermodynamic Consistency (Tc) Linesmentioning

confidence: 99%

“…Based on this fact, an intrinsic TC test was proposed [10] using the A = B relationship, i.e., a one-binary parameter Margules equation. It was shown that non-polar binaries mainly satisfy the intrinsic test [10]. In addition to the previous intrinsic TC test, the present investigation develops an empirical consistency test on the basis of the GD equation, D = 0, satisfied at x 1 = 0 in spite of the notable differences in the binary parameters, A / = B, which holds in polar binaries.…”

Section: Thermodynamic Consistency (Tc) Linesmentioning

confidence: 99%

“…However, experimental errors prevent us from a direct comparison between the accurate data and the Gibbs-Duhem (GD) equation; therefore, conventional data correlations using activity coefficient equations have a fault that the effect of the experimental errors on the deviation from the GD equation cannot be identified. On the other hand, by applying a finite difference method to the GD equation combined with the three-suffix Margules equation, Kato [10] showed that the deviation from the GD equation, D, resulting from the experimental errors involved in the liquid phase composition, x 1 , is explicitly formulated as D = 2(B − A) x 1 2 , where A E-mail address: kato-satoru@tmu.ac.jp and B denote the binary parameters of the Margules equation representing the experimental data. Using this formula, a TC test was proposed; however, its application is limited to simple or non-polar liquid mixtures.…”

Section: Introductionmentioning

confidence: 99%

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An empirical consistency test using thermodynamic consistency lines for the VLE data of 7262 constant-temperature and 5167 constant-pressure binaries

Kato

2011

Fluid Phase Equilibria

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“…(12). In a previous investigation [10], the D value was approximated using a finite difference method as follows:…”

Section: Thermodynamic Consistency (Tc) Linesmentioning

confidence: 99%

Section: Thermodynamic Consistency (Tc) Linesmentioning

confidence: 99%

Section: Thermodynamic Consistency (Tc) Linesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An empirical consistency test using thermodynamic consistency lines for the VLE data of 7262 constant-temperature and 5167 constant-pressure binaries

Kato

2011

Fluid Phase Equilibria

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“…(10). In a previous investigation [5], D was approximated using a finite difference method, and it was shown that D is simply formulated as follows:…”

Section: Determination Of the Tc Linesmentioning

confidence: 99%

Thermodynamic Consistency Lines of the 511 Mutual Solubility Data and the VLE Data of 7262 Constant-Temperature and 5167 Constant-Pressure Binaries

Kato

Tachibana

2011

SERDJ

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It has already been shown that the binary vapor-liquid equilibrium (VLE) data form thermodynamic consistency (TC) lines, defined using the polarity exclusion factor; i.e., the ratio of data deviation from the Gibbs-Duhem equation, F, to |B-A|, where A and B denote Margules parameters representing the VLE data. The present investigation shows that the mutual solubility data from the literature converge to TC lines. It was shown that fluctuations of the TC lines from the LLE data are less than those from the VLE data. IntroductionMutual solubility data are of practical importance for the rational design of solvent selection and the prediction of ternary liquid-liquid equilibria (LLE). A significant number of mutual solubility data can be found in the literature [1]. However, a method for determining the thermodynamic consistency of the mutual solubility data has not yet been established. Meanwhile, Kato [2] recently showed that TC lines are useful for the thermodynamic consistency (TC) identification of the binary vapor-liquid equilibrium (VLE) data [3]; i.e., it was shown that each binary has a straight TC line represented as β = aP b , where β and P denote the polarity exclusion factor and the system pressure, respectively, while a and b are constants. It has already been shown that the TC line for the 1-butanol(1)-water(2) binary determined from the VLE data is identical with that determined from the binary LLE data. It was also suggested that the data convergence of the TC line from the LLE data are much better than that from the VLE data [2].The purpose of the present investigation is to show that all of the mutual solubility data from the literature conform to their TC lines, and that their data convergences are excellent.

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A rigorous method to evaluate the consistency of experimental data in phase equilibria. Application to VLE and VLLE

2017

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This work forms part of a broader study that describes a methodology to validate experimental data of phase equilibria for multicomponent systems from a thermodynamic‐mathematical perspective. The goal of this article is to present and justify this method and to study its application to vapor–liquid equilibria (VLE) and vapor–liquid–liquid equilibria (VLLE), obtained under isobaric/isothermal conditions. A procedure based on the Gibbs‐Duhem equation is established which presents two independent calculation paths for its resolution: (a) an integral method and (b) a differential method. Functions are generated for both cases that establish the verification or consistency of data, δψ for the integral test and δζ for the differential approach, which are statistically evaluated by their corresponding average values [ δtrueψ¯, δtrueζ¯], and the standard deviations [ strue(δψtrue), strue(δζtrue)]. The evaluation of these parameters for application to real cases is carried out using a set of hypothetical systems (with data generated artificially), for which the values are adequately changed to determine their influence on the method. In this way, the requirements of the proposed method for the data are evaluated and their behavior in response to any disruption in the canonical variables (p,T, phase compositions). The conditions for thermodynamic consistency of data are: δtrueψ¯<2, strue(δψtrue)<0.2, δtrueζ¯<5, and s(δξ)<0.2. In systems with VLLE, in addition to the previous criteria, must occur that: δxLLE<0.05 and δTLLE<0.5 K. The new proposed method has been tested with a set of 300 experimental binary systems, biphasic and triphasic, obtained from published bibliography, and the results are compared with those of other tests commonly used for testing thermodynamic consistency. The results show that the greater rigor of the proposed method is mainly due to the simultaneous verification of various independent variables. As a result, the conditions for the new test are verified for fewer systems than using other tests mentioned in the literature (i.e., Fredenslund‐test and direct of Van Ness). Its unique application is sufficient to ensure the consistency of experimental data, without using other tests. © 2017 American Institute of Chemical Engineers AIChE J, 2017

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A thermodynamic consistency test for the binary constant-temperature VLE data using numerically optimized binary parameters

Cited by 9 publications

References 15 publications

An empirical consistency test using thermodynamic consistency lines for the VLE data of 7262 constant-temperature and 5167 constant-pressure binaries

An empirical consistency test using thermodynamic consistency lines for the VLE data of 7262 constant-temperature and 5167 constant-pressure binaries

Thermodynamic Consistency Lines of the 511 Mutual Solubility Data and the VLE Data of 7262 Constant-Temperature and 5167 Constant-Pressure Binaries

A rigorous method to evaluate the consistency of experimental data in phase equilibria. Application to VLE and VLLE

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