vle consistency pitfalls

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ArticlePITFALLS IN THE EVALUATION OF THE THERMODYNAMIC

CONSISTENCY OF EXPERIMENTAL VLE DATA SETSantonio marcilla, Maria del Mar Olaya, Mara Dolores Serrano, and MARA ANGELES GARRIDO

Ind. Eng. Chem. Res., Just Accepted Manuscript DOI: 10.1021/ie401646j Publication Date (Web): 29 Jul 2013Downloaded from http://pubs.acs.org on August 2, 2013

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1

PITFALLS IN THE EVALUATION OF THE THERMODYNAMIC

CONSISTENCY OF EXPERIMENTAL VLE DATA SETS

Antonio Marcilla*, Mara del Mar Olaya, Mara Dolores Serrano and

Mara Angeles Garrido

Chemical Engineering Department, University of Alicante, Apdo. 99, Alicante 03080,

Spain. Tel. (34) 965 903789 Fax (34) 965 903826, *e-mail: [email protected]

ABSTRACT

The thermodynamic consistency of almost ninety VLE data series, including isothermal and

isobaric conditions for systems of both total and partial miscibility in the liquid phase, has

been examined by means of the area and point-to-point tests. In addition, the Gibbs energy

of mixing function calculated from these experimental data has been inspected, with some

rather surprising results: certain data sets exhibiting high dispersion or leading to Gibbs

energy of mixing curves inconsistent with the total or partial miscibility of the liquid phase,

surprisingly, pass the tests. Several possible inconsistencies in the tests themselves or in

their application are discussed. Related to this is a very interesting and ambitious initiative

that arose within the NIST organization: the development of an algorithm to assess the

quality of experimental VLE data. The present paper questions the applicability of two of

the five tests that are combined in the algorithm. It further shows that the deviation of the

experimental VLE data from the correlation obtained by a given model, the basis of some

point-to-point tests, should not be used to evaluate the quality of these data.

KEYWORDS

Thermodynamic consistency, Consistency tests, VLE data, NRTL, Gibbs energy of mixing.

1. INTRODUCTION

Vapor-liquid equilibrium (VLE) data are essential for the simulation and design of many

separation processes. These data are compiled in data banks such as, for example, Dortmunt

Data Bank DBB1 and NIST Source Data Archival System

2. Accurate VLE data are

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demanded for separation process design. VLE data are usually measured under isobaric or

isothermal conditions and require the equilibrium vapor (y) or liquid (x) compositions as

well as the temperature (T) or pressure (P) of the system, respectively. Accurate

measurement of y is by far the most difficult and, therefore, many P - x or T x data sets

are frequently published. Only when a full set of measurements P x, y or T x, y (over

determined system) is available is it possible to check whether they satisfy certain

thermodynamic relationships (thermodynamic consistency tests or TC tests). In these cases,

the VLE experimental data are declared thermodynamically consistent, but not necessarily

correct. Conversely, if the experimental VLE data do not obey these conditions then they

will be inconsistent and can always be considered as such providing the thermodynamic

consistency tests are applied rigorously. The fundamental Gibbs-Duhem (GD) equation is

the most widely referenced condition for consistency of the experimental data. This

equation can be handled in a number of ways, leading to a variety of consistency tests that

can be broadly classified as: area or integral test3, point-to-point tests

4-6, L-W test

7, infinite

dilution test6,8

and differential test9. Experimental error propagates differently in each test

and, therefore, some authors propose certain combinations of these tests as an overall check

of the data. For example, Kojima et al. propose the PAI test that is a combination of the

point-to-point, area and infinite dilution tests6,8,10

. Eubank and Lamonte11

advise about the

advantages of a two-step method to check the consistency of the VLE data via the GD

equation. A recent and ambitious initiative is proposed in a paper by Kang et al.12

: the

development of an algorithm to assess the quality of experimental VLE data. This

algorithm combines compliance of the data with the general Gibbs-Duhem equation on the

one hand, with consistency between the VLE data and the pure-compound vapor pressures

on the other. It employs four consistency tests based on the GD equation: area test3, point-

to-point test by van Ness4 and Kojima

6, and infinite dilution test

8. The results of these four

tests plus consistency with pure-compound vapor pressures are represented numerically by

their corresponding individual quality factors (Fi). These are then further combined to

obtain a global quality factor (QVLE) for each one of the evaluated VLE data sets.

Many efforts have been devoted to developing TC tests and applying them to large numbers

of data series. One of the most extensive applications of TC tests and the results thereof is

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contained in the DECHEMA Chemistry Data Series13

compilation, where the area test3

(with the Herington approximation) is used in combination with the Fredenslund point-to-

point test5 to check the consistency of about ten thousand VLE data sets. Another more

recent example of the application of TC tests is the NIST Thermodata Engine (TDE)

software package. It represents the first full-scale implementation of the dynamic data

evaluation concept for thermophysical properties (including phase equilibria) and has led to

the ability to produce critically evaluated data dynamically14

. For example, TDE 3.015

provides area test results for the VLE data sets of binary systems and TDE 6.016

includes

the algorithm proposed by Kang et al.12

to assess the quality of the experimental VLE data

for binary and ternary mixtures.

However, existing TC tests possess many drawbacks, some of which have already been

discussed in the literature17,18

, and others that are partially the subject of the present paper.

It is known that the widely used area test can involve cancellation errors19

. Moreover, the

method is not sensitive at all to the measured total pressure data4,19

. Besides, some of the

data required by the tests are not available and, as a result, recourse is usually made to

approximations. Jackson and Wilsak17

comment that there has not yet been a

thermodynamic consistency test rigorously applied to VLE data nor does there exist a set of

data that is known a priori to be absolutely accurate. The consequences of using some of

the very popular approximations are not sufficiently known and will be discussed in the

present paper. Finally, another very important question to be considered is the fact that

some of the TC tests require models in order to be applied, e.g. excess Gibbs energy (gE)

models. Several issues derived from this fact are already mentioned in the literature, such as

that the test results are highly sensitive to the model that is used17

. Here, we go further by

attempting to present conclusive reasoning to demonstrate that TC tests, combined with the

existing gE models (i.e. local composition models), are not suitable for the evaluation of

experimental VLE data.

Two of the most commonly used TC tests, the area and point-to-point (Fredenslund) tests,

have been used to check the thermodynamic consistency of almost ninety VLE data sets as

examples. These data sets include isothermal and isobaric conditions for both completely

and partially miscible liquid phases. In this regard, the information supplied by a graphical

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representation of the Gibbs energy of mixing (gM

) versus the liquid composition (x) is

highly relevant. Some important inconsistencies found with the cited tests or in their

application are illustrated using selected examples. This discussion is directly related to the

initiative by Kang et al.12

, arising within the National Institute of Standards and Technology

(NIST), to develop an algorithm to assess the quality of published experimental VLE data

sets, which has already been implemented in the TDE 6.0 software16

.

This initiative is not only valuable but also absolutely necessary and represents an advance

toward the final objective of ensuring the quality of published experimental data. In this

sense, some important steps have already been taken. An example of this is the joint

statement by the editors of some journals and the Thermodynamics Research Center (TRC)

of the NIST, which serves to facilitate the searching process when experimental data in

submitted manuscripts must be compared with previously reported literature values20

. This

is the context in which can be better understood the significance of the consistency

algorithm proposed by Kang et al.12

and the importance of the discussion presented in this

paper, which questions the applicability of two of the tests included in that algorithm

because they can lead to a distorted picture of the quality of the experimental data, as

conveniently illustrated by the examples below.

2. THE AREA AND POINT-TO-POINT TC TESTS

In this section, a brief description of the area and the point-to-point tests is presented. For

more details about these and other TC tests several other reference works can be

consulted10,17,18

.

2.1. Area test

The general Gibbs-Duhem equation can be expressed as follows21

:

0dPRT

vdT

RT

Hlndx

i

E

2

E

ii =+

(1)

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where is the activity coefficient of component i, xi is its molar fraction, HE is the excess

enthalpy and vE is the excess volume of the mixture, while R, T and P retain their usual

meaning. For a binary system, the integrated form of eq 1 becomes:

0dPRT

vdT

RT

Hdxln

o1

o2

o1

o2

P

P

ET

T 2

E

11

02

1 =+

(2)

where 0iT and 0iP

are the boiling points and the vapor pressures of pure component i,

respectively.

Under isothermal conditions, the second term in eq 2 vanishes22

and the third can be

neglected8. Then, the area test can be performed according to the Redlich-Kister method

(eq 3) that verifies whether the positive (A) and negative (B) areas in the ln 1/ 2 versus x1

graph are equal3. The condition for passing this test is given by eq 4 using a deviation

parameter D:

0dxln 11

02

1 =

(3)

2BA

BA100D

+

= (4)

Under isobaric conditions, the third term in eq 2 vanishes, but the second one now cannot

be neglected. The evaluation of this term requires excess enthalpy HE data as a function of

the temperature and composition. This information is scarce and rarely available and

impedes rigorous calculation of eq 2. To overcome this problem, Herington23

proposed an

empirical equation (eq 5) to approximately evaluate the integral term depending on HE.

min

minmax

T

TT150J

= (5)

The derivation of this equation was examined by Wisniak18

, who showed that it contained

errors due to the very limited experimental information available to Herington at the time.

Wisniak used an extensive database to show that the J parameter is better represented as

indicated in eq 6:

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( )min

minmax

Emax

Ea

T

TT

G

H34J

= (6)

where Tmax and Tmin are the maximum and minimum boiling temperatures over the entire

concentration range, EaH

is the average heat of excess and EmaxG

is the maximum Gibbs

energy of excess. Eq 6 can be only used when heats of excess data (or their average values)

are available. In the absence of this kind of data a correlation to calculate the ratio

Emax

Ea G/H has been proposed

18. The criterion for the VLE data set to pass the test is

.10JD

7

i

ii0ical

i P

xfy

= (7)

where 0if is the fugacity of pure component i as liquid and i is the fugacity coefficient for i

in the vapor phase. In order to use eq 7, it is necessary to calculate the activity coefficients,

and for this an expression for the excess Gibbs energy (gE) is required.

These authors used the four-suffix Margules (three-parameter) equation

( )211221E

E xCxBxAxxxRT

Gg +=

= (8)

The activity coefficients are calculated from the gE function and its derivative as

1

E

2E

1dx

dgxgln += (9)

1

E

1E

2dx

dgxgln = (10)

The coefficients A, B and C in the gE function are calculated by fitting, using a comparison

between the experimental and calculated total pressure

220211

01

cal xpxpP += (11)

for which eqs 9 and 10 are used to obtain the activity coefficients.

Next, the deviation between the calculated and experimental vapor composition is

evaluated (eq 12). These authors did not place any numerical limit on y in order to

establish whether VLE data are consistent but, obviously, this quantity must be small. They

recommended inspecting the P and y versus x plots to verify that a random scatter about

zero occurs, enabling one to establish consistency of the experimental VLE data.

expi

calii yyy = (12)

2.2.2. The Fredenslund test

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Fredenslund et al.5 proposed several modifications to the van Ness test, such as the use of

the highly flexible Legendre orthogonal polynomials (eq 13) to represent the Gibbs energy

of excess:

( )=

=

=n

1k

1kk21

EE xLaxx

RT

Gg (13)

where ak are the coefficients of order k and Lk(x1) are the Legendre polynomials (eq 14)

( ) ( ) ( ) ( ) ( ) ( )[ ]12k11k11k xL1kxL1x21k2k

1xL = (14)

In addition, for the VLE data to be considered consistent the deviation between the

experimental and calculated vapor compositions (eq 15) should not exceed a certain

maximum established value:

01.0yyyexpi

calii = (15)

This is a widely used test, e.g., DECHEMA Chemistry Data Series13

applies this test

together with the area test to check the consistency of all the VLE data sets it contains, but

the evaluation of the data set is carried out globally by means of eq 16 instead of eq 15:

01.0n

yyn

1i

expi

cali

=

(16)

3. APPLICATION OF TC TESTS TO VLE DATA SETS

The main goal of this work has been to apply several TC tests to VLE data sets for

isothermal and isobaric systems that exhibit both total and partial miscibility in liquid

phase, with the aim of detecting problematic cases that allow identifying suspected

limitations of the tests or in their application.

The source of the experimental VLE data has been the book collection DECHEMA

Chemistry Data Series13

. 72 isothermal systems and 17 isobaric systems have been studied

and are summarized in Tables S1 and S2, respectively, in the Supporting Information. The

area and the Frendenslund point-to-point5 tests have been applied to these systems. Results

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are given as + (consistent) and (inconsistent) in accordance with the corresponding test

criteria. Blanks appear when the number of experimental points is too low or their

distribution is not suitable. Results for these same TC tests are published in the data bank

used13

, but the information for the point-to-point test results given there is for the overall

data set and our study required detailed information of the individual data points. In

addition, the following relationships have been inspected graphically: vapor (y) versus

liquid (x) compositions (equilibrium curve), P versus x and y, and also the Gibbs energy of

mixing for the liquid phase (gM,liq

or gM

) versus x, with the aim of checking the trends and

dispersion of the experimental points (i.e. smoothness, moderate or high dispersion). The

following equation is used to obtain the gM,liq

curve:

( ) ( )222111liq,M

xlnxxlnxRT

G+= (17)

where i is calculated from the experimental equilibrium data.

It is important to remark that the gM

versus x curve is not usually analyzed, in spite of the

fact that it provides highly valuable information about the quality of the data, as we show in

the present paper. A set of good VLE data should necessarily generate a gM

curve

possessing the following two characteristics: a) a smooth tendency and b) consistency with

the total or partial miscibility of the liquid phase. That is to say, if the system presents a

homogeneous liquid phase, the gM

curve must be convex throughout the composition space

(Figure 1a), but if the liquid phase is partially miscible, the gM

curve must be concave in a

region to allow for the existence of a common tangent line between the two liquid mixtures

at equilibrium (points I and II in Figure 1b).

The following represents some relevant data that summarize the information collected in

Tables S1 and S2 (Supporting Information). Among the 89 data sets selected, 25 pass both

tests, 20 data sets pass the area test but do not pass the point-to-point test, and 9 data sets

pass the point-to-point test but not the area test. For 7 data sets the results of the area test

obtained in this study are not in agreement with those published in DECHEMA. This

number increases to 11 for the point-to-point test. As regards the gM

curve obtained from

the experimental VLE data, 22 data sets show a smooth tendency, 28 data sets present a

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moderate dispersion and 39 exhibit a high dispersion or no trend at all. Besides, some of

them (e.g., no. 46, 47 and 60 in Table S1 Supporting Information) correspond to the VLE

data that are inconsistent with the total or partial miscibility of the liquid mixture, as is

shown next.

We reconciled the results of the TC tests with the aforementioned graphical representations

for every one of the VLE data sets included in this study. This produced some rather

unexpected results: some data sets exhibiting a smooth trend did not pass the tests, whereas

others exhibiting high dispersion did. Furthermore, even data sets reproducing gM

curves

that are inconsistent with the total or partial miscibility of the liquid passed the tests.

Obviously, a smooth trend in the data when represented graphically and consistency with

the total or partial miscibility of the liquid phase do not guarantee thermodynamic

consistency of the data. However, the opposite situation, high dispersion or inconsistent

data that do pass the tests, is more difficult to justify. For example, the data sets for acetone

+ water at 100C and ethylene oxide + water at 20C (no. 24 and 7 in Table S1 Supporting

Information), represented graphically in Figures 2 and 3, respectively, show dispersion in

their gM

curves. Nonetheless, both data sets do pass the point-to-point test and the former

even the area test. In relation to the point-to-point test, the data set shown in Figure 2 passes

the overall (but non-individual) test. However, all the points plotted in Figure 3 are

individually thermodynamically consistent according to this test. Figure 4 shows the

water(1) + 1-hexanol(2) system at 40C, whose liquid phase is partially miscible. The data

set selected for this example (no. 60 in Table S1 Supporting Information) generates a gM

curve that is inconsistent because it reproduces a false LL splitting where the system is

actually homogeneous. Conversely, in the composition interval where the system has a true

LL equilibrium26

x1I=0.305 and x1

II=0.998, a point with a homogeneous liquid phase is

obtained. Despite all the inconsistencies in this data set, these experimental points still pass

the (individual) point-to-point test. A possible gM

curve that is consistent with the liquid

behavior of the system has been included, just for the sake of illustration.

The following partial conclusions are deduced from the study summarized in the present

section:

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1. The gM

vs. x curve reveals important information about the quality of the VLE data

that is neither apparent in other typical representations nor in the test results.

2. Some inconsistencies in the TC tests or in their application should exist that justify

the obtained results.

It is especially important to clarify this last point because the area and point-to-point tests

(by van Ness or Frendenslund) are used too often. For example, both are included in the

algorithm proposed by Kang et al.12

whose end purpose is use in the quality evaluation of

the main VLE data banks. In the next section, the area and van Ness point-to-point tests,

such as they are used in the algorithm proposed by Kang et al., are analyzed and important

inconsistencies discussed.

4. SOME INCONSISTENCES IN THE APPLICATION OF TC TESTS

4.1. Area test (with the Herington approximation)

As was explained in section 2, when the area test is applied to isobaric VLE data,

experimental information about the excess enthalpy as a function of the temperature and

composition is required. The approximation proposed by Herington to circumvent the

necessity of these hard-to-come-by data, is still widely used despite having been proved to

be incorrect18,25

. A sign of its popularity is that the Herington equation is included in test 1

of the algorithm proposed by Kang et al.12,27

for the global numerical evaluation of VLE

data sets. In this paper, we present a different approach that invalidates this equation and

corroborates the conclusions reached by Wisniak many years ago18

.

The VLE data of any system, for example water + 1,2-propanediol at 50 mmHg, can be

generated using the NRTL equation based on the parameter values published in

DECHEMA Chemistry Data Series (reference no. 80 in Table S2 Supporting Information).

Because these equilibrium data are obtained by means of a thermodynamically consistent

model, they are totally consistent according to the area test when it is applied rigorously

using eq 2; the second term is evaluated by means of the NRTL equation using the relation

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( )2

EE

RT

H

T

RT/G=

(18)

In contrast, when the Herington approximation is used in the application of the area test to

these same VLE data (generated with the NRTL model), the result is negative: these data

are now thermodynamically inconsistent! This demonstrates the complete unreliability of

the results obtained when the Herington approximation is used to evaluate experimental

VLE data. As a consequence, this equation should not be used in any procedure, algorithm,

etc. whose purpose it is to evaluate such data sets. It may erroneously invalidate correctly

obtained VLE data (such as the data obtained with the NRTL equation in the above

example), or do the opposite of that, i.e. validate spurious data, as has been pointed out by

Wisniak18

. If eq 6 is used instead of eq 5 to evaluate the J parameter, the VLE data set

considered here produces the consistent result, showing that this equation is a better

approximation of the rigorous one than the Herington equation.

4.2. Point-to-point test (van Ness)

In this section, we present strong arguments to demonstrate that point-to-point tests based

on models (i.e. local composition models such as NRTL) and used to verify the quality of

experimental VLE data, should no longer be used without due consideration to their

limitations in representing the phase equilibria of many systems.

The van Ness test (as well as the one by Fredenslund) is regarded as a modeling capability

test. Kang et al.12

state literally that This test shows how a mathematical activity

coefficient model can reproduce the experimental data accurately. These authors include

the van Ness test as part of their proposed algorithm and suggest using the five-parameter

NRTL equation as the required model. Jackson et al.17

note that the required model may be

empirical functions such as spline fits, although the traditional equations are generally

preferred since proper limiting characteristics are already built into them.

However, for far too many systems a satisfactory fitting is not obtained, and regrettably, not

with any model either, at least not good enough to justify using the model as the standard of

comparison for validating experimental data. In these cases, are the data inconsistent or is

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the model unable to represent the experimental phase behavior? The thermodynamic

consistency tests, such as the van Ness point-to-point test, penalize the experimental data

when the model is not capable of fitting them. Some authors17

have noticed that it is

necessary to first find a thermodynamically consistent model that is capable of fitting the

experimental data before the test can be applied, but this important observation is usually

obviated. Furthermore, especially strict consideration should be given to a models ability

to adequately fit a VLE data set when it is to be used as a standard of comparison, i.e. P and

y residuals should be inspected to check that random distributions exist. Only in the paper

by Jackson and Wilsak17

have we found some of these shortcomings of the test

appropriately discussed. However, this excellent paper does not deduce anything regarding

the very limited number of VLE data sets that could be evaluated if all these necessary

requirements were taken into account.

The test is based on an excessive reliance on the existing excess Gibbs energy models,

unfounded from our point of view as we have already demonstrated. In a previous paper28

,

we carried out a systematic topological study of the Gibbs energy of mixing as a function of

composition and demonstrated that the NRTL model exhibits gaps or regions where

NRTL solutions for miscible binaries do not exist. In Figure 5a an example of these gaps is

shown for which the minimum value of gM

(NRTL) is located at x1= 0.35. Similar

representations28

would show that the gap becomes progressively smaller as the minimum

goes from 0.35 to 0.5. But what is more important is that the gaps themselves are

responsible for the poor correlation of the LLE and VLE data of many systems. The above

cited paper contains an example of the relationship between the gaps and the

impossibility of fitting the experimental LLE data for a type I ternary system. This idea has

been schematically represented in Figure 5b, where the fitting of the experimental tie-lines

(LLE) requires that the gM

binary curve of the 2-3 binary subsystem is exactly located

where the model produces a gap and, as a consequence, no solution can be found using the

model. This explains the poor LLE data correlation obtained for many systems using

different models, e.g. methanol + diphenylamine + cyclohexane at 298K with the NRTL

model. In what follows, a similar case is presented but, now, for a VLE data correlation.

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The correlation of a unique experimental VLE data point, using the NRTL model as being

representative of the local composition models, is considered in this example. This

experimental point, specified below, belongs to the experimental data set of the water(1) +

1,2-propanediol(2) system at 25mmHg (no. 79 in Table S2 Supporting Information),

plotted in Figure 6a:

x1 = 0.030; y1 = 0.775; T = 83.5C

The NRTL model is unable to fit this point because the vapor phase composition calculated

using it deviates greatly from the experimental one. The best correlation that can be

achieved uses the following NRTL binary interaction parameters A12= 145.85K; A21=

41.307K and =3.032. This yields the calculated point:

x1(cal) = 0.030; y1(cal) = 0.612; T(cal) = 83.5C

The explanation for this poor correlation is, again, the existence of gaps in the NRTL

model. This can be understood by taking into account that for a vapor and liquid phase to

be in equilibrium, a common tangent line to the respective vapor and liquid Gibbs energy of

mixing functions (gM,V

and gM,L

) must exist at the vapor and liquid equilibrium

compositions. The gM,V

curve for the vapor phase has been calculated using eq 19, and is

shown in Figure 6b. The reference state in this equation is the pure component as liquid at

the same T and P of the system, and the vapor phase is considered to be ideal.

+==i i

iioi

i

V,MV,M ylny

)T(p

Plny

RT

Gg (19)

Both the composition of the experimental vapor phase and the tangent line to the gM,V

curve

at the point in question are plotted in Figure 6b. For a perfect fitting of the specified VLE

data point, the model should be able to generate a gM,L

curve for the liquid phase, having

the same tangent line in the experimental liquid composition as in the experimental vapor

composition. A possible gM,L

curve that satisfies this condition is also plotted in Figure 6b.

However, the NRTL model is unable to generate a curve of these characteristics because it

produces a gap in that region. In other words, the NRTL model cannot provide a solution

for the following conditions:

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15

47.2dx

dg

expx1

L,M

=

(20)

65.0g

expx

L,M = (21)

The closest to the required gM,L

curve that can be generated by the model is also shown in

Figure 6b. The common tangent line between this curve for the liquid and the one for the

vapor produces the large deviation in the calculated vapor composition cited previously:

y1 = 0.775 - 0.610 = 0.165. The gM,L

curve obtained based on the NRTL parameters

published in DECHEMA Chemistry Data Series (no. 79 in Table S2 Supporting

Information), obtained from the global correlation of all the experimental VLE data

included in that series, has also been plotted in Figure 6b. Obviously, this non-isothermal

curve is somewhat different to that obtained by correlation of a single point. However, the

solution for the specific point considered in this example is identical in both cases, as can

be ascertained from the figure.

At this point, we might wonder if we could resolve the problem by only increasing the

number of parameters in the model, for example by taking into account the temperature or

the composition dependence of the NRTL binary interaction parameters, as suggested by

Kang et al.12

. The reply would be no: the correlation of the above experimental VLE data

set is not significantly improved when five, instead of three, interaction parameters are

used; nor is it improved by incorporating temperature or composition dependencies into the

model. The reason for this is that, although the additional parameters provide some

additional flexibility, the gaps in the model are not filled in and, therefore, the capability of

the model continues to be very limited.

Given all these limitations of the existing gE models, such as NRTL, in correlating the

experimental phase equilibrium data, i.e. LLE or VLE, it does not seem reasonable to

penalize any experimental VLE data if it cannot be correlated by a given model or results in

large deviations. Other different arguments can be used that reinforce this idea:

- A comparison of the experimental and the calculated data is usually the procedure

followed to check the capability of the models. Therefore, it does not seem logical to

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16

swap the role of every element in the comparison to the extent of turning the model

into the standard of comparison.

- The results can vary greatly when different gE models are used in the same TC tests

(i.e. van Ness or Fredenslund point-to-point test), a fact that is acknowledged by other

authors17

.

The problems discussed in this paper have important practical repercussions. The following

example illustrates how an excess of confidence in the existing consistency tests may lead

to a selection of the wrong model parameters. Seven data sets for the water + 1-propanol

binary system at 760 mmHg are compiled in the DECHEMA data collection13

. Table 1

shows the NRTL binary parameters obtained by fitting the available experimental data for

every one of these sets. Moreover, only one of these data sets passes both area and point-to-

point consistency tests (set number 2), but in this case the NRTL parameters reproduce data

consistent with a type IV binary azeotrope (Figure 7), whereas the real behavior of the

system corresponds to type I data, which means that there should be no LL miscibility gap

present29

. Chemical process simulation software packages obtain information from that

which is available in data banks, compilations, and use the existing procedures to select

data. Therefore, all the problems discussed here affect the results obtained when using

chemical process simulation programs. Continuing with the previous example, the NRTL

parameters in the database used by CHEMCAD 6.4.0 for this system coincide with those

classified as set 2 shown in Table 1. They reproduce the inconsistent system plotted in

Figure 7. Among the other parameter sets in Table 1 there are some that do not reproduce

liquid-liquid splitting but rather Type 1 binary data consistent with the behavior of this

system, e.g. set 3. Most likely, the selection criterion to include set number 2, and no other

parameters, is that this experimental data set is the only one that passes both the area and

point-to-point consistency tests. An unfounded overconfidence in these consistency tests

may have negative consequences, as just illustrated by the above example. Initiatives such

as the one arising within the NIST12

are absolutely necessary, but in order to avoid

inconsistencies, the tests and their application to the data must be thoroughly revised, as

discussed in the present paper.

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5. CONCLUSIONS

The main conclusions of the present paper are the following:

1. Consistency tests not developed and/or applied with the required degree of rigor may

erroneously invalidate correctly obtained VLE data or do the opposite, i.e. validate spurious

data.

2. The deviation of the experimental VLE data with regard to correlation by means of a

given model should not be used to assess the quality of these data until gE models capable

of fitting all existing phase equilibrium behaviors are developed. The consistency tests

based on this idea should not be applied.

3. Therefore, the applicability of two of the five test that are combined in the algorithm

propose by Kang et al.12

is questioned. A thorough revision of the strategies to develop and

apply sound consistency tests is required that guarantees utility and reliability, as well as

the quality of the experimental equilibrium data. In the mean time, inspection of the Gibbs

energy of mixing curve for the liquid (gM,L

) versus the liquid composition, obtained from

the experimental VLE data, can reveal important information about the quality of these data

that should be taken into account. This curve must be both smooth and consistent with the

partial or total miscibility behavior of the liquid mixture.

NOMENCLATURE

ak = Legendre polynomial coefficients

i,j = binary interaction parameters (K) for components i and j

A, B, C = Margules coefficients

fio = fugacity of pure component i

Fi = individual quality factor

GE (g

E) = Gibbs energy of excess (dimensionless)

GM

(gM

) = Gibbs energy of mixing (dimensionless)

HE = enthalpy of excess

HaE = average enthalpy of excess

Lk = Legendre polynomials

P = pressure

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18

pio = vapour pressure of pure component i

QVLE = global quality factor for VLE data

T = temperature

Tio = boiling point of pure component i

vE = excess volume

xi = mole fraction of component i in liquid phase

yi = mole fraction of component i in vapour phase

Greek letters

i,j = non-randomness NRTL factor

i = activity coefficient of component i

i = fugacity coefficient for i in the vapour phase

ASSOCIATED CONTENT

Supporting Information

Supplemental tables (S1 and S2) referenced in the text. This information is available free of

charge via the Internet at http://pubs.acs.org/.

ACKNOWLEDGEMENTS

We gratefully acknowledge financial support from the Vice-Presidency of Research

(University of Alicante, Spain).

LITERATURE

(1) Dortmund Data Bank Software Package (DDBSP). Dortmund Data Bank Software and

Separation Technology Gmbh. 2001

(2) Frenkel, M.; Dong, Q.; Wilhoit, R.C.; Hall, K.R. TRC SOURCE Database: A Unique

Tool for Automatic Production of Data Compilations. Int. J. Thermophys. 2001, 22, 215.

(3) Redlich, O.; Kister, A.T. Algebraic representation of thermodynamic properties and the

classification of solutions, Ind. Eng. Chem., 1948, 40, 345348.

(4) Van Ness , H.C.; Byer, S.M.; Gibbs, R.E. Vapor-Liquid equilibrium: Part I. An

appraisal of data reduction methods, AIChE J., 1973, 19, 238.

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(5) Fredenslund, A.; Gmehling, J.; Rasmunssen, P. Vapor-Liquid Equilibria Using

UNIFAC, Elsevier, Amsterdam, 1977.

(6) Kojima, K.; Moon, H.M.; Ochi, K. Thermodynamic Consistency Test of Vapor-Liquid

Equilibrium Data, Fluid Phase Equilib. 1990, 56, 269284.

(7) Wisniak, J. A New Test for the Thermodynamic Consistency of Vapor-Liquid

Equilibrium, Ind. Eng. Chem. Res. 1993, 32, 15311533.

(8) Kurihara, K.; Egawa, Y.; Ochi, K.; Kojima, K. Evaluation of thermodynamic

consistency of isobaric and isothermal binary vapor-liquid equilibrium data using the PAI

test, Fluid Phase Equilib. 2004, 219, 7585.

(9) Prausnitz, J.M.; Lichtenthaler, R.N.; Gomes de Azevedo, E. Molecular

Thermodynamics of fluid-phase equilibria, 3rd ed., Prentice Hall Ptr, New Jersey, 1999.

(10) Kurihara, K.; Egawa, Y.; Iino, S.; Ochi, K.; Kojima, K. Evaluation of thermodynamic

consistency of isobaric and isothermal binary vapor-liquid equilibrium data using the PAI

test II, alcohol+n-alkane, +aromatic, +cycloalkane systems, Fluid Phase Equilib. 2007,

257, 151162.

(11) Eubank, P.T.; Lamonte, B.G. Consistency Tests for Binary VLE Data, J. Chem. Eng.

Data. 2000, 45, 1040-1048.

(12) Kang, J.W.; Diky, V.; Chirico, R.D.; Magee, J.W.; Muzny, C.D.; Abdulagatov, I.;

Kazakov, A.F.; Frenkel, M. Quality assessment algorithm for vapor-liquid equilibrium data.

J. Chem. Eng. Data 2010, 55, 36313640.

(13) Gmehling, J.; Onken, U.; Arlt, W. Vapor-Liquid Equilibrium Data Collection.

Chemistry Data Series. DECHEMA: Frankfurt, 1977-1984.

(14) Frenkel, M.; Chirico, R.D.; Diky, V.; Yan, X.; Dong, Q.; Muzny, C. ThermoData

Engine (TDE): Software Implementation of the Dynamic Data Evaluation Concept, J.

Chem. Inf. Model. 2005, 45, 816-838.

(15) Diky, V.; Chirico, R.D.; Kazakov, A.F.; Muzny, C.D.; Frenkel, M. ThermoData

Engine (TDE): Software Implementation of the Dynamic Data Evaluation Concept. 3.

Binary Mixtures, J. Chem. Inf. Model., 2009, 49, 503-517.

(16) Diky, V.; Chirico, R.D.; Muzny, C.D.; Kazakov, A.F.; Kroenlein, K.; Magee, J.W.;

Abdulagatov, I.; Kang, J.W.; Frenkel, M. ThermoData Engine (TDE): Software

Implementation of the Dynamic Data Evaluation Concept. 7. Ternary Mixtures, J. Chem.

Inf. Model., 2012, 52, 260-276.

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20

(17) Jackson, P.L.; Wilsak, R.A. Thermodynamic consistency tests based on the Gibbs-

Duhem equation applied to isothermal, binary vapor-liquid equilibrium data: data

evaluation and model testing, Fluid Phase Equilib., 1995, 103, 155197.

(18) Wisniak, J. The Herington Test for Thermodynamic Consistency, Ind. Eng. Chem.

Res. 1994, 33, 177-180.

(19) Van Ness, H.C. Thermodynamics in the treatment of vapor/liquid equilibrium (VLE)

data, Pure & Appl. Chem. 1995, 67, 6, 859-872.

(20) Cummings, P.T.; de Loos, Th.W.; OConnell, J.P. Joint Statement of Editors of

Journals Publishing Thermophysical Property Data Process for Article Submission, Fluid

Phase Equilib. 2009, 276, 165-166.

(21) Van Ness, H.C. Classical Thermodynamics of Non-electrolyte Solutions. Pergamon.

Oxford, 1964, 79.

(22) Tassios, D. Applied Chemical Engineering Thermodynamics, Springer, Berlin, 1993.

(23) Herington, E.F.G. A Thermodynamic Consistency Test for the Internal Consistency of

Experimental Data of Volatility Ratios, Nature, 1947, 160, 610611.

(24) Wang, H.; Xiao, J.; Shen, Y.; Ye, C.; Li, L.; Qiu, T. Experimental Measurements of

VaporLiquid Equilibrium Data for the Binary Systems of Methanol + 2-Butyl Acetate, 2-

Butyl Alcohol + 2-Butyl Acetate, and Methyl Acetate + 2-Butyl Acetate at 101.33 kPa, J.

Chem. Eng. Data, 2013,Volume 58, issue 6, 1827-1832.

(25) Wisniak, J. Comment on ref (12), J. Chem. Eng. Data, 2010, 55, 5394.

(26) Srensen, J.M.; Artl, W. Liquid-Liquid Equilibrium Data Collection. Vol V, Part 1 (p

419, 422), Chemistry Data Series, DECHEMA, Frankfurt.

(27) Kang, J.W.; Diky, V.; Chirico, R.D.; Magee, J.W.; Muzny, C.D.; Abdulagatov, I.;

Kazakov, A.F.; Frenkel, M. Reply to Comments by J. Wisniak on ref (12), J. Chem. Eng.

Data, 2010, 55, 5395.

(28) Marcilla, A.; Olaya, M.M.; Serrano, M.D.; Reyes-Labarta, J.A. Methods for improving

models for condensed phase equilibrium calculations, Fluid Phase Equilib., 2010, 296, 15-

24.

(29) Gmehling, J.; Menke, J.; Krafczyk, J.; Fischer, K. Azeotropic data. Part I., VCH,

Weinheim, 1994.

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Table 1. NRTL parameters values obtained by fitting different experimental VLE data sets

for 1-propanol (1) + water (2) system at 760 mmHg.

Data source Num. A12 (cal/mol) A21 (cal/mol)

DECHEMA [13] 1 152,5084 1866,3369 0,3747

2 444,3339 1997,5504 0,4850

3 412,0253 1735,4304 0,4465

4 152,5084 1866,3369 0,3747

5 294,7832 1893,5152 0,4276

6 619,3422 2708,5773 0,6185

7 -13,0045 1872,0758 0,2803

ChemCAD 6.4.0. 444.3322 1997.6031 0.4850

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a)

x1

RT

GM

b)

x1I x1

II

II

I

commontangent line

RT

GM

Figure 1. Gibbs energy of mixing (dimensionless) curves as a function of the molar fraction

of the 1-component: a) for a completely miscible binary system, and b) for a partially

miscible binary system with LL splitting (I and II points).

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a)

b)

Figure 2. VLE experimental data for the binary system acetone (1) + water (2) at 100C

(no. 24 in Table S1 Supporting Information): a) Pressure vs. x and y (molar fractions), and

b) gM

as a function of the composition for the liquid phase.

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a)

b)

Figure 3. VLE experimental data for the binary system ethylene oxide (1) + water (2) at

20C (no. 7 in Table S1 Supporting Information): a) Pressure vs. x and y (molar fractions),

and b) gM


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a)

b)

Figure 4. VLE experimental data for the binary system water (1) + 1-hexanol (2) at 40C

(no. 60 in Table S1 Supporting Information): a) Pressure vs. x and y (molar fractions), and

b) gM


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a)

b)

Figure 5. Schematic representation of the limitations of the NRTL model: a) systematic

study of the homogeneous gM

binary curves for x2min=0.35, and b) gM

binary curves for a

type 1 ternary system where the existence of gaps constrains the LL region calculated by

the model.

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a)

b)

Figure 6. Experimental VLE data for the binary system water (1) + 1,2-propanediol (2) at

25 mmHg (no. 79 in Table S1 Supporting Information): a) Temperature vs. x and y (molar

fractions), and b) gM,V

(vapour) and gM

NRTL (liquid) functions for the selected VLE point

at T=83.5C (the non-isothermal gML

curve for all data set has been included).

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a)

b)

Figure 7. Equilibrium data for the 1-propanol (1) + water (2) binary system at 760 mmHg

using the NRTL parameters in ChemCAD 6.4.0 (see Table 1): a) y vs. x b) Temperature vs.

x and y (molar fractions). A false VLLE data point is generated leading to a Type IV

instead a Type I system.

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vle consistency pitfalls

Documents

experimental data

mara dolores serrano

vle data series

american chemicalsociety

mara angeles garridoind

certain data sets

manuscript doi

partial miscibility