J. of Supercritical Fluids 115 (2016) 65–78
Contents lists available at ScienceDirect
The Journal of Supercritical Fluids
journal homepage: www.elsevier.com/locate/supflu
Implementation of GC-PPC-SAFT and CP-PC-SAFT for predicting
thermodynamic properties of mixtures of weakly- and non-associated
oxygenated compounds
Helena Lubarsky a , Ilya Polishuk a,∗ , Dong NguyenHuynh b,∗
a
b
Department of Chemical Engineering & Biotechnology, Ariel University, 40700, Ariel, Israel
Petrovietnam Manpower Training College, No.43 30/4(A1) Street, Ward 9, Vung Tau City, Vietnam
a r t i c l e
i n f o
Article history:
Received 29 February 2016
Received in revised form 23 April 2016
Accepted 23 April 2016
Available online 30 April 2016
Keywords:
Predictive modeling
SAFT
Thermodynamic properties
Global phase behavior
a b s t r a c t
This study continues a comprehensive comparison between the Critical Point-based Modified PC-SAFT
(CP-PC-SAFT) and the Group Contribution Polar PC-SAFT (GC-PPC-SAFT). The predictive values of these
approaches are enhanced by reducing their referring to the experimental pure compound data. The
mixtures comprising aromatic and aliphatic alkanols, esters, ethers and ketones have been treated in
the entirely predictive manner, without adjusting any binary parameters. The results indicate that both
models under consideration are particularly accurate estimators of single phase liquid densities at high
pressures, usually with slight superiority of GC-PPC-SAFT. Nevertheless the universality of CP-PC-SAFT
could be considered as more advanced since this model yields accurate predictions also for sound velocities and compressibilities. In addition, the results indicate that GC-PPC-SAFT is often a superior estimator
of phase equilibria in symmetric systems. At the same time, CP-PC-SAFT typically has a clear advantage
in predicting the global phase behavior of asymmetric systems.
© 2016 Elsevier B.V. All rights reserved.
1. Introduction
Simultaneous estimation of various kinds of fluid phase equilibria and the single phase thermodynamic properties in wide range
of operating conditions is one of the major industrial requirements
posed to modern thermodynamic approaches [1]. The literature
dealing with modeling of phase equilibria by Equation of State (EoS)
approaches is virtually immense and it has been surveyed by several comprehensive reviews and monographs [2–7]. In the recent
years accurate estimation of the auxiliary thermodynamic properties by the EoS models receives major attention as well. In this
respect several versions of the Statistical Association Fluid Theory (SAFT) present particular interest. Among the recent studies,
the applications of SAFT-VR [8–12], Soft-SAFT [13–17], SAFT + cubic
[18–25], PC-SAFT [26,27], modified PC-SAFT [28,29], and other
versions of SAFT [30–33] for estimating the derivative thermodynamic properties should be noticed. Unfortunately, wide industrial
implementation of most SAFT approaches is hindered by lacking of
∗ Corresponding authors.
E-mail addresses: polishuk@ariel.ac.il (I. Polishuk), dongnh@pvmtc.com.vn
(D. NguyenHuynh).
http://dx.doi.org/10.1016/j.supflu.2016.04.013
0896-8446/© 2016 Elsevier B.V. All rights reserved.
standardization in evaluating their substance-specific parameters
[1], while fitting of large experimental databases diminishes their
predictive values. This problem can be addressed by a standardized numerical solution of the substance-dependent parameters at
the characteristic states, namely the pure compound critical and
triple points, as proposed by the critical point-based modified version of PC-SAFT (CP-PC-SAFT). Thus far it has been demonstrated
that CP-PC-SAFT yields accurate predictions of various thermodynamic properties of substances such as light compounds, n-alkanes,
1-alkenes [34], 1-alkanols [35], aromatic and haloaromatic compounds [36], some haloalkanes [37,38], and their mixtures in
wide range of conditions. In addition, it has been found that this
model can be applied in predictive manner for estimating solubility of metallic mercury in hydrocarbons [39]. A conceptually
different method for enhancing the predictive character of SAFT
models is evaluation of their substance-specific parameters by
the group contribution approaches. One of these approaches is
the Group Contribution Polar PC-SAFT (GC-PPC-SAFT). Thus far
GC-PPC-SAFT has been successfully implemented for modeling
various phase equilibria in mixtures of polycyclic aromatic hydrocarbons [40], heavy esters [41], CO2 -n-alkanes, methane-n-alkanes,
and ethane-n-alkanes [42], CO2 , N2 , and H2 S-aromatic hydrocarbons and n-alkanes, [43], H2 -hydrocarbon mixtures [44], methyl
66
Table 1
Accuracy of predicting thermophysical data in mixtures in the single-phase region (k12 = 0).
Property
AAD% CP-PC-SAFT
AAD% GC-PC-SAFT
T range (K)
P range (bar)
No. pts.
Refs.
ethylene(1) – 1-pentanol(2)
ethylene(1) – 1-heptanol(2)
ethylene(1) – 1-nonanol(2)
ethylene(1) – vinyl acetate(2)
cyclohexane(1) – 1-butanol(2)
1-hexene(1) – 1-butanol(2)
n-hexane(1) – 1-hexanol(2)
n-hexane (1) – 1-hexanol(2)
n-heptane(1) – 1-heptanol(2)
n-heptane(1) – 1-heptanol(2)
n-heptane(1) – 1-heptanol(2)
n-heptane(1) – 2-methyl-2-butanol(2)
n-heptane(1) – 2-methyl-2-butanol(2)
n-heptane (1) – 1-decanol(2)
isooctane(1) – 1-butanol(2)
n-nonane(1) – 1-octanol(2)
n-nonane(1) – 1-octanol(2)
n-nonane(1) –1-octanol(2)
dimethyl carbonate(1) – n-hexane(2)
dimethyl carbonate(1) – n-octane(2)
dimethyl carbonate(1) – n-decane(2)
dimethyl carbonate(1) – p-xylene(2)
diethyl carbonate(1) – n-octane(2)
diethyl carbonate(1) – n-C10 H22 (2)
diethyl carbonate(1) – p-xylene(2)
dibutyl ether(1) – 1-butanol(2)
dibutyl ether(1) – 1-butanol(2)
dibutyl ether(1) – 1-butanol(2)
dibutyl ether(1) – 1-hexanol(2)
dibutyl ether(1) – 1-hexanol(2)
dibutyl ether(1) – 1-hexanol(2)
methyl benzoate(1) – 1-hexanol(2)
methyl benzoate(1) – 1-hexanol(2)
methyl benzoate(1) – 1-hexanol(2)
density
density
density
density
density
density
density
isobaric thermal expansivity
density
isothermal compressibility
isobaric thermal expansivity
density
sound velocity
sound velocity
density
sound velocity
density
adiabatic compressibility
density
density
density
density
density
density
density
density
isothermal compressibility
isobaric thermal expansivity
density
isothermal compressibility
isobaric thermal expansivity
density
isothermal compressibility
isobaric thermal expansivity
3.37
4.17
3.49
3.595
1.180
1.58
0.650
11.0
0.913
3.53
5.28
1.25
1.26
1.90
1.83
1.23
0.670
3.13
1.38
1.36
0.968
0.419
0.993
0.951
0.284
0.896
3.23
6.32
0.952
5.74
4.41
0.433
5.91
5.14
1.53
2.09
2.02
–
0.956
1.17
1.11
6.08
0.785
20.5
5.20
–
–
9.92
–
9.56
0.639
20.8
–
–
–
–
–
–
–
2.34
16.1
3.18
2.20
22.9
6.00
2.05
25.9
7.12
298–373
298–373
298–413
298–373
293–333
273–333
303–423
303–503
298–393
298–393
298–393
293–318
292–318
293–319
273–333
293–423
303–453
333–453
293–313
278–353
288–308
288–308
288–308
288–308
288–308
293–393
293–393
293–393
293–353
293–353
293–353
278–358
278–358
278–358
500–1950
500–1950
500–1950
500–1950
1–1000
1–500
0.9–506
69–3476
1–1400
1–1400
1–1400
1–1000
1–1013
1–1013
1–500
0.98–1013
0–980
0–980
1–400
1–400
1–400
1–400
1–400
1–400
1–400
1–1400
1–1400
1–1400
1–1400
1–1400
1–1400
1–600
1–600
1–600
75
75
99
75
495
200
160
660
680
680
680
696
450
401
360
325
185
171
360
905
144
180
180
162
216
445
445
445
300
300
300
1134
1134
1134
[54]
[54]
[54]
[54]
[55]
[56]
[57]
[58]
[59]
[59]
[59]
[60]
[60]
[61]
[62]
[63,64]
[65]
[65]
[66]
[67,68]
[68]
[69]
[68]
[68]
[69]
[70]
[70]
[70]
[71]
[71]
[71]
[72]
[72]
[72]
H. Lubarsky et al. / J. of Supercritical Fluids 115 (2016) 65–78
System
H. Lubarsky et al. / J. of Supercritical Fluids 115 (2016) 65–78
67
6
2400
(b)
(a)
P(bar)
P(bar)
1600
4
800
2
0
0
100
T (K)
180
260
0.0
340
150
.2
.4
x1,y1 .6
.8
1.0
150
P(bar)
100
(d)
P(bar)
318.15
K
100
298.15 K
(c)
50
50
K
343.8
K
313.3
282.9 K
0
0
0.0
.2
.4
x1,y1 .6
.8
1.0
0.0
.2
.4
x1,y1 .6
.8
1.0
Fig. 1. Phase equilibria in the systems of nitrogen(1), methane(1), krypton(1) and xenon(1) – dimethyl ether (DME)(2). (a) the near-critical isopleths: 䊎 – N2 (1) – DME(2)
– CH4 (1) – DME(2) (x1 = 0.38),
– Kr(1) – DME(2) (x1 = 0.69). The isotherms: (b) Xe(1) – DME(2) at 182.33 K, (c) CH4 (1) – DME(2), (d) N2 (1) – DME(2). Points
(x1 = 0.6),
– experimental data [73–75,96–98]. Dashed lines – predictions of CP-PC-SAFT, solid lines – of GC-PPC-SAFT (k12 = 0 for both models and all the current and the furtherly
considered systems).
benzoate-alkanes [45], methanol-n-alkanes [46], water-alkanes,
aromatic hydrocarbons, alcohols and gases [47], ethers, aldehydes
and ketones [48], CO2 -1, 2, 3 and 4-alkanols [49], and additional
polar compounds [50–52].
In the previous study [53] we have compared the performances
of CP-PC-SAFT and GC-PPC-SAFT in estimating various thermodynamic properties of the pure weakly- and non-associated alkanols,
ethers, esters and ketones in wide range of temperatures and pressures. It has been demonstrated that both models are capable of
predicting reasonable accurate results for various thermodynamic
properties in the particularly wide range of conditions. It has also
been found that CP-PC-SAFT typically has an advantage in predicting sound velocity and compressibility data. At the same time
GC-PPC-SAFT is superior in qualitative estimating the isobaric thermal expansion coefficients and the vapor pressures away from the
critical points. The current investigation aims at comparing the predictions of CP-PC-SAFT and GC-PPC-SAFT for the mixtures of the
previously considered [53] compounds, and it continues paying
a major attention to the high pressure range. Unlike the relative
paucity of the pertinent data on the single phase thermodynamic
properties [54–72], vast number of references report phase equilibria in various mixtures of the compounds under consideration.
Some of these references [73–78] provide information concerning
the global phase behavior in several systems of these substances.
Obviously, such data are essential for the fundamental comparison
between the models and, consequently, they are considered as a
primary subject of the current investigation.
At the same time, it should be emphasized that a very accurate modeling of even the most sophisticated phase equilibria can
be achieved by fitting the binary adjustable parameters. Although
the predictive values of EoS models can be recovered by further generalization of these parameters, this practice may hinder
a comparison between the EoS models. Therefore, similarly to
the recent studies of Bender et al. [79,80], here the values of all
binary adjustable parameters are also set to zero in all the considered cases. The subsequent discussion provides some additional
information on the current implementation of CP-PC-SAFT and GCPPC-SAFT.
2. Theory
Both approaches under considerations have been described in
great details in the previous references [34–52]. Hence the current
discussion is restricted to the mean features of these models and
the major differences between them.
The predictive character of CP-PC-SAFT is enhanced by a
substantial reduce of the data required for evaluating its substancespecific parameters. Instead of fitting these parameters to large and
vague experimental databases, they are solved at two characteristic
states, namely the critical and the triple points, by implementing a
standardized numerical procedure. Unfortunately, the original version of PC-SAFT [81] cannot generate the simultaneously accurate
description of the critical temperature and pressures along with
the sub-critical data [82]. In addition, this model is affected by
68
H. Lubarsky et al. / J. of Supercritical Fluids 115 (2016) 65–78
(a)
(b)
Fig. 2. Phase equilibria in: (a) nitrogen(1) – 1-decanol(2), (b) methane(1) – 1-butanol(2). Points – experimental data [99,100]. Dashed lines – predictions of CP-PC-SAFT, solid
lines – of GC-PPC-SAFT.
10
8
UCEP
EP
LC
n
240
6
P(bar)
4
270
160
290
310
330
80
0
270
380
T(K)
Fig. 3. Critical loci and endpoints of ethane(1) – 1-alkanols(2) systems: 䊎 – 1-butanol,
data [76,77]. Dashed lines – predictions of CP-PC-SAFT, solid lines – of GC-PPC-SAFT.
certain undesired numerical artefacts [83–91]. In order to address
these issues and to improve the over-all accuracy of CP-PC-SAFT,
the original version of PC-SAFT [81] has been substantially revised
[34]. In particular, its universal parameters of the radial distribution function in 1st order perturbation term have been transformed,
the expressions of the hard sphere contribution and the tempera-
490
– 1-pentanol,
600
– 1-octanol. Experimental endpoints – LCEP 䊉 – UCEP. Experimental
ture dependence of the segment diameter have been changed, and
the mixing rules have been slightly modified. Besides the advantages of CP-PC-SAFT in estimating thermodynamic properties in
particularly wide range of conditions for large variety of compounds [34–39], there is a price to pay for implementation of its
standardized predictive procedure. In particular, this model may
H. Lubarsky et al. / J. of Supercritical Fluids 115 (2016) 65–78
(a)
69
(b)
(d)
(c)
Fig. 4. LLVE in: (a,b) ethane(1) – 1-octanol(2), (c,d) xenon(1) – 1-decanol(2) systems. Points – experimental data [77,78]. Dashed lines – predictions of CP-PC-SAFT, solid
lines – of GC-PPC-SAFT.
generate imprecise estimations of the vapor pressures away from
the critical points. In addition, an accuracy of the CP-approach deteriorates in the cases of heavy compounds whose critical data are
imaginary, and the strongly associated substances. Unfortunately,
attaching this model by an association contribution does not result
in substantial improvement of its accuracy. Therefore the current
version of CP-PC-SAFT [34–39] neglects these interactions, while
the strongly associated compounds are excluded from its applicability range.
Unlike CP-PC-SAFT, GC-PPC-SAFT does not revise the original
version of PC-SAFT [81], but comprises two additional contributions, namely the association and the multi-polar terms. The latter
contribution has been obtained by extending the theory of Gubbins
and Twu [92] to chain molecules using the “segment approach” of
Jog and Chapman [93] and Jog et al. [94]. The current GC method
has been originally proposed by Tamouza et al. [95] and furtherly
expanded to various chemical groups [40–52]. The latter references also list the experimental data selected for developing this
approach. Currently it is implemented for evaluating ε (the segment
energy parameter), (the segment diameter), and m (the number
of segments), while other model’s parameters are kept constant for
the homologies series of compounds in order to maintain its predictive character. Notwithstanding of its advantageous accuracy and
significant predictive capacity, GC-PPC-SAFT has two major drawbacks. In particular, being based on the original form of PC-SAFT
[81], this model overestimates the pure compound critical temperature and pressures. In addition, the current GC method does
evolve most 2nd order functional groups, which typically affects its
predictions for the branched molecules. Moreover, the GC method
cannot be implemented for the first members of the homologues
series of compounds. In all these cases the molecular parameters of
the model are not predicted, but fitted to the available experimental
data. Unfortunately, some particularly important data reporting the
global phase behavior are available specifically for the systems of
compounds, such as dimethyl ether and benzyl alcohol, which cannot be appropriately treated by the current version of GC-PPC-SAFT
in predictive manner. Although in the latter cases the comparison
with CP-PC-SAFT can hardly be recognized as entirely equivalent,
such systems have still been included in this study. The GC-PPCSAFT parameters for the gases have been adopted from the original
version of PC-SAFT [81]. The values of the molecular parameters,
either solved by CP-PC-SAFT, predictively assembled and the fitted
for GC-PPC-SAFT are listed in the Supplementary Content (Tables S1
and S2). All the calculations have been performed in Mathematica®
7 software and the pertinent routines can be obtained from the
corresponding authors by request.
3. Results
In order to compare the performances of the models under
consideration in comprehensive manner, we have implemented
them for predicting various data thus far reported for the mixtures
of oxygenated compounds. First of all, the available single phase
thermodynamic properties in wide range of conditions have been
considered. Afterwards the models under consideration have been
implemented for predicting the existing information on the global
phase behavior, the representative high pressure VLE in systems
of gases such as nitrogen, methane, ethane, carbon dioxide, etc.
70
H. Lubarsky et al. / J. of Supercritical Fluids 115 (2016) 65–78
180
180
P(bar)
(a)
P(bar)
120
120
60
60
(b)
323.1 K
323
.1 K
313.15 K
5K
313.1
0
0
0.0
.2
.4
x1,y1 .6
.8
1.0
0
ρ (g/L)
300
600
900
210
200
P(bar)
(c)
P(bar)
(d)
150
140
K
15
8.
4
4
K
3.3
35
100
5 K 328
.1
338
50
5
318.1
.15
70
K
309 K
K
0
0
0.0
.2
.4
x1,y1 .6
.8
1.0
0.0
.2
.4
x1,y1 .6
.8
1.0
Fig. 5. VLE in ethane(1) – 1-alkanols(2) systems: (a and b) 1-butanol, (c) 1-octanol, (d) 1-decanol. Points – experimental data [100–104]. Dashed lines – predictions of
CP-PC-SAFT, solid lines – of GC-PPC-SAFT.
and the oxygenated organic compounds (furtherly designated as
asymmetric), systems of compounds existing in the liquid phase
at the ambient conditions or having comparable critical constants
(furtherly designated as symmetric), and, finally, the characteristic
low pressure phase equilibria data.
Table 1 compares the absolute average deviations (AAD%)
yielded for the single phase densities, isobaric thermal expansivities, isothermal and adiabatic compressibilities, and sound
velocities covering the high pressure range. Unfortunately, the
current version of GC-PPC-SAFT cannot be applied in predictive
manner for the particularly important systems of vinyl acetate,
2-methyl-2-butanol, dimethyl carbonate and diethyl carbonate. In
these cases we report only the results of CP-PC-SAFT. As seen, both
models yield satisfactorily accurate predictions for the densities.
Remarkable, in most of the cases GC-PPC-SAFT has a slight superiority in estimating these data. At the same time, the precision
of CP-PC-SAFT in predicting the densities of n-hexane(1) – 1hexanol(2), dimethyl and diethyl carbonates(1) – p-xylene(2) and
methyl benzoate(1) – 1-hexanol(2) should be noticed. In addition,
both models typically exhibit the comparable over-all results for
the isobaric thermal expansivities. However in the cases of sound
velocities and compressibilities the picture is different. Yet CPPC-SAFT has a major advantage, confirming the previously drown
conclusion [53] concerning its universality in the elevated pressure
range.
In the following discussion let us proceed to consideration of
phase equilibria. Fig. 1 depicts phase equilibria in the systems
of dimethyl ether with nitrogen, methane, krypton and xenon,
including the global phase behavior represented by the near-critical
isopleths. Wallbruch et al. [73] have related the extent of phase separation in these systems to the polarizability of the pertinent gases.
In particular, it has been explained that the smaller polarizability of
nitrogen resulting in the relatively large excess functions in its mixtures with the polar dimethyl ether, and, consequently, wide region
of phase separation (phase behavior of Type III). At the same time,
the bigger polarizabilities of the other gases reduce the extent of
phase separation, resulting in phase behavior of Type II for methane
and krypton systems, and, apparently, Type I in the case of xenon. In
spite of the fact that CP-PC-SAFT does not consider the polar interactions, it correctly predicts the topology of the global phase behavior
for all these systems. Unfortunately, this is not a case of GC-PPCSAFT. Although its predictions are similar to CP-PC-SAFT for the
nitrogen system (Fig. 1A and D), GC-PPC-SAFT erroneously predicts
the Type III topology for other systems as well, substantially overestimating the extent of their phase separation (Fig. 1A–C). At the
same time, although the over-all quantitative predictions of CP-PCSAFT can be considered as satisfactorily accurate, it exhibits a minor
underestimation of the phase split in methane (Fig. 1A) and xenon
(Fig. 1B) systems.
As seen, the latter tendencies are valid also in the cases of 1alkanols. In particular, both models continue yielding alike results
for nitrogen(1) – 1-decanol (Fig. 2A) with certain superiority of
CP-PC-SAFT. In the case of methane(1) – 1-butanol (Fig. 2B) GCPPC-SAFT once again overestimates the phase equilibria. Although
CP-PC-SAFT predicts these data more accurately, apparently it
slightly underestimates them. Similar results are obtained also for
ethane(1) – 1-alkanols(2). As seen (Fig. 3), GC-PPC-SAFT continues
predicting the Type III for these systems, substantially overes-
H. Lubarsky et al. / J. of Supercritical Fluids 115 (2016) 65–78
71
330
300
P(bar)
(a)
P(bar)
(b)
220
200
100
3
37
.15
K
110
.1 5
338
K
.15
343
K
1
318.
5K
0
0
0.0
.2
.4
x1,y1 .6
.8
0.0
1.0
.2
.4
x1,y1 .6
.8
1.0
100
(c)
P(bar)
(d)
44
8.1
5
P(bar)
K
330
75
220
8.1
40
5K
50
110
25
15 K
318.
5K
308.1
0
0
0.0
.2
.4
x1,y1 .6
.8
1.0
0.0
.2
.4
x1,y1 .6
.8
1.0
Fig. 6. VLE in: (a) ethylene(1) – 1-pentanol(2), (b) ethylene(1) – 1-octanol(2), (c) ethylene(1) – 1-decanol(2) and (d) propane – 1-decanol(2) systems. Points – experimental
data [103–106]. Dashed lines – predictions of CP-PC-SAFT, solid lines – of GC-PPC-SAFT.
timating an extent of the phase split at the low temperature
range. Although CP-PC-SAFT correctly estimates their Type IV phase
behavior, its tendency of minor underestimating of the phase equilibria takes place also in this case. Fig. 4A–B provide additional
details concerning the three-phase equilibria in the representative system ethane(1) – 1-octanol(2) and Fig. 4C–D – in xenon(1)
– 1-decanol(2). As seen, similarly to the previously considered
system xenon(1) – dimethyl ether(2), GC-PPC-SAFT substantially
over-estimates the phase split. Although CP-PC-SAFT truthfully
estimates the equilibria compositions of the liquid phases and the
loop created by the densities, its quantitative predictions the latter property are less accurate. Fig. 5 depicts the predictions of VLE
in ethane(1) – 1-alkanols(2). As seen, although CP-PC-SAFT exhibits
the superior over-all quality of predictions, GC-PPC-SAFT estimates
slightly more accurately the phase equilibria at the moderated
pressures. In addition, it can be seen (Fig. 5D), that at the high
temperature (448.15 K) both models yield nearly identical results,
overestimating the solubility of ethane in the liquid 1-decanol rich
phase. Fig. 6A–C demonstrate that a tendency detected for the previously considered systems of light alkanes and polar compounds,
namely the overestimation of phase equilibria by GC-PPC-SAFT
and the superior over-all accuracy of CP-PC-SAFT, are valid also
in the case of ethylene(1) – 1-alkanol(2) systems. Once again, the
performances of both models under consideration become hardly
distinguishable at the elevated temperatures (Fig. 6D). However,
unlike the previously considered ethane(1) – 1-decanol(2), in the
case of propane(1) their predictions are particularly accurate.
In addition to the discussed above mixtures of 1-alkanols,
comprehensive experimental data are available also for their carbon dioxide systems. Unfortunately, accurate modeling of these
systems requires fitting of two binary adjustable parameters of
CP-PC-SAFT [36] and implementation of a sophisticated crossassociation interaction scheme for GC-PPT-SAFT [49]. Since this
study examines only the entirely predictive capacities of these
models without adjusting any binary parameters, we treat here
CO2 as a non-associative and non-polar molecule, and, therefore,
omit the carbon dioxide(1)–alkanol(2) systems.
In the following discussion the results for the systems of additional oxygenated compounds are presented. Fig. 7 depicts the
high pressure phase diagrams of the systems of two aromatic compounds, namely methyl benzoate and benzyl alcohol with ethane
and carbon dioxide. As indicated previously, the molecular parameters of GC-PPC-SAFT for these aromatic compounds have not been
assembled by the GC method, but fitted to the experimental data.
The figure shows that this time the tendencies exhibited by the
approaches under consideration become quite opposite. In particular, unlike the previously considered cases, yet CP-PC-SAFT predicts
a larger extent of phase equilibria in comparison to GC-PPC-SAFT.
As seen, in the cases of ethane(1) – benzyl alcohol(2) (Fig. 7A), carbon dioxide(1) – benzyl alcohol(2) (Fig. 7C) and carbon dioxide(1)
– methyl benzoate(2) (Fig. 7D) this tendency of CP-PC-SAFT is in
a better over-all agreement with the experimental data. Fig. S1 in
the Supplementary Content demonstrates that CP-PC-SAFT truthfully predicts the phase equilibria in ethane and carbon dioxide
systems of additional aromatic compounds. Nevertheless, Fig. 7B
72
H. Lubarsky et al. / J. of Supercritical Fluids 115 (2016) 65–78
330
300
P(bar)
(a)
P(bar)
(b)
220
200
100
3
37
.15
K
110
.1 5
338
K
.15
343
K
1
318.
5K
0
0
0.0
.2
.4
x1,y1 .6
.8
0.0
1.0
.2
.4
x1,y1 .6
.8
1.0
100
(c)
P(bar)
(d)
44
8.1
5
P(bar)
K
330
75
220
8.1
40
5K
50
110
15
318.
25
K
5K
308.1
0
0
0.0
.2
.4
x1,y1 .6
.8
1.0
0.0
.2
.4
x1,y1 .6
.8
1.0
Fig. 7. VLE in: (a) ethane(1) – benzyl alcohol(2), (b) ethane(1) – methyl benzoate(2), (c) carbon dioxide(1) – benzyl alcohol(2) and (d) carbon dioxide(1) – methyl benzoate(2)
systems. Points – experimental data [107–111]. Dashed lines – predictions of CP-PC-SAFT, solid lines – of GC-PPC-SAFT.
indicates that this tendency of CP-PC-SAFT to predict a wider area
of VLE is not always in better agreement with the data. Although
this model is slightly more accurate in estimating the solubility of
ethane in methyl benzoate at the moderated pressures, GC-PPCSAFT yields the advantageous over-all results for this system. In
addition, GC-PPC-SAFT is apparently a better estimator of the vapor
phase compositions.
Unlike the relative scarcity of the high pressure phase equilibria
of oxygenated aromatic compounds, a more significant experimental data base is available for the systems of carbon dioxide
and some oxygenated aliphatic compounds. Fig. 8 depicts the representative results for the saturated linear esters and ketones.
Additional examples of CP-PC-SAFT’s predictions including inter
alia the unsaturated and branched compounds can be found in the
Supplementary Content (Figs. S2 and S3). As seen, this model is
capable of particularly accurate predictions for these systems. At
the same time, GC-PPC-SAFT tends to overestimate the solubility
of CO2 in the liquid phases. Some hints probably explaining these
results can be found in Fig. 8A depicting the critical loci of carbon
dioxide – ethyl alkylate(2) systems. As seen, the overestimation of
the pure compound critical points characteristic for GC-PPC-SAFT
moves up also the binary critical loci, which apparently affects the
subcritical VLE as well.
Unsurprisingly, the effect of pure compound critical points on
the high pressure phase equilibria increases in the cases of the more
symmetric systems such as carbon dioxide(1) – dimethyl ether(2),
diethyl ether(1) – 1-butanol(2) and 1-hexane(1) – 1-hexadecanol
(Fig. 9A–C). As seen, the overestimation of the critical data notable
affects the accuracy of GC-PPC-SAFT in the near-critical range. At
the same time, the results of both models are nearly identical away
from the critical states (see also Fig. 9D).
And, finally, Fig. 10 depicts the representative examples of the
low pressure phase equilibria. Since these phase equilibria are
demarcated by the pure compound vapor pressures remote from
the critical points, yet the advantage of GC-PPC-SAFT over CP-PCSAFT is obvious. As seen, the overestimation of the vapor pressure
of the compounds such as n-alkanes, 1-dodecanol and butyl acetate
(Fig. 10A and B) characteristic for CP-PC-SAFT leads to overestimation of their binary VLE as well. Unsurprisingly, the predictions of
GC-PPC-SAFT for these data are nearly precise. At the same time,
in the cases of substances such as dipropyl ether and 1-hexanol,
whose pure compound vapor pressure data are decently estimated
by CP-PC-SAFT in the entire temperature range, this model yields
reasonable predictions of the low pressure VLE as well. Nevertheless even in such cases GC-PPC-SAFT apparently exhibits a better
over-all accuracy (Fig. 10C). However a major advantage of GC-PPCSAFT is its outstanding potential in simultaneous predicting of VLE
and LLE in symmetric systems [51]. Fig. 10D presents an example
of this remarkable feature, namely the system n-heptane(1) – benzyl alcohol(2) at the atmospheric pressure. Although CP-PC-SAFT is
also capable of qualitatively correct predicting the over-all picture
of these phase equilibria, its quantitative performance is substantially less accurate. At the same time, it should be kept in mind that
the GC-PPC-SAFT parameters for benzyl alcohol have been fitted,
while CP-PC-SAFT appears here as an entirely predictive model.
H. Lubarsky et al. / J. of Supercritical Fluids 115 (2016) 65–78
73
150
180
(a)
P(bar)
P(bar)
(b)
39
3.
2
K
100
120
3.2
35
CO2
60
50
31
K
K
3.2
0
0
300
400
500
T(K)
0.0
600
.2
.4
x1,y1 .6
.8
1.0
120
180
(d)
(c)
P(bar)
P(bar)
80
120
3.2
39
K
K
.15
3
33
K
3.2
35
60
5K
3 .1
1
3
40
.2 K
313
0
0
0.0
.2
.4
x1,y1 .6
.8
0.0
1.0
150
.2
.4
x1,y1 .6
.8
1.0
.8
1.0
90
P(bar)
(e)
P(bar)
15
3.
5
3
100
K
60
5K
3.1
3
3
K
.15
313
50
(f)
5
3.1
31
K
30
0
0
0.0
.2
.4
x1,y1 .6
.8
1.0
0.0
.2
.4
x1,y1 .6
Fig. 8. Phase equilibria in the systems of carbon dioxide(1). (a) the critical loci: 䊎 – ethyl acetate(2), - ethyl propionate(2), – ethyl butyrate(2). The isotherms: (b) propyl
acetate(2), (c) butyl acetate(2), (d) ethyl butyrate(2), (e) 3-pentanone(2), (f) 2-hexanone(2). Points – experimental data [112–118]. Dashed lines − predictions of CP-PC-SAFT,
solid lines – of GC-PPC-SAFT.
4. Conclusions
In this study we have performed a comprehensive comparison
between two SAFT approaches whose parameterization substantially diminishes referring to the experimental pure compound
data, which radically increases their predictive values. In the case
of CP-PC-SAFT, the only required information is the critical constants and triple point densities, which are available for large
variety of compounds. Parameterization of GC-PPC-SAFT does not
require any experimental information for the compounds comprised of the chemical groups included in its current parameter
matrix. At the same time, implementation of this model to the
first members of the homologues series of compounds and the
branched molecules still requires fitting. In this study the models under consideration have been implemented to the mixtures
of weakly- and non-associated oxygenated compounds, such as
aromatic and aliphatic alkanols, esters, ethers and ketones in the
entirely predictive manner, without adjusting any binary parameters. The considered data have included the available single phase
thermodynamic properties in wide range of conditions, the existing
information on the global phase behavior, the representative high
pressure VLE in asymmetric and symmetric systems, and, finally,
the characteristic low pressure phase equilibria data.
74
60
=
K
x1
39
74
0.
1
40
0.1
31
=
30
=
33
K
(b)
x
3
0.1
37
60
P(bar)
5K
8.6
5K
3.1
1
(a)
x
P(bar)
0.
47
65
90
28
8. 2
20
A
0
0
0.0
.2
.4
x1,y1 .6
.8
1.0
400
460
T(K)
520
580
27
60
P(bar)
P(bar)
(c)
3K
62
K
2.4
57
.4 K
524
40
20
(d)
.15
453
K
18
15 K
423.
K
393.15
9
K
472.1
373.15 K
0
0
0.0
.2
.4
x1,y1 .6
.8
1.0
0.0
.2
.4
x1,y1 .6
.8
1.0
Fig. 9. High pressure phase equilibria in symmetric systems. (a) carbon dioxide(1) – dimethyl ether(2), (b) diethyl ether(1) – 1-butanol(2), (c) n-hexane (1) – 1-hexadecanol(2), (d) n-pentane(1) – methyl benzoate(2). Points –
experimental data [119–125]. Dashed lines – predictions of CP-PC-SAFT, solid lines − of GC-PPC-SAFT.
H. Lubarsky et al. / J. of Supercritical Fluids 115 (2016) 65–78
30
H. Lubarsky et al. / J. of Supercritical Fluids 115 (2016) 65–78
75
420
600
(a)
T (K)
(b)
T (K)
395
500
370
VLE
400
345
320
300
0.0
.2
.4
x1,y1
.6
.8
0.0
1.0
.2
.4
x1,y1
.6
.8
1.0
550
.3
P(bar)
(c)
5K
3.1
32
(d)
T(K)
450
.2
K
.15
313
303.1
.1
VLE
5K
350
293.15 K
LLE
250
0.0
0.0
.2
.4
x1,y1 .6
.8
1.0
0.0
.2
.4
x1
.6
.8
1.0
Fig. 10. Low pressure phase equilibria in symmetric systems. (a) n-hexane(1) – 1-dodecanol(2) at 1.013 bar, (b) n-hexane(1) – butyl acetate(2) at 1.013 bar, (c) dipropyl
ether(1) – 1-hexanol(2), (d) n-heptane(1) – benzyl alcohol(2) at 1.013 bar. Points – experimental data [126–133]. Dashed lines – predictions of CP-PC-SAFT, solid lines – of
GC-PPC-SAFT.
The results indicate that both models under consideration are
particularly accurate estimators of the single phase liquid densities
at high pressures, typically with slight superiority of GC-PPC-SAFT.
Although these results outline the universality of both approaches,
this feature of CP-PC-SAFT can be considered as more advanced
since this model yields accurate predictions also for sound velocities and compressibilities.
No one of the considered approaches has exhibited a clear and
over-all superiority in the case of phase equilibria. In this study
we have considered the representative examples of VLE and LLE
in various systems and conditions. The results indicate that GCPPC-SAFT is typically advantageous for the symmetric systems. This
advantage is particularly pronounced at the low pressures since
this model is a better estimator of pure compound vapor pressures
away from the critical points. In addition, GC-PPC-SAFT is capable of
particularly accurate estimations of the LLE in these systems. At the
same time, unlike GC-PPC-SAFT, CP-PC-SAFT reproduces the experimental values of critical temperatures and pressures. Therefore the
latter model is a more reliable estimator of the near-critical VLE,
which probably supports its accuracy in predicting of the global
phase behavior. Consequently, while exhibiting the less impressive
over-all results for the symmetric systems, CP-PC-SAFT typically
has a clear superiority in the cases of the asymmetric ones. In particular, unlike GC-PPC-SAFT, this model yields truthful predictions
of the balance between LLE and VLE and more accurate estimations
of solubility of gases in liquids under elevated pressures. At the
same time, GC-PPC-SAFT can sometimes be advantageous in estimating the vapor phase compositions. The results also indicate that
the more precise adjustment of both models under consideration
to the data could not be achieved by a universal value of the binary
parameter k12 . This is because in some cases positive, and in other
negative values of this parameter are required. At the same time,
predictive group-contribution methods for estimating these values
for additional improvement of the precision of both models should
be considered in future.
Acknowledgements
The authors would like to express their deepest thanks to Professor Dan Meyerstein for his fruitful discussion.
Appendix A. Supplementary data
Supplementary data associated with this article can be found,
in the online version, at http://dx.doi.org/10.1016/j.supflu.2016.04.
013.
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