Available online at www.sciencedirect.com
Fluid Phase Equilibria 261 (2007) 343–350
An evaluation of the performance of the Cubic-Plus-Association
equation of state in mixtures of non-polar, polar and associating
compounds: Towards a single model for non-polymeric systems
Epaminondas Voutsas ∗ , Christophoros Perakis,
Georgia Pappa, Dimitrios Tassios
Laboratory of Thermodynamics and Transport Phenomena, School of Chemical Engineering, National Technical University of Athens 9,
Heroon Polytechniou Str., Zografou Campus, 15780 Athens, Greece
Received 8 May 2007; received in revised form 13 July 2007; accepted 18 July 2007
Available online 24 July 2007
Abstract
The aim of this work is to investigate the possibility of identifying a single model that will be able to accurately describe the phase equilibrium
in non-polymeric systems, which involve non-polar, polar and hydrogen bonding compounds. To this purpose the Cubic-Plus-Association (CPA)
EoS, developed in this laboratory about 10 years ago, is examined in the correlation of phase equilibrium in binary systems and prediction of
multicomponent phase equilibrium from binary data. When possible the results of the CPA EoS are compared with those obtained from the
PC-SAFT EoS.
To account for dipolar or quadrupolar interactions, present when molecules such as acetone or carbon dioxide are involved, these molecules are
treated using the concept of “pseudo-association”, i.e. as being able to act as associating compounds. This approach renders CPA applicable to
systems that involve polar compounds without the need of extra terms to account for polar and/or quadrupolar interactions.
It is concluded that CPA, coupled with the “pseudo-association” approach for polar molecules, represents a model that is able to accurately
describe the phase equilibrium in a variety of binary systems involving non-polar, polar and hydrogen bonding compounds and provide satisfactory
prediction of multicomponent phase equilibrium from binary data.
© 2007 Elsevier B.V. All rights reserved.
Keywords: CPA; PC-SAFT; Polar; Association; Phase equilibrium; Binary; Multicomponent
1. Introduction
Mixtures containing associating compounds, such as mixtures of alcohols with hydrocarbons, water with hydrocarbons,
etc., exhibit extremely non-ideal phase behavior, due to the
strong hydrogen bonding interactions present. Moreover, dipolar
and/or quadrupolar interactions, are known to have a significant
effect on the phase behavior of mixtures containing polar compounds. For example, the dipolar interactions are responsible
for the non-ideal behavior observed in mixtures in which one
of the components is polar, e.g. ether, ketone or ester, and the
other is non-polar like a hydrocarbon. Also, due to the strong
quadrupolar moment of carbon dioxide, relatively high solubil-
∗ Corresponding author. Tel.: +30 210 772 3971; fax: +30 210 772 3155.
E-mail address: evoutsas@chemeng.ntua.gr (E. Voutsas).
0378-3812/$ – see front matter © 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.fluid.2007.07.051
ities of polar compounds such as ketones or esters are observed
in carbon dioxide.
In the last about 15 years, hydrogen bonding (HB), or associating, fluids are modeled successfully using the Statistical
Association Fluid Theory (SAFT) equation of state (EoS),
whose development started with the application of Weirtheim’s
theory [1,2] to associating spheres with multiple association
sites, and since then various SAFT versions have been proposed
[3,4]. On the other hand, Weirtheim’s association theory has
been successfully coupled with a cubic equation of state in the
so-called Cubic-Plus-Association (CPA) EoS [5]. Application of
these models to mixtures containing HB molecules is straightforward, after the decision of how many association sites (electron
donor and acceptor) exist on a self-associating molecule. In
all these cases the physical term of SAFT-type models or
that of the CPA EoS takes into account the non-polar interactions.
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E. Voutsas et al. / Fluid Phase Equilibria 261 (2007) 343–350
Many attempts have been made for the extension of SAFTtype models to mixtures containing dipolar or quadrupolar
molecules [6–10]. However, even though a significant complexity is introduced in these models, the results are not always
encouraging. For example, de Hemptinne et al. [11] presented
phase equilibria calculations of the cis-2-butene/n-butane mixture with a polar PC-SAFT model, using a fitted value for the
dipole moment of cis-butene equal to 1.55 D, which is three
times higher than the experimental value, in order to account for
the dipolar interactions developed by cis-2-butene. Moreover,
they comment that when dipole moment values below 1 D were
used, their equation was insensitive to the presence of the dipolar
term.
A different approach has been used by the Lyngby group
[12,13] and our laboratory [14,15], whereby polar or quadrupolar molecules, like ketones, esters and carbon dioxide, are treated
as if they were associating molecules, i.e. as pseudo-associating
molecules. Although this approach does not correspond to the
physical picture, it represents a simple and very useful approach
in using the same model to treat the dipolar and quadrupolar
interactions present in a mixture.
From the engineering point of view it is desirable to have a
single model that is applicable over a wide range of conditions
(temperatures and pressures) and for mixtures that contain various kinds of molecules from non-polar up to strongly polar or
even HB molecules. To this purpose, in this paper, the performance of the CPA EoS is evaluated in all type of non-polymeric
systems, from non-polar up to those involving polar and HB
molecules, using for polar compounds the aforementioned
pseudo-association approach. When possible the performance
of the CPA EoS is compared to the one of a commonly used
SAFT version, the PC-SAFT EoS. This work represents, thus,
a continuation of our earlier study [16] where the PR-fit and
the PC-SAFT EoS were evaluated in systems involving mixtures of alkanes only. Towards the objective of identifying a
single model applicable in all kind of non-polymeric mixtures,
the phase equilibrium of a great variety of binary systems is
examined, including hydrocarbon systems, polar (non-HB)/nonpolar, polar (non-HB)/polar (non-HB), HB/non-polar, polar/HB
and HB/HB systems. Finally, the prediction of vapor–liquid
equilibrium (VLE) of ternary systems that include non-polar,
polar and HB compounds is examined.
2. The models
2.1. The CPA EoS
The modified version of the CPA EoS proposed by Perakis et al. [14] is used in this work. The detailed description
of the model and the equations can be found in two recent
publications by Perakis et al. [14,15]. CPA requires three purecomponent parameters for non-associating compounds, namely
Tc , Pc and ω , while for pure self-associating compounds two
additional parameters are needed: the association energy, εAB ,
and the association volume, βAB . In both cases, the pure compound parameters are determined by fitting experimental vapor
pressure (Ps ) and saturated liquid volume (Vl ) data.
When the CPA EoS is applied to mixtures, the classical van
der Waals one-fluid mixing and combing rules are used for the
attractive term and co-volume parameters of the physical part:
√
xi xj aij ,
aij = ai aj (1 − kij )
(1)
a=
i
b=
j
xi bi
(2)
i
For the extension of the CPA EoS to mixtures containing two
associating compounds, combining rules for the association
energy and association volume parameters are also required.
In this work, the geometric mean is used for both the crossassociation energy, εAi Bj , and the cross-association volume,
βAi Bj , parameters as proposed by Perakis et al. [14]:
√
εAi Bj = εAi Bi εAj Bj and βAi Bj = βAi Bi βAj Bj
(3)
The binary interaction parameter, kij , in Eq. (1) is an adjustable
parameter, and it is determined by fitting experimental binary
phase equilibrium data.
2.2. The PR-fit EoS
The PR-fit EoS [16] is in fact the PR EoS [17], where, however, the critical properties and the acentric factor of the pure
compound are treated as adjustable parameters, denoted as Tc ,
Vc and ω , and they are determined as in CPA and PC-SAFT
by fitting pure compound vapor pressure and saturated liquid
density data. Obviously PR-fit and CPA is the same model for
pure non-associating compounds or mixtures containing only
non-associating compounds.
2.3. The PC-SAFT EoS
One of the most successful SAFT versions, the so-called perturbed chain-SAFT (PC-SAFT) EoS, has been considered in
this work. Details about this model can be found in the original
publications of Gross and Sadowski [18,19].
3. Pure compound parameters
When available the pure compound parameters for all models
were taken from the literature. When not available, they were
determined in this work by fitting experimental pure compound
vapor pressure and liquid volume data taken from the DIPPR
data compilation [20].
The quadrupolar carbon dioxide molecule has been treated
either as a non-associating molecule with PR-fit and PC-SAFT
or as a 4-site associating molecule having two electron donor and
two electron acceptor sites (4C association scheme as defined
by Huang and Radosz [21]) with CPA. The dipolar ketone,
ether and ester molecules were treated either as non-associating
compounds with PR-fit and PC-SAFT or as 2-site associating
molecules having one electron donor and one electron acceptor sites (2B association scheme according to the definition of
Huang and Radosz) with CPA. Alcohols have also been treated
as 2-site associating molecules with CPA and PC-SAFT. Water
E. Voutsas et al. / Fluid Phase Equilibria 261 (2007) 343–350
345
Table 1
Pure compound parameters for PR-fit
Compound
Tr range
Tc (K)
Pc (bar)
ω
%AAD in Ps
%AAD in Vl
Propane
n-Pentane
n-Hexane
n-Heptane
n-Dodecane [16]
Cyclohexane
Benzene
Toluene
CO2 [14]
Diethyl ether
Methyl acetate
Acetone
0.33–0.98
0.40–0.99
0.40–0.99
0.51–0.95
368.59
470.06
508.56
542.42
640.89
551.66
559.43
590.58
306.97
468.05
512.20
518.63
41.56
33.74
31.13
28.25
18.95
39.80
47.81
41.50
75.29
37.15
50.42
54.16
0.1676
0.2567
0.3166
0.3492
0.5684
0.2216
0.2277
0.2785
0.1832
0.2856
0.3142
0.2748
2.2
1.7
3.2
0.9
–
1.1
1.3
1.0
1.9
1.4
1.1
1.2
4.1
3.3
3.7
2.2
–
3.3
1.7
1.3
3.2
3.0
2.0
1.4
0.50–0.96
0.48–0.92
0.45–0.90
0.72–0.98
0.50–0.97
0.50–0.97
0.40–0.99
in CPA has been treated as a 4-site associating molecule and
in PC-SAFT as a 2-site associating molecule as suggested by
Gross and Sadowski [19].
All pure compound parameters for PR-fit and CPA are presented in Tables 1 and 2. For PC-SAFT the parameters reported
by Gross and Sadowski [18,19] were used.
does not offer any advantage over the simple PR-fit cubic EoS
when non-polymeric mixtures are involved. Similar conclusions
were also derived in a recent study by Alfradique and Castier
[22].
4. Results
Fig. 1 presents VLE correlation results for the system methyl
acetate/cyclohexane. Methyl acetate is a weakly polar compound
(dipole moment = 1.7 D), and its treatment as an associating
compound with CPA leads to only a slightly improved VLE
description over this obtained with PR-fit or PC-SAFT, especially for the bubble point curve. Significant improvement
is, however, achieved by treating a strongly polar compound
like acetone (2.9 D) as an associating molecule, as demonstrated in Fig. 2, which presents the VLE description of
the n-pentane/acetone mixture with the various equations of
state. CPA gives better results than PR-fit and PC-SAFT,
matching very well the azeotropic points at all temperatures. It should be noted that Tumakaka and Sadowski [25]
using a polar PC-SAFT model and zero interaction parameter obtained similar results with those obtained by CPA with
zero kij .
Fig. 3 presents VLE correlation results for the carbon dioxide/benzene system, with PR-fit, PC-SAFT and CPA EoS.
CPA, by treating CO2 as an associating molecule in order
to account for the quadrupolar interactions, gives improved
description of the CO2 solubilities in the liquid phase over
PR-fit and PC-SAFT. It is worth noticing that Gross [6] was
not able to get better results for this particular system with
4.3. Non-polar/polar (non-HB) systems
4.1. Binary mixture calculations
In all binary mixture calculations, one binary adjustable interaction parameter was used for all models: for PR-fit and CPA in
the attractive term (Eq. (1)), and for PC-SAFT in the dispersion
term.
4.2. Binary hydrocarbon mixtures
In a recent publication by our laboratory [16], the original
PR EoS, the PR-fit EoS and two versions of SAFT, the one
proposed by Huang and Radosz [21] and the PC-SAFT, have
been thoroughly examined in terms of their performance in the
correlation/prediction of vapor–liquid equilibria of binary systems containing methane or ethane and n-alkanes of various
degree of asymmetry, and in the prediction of multicomponent
vapor–liquid equilibria in mixtures containing these components. It was concluded that the PR-fit model performed better
than these SAFT-type models, except from highly asymmetric
systems, such as the ones of methane with very large alkanes,
which suggests that the physical term of the PC-SAFT model
Table 2
Pure compound parameters for CPA
Compound
Tr range
Tc (K)
Pc (bar)
ω
εAB /R (K)
βAB
%AAD in Ps
%AAD in Vl
CO2 (4-site) [14]
Diethyl ether (2-site)
Methyl acetate (2-site)
Acetone (2-site)
Methanol
Ethanol [14]
H2 O [14]
0.72–0.98
0.50–0.97
0.50–0.97
0.50–0.95
0.50–0.95
0.50–0.99
0.43–0.99
259.44
435.10
496.83
429.82
346.61
429.49
305.40
58.42
33.57
47.79
44.94
72.57
57.48
135.62
0.1290
0.1752
0.2286
0.2873
0.0640
0.1795
0.1609
481.1
1080.5
1080.2
942.2
2771.2
2625.3
1811.2
0.0457
0.0423
0.0222
0.3103
0.0265
0.0099
0.1062
0.3
0.5
0.3
0.1
1.2
0.6
1.5
0.3
1.1
1.0
1.1
2.0
0.9
0.7
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E. Voutsas et al. / Fluid Phase Equilibria 261 (2007) 343–350
Fig. 1. VLE correlation results for the methyl acetate/cyclohexane system at
308.15 K. Experimental data were taken from [23].
the polar PC-SAFT even when a mixing rule for the crossquadrupolar interactions in the mixture was employed. Also,
Fig. 4 presents liquid–liquid equilibrium (LLE) correlation of
the asymmetric CO2 /n-dodecane system. CPA, by treating CO2
as a self-associating molecule, although it cannot reproduce
very accurately the solubilities in the CO2 -rich phase, provides
a substantial improvement over the PR-fit and PC-SAFT EoS.
Similarly, improved results over those obtained with the original PC-SAFT were presented by Gross [6] with the polar-PCSAFT.
Fig. 2. VLE results for the n-pentane/acetone system. Experimental data were
taken from [24].
Fig. 3. VLE correlation results for the CO2 /benzene system. Experimental data
were taken from [26].
4.4. Polar (non-HB)/polar (non-HB) systems
For the application of CPA in such systems, following the
approach described in Section 4.3, polar compounds were
treated as if they were associating molecules. Figs. 5 and 6
present VLE correlation results for systems containing carbon
dioxide with diethyl ether and acetone. It is shown that the use
of CPA leads to a better description of the bubble point curve
than PR-fit and PC-SAFT.
Fig. 4. Liquid–liquid equilibrium correlation results for the carbon dioxide/ndodecane mixture. Experimental data were taken from [27].
E. Voutsas et al. / Fluid Phase Equilibria 261 (2007) 343–350
Fig. 5. VLE correlation results for the diethyl ether/CO2 system at 298.15 K.
Experimental data were taken from [28].
4.5. Non-polar/HB systems
Mixtures of methanol with alkanes are very important in the
petroleum industry since methanol is widely used as a gashydrate inhibitor. Fig. 7 presents isothermal VLE correlation
results with CPA and PC-SAFT for the methanol/propane system at 313.1 K. Both CPA and PC-SAFT predict an azeotropic
behavior, which however is not confirmed by this particular set of experimental data. Using these kij values, the
azeotropic compositions and pressures at 310.7 and 352.2 K
were predicted with the two models and they were compared
Fig. 6. VLE correlation results for the acetone/CO2 system at 333.15 K. Experimental data were taken from [29].
347
Fig. 7. VLE correlation results for the methanol/propane system at 313 K. Experimental data were taken from [30].
with the experimental values given by Leu et al. [31]. At
310.7 K CPA predicts xaz = 0.988, Paz = 12.9 bar and PC-SAFT
xaz = 0.986, Paz = 13.1 bar, while the corresponding experimental values are xaz = 0.979 and Paz = 13.5 bar. At 352.2 K CPA
predicts xaz = 0.975, Paz = 31.3 bar and PC-SAFT xaz = 0.972,
Paz = 31.3 bar, while the corresponding experimental values are
xaz = 0.958 and Paz = 31.8 bar. Both models provide satisfactory
azeotropic point predictions. An interesting discussion on the
VLE behavior of methanol/alkane systems and the good performance of models that include the association term of SAFT in
this kind of systems is given by Chapman et al. [32].
The methanol/n-hexane system is very interesting since it
exhibits a homoazeotropic VLE behavior at high temperatures
and LLE phase behavior at lower temperatures. Fig. 8 presents
VLE and LLE calculations with CPA and PC-SAFT, where for
both models a single binary interaction parameter, fitted only
to the LLE data, was used. Both models predict very well the
VLE of this system indicating that they are able to satisfactorily
describe the phase equilibria in such systems over a wide temperature range, but CPA gives better LLE results for the alkane-rich
phase.
Modeling of phase equilibria of water/hydrocarbon mixtures, which is very important for industrial and environmental
applications, is a very stringent test for the performance of thermodynamic models due to the extremely non-ideal behavior
exhibited by these systems. The solubilities in the coexisting
phases are strongly asymmetric: the solubility of the hydrocarbon in the water-rich phase is several orders of magnitude lower
than the solubility of water in the hydrocarbon-rich phase. Fig. 9
presents mutual solubility calculations for the n-hexane/water
system with the CPA and PC-SAFT. A single binary interaction
parameter has been used for both models, fitted to the solubility
of water in the hexane-rich phase. CPA gives fairly good predictions of the solubilities of n-hexane in the water-rich phase, while
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E. Voutsas et al. / Fluid Phase Equilibria 261 (2007) 343–350
Fig. 8. Isobaric (1 atm) homoazeotropic VLE and LLE of the methanol/n-hexane
mixture with CPA and PC-SAFT EoS. kij ’s were obtained by fitting the LLE data.
Experimental data were taken from [33,34].
PC-SAFT underestimates by orders-of-magnitude the experimental data. Voutsas et al. [36] also concluded that CPA provides
significantly better results over the SAFT version of Huang and
Radosz [21] for water/alkane systems.
4.6. Polar (non-HB)/HB systems
Fig. 10 presents correlation results for the ethanol/CO2 mixture with the CPA and PC-SAFT models. In CPA, CO2 has
been treated either as a non-associating or as a self-associating
Fig. 9. LLE correlation results for the system water/n-hexane with CPA and
PC-SAFT at the three-phase equilibrium pressure. Experimental data were taken
from [35].
Fig. 10. VLE correlation results for the ethanol/CO2 mixture at 313.4 K. Experimental data were taken from [37]. CPA-na: CO2 is treated as non-associating
compound; CPA-a: CO2 is treated as associating compound.
molecule. Satisfactory results are obtained only with CPA when
CO2 is treated as a self-associating molecule. Similar conclusions have been also derived for the CO2 /water system, which
has been thoroughly investigated in two recent publications by
Perakis et al. [14,15].
Fig. 11 presents VLE correlation for the acetone/methanol
binary system. When the polar interactions developed by acetone are ignored, i.e. if acetone is treated as a non-associating
molecule, a very poor correlation is obtained by both CPA and
Fig. 11. VLE correlation results for the acetone/methanol mixture at 1 atm.
Experimental data were taken from [38]. CPA-na: acetone is treated as nonassociating compound; CPA-a: acetone is treated as associating compound.
E. Voutsas et al. / Fluid Phase Equilibria 261 (2007) 343–350
349
Table 3
VLE results for the water/ethanol system in the T range of 298–623 K with the
CPA (kij = −0.1) [14] and tPC-SAFT EoS (kij = 0.0085) [41]
CPA
tPC-SAFT
%AAD in P
%AAD in y
2.6
5.7
6.9
7.3
Experimental data were taken from [42,43].
Table 4
VLE predictions for ternary systems with the CPA EoS
System
%AAD in P
y1
y2
y3
n-Pentane (1)/methanol (2)/
acetone (3)a [39]
Acetone (1)/methanol (2)/
water (3)b [44]
1.4
1.0
0.9
0.7
3.6
2.1
1.9
1.3
a k = 0.0549 (obtained by fitting experimental VLE data at 372.7 K [44]);
12
k13 = 0.0132; k23 = 0.0528.
b k = 0.0528; k = −0.1185 (obtained by fitting experimental VLE data at
12
13
373.15 K [39]); k23 = −0.1442.
Fig. 12. VLE correlation and prediction results with CPA and PC-SAFT for the
methanol/water system. kij ’s were obtained by fitting the VLE data at 373.15 K.
Experimental data were taken from [39,40].
PC-SAFT. On the other hand, treatment of acetone as an associating molecule with CPA leads to improved results, i.e. CPA
underpredicts the azeotropic temperature only about 1.4 K. Similar behavior was observed for the acetone/water binary.
4.7. Binary mixtures of hydrogen bonding molecules
Fig. 12 presents VLE calculations with the CPA and PCSAFT EoS for the methanol/water system over a wide range
of temperatures and pressures, using a single binary interaction
parameter that was fitted to the 373 K isotherm since it will be
used later in ternary VLE predictions. Both models give satisfactory correlation/prediction results, with CPA to be overall
superior to PC-SAFT. It is worth noticing that PC-SAFT does
not predict a mixture critical point for the 523.15 K isotherm,
i.e. it predicts that pure liquid methanol exists at this temperature, which, however, is higher than the critical temperature of
methanol (512.6 K). On the other hand CPA correctly predicts a
mixture critical point at this isotherm. This is due to the fact that
PC-SAFT overpredicts the critical temperature of methanol by
18.9 K, while CPA only by 7.8 K.
Finally, it is interesting to compare the results obtained with
CPA for the water/ethanol system with those presented for the
same system by Karakatsani et al. [41] with the tPC-SAFT EoS,
which is a truncated version of the polar PC-SAFT EoS. For
CPA and tPC-SAFT a single temperature independent interaction parameter for all isotherms in the range of 298–623 K
has been employed. The overall results, presented in Table 3,
indicate a superior performance of CPA.
5. Prediction of ternary phase equilibria
Multicomponent phase equilibrium prediction is a very strict
test for the performance of thermodynamic models. Table 4
demonstrates ternary VLE predictions with the CPA EoS for npentane/methanol/acetone and acetone/methanol/water, where
acetone was treated as an associating molecule. The binary interaction parameters that were determined from the binary VLE
data were used without further fitting. CPA gives predictions
which are in very good agreement with the experimental data
both for the bubble point pressures and for the vapor phase
compositions.
6. Discussion and conclusions
The following comments summarize the observations on the
obtained results:
a. The PR-fit EoS, i.e. CPA without the association term, is a
powerful tool for VLE calculations in mixtures containing
non-polar or weakly polar compounds.
b. For strongly dipolar molecules like acetone or a quadrupolar
one like carbon dioxide, the use of the “pseudo-association”
concept in CPA provides very satisfactory results for their
mixtures with non-polar, polar and associating compounds.
This approach renders CPA applicable to systems involving
polar compounds without the need of extra terms to account
for polar and quadrupolar interactions.
c. For mixtures of hydrocarbons with a self-associating
molecule, like alcohols or water, CPA gives very good
results. The same applies for mixtures containing two selfassociating compounds, such as mixtures of alcohols with
water.
d. There is evidence that the inclusion of an extra term in the
PC-SAFT to account for dipolar or quadrupolar interactions,
does not appear to provide any advantage over CPA coupled with the pseudo-association scheme, as suggested by the
comparison with literature results for the acetone/n-pentane,
CO2 /benzene, CO2 /dodecane and water/ethanol systems.
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E. Voutsas et al. / Fluid Phase Equilibria 261 (2007) 343–350
e. CPA provides reliable multicomponent phase equilibrium
predictions as suggested by the results presented here and
the recent ones presented by Perakis et al. [14,15].
In conclusion, the CPA model, coupled with the pseudoassociation approach for polar molecules, represents a single
model that is able to accurately describe the binary phase equilibrium in systems involving non-polar, polar and hydrogen
bonding compounds and provides satisfactory prediction of multicomponent equilibrium from binary data.
List of symbols
Ai
site A in molecule i
AAD average absolute deviation,
np
|exp. value−calc. value|
1
np
b
Bj
kij
np
Ps
R
Vl
xi
yi
%AAD = 100 ×
exp . value
i=1
co-volume parameter (dm3 mol−1 )
site B in molecule j
binary interaction parameter
number of experimental data points
vapor pressure (bar)
gas constant (bar dm3 mol−1 K−1 )
saturated liquid volume (dm3 mol−1 )
liquid mole fraction of component i
vapor mole fraction of component i
Greek letters
β
association volume parameter
Δ
association strength (dm3 mol−1 )
y
deviation in the calculated vapor mole fractions, y =
np
exp
1
100 × np
|yi − yicalc |
ε
ε/k
ω
i=1
association energy parameter (bar dm3 mol−1 )
energy of association (K)
acentric factor
Subscripts and superscripts
c
critical
calc
calculated
exp
experimental
r
reduced
Acknowledgement
We acknowledge the use of the SPECS program (V5.3),
developed in IVCSEP-Lyngy, for performing some of the calculations with PC-SAFT.
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