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December 2012, Volume 3, No.6Inte rnational Journal of Chemical and Environmental Engineering
Thermodynamic analysis of vapor- liquid
equilibrium for (water-acrylic acid) and (aceticacid-acrylic acid) systems at moderate pressure
A. Attiaa.b
, F. Muteleta*
, J.C Moise a
. R. Solimandoa*
, Med. R Jedayb
aUniversité de Lorraine, Laboratoire de Réactions et Génie des Procédés (UPR CNRS 3349),
1 rue Grandville, BP 20451 54001 Nancy, France.b
University of Gabes, National Engineering school, Research unit of Energetic and Environment UR/99, ,Street of’Omar El Khattab, 6029, Gabes, TUNISIA. a Fabrice MUTELET
*Corresponding author E-mail :[email protected]
Abstract: In this paper, experimental vapor-liquid equilibria data for two binary systems {water + acrylic acid} and {acetic acid + acrylic acid}
are determined at low pressure by ebulliometer apparatus. Our experimental data are also in good agreement with those published in
the literature. The vapor-liquid equilibria of binary systems are represented using NRTL-HOC and UNIQUAC-HOC models. A goodquantitative agreement was obtained with both models. It was found that the average deviation from the NRTL model is slightly
greater than those from the UNIQUAC model. Selected thermodynamic models can now represent with a good accuracy the relative
volatility.
Keywords: carboxylic acids, vapor-liquid equilibria, acrylic acid, NRTL-HOC, UNIQUAC-HOC, relative volatility.
1. Introduction
Acrylic acid and its esters are among the most versatilemono mers for providing performance properties to a wide
variety of polymers. An important part of acrylic acid isusual in the production of acrylate esters which include
methyl, ethyl, n-butyl, and 2-ethylhexyl acrylate, else is
purified into glacial acrylic acid and subsequently utilizedfor the production of poly-acrylic acid or copolymers
which find applications in super absorbents, detergent co-
builders, dispersants, flocculants , and thickeners. Acrylate
esters impart many desirable qualities to polymeric
materials, such as color stability and clarity when exposed
to light, heat and aging resistance, good weather ability,low temperature flexibility, and base resistance [1-3].
A current process for producing acrylic acid has been
practiced by catalytic oxidation of propylene or acrolein
in gaseous phase. Purification steps consist of collect,separate and recover of acrylic acid from impurities like
as acetic acid, water.
For the development of actual separation processes of
acrylic acid, there is a need for insight into the
fundamental phenomena of non ideal phase equilibria.
The determination of an adequate thermodynamic model
for wide range of temperature and pressure is necessary
for modeling and optimizing an industrial purification.
For these reasons, the evaluation and accuracy of the
experimental data reported in literature for different
systems is absolutely necessary. Interesting binary
systems such as {water-acrylic acid} and {acetic acid-
acrylic acid} are s tudied in this work. These s ystems were
limited reported in the literature. For e xample, the {water-acrylic acid} system has been studied only by Olson et
al.[4-8]. The {acetic acid-acrylic acid} has been
investigated by Chubarov et al [5], Linek et al. [9] and by
Trybula et al. [10]. Unfortunately, acids form particular
complexes that are due to hydrogen bonding interactions
[11-12]. Dimerization of carboxylic acid is as a result of
these specific chemical forces acting between molecules.
This paper evaluates the reliability of experimental points
in a large range of the interval of pressure and
temperature. Thermodynamic behavior for carboxylic
acids is characterized by complexity and non ideality of
vapor phase that cannot be neglected at low pressure [11-
13]. Hayden O’Connell [12] correlation was used tocompute fugacity coefficients of vapor phase. All
equilibrium data were correlated with NRTL [14] and
UNIQUAC [15] activity coefficient models which were
introduced to obtain adequate parameters in order to
represent the relative volatilities. All binary interaction
parameters of these models were taken from Aspen plus
commercial software.
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The rmodynamic analysis of vapor- liquid equilibrium for {water-acrylic acid} and {acetic acid- acrylic acid} systems at modera te pressure
387
2. Materials and Method
2.1. Materi als
In this work, all compounds were purchased from
commercial sources and used without any further
purification. Acry lic acid stabilized with 200 pp m 4-
methoxyphenol (CAS 79-10-7) and acetic acid (CAS 64-
19-7) were from Sigma Aldrich. The mole fraction
purities stated by the manufacturers were greater than0.99 and 0.998 for acrylic acid and acid acetic
respectively. Water was purified by a M illi-Q system with
resistivity lesser than 18Ω.cm.
2.2.
Apparatus and procedure
Ebulliometer is designed to accurately measure isobaric
vapor-liquid equilibria of pure component and mixtures
[16-23]. This apparatus (EEA/3000) is based on dynamic
recirculation of liquid and vapor phase allowing it to
reach thermodynamic equilibria. It is operated in a batch
mode at atmospheric and reduced pressure up 0.13 kPa. Adetailed diagram of this experimental system is presented
in figure 1.
The stainless steel/glass and PTFE design of the unitallows to study of a large range of products. The pressure
is fixed and constant by using a vacuum pump. The
accuracy of the pressure calibrator was ±0.01kPa.
Firstly, a mixture is introduced through loaded 150 cm3
feed flask (1) and passed into a buffering reserve equiped
by magnetic stirrer (5). Then, mixture pas sed directly into
a boiler (2) and is heated by mean of an electrical
resistance generating evaporation calibrated 0 to 100%
with maximum power 500 W. Adiabatic double envelope
equilibrium chambers (3) ensure a thermodynamic
equilibrium and provide a contact between two phases.
The temperature is measured using temperature probe
which is placed on the equilibrium chamber. Theuncertainty in the temperature measurement is estimated
to ± 0.01 K. when thermodynamic equilibria is reached.
Vapor phase is condensed in condenser (8) and the
dropped in the buffering reserve, while a liquid phase is
recycled directly in the buffering cell. Vapor phase
sampling and liquid phase sampling are taken from
sampling ports (6) and (7) and are analyzed by gas
chromatography. A vacuum pump (9), assures
measurement of VLE at low pressure. A trap of dry ice
(4) can also be used to protect the pump of any contact
with the fluid‘s s tudied.
Figure1.Experimental apparatus of VLE measurement
The gas chromatography (Agilent technology) was
equipped with a FID detector and the column used was
capillary column (10 m 0.53 mm 0.7 mm, Agilent)
packed with polyethyleneglycol. The carrier gas was
helium flowing at 20 mL3/min, and the operating
conditions were as follows: injector temperature, 543.15
K, detector temperature, 573.15 K. The initial temperature
of the oven was fired at 333.15 K during 4 min andgradient of 10K/min was impos ed up to 453.15K.
3. Results and Discussions
To test the performance of the equilibrium apparatus, we
measured vapor pressure of pure compound such as
ethanol. Table 1 shows that measured values and the
literature data [26] are in good agreement. In general an
average s tarted deviation lower than 0.23%.
Isobaric vapor liquid equilibria data of {water
(1) + acrylic acid (2)} and {acetic acid (1) + acrylic acid
(2)} measured in this work but also data taken for the
literature are presented in figures 2 and 3.Acetic acid and water vapor pressure data were found in
the DIPPR databank are listed in table 2. Acrylic acid
parameters are obtained by fitting experimental data [9,
25-28].
Table 1 . Vapor press ure of Ethanol
Table 2 . Parameter of the extended Antoin e equ ation ( l nP/kPa=
A+B/T+ClnT+DTE)
The equation that describes thermodynamic equilibrium between phases at temperature T and pressure P is:
( )exp( )
L S S S i i
i i i i i i
V P P Py P x
RT
(1)
Where i is the fugacity coefficient of component i in the
vapor phase, yi and xi are the molar fractions in the vapor
and liquid phases respectively, γi is the activity coefficient
of i with respect to the reference fugacity, is is the
fugacity coefficient of the pure saturated vapor of
component i, Psi is the saturated vapor pressure of
P/PaMeasuredT/K [26]
calculatedT/K Errors %
3199.70 283.15 283.75 0.21
5946.20 293.15 293.29 0.05
7972.70 298.15 298.11 0.01
10600.00 303.15 303.03 0.04
18000.00 313.15 312.91 0.0729500.00 323.15 322.91 0.07
46900.00 333.15 332.77 0.11
72300.00 343.15 342.36 0.23
Compound A B C D E
Acetic Acid 46.3622 -6304.5 -4.2985 8.88*10-18
2
Acrylic acid 40.7143 -6738.33 -3.22080 5.22*10-7
2
Water 66.7412 -7258 .20 -7.3037 4.16*10-6
2
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The rmodynamic analysis of vapor- liquid equilibrium for {water-acrylic acid} and {acetic acid- acrylic acid} systems at modera te pressure
388
component i at temperature T, and Vil is the mo lar
volume of component i is equal to the partial molar
volume of component i at these conditions. At low
pressure, the term ( )exp( )
L S
i iV P P
RT
is approximately
equal to unit thus equation (1) can be rewritten as :
ii
S
i
S
iii x P Py (2)
The vapor phase fugacity coefficients of acetic acid and
acrylic acid were obtained by using the virial equation ofstate truncated after the second term. The second virial
coefficients were determined by the Hayden and
O’Connell corre lation. The phys ical properties [29-30] of
the pure components required in calculation are presented
in table 3.
Table 3. Properties of pure compone nts use d in calcu lati ng th e
second virial coefficie nt
T c critical temperature, P c critical pressure. V c critical volume, wacentric factor, RD gyration radius, DM dipole moment.
Figu re 2. T – x (1)-y(1) diagrams of {water(1)-acryli c acid(2)} at
diffe rent pressures: (A) 101.325 kPa , (B) 50 kPa, (C) 6 .67 kPa,experimental values, ■[4], ▲ [5] and --- UNIQUAC.
Figu re 3. T – x (1) -y(1) diagrams of {acetic acid(1)-acrylic acid(2)} at
diffe rent pressures: (A) 101.325 kPa , 26.7 kPa, experi me nta lvalues, ■[9], ♦ [5] and --- UNIQUAC.
Activity coefficients data investigated are computed using
the NonRandom Two-Liquid equation (NTRL) proposed
by Renon and Prausnitz [14] and the UNIversal QUAs i-
Chemical (UNIQUAC) theory developed by Abrams and
Prausnitz [15].
For the NRTL Model, the activity coefficient γ i, for any
component i of the binary sys tem is given by:
)(ln
1
1
1
11
1
m
l
l li
m
r r rjrj
ji
m
jm
l
l ij
j ji
m
l
l li
m
j j ji ji
i
x
xG
xG
xG
x
xG
(3)
With )exp( ji ji jiG ,T
ba
ji
ji ji and
ij ji
Where g is an energy parameter characterizing the
interaction of species i and j,i
x is the mole fraction of
component i. the nonrandomness parameter. Although
can be treated as an adjustable parameter, in this study
was set equal to 0.3 according the literature [14].
For the UNIQUAC Model, the activity coefficient γ i, forany component i of the binary system is given by:
m
jm
k
kjk
ji j
ii jiiii
i
i
i
i
i qqql q z
x 1
1
lnln2
lnln
(4)
Where
m
j j j
ii
i
xr
xr
1
,
m
j j j
ii
i
xq
xq
1
)1()(2
j j j j r qr z
l andT
ba
ji
ji ji
Here, the lattice coordination number z is assumed to beequal to 10. r i and q i are respectively a relative volume
and surface area of the pure component i. Parameters r i
and qi are respectively relative to molecular Van derWaals volumes and molecular surface areas. They a re
calculated as the sum o f the group volume and group area
parameters R k and Qk :i
i k k
k
r R andi
i k k
k
q Q (5)
Where i
k the number of is groups of type k in molecule i.
The group parameters R k and Qk are obtained from van
der Waals group volumes and surface areas. Vk and Ak
taken from the UNIFAC group contributions [31]:
15.17
k
k
V R and
92.5 10
k k
AQ
(6)
The values of 15.17 and 2.5109 are respectively the
standard segment volume and standard segment area of a
methylene group [31].
The maximum Likelihood method and Britt-Luecke
algorithm were used [32-33]. The binary VLE problem
the maximum likelihood objective function is:
Acetic Acid Acrylic Acid Water
T c /K 591.95 615 647 .096
P c /kPa 5786 5660 22064
V c /m
3
.Kmol
-1
0.1797 0.208 0.05595w 0.2640 0.4665 0 .345
RD .10-10
/m 2.61 2.978 61.5
DM .10-30
/C.m 5.8 4.67 6.17
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The rmodynamic analysis of vapor- liquid equilibrium for {water-acrylic acid} and {acetic acid- acrylic acid} systems at modera te pressure
389
))()(( 2
,
,,
2
1 ,
,,
im
iest im N
i im
iest im
obj y
y y
T
T T F
(7)
Where N is the number of experimental and calculated
mole fractions of one phase and y designed a vapour mole
fraction estimated and measured.
From table 4to table 7, we present T- data for different
systems at different pressures.
Table 4. T- data for {water (1) -acrylic acid (2)} at 50 k Pa
Table 5. T- data for {water (1)-acryli c acid(2)} at 101, 325 kPa
Table 6. T- data for {acetic acid (1)-acrylic acid(2)} at 26.67 KPa
Table 7. T- data for {acetic acid (1)-acrylic acid(2)} at 100.44 kPa
The binary interaction parameters of NRTL and
UNIQUAC models were obtained using ASPEN PLUS
V7.2. The estimated NRTL and UNIQUAC binaryinteraction parameters for the systems studied here are
presented in table 8.
Table 8. Correlation Parameters for Activity Coefficients
All data show c that no extremum and hence no azeotropeexists for {water + acrylic acid} at 101.325 kPa [4].
The use of Hayden O’Connell second virial coefficient to
calculate vapor phase fugacity coefficients and
compositions is essential for systems containing organic
acids.
All the activity coefficient models provide a similar
correlation of experimental data. The value of average
means of vapor molar fraction Δy <0.033, temperature (ΔT/T)
<0.3% and the average absolute deviation of activity
coefficients Δγ1<0.09 and Δγ2<0.26 are listed in table 9.
T/K
354.29 1.01 -
354.36 1.04 3.66
354.595 1.18 2.21
356.10 1.29 1.76
358.35 1.25 1.58
359.50 1.23 1.55
361.32 1.36 1.37
362.75 1.32 1.36
366.53 1.39 1.23
381.22 1.45 1.07394.20 - 0.96
T/K
372.50 1.01 -
372.70 1.02 4.91
372.77 1.01 5.62
372.87 1.01 4.94
372.97 1.03 3.91
373.07 1.05 3.34
373.21 1.05 3.15
373.30 1.06 2.86
373.48 1.08 2.57
373.89 1.12 2.21
374.84 1.17 1.89
375.74 1.23 1.63
377.45 1.35 1.35
380.05 1.35 1.27
385.80 1.57 1.10
383.03 1.51 1.13
391.45 1.76 1.03
402.00 2.17 0.97
414.40 - 1.00
T/K
352.31 1.00 -
354.96 1.03 2.72
359.03 1.11 1.79
359.51 1.13 1.72
361.00 1.16 1.59
362.94 1.21 1.46
365.63 1.32 1.29
367.47 1.43 1.21
371.36 1.79 1.08
375.52 - 1.00
T/K 1 2
390.75 1.01 -
393.65 1.05 2.09
396.18 1.11 1.68
399.31 1.14 1.53
400.26 1.14 1.50
406.14 1.3684 1.17
407.08 1.4066 1.15
410.26 1.6985 1.05
414.00 - 1.01
aij a ji bij b ji
Water (1) +acrylic acid(2)
UNIQUAC -0.8068 2.0793 327.5566 -913.8214
NRTL 2.7911 -2.1478 -275.1986 665.3429
Acetic acid(1) + acrylic acid(2)
UNIQUAC -0.747 8 1.6879 310.8726 -864.3531 NRTL 1.7676 -3.4119 -575.837 1606.8865
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The rmodynamic analysis of vapor- liquid equilibrium for {water-acrylic acid} and {acetic acid- acrylic acid} systems at modera te pressure
390
All activity coefficients obtained are greater than 1. It
designed that mixtures have positive deviation (γ 1>1)
from Raoult’s law; the co mpounds dislike each other. The
attraction between identical molecules (A-A and B-B) is
stranger than between different molecules (A-B) this may
cause the formation of minimum-boiling azeotrope and
heterogeneity.
The VLE properties of binary systems studied in this
work a well represented with both models. Themeasurement of the degree of enrichment, or the ease of
separation, is the relative volatility between pair of
components.
Table 9. Averages deviations
Figure 4 and 5 illustrate evolution of relative volatilities.
Then, the tendency of acrylic acid to vaporize is greater
compared to water and acid acetic. In fact, volatility is
directly related to a substance's vapor pressure. At lower
vapor pressure, volatility increases slightly.
Figure 4. Relative volatility – x (1) diagrams o f {water (1)-acryl icacid(2)} at different pressures: (A) 101.325 kPa . (B) 50 kPa. (C)
6.67 kPa. experimental values. ■[7]. ▲ [5] and --- UNIQUAC.
Figu re 5. Relative vola til ity – x (1) diagrams of {acetic acid(1)-acrylic acid(2)} at different pressures : (A) 101.325 kPa . (B) 26.7
kPa . (C) 6.67 kPa, experimental values♦ [5],■[9],▲ [10] and ---
UNIQUAC.
4.
Conclusions
In this paper, measurement of the isobaric vapor – liquid
equilibrium of two interesting indus trial systems {water +
acrylic acid} and {acetic acid-acrylic acid} were carried
out. The NRTL and UNIQUAC models accurately
correlate the experimental data. A good quantitative
agreement was obtained with these models and the
average deviation from the NRTL model greater than
those from the UNIQUAC model.
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