Fluid Phase Equilibria 338 (2013) 30–36
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Vapor–liquid equilibrium for the ternary carbon dioxide–ethanol–nonane and decane systems Miguel G. Arenas-Quevedo a , Luis A. Galicia-Luna a,∗ , Octavio Elizalde-Solis b , José A. Pérez-Pimienta c a
Laboratorio de Termodinámica, SEPI-ESIQIE, Instituto Politécnico Nacional, UPALM, Ed. Z, Secc. 6, 1ER piso, Lindavista, C.P. 07738 México, D.F., Mexico Departamento de Ingeniería Química Petrolera, ESIQIE, Instituto Politécnico Nacional, UPALM, Edif. 8, 2◦ piso, Lindavista, C.P. 07738 México, D.F., Mexico c Departamento de Ingeniería Química, Área de Ciencias Básicas e Ingenierías, Universidad Autónoma de Nayarit, Edificio E2, Ciudad de la Cultura Amado Nervo, C.P. 63155 Tepic, Nayarit, Mexico b
a r t i c l e
i n f o
Article history: Received 18 May 2012 Received in revised form 8 October 2012 Accepted 16 October 2012 Available online 23 October 2012 Keywords: Vapor–liquid equilibrium Carbon dioxide Ethanol Nonane Decane
a b s t r a c t In this work, experimental vapor–liquid equilibrium (T, p, xi , yi ) data for the ternary carbon dioxide–ethanol–nonane and carbon dioxide–ethanol–decane systems are reported in the temperature range of 313–373 K from low pressures to the nearest of the corresponding critical pressure. Measurements were performed in an apparatus based on the static-analytic method with an on-line ROLSI sampler-injector device. Vapor–liquid equilibrium (VLE) data for both ternary systems are predicted using the Peng–Robinson equation of state coupled to the Wong–Sandler, one parameter van der Waals and two parameters van der Waals mixing rules. Binary interaction parameters are obtained from the VLE data of binary mixtures reported in the literature. © 2012 Elsevier B.V. All rights reserved.
1. Introduction The study of phase equilibrium behavior of multicomponent systems is necessary in order to understand and establish the temperature (T) and pressure (p) conditions where phases coexist. Thermodynamic models are used to represent the phase behavior of multicomponent mixtures; however, in some cases these models are not enough accurate and give an approximation of the phase behavior. Therefore, experimental data is the basic information that can be obtained accurately [1,2]. Experimental methods for the determination of phase equilibrium data are classified with the aim of selecting the one suitable based on the involved phases [3,4]. The vapor liquid equilibrium behavior for carbon dioxide + alkanol + alkane systems is scarcely available in the literature [5–9]. These studies are about critical end points, critical lines, miscibility windows and isothermal phase diagrams utilizing linear alkanols (pentanol to dodecanol) and alkanes (tetradecane to tetracosane). However, there is a lack of VLE data for short carbon chains of alkanes and alkanols. As a continuation of a previous work, we present the vapor–liquid equilibrium behavior for the ternary systems carbon
∗ Corresponding author. Tel.: +52 55 5729 6000x55133; fax: +52 55 5586 2728. E-mail address:
[email protected] (L.A. Galicia-Luna). 0378-3812/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.fluid.2012.10.012
dioxide + ethanol + nonane or decane at three temperatures in a wide range of pressure. The experimental VLE results are compared with the prediction using the Peng–Robinson equation of state with classical and Wong–Sandler mixing rules. Separation factors between solutes are calculated from experimental vapor and liquid phase compositions. 2. Experimental 2.1. Materials Properties of chemicals [10] are listed in Table 1. Carbon dioxide of supercritical grade was supplied from Infra Air-Products. Ethanol was purchased from Merck Chemicals and alkanes were provided by Sigma–Aldrich. These were used as received with no previous purification stage. Water content was determined in a Karl–Fisher coulometer and are presented in Table 1 as well as certified purities. 2.2. Apparatus The experimental apparatus where measurements were carried out is based on the static–analytic technique. Details of the operating principle and its reliability for VLE measurements were described in previous papers [11,12]. The apparatus is mainly constituted by a 100 cm3 high-pressure view-cell made of titanium alloy, a gas chromatograph (Hewlett-Packard, 5890 series II). Both
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31
Table 1 Properties of chemicals [10]. Chemicals
CAS
Mole fraction purity
Carbon dioxide Ethanol Nonane Decane
[124-38-9] [64-17-5] [111-84-2] [124-18-5]
0.999999 >0.998 0.991 0.997
Mole fraction water – 22 × 10−5 21 × 10−5 26 × 10−5
devices are connected with a thermo-regulated tubing that allows taking samples on-line with a ROLSI [13] sampler-injector. Pressure in the system is measured by a transducer (Druck, PDCR) connected to an indicator (Druck, DPI 145) previously calibrated with an uncertainty of ±0.008 MPa. Two calibrated temperature resistance probes PT 100- coupled to a digital indicator (Hart Scientific, CHUB E4 1529) are located in the top and bottom of the equilibrium cell. Their corresponding uncertainties are within 0.02 K. The analytical equipment used helium as carrier gas at a flowrate of 30 cm3 min−1 through a packed column (Alltech, Porapak Q 80/100) with 4 ft of length, 1/8 in of outlet diameter and reference gas at 45 cm3 min−1 . The thermal conductivity detector (TCD) was calibrated using high purity chemicals listed in Table 1 with the same conditions than the corresponding for the equilibrium measurements. 2.3. VLE measurements The apparatus was totally washed with organic solvents before experiments. Carbon dioxide flowed through the entire lines and
Tc (K)
pc (MPa)
ω
304.12 513.92 594.60 617.70
7.374 6.148 2.290 2.110
0.225 0.649 0.445 0.490
cell to remove any contaminants and finally these were dried with high purity nitrogen. About 50 cm3 of the binary mixtures ethanol–alkane were loaded into the equilibrium cell at equimolar relation. The cell was placed into the air bath and degassed by means of a vacuum pump under stirring. The air bath temperature was set to the selected value. After temperature was stable, carbon dioxide was carefully fed to the cell from the supply cylinder through a syringe pump (Isco, 100 DM). The stirring was permanently activated in order to ensure the correct mixing of the compounds in both phases. Within thermal and mechanical equilibrium, samples of the vapor or liquid phase were sent to the gas chromatograph for quantifying their composition using the ROLSI sampler. This device has a capillary which is immersed into the cell from the cap and can be moved up to the bottom in vertical position to sample each phase. Several samples of each phase had to be taken at constant pressure and temperature in order to have a suitable value of the composition. Then, the last five consecutive samples within 1% of deviation with respect to CO2 composition were considered to reduce the uncertainty.
Table 2 Experimental vapor–liquid equilibria for the carbon dioxide (1)–ethanol (2)–nonane (3). p (MPa)
x1
x2
x3
y1
y2
y3
U(x1 )
U(y1 )
T (K) = 313.33 2.041 2.867 3.516 4.563 5.517 6.391 6.569 7.187 7.463 7.730
0.1760 0.2497 0.3072 0.4098 0.5106 0.6592 0.6804 0.8258 0.8832 0.9222
0.5263 0.4853 0.4440 0.3767 0.3106 0.2136 0.2002 0.1062 0.0704 0.0476
0.2977 0.2650 0.2488 0.2135 0.1788 0.1272 0.1194 0.0680 0.0464 0.0302
0.9863 0.9887 0.9903 0.9916 0.9917 0.9907 0.9904 0.9888 0.9876 0.9861
0.0105 0.0089 0.0078 0.0068 0.0065 0.0072 0.0074 0.0086 0.0093 0.0102
0.0032 0.0024 0.0019 0.0016 0.0018 0.0021 0.0022 0.0026 0.0031 0.0037
0.0024 0.0026 0.0030 0.0014 0.0028 0.0020 0.0016 0.0015 0.0017 0.0018
0.0011 0.0017 0.0014 0.0012 0.0010 0.0016 0.0010 0.0012 0.0013 0.0009
T (K) = 344.61 2.079 2.922 4.016 5.002 5.654 6.568 7.609 8.598 9.565 10.597 11.044
0.1600 0.2049 0.2697 0.3138 0.3504 0.4021 0.4630 0.5408 0.6711 0.7826 0.8291
0.5454 0.5207 0.4751 0.4442 0.4258 0.3961 0.3602 0.3070 0.2060 0.1345 0.1117
0.2946 0.2744 0.2552 0.2420 0.2238 0.2018 0.1768 0.1522 0.1229 0.0829 0.0592
0.9610 0.9696 0.9730 0.9741 0.9737 0.9732 0.9719 0.9689 0.9629 0.9465 0.9233
0.0342 0.0264 0.0232 0.0218 0.0219 0.0220 0.0226 0.0243 0.0266 0.0367 0.0513
0.0048 0.0040 0.0038 0.0041 0.0044 0.0048 0.0055 0.0068 0.0105 0.0168 0.0254
0.0021 0.0026 0.0021 0.0022 0.0024 0.0028 0.0025 0.0022 0.0019 0.0021 0.0021
0.0016 0.0016 0.0015 0.0019 0.0017 0.0018 0.0015 0.0010 0.0011 0.0016 0.0009
T (K) = 373.94 1.974 3.030 4.021 4.974 6.049 6.925 7.975 9.071 10.041 11.051 12.063 12.984 13.059
0.1233 0.1786 0.2271 0.2723 0.3171 0.3596 0.4120 0.4588 0.5098 0.5807 0.6555 0.7350 0.7933
0.6249 0.5861 0.5489 0.5182 0.4869 0.4528 0.4112 0.3841 0.3411 0.2829 0.2332 0.1836 0.1432
0.2518 0.2353 0.2240 0.2095 0.1960 0.1876 0.1768 0.1571 0.1491 0.1364 0.1113 0.0814 0.0635
0.8692 0.9057 0.9260 0.9422 0.9500 0.9571 0.9639 0.9620 0.9591 0.9537 0.9440 0.9143 0.8505
0.1173 0.0833 0.0643 0.0498 0.0426 0.0356 0.0291 0.0306 0.0324 0.0355 0.0416 0.0603 0.1053
0.0135 0.0110 0.0097 0.0080 0.0074 0.0073 0.0070 0.0074 0.0085 0.0108 0.0144 0.0254 0.0442
0.0021 0.0028 0.0028 0.0025 0.0023 0.0027 0.0026 0.0027 0.0020 0.0029 0.0021 0.0025 0.0020
0.0013 0.0012 0.0011 0.0013 0.0013 0.0014 0.0015 0.0012 0.0010 0.0011 0.0014 0.0013 0.0010
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Table 3 Experimental vapor–liquid equilibria for the carbon dioxide (1)–ethanol (2)–decane (3). p (MPa)
x1
x2
x3
y1
y2
y3
U(x1 )
U(y1 )
T (K) = 314.98 2.072 3.039 4.112 5.063 6.234 7.039 7.413 7.770 8.164
0.1972 0.2630 0.3974 0.4915 0.6019 0.7407 0.8333 0.8992 0.9308
0.4619 0.4299 0.3471 0.2905 0.2278 0.1411 0.0886 0.0560 0.0387
0.3409 0.3071 0.2555 0.2180 0.1703 0.1182 0.0781 0.0448 0.0305
0.9914 0.9926 0.9931 0.9925 0.9915 0.9899 0.9878 0.9869
0.0078 0.0067 0.0062 0.0067 0.0074 0.0081 0.0093 0.0100
0.0008 0.0007 0.0007 0.0008 0.0011 0.0020 0.0029 0.0031
0.0021 0.0030 0.0020 0.0025 0.0026 0.0021 0.0020 0.0014 0.0021
0.0013 0.0017 0.0015 0.0010 0.0012 0.0009 0.0011 0.0011
T (K) = 344.77 2.117 3.259 4.194 5.204 6.033 7.011 8.075 9.074 10.067 10.544 11.104 11.407
0.1417 0.2118 0.2568 0.2949 0.3486 0.4170 0.4926 0.5829 0.7097 0.7805 0.8478 0.8883
0.5270 0.4825 0.4586 0.4405 0.4126 0.3661 0.3281 0.2791 0.1808 0.1272 0.0885 0.0644
0.3313 0.3057 0.2846 0.2646 0.2388 0.2169 0.1793 0.1380 0.1095 0.0923 0.0637 0.0473
0.9621 0.9690 0.9728 0.9765 0.9759 0.9754 0.9750 0.9697 0.9629 0.9582 0.9442 0.9275
0.0349 0.0283 0.0247 0.0212 0.0217 0.0218 0.0220 0.0262 0.0301 0.0318 0.0389 0.0472
0.0030 0.0027 0.0025 0.0023 0.0024 0.0028 0.0030 0.0041 0.0070 0.0100 0.0169 0.0253
0.0017 0.0028 0.0022 0.0027 0.0023 0.0028 0.0029 0.0026 0.0021 0.0023 0.0027 0.0030
0.0015 0.0010 0.0009 0.0015 0.0010 0.0014 0.0006 0.0016 0.0013 0.0011 0.0011 0.0012
T (K) = 373.98 1.917 3.233 4.785 5.996 7.016 8.457 9.840 11.174 12.075 12.882 13.255 13.541 13.650
0.1007 0.1688 0.2407 0.3085 0.3472 0.4199 0.4872 0.5541 0.6086 0.6663 0.7300 0.7944 0.8035
0.6160 0.5651 0.5182 0.4647 0.4339 0.3888 0.3541 0.3084 0.2849 0.2416 0.1897 0.1384 0.1356
0.2833 0.2661 0.2411 0.2268 0.2189 0.1913 0.1587 0.1375 0.1065 0.0921 0.0803 0.0672 0.0609
0.8637 0.8953 0.9281 0.9453 0.9472 0.9460 0.9400 0.9318 0.9152 0.9014 0.8826 0.8648 0.8360
0.1295 0.0991 0.0669 0.0501 0.0478 0.0480 0.0525 0.0579 0.0700 0.0786 0.0892 0.0989 0.1165
0.0068 0.0056 0.0050 0.0046 0.0050 0.0060 0.0075 0.0103 0.0148 0.0200 0.0282 0.0363 0.0475
0.0020 0.0019 0.0028 0.0029 0.0024 0.0026 0.0026 0.0025 0.0021 0.0028 0.0030 0.0025 0.0021
0.0006 0.0006 0.0013 0.0016 0.0013 0.0013 0.0017 0.0011 0.0010 0.0015 0.0012 0.0017 0.0010
Sampling procedure was repeated at different pressures isothermally for the vapor and liquid phase. Pressure was changed by adding or removing CO2 to the cell up to near the critical pressure of the mixture. Finally, temperature was set to another value to obtain the following isothermal phase envelope and accomplish VLE measurements. Uncertainties for composition with respect to carbon dioxide in mole fraction were estimated to be within 0.0030 in the liquid phase u(xCO2 ) and 0.0017 in the vapor phase u(yCO2 ). These were rigorously computed following procedure of the error propagation law reported by National Institute of Standards and Technology (NIST) [14]. Mole fraction for each sample zi = xi , yi is a function of the mole number zi = ni /nt ; therefore, its uncertainty u(zi ) associates the variances of the mole number u2 (ni ) using the general expression:
u2 (zi ) =
Nc n / i k k=
2
u2 (ni ) + n2i
Nc
Nc u2 (nk ) / i k=
(1)
n i=1 i
The variances for the mole number of chemicals were calculated from the TCD calibration. This calibration curve was obtained from the response area (Ai ) against mole number (ni ) plot. The best fit was obtained using the following function: ni = ci A2i + di Ai
(2)
where ci and di are the optimized parameters. The associated errors for ni were computed including the sensitivity coefficients, variances and covariance matrix as presented in the following
equation:
2
u (ni ) =
∂ni ∂Ai
2
2
u (Ai ) +
∂ni ∂ci
2
2
u (ci ) +
∂ni ∂di
2 u2 (di )
∂ni ∂ni ∂ni ∂ni ∂ni ∂ni +2 u(Ai , ci ) + u(Ai , di ) + u(ci , di ) ∂Ai ∂ci ∂Ai ∂di ∂ci ∂di
(3)
3. Results and discussion Liquid and vapor equilibrium phase compositions for the carbon dioxide–ethanol–nonane are listed in Table 2 at 313.33, 344.61, and 373.94 K. The corresponding data for the carbon dioxide–ethanol–decane are summarized in Table 3 at 314.98, 344.77, and 373.98 K; uncertainties in composition are also reported at each pressure in both tables based on the carbon dioxide. Equilibrium ratios Ki = yi /xi for the carbon dioxide–ethanol–nonane are depicted in Fig. 1 and for the carbon dioxide–ethanol–decane in Fig. 2. Ki values tend to the unit at the critical point, for carbon dioxide, these are higher than the unit due to its rich content in the vapor phase, the low solubility of alkanes in the vapor phase causes their Ki values are lower than those obtained for ethanol. The solubility of decane in the vapor phase is lower than the values obtained for nonane at fixed temperature and pressure. This behavior is presented in Fig. 3 where the illustrated temperatures are 344.61, 344.77, 373.94, and 373.98 K. Therefore, it can be
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33
10 X
+
KCO
X
+
2
+
X
+
X
X
X
+
++
1
X
X
X
+++
X X
Ki
0.1
KC H OH 2
0.01
5
1
0.1
0.01
0.001
KC H 9
0
3
6
9
12
20
15
p / MPa Fig. 1. Equilibrium ratios Ki for carbon dioxide–ethanol–nonane system at: (+, 䊉, ) 313.33 K, (×, , ) 344.61 K, and (夽, , ) 373.94 K. Solid lines represent prediction of VLE using the PR EoS + two parameter classical mixing rules.
considered that as the carbon chain increases the solubility of the solute is low. Experimental VLE for the ternary systems was predicted using the Peng–Robinson equation of state [15] (Eq. (4)) coupled to three mixing rules: one parameter classical (Eqs. (5) and (6)), two parameter classical (Eqs. (5) and (7)) and Wong–Sandler [16] (Eqs. (10) and (12)). p=
RT
v−b
am =
a(T )
(5)
xi bi
(6)
xi xj
bi + bj 2
(1 − lij )
(7)
R2 Tc2 1/2 2 a(T ) = 0.45724 [1 + (0.37464 + 1.54226ω − 0.26992ω2 )(1 − Tr )] Pc
RTc Pc
(8) (9)
ij
=
(bi − (ai /RT )) + (bj − (aj /RT )) 2
a i xi
xi xj (b − (a/RT ))ij i j exc x ((ai /bi RT ) − (G i i
bi
+
Gexc
(1 − kij )
/CRT ))
(12)
C
√ √ where C = ln( 2 − 1)/ 2. The NRTL model was selected to obtain the excess Gibbs energy Gexc [17]:
RT
=
g x j ji ji j xi
(13)
g x k ki k
i
ıij
(14)
RT
(15)
The nonrandomness parameter ˛ji for the NRTL model was fixed to 0.3. Binary interaction parameters were optimized by minimizing the following objective function:
⎡
2
2 ⎤ exptl exptl NP Nc yijcalcd − yij pcalcd − pj j ⎣ ⎦ + OF = j=1
(10)
(11)
exptl
The Wong–Sandler mixing rules are expressed as:
1−
gij = exp(−˛ij ij )
where the parameters a and b are related to:
bm =
a RT
am = bm
ij =
j
b = 0.07780
b−
Gexc
j
i
(4)
xi xj (ai aj )1/2 (1 − kij )
i
bm =
i
v(v + b) + b(v − b)
i
bm =
−
with
i=1
yij
exptl
(16)
pj
where NP is the number of data points, Nc is the number of components, y is the vapor mole fraction, and the superscripts calcd and
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10
KCO
X
+
X
+
X
+
X
+
X
+
1
X
++
X
X
+
X X
2
XX
0.1
Ki
KC H OH 2
5
0.01 1
0.1
0.01
KC 0.001
0
3
6
9
12
10H22
15
p / MPa Fig. 2. Equilibrium ratio Ki for carbon dioxide–ethanol–decane system at: (+, 䊉, ) 314.98 K, (×, , ) 344.77 K, and (夽, , ) 373.98 K. Solid lines represent prediction of VLE using the PR EoS + two parameter classical mixing rules.
exptl denotes the calculated and experimental values, respectively. Deviations in pressure and composition were computed with %p =
NP 100 |p exptl − p calcd | i
NP i=1
%yi =
i
(17)
pi exptl
NP 100 yi exptl − yi calcd NP yi exptl
(18)
i=1
14 12
p / MPa
10 8 6 4 2 0 0.00
0.01
0.02
y3
0.03
0.04
0.05
Fig. 3. Experimental vapor phase composition for the alkane y3 in the ternary system: () 344.61 K, nonane; (䊉) 344.77, decane; () 373.94 K, nonane; () 373.98 K, decane.
VLE prediction for the ternary systems consisted on the correlation of VLE data for binary systems reported in the literature [18–23] with the aim of obtaining the interaction parameters. Optimized parameters which are temperature independent as well as deviations for the VLE of binary systems are listed in Tables 4–6 for each mixing rules. The best results were found with the two parameter classical mixing rules. Afterwards, the vapor–liquid equilibrium for both ternary systems were predicted using the PR EoS coupled to each one of the three mixing rules. Bubble pressure calculations were performed by fitting the experimental VLE data for ternary systems and the optimized interaction parameters of binary systems. The two parameter (kij and lij ) classical mixing rules for the ethanol + nonane and ethanol + decane had to be set to zero since the corresponding parameters reported in Table 5 provide higher deviations; therefore, these binary VLE data reported at atmospheric pressure are not affordable to be used in the two parameter classical mixing rules for VLE calculations at high pressure. Results of VLE predictions are presented in Table 7. According to these results, deviations in pressure and composition are lower for the two parameter classical mixing rules than the obtained for the one parameter classical and Wong–Sandler mixing rules. Equilibrium ratios from these calculations are also presented in Figs. 1 and 2 for the two parameter classical mixing rules. This is attributed to the binary interaction parameters obtained with low deviations for the VLE data. Separation factor between both solutes Sij = Ki /Kj are depicted in Figs. 4 and 5 for the ternary systems as a function of pressure. The separation factor for ethanol (2) over nonane (3) S2/3 at 313.33 K plotted in Fig. 4 do not have gradual change and
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35
Table 4 VLE correlation for binary systems using the PR-EoS + one parameter classical mixing rule. Refs.
Data points
Binary system
T (K)
%p
%yCO2
kij
[19] [20] [21] [22] [23]
41 38 26 29 13
CO2 –ethanol CO2 –nonane Ethanol–nonane CO2 –decane Ethanol–decane
312.82–373.00 315.12–418.82 343.17 319.11–372.94 351.45–447.15
5.4 5.9 10.2 2.5 26.2
1.4 3.2 2.7 0.5 5.6
0.0950 0.1585 0.0410 0.1058 0.1225
Table 5 VLE correlation for binary systems using the PR-EoS + two parameter classical mixing rules. Refs.
Data points
Binary system
T (K)
%p
%yCO2
kij
lij
[19] [20] [21] [22] [23]
43 38 26 29 13
CO2 –ethanol CO2 –nonane Ethanol–nonane CO2 –decane Ethanol–decane
312.82–373.00 315.12–418.82 343.17 319.11–372.94 351.45–447.15
3.2 1.5 7.7 1.5 0.0
0.5 0.6 1.8 0.2 2.2
0.0822 0.0917 −0.5969 0.0981 −0.3511
−0.0169 −0.0070 −0.7021 −0.0126 −0.4510
Table 6 VLE correlation for binary systems using the PR-EoS + Wong–Sandler mixing rule. Refs.
Data points
[19] [20] [21] [22] [23]
Binary system
38 38 26 29 13
T (K)
CO2 –ethanol CO2 –nonane Ethanol–nonane CO2 –decane Ethanol–decane
%p
312.82–373.00 315.12–418.82 343.17 319.11–372.94 351.45–477.15
%yCO2
5.3 4.3 0.5 3.9 10.8
kij
0.5 0.5 0.3 0.4 4.6
NRTL
0.3084 0.6841 0.4020 0.7155 0.4812
12 (kJ mol−1 )
21 (kJ mol−1 )
34.0826 8.2741 3.8707 11.8841 5.6630
2.3964 −2.0510 7.1189 −1.9705 4.5744
Table 7 VLE predictions for the ternary systems using the PR-EoS. Ternary system
T (K)
Mixing rules One parameter classical
Two parameter classical
Wong–Sandler
%p
%yCO2
%p
%yCO2
%p
%yCO2
CO2 –ethanol–nonane
313.33 344.61 373.94
2.3 6.2 9.6
0.1 1.3 2.2
5.1 6.0 6.2
0.1 0.5 1.9
5.2 6.6 14.7
0.1 0.5 4.0
CO2 –ethanol–decane
314.98 344.77 373.98
12.9 16.0 12.7
0.6 1.3 2.2
2.0 7.4 3.9
0.2 0.1 1.5
3.9 5.7 11.0
0.2 1.6 2.9
4.0
10
3.5 8 3.0 6
S2/3
S 2/3
2.5 2.0
4
1.5 2
1.0 0.5
0
2
4
6
8
10
12
14
p / MPa Fig. 4. Experimental separation factor for ethanol over nonane S2/3 as a function of pressure using carbon dioxide as solvent media at (䊉) 313.33 K, () 344.61 K, and () 373.94 K.
0
0
2
4
6
8
10
12
14
p / MPa Fig. 5. Experimental separation factor for ethanol over decane S2/3 as a function of pressure using carbon dioxide as solvent media at (䊉) 314.98 K, () 344.77 K, and () 373.98 K.
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values are between 1.5 and 2.5; higher S2/3 values are obtained at 344.61 K compared with the values obtained at 373.94 K. Separation factors for ethanol (2) over decane (3) S2/3 are depicted in Fig. 5; high S2/3 values are presented at low pressures and do not have significant difference at 314.98 and 344.77 K. Ethanol is preferable to be separated from decane at 373.98 K and low pressures. 4. Conclusions Equilibrium liquid and vapor phase compositions are reported for the ternary carbon dioxide–ethanol–nonane and carbon dioxide–ethanol–decane systems at temperatures ranging from 313.33 to 373.94 K and 314.98 to 373.98 K, respectively. The Peng–Robinson equation of state using the classical (one and two parameters) and Wong–Sandler mixing rules predict acceptable deviations in pressure and composition the experimental VLE data; nevertheless, two parameter classical mixing rules have a better representation of this behavior. High separation factors are obtained at low pressure using carbon dioxide. Ethanol is feasible to be separated from nonane at the intermediate temperature 344.61 K but is similar to the corresponding magnitude at 373.94. On the case of the separation of ethanol over decane, high values are obtained at 373.98 K. List of symbols Ai response area of the gas chromatograph a, b, C parameters to Eqs. (4)–(12) ci , di parameters to Eqs. (2) and (3) Gexc excess Gibbs energy g parameter to Eqs. (13)–(15) Ki equilibrium ratio kij binary interaction parameter to Eq. (5) lij binary interaction parameter to Eq. (7) ni mole number of component i nt total mole number Nc number of components NP number of data points p pressure (MPa) R ideal gas constant (MPa m3 K−1 kmol−1 ) separation factor Si/j T temperature (K) liquid mole fraction of component i xi yi vapor mole fraction of component i mole fraction of component i zi u uncertainty v molar volume (m3 kmol−1 )
Greek letters ˛ NRTL parameter to Eq. (15) ı NRTL parameter to Eq. (14) NRTL parameter to Eqs. (13)–(15) ω acentric factor Subscripts c critical property i, j, k components m mixture reduced property r Superscripts calcd calculated value exptl experimental value Acknowledgments Instituto Politécnico Nacional and CONACyT are acknowledged for the financial support of this research. Miguel G. Arenas-Quevedo thanks the grant provided by “Programa DELFIN” in 2011. References [1] G. Brunner, Gas Extraction. An Introduction to Fundamentals of Supercritical Fluids and the Application to Separation Processes, Springer, New York, 1994. [2] M.A. McHugh, V.J. Krukonis, Supercritical Fluid Extraction Principles and Practice, 2nd ed., Butterworth-Heinemann, USA, 1994. [3] R. Dohrn, S. Peper, J.S.M. Fonseca, Fluid Phase Equilib. 288 (2010) 1–54. [4] J.S.M. Fonseca, R. Dohrn, S. Peper, Fluid Phase Equilib. 300 (2011) 1–69. [5] C.J. Peters, L.J. Florusse, S. Hähre, J. Supercrit. Fluids 9 (1996) 135–140. [6] C.J. Peters, L.J. Florusse, S. Hähre, J. de Swaan Arons, Fluid Phase Equilib. 110 (1995) 157–173. [7] A. Kordikowski, G.M. Schneider, Fluid Phase Equilib. 90 (1993) 149–162. [8] H. Pöler, A.L. Scheidgen, G.M. Schneider, Fluid Phase Equilib. 115 (1996) 165–177. [9] A.L. Scheidgen, G.M. Schneider, J. Chem. Thermodyn. 32 (2000) 1183–1201. [10] B.E. Poling, J.M. Prausnitz, J.P. O’Connell, The Properties of Gases and Liquids, 5th ed., McGraw-Hill, New York, 2001, pp. A6, A7, A15, A16. [11] O. Elizalde-Solis, L.A. Galicia-Luna, Ind. Eng. Chem. Res. 44 (2005) 5757–5760. [12] O. Elizalde-Solis, L.A. Galicia-Luna, Fluid Phase Equilib. 236 (2005) 178–183. [13] P. Guilbot, A. Valtz, H. Legendre, D. Richon, Analusis 28 (2000) 426–431. [14] B.N. Taylor, C.E. Kuyatt, Guidelines for evaluating and expressing the uncertainty of NIST measurement results, NIST Technical Note 1297, 1994 Edition. [15] D.Y. Peng, D.B. Robinson, Ind. Eng. Chem. Fundam. 15 (1976) 59–64. [16] D.S.H. Wong, S.I. Sandler, AIChE J. 38 (1992) 671–680. [17] H. Renon, J.M. Prausnitz, AIChE J. 14 (1968) 135–144. ˇ L. Iliˇc, C. Lütge, J. Supercrit. Fluids 43 (2008) 383–389. [18] Z. Knez, M. Skerget, [19] L.A. Galicia-Luna, A. Ortega-Rodriguez, D. Richon, J. Chem. Eng. Data 45 (2000) 265–271. [20] L.E. Camacho-Camacho, L.A. Galicia-Luna, O. Elizalde-Solis, Z. MartínezRamírez, Fluid Phase Equilib. 259 (2007) 45–50. [21] C. Berro, M. Rogalski, A. Peneloux, Fluid Phase Equilib. 8 (1982) 55–73. [22] R. Jiménez-Gallegos, L.A. Galicia-Luna, O. Elizalde-Solis, J. Chem. Eng. Data 51 (2006) 1624–1628. [23] S.R.M. Ellis, M.J. Spurr, Brit. Chem. Eng. 6 (1961) 92–95.
