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(Vapour + liquid) equilibria of the {trifluoromethane (HFC-23) + propane} and {trifluoromethane (HFC-23) + n-butane} systems
J. Chem. Thermodynamics 41 (2009) 1339–1342
Contents lists available at ScienceDirect
J. Chem. Thermodynamics journal homepage: www.elsevier.com/locate/jct
(Vapour + liquid) equilibria of the {trifluoromethane (HFC-23) + propane} and {trifluoromethane (HFC-23) + n-butane} systems Mincheol Ju a, Yongju Yun a, Moon Sam Shin b, Hwayong Kim a,* a b
School of Chemical and Biological Engineering and Institute of Chemical Processes, Seoul National University, Shinlim-dong, Gwanak-gu, Seoul 151-744, Republic of Korea Department of Cosmetic Science, Chungwoon University, Chungnam 350-701, Republic of Korea
a r t i c l e
i n f o
Article history: Received 7 April 2009 Received in revised form 8 June 2009 Accepted 8 June 2009 Available online 12 June 2009 Keywords: (Vapour + liquid) equilibria Trifluoromethane (HFC-23) Propane n-Butane
a b s t r a c t Isothermal (vapour + liquid) equilibrium data were measured for the two systems, {trifluoromethane (HFC-23) + propane} and {trifluoromethane (HFC-23) + n-butane}, at temperatures ranging from 283.15 K to 313.15 K at 10 K intervals. These experiments were performed with a circulating-type apparatus and on-line gas chromatography. Experimental data were well correlated by the Peng–Robinson equation of state using the Wong–Sandler mixing rules and the NRTL model. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction Chlorofluorocarbons (CFCs) are non-toxic, non-flammable compounds that do not react with other chemical compounds. Due to these characteristics, CFCs have been used as commercial and home refrigerants, solvents, and blowing agents. However, in recent years depletion of the ozone layer has become a major environmental problem. The principal cause of this is the release of CFCs, which have high ozone depletion potentials (ODPs). CFCs are therefore being phased out as a result of the Montreal Protocol on Substances that Deplete the Ozone Layer enacted in 1987. This has lead to the urgent need in refrigeration industry to find alternative CFCs. One possible class of refrigerants is hydrofluorocarbons (HFCs) on account of their near zero ODPs. However, these substances are also regulated by the Kyoto Protocol of 1997 due to their global warming potentials (GWPs). The least environmental problematic refrigerants are hydrocarbon (HCs), which have zero ODPs and near zero GWPs in addition to being relatively cheap compared with HFCs. Unfortunately, HCs are prone to explosion because of a low flammability level. Therefore, refrigerants thus far do not satisfy environmental conditions or safety standards. A compound consisting of HFCs and HCs could be an alternative and solve those problems. [1–10]. Isothermal (vapour + liquid) equilibrium data are important in deciding the optimal composition of mixtures and to evaluate the performance of refrigeration cycles. In this study, isothermal * Corresponding author. Tel.: +82 2 880 7406; fax: +82 2 888 6695. E-mail address: [email protected] (H. Kim). 0021-9614/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jct.2009.06.009
(vapour + liquid) equilibrium data were measured in two systems, {trifluoromethane (HFC-23) + propane} and {trifluoromethane (HFC-23) + n-butane}, tested as alternative refrigerants in a temperature range from 283.15 K to 313.15 K at 10 K intervals. The experimental data were correlated by the Peng–Robinson equation of state (PR EoS) [11] with the Wong–Sandler mixing rules [12] using the NRTL model [13]. 2. Experimental 2.1. Materials HFC-23 of 99.7% purity was supplied by Daikin industries, Ltd. Propane and n-butane of 99.5% purity were supplied by Korea industrial gases. All components were used without further purification in these experiments. 2.2. Experimental apparatus Measurement of isothermal (vapour + liquid) equilibrium data was conducted in a circulation type apparatus, the details of which were given in our previous studies [8]. Inner volume of the equilibrium cell is about 200 cm3 made out of 316-stainless steel. In addition, two windows were set up on two sides of the cell to observe the inside. To reach equilibrium quickly, a pair of magnetic pumps circulated both the vapour and liquid phases. In order to trap the liquid and vapour samples for injection into the gas chromatograph, two sampling valves (Rheodyne Instruments, model 7413 with a 1.0 lL sampling loop for liquid and model 7010 with a
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M. Ju et al. / J. Chem. Thermodynamics 41 (2009) 1339–1342
10 lL sampling loop for vapour) were used. A gas chromatograph, equipped with a thermal conductivity detector (TCD) and a Porapak-Q column (1.83-m long; 3.18-mm diameter; mesh range, 80/ 100), was connected on-line to the equilibrium apparatus. Helium was used as a carrier gas. The temperature in the cell was measured with a 100 X platinum resistance thermometer (Hart Scientific Co., model 5614) and a digital indicator (Hart Scientific Co., model 1502A) with an accuracy of ±0.018 K. The pressure of the cell was measured with a pressure transducer (Sensotec Co., model Super TJE (0 to 6895) kPa) connected to a digital indicator (Laurel, model L20001WM1). Accuracy of the digital pressure gauge is 0.05%. Calibration of the pressure transducer and thermometer was done by Korea Testing Laboratory (KTL), a national calibration
TABLE 1 Critical properties and acentric factors of each pure component [14].
Tc/K pc/MPa
x
HFC-23
Propane
n-Butane
299.29 4.832 0.263
369.89 4.2512 0.1521
425.13 3.796 0.201
TABLE 2 (Vapour + liquid) equilibrium measurements for the {xHFC-23 + (1 x)propane} system. ycal
4pa/MPa
4yb
T = 283.15 K 0.635 0.902 1.157 1.470 1.690 1.913 2.304 2.538 2.769 3.013 3.269
0.0000 0.2750 0.4225 0.5355 0.5909 0.6351 0.6954 0.7269 0.7598 0.8059 1.0000
0.003 0.006 0.000 0.000 0.014 0.017 0.016 0.002 0.001 0.000 0.023
0.0000 0.0140 0.0114 0.0169 0.0044 0.0008 0.0026 0.0009 0.0023 0.0097 0.0000
0.0000 0.3084 0.4784 0.5645 0.6148 0.6606 0.7082 0.7527 0.7921 0.8414 1.0000
T = 293.15 K 0.835 1.283 1.753 2.120 2.445 2.794 3.143 3.442 3.686 3.900 4.183
0.0000 0.3207 0.4896 0.5727 0.6280 0.6761 0.7190 0.7569 0.7945 0.8407 1.0000
0.005 0.000 0.000 0.014 0.003 0.000 0.001 0.025 0.041 0.053 0.025
0.0000 0.0123 0.0112 0.0082 0.0132 0.0155 0.0108 0.0042 0.0024 0.0007 0.0000
0.0000 0.0427 0.1061 0.1543 0.2301 0.3056 0.4332 0.5318 0.6962
0.0000 0.2397 0.4226 0.4980 0.5674 0.6110 0.6699 0.7007 0.7548
T = 303.15 K 1.079 1.503 2.049 2.404 2.877 3.261 3.769 4.088 4.576
0.0000 0.2511 0.4286 0.5031 0.5754 0.6205 0.6702 0.7000 0.7532
0.004 0.000 0.007 0.006 0.015 0.007 0.000 0.025 0.041
0.0000 0.0114 0.0060 0.0051 0.0080 0.0095 0.0003 0.0007 0.0016
0.0000 0.0526 0.1485 0.2203 0.3233 0.4263 0.4831
0.0000 0.2508 0.4420 0.5143 0.5759 0.6183 0.6274
T = 313.15 K 1.372 1.961 2.819 3.325 3.914 4.395 4.630
0.0000 0.2573 0.4497 0.5194 0.5801 0.6197 0.6369
0.003 0.000 0.013 0.009 0.000 0.013 0.041
0.0000 0.0065 0.0077 0.0051 0.0042 0.0014 0.0095
pexp/MPa
xexp
yexp
0.638 0.908 1.157 1.470 1.676 1.896 2.288 2.540 2.770 3.013 3.246
0.0000 0.0317 0.0657 0.1142 0.1545 0.2030 0.3190 0.4203 0.5494 0.7001 1.0000
0.0000 0.2610 0.4111 0.5186 0.5865 0.6343 0.6928 0.7260 0.7622 0.8156 1.0000
0.840 1.283 1.753 2.106 2.442 2.794 3.144 3.467 3.727 3.953 4.158
0.0000 0.0487 0.1110 0.1711 0.2366 0.3251 0.4409 0.5662 0.6814 0.7873 1.0000
1.083 1.503 2.056 2.410 2.862 3.254 3.769 4.113 4.617 1.375 1.961 2.806 3.316 3.914 4.408 4.671 a b
4p = pcal pexp. 4y = ycal yexp.
pcal/MPa
laboratory. The temperature was read to an uncertainty of ±0.04 K and the estimated uncertainty of the pressure was ±1.0 kPa. 2.3. Experimental procedure In order to measure the isothermal (vapour + liquid) equilibrium data for the binary mixture, the whole system was first evacuated with a vacuum pump to remove all impurities. A less volatile component, HCs, was added into the cell next, followed by a proper amount of HFC-23 being charged. The vapour and liquid phases of the mixture were circulated separately by two magnetic pumps with the intention to reach equilibrium quickly. After the system reached equilibrium, each sample of the binary mixture was injected into the gas chromatograph to analyze the composition and measure pressure of the inner cell. At least five samples of composition of vapour and liquid were measured to obtain reliable data at each equilibrium state. The uncertainty of the equilibrium
TABLE 3 (Vapour + liquid) equilibrium measurements for the {xHFC-23 + (1 x)n-butane} system. ycal
4pa/MPa
T = 283.15 K 0.148 0.447 0.798 1.096 1.383 1.674 1.955 2.256 2.554 2.706 2.949 3.269
0.0000 0.6532 0.7978 0.8480 0.8759 0.8945 0.9075 0.9183 0.9286 0.9358 0.9545 1.0000
0.000 0.000 0.002 0.003 0.003 0.001 0.000 0.002 0.000 0.021 0.010 0.027
0.0000 0.0281 0.0166 0.0147 0.0109 0.0096 0.0067 0.0071 0.0050 0.0032 0.0029 0.0000
0.0000 0.6164 0.7566 0.8158 0.8536 0.8790 0.8875 0.9004 0.9064 0.9385 1.0000
T = 293.15 K 0.207 0.608 1.029 1.392 1.800 2.257 2.571 2.976 3.194 3.650 4.183
0.0000 0.6383 0.7760 0.8277 0.8609 0.8838 0.8950 0.9073 0.9144 0.9390 1.0000
0.001 0.000 0.006 0.005 0.001 0.003 0.000 0.000 0.009 0.032 0.021
0.0000 0.0219 0.0194 0.0119 0.0073 0.0048 0.0075 0.0069 0.0080 0.0005 0.0000
0.0000 0.0430 0.0825 0.1374 0.2060 0.3028 0.4723 0.6108 0.7114 0.3746
0.0000 0.5799 0.7146 0.7831 0.8295 0.8563 0.8773 0.8857 0.8967 0.8691
T = 303.15 K 0.282 0.775 1.182 1.679 2.200 2.774 3.439 3.798 4.037 3.099
0.0000 0.6079 0.7304 0.7995 0.8378 0.8627 0.8811 0.8897 0.8966 0.8725
0.000 0.000 0.008 0.000 0.005 0.000 0.018 0.003 0.035 0.016
0.0000 0.0280 0.0158 0.0164 0.0083 0.0064 0.0038 0.0040 0.0001 0.0034
0.0000 0.0283 0.0597 0.1032 0.1443 0.1979 0.3196 0.4195 0.5472 0.6942
0.0000 0.4349 0.6022 0.7088 0.7598 0.7956 0.8331 0.8470 0.8562 0.8586
T = 313.15 K 0.377 0.738 1.114 1.589 1.994 2.462 3.303 3.808 4.287 4.735
0.0000 0.4583 0.6240 0.7215 0.7675 0.8011 0.8356 0.8476 0.8554 0.8611
0.001 0.002 0.000 0.000 0.000 0.010 0.015 0.016 0.000 0.045
0.0000 0.0234 0.0218 0.0127 0.0077 0.0055 0.0025 0.0006 0.0008 0.0025
pexp/MPa
xexp
yexp
0.148 0.447 0.796 1.099 1.386 1.673 1.955 2.254 2.554 2.727 2.959 3.242
0.0000 0.0309 0.0720 0.1123 0.1578 0.2139 0.2842 0.3943 0.5938 0.7303 0.8779 1.0000
0.0000 0.6251 0.7812 0.8333 0.8650 0.8849 0.9008 0.9112 0.9236 0.9326 0.9516 1.0000
0.208 0.608 1.035 1.397 1.799 2.254 2.571 2.976 3.203 3.682 4.162
0.0000 0.0376 0.0825 0.1273 0.1877 0.2751 0.3569 0.5157 0.6377 0.8563 1.0000
0.282 0.775 1.190 1.679 2.205 2.774 3.421 3.801 4.072 3.083 0.378 0.736 1.114 1.589 1.994 2.472 3.288 3.792 4.287 4.780 a b
4p = pcal pexp. 4y = ycal yexp.
pcal/MPa
4yb
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M. Ju et al. / J. Chem. Thermodynamics 41 (2009) 1339–1342
compositions in the mole fraction was estimated to less than ±0.001
properties and acentric factors of each component are given in table 1. The Wong–Sandler mixing rule is represented as
PP
3. Correlations
bm ¼ In this study, the experimental (vapour + liquid) equilibrium data were correlated with the Peng–Robinson equation of state (PR EoS) [11] using the Wong–Sandler mixing rules [12]. The PR EoS and the Wong–Sandler mixing rules are expressed as follows:
p¼
RT aðTÞ ; V b VðV þ bÞ þ bðV bÞ
ð1Þ
R2 T 2c aðTÞ; pc RT c bðT c Þ ¼ 0:077796 ; pc
aðTÞ ¼ 0:457235
ð2Þ ð3Þ
2 aðTÞ ¼ ½1 þ jð1 T 0:5 r Þ ; j ¼ 0:37464 þ 1:54226x 0:26992x2 ;
ð4Þ ð5Þ
where Tc is the critical temperature, pc is the critical pressure, Tr is the reduced temperature, and x is the acentric factor. The critical
P
a b RT
ij E
A1 ai i xi b RT CRT
ð7Þ
;
i
! ai AE1 ; xi þ am ¼ bm bi C i a ai þ bj RTj bi RT a b ¼ ð1 kij Þ; 2 RT ij
ð8Þ ð9Þ
pffiffiffi pffiffiffi where C ¼ lnð 2 1Þ= 2 for the PR EoS. Since the excess Helmholtz free energy of mixing at infinite pressure is assumed equal to the excess Gibbs free energy (GE) at low pressure, the GE model is used in place of AE1 . We selected the NRTL model [13] as an activity coefficient model in this study:
P GE X xi sji Gji xi Pi ; ¼ RT k xk Gki i
ð10Þ
Gij ¼ expðaij sij Þ;
ð11Þ
aij ¼ aji
Aij ¼ ; T
ð12Þ
where sij and sji are the interaction parameters and aij is the nonrandomness parameter. The non-randomness parameter aij was fixed on 0.3.
5.0
4.0
p/MPa
1
X
sij 6.0
j xi xj
i
a
2
3.0
1
1.0
0.0 0.0
0.2
0.4
0.6
0.8
1.0
(pcal-pexp)/pexpX100
2.0
x, y
0
-1
FIGURE 1. (Vapour + liquid) equilibria of the {xHFC-23 + (1 x)propane} binary system. Symbols are for experimental data: H, at 283.15 K; j, at 293.15 K; N, at 303.15 K; and d, at 313.15 K. Solid lines correspond to calculation with the PR EoS using the Wong–Sandler mixing rules.
-2 0.0
0.2
0.4
0.6
0.8
1.0
x
b
5.0
0.01
3.0
ycal-yexp
p/MPa
4.0
0.02
0.00
2.0
-0.01
1.0
0.0 0.0
0.2
0.4
0.6
0.8
1.0
x, y
-0.02 0.0
0.2
0.4
0.6
0.8
1.0
x FIGURE 2. (Vapour + liquid) equilibria of the {xHFC-23 + (1 x)n-butane} binary system. Symbols are for experimental data: j, at 283.15 K; N, at 293.15 K; , at 303.15 K; and d, at 313.15 K. Solid lines correspond to calculation with the PR EoS using the Wong–Sandler mixing rules.
FIGURE 3. Deviation of the {xHFC-23 + (1 x)propane} system: (a) deviation of pressure and (b) deviation of vapour mole fraction: d, at 283.15 K; s, at 293.15 K; ., at 303.15 K; 4, at 313.15 K.
1342
a
M. Ju et al. / J. Chem. Thermodynamics 41 (2009) 1339–1342 TABLE 4 Binary parameters, MRD-p and MD-y.
2
(pcal-pexp)/pexpX100
1
0.4
0.6
0.8
(HFC-23 + n-butane) 388.82 220.91 384.17 217.34 397.60 189.60 409.87 178.63
0.20 0.26 0.32 0.28
0.0105 0.0098 0.0096 0.0086
283.15 293.15 303.15 313.15
0.397 0.389 0.391 0.390
P MRD-p ¼ ð100=NÞ N ðjpi;cal pi;exp j=pi;exp Þ. PN i MD-y ¼ ð1=NÞ i jyi;cal yi;exp j.
measured data at each temperature. Both systems show positive deviation from the Raoult’s law. Figures 3 and 4 illustrates the deviation of pressure and deviation of vapour mole fraction for each system between the experimental data and the calculated values. The results showed a tendency to overestimate vapour composition in the dilute x region and the deviations of vapour composition were less than 0.0169 and 0.0281, respectively, for {HFC-23 + propane} system and {HFC-23 + n-butane} system. The mean relative deviations (MRD) of pressure and mean deviations (MD) of vapour composition were less than 0.36% and 0.0087, respectively, for {HFC-23 + propane} and 0.32% and 0.0105, respectively, for {HFC23 + n-butane}. Binary parameters and the MRD of p and y are given in table 4.
0.04
0.02
ycal-yexp
0.0070 0.0087 0.0053 0.0057
0.245 0.357 0.323 0.349
Aji/K
1.0
x
b
0.35 0.36 0.36 0.31
283.15 293.15 303.15 313.15
b
0.2
(HFC-23 + propane) 507.18 214.72 154.67 306.60 303.76 206.67 125.36 338.11
Aij/K
a
-2 0.0
MD-yb
kij
0
-1
MRD-pa/%
T/K
0.00
-0.02
Acknowledgements -0.04 0.0
0.2
0.4
0.6
0.8
1.0
x FIGURE 4. Deviation of the {xHFC-23 + (1 x)n-butane} system: (a) deviation of pressure and (b) deviation of vapour mole fraction: d, at 283.15 K; s, at 293.15 K; ., at 303.15 K; 4, at 313.15 K.
4. Results and discussion Isothermal (vapour + liquid) equilibrium data for the (HFC23 + propane) and (HFC-23 + n-butane} systems were measured at temperatures ranging from 283.15 K to 313.15 K at 10 K intervals. Experimental and calculated data are provided in tables 2 and 3. Parameters were obtained by minimizing the following objective function through the simplex algorithm:
N X pexp pcal F¼ pexp i
ð13Þ
where N is the number of data points, pexp is the measured pressures and pcal is the calculated pressures. As shown in figures 1 and 2, the calculated results represent a good agreement with the
This work was supported by the Brain Korea 21 Program supported by the Ministry of Education and by Korea institute of Energy and resources Technology Evaluation and Planning (KETEP). References [1] J. McMullan, Int. J. Refrig. 25 (2002) 89–99. [2] J. Im, G. Lee, J. Lee, H. Kim, J. Chem. Thermodyn. 39 (2007) 1164–1167. [3] J. Im, G. Lee, M.S. Shin, J. Lee, H. Kim, Fluid Phase Equilibr. 248 (2006) 19– 23. [4] C. Coquelet, A. Chareton, D. Richon, Fluid Phase Equilibr. 218 (2004) 209– 214. [5] S. Bobbo, R. Camporese, R. Stryjek, J. Chem. Thermodyn. 32 (2000) 1647–1656. [6] J.S. Lim, J.Y. Park, J.W. Kang, B.G. Lee, Fluid Phase Equilibr. 243 (2006) 57–63. [7] S. Bobbo, R. Stryjek, N. Elvassore, A. Bertucco, Fluid Phase Equilibr. 150–151 (1998) 343–352. [8] Y. Yun, J. Im, H. Kim, J. Chem. Thermodyn. 40 (2008) 766–769. [9] J.Y. Park, J.S. Lim, B.G. Lee, Fluid Phase Equilibr. 194–197 (2002) 981–993. [10] Y. Yun, J. Im, M.S. Shin, Y. Lee, H. Kim, Fluid Phase Equilibr. 271 (2008) 34–37. [11] D. Peng, D.B. Robinson, Ind. Eng. Chem. Fundam. 15 (1976) 59–64. [12] D.S. Wong, S.I. Sandler, AIChE J. 38 (1992) 671–680. [13] H. Renon, J.M. Prausnitz, AIChE J. 14 (1968) 135–144. [14] M. McLinden, M. Huber, E. Lemmon, NIST Thermodynamic and Transport Properties of Refrigerants and Refrigerant Mixtures Database (REFPROP), Version 8.0.
JCT 09-118
Contents lists available at ScienceDirect
J. Chem. Thermodynamics journal homepage: www.elsevier.com/locate/jct
(Vapour + liquid) equilibria of the {trifluoromethane (HFC-23) + propane} and {trifluoromethane (HFC-23) + n-butane} systems Mincheol Ju a, Yongju Yun a, Moon Sam Shin b, Hwayong Kim a,* a b
School of Chemical and Biological Engineering and Institute of Chemical Processes, Seoul National University, Shinlim-dong, Gwanak-gu, Seoul 151-744, Republic of Korea Department of Cosmetic Science, Chungwoon University, Chungnam 350-701, Republic of Korea
a r t i c l e
i n f o
Article history: Received 7 April 2009 Received in revised form 8 June 2009 Accepted 8 June 2009 Available online 12 June 2009 Keywords: (Vapour + liquid) equilibria Trifluoromethane (HFC-23) Propane n-Butane
a b s t r a c t Isothermal (vapour + liquid) equilibrium data were measured for the two systems, {trifluoromethane (HFC-23) + propane} and {trifluoromethane (HFC-23) + n-butane}, at temperatures ranging from 283.15 K to 313.15 K at 10 K intervals. These experiments were performed with a circulating-type apparatus and on-line gas chromatography. Experimental data were well correlated by the Peng–Robinson equation of state using the Wong–Sandler mixing rules and the NRTL model. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction Chlorofluorocarbons (CFCs) are non-toxic, non-flammable compounds that do not react with other chemical compounds. Due to these characteristics, CFCs have been used as commercial and home refrigerants, solvents, and blowing agents. However, in recent years depletion of the ozone layer has become a major environmental problem. The principal cause of this is the release of CFCs, which have high ozone depletion potentials (ODPs). CFCs are therefore being phased out as a result of the Montreal Protocol on Substances that Deplete the Ozone Layer enacted in 1987. This has lead to the urgent need in refrigeration industry to find alternative CFCs. One possible class of refrigerants is hydrofluorocarbons (HFCs) on account of their near zero ODPs. However, these substances are also regulated by the Kyoto Protocol of 1997 due to their global warming potentials (GWPs). The least environmental problematic refrigerants are hydrocarbon (HCs), which have zero ODPs and near zero GWPs in addition to being relatively cheap compared with HFCs. Unfortunately, HCs are prone to explosion because of a low flammability level. Therefore, refrigerants thus far do not satisfy environmental conditions or safety standards. A compound consisting of HFCs and HCs could be an alternative and solve those problems. [1–10]. Isothermal (vapour + liquid) equilibrium data are important in deciding the optimal composition of mixtures and to evaluate the performance of refrigeration cycles. In this study, isothermal * Corresponding author. Tel.: +82 2 880 7406; fax: +82 2 888 6695. E-mail address: [email protected] (H. Kim). 0021-9614/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jct.2009.06.009
(vapour + liquid) equilibrium data were measured in two systems, {trifluoromethane (HFC-23) + propane} and {trifluoromethane (HFC-23) + n-butane}, tested as alternative refrigerants in a temperature range from 283.15 K to 313.15 K at 10 K intervals. The experimental data were correlated by the Peng–Robinson equation of state (PR EoS) [11] with the Wong–Sandler mixing rules [12] using the NRTL model [13]. 2. Experimental 2.1. Materials HFC-23 of 99.7% purity was supplied by Daikin industries, Ltd. Propane and n-butane of 99.5% purity were supplied by Korea industrial gases. All components were used without further purification in these experiments. 2.2. Experimental apparatus Measurement of isothermal (vapour + liquid) equilibrium data was conducted in a circulation type apparatus, the details of which were given in our previous studies [8]. Inner volume of the equilibrium cell is about 200 cm3 made out of 316-stainless steel. In addition, two windows were set up on two sides of the cell to observe the inside. To reach equilibrium quickly, a pair of magnetic pumps circulated both the vapour and liquid phases. In order to trap the liquid and vapour samples for injection into the gas chromatograph, two sampling valves (Rheodyne Instruments, model 7413 with a 1.0 lL sampling loop for liquid and model 7010 with a
1340
M. Ju et al. / J. Chem. Thermodynamics 41 (2009) 1339–1342
10 lL sampling loop for vapour) were used. A gas chromatograph, equipped with a thermal conductivity detector (TCD) and a Porapak-Q column (1.83-m long; 3.18-mm diameter; mesh range, 80/ 100), was connected on-line to the equilibrium apparatus. Helium was used as a carrier gas. The temperature in the cell was measured with a 100 X platinum resistance thermometer (Hart Scientific Co., model 5614) and a digital indicator (Hart Scientific Co., model 1502A) with an accuracy of ±0.018 K. The pressure of the cell was measured with a pressure transducer (Sensotec Co., model Super TJE (0 to 6895) kPa) connected to a digital indicator (Laurel, model L20001WM1). Accuracy of the digital pressure gauge is 0.05%. Calibration of the pressure transducer and thermometer was done by Korea Testing Laboratory (KTL), a national calibration
TABLE 1 Critical properties and acentric factors of each pure component [14].
Tc/K pc/MPa
x
HFC-23
Propane
n-Butane
299.29 4.832 0.263
369.89 4.2512 0.1521
425.13 3.796 0.201
TABLE 2 (Vapour + liquid) equilibrium measurements for the {xHFC-23 + (1 x)propane} system. ycal
4pa/MPa
4yb
T = 283.15 K 0.635 0.902 1.157 1.470 1.690 1.913 2.304 2.538 2.769 3.013 3.269
0.0000 0.2750 0.4225 0.5355 0.5909 0.6351 0.6954 0.7269 0.7598 0.8059 1.0000
0.003 0.006 0.000 0.000 0.014 0.017 0.016 0.002 0.001 0.000 0.023
0.0000 0.0140 0.0114 0.0169 0.0044 0.0008 0.0026 0.0009 0.0023 0.0097 0.0000
0.0000 0.3084 0.4784 0.5645 0.6148 0.6606 0.7082 0.7527 0.7921 0.8414 1.0000
T = 293.15 K 0.835 1.283 1.753 2.120 2.445 2.794 3.143 3.442 3.686 3.900 4.183
0.0000 0.3207 0.4896 0.5727 0.6280 0.6761 0.7190 0.7569 0.7945 0.8407 1.0000
0.005 0.000 0.000 0.014 0.003 0.000 0.001 0.025 0.041 0.053 0.025
0.0000 0.0123 0.0112 0.0082 0.0132 0.0155 0.0108 0.0042 0.0024 0.0007 0.0000
0.0000 0.0427 0.1061 0.1543 0.2301 0.3056 0.4332 0.5318 0.6962
0.0000 0.2397 0.4226 0.4980 0.5674 0.6110 0.6699 0.7007 0.7548
T = 303.15 K 1.079 1.503 2.049 2.404 2.877 3.261 3.769 4.088 4.576
0.0000 0.2511 0.4286 0.5031 0.5754 0.6205 0.6702 0.7000 0.7532
0.004 0.000 0.007 0.006 0.015 0.007 0.000 0.025 0.041
0.0000 0.0114 0.0060 0.0051 0.0080 0.0095 0.0003 0.0007 0.0016
0.0000 0.0526 0.1485 0.2203 0.3233 0.4263 0.4831
0.0000 0.2508 0.4420 0.5143 0.5759 0.6183 0.6274
T = 313.15 K 1.372 1.961 2.819 3.325 3.914 4.395 4.630
0.0000 0.2573 0.4497 0.5194 0.5801 0.6197 0.6369
0.003 0.000 0.013 0.009 0.000 0.013 0.041
0.0000 0.0065 0.0077 0.0051 0.0042 0.0014 0.0095
pexp/MPa
xexp
yexp
0.638 0.908 1.157 1.470 1.676 1.896 2.288 2.540 2.770 3.013 3.246
0.0000 0.0317 0.0657 0.1142 0.1545 0.2030 0.3190 0.4203 0.5494 0.7001 1.0000
0.0000 0.2610 0.4111 0.5186 0.5865 0.6343 0.6928 0.7260 0.7622 0.8156 1.0000
0.840 1.283 1.753 2.106 2.442 2.794 3.144 3.467 3.727 3.953 4.158
0.0000 0.0487 0.1110 0.1711 0.2366 0.3251 0.4409 0.5662 0.6814 0.7873 1.0000
1.083 1.503 2.056 2.410 2.862 3.254 3.769 4.113 4.617 1.375 1.961 2.806 3.316 3.914 4.408 4.671 a b
4p = pcal pexp. 4y = ycal yexp.
pcal/MPa
laboratory. The temperature was read to an uncertainty of ±0.04 K and the estimated uncertainty of the pressure was ±1.0 kPa. 2.3. Experimental procedure In order to measure the isothermal (vapour + liquid) equilibrium data for the binary mixture, the whole system was first evacuated with a vacuum pump to remove all impurities. A less volatile component, HCs, was added into the cell next, followed by a proper amount of HFC-23 being charged. The vapour and liquid phases of the mixture were circulated separately by two magnetic pumps with the intention to reach equilibrium quickly. After the system reached equilibrium, each sample of the binary mixture was injected into the gas chromatograph to analyze the composition and measure pressure of the inner cell. At least five samples of composition of vapour and liquid were measured to obtain reliable data at each equilibrium state. The uncertainty of the equilibrium
TABLE 3 (Vapour + liquid) equilibrium measurements for the {xHFC-23 + (1 x)n-butane} system. ycal
4pa/MPa
T = 283.15 K 0.148 0.447 0.798 1.096 1.383 1.674 1.955 2.256 2.554 2.706 2.949 3.269
0.0000 0.6532 0.7978 0.8480 0.8759 0.8945 0.9075 0.9183 0.9286 0.9358 0.9545 1.0000
0.000 0.000 0.002 0.003 0.003 0.001 0.000 0.002 0.000 0.021 0.010 0.027
0.0000 0.0281 0.0166 0.0147 0.0109 0.0096 0.0067 0.0071 0.0050 0.0032 0.0029 0.0000
0.0000 0.6164 0.7566 0.8158 0.8536 0.8790 0.8875 0.9004 0.9064 0.9385 1.0000
T = 293.15 K 0.207 0.608 1.029 1.392 1.800 2.257 2.571 2.976 3.194 3.650 4.183
0.0000 0.6383 0.7760 0.8277 0.8609 0.8838 0.8950 0.9073 0.9144 0.9390 1.0000
0.001 0.000 0.006 0.005 0.001 0.003 0.000 0.000 0.009 0.032 0.021
0.0000 0.0219 0.0194 0.0119 0.0073 0.0048 0.0075 0.0069 0.0080 0.0005 0.0000
0.0000 0.0430 0.0825 0.1374 0.2060 0.3028 0.4723 0.6108 0.7114 0.3746
0.0000 0.5799 0.7146 0.7831 0.8295 0.8563 0.8773 0.8857 0.8967 0.8691
T = 303.15 K 0.282 0.775 1.182 1.679 2.200 2.774 3.439 3.798 4.037 3.099
0.0000 0.6079 0.7304 0.7995 0.8378 0.8627 0.8811 0.8897 0.8966 0.8725
0.000 0.000 0.008 0.000 0.005 0.000 0.018 0.003 0.035 0.016
0.0000 0.0280 0.0158 0.0164 0.0083 0.0064 0.0038 0.0040 0.0001 0.0034
0.0000 0.0283 0.0597 0.1032 0.1443 0.1979 0.3196 0.4195 0.5472 0.6942
0.0000 0.4349 0.6022 0.7088 0.7598 0.7956 0.8331 0.8470 0.8562 0.8586
T = 313.15 K 0.377 0.738 1.114 1.589 1.994 2.462 3.303 3.808 4.287 4.735
0.0000 0.4583 0.6240 0.7215 0.7675 0.8011 0.8356 0.8476 0.8554 0.8611
0.001 0.002 0.000 0.000 0.000 0.010 0.015 0.016 0.000 0.045
0.0000 0.0234 0.0218 0.0127 0.0077 0.0055 0.0025 0.0006 0.0008 0.0025
pexp/MPa
xexp
yexp
0.148 0.447 0.796 1.099 1.386 1.673 1.955 2.254 2.554 2.727 2.959 3.242
0.0000 0.0309 0.0720 0.1123 0.1578 0.2139 0.2842 0.3943 0.5938 0.7303 0.8779 1.0000
0.0000 0.6251 0.7812 0.8333 0.8650 0.8849 0.9008 0.9112 0.9236 0.9326 0.9516 1.0000
0.208 0.608 1.035 1.397 1.799 2.254 2.571 2.976 3.203 3.682 4.162
0.0000 0.0376 0.0825 0.1273 0.1877 0.2751 0.3569 0.5157 0.6377 0.8563 1.0000
0.282 0.775 1.190 1.679 2.205 2.774 3.421 3.801 4.072 3.083 0.378 0.736 1.114 1.589 1.994 2.472 3.288 3.792 4.287 4.780 a b
4p = pcal pexp. 4y = ycal yexp.
pcal/MPa
4yb
1341
M. Ju et al. / J. Chem. Thermodynamics 41 (2009) 1339–1342
compositions in the mole fraction was estimated to less than ±0.001
properties and acentric factors of each component are given in table 1. The Wong–Sandler mixing rule is represented as
PP
3. Correlations
bm ¼ In this study, the experimental (vapour + liquid) equilibrium data were correlated with the Peng–Robinson equation of state (PR EoS) [11] using the Wong–Sandler mixing rules [12]. The PR EoS and the Wong–Sandler mixing rules are expressed as follows:
p¼
RT aðTÞ ; V b VðV þ bÞ þ bðV bÞ
ð1Þ
R2 T 2c aðTÞ; pc RT c bðT c Þ ¼ 0:077796 ; pc
aðTÞ ¼ 0:457235
ð2Þ ð3Þ
2 aðTÞ ¼ ½1 þ jð1 T 0:5 r Þ ; j ¼ 0:37464 þ 1:54226x 0:26992x2 ;
ð4Þ ð5Þ
where Tc is the critical temperature, pc is the critical pressure, Tr is the reduced temperature, and x is the acentric factor. The critical
P
a b RT
ij E
A1 ai i xi b RT CRT
ð7Þ
;
i
! ai AE1 ; xi þ am ¼ bm bi C i a ai þ bj RTj bi RT a b ¼ ð1 kij Þ; 2 RT ij
ð8Þ ð9Þ
pffiffiffi pffiffiffi where C ¼ lnð 2 1Þ= 2 for the PR EoS. Since the excess Helmholtz free energy of mixing at infinite pressure is assumed equal to the excess Gibbs free energy (GE) at low pressure, the GE model is used in place of AE1 . We selected the NRTL model [13] as an activity coefficient model in this study:
P GE X xi sji Gji xi Pi ; ¼ RT k xk Gki i
ð10Þ
Gij ¼ expðaij sij Þ;
ð11Þ
aij ¼ aji
Aij ¼ ; T
ð12Þ
where sij and sji are the interaction parameters and aij is the nonrandomness parameter. The non-randomness parameter aij was fixed on 0.3.
5.0
4.0
p/MPa
1
X
sij 6.0
j xi xj
i
a
2
3.0
1
1.0
0.0 0.0
0.2
0.4
0.6
0.8
1.0
(pcal-pexp)/pexpX100
2.0
x, y
0
-1
FIGURE 1. (Vapour + liquid) equilibria of the {xHFC-23 + (1 x)propane} binary system. Symbols are for experimental data: H, at 283.15 K; j, at 293.15 K; N, at 303.15 K; and d, at 313.15 K. Solid lines correspond to calculation with the PR EoS using the Wong–Sandler mixing rules.
-2 0.0
0.2
0.4
0.6
0.8
1.0
x
b
5.0
0.01
3.0
ycal-yexp
p/MPa
4.0
0.02
0.00
2.0
-0.01
1.0
0.0 0.0
0.2
0.4
0.6
0.8
1.0
x, y
-0.02 0.0
0.2
0.4
0.6
0.8
1.0
x FIGURE 2. (Vapour + liquid) equilibria of the {xHFC-23 + (1 x)n-butane} binary system. Symbols are for experimental data: j, at 283.15 K; N, at 293.15 K; , at 303.15 K; and d, at 313.15 K. Solid lines correspond to calculation with the PR EoS using the Wong–Sandler mixing rules.
FIGURE 3. Deviation of the {xHFC-23 + (1 x)propane} system: (a) deviation of pressure and (b) deviation of vapour mole fraction: d, at 283.15 K; s, at 293.15 K; ., at 303.15 K; 4, at 313.15 K.
1342
a
M. Ju et al. / J. Chem. Thermodynamics 41 (2009) 1339–1342 TABLE 4 Binary parameters, MRD-p and MD-y.
2
(pcal-pexp)/pexpX100
1
0.4
0.6
0.8
(HFC-23 + n-butane) 388.82 220.91 384.17 217.34 397.60 189.60 409.87 178.63
0.20 0.26 0.32 0.28
0.0105 0.0098 0.0096 0.0086
283.15 293.15 303.15 313.15
0.397 0.389 0.391 0.390
P MRD-p ¼ ð100=NÞ N ðjpi;cal pi;exp j=pi;exp Þ. PN i MD-y ¼ ð1=NÞ i jyi;cal yi;exp j.
measured data at each temperature. Both systems show positive deviation from the Raoult’s law. Figures 3 and 4 illustrates the deviation of pressure and deviation of vapour mole fraction for each system between the experimental data and the calculated values. The results showed a tendency to overestimate vapour composition in the dilute x region and the deviations of vapour composition were less than 0.0169 and 0.0281, respectively, for {HFC-23 + propane} system and {HFC-23 + n-butane} system. The mean relative deviations (MRD) of pressure and mean deviations (MD) of vapour composition were less than 0.36% and 0.0087, respectively, for {HFC-23 + propane} and 0.32% and 0.0105, respectively, for {HFC23 + n-butane}. Binary parameters and the MRD of p and y are given in table 4.
0.04
0.02
ycal-yexp
0.0070 0.0087 0.0053 0.0057
0.245 0.357 0.323 0.349
Aji/K
1.0
x
b
0.35 0.36 0.36 0.31
283.15 293.15 303.15 313.15
b
0.2
(HFC-23 + propane) 507.18 214.72 154.67 306.60 303.76 206.67 125.36 338.11
Aij/K
a
-2 0.0
MD-yb
kij
0
-1
MRD-pa/%
T/K
0.00
-0.02
Acknowledgements -0.04 0.0
0.2
0.4
0.6
0.8
1.0
x FIGURE 4. Deviation of the {xHFC-23 + (1 x)n-butane} system: (a) deviation of pressure and (b) deviation of vapour mole fraction: d, at 283.15 K; s, at 293.15 K; ., at 303.15 K; 4, at 313.15 K.
4. Results and discussion Isothermal (vapour + liquid) equilibrium data for the (HFC23 + propane) and (HFC-23 + n-butane} systems were measured at temperatures ranging from 283.15 K to 313.15 K at 10 K intervals. Experimental and calculated data are provided in tables 2 and 3. Parameters were obtained by minimizing the following objective function through the simplex algorithm:
N X pexp pcal F¼ pexp i
ð13Þ
where N is the number of data points, pexp is the measured pressures and pcal is the calculated pressures. As shown in figures 1 and 2, the calculated results represent a good agreement with the
This work was supported by the Brain Korea 21 Program supported by the Ministry of Education and by Korea institute of Energy and resources Technology Evaluation and Planning (KETEP). References [1] J. McMullan, Int. J. Refrig. 25 (2002) 89–99. [2] J. Im, G. Lee, J. Lee, H. Kim, J. Chem. Thermodyn. 39 (2007) 1164–1167. [3] J. Im, G. Lee, M.S. Shin, J. Lee, H. Kim, Fluid Phase Equilibr. 248 (2006) 19– 23. [4] C. Coquelet, A. Chareton, D. Richon, Fluid Phase Equilibr. 218 (2004) 209– 214. [5] S. Bobbo, R. Camporese, R. Stryjek, J. Chem. Thermodyn. 32 (2000) 1647–1656. [6] J.S. Lim, J.Y. Park, J.W. Kang, B.G. Lee, Fluid Phase Equilibr. 243 (2006) 57–63. [7] S. Bobbo, R. Stryjek, N. Elvassore, A. Bertucco, Fluid Phase Equilibr. 150–151 (1998) 343–352. [8] Y. Yun, J. Im, H. Kim, J. Chem. Thermodyn. 40 (2008) 766–769. [9] J.Y. Park, J.S. Lim, B.G. Lee, Fluid Phase Equilibr. 194–197 (2002) 981–993. [10] Y. Yun, J. Im, M.S. Shin, Y. Lee, H. Kim, Fluid Phase Equilibr. 271 (2008) 34–37. [11] D. Peng, D.B. Robinson, Ind. Eng. Chem. Fundam. 15 (1976) 59–64. [12] D.S. Wong, S.I. Sandler, AIChE J. 38 (1992) 671–680. [13] H. Renon, J.M. Prausnitz, AIChE J. 14 (1968) 135–144. [14] M. McLinden, M. Huber, E. Lemmon, NIST Thermodynamic and Transport Properties of Refrigerants and Refrigerant Mixtures Database (REFPROP), Version 8.0.
JCT 09-118