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An experimental study of PVTx properties in the gas phase for binary mixtures of HFC-161 and HFC-32
Fluid Phase Equilibria 243 (2006) 156–160
An experimental study of PVTx properties in the gas phase for binary mixtures of HFC-161 and HFC-32 Qi Chen, Rong-hua Hong, Guang-ming Chen ∗ College of Mechanical and Energy Engineering, Zhejiang University, Hangzhou 310027, PR China Received 18 December 2005; received in revised form 23 February 2006; accepted 6 March 2006
Abstract An experimental study of the pressure–volume–temperature–composition (PVTx) properties in the gas phase for binary mixtures of ethyl fluoride (HFC-161) + difluoromethane (HFC-32) was conducted in the range of temperatures from 303.179 to 403.190 K, pressures from 1182.9 to 5918.2 kPa, densities from 0.5754 to 3.2174 mol dm−3 , and compositions from 0.1597 to 0.8989 mole fractions of HFC-161. The measurements were performed with an isochoric cell apparatus. The uncertainties in the present work were estimated to be ±1.5 kPa for pressure, ±6 mK for temperature, and ±0.15% for composition. On the basis of the experimental PVTx property data, a truncated virial equation of state was developed for the binary HFC-161/32 system. This equation reproduced the experimental data in the gas phase within ±0.457% in pressure. The temperature dependence of the second virial coefficients, including the cross-virial coefficients for this system is also discussed. © 2006 Elsevier B.V. All rights reserved. Keywords: Gas phase; PVTx properties; Equation of state; HFC-161/32 mixtures
1. Introduction The Montreal Protocol establishes schedules for phasing out the manufacture of chlorine-containing refrigerants, chlorofluorocarbons (CFCs) and hydrochlorofluorocarbons (HCFCs), which have been implicated in stratospheric ozone depletion. It is strongly recommended to replace remaining CFCs and HCFCs with zero ozone depletion potential (ODP) refrigerants such as hydrofluorocarbons (HFCs). Xuan has proposed a new ternary mixture of HFC-161, HFC-125, and HFC-32 as a promising candidate to replace HCFC-22 [1]. Reliable information about the thermodynamic properties of HFC-161/32, HFC-161/125, and HFC-32/125 is essential for its application as a working fluid in refrigeration system. Gas phase PVTx properties for the binary HFC-32/125 and HFC-161/125 systems are available in literatures [2,3]. However, for the binary HFC-161/32 system, there are no published reports on its gas phase PVTx properties. In the present study, we aim to measure a first set of PVTx properties in the gas phase of this important binary blend. A total of 140 gaseous PVTx data for the binary HFC-161/32 sys-
∗
Corresponding author. Tel.: +86 571 87951680; fax: +86 571 87952464. E-mail address: [email protected] (G.-m. Chen).
0378-3812/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2006.03.003
tem were measured using an isochoric method in a wide range of temperatures from 303.179 to 403.190 K and corresponding pressures from 1182.9 to 5918.2 kPa. 2. Experimental The experimental apparatus includes a sample cell, a highaccuracy thermostatic bath, a pressure measurement system, a temperature measurement system, and a vacuum system. It is the same as the one described previously [4]. The temperature in the thermostatic bath can be varied from 230.15 to 453.15 K. The overall temperature uncertainty is ±6 mK. The whole pressure measurement system has an uncertainty of ±1.5 kPa in the pressure range of 0.1–6.0 MPa. The uncertainty in density values is estimated to be within ±0.15% in present work. Considering all the possible effects on the composition determination, the uncertainty of the sample compositions determined in the present measurements was estimated to be ±0.1 mol%. The samples of the HFC-161 and HFC-32, provided by Zhejiang Chemical Industry Research Institute, have a purity of 99.74 mass% for the HFC-161 with the principal impurities of ethylene and isobutane, and 99.98 mass% for the HFC-32. They were used without further purification.
Q. Chen et al. / Fluid Phase Equilibria 243 (2006) 156–160
157
3. Results and discussion In this study, a total of 140 PVTx data were obtained at temperatures from 303.179 to 403.190 K along nine independent isopleths: 0.1597, 0.2227, 0.3830, 0.5084, 0.5194, 0.5399, 0.5760, 0.6132, and 0.8989 mole fractions of HFC-161. A temperature correction to the densities was made to compensate for the thermal expansion of the sample cell. Results of the isochoric measurements are given in Table 1 . To represent the experimental PVTx data in the gas phase of the binary HFC-161/32 system, a truncated virial equation of state was developed. Since the applicable density range of the present model is up to 3.2174 mol dm−3 , the fourth and higher viral terms are truncated [5]. The virial-type equation of state thus developed is [6]: Z=
P = 1 + Bm ρ + C m ρ 2 ρRT
(1)
where Z, P, T, and ρ denote the compressibility factor, pressure, temperature, and molar density, respectively; R the universal gas constant; and the second and third virial coefficients of the binary HFC-161/32 mixture, Bm and Cm , are calculated with the following mixing rules: Bm =
2 2
xi xj Bij
(2)
i=1 j=1
and Cm =
2 2 2
xi xj xk Cijk
(3)
i=1 j=1 k=1
Bij in Eq. (2) and Cijk in Eq. (3) are expressed as follows: −1 −1 + b3 exp(Tr,1 ) B11 = b1 + b2 Tr,1
(4)
−1 −1 B22 = b4 + b5 Tr,2 + b6 exp(Tr,2 )
(5)
−1 −1 + b9 exp(Tr,12 ) B12 = B21 = b7 + b8 Tr,12
(6)
−3 −13 C111 = c1 + c2 Tr,1 + c3 Tr,1
(7)
−5 −12 C222 = c4 + c5 Tr,2 + c6 Tr,2
(8)
−5 −7 + c9 Tr,112 C112 = C211 = C121 = c7 + c8 Tr,112
(9)
−5 −6 C221 = C122 = C212 = c10 + c11 Tr,221 + c12 Tr,221
Fig. 1. Deviations of measured PVT data from values calculated from Eq. (1): () HFC-32, Fu et al. [9] () HFC-161, Chen et al. [4].
Tc,ijk = (Tc,i Tc,j Tc,k )1/3
(15)
where Tr is the reduced temperature and the critical temperatures, Tc,1 = 375.31 K for HFC-161 and Tc,2 =351.26 K for HFC32, were reported by Booth and Swinehart [7] and Higashi [8], respectively. Note that Tc,ij and Tc,ijk are not real critical temperature but parameters used in the present model. The values of numerical coefficients bi , and ci in Eqs. (4)–(10) for HFC161/32 were determined by fitting the present PVTx data into the EOS. The numerical constants are listed in Table 2. In Fig. 1, the data for HFC-161 [4] and HFC-32 [9] are compared with Eq. (1) in the range where Eq. (1) is effective. The maximum and average absolute pressure deviations of Eq. (1) from Chen et al. [3] are 0.472% and 0.085%, respectively, and 0.551% and 0.214% for the results of Fu et al. [9]. Deviations of the experimental PVTx data from the present model in the gas phase of the binary HFC-161/32 system are shown in Fig. 2. The maximum and average absolute pressure deviations from Eq. (1)
(10)
and Tr,i =
T Tc,i
(11)
Tr,ij =
T Tc,ij
(12)
Tr,ijk =
T Tc,ijk
(13)
with Tc,ij = (Tc,i Tc,j )1/2
(14)
Fig. 2. Deviations of measured PVTx data from values calculated from Eq. (1).
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Q. Chen et al. / Fluid Phase Equilibria 243 (2006) 156–160
Table 1 Experimental PVTx properties of HFC-161/32 system T (K)
P (kPa)
ρ (mol dm−3 )
x1∗
T (K)
P (kPa)
ρ (mol dm−3 )
x1∗
366.249 368.137 370.162 372.181 374.207 376.224 378.155 380.152 382.149 384.164 363.160 368.190 371.138 374.203 377.165 380.265 383.223 386.191 389.187 392.164 395.215 398.180 401.184 403.190 358.168 363.148 368.128 328.161 333.156 338.156 343.156 348.157 353.154 358.198 363.164 368.139 373.160 378.244 383.219 388.205 393.182 398.169 403.157 318.163 323.157 328.162 333.144 338.157 343.147 348.157 353.155 358.151 363.149 368.150 343.164 348.160 353.159 358.178 363.155 368.132 373.144 378.133 383.257 388.188
5121.2 5208.2 5300.1 5391.1 5481.1 5571.3 5656.4 5744.1 5830.6 5918.2 4411.2 4589.1 4692.0 4796.7 4898.0 5002.5 5101.5 5200.4 5298.9 5396.6 5495.6 5591.7 5688.1 5752.9 3771.6 3899.7 4026.0 2279.9 2347.7 2414.0 2479.0 2543.5 2606.9 2670.0 2732.0 2794.0 2855.6 2916.9 2976.3 3035.1 3094.8 3153.4 3212.1 2131.5 2198.6 2263.4 2327.5 2390.9 2452.5 2513.6 2574.4 2634.6 2693.7 2752.8 2154.4 2203.9 2252.8 2301.6 2350.2 2398.1 2445.5 2492.5 2540.3 2586.3
3.2174 3.2171 3.2168 3.2164 3.2161 3.2158 3.2155 3.2152 3.2148 3.2145 2.6007 2.6001 2.5997 2.5993 2.5989 2.5985 2.5982 2.5978 2.5974 2.5970 2.5966 2.5962 2.5958 2.5956 2.0017 2.0012 2.0007 1.1328 1.1325 1.1322 1.1320 1.1317 1.1314 1.1311 1.1308 1.1306 1.1303 1.1299 1.1297 1.1294 1.1292 1.1289 1.1286 1.1040 1.1038 1.1035 1.1032 1.1029 1.1027 1.1024 1.1021 1.1018 1.1016 1.1013 0.9271 0.9268 0.9266 0.9264 0.9261 0.9259 0.9257 0.9255 0.9252 0.9250
0.5194 0.5194 0.5194 0.5194 0.5194 0.5194 0.5194 0.5194 0.5194 0.5194 0.6132 0.6132 0.6132 0.6132 0.6132 0.6132 0.6132 0.6132 0.6132 0.6132 0.6132 0.6132 0.6132 0.6132 0.5760 0.5760 0.5760 0.3830 0.3830 0.3830 0.3830 0.3830 0.3830 0.3830 0.3830 0.3830 0.3830 0.3830 0.3830 0.3830 0.3830 0.3830 0.3830 0.2227 0.2227 0.2227 0.2227 0.2227 0.2227 0.2227 0.2227 0.2227 0.2227 0.2227 0.1597 0.1597 0.1597 0.1597 0.1597 0.1597 0.1597 0.1597 0.1597 0.1597
373.143 376.215 379.180 382.144 385.233 388.193 391.159 394.189 397.221 400.183 403.149 338.176 343.167 348.165 353.166 358.174 361.135 363.160 368.128 373.186 378.131 383.225 388.189 393.177 398.159 403.144 323.170 373.194 378.178 383.218 388.198 393.183 398.162 403.144 338.174 343.166 348.177 353.180 358.182 363.187 368.162 373.146 378.159 383.201 388.189 393.173 398.161 403.140 313.157 318.188 323.155 328.158 333.154 338.156 318.154 323.147 328.152 333.149 338.147 343.156 348.159 353.149 358.152 363.157
4150.9 4226.5 4299.3 4371.4 4446.2 4517.5 4588.7 4660.6 4732.3 4802.3 4872.2 2630.9 2712.8 2792.7 2871.3 2949.0 2995.0 3026.2 3102.1 3177.9 3251.3 3326.2 3398.8 3471.2 3543.3 3614.4 2210.3 2811.5 2869.2 2927.4 2984.7 3041.7 3098.3 3154.3 2090.9 2149.6 2207.5 2264.1 2319.9 2375.4 2429.8 2484.1 2537.8 2591.2 2643.6 2695.7 2747.5 2799.0 1847.3 1901.8 1954.5 2002.7 2054.0 2104.4 1280.2 1310.7 1341.1 1371.0 1400.5 1429.4 1458.6 1487.1 1515.5 1545.2
2.0002 1.9999 1.9996 1.9993 1.9990 1.9987 1.9985 1.9982 1.9979 1.9976 1.9973 1.3324 1.3321 1.3317 1.3314 1.3311 1.3309 1.3307 1.3304 1.3301 1.3297 1.3294 1.3291 1.3288 1.3284 1.3281 1.1331 1.1010 1.1007 1.1005 1.1002 1.0999 1.0997 1.0994 1.0024 1.0021 1.0019 1.0016 1.0014 1.0011 1.0009 1.0006 1.0004 1.0001 0.9999 0.9996 0.9994 0.9991 0.9285 0.9282 0.9280 0.9278 0.9275 0.9273 0.5775 0.5774 0.5772 0.5771 0.5769 0.5768 0.5766 0.5765 0.5764 0.5762
0.5760 0.5760 0.5760 0.5760 0.5760 0.5760 0.5760 0.5760 0.5760 0.5760 0.5760 0.5399 0.5399 0.5399 0.5399 0.5399 0.5399 0.5399 0.5399 0.5399 0.5399 0.5399 0.5399 0.5399 0.5399 0.5399 0.3830 0.2227 0.2227 0.2227 0.2227 0.2227 0.2227 0.2227 0.8989 0.8989 0.8989 0.8989 0.8989 0.8989 0.8989 0.8989 0.8989 0.8989 0.8989 0.8989 0.8989 0.8989 0.1597 0.1597 0.1597 0.1597 0.1597 0.1597 0.5084 0.5084 0.5084 0.5084 0.5084 0.5084 0.5084 0.5084 0.5084 0.5084
Q. Chen et al. / Fluid Phase Equilibria 243 (2006) 156–160
159
Table 1 (Continued ) T (K)
P (kPa)
ρ (mol dm−3 )
x1∗
T (K)
P (kPa)
ρ (mol dm−3 )
x1∗
393.177 398.162 403.170 303.179 308.151 313.152
2632.1 2678.2 2724.0 1182.9 1216.7 1248.7
0.9248 0.9245 0.9243 0.5779 0.5778 0.5776
0.1597 0.1597 0.1597 0.5084 0.5084 0.5084
368.148 373.254 378.145 383.214 388.193 393.183
1573.6 1602.1 1629.7 1657.5 1685.4 1713.3
0.5761 0.5759 0.5758 0.5756 0.5755 0.5754
0.5084 0.5084 0.5084 0.5084 0.5084 0.5084
x1∗ denotes the mole fraction of HFC-161. Table 2 Numerical coefficients in Eqs. (4)–(10) for HFC-161/32 system I
bi (dm3 mol−1 )
ci (dm6 mol−2 )
1 2 3 4 5 6 7 8 9 10 11 12
0.325429 −0.623934 0.028661 0.340609 1.30265 −0.673922 0.355141 0.336066 −0.330869
−0.014195 0.036759 −4.774543 × 10−3 9.403127 × 10−3 −9.381096 × l0−4 5.079966 × 10−3 −4.720998 × l0−3 0.03007 −0.010709 0.016354 −4.888886 × l0−3 9.984015 × l0−3
are 0.457% and 0.171%, respectively. The suitable range of Eq. (1) is from 1182.9 to 5918.2 kPa in pressure, from 303.179 to 403.190 K in temperature and from 0.5754 to 3.2174 mol dm−3 in density. The temperature dependence of the second virial coefficients for pure components and of the cross-second virial coefficients for the HFC-161/32 system described by the present model is shown in Fig. 3. It is apparent that the second virial coefficient of HFC-32 by Defibaugh et al. [10] and HFC-161 by Chen et
al. [4] are represented well by the present model. And the curve of the second virial coefficient calculated at 0.5 mole fraction of HFC-161 is very close to the cure of the cross-virial coefficients B12 at higher temperatures. 4. Conclusion A total of 140 PVTx property measurements in the gas phase of the binary HFC-161/32 system along nine independent isopleths were performed using the isochoric method. The maximum uncertainties in the present work were estimated to be ±1.5 kPa, ±6 mK, and ±0.15% for pressure, temperature, and density, respectively. A thermodynamic model that represents the PVTx properties of the binary HFC-161/32 system has been developed. The model has a form of a truncated virial equation of state, and the numerical constants for its virial terms were obtained on the basis of the experimental PVTx data. The reproducibility of the present model has been confirmed to be satisfactory, within ±0.457% in pressure for the range of temperatures from 303.179 to 403.190 K and pressures up to 5918.2 kPa. The present model for the binary HFC-161/32 system is valid for the entire range of compositions. Acknowledgements We are greatly indebted to Zhejiang Chemical Industry Research Institute for providing the ethyl fluoride (HFC161) and difluoromethane (HFC-32) samples. Financial support of Zhejiang Provincial Natural Science Foundation of China (Project No. Z105034) is also gratefully acknowledged. References
Fig. 3. Temperature dependence of the second virial coefficient for HFC-161/32 system: () Bm (0.5 mole fraction of HFC-161); () B12 ; (×) HFC-32 [10]; () HFC-161 [4].
[1] Y.M. Xuan, Theoretical and experimental study on new alternative refrigerants. Ph.D. Thesis, Zhejiang University, China, 2004. [2] H.L. Zhang, H. Sato, K. Watanabe, Gas phase PVT properties for the difluoromethane + pentafluoroethane (R-32 + 125) system, J. Chem. Eng. Data 41 (1996) 1401–1408. [3] Q. Chen, R.H. Hong, G.M. Chen, PVTx properties in the gas phase for binary HFC-161/125 system, Fluid Phase Equilib. 240 (1) (2006) 63– 66. [4] Q. Chen, R.H. Hong, G.M. Chen, Gaseous PVT properties of ethyl fluoride, Fluid Phase Equilib. 237 (2005) 111–116. [5] W.M. Righter, K.R. Hall, Optimal truncation of the virial equation, AIChE J. 21 (1975) 406–407. [6] H.L. Zhang, S. Tada, H. Sato, K. Watanabe, PVTx properties in the gas phase for binary R-125/143a system, Fluid Phase Equilib. 150–151 (1998) 333–341.
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[7] H.S. Booth, C.F. Swinehart, Critical constants and vapor pressure of some gaseous fluorides of group IV, J. Am. Chem. Soc. 57 (1935) 1337–1342. [8] Y. Higashi, Critical parameters for HFC134a, HFC32 and HFC125, Int. J. Refrig. 17 (1994) 524–531.
[9] Y.D. Fu, L.Z. Han, M.S. Zhu, PVT properties, vapor pressures and critical parameters of HFC-32, Fluid Phase Equilib. 111 (1995) 273– 286. [10] K.A. Defibaugh, G. Morrison, L.A. Weber, Thermodynamic properties of difluoromethane, J. Chem. Eng. Data 39 (1994) 333–340.
An experimental study of PVTx properties in the gas phase for binary mixtures of HFC-161 and HFC-32 Qi Chen, Rong-hua Hong, Guang-ming Chen ∗ College of Mechanical and Energy Engineering, Zhejiang University, Hangzhou 310027, PR China Received 18 December 2005; received in revised form 23 February 2006; accepted 6 March 2006
Abstract An experimental study of the pressure–volume–temperature–composition (PVTx) properties in the gas phase for binary mixtures of ethyl fluoride (HFC-161) + difluoromethane (HFC-32) was conducted in the range of temperatures from 303.179 to 403.190 K, pressures from 1182.9 to 5918.2 kPa, densities from 0.5754 to 3.2174 mol dm−3 , and compositions from 0.1597 to 0.8989 mole fractions of HFC-161. The measurements were performed with an isochoric cell apparatus. The uncertainties in the present work were estimated to be ±1.5 kPa for pressure, ±6 mK for temperature, and ±0.15% for composition. On the basis of the experimental PVTx property data, a truncated virial equation of state was developed for the binary HFC-161/32 system. This equation reproduced the experimental data in the gas phase within ±0.457% in pressure. The temperature dependence of the second virial coefficients, including the cross-virial coefficients for this system is also discussed. © 2006 Elsevier B.V. All rights reserved. Keywords: Gas phase; PVTx properties; Equation of state; HFC-161/32 mixtures
1. Introduction The Montreal Protocol establishes schedules for phasing out the manufacture of chlorine-containing refrigerants, chlorofluorocarbons (CFCs) and hydrochlorofluorocarbons (HCFCs), which have been implicated in stratospheric ozone depletion. It is strongly recommended to replace remaining CFCs and HCFCs with zero ozone depletion potential (ODP) refrigerants such as hydrofluorocarbons (HFCs). Xuan has proposed a new ternary mixture of HFC-161, HFC-125, and HFC-32 as a promising candidate to replace HCFC-22 [1]. Reliable information about the thermodynamic properties of HFC-161/32, HFC-161/125, and HFC-32/125 is essential for its application as a working fluid in refrigeration system. Gas phase PVTx properties for the binary HFC-32/125 and HFC-161/125 systems are available in literatures [2,3]. However, for the binary HFC-161/32 system, there are no published reports on its gas phase PVTx properties. In the present study, we aim to measure a first set of PVTx properties in the gas phase of this important binary blend. A total of 140 gaseous PVTx data for the binary HFC-161/32 sys-
∗
Corresponding author. Tel.: +86 571 87951680; fax: +86 571 87952464. E-mail address: [email protected] (G.-m. Chen).
0378-3812/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2006.03.003
tem were measured using an isochoric method in a wide range of temperatures from 303.179 to 403.190 K and corresponding pressures from 1182.9 to 5918.2 kPa. 2. Experimental The experimental apparatus includes a sample cell, a highaccuracy thermostatic bath, a pressure measurement system, a temperature measurement system, and a vacuum system. It is the same as the one described previously [4]. The temperature in the thermostatic bath can be varied from 230.15 to 453.15 K. The overall temperature uncertainty is ±6 mK. The whole pressure measurement system has an uncertainty of ±1.5 kPa in the pressure range of 0.1–6.0 MPa. The uncertainty in density values is estimated to be within ±0.15% in present work. Considering all the possible effects on the composition determination, the uncertainty of the sample compositions determined in the present measurements was estimated to be ±0.1 mol%. The samples of the HFC-161 and HFC-32, provided by Zhejiang Chemical Industry Research Institute, have a purity of 99.74 mass% for the HFC-161 with the principal impurities of ethylene and isobutane, and 99.98 mass% for the HFC-32. They were used without further purification.
Q. Chen et al. / Fluid Phase Equilibria 243 (2006) 156–160
157
3. Results and discussion In this study, a total of 140 PVTx data were obtained at temperatures from 303.179 to 403.190 K along nine independent isopleths: 0.1597, 0.2227, 0.3830, 0.5084, 0.5194, 0.5399, 0.5760, 0.6132, and 0.8989 mole fractions of HFC-161. A temperature correction to the densities was made to compensate for the thermal expansion of the sample cell. Results of the isochoric measurements are given in Table 1 . To represent the experimental PVTx data in the gas phase of the binary HFC-161/32 system, a truncated virial equation of state was developed. Since the applicable density range of the present model is up to 3.2174 mol dm−3 , the fourth and higher viral terms are truncated [5]. The virial-type equation of state thus developed is [6]: Z=
P = 1 + Bm ρ + C m ρ 2 ρRT
(1)
where Z, P, T, and ρ denote the compressibility factor, pressure, temperature, and molar density, respectively; R the universal gas constant; and the second and third virial coefficients of the binary HFC-161/32 mixture, Bm and Cm , are calculated with the following mixing rules: Bm =
2 2
xi xj Bij
(2)
i=1 j=1
and Cm =
2 2 2
xi xj xk Cijk
(3)
i=1 j=1 k=1
Bij in Eq. (2) and Cijk in Eq. (3) are expressed as follows: −1 −1 + b3 exp(Tr,1 ) B11 = b1 + b2 Tr,1
(4)
−1 −1 B22 = b4 + b5 Tr,2 + b6 exp(Tr,2 )
(5)
−1 −1 + b9 exp(Tr,12 ) B12 = B21 = b7 + b8 Tr,12
(6)
−3 −13 C111 = c1 + c2 Tr,1 + c3 Tr,1
(7)
−5 −12 C222 = c4 + c5 Tr,2 + c6 Tr,2
(8)
−5 −7 + c9 Tr,112 C112 = C211 = C121 = c7 + c8 Tr,112
(9)
−5 −6 C221 = C122 = C212 = c10 + c11 Tr,221 + c12 Tr,221
Fig. 1. Deviations of measured PVT data from values calculated from Eq. (1): () HFC-32, Fu et al. [9] () HFC-161, Chen et al. [4].
Tc,ijk = (Tc,i Tc,j Tc,k )1/3
(15)
where Tr is the reduced temperature and the critical temperatures, Tc,1 = 375.31 K for HFC-161 and Tc,2 =351.26 K for HFC32, were reported by Booth and Swinehart [7] and Higashi [8], respectively. Note that Tc,ij and Tc,ijk are not real critical temperature but parameters used in the present model. The values of numerical coefficients bi , and ci in Eqs. (4)–(10) for HFC161/32 were determined by fitting the present PVTx data into the EOS. The numerical constants are listed in Table 2. In Fig. 1, the data for HFC-161 [4] and HFC-32 [9] are compared with Eq. (1) in the range where Eq. (1) is effective. The maximum and average absolute pressure deviations of Eq. (1) from Chen et al. [3] are 0.472% and 0.085%, respectively, and 0.551% and 0.214% for the results of Fu et al. [9]. Deviations of the experimental PVTx data from the present model in the gas phase of the binary HFC-161/32 system are shown in Fig. 2. The maximum and average absolute pressure deviations from Eq. (1)
(10)
and Tr,i =
T Tc,i
(11)
Tr,ij =
T Tc,ij
(12)
Tr,ijk =
T Tc,ijk
(13)
with Tc,ij = (Tc,i Tc,j )1/2
(14)
Fig. 2. Deviations of measured PVTx data from values calculated from Eq. (1).
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Q. Chen et al. / Fluid Phase Equilibria 243 (2006) 156–160
Table 1 Experimental PVTx properties of HFC-161/32 system T (K)
P (kPa)
ρ (mol dm−3 )
x1∗
T (K)
P (kPa)
ρ (mol dm−3 )
x1∗
366.249 368.137 370.162 372.181 374.207 376.224 378.155 380.152 382.149 384.164 363.160 368.190 371.138 374.203 377.165 380.265 383.223 386.191 389.187 392.164 395.215 398.180 401.184 403.190 358.168 363.148 368.128 328.161 333.156 338.156 343.156 348.157 353.154 358.198 363.164 368.139 373.160 378.244 383.219 388.205 393.182 398.169 403.157 318.163 323.157 328.162 333.144 338.157 343.147 348.157 353.155 358.151 363.149 368.150 343.164 348.160 353.159 358.178 363.155 368.132 373.144 378.133 383.257 388.188
5121.2 5208.2 5300.1 5391.1 5481.1 5571.3 5656.4 5744.1 5830.6 5918.2 4411.2 4589.1 4692.0 4796.7 4898.0 5002.5 5101.5 5200.4 5298.9 5396.6 5495.6 5591.7 5688.1 5752.9 3771.6 3899.7 4026.0 2279.9 2347.7 2414.0 2479.0 2543.5 2606.9 2670.0 2732.0 2794.0 2855.6 2916.9 2976.3 3035.1 3094.8 3153.4 3212.1 2131.5 2198.6 2263.4 2327.5 2390.9 2452.5 2513.6 2574.4 2634.6 2693.7 2752.8 2154.4 2203.9 2252.8 2301.6 2350.2 2398.1 2445.5 2492.5 2540.3 2586.3
3.2174 3.2171 3.2168 3.2164 3.2161 3.2158 3.2155 3.2152 3.2148 3.2145 2.6007 2.6001 2.5997 2.5993 2.5989 2.5985 2.5982 2.5978 2.5974 2.5970 2.5966 2.5962 2.5958 2.5956 2.0017 2.0012 2.0007 1.1328 1.1325 1.1322 1.1320 1.1317 1.1314 1.1311 1.1308 1.1306 1.1303 1.1299 1.1297 1.1294 1.1292 1.1289 1.1286 1.1040 1.1038 1.1035 1.1032 1.1029 1.1027 1.1024 1.1021 1.1018 1.1016 1.1013 0.9271 0.9268 0.9266 0.9264 0.9261 0.9259 0.9257 0.9255 0.9252 0.9250
0.5194 0.5194 0.5194 0.5194 0.5194 0.5194 0.5194 0.5194 0.5194 0.5194 0.6132 0.6132 0.6132 0.6132 0.6132 0.6132 0.6132 0.6132 0.6132 0.6132 0.6132 0.6132 0.6132 0.6132 0.5760 0.5760 0.5760 0.3830 0.3830 0.3830 0.3830 0.3830 0.3830 0.3830 0.3830 0.3830 0.3830 0.3830 0.3830 0.3830 0.3830 0.3830 0.3830 0.2227 0.2227 0.2227 0.2227 0.2227 0.2227 0.2227 0.2227 0.2227 0.2227 0.2227 0.1597 0.1597 0.1597 0.1597 0.1597 0.1597 0.1597 0.1597 0.1597 0.1597
373.143 376.215 379.180 382.144 385.233 388.193 391.159 394.189 397.221 400.183 403.149 338.176 343.167 348.165 353.166 358.174 361.135 363.160 368.128 373.186 378.131 383.225 388.189 393.177 398.159 403.144 323.170 373.194 378.178 383.218 388.198 393.183 398.162 403.144 338.174 343.166 348.177 353.180 358.182 363.187 368.162 373.146 378.159 383.201 388.189 393.173 398.161 403.140 313.157 318.188 323.155 328.158 333.154 338.156 318.154 323.147 328.152 333.149 338.147 343.156 348.159 353.149 358.152 363.157
4150.9 4226.5 4299.3 4371.4 4446.2 4517.5 4588.7 4660.6 4732.3 4802.3 4872.2 2630.9 2712.8 2792.7 2871.3 2949.0 2995.0 3026.2 3102.1 3177.9 3251.3 3326.2 3398.8 3471.2 3543.3 3614.4 2210.3 2811.5 2869.2 2927.4 2984.7 3041.7 3098.3 3154.3 2090.9 2149.6 2207.5 2264.1 2319.9 2375.4 2429.8 2484.1 2537.8 2591.2 2643.6 2695.7 2747.5 2799.0 1847.3 1901.8 1954.5 2002.7 2054.0 2104.4 1280.2 1310.7 1341.1 1371.0 1400.5 1429.4 1458.6 1487.1 1515.5 1545.2
2.0002 1.9999 1.9996 1.9993 1.9990 1.9987 1.9985 1.9982 1.9979 1.9976 1.9973 1.3324 1.3321 1.3317 1.3314 1.3311 1.3309 1.3307 1.3304 1.3301 1.3297 1.3294 1.3291 1.3288 1.3284 1.3281 1.1331 1.1010 1.1007 1.1005 1.1002 1.0999 1.0997 1.0994 1.0024 1.0021 1.0019 1.0016 1.0014 1.0011 1.0009 1.0006 1.0004 1.0001 0.9999 0.9996 0.9994 0.9991 0.9285 0.9282 0.9280 0.9278 0.9275 0.9273 0.5775 0.5774 0.5772 0.5771 0.5769 0.5768 0.5766 0.5765 0.5764 0.5762
0.5760 0.5760 0.5760 0.5760 0.5760 0.5760 0.5760 0.5760 0.5760 0.5760 0.5760 0.5399 0.5399 0.5399 0.5399 0.5399 0.5399 0.5399 0.5399 0.5399 0.5399 0.5399 0.5399 0.5399 0.5399 0.5399 0.3830 0.2227 0.2227 0.2227 0.2227 0.2227 0.2227 0.2227 0.8989 0.8989 0.8989 0.8989 0.8989 0.8989 0.8989 0.8989 0.8989 0.8989 0.8989 0.8989 0.8989 0.8989 0.1597 0.1597 0.1597 0.1597 0.1597 0.1597 0.5084 0.5084 0.5084 0.5084 0.5084 0.5084 0.5084 0.5084 0.5084 0.5084
Q. Chen et al. / Fluid Phase Equilibria 243 (2006) 156–160
159
Table 1 (Continued ) T (K)
P (kPa)
ρ (mol dm−3 )
x1∗
T (K)
P (kPa)
ρ (mol dm−3 )
x1∗
393.177 398.162 403.170 303.179 308.151 313.152
2632.1 2678.2 2724.0 1182.9 1216.7 1248.7
0.9248 0.9245 0.9243 0.5779 0.5778 0.5776
0.1597 0.1597 0.1597 0.5084 0.5084 0.5084
368.148 373.254 378.145 383.214 388.193 393.183
1573.6 1602.1 1629.7 1657.5 1685.4 1713.3
0.5761 0.5759 0.5758 0.5756 0.5755 0.5754
0.5084 0.5084 0.5084 0.5084 0.5084 0.5084
x1∗ denotes the mole fraction of HFC-161. Table 2 Numerical coefficients in Eqs. (4)–(10) for HFC-161/32 system I
bi (dm3 mol−1 )
ci (dm6 mol−2 )
1 2 3 4 5 6 7 8 9 10 11 12
0.325429 −0.623934 0.028661 0.340609 1.30265 −0.673922 0.355141 0.336066 −0.330869
−0.014195 0.036759 −4.774543 × 10−3 9.403127 × 10−3 −9.381096 × l0−4 5.079966 × 10−3 −4.720998 × l0−3 0.03007 −0.010709 0.016354 −4.888886 × l0−3 9.984015 × l0−3
are 0.457% and 0.171%, respectively. The suitable range of Eq. (1) is from 1182.9 to 5918.2 kPa in pressure, from 303.179 to 403.190 K in temperature and from 0.5754 to 3.2174 mol dm−3 in density. The temperature dependence of the second virial coefficients for pure components and of the cross-second virial coefficients for the HFC-161/32 system described by the present model is shown in Fig. 3. It is apparent that the second virial coefficient of HFC-32 by Defibaugh et al. [10] and HFC-161 by Chen et
al. [4] are represented well by the present model. And the curve of the second virial coefficient calculated at 0.5 mole fraction of HFC-161 is very close to the cure of the cross-virial coefficients B12 at higher temperatures. 4. Conclusion A total of 140 PVTx property measurements in the gas phase of the binary HFC-161/32 system along nine independent isopleths were performed using the isochoric method. The maximum uncertainties in the present work were estimated to be ±1.5 kPa, ±6 mK, and ±0.15% for pressure, temperature, and density, respectively. A thermodynamic model that represents the PVTx properties of the binary HFC-161/32 system has been developed. The model has a form of a truncated virial equation of state, and the numerical constants for its virial terms were obtained on the basis of the experimental PVTx data. The reproducibility of the present model has been confirmed to be satisfactory, within ±0.457% in pressure for the range of temperatures from 303.179 to 403.190 K and pressures up to 5918.2 kPa. The present model for the binary HFC-161/32 system is valid for the entire range of compositions. Acknowledgements We are greatly indebted to Zhejiang Chemical Industry Research Institute for providing the ethyl fluoride (HFC161) and difluoromethane (HFC-32) samples. Financial support of Zhejiang Provincial Natural Science Foundation of China (Project No. Z105034) is also gratefully acknowledged. References
Fig. 3. Temperature dependence of the second virial coefficient for HFC-161/32 system: () Bm (0.5 mole fraction of HFC-161); () B12 ; (×) HFC-32 [10]; () HFC-161 [4].
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