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Measurement of vapor–liquid equilibria for the binary mixture of propylene (R-1270) + propane (R-290)
Fluid Phase Equilibria 245 (2006) 63–70
Measurement of vapor–liquid equilibria for the binary mixture of propylene (R-1270) + propane (R-290) Quang Nhu Ho a , Kye Sang Yoo a , Byung Gwon Lee a,∗ , Jong Sung Lim b a
Division of Environment and Process Technology, Korea Institute of Science and Technology (KIST), P.O. Box 131, Cheongryang, Seoul 130-650, South Korea b Department of Chemical and Biomolecular Engineering, Sogang University, P.O. Box 1142, Seoul 100-611, South Korea Received 12 September 2005; received in revised form 19 March 2006; accepted 20 March 2006 Available online 27 March 2006
Abstract Isothermal vapor–liquid equilibria data for the binary mixture of propylene (R-1270) + propane (R-290) at 273.15, 278.15, 283.15, 293.15, 303.15 and 313.15 K were measured by using a circulation-type equilibrium apparatus. The experimental data were correlated with the Peng–Robinson equation of state (PR-EOS) combined with the Wong–Sandler mixing rule. It is confirmed that the data calculated by this equations of state are in good agreement with experimental data. The azeotropic behavior was not found in this mixture over range of temperature studied here. © 2006 Published by Elsevier B.V. Keywords: Propane (R-290); Propylene (R-1270); Hydrocarbon mixture; Vapor–liquid equilibria (VLE); Peng–Robinson equation of state (PR-EOS)
1. Introduction Much effort has been made to find the suitable replacement for CFCs and HCHCs due to their high ozone depletion potentials (ODPs) and global warming potentials (GWPs). In recent years, the utilization of light hydrocarbons, such as propane, butane, propylene, etc., as effective refrigerants is believed as an alternative solution because these hydrocarbons are rather cheap, plentiful and environmentally benign chemicals (zero ODPs and near zero GWPs) and have many outstanding properties. Even though flammability of these materials has caused some concerns, but it was found that hydrocarbons are quite safe in small applications such as domestic refrigeration and car air-conditioning, due to very small amounts involved [1]. For the binary mixture of propylene (R-1270) + propane (R290), vapor–liquid equilibria (VLE) data at various temperatures were previously reported by some authors [2–8]. However, some of them were not in detail. In this work, isothermal vapor–liquid equilibria data for the binary mixture of propylene (R1270) + propane (R-290), which are very important basic information in evaluating the performance refrigeration cycles and
in determining optimal composition of this mixture, were measured at 273.15, 278.15, 283.15, 293.15, 303.15 and 313.15 K by using a circulation-type equilibrium apparatus. The experimental data were correlated with the Peng–Robinson [9] equation of state (PR-EOS) combined with the Wong–Sandler [10] mixing rule. The interaction parameters and average deviations in pressures and in vapor phase compositions obtained from this correlation were presented. The deviations of other published data to the equation of state above are also reported in this paper. 2. Experimental 2.1. Chemicals High-grade chemicals of propane and propylene were used for this investigation. Propylene of purity higher than 99.5% by mass was supplied by Conley Gas Ltd., U.S.A. Propane produced by M.G. Industries, U.S.A., had purity higher than 99.8 mass%. The purity of each chemical was validated by using gas chromatograph. 2.2. Vapor–liquid equilibrium apparatus
∗
Corresponding author. Tel.: +82 2 958 5857. E-mail address: [email protected] (B.G. Lee).
0378-3812/$ – see front matter © 2006 Published by Elsevier B.V. doi:10.1016/j.fluid.2006.03.009
The vapor–liquid equilibrium apparatus used in this work was a circulation-type one in which both liquid and vapor phases
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were continuously recirculated. Description of the experimental apparatus has been reported in our previous work [11,12] and is only briefly discussed here. The equilibrium cell was a 316 stainless steel with an inner volume of about 85 mL. A pair of Pyrex glass windows was installed on two sides of the cell to observe the inside during operation. Inside the cell, a stirring bar rotated at variable speeds was used to accelerate the attainment of the equilibrium state and to reduce concentration gradients in both phases. The temperature of the equilibrium cell in the bath was maintained by a bath circulator (RCB-20, Jeio Tech, Korea). The temperature in the cell was measured with a platinum resistance sensor connected to a digital temperature indicator (F250 precision thermometer, Automatic Systems Laboratories Ltd., UK). They were calibrated by NAMAS accredited calibration laboratory. The total error is estimated to be within ±0.02 K, including sensor uncertainty, ±0.01 K, temperature resolution, ±0.001 K, and measurement uncertainty, ±0.001 K. The pressure was measured with a pressure transducer (model XPM60) and digital pressure calibrator indicator (C106 model, Beamax, Finland). Pressure calibrations are traceable to national standards (Center for Metrology and Accreditation Certificate Nos. M-95P077 dated 14 November 1995, M-M730 dated 16 November 1995 and M-95P078 dated 16 November 1995), and total errors were estimated to be within ±1 kPa, including calibrator uncertainty, ±0.5 kPa, sensor uncertainty, ±0.1 kPa, and measurement uncertainty, ±0.1 kPa. The vapor and liquid phases in the equilibrium cell were continuously recirculated by a dual-head circulation pump (Milton Roy Co., U.S.A.). After equilibrium was reached, the vapor and liquid samples were withdrawn from the recycling loop and injected on-line into a gas chromatograph (Gow-Mac model 550P) equipped with a thermal conductivity detector (TCD) and an Unibead 2S column (Altech Co.). The signals from GC were processed and converted to data by D520B computing integrator (Young In Co., Korea).
estimated within ±0.002 mole fraction for both liquid and vapor phases. 3. Correlation In this work, the experimental VLE data were correlated with the Peng–Robinson [9] equation of state combined with the Wong–Sandler mixing rule. The Peng–Robinson equation of state is expressed as follows: RT a(T ) − VM − b VM (VM + b) + b(VM − b) R2 Tc2 a(T ) = 0.457235 α(T ) Pc
P=
b = 0.077796
RTc Pc
(2) (3)
α(T ) = 1 + k 1 −
T Tc
2 (4)
Table 1 Characteristic properties of R-290 and R-2170 Characteristic property
R-290
R-1270
Chemical formula Molar mass Boiling point, Tb (K) Critical temperature, Tc (K) Critical pressure, Pc (MPa) Critical density, ρc (kg/m3 ) Acentric factor, ω
CH3 CH2 CH3 44.10 231.06 369.85 4.248 220.5 0.1524
CH2 CHCH3 42.08 225.46 365.57 4.665 223.4 0.1408
Source: Database REFPROP 6.01 (1998) [15].
2.3. Experimental procedures Experiments to measure VLE data for the binary mixture R-290 + R-1270 at certain temperature were performed by the following procedures. At first, the system was evacuated to remove all inert gases. A certain amount of R-290 (less volatile than R-1270) was introduced into the cell, and then the temperature of the entire system was maintained by controlling the temperature of water bath system. After desired temperature was achieved, the vapor pressure of the R-290 was measured. Then, a targeted amount of R-1270 was supplied into the cell. Both the dual-head pump and stirrer should be turned on continuously until the equilibrium state of the mixture in the cell was established. As soon as the equilibrium state was confirmed, the compositions of sample and the pressure in the cell were measured. Finally, the vapor pressure of pure R-2170 was measured in the same procedure mentioned above for R-290. The GC was calibrated with pure components of known purity and with mixtures of known compositions that were prepared gravimetrically. The composition uncertainty of composition measurement was
(1)
Fig. 1. Vapor pressures of pure components.
Q.N. Ho et al. / Fluid Phase Equilibria 245 (2006) 63–70
k = 0.37464 + 1.54226ω − 0.26992ω2
(5)
where the parameter ‘a’ is a function of temperature, ‘b’ the constant, k a constant characteristic of each substance, ω the acentric factor, P and Pc (MPa) the absolute and critical pressures, T and Tc (K) the absolute and critical temperatures, Tr the reduced temperature and VM is the molar volume. The Wong–Sandler [10] mixing rule was used in this work to obtain equation of state parameters for a mixture from those of the pure components. Wong and Sandler equated the excess Helmholtz free energy at infinite pressure from an equation of state to the excess Helmholtz free energy from any activity coefficient model, in such a way that a mixing rule is obtained which simultaneously satisfies the quadratic composition dependence of the second virial coefficient but also behaves like an activity coefficient model at high density. This mixing rule for a cubic
65
equation of state can be written as i j xi xj ((b − a)/RT )ij bm = (1 − AE∞ )/CRT − i xi ai /RTbi
(6)
with 1 b−a b−a b−a (1 − kij ) = + RT ij 2 RT i RT j
(7)
and ai AE am = xi + ∞ bm bi C
(8)
i
√ √ where C is a constant equal to ln( 2 − 1)/ 2 for the PR-EOS used in this work and kij is binary interaction parameter. Also, AE∞ is an excess Helmholtz free energy model at infinite pressure
Table 2 Comparisons of pure component vapor pressures at various temperatures T (K)
273.15b 278.15b 283.15b 293.15b 303.15b 313.15b
Propane (R-290)
Propylene (R-1270)
Pv,exp (MPa)
Pv,REF (MPa)
0.4740 0.5508 0.6360 0.8362 1.0776 1.3680
0.4743 0.5510 0.6364 0.8362 1.0787 1.3690
|Pv |a (MPa) 0.0003 0.0002 0.0004 0.0000 0.0011 0.0010
|Pv |/ Pv,exp (%)
Pv,exp (MPa)
Pv,REF (MPa)
0.06 0.04 0.06 0.00 0.10 0.07
0.5860 0.6785 0.7808 1.0190 1.3076 1.6522
0.5859 0.6782 0.7809 1.0199 1.3084 1.6520
|Pv | (MPa) 0.0001 0.0003 0.0001 0.0009 0.0008 0.0002
0.06c 260.93d 277.59d 310.93d 344.26d 360.93d
0.3247 0.5447 1.3031 2.6469 3.6197
0.3204 0.5420 1.3001 2.6430 3.6147
0.0043 0.0027 0.0030 0.0039 0.0050
1.34 0.49 0.23 0.15 0.14
0.4251 1.0335 2.0002
0.4241 1.0308 1.9955
0.0010 0.0027 0.0047
0.23 0.26 0.23
0.3999 0.6660 1.5672 3.1392 4.2830
0.3994 0.6675 1.5708 3.1507 4.2916
0.0005 0.0015 0.0036 0.0115 0.0086
1.3005 1.4757 1.6703 1.8830 2.1166 2.3655 2.6382
1.3001 1.4774 1.6718 1.8844 2.1163 2.3687 2.643
0.0004 0.0017 0.0015 0.0014 0.0003 0.0032 0.0048
0.03 0.12 0.09 0.07 0.02 0.14 0.18
0.5264 1.2466 2.3890
0.5252 1.2515 2.3906
0.0012 0.0049 0.0016
0.4730 0.8360
0.4743 0.8362
−0.0013 −0.0002
0.27 0.02 0.15c
a b c d e f g
Pv = Pv,exp − Pv,REF . This study. Average. Reference [2]. Reference [3]. Reference [5]. Reference [6].
0.23 0.40 0.07 0.23c
1.5694 1.7802 2.0120 2.2597 2.5313 2.8228 3.1350
1.5708 1.7803 2.0096 2.2599 2.5326 2.8289 3.1507
0.0014 0.0001 0.0024 0.0002 0.0013 0.0061 0.0157
0.09c 273.15g 293.15g
0.12 0.22 0.23 0.37 0.20 0.23c
0.24c 310.93f 316.48f 322.04f 327.59f 333.15f 338.71f 344.26f
0.02 0.04 0.01 0.09 0.06 0.01 0.04c
0.47c 269.54e 301.32e 330.32e
|Pv |/ Pv,exp (%)
0.09 0.00 0.12 0.01 0.05 0.22 0.50 0.14c
0.5840 1.0170
0.5859 1.0199
−0.0019 −0.0029
0.33 0.29 0.31c
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Table 3 Comparison of deviations in pressure and in vapor phase compositions between experimental and calculated VLE data for the mixture of R-1270 (1) + R-290 (2) at various temperatures x1,exp
y1,exp
Pexp (MPa)
y1,cal
Pcal (MPa)
P/Pexp (%)a
y1 /y1,exp (%)b
T1 = 273.15 K 0.000 0.092 0.162 0.261 0.355 0.442 0.531 0.657 0.758 0.825 0.917 0.994 1.000
0.000 0.112 0.191 0.299 0.394 0.483 0.568 0.687 0.780 0.840 0.923 0.995 1.000
0.4740 0.4890 0.4985 0.5116 0.5232 0.5338 0.5437 0.5574 0.5675 0.5736 0.5805 0.5856 0.5860
0.000 0.115 0.196 0.307 0.405 0.492 0.577 0.692 0.784 0.843 0.925 0.995 1.000
0.4735 0.4877 0.4978 0.5117 0.5239 0.5345 0.5446 0.5575 0.5668 0.5723 0.5792 0.5844 0.5847
0.10 0.28 0.14 −0.02 −0.14 −0.13 −0.16 −0.02 0.13 0.22 0.22 0.21 0.22
– −2.50 −2.83 −2.85 −2.69 −1.78 −1.48 −0.73 −0.49 −0.30 −0.18 −0.01 0.00
T2 = 278.15 K 0.000 0.049 0.077 0.153 0.233 0.326 0.430 0.528 0.622 0.705 0.799 0.871 0.921 0.960 1.000
0.000 0.060 0.093 0.181 0.270 0.366 0.470 0.566 0.656 0.732 0.817 0.882 0.928 0.964 1.000
0.5508 0.5601 0.5647 0.5765 0.5886 0.6017 0.6155 0.6283 0.6399 0.6493 0.6595 0.6669 0.6717 0.6745 0.6785
0.000 0.061 0.095 0.184 0.274 0.372 0.476 0.571 0.659 0.735 0.820 0.884 0.929 0.964 1.000
0.5501 0.5587 0.5634 0.5760 0.5886 0.6022 0.6164 0.6290 0.6402 0.6494 0.6590 0.6658 0.6704 0.6737 0.6770
0.12 0.25 0.22 0.09 0.01 −0.08 −0.15 −0.11 −0.04 −0.01 0.08 0.16 0.20 0.12 0.22
– −1.66 −1.93 −1.88 −1.59 −1.61 −1.32 −1.01 −0.53 −0.44 −0.38 −0.20 −0.15 0.01 0.00
T3 = 283.15 K 0.000 0.075 0.116 0.170 0.233 0.328 0.424 0.530 0.612 0.703 0.774 0.856 0.914 0.973 1.000
0.000 0.090 0.138 0.199 0.268 0.366 0.463 0.567 0.646 0.732 0.793 0.869 0.923 0.975 1.000
0.6360 0.6518 0.6592 0.6691 0.6801 0.6956 0.7111 0.7268 0.7386 0.7505 0.7590 0.7680 0.7735 0.7787 0.7808
0.000 0.092 0.142 0.204 0.274 0.374 0.470 0.573 0.649 0.732 0.796 0.870 0.922 0.975 1.000
0.6357 0.6505 0.6586 0.6686 0.6801 0.6965 0.7119 0.7277 0.7388 0.7502 0.7583 0.7669 0.7724 0.7775 0.7797
0.05 0.20 0.10 0.07 0.00 −0.12 −0.11 −0.12 −0.03 0.04 0.09 0.15 0.15 0.16 0.14
– −2.78 −2.83 −2.47 −2.24 −2.07 −1.60 −1.09 −0.51 −0.05 −0.30 −0.01 0.10 0.04 0.00
T4 = 293.15 K 0.000 0.037 0.097 0.167 0.259 0.350 0.436 0.518 0.590 0.658 0.709 0.772 0.838 0.902
0.000 0.046 0.118 0.198 0.298 0.388 0.474 0.554 0.627 0.688 0.738 0.792 0.854 0.911
0.8362 0.8474 0.8612 0.8761 0.8949 0.9132 0.9309 0.9466 0.9604 0.9725 0.9815 0.9910 1.0005 1.0082
0.000 0.045 0.116 0.197 0.297 0.392 0.479 0.559 0.627 0.690 0.737 0.793 0.854 0.911
0.8360 0.8448 0.8590 0.8752 0.8956 0.9148 0.9322 0.9478 0.9606 0.9721 0.9803 0.9898 0.9992 1.0076
0.02 0.31 0.26 0.11 −0.07 −0.18 −0.14 −0.12 −0.02 0.04 0.12 0.12 0.13 0.06
– 2.18 1.11 0.46 0.10 −1.11 −1.16 −0.85 0.10 −0.17 0.20 −0.20 0.02 0.01
Q.N. Ho et al. / Fluid Phase Equilibria 245 (2006) 63–70
67
Table 3 (Continued ) x1,exp
y1,exp
Pexp (MPa)
y1,cal
Pcal (MPa)
P/Pexp (%)a
0.951 1.000
0.956 1.000
1.0139 1.0190
0.955 1.000
1.0136 1.0192
0.03 −0.02
0.05 0.00
T3 = 303.15 K 0.000 0.037 0.104 0.169 0.232 0.283 0.358 0.432 0.511 0.587 0.681 0.765 0.838 0.905 1.000
0.000 0.045 0.124 0.198 0.266 0.318 0.396 0.472 0.550 0.622 0.708 0.785 0.853 0.912 1.000
1.0776 1.0891 1.1074 1.1253 1.1415 1.1544 1.1738 1.1924 1.2118 1.2290 1.2503 1.2678 1.2818 1.293 1.3076
0.000 0.044 0.121 0.195 0.264 0.318 0.397 0.472 0.550 0.622 0.710 0.787 0.854 0.914 1.000
1.0798 1.0896 1.1072 1.1247 1.1414 1.1546 1.1740 1.1927 1.2119 1.2294 1.2500 1.2673 1.2815 1.2935 1.3092
−0.20 −0.05 0.01 0.06 0.01 −0.02 −0.02 −0.02 0.00 −0.03 0.03 0.04 0.03 −0.04 −0.12
– 2.00 2.11 1.62 0.53 −0.13 −0.15 −0.04 0.00 −0.10 −0.20 −0.27 −0.12 −0.25 0.00
T4 = 313.15 K 0.000 0.050 0.120 0.204 0.293 0.366 0.429 0.517 0.615 0.678 0.754 0.817 0.875 0.930 0.956 1.000
0.000 0.059 0.138 0.231 0.320 0.397 0.463 0.550 0.645 0.703 0.772 0.830 0.884 0.935 0.960 1.000
1.3680 1.3857 1.4098 1.4377 1.4672 1.4890 1.5094 1.5366 1.5640 1.5811 1.6000 1.6150 1.6289 1.6407 1.6465 1.6522
0.000 0.058 0.138 0.232 0.328 0.404 0.469 0.555 0.647 0.706 0.776 0.834 0.886 0.936 0.960 1.000
1.3725 1.3876 1.4096 1.4371 1.4663 1.4897 1.5099 1.5365 1.5641 1.5809 1.6001 1.6154 1.6285 1.6407 1.6465 1.6558
−0.33 −0.14 0.02 0.04 0.06 −0.05 −0.03 0.01 0.00 0.02 −0.01 −0.02 0.03 0.00 0.00 −0.22
– 2.36 0.65 −0.39 −2.72 −1.76 −1.30 −0.84 −0.42 −0.33 −0.49 −0.47 −0.24 −0.10 −0.04 0.00
a b
y1 /y1,exp (%)b
P = Pexp − Pcal . y1 = y1,exp − y1,cal .
which can be equated to a low-pressure excess Gibbs free energy [13]. In this study we use the NRTL model [14] given by
AE∞ j xj Gji τji = xi RT r xr Gri
(9)
i
and τji =
N
1 Objective function = N i=1
|Pi,exp − Pi,cal | Pi,exp
2 100
(11)
where N is the number of experimental points and Pexp and Pcal are experimental and calculated pressures.
with Gji = exp(−αji τji )
function:
Aji RT
(10)
where Gji is the local composition factor for the NRTL model, τ ji the NRTL model binary interaction parameter, Aji = gji − gii , where gji is interaction energy between an i–j pair of molecules, αji a non-randomness parameter and R is the universal gas constant (8.314 J K−1 mol−1 ). The critical properties (Tc and Pc ) and acentric factors (ω) of R-290 and R-1270 used to calculate the parameters for the PR-EOS are summarized in Table 1. We have set the non-randomness parameter, αij , equal to 0.3 for the binary mixture investigated here. The parameters of these equations were obtained by minimizing the following objective
4. Results and discussion 4.1. Saturated vapor pressures of pure compounds The experimental vapor pressures (Pv ) of pure R-290 and R-1270 measured at 273.15, 278.15, 283.15, 293.15, 303.15 and 313.15 K in this study and other published data at different temperatures are presented in Fig. 1. The comparisons of these values with the calculations obtained from database REFPROP 6.01 [15] are illustrated in Table 2. It is found that the absolute deviations of vapor pressure (Pv ) between experimental and cited data are within ±0.001 MPa for both R-290 and R-1270 and the average absolute deviations (AAD%–Pv )
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Q.N. Ho et al. / Fluid Phase Equilibria 245 (2006) 63–70
are 0.04% for R-1270 and 0.06% for R-290. In the same temperatures we investigated, particularly at 273.15 and 293.15 K, some data were also reported by Noda et al. [6]. However, the values of AAD%–Pv for these data are somewhat higher than those of our experimental data: 0.15% for R-290 and 0.31% for R-1270. For the vapor pressure data from 100 to 160 ◦ F (310.93–344.26 K) reported by Laurance and Swift [5], the average deviations in vapor pressure are rather small, about 0.09 and 0.14% for propane and propylene, respectively. In case of the published values introduced by Reamer and Sage [2] and Hanson et al. [3], it is found that the values of AAD%–Pv both R-1270 and R-290 are higher than 0.23%. Generally, all values are rather low and acceptable. 4.2. Vapor–liquid equilibria of the binary mixture The measured and calculated VLE data for the binary mixture R-1270 (1) + R-290 (2) at 273.15, 278.15, 283.15, 293.15, 303.15 and 313.15 K as well as their deviations in pressure and in vapor phase compositions are presented in Table 3. The results of correlation including all the values of determined k12 , NRTL parameters (τ 12 and τ 12 ) and the average absolute percentage deviations in pressure and in vapor phase compositions (AAD%–P and AAD%–y) between calculated and experimental data for this binary mixture are reported in Table 4. The P–x–y diagrams for this system are shown in Fig. 2 where the experimental data are presented as symbols and the dashed lines represent the calculated values by PR-EOS. Both experimental and calculated diagrams clearly indicated that the azeotropic behavior was not found in this mixture over range of temperature studied here. The deviations in vapor phase composition and in pressure of the calculated data compared with experimental values at each point are shown in Figs. 3 and 4. From the results summarized in Table 4, it was found that in the temperature range between 273.15 and 313.15 K, the values of AAD%–P varied within 0.06–0.15%; meanwhile, the values of AAD%–y varied within 0.51–1.3%. Generally, all values are relatively small and acceptable. In other way, the data calculated by using PR-EOS combined with the Wong–Sandler mixing rule are in good agreement with the experimental data.
Fig. 2. P–x–y diagram for the mixture of R-1270 (1) + R-290 (2) at various temperatures.
As we mentioned in Section 1, the vapor–liquid equilibria data for the binary mixture of R-1270 + R-290 at various temperatures were previously reported by some authors [2–8]. However, some of them were reported as isobaric data without temperatures by Mann et al. [4] or as calculated data by Harmens [7] and Eubank et al. [8]. Laurance and Swift [5] and Noda et al. [6] reported experimental isothermal VLE data for this mixture but not including measured vapor phase composition. Only actually measured isothermal VLE data introduced by Reamer and Sage [2] for 10, 40, 100, 160 and 190 ◦ F and by Hanson et al. [3] for 25.5, 82.7 and 134.9 ◦ F are concerned. The average absolute percentage deviations in
Table 4 Interaction parameters k12 , NRTL parameters (τ 12 and τ 21 ), average absolute deviations in pressures (AAD%–P) and in vapor phase composition (AAD%–y) T (K)
k12
τ 12
τ 21
AAD%–Pa
AAD%–yb
273.15 278.15 283.15 293.15 303.15 313.15
0.06497 −0.00651 0.06546 0.06561 0.07347 0.17985
0.29532 −0.04485 0.30697 0.34273 0.37903 −0.27589
−0.31633 0.20684 −0.33060 −0.38285 −0.46805 −0.22214
0.15 0.13 0.10 0.11 0.05 0.06
1.30 0.91 1.15 0.51 0.54 0.81
a b
Pexp,i −Pcal,i . P exp,i y −ycal,i N AAD% − y = N1 100 exp,i . yexp,i i=1 AAD% − P =
1 N
N
100 i=1
Q.N. Ho et al. / Fluid Phase Equilibria 245 (2006) 63–70
69
Table 5 Deviations of published data to the PR-EOS for the binary mixture of R1270 + R-290 at various temperatures T (K)
Number of experimental points
AAD%–P
AAD%–y
260.93a 277.59a 310.93a 344.26a 360.93a 269.54b 301.32b 330.32b
8 7 4 4 4 6 4 5
0.21 0.13 0.02 0.02 0.13 0.33 0.01 0.03
1.11 1.02 1.23 2.65 1.18 0.63 0.83 0.97
a b
Reference [2]. Reference [3].
from the mixture of propane + propylene by distillation due to the very close distance between dew-point curve and bubblepoint curve. Fig. 3. Deviations in pressure between experimental and calculated for the mixture of R-1270 (1) + R-290 (2) at various temperatures.
pressure and in vapor phase compositions between calculated and these experimental data for this binary mixture are summarized in Table 5. It indicates that the values of AAD%–P and AAD%–y vary within 0.02–0.21 and 1.02–2.56% for Reamer et al.’s data; meanwhile; these values for Hanson et al.’s data vary within 0.01–0.33 and 0.63–0.97%. All of them are small and acceptable. However, just few experimental points measured at several temperatures are not enough to obtain the reliable binary interaction parameter, kij . Based on the P–x–y diagram in Fig. 2, it could be realized that it is really difficult to produce high purity propane (or propylene)
5. Conclusions Measurements of the vapor–liquid equilibria for the binary mixture R-290 + R-1270 at 273.15, 278.15, 283.15, 293.15, 303.15 and 313.15 K were carried out by using a circulationtype equilibrium apparatus and 90 isothermal VLE data for this mixture were reported in detail in this paper. It was confirmed that this mixture did not exhibit azeotropic behavior in the studied temperature range. The experimental and published isothermal VLE data were correlated with the PR-EOS combined with the Wong–Sandler mixing rule and good agreements between calculated and experimental data were confirmed. The result means that the model equation used in this study can be used to estimate the thermodynamic properties of the binary mixture R-1270 + R-290 in the range of temperature from 273.15 to 313.15 K. It could be also used for other ranges but additional experiments are necessary to confirm that. List of symbols x mole fraction in liquid phase y mole fraction in vapor phase Greek letters α(T) temperature dependent α12 non-randomless parameter , ␦ change in a quantity ω acentric factor
Fig. 4. Deviations in vapor phase composition between experimental and calculated data for the mixture of R-1270 (1) + R-290 (2) at various temperatures.
Subscripts Ave. average c critical property cal. calculated exp. experimental i, j ith and jth components of the mixture m mixture v vapor phase
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References [1] E. Aisbeet, T. Pham, Seminar on Environment and Development in Vietnam National Center for Development Studies, December 6–7, Australian National University, 1996. [2] H.H. Reamer, B.H. Sage, Ind. Eng. Chem. 43 (1951) 1628–1634. [3] G.H. Hanson, R.J. Hogan, W.T. Nelson, M.R. Cines, Ind. Eng. Chem. 44 (1952) 604–608. [4] A.N. Mann, W.A. Pardee, R.W. Smyth, Chem. Eng. Data J. 8 (4) (1963) 499–502. [5] D.R. Laurance, G.W. Swift, Chem. Eng. Data J. 17 (1972) 333–337. [6] K. Noda, M. Sakai, K. Ishida, Chem. Eng. Data J. 27 (1982) 32–34. [7] A. Harmens, Chem. Eng. Data J. 30 (2) (1985) 230–233.
[8] P.T. Eubank, M.A. Barrufet, H. Duarte-Garza, L. Yurttas, Fluid Phase Equilib. 52 (1989) 219–227. [9] D.Y. Peng, D.B. Robinson, Ind. Eng. Chem. Fundam. 15 (1976) 59–64. [10] D.S.H. Wong, S.I. Sandler, AIChE J. 38 (1992) 671–680. [11] J.S. Lim, Q.N. Ho, J.Y. Park, B.G. Lee, Chem. Eng. Data J. 49 (2004) 192–198. [12] Q.N. Ho, B.G. Lee, J.Y. Park, J.D. Kim, J.S. Lim, Fluid Phase Equilib. 225 (2004) 125–132. [13] D.S.H. Wong, H. Orbey, S.I. Sandler, Ind. Eng. Chem. Res. 31 (1992) 2033–2039. [14] H. Renon, J.M. Prausnitz, AIChE J. 14 (1968) 135–144. [15] M.O. McLinden, S.A. Klein, E.W. Lemmon, A.P. Peskin, REFPROP V.6.01, NIST, 1998.
Measurement of vapor–liquid equilibria for the binary mixture of propylene (R-1270) + propane (R-290) Quang Nhu Ho a , Kye Sang Yoo a , Byung Gwon Lee a,∗ , Jong Sung Lim b a
Division of Environment and Process Technology, Korea Institute of Science and Technology (KIST), P.O. Box 131, Cheongryang, Seoul 130-650, South Korea b Department of Chemical and Biomolecular Engineering, Sogang University, P.O. Box 1142, Seoul 100-611, South Korea Received 12 September 2005; received in revised form 19 March 2006; accepted 20 March 2006 Available online 27 March 2006
Abstract Isothermal vapor–liquid equilibria data for the binary mixture of propylene (R-1270) + propane (R-290) at 273.15, 278.15, 283.15, 293.15, 303.15 and 313.15 K were measured by using a circulation-type equilibrium apparatus. The experimental data were correlated with the Peng–Robinson equation of state (PR-EOS) combined with the Wong–Sandler mixing rule. It is confirmed that the data calculated by this equations of state are in good agreement with experimental data. The azeotropic behavior was not found in this mixture over range of temperature studied here. © 2006 Published by Elsevier B.V. Keywords: Propane (R-290); Propylene (R-1270); Hydrocarbon mixture; Vapor–liquid equilibria (VLE); Peng–Robinson equation of state (PR-EOS)
1. Introduction Much effort has been made to find the suitable replacement for CFCs and HCHCs due to their high ozone depletion potentials (ODPs) and global warming potentials (GWPs). In recent years, the utilization of light hydrocarbons, such as propane, butane, propylene, etc., as effective refrigerants is believed as an alternative solution because these hydrocarbons are rather cheap, plentiful and environmentally benign chemicals (zero ODPs and near zero GWPs) and have many outstanding properties. Even though flammability of these materials has caused some concerns, but it was found that hydrocarbons are quite safe in small applications such as domestic refrigeration and car air-conditioning, due to very small amounts involved [1]. For the binary mixture of propylene (R-1270) + propane (R290), vapor–liquid equilibria (VLE) data at various temperatures were previously reported by some authors [2–8]. However, some of them were not in detail. In this work, isothermal vapor–liquid equilibria data for the binary mixture of propylene (R1270) + propane (R-290), which are very important basic information in evaluating the performance refrigeration cycles and
in determining optimal composition of this mixture, were measured at 273.15, 278.15, 283.15, 293.15, 303.15 and 313.15 K by using a circulation-type equilibrium apparatus. The experimental data were correlated with the Peng–Robinson [9] equation of state (PR-EOS) combined with the Wong–Sandler [10] mixing rule. The interaction parameters and average deviations in pressures and in vapor phase compositions obtained from this correlation were presented. The deviations of other published data to the equation of state above are also reported in this paper. 2. Experimental 2.1. Chemicals High-grade chemicals of propane and propylene were used for this investigation. Propylene of purity higher than 99.5% by mass was supplied by Conley Gas Ltd., U.S.A. Propane produced by M.G. Industries, U.S.A., had purity higher than 99.8 mass%. The purity of each chemical was validated by using gas chromatograph. 2.2. Vapor–liquid equilibrium apparatus
∗
Corresponding author. Tel.: +82 2 958 5857. E-mail address: [email protected] (B.G. Lee).
0378-3812/$ – see front matter © 2006 Published by Elsevier B.V. doi:10.1016/j.fluid.2006.03.009
The vapor–liquid equilibrium apparatus used in this work was a circulation-type one in which both liquid and vapor phases
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were continuously recirculated. Description of the experimental apparatus has been reported in our previous work [11,12] and is only briefly discussed here. The equilibrium cell was a 316 stainless steel with an inner volume of about 85 mL. A pair of Pyrex glass windows was installed on two sides of the cell to observe the inside during operation. Inside the cell, a stirring bar rotated at variable speeds was used to accelerate the attainment of the equilibrium state and to reduce concentration gradients in both phases. The temperature of the equilibrium cell in the bath was maintained by a bath circulator (RCB-20, Jeio Tech, Korea). The temperature in the cell was measured with a platinum resistance sensor connected to a digital temperature indicator (F250 precision thermometer, Automatic Systems Laboratories Ltd., UK). They were calibrated by NAMAS accredited calibration laboratory. The total error is estimated to be within ±0.02 K, including sensor uncertainty, ±0.01 K, temperature resolution, ±0.001 K, and measurement uncertainty, ±0.001 K. The pressure was measured with a pressure transducer (model XPM60) and digital pressure calibrator indicator (C106 model, Beamax, Finland). Pressure calibrations are traceable to national standards (Center for Metrology and Accreditation Certificate Nos. M-95P077 dated 14 November 1995, M-M730 dated 16 November 1995 and M-95P078 dated 16 November 1995), and total errors were estimated to be within ±1 kPa, including calibrator uncertainty, ±0.5 kPa, sensor uncertainty, ±0.1 kPa, and measurement uncertainty, ±0.1 kPa. The vapor and liquid phases in the equilibrium cell were continuously recirculated by a dual-head circulation pump (Milton Roy Co., U.S.A.). After equilibrium was reached, the vapor and liquid samples were withdrawn from the recycling loop and injected on-line into a gas chromatograph (Gow-Mac model 550P) equipped with a thermal conductivity detector (TCD) and an Unibead 2S column (Altech Co.). The signals from GC were processed and converted to data by D520B computing integrator (Young In Co., Korea).
estimated within ±0.002 mole fraction for both liquid and vapor phases. 3. Correlation In this work, the experimental VLE data were correlated with the Peng–Robinson [9] equation of state combined with the Wong–Sandler mixing rule. The Peng–Robinson equation of state is expressed as follows: RT a(T ) − VM − b VM (VM + b) + b(VM − b) R2 Tc2 a(T ) = 0.457235 α(T ) Pc
P=
b = 0.077796
RTc Pc
(2) (3)
α(T ) = 1 + k 1 −
T Tc
2 (4)
Table 1 Characteristic properties of R-290 and R-2170 Characteristic property
R-290
R-1270
Chemical formula Molar mass Boiling point, Tb (K) Critical temperature, Tc (K) Critical pressure, Pc (MPa) Critical density, ρc (kg/m3 ) Acentric factor, ω
CH3 CH2 CH3 44.10 231.06 369.85 4.248 220.5 0.1524
CH2 CHCH3 42.08 225.46 365.57 4.665 223.4 0.1408
Source: Database REFPROP 6.01 (1998) [15].
2.3. Experimental procedures Experiments to measure VLE data for the binary mixture R-290 + R-1270 at certain temperature were performed by the following procedures. At first, the system was evacuated to remove all inert gases. A certain amount of R-290 (less volatile than R-1270) was introduced into the cell, and then the temperature of the entire system was maintained by controlling the temperature of water bath system. After desired temperature was achieved, the vapor pressure of the R-290 was measured. Then, a targeted amount of R-1270 was supplied into the cell. Both the dual-head pump and stirrer should be turned on continuously until the equilibrium state of the mixture in the cell was established. As soon as the equilibrium state was confirmed, the compositions of sample and the pressure in the cell were measured. Finally, the vapor pressure of pure R-2170 was measured in the same procedure mentioned above for R-290. The GC was calibrated with pure components of known purity and with mixtures of known compositions that were prepared gravimetrically. The composition uncertainty of composition measurement was
(1)
Fig. 1. Vapor pressures of pure components.
Q.N. Ho et al. / Fluid Phase Equilibria 245 (2006) 63–70
k = 0.37464 + 1.54226ω − 0.26992ω2
(5)
where the parameter ‘a’ is a function of temperature, ‘b’ the constant, k a constant characteristic of each substance, ω the acentric factor, P and Pc (MPa) the absolute and critical pressures, T and Tc (K) the absolute and critical temperatures, Tr the reduced temperature and VM is the molar volume. The Wong–Sandler [10] mixing rule was used in this work to obtain equation of state parameters for a mixture from those of the pure components. Wong and Sandler equated the excess Helmholtz free energy at infinite pressure from an equation of state to the excess Helmholtz free energy from any activity coefficient model, in such a way that a mixing rule is obtained which simultaneously satisfies the quadratic composition dependence of the second virial coefficient but also behaves like an activity coefficient model at high density. This mixing rule for a cubic
65
equation of state can be written as i j xi xj ((b − a)/RT )ij bm = (1 − AE∞ )/CRT − i xi ai /RTbi
(6)
with 1 b−a b−a b−a (1 − kij ) = + RT ij 2 RT i RT j
(7)
and ai AE am = xi + ∞ bm bi C
(8)
i
√ √ where C is a constant equal to ln( 2 − 1)/ 2 for the PR-EOS used in this work and kij is binary interaction parameter. Also, AE∞ is an excess Helmholtz free energy model at infinite pressure
Table 2 Comparisons of pure component vapor pressures at various temperatures T (K)
273.15b 278.15b 283.15b 293.15b 303.15b 313.15b
Propane (R-290)
Propylene (R-1270)
Pv,exp (MPa)
Pv,REF (MPa)
0.4740 0.5508 0.6360 0.8362 1.0776 1.3680
0.4743 0.5510 0.6364 0.8362 1.0787 1.3690
|Pv |a (MPa) 0.0003 0.0002 0.0004 0.0000 0.0011 0.0010
|Pv |/ Pv,exp (%)
Pv,exp (MPa)
Pv,REF (MPa)
0.06 0.04 0.06 0.00 0.10 0.07
0.5860 0.6785 0.7808 1.0190 1.3076 1.6522
0.5859 0.6782 0.7809 1.0199 1.3084 1.6520
|Pv | (MPa) 0.0001 0.0003 0.0001 0.0009 0.0008 0.0002
0.06c 260.93d 277.59d 310.93d 344.26d 360.93d
0.3247 0.5447 1.3031 2.6469 3.6197
0.3204 0.5420 1.3001 2.6430 3.6147
0.0043 0.0027 0.0030 0.0039 0.0050
1.34 0.49 0.23 0.15 0.14
0.4251 1.0335 2.0002
0.4241 1.0308 1.9955
0.0010 0.0027 0.0047
0.23 0.26 0.23
0.3999 0.6660 1.5672 3.1392 4.2830
0.3994 0.6675 1.5708 3.1507 4.2916
0.0005 0.0015 0.0036 0.0115 0.0086
1.3005 1.4757 1.6703 1.8830 2.1166 2.3655 2.6382
1.3001 1.4774 1.6718 1.8844 2.1163 2.3687 2.643
0.0004 0.0017 0.0015 0.0014 0.0003 0.0032 0.0048
0.03 0.12 0.09 0.07 0.02 0.14 0.18
0.5264 1.2466 2.3890
0.5252 1.2515 2.3906
0.0012 0.0049 0.0016
0.4730 0.8360
0.4743 0.8362
−0.0013 −0.0002
0.27 0.02 0.15c
a b c d e f g
Pv = Pv,exp − Pv,REF . This study. Average. Reference [2]. Reference [3]. Reference [5]. Reference [6].
0.23 0.40 0.07 0.23c
1.5694 1.7802 2.0120 2.2597 2.5313 2.8228 3.1350
1.5708 1.7803 2.0096 2.2599 2.5326 2.8289 3.1507
0.0014 0.0001 0.0024 0.0002 0.0013 0.0061 0.0157
0.09c 273.15g 293.15g
0.12 0.22 0.23 0.37 0.20 0.23c
0.24c 310.93f 316.48f 322.04f 327.59f 333.15f 338.71f 344.26f
0.02 0.04 0.01 0.09 0.06 0.01 0.04c
0.47c 269.54e 301.32e 330.32e
|Pv |/ Pv,exp (%)
0.09 0.00 0.12 0.01 0.05 0.22 0.50 0.14c
0.5840 1.0170
0.5859 1.0199
−0.0019 −0.0029
0.33 0.29 0.31c
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Table 3 Comparison of deviations in pressure and in vapor phase compositions between experimental and calculated VLE data for the mixture of R-1270 (1) + R-290 (2) at various temperatures x1,exp
y1,exp
Pexp (MPa)
y1,cal
Pcal (MPa)
P/Pexp (%)a
y1 /y1,exp (%)b
T1 = 273.15 K 0.000 0.092 0.162 0.261 0.355 0.442 0.531 0.657 0.758 0.825 0.917 0.994 1.000
0.000 0.112 0.191 0.299 0.394 0.483 0.568 0.687 0.780 0.840 0.923 0.995 1.000
0.4740 0.4890 0.4985 0.5116 0.5232 0.5338 0.5437 0.5574 0.5675 0.5736 0.5805 0.5856 0.5860
0.000 0.115 0.196 0.307 0.405 0.492 0.577 0.692 0.784 0.843 0.925 0.995 1.000
0.4735 0.4877 0.4978 0.5117 0.5239 0.5345 0.5446 0.5575 0.5668 0.5723 0.5792 0.5844 0.5847
0.10 0.28 0.14 −0.02 −0.14 −0.13 −0.16 −0.02 0.13 0.22 0.22 0.21 0.22
– −2.50 −2.83 −2.85 −2.69 −1.78 −1.48 −0.73 −0.49 −0.30 −0.18 −0.01 0.00
T2 = 278.15 K 0.000 0.049 0.077 0.153 0.233 0.326 0.430 0.528 0.622 0.705 0.799 0.871 0.921 0.960 1.000
0.000 0.060 0.093 0.181 0.270 0.366 0.470 0.566 0.656 0.732 0.817 0.882 0.928 0.964 1.000
0.5508 0.5601 0.5647 0.5765 0.5886 0.6017 0.6155 0.6283 0.6399 0.6493 0.6595 0.6669 0.6717 0.6745 0.6785
0.000 0.061 0.095 0.184 0.274 0.372 0.476 0.571 0.659 0.735 0.820 0.884 0.929 0.964 1.000
0.5501 0.5587 0.5634 0.5760 0.5886 0.6022 0.6164 0.6290 0.6402 0.6494 0.6590 0.6658 0.6704 0.6737 0.6770
0.12 0.25 0.22 0.09 0.01 −0.08 −0.15 −0.11 −0.04 −0.01 0.08 0.16 0.20 0.12 0.22
– −1.66 −1.93 −1.88 −1.59 −1.61 −1.32 −1.01 −0.53 −0.44 −0.38 −0.20 −0.15 0.01 0.00
T3 = 283.15 K 0.000 0.075 0.116 0.170 0.233 0.328 0.424 0.530 0.612 0.703 0.774 0.856 0.914 0.973 1.000
0.000 0.090 0.138 0.199 0.268 0.366 0.463 0.567 0.646 0.732 0.793 0.869 0.923 0.975 1.000
0.6360 0.6518 0.6592 0.6691 0.6801 0.6956 0.7111 0.7268 0.7386 0.7505 0.7590 0.7680 0.7735 0.7787 0.7808
0.000 0.092 0.142 0.204 0.274 0.374 0.470 0.573 0.649 0.732 0.796 0.870 0.922 0.975 1.000
0.6357 0.6505 0.6586 0.6686 0.6801 0.6965 0.7119 0.7277 0.7388 0.7502 0.7583 0.7669 0.7724 0.7775 0.7797
0.05 0.20 0.10 0.07 0.00 −0.12 −0.11 −0.12 −0.03 0.04 0.09 0.15 0.15 0.16 0.14
– −2.78 −2.83 −2.47 −2.24 −2.07 −1.60 −1.09 −0.51 −0.05 −0.30 −0.01 0.10 0.04 0.00
T4 = 293.15 K 0.000 0.037 0.097 0.167 0.259 0.350 0.436 0.518 0.590 0.658 0.709 0.772 0.838 0.902
0.000 0.046 0.118 0.198 0.298 0.388 0.474 0.554 0.627 0.688 0.738 0.792 0.854 0.911
0.8362 0.8474 0.8612 0.8761 0.8949 0.9132 0.9309 0.9466 0.9604 0.9725 0.9815 0.9910 1.0005 1.0082
0.000 0.045 0.116 0.197 0.297 0.392 0.479 0.559 0.627 0.690 0.737 0.793 0.854 0.911
0.8360 0.8448 0.8590 0.8752 0.8956 0.9148 0.9322 0.9478 0.9606 0.9721 0.9803 0.9898 0.9992 1.0076
0.02 0.31 0.26 0.11 −0.07 −0.18 −0.14 −0.12 −0.02 0.04 0.12 0.12 0.13 0.06
– 2.18 1.11 0.46 0.10 −1.11 −1.16 −0.85 0.10 −0.17 0.20 −0.20 0.02 0.01
Q.N. Ho et al. / Fluid Phase Equilibria 245 (2006) 63–70
67
Table 3 (Continued ) x1,exp
y1,exp
Pexp (MPa)
y1,cal
Pcal (MPa)
P/Pexp (%)a
0.951 1.000
0.956 1.000
1.0139 1.0190
0.955 1.000
1.0136 1.0192
0.03 −0.02
0.05 0.00
T3 = 303.15 K 0.000 0.037 0.104 0.169 0.232 0.283 0.358 0.432 0.511 0.587 0.681 0.765 0.838 0.905 1.000
0.000 0.045 0.124 0.198 0.266 0.318 0.396 0.472 0.550 0.622 0.708 0.785 0.853 0.912 1.000
1.0776 1.0891 1.1074 1.1253 1.1415 1.1544 1.1738 1.1924 1.2118 1.2290 1.2503 1.2678 1.2818 1.293 1.3076
0.000 0.044 0.121 0.195 0.264 0.318 0.397 0.472 0.550 0.622 0.710 0.787 0.854 0.914 1.000
1.0798 1.0896 1.1072 1.1247 1.1414 1.1546 1.1740 1.1927 1.2119 1.2294 1.2500 1.2673 1.2815 1.2935 1.3092
−0.20 −0.05 0.01 0.06 0.01 −0.02 −0.02 −0.02 0.00 −0.03 0.03 0.04 0.03 −0.04 −0.12
– 2.00 2.11 1.62 0.53 −0.13 −0.15 −0.04 0.00 −0.10 −0.20 −0.27 −0.12 −0.25 0.00
T4 = 313.15 K 0.000 0.050 0.120 0.204 0.293 0.366 0.429 0.517 0.615 0.678 0.754 0.817 0.875 0.930 0.956 1.000
0.000 0.059 0.138 0.231 0.320 0.397 0.463 0.550 0.645 0.703 0.772 0.830 0.884 0.935 0.960 1.000
1.3680 1.3857 1.4098 1.4377 1.4672 1.4890 1.5094 1.5366 1.5640 1.5811 1.6000 1.6150 1.6289 1.6407 1.6465 1.6522
0.000 0.058 0.138 0.232 0.328 0.404 0.469 0.555 0.647 0.706 0.776 0.834 0.886 0.936 0.960 1.000
1.3725 1.3876 1.4096 1.4371 1.4663 1.4897 1.5099 1.5365 1.5641 1.5809 1.6001 1.6154 1.6285 1.6407 1.6465 1.6558
−0.33 −0.14 0.02 0.04 0.06 −0.05 −0.03 0.01 0.00 0.02 −0.01 −0.02 0.03 0.00 0.00 −0.22
– 2.36 0.65 −0.39 −2.72 −1.76 −1.30 −0.84 −0.42 −0.33 −0.49 −0.47 −0.24 −0.10 −0.04 0.00
a b
y1 /y1,exp (%)b
P = Pexp − Pcal . y1 = y1,exp − y1,cal .
which can be equated to a low-pressure excess Gibbs free energy [13]. In this study we use the NRTL model [14] given by
AE∞ j xj Gji τji = xi RT r xr Gri
(9)
i
and τji =
N
1 Objective function = N i=1
|Pi,exp − Pi,cal | Pi,exp
2 100
(11)
where N is the number of experimental points and Pexp and Pcal are experimental and calculated pressures.
with Gji = exp(−αji τji )
function:
Aji RT
(10)
where Gji is the local composition factor for the NRTL model, τ ji the NRTL model binary interaction parameter, Aji = gji − gii , where gji is interaction energy between an i–j pair of molecules, αji a non-randomness parameter and R is the universal gas constant (8.314 J K−1 mol−1 ). The critical properties (Tc and Pc ) and acentric factors (ω) of R-290 and R-1270 used to calculate the parameters for the PR-EOS are summarized in Table 1. We have set the non-randomness parameter, αij , equal to 0.3 for the binary mixture investigated here. The parameters of these equations were obtained by minimizing the following objective
4. Results and discussion 4.1. Saturated vapor pressures of pure compounds The experimental vapor pressures (Pv ) of pure R-290 and R-1270 measured at 273.15, 278.15, 283.15, 293.15, 303.15 and 313.15 K in this study and other published data at different temperatures are presented in Fig. 1. The comparisons of these values with the calculations obtained from database REFPROP 6.01 [15] are illustrated in Table 2. It is found that the absolute deviations of vapor pressure (Pv ) between experimental and cited data are within ±0.001 MPa for both R-290 and R-1270 and the average absolute deviations (AAD%–Pv )
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Q.N. Ho et al. / Fluid Phase Equilibria 245 (2006) 63–70
are 0.04% for R-1270 and 0.06% for R-290. In the same temperatures we investigated, particularly at 273.15 and 293.15 K, some data were also reported by Noda et al. [6]. However, the values of AAD%–Pv for these data are somewhat higher than those of our experimental data: 0.15% for R-290 and 0.31% for R-1270. For the vapor pressure data from 100 to 160 ◦ F (310.93–344.26 K) reported by Laurance and Swift [5], the average deviations in vapor pressure are rather small, about 0.09 and 0.14% for propane and propylene, respectively. In case of the published values introduced by Reamer and Sage [2] and Hanson et al. [3], it is found that the values of AAD%–Pv both R-1270 and R-290 are higher than 0.23%. Generally, all values are rather low and acceptable. 4.2. Vapor–liquid equilibria of the binary mixture The measured and calculated VLE data for the binary mixture R-1270 (1) + R-290 (2) at 273.15, 278.15, 283.15, 293.15, 303.15 and 313.15 K as well as their deviations in pressure and in vapor phase compositions are presented in Table 3. The results of correlation including all the values of determined k12 , NRTL parameters (τ 12 and τ 12 ) and the average absolute percentage deviations in pressure and in vapor phase compositions (AAD%–P and AAD%–y) between calculated and experimental data for this binary mixture are reported in Table 4. The P–x–y diagrams for this system are shown in Fig. 2 where the experimental data are presented as symbols and the dashed lines represent the calculated values by PR-EOS. Both experimental and calculated diagrams clearly indicated that the azeotropic behavior was not found in this mixture over range of temperature studied here. The deviations in vapor phase composition and in pressure of the calculated data compared with experimental values at each point are shown in Figs. 3 and 4. From the results summarized in Table 4, it was found that in the temperature range between 273.15 and 313.15 K, the values of AAD%–P varied within 0.06–0.15%; meanwhile, the values of AAD%–y varied within 0.51–1.3%. Generally, all values are relatively small and acceptable. In other way, the data calculated by using PR-EOS combined with the Wong–Sandler mixing rule are in good agreement with the experimental data.
Fig. 2. P–x–y diagram for the mixture of R-1270 (1) + R-290 (2) at various temperatures.
As we mentioned in Section 1, the vapor–liquid equilibria data for the binary mixture of R-1270 + R-290 at various temperatures were previously reported by some authors [2–8]. However, some of them were reported as isobaric data without temperatures by Mann et al. [4] or as calculated data by Harmens [7] and Eubank et al. [8]. Laurance and Swift [5] and Noda et al. [6] reported experimental isothermal VLE data for this mixture but not including measured vapor phase composition. Only actually measured isothermal VLE data introduced by Reamer and Sage [2] for 10, 40, 100, 160 and 190 ◦ F and by Hanson et al. [3] for 25.5, 82.7 and 134.9 ◦ F are concerned. The average absolute percentage deviations in
Table 4 Interaction parameters k12 , NRTL parameters (τ 12 and τ 21 ), average absolute deviations in pressures (AAD%–P) and in vapor phase composition (AAD%–y) T (K)
k12
τ 12
τ 21
AAD%–Pa
AAD%–yb
273.15 278.15 283.15 293.15 303.15 313.15
0.06497 −0.00651 0.06546 0.06561 0.07347 0.17985
0.29532 −0.04485 0.30697 0.34273 0.37903 −0.27589
−0.31633 0.20684 −0.33060 −0.38285 −0.46805 −0.22214
0.15 0.13 0.10 0.11 0.05 0.06
1.30 0.91 1.15 0.51 0.54 0.81
a b
Pexp,i −Pcal,i . P exp,i y −ycal,i N AAD% − y = N1 100 exp,i . yexp,i i=1 AAD% − P =
1 N
N
100 i=1
Q.N. Ho et al. / Fluid Phase Equilibria 245 (2006) 63–70
69
Table 5 Deviations of published data to the PR-EOS for the binary mixture of R1270 + R-290 at various temperatures T (K)
Number of experimental points
AAD%–P
AAD%–y
260.93a 277.59a 310.93a 344.26a 360.93a 269.54b 301.32b 330.32b
8 7 4 4 4 6 4 5
0.21 0.13 0.02 0.02 0.13 0.33 0.01 0.03
1.11 1.02 1.23 2.65 1.18 0.63 0.83 0.97
a b
Reference [2]. Reference [3].
from the mixture of propane + propylene by distillation due to the very close distance between dew-point curve and bubblepoint curve. Fig. 3. Deviations in pressure between experimental and calculated for the mixture of R-1270 (1) + R-290 (2) at various temperatures.
pressure and in vapor phase compositions between calculated and these experimental data for this binary mixture are summarized in Table 5. It indicates that the values of AAD%–P and AAD%–y vary within 0.02–0.21 and 1.02–2.56% for Reamer et al.’s data; meanwhile; these values for Hanson et al.’s data vary within 0.01–0.33 and 0.63–0.97%. All of them are small and acceptable. However, just few experimental points measured at several temperatures are not enough to obtain the reliable binary interaction parameter, kij . Based on the P–x–y diagram in Fig. 2, it could be realized that it is really difficult to produce high purity propane (or propylene)
5. Conclusions Measurements of the vapor–liquid equilibria for the binary mixture R-290 + R-1270 at 273.15, 278.15, 283.15, 293.15, 303.15 and 313.15 K were carried out by using a circulationtype equilibrium apparatus and 90 isothermal VLE data for this mixture were reported in detail in this paper. It was confirmed that this mixture did not exhibit azeotropic behavior in the studied temperature range. The experimental and published isothermal VLE data were correlated with the PR-EOS combined with the Wong–Sandler mixing rule and good agreements between calculated and experimental data were confirmed. The result means that the model equation used in this study can be used to estimate the thermodynamic properties of the binary mixture R-1270 + R-290 in the range of temperature from 273.15 to 313.15 K. It could be also used for other ranges but additional experiments are necessary to confirm that. List of symbols x mole fraction in liquid phase y mole fraction in vapor phase Greek letters α(T) temperature dependent α12 non-randomless parameter , ␦ change in a quantity ω acentric factor
Fig. 4. Deviations in vapor phase composition between experimental and calculated data for the mixture of R-1270 (1) + R-290 (2) at various temperatures.
Subscripts Ave. average c critical property cal. calculated exp. experimental i, j ith and jth components of the mixture m mixture v vapor phase
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