Article pubs.acs.org/jced
pvT Property of HFE 7100 in the Gaseous Phase Baolin An, Yuanyuan Duan,* Fufang Yang, and Zhen Yang Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Beijing Key Laboratory for CO2 Utilization and Reduction Technology, Tsinghua University, Beijing 100084, China ABSTRACT: HFE 7100 (C4F9OCH3) is a promising working fluid for organic Rankine cycles (ORC). However, there are no available published experimental gaseous pvT data. Thus, pvT data of HFE 7100 in the gaseous phase were measured with a Burnett apparatus. High purity helium was used to calibrate the cell constant of the Burnett apparatus. Then, the gaseous pvT data of HFE 7100 were measured from (363 to 431) K for pressures from (148 to 878) kPa. The temperature measurement standard uncertainty was estimated to be 2.3 mK, the pressure standard uncertainty was estimated to be 240 Pa, and the density relative standard uncertainty was estimated to be 0.0006. A truncated virial equation of state (EOS) for HFE 7100 was used to correlate the experimental data with a relative root-mean-square deviation of 0.00042.
1. INTRODUCTION Organic Rankine cycles (ORCs) can make good use of lowgrade heat sources and have been researched for the past 20 years.1−6 The working fluid is very important for the ORCs and much work has been done to identify applicable working fluids.2−6 HFE 7100 is a promising working fluid for ORCs because it has low GWP (global warming potentials), zero ODP (ozone depletion potentials), is nonflammable, and has low viscosity. HFE 7100 has often been selected as the working fluid for ORC systems, especially for micro-CHP (combined heat and power) systems.3−5 The fluid thermophysical properties must be accurately measured for the design and operation of ORC systems. Li et al.7 measured the liquid density and surface tension of HFE 7100 from (279.15 to 321.15) K at atmospheric pressure, while Tsai8 predicted the critical properties of HFE 7100 theoretically and An et al.9 measured the vapor pressure of HFE 7100 from (306 to 431) K. Gaseous pvT property of working fluids is one of the most fundamental thermophysical properties and thus has been extensively researched.10−15 For ORC systems, the gaseous pvT property directly influences the system performance through the expansion processes. Thus, accurate ORC designs using HFE 7100 need reliable gaseous pvT data. However, to the best of the authors’ knowledge, there are no published reports of gaseous pvT data for HFE 7100. Therefore, the pvT data for HFE 7100 were measured from (363 to 431) K for pressures from (148 to 878) kPa, using a Burnett apparatus.
Table 1. Fluid Used in This Work
source
HFE 7100
3M Company
mole purity
purification method
99.91 %
37.7:62.3
none
without further purification after being degassed. Before the pvT measurements, the HFE 7100 sample was transferred to a stainless steel vessel which was cooled by liquefied nitrogen to remove the noncondensable gases (such as air). The procedure was repeated several times to improve the HFE 7100 purity. The HFE 7100 sample was measured with an ISQ Trance 1300 to test the main compositions and impurities. The initial temperature was set as 30 °C, the final temperature was set as 50 °C, and the heating rate was set as 2 °C·min−1. The result shows that the mole fraction of HFE 7100 is 0.9991, the mole fraction of 1,1,1,2,3,3,3,-heptafluoro-2-methoxypropane is 0.0003, and the mole fraction of 1,1,2,3,3,3-hexafluoropropyl methyl ether is 0.0006. A 19F nuclear magnetic resonance was performed on the HFE 7100 sample with a Bruker AVANCE III 400 HD NMR to measure the ratio of methyl nonafluoroisobutyl ether and methyl nonafluorobutyl ether. The NMR result shows that the mass ratio of methyl nonafluorobutyl ether and methyl nonafluoroisobutyl ether is 37.7:62.3. Apparatus. A Burnett apparatus was used to measure the pvT data. A diagram of the apparatus is shown in Figure 1. The system included thermostatic baths, a temperature measurement system, a pressure measurement system, a vacuum
2. EXPERIMENT Chemicals. The HFE 7100 was supplied by the 3 M Company (Table 1). The HFE 7100 consists of two inseparable isomers (methyl nonafluoroisobutyl ether and methyl nonafluorobutyl ether) with essentially identical properties according to the 3 M Company. The samples were used © 2015 American Chemical Society
fluid name
chemical composition (methyl nonafluorobutyl ether/ methyl nonafluoroisobutyl ether)
Received: June 19, 2015 Accepted: October 9, 2015 Published: October 27, 2015 3289
DOI: 10.1021/acs.jced.5b00513 J. Chem. Eng. Data 2015, 60, 3289−3295
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uncertainty of the differential pressure detector is 20 Pa. So, the combined pressure standard uncertainty was 240 Pa below 900 kPa. Procedure. The Burnett apparatus included two cells made of 316 stainless steel. The insides of the sample cell, B2, with a volume of 500 mL and the expansion cell, B1, with a volume of 200 mL were polished to reduce physical adsorption. The two Burnett cells and the connections were then evacuated by the vacuum pump to remove impurities. The vacuum in the system was better than 1·10 −4 Pa and was maintained for at least 6 h. Then, a selected amount of HFE 7100 was introduced into cell B2. After the sample cell was filled, the apparatus was heated by controlling the thermostatic bath temperature. The heating process continued until the HFE 7100 sample was in the gaseous phase. The HFE 7100 vapor pressures were obtained from a previous work to verify that the states of the HFE 7100 sample were in the gaseous phase.9 The pvT data measurements were then started. The thermostat bath temperature was controlled to the experimental temperature. The sample was assumed to be in thermal equilibrium with the bath fluid when the pressure remained the same. Then, the sample temperature and pressure were measured. The temperature and pressure at each state point were measured three times to reduce the experimental error, with the average value of the three measurements used as the final value. When a series of pressure measurements at different temperatures were completed along one isochore, valve V1 (as shown in Figure 1) was opened and the working fluid was expanded into cell B1 at 431.15 K, the highest experimental temperature. Before the expansion, cell B1 was evacuated to less than 1·10 −4 Pa with valve V2 open and V1 and V3 closed. Then V2 was closed and V1 was opened to expand part of the sample fluid into the expansion cell in the gaseous phase. Valve V1 was kept open for at least 1 h to ensure uniform density. During the expansion, the bath temperature was kept stable at the highest experimental temperature. Then the apparatus was cooled along the isochorefor the pvT measurements. After the lowest temperature pvT measurement on each isochore, the apparatus was cooled to the vapor−liquid equilibrium states to measure the vapor pressures. The measured vapor pressure data were compared with the Wagner-type vapor pressure equation for HFE 7100 proposed by An et al. to evaluate the sample purity, especially whether the sample contained any air impurities.9 After the vapor pressures were measured, the apparatus was again heated to the highest experimental temperature for the isothermal expansion procedure with the procedure repeated for several isochores. Density Calculation. The densities were calculated as
Figure 1. pvT pressure measurement apparatus: B, thermostatic bath; H/CP, heater/cooler; MS, mechanical stirrer; DPI, differential pressure detector; MTa, absolute pressure digital manometer; MTgL/MTgH, gauge pressure digital manometer for low and high pressures; PC, personal computer; SC, sample cylinder; ST, super thermometer; T, platinum resistance thermometer; TB, thermometer bridge; VP, vacuum; B1, expansion cell (200 mL) ; B2, sample cell (500 mL) ; V1−V9, valves.
system, and a data acquisition system. The system details were described by Feng et al.13 and Liu et al.;14 only a brief description is given below. The thermostatic baths provided a uniform, stable temperature field. The temperature range for the thermostatic baths was from (273 to 453) K. The temperature measurement system included platinum resistance thermometers, a precise thermometer bridge (MI: 6242T), a selector switch and a super thermometer (HART: 1590). The temperature was determined on the basis of the International Temperature Scale of 1990 (ITS-90). The pressure measurement system, which could measure pressures from (0 to 10) MPa, included an absolute digital manometer (Yokogawa: MT210), two gauge pressure digital manometers (Yokogawa: MT210; Ruska: 7050i), and a very sensitive diaphragm pressure transducer (Rousemount: 3051S). A turbo-molecular pump (KYKY: FD110) with a vacuum of 1· 10 −6 Pa provided the vacuum for the experimental apparatus. Before the experiments, the platinum resistance thermometers, the thermometer bridge, and the digital manometers were calibrated by the National Institute of Metrology (NIM), China. The overall temperature standard uncertainty including the variation of the thermostatic bath temperature and the temperature measurement standard uncertainty was estimated to be 2.3 mK, including the 1 mK standard uncertainty of the platinum resistance thermometer, the 0.3 mK standard uncertainty of the thermometer bridge, and the 2 mK stability and uniformity of the thermostatic bath. The combined standard uncertainty of the pressure measurements included the standard uncertainty of the absolute digital manometer, the gauge pressure digital manometer, the Ruska manometer, and the differential pressure detector. The relative standard uncertainty of the absolute digital manometer is 0.0001 of reading and 0.00005 of full scale from (0 to 130) kPa, the relative standard uncertainty of the gauge pressure digital manometer is 0.0001 of reading and 0.00005 of full scale up to 3000 kPa, the relative standard uncertainty of the Ruska manometer is 0.00005 from (0 to 10000) kPa and the standard
ρi =
pi ZiRT
=
1 1 = i v ART ∏k = 0 Nk
(1)
where ρi is the molar density, pi is the pressure, Zi is the compressibility, R is the universal gas constant, T is the temperature, N is the cell constant, A is the gas-filled constant, v is molar specific volume, and i is the expansion number The cell constant in the data processing constant, N, is a weak function of pressure. Ni(pi − 1 , pi ) = N0 3290
1 + mpi 1 + mpi − 1
(2) DOI: 10.1021/acs.jced.5b00513 J. Chem. Eng. Data 2015, 60, 3289−3295
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Comparison of Vapor Pressures. The vapor pressures were measured for every isochore with the measured values listed in Table 2. The measured vapor pressure data were
where m is a constant and cell constant N0 is the ratio of the sum of the volumes of cells B1 and B2 to the volume of cell B2 at a vacuum state. The gas-filled constant was determined as
Table 2. Vapor Pressures for HFE 7100
i p 1 ≡ 0 = lim pi ∏ Nk pi → 0 A Z0 k=0
(3)
where Z0 is the initial compressibility and p0 denotes the initial pressure.
3. RESULTS AND DISCUSSION Calibration of Cell Constant N0. A helium sample was used to calibrate the cell constant of the Burnett apparatus. The helium was provided by Beiwen Gas Coporation with a stated mole purity of higher than 99.999 %.The cell constant, N0, was determined from the following equation: p N0 = lim i − 1 p→0 p (4) i
T
pexp
pcal
pexp − pcal
K
kPa
kPaa
kPa
100(pexp − pcal)/pcal
338.152 347.895 358.151 368.150 377.897 396.147 406.246
120.14 163.08 220.01 289.31 371.99 572.54 714.05
120.14 163.03 220.10 289.43 371.94 572.00 714.57
0.00 0.05 −0.09 −0.12 0.05 −0.46 −0.52
0.000 0.031 −0.041 −0.041 0.013 −0.080 −0.073
Temperature measurement standard uncertainty was 2.3 mK and 240 Pa for pressure measurement. aVapor pressures calculated from An et al.9
compared with the Wagner-type vapor pressure equation for HFE 7100 proposed by An et al.9 in Table 2. The present experimental data points are well represented by the equation with the maximum relative deviation being 0.08 % at 396.147 K. Gaseous pvT Data for HFE 7100. The densities of the HFE 7100 sample along different isochores were determined from the cell constant and gas-filled constant along each isotherm, according to eq 1. To examine the agreement of the experimental data, the HFE 7100 sample densities at 431.15 K were obtained from the densities determined at (431.15, 429.15, 427.15, 425.15, 423.15, 418.15, and 413.15 K, by correcting for the influence of the cell distortion due to pressure and, more importantly, temperature.17 All the densities at 431.15 K determined from different isotherms were compared and the result is shown in Figure 3. To express the
The cell constant calibration experiment was conducted at temperatures of 413.153 K and 418.155 K. The cell constant calibration values were calculated to be 1.349734 ± 0.00006 for 413.153 K and 1.349748 ± 0.00005 for 418.155 K. The relative deviation of the two constant calibration values is less than 0.001 %. The experimental data were used to calculate the helium sample densities. The helium pvT data were then compared to the helium equation of state from REFPROP (ver. 9.1)16 with the result shown in Figure 2.
Figure 2. Deviations of helium gaseous pvT data from the helium equation of state16: □, 418.155 K; ○, 413.153 K.
The root-mean-square (RMS) deviation relative to the helium equation of state was defined as ⎡ 1 RMS = ⎢ ⎢⎣ n − 1
⎤ 2⎥ ρ ρ − ( / 1) ∑ j ,exp j ,cal ⎥⎦ j=1 n
Figure 3. Comparison of the densities at 431.15 K determined from different isotherms: −, 431.15 K; □, 429.15 K; ○, 427.15 K; △, 425.15 K; ▽, 423.15 K; ◊, 418.15 K; ◁, 413.15 K.
1/2
(5)
where n is the number of experimental points, ρj,cal is the density calculated from the helium equation of state, and ρj,exp is the measured density. The RMS differences relative to the helium equation of state are both 0.00006 at 413.153 K and 418.155 K.
differences clearly, the sample densities determined from the isotherm of 431.15 K were selected to be the baseline. The maximum relative deviation of the densities determined from other isotherms to the baseline is less than 0.1 %, which shows that the experimental data is consistent. 3291
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Table 3. pvT Data for HFE 7100 in the Gaseous Phase T/Ka
p/kPab
ρ/mol·m−3c
T/Ka
p/kPab
ρ/mol·m−3c
431.15 431.15 431.15 431.15 431.15 431.15 431.15 429.15 429.15 429.15 429.15 429.15 429.15 429.15 427.15 427.15 427.15 427.15 427.15 427.15 427.15 425.15 425.15 425.15 425.15 425.15 425.15 425.15 423.15 423.15 423.15 423.15 423.15 421.15 421.15 421.15 421.15 418.15 418.15 418.15 418.15 418.15 416.15 416.15 414.15 413.15
877.86 696.89 542.65 416.82 317.09 239.54 180.05 870.54 691.91 539.17 414.37 315.38 238.29 179.14 863.18 686.89 535.69 411.93 313.64 237.03 178.24 855.75 681.86 532.20 409.48 311.88 235.78 177.33 676.78 528.70 407.01 310.13 234.51 671.73 525.20 404.55 308.37 664.06 519.90 400.84 305.74 231.36 658.93 516.36 653.76 651.15
316.50 234.49 173.73 128.71 95.36 70.65 52.34 316.54 234.52 173.75 128.73 95.37 70.66 52.35 316.57 234.54 173.77 128.74 95.38 70.67 52.35 316.60 234.56 173.78 128.75 95.39 70.67 52.36 234.59 173.80 128.77 95.40 70.68 234.61 173.82 128.78 95.41 234.65 173.85 128.80 95.43 70.70 234.67 173.86 234.69 234.71
413.15 413.15 413.15 413.15 413.15 411.15 411.15 408.15 408.15 408.15 406.15 406.15 403.15 403.15 403.15 403.15 403.15 401.15 398.15 398.15 398.15 396.15 393.15 393.15 393.15 393.15 393.15 391.15 388.15 388.15 383.15 383.15 383.15 383.15 378.15 378.15 373.15 373.15 373.15 368.15 363.15 363.15
511.18 394.62 301.31 228.19 171.97 645.96 507.44 502.05 388.34 296.87 632.76 498.43 624.65 492.98 382.03 292.40 221.80 489.34 483.81 375.65 287.90 480.10 474.46 369.23 283.39 215.36 162.67 470.64 362.74 278.82 356.13 274.23 209.10 157.94 349.33 269.59 264.87 202.27 153.22 260.04 195.54 148.41
173.89 128.83 95.45 70.72 52.39 234.73 173.91 173.93 128.86 95.47 234.79 173.95 234.82 173.98 128.90 95.50 70.75 173.99 174.02 128.93 95.52 174.04 174.07 128.96 95.55 70.79 52.45 174.08 128.99 95.57 129.03 95.59 70.82 52.47 129.06 95.62 95.64 70.86 52.50 95.67 70.89 52.52
a The temperature standard uncertainty was 2.3 mK. bThe pressure standard uncertainty was 240 Pa. cThe density relative standard uncertainty was 0.0006.
where ρ is density, mol·m−3, and B and C denote the second and third virial coefficients given by
Since the adsorption has the least effect at the highest experimental temperature on the pressure measurements, the densities determined at 431.15 K were chosen to calculate the densities along the isochores. The densities along other isotherms were obtained by correcting for the influence of cell distortion. The measurement results are shown in Table 3 and Figure 4. A truncated virial EOS for HFE 7100 was developed by fitting the data listed in Table 3. The equation was based on the following functional form to facilitate the calculation of thermodynamic properties:
Z = 1 + Bρ + Cρ2
B = B0 + B1/Tr + B2 /Tr2 + B3 /Tr 3 + B4 /Tr 6 + B5 /Tr 8 (7)
C = C0 + C1/Tr 0.5 + C2/Tr + C3/Tr 2
(8)
where Tr = T/Tc, the critical temperature Tc = 468.5 K,8 and Bi and Ci for HFE 7100 were determined by fitting the experimental data to the virial EOS. The coefficients in eqs 7 and 8 are listed in Table4. The suitable range of this equation is from (363 to 431) K in temperature, from (148 to 878) kPa in pressure and from (52.3
(6) 3292
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Figure 4. Distribution of HFE 7100 pvT data in the gaseous phase: ○, HFE 7100 experimental data in the gaseous phase; −, HFE 7100 vapor pressure9.
Figure 5. Deviations between the experimental data and the value calculated using eq 6.
Table 5. HFE 7100 Second and Third Virial Coefficients to 316.6) mol·m−3 in density. The pressures calculated from eq 6 were compared with the experimental data in Figure5. The RMS deviation of the HFE 7100 gaseous pvT experimental data relative to the virial EOS is 0.00042. The HFE 7100 s and third virial coefficients were obtained from the experimental data and listed in Table 5. Since there are no available experimental data, the obtained second and third virial coefficients were compared with the calculation results from the empirical correlating methods proposed in the literature. The second virial coefficients can be calculated from the equation as18,19 Bp Br = c = f (0) (Tr) + ωf (1) (Tr) + f (2) (Tr) RTc (9)
2nd virial coefficients uncertainty
3rd virial coefficients
3rd virial coefficients uncertainty
T/K
dm3·mol−1
dm3·mol−1
dm6·mol−2
dm6·mol−2
431.15 429.15 427.15 425.15 423.15 418.15 413.15 403.15 393.15
−0.777 −0.786 −0.795 −0.805 −0.817 −0.842 −0.867 −0.925 −0.989
0.004 0.004 0.004 0.004 0.004 0.004 0.006 0.006 0.006
0.197 0.196 0.196 0.195 0.216 0.214 0.202 0.197 0.199
0.02 0.02 0.02 0.02 0.02 0.02 0.03 0.03 0.04
The uncertainties here are expanded uncertainties with 0.95 level of confidence.
where pc is the critical pressure,8 ω is the acentric factor, f(0) was obtained by fitting data for small spherical molecules (ω = 0), such as argon, f(1) was obtained from data for larger, nonspherical, nonpolar molecules (ω ≠ 0), such as butane and octane, f(2) was obtained from data for nonhydrogen bonding polar molecules and related to the dipole moment. An empirical correlation of the third virial coefficients was given by Weber as20 C = C h + (B − B h )2 δc ϑ(Tr)
2nd virial coefficients
where c0 = 5.476·10−3, c1 = 0.0936, and μr is related to the dipole moment. The comparison results of HFE 7100 s and third virial coefficients were shown in Figures 6 and 7. Because there is no available dipole moment data for HFE 7100, only the f(0) and f(1) terms in eq 9 were used for calculation of the second virial coefficients. The results from Meng et al. and Tsonopoulos are both higher than experimental results in this work, with relative deviations within 5 % and 7 %, respectively.18,19 Therefore, the HFE 7100 s virial coefficients in this work are satisfactory. Because of a similar reason, the dipole moment was not used for the third virial coefficient calculation. The results from Meng et al. and Weber are lower than experimental results in this work, while results from Meng et al. are closer to experimental results.18,20 However, the results show the same trend and order of magnitude. Hence, the experimental third virial coefficients are reasonable.
(10)
where Bh = b, Ch = 0.625b , b = 0.36vc, vc is the critical volume,8 δc is a function of the dipole moment, and ϑ(Tr) is a strong functions of Tr. Another empirical correlation was given by Meng et al. as18 2
⎛ P ⎞2 Cr = C ⎜ c ⎟ = c0 + (Br − c1)2 [f0 (Tr) + μr4 f1 (Tr)] ⎝ RTc ⎠ (11)
Table 4. Coefficients in eqs 7 and 8 B0
B1
B2
B3
B4
−2.527091 B5
8.830768 C0
−10.92568 C1
4.937171 C2
−0.3728284 C3
0.05673892
1.551586·10−6
−1.262862·10−5 3293
1.536489·10−5
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from the impurities was estimated to be 0.00011. The density relative standard uncertainty from the experimental measurement was estimated to be 0.00056. So, the combined relative standard uncertainty of density was estimated to be 0.0006
4. CONCLUSION The cell constant of the Burnett apparatus was first calibrated with helium. Then, the gaseous pvT data of HFE 7100 were measured from (363 to 431) K for pressures from (148 to 878) kPa. The temperature measurement standard uncertainty was 2.3 mK, the pressure standard uncertainty was 240 Pa, and the density relative standard uncertainty was 0.0006. A truncated virial EOS for HFE 7100 was used to correlate the experimental data with the second and third virial coefficients as functions of temperature. The RMS deviation between the experimental data and the virial EOS is 0.00042 and a comparison with empirical correlations verified the experimental second and third virial coefficients.
Figure 6. Second virial coefficients for HFE 7100: , eq 7; ●, experimental data; ---, Meng et al.;18 -·-·-, Tsonopoulos.19
■
AUTHOR INFORMATION
Corresponding Author
*Tel +86 10 6279 6318. E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
■
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Figure 7. Third virial coefficients for HFE 7100: , eq 8; ●, experimental data; ---, Meng et al. ;18 -·-·-, Weber.20
The ideal solution model was used to estimate the contribution of impurities to the density standard uncertainty, because the mole fractions of 1,1,1,2,3,3,3,-heptafluoro-2methoxypropane and 1,1,2,3,3,3-hexafluoropropyl methyl ether were very small.
Vm =
∑ xiVm,i i
REFERENCES
(12)
where Vm is the mole specific volume of the mixture, xi is the mole fraction of the composition, and Vm,i is the mole specific volume of the composition. The second virial coefficients of HFE 7100 and 1,1,2,3,3,3hexafluoropropyl methyl ether were calculated by eq 9 with the critical parameters from previous literature.8,18,21 Then, the calculated second virial coefficients were used to estimate the mole specific volume differences between HFE 7100 and 1,1,2,3,3,3-hexafluoropropyl methyl. The result shows that the maximum mole specific volume difference is 12 % among all the data points in this paper. The differences between the HFE 7100 and 1,1,1,2,3,3,3,-heptafluoro-2-methoxypropane was estimated to be 12 % because 1,1,2,3,3,3-hexafluoropropyl methyl ether and 1,1,1,2,3,3,3,-heptafluoro-2-methoxypropane were isomers. Then, the density relative standard uncertainty 3294
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