Article pubs.acs.org/jced
Vapor Pressure of HFE 7100 Baolin An, Yuanyuan Duan,* Longshan Tan, and Zhen Yang Key Laboratory for Thermal Science and Power Engineering of the Ministry of Education, Beijing Key Laboratory for CO2 Utilization and Reduction Technology, Tsinghua University, Beijing 100084, China ABSTRACT: The vapor pressure of HFE 7100 was measured from (306 to 431) K for pressures from (36 to 1180) kPa using a Burnett apparatus. The temperature measurement uncertainty was estimated to be ± 5 mK, and the pressure uncertainty was estimated to be ± 300 Pa. A Wagner-type equation was used for the vapor pressure of HFE 7100 based on the experimental data. This equation contains five coefficients and correlates the measured vapor pressures within 0.11 %.
1. INTRODUCTION The utilization of low-grade heat sources has great importance for energy conservation, because they account for 50% or more of the total heat generated in the world.1 Organic Rankine cycles (ORCs) can make good use of low-grade heat sources and have been researched for the past 20 years.1−7The 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 used for ORCs due to its low GWP (global warming potential), zero ODP (ozone depletion potential), nonflammability, and low viscosity. HFE 7100 has recently been frequently 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.8 measured the liquid density and surface tension of HFE 7100 from (279.15 to 321.15) K at atmospheric pressure, while Tsai 9 predicted the critical properties of HFE 7100 theoretically. The working fluid vapor pressure is one of the most fundamental thermophysical properties that has been extensively researched.10−15 For ORC systems, the vapor pressure directly influences the system performance through the evaporation and condensation processes. Thus, the accurate ORC design using HFE 7100 needs reliable vapor pressure data. However, to the best of the authors’ knowledge, there are no reports for the vapor pressure of pure HFE 7100. Therefore, the vapor pressures of HFE 7100 were measured from (36 to 1180) kPa and temperatures from (306 to 431) K using a Burnett apparatus. Then, a Wagner-type equation was used for the HFE 7100 vapor pressure from the experimental data.
inseparable isomers (methyl nonafluoroisobutyl ether and methyl nonafluorobutyl ether) with essentially identical properties, according to 3M Co. A 19F nuclear magnetic resonance was performed on the purchased 3M HFE 7100 with a Bruker AVANCE III 400 HD NMR to measure the ratio of the two isomers. The NMR result shows that the ratio of the amount of methyl nonafluorobutyl ether and methyl nonafluoroisobutyl ether is 37.7:62.3. The samples were used without further purification after being degassed. Before the vapor pressure 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 for several times to improve the HFE 7100 purity. Apparatus. A Burnett apparatus was used to measure the vapor pressures. 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 system, and a data acquisition system. The system details were described by Feng et al. and Liu et al.,13,14 with only a brief description given in following text. The thermostatic baths provided a uniform, stable temperature field. The temperature range for the thermostatic baths was from (273 to 453) K. The stability of the thermostatic baths was estimated to be within ± 3 mK·h−1. 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, including an absolute digital
2. EXPERIMENT Chemicals. HFE 7100 was supplied by 3M Co., with a stated mass fraction of 99.5%. HFE 7100 consists of two
Received: January 28, 2015 Accepted: March 22, 2015 Published: April 1, 2015
© 2015 American Chemical Society
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DOI: 10.1021/acs.jced.5b00089 J. Chem. Eng. Data 2015, 60, 1206−1210
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the measurement at one state point was finished, the bath temperature would be controlled to a new experimental temperature. The sample pressure always changes before the equilibrium was achieved. The experimental data at this point were recorded at least 1 h after the sample pressure did not change at the experimental temperature. After the state point data with the highest temperature was recorded, the pressure in the sample was much higher than atmospheric pressure. The valve on the sample cell was then opened at the highest temperature to release a small amount of gaseous HFE 7100. Then, the valve was closed. The measured vapor pressures before opening the valve are compared with the measured vapor pressures after opening the valve. This is used to confirm that there were no noncondensable gases (such as air) in the sample cell and the HFE 7100 sample was in the two phase vapor−liquid region. Several sets of experimental measurements were carried out to eliminate the random or systematic errors.
Figure 1. Vapor pressure measurement apparatus: B, thermostatic bath; PS, pressure sensor; H/CP, heater/cooler; MS, mechanical stirrer; PC, personal computer; SC, sample cylinder; ST, superthermometer; T, platinum resistance thermometer; TB, thermometer bridge; VP, vacuum; B1, expansion cell (200 mL); B2, sample cell (500 mL); V1−V9, valves.
3. RESULTS AND DISCUSSION The HFE 7100 vapor pressures were measured at temperatures from (306 to 431) K to obtain the 226 data points shown in Table 1 and Figure 2. The uncertainties in the vapor pressures were estimated with the following equation:
manometer (Yokogawa, MT210), two gauge pressure digital manometers (Yokogawa, MT210; Ruska, 7050i), and a very sensitive diaphragm pressure transducer (Rousemount, 3051S). Pressures below 130 kPa were measured directly by the absolute digital manometer, while pressures of (130 to 3500) kPa were measured by the gauge pressure digital manometer MT210 and the absolute digital manometer. A turbomolecular 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), Beijing, China. The overall temperature uncertainty including the variation of the thermostatic bath temperature and the temperature measurement was estimated to be within ± 5 mK, including the ± 2 mK uncertainty of the platinum resistance thermometer, the ± 0.3 mK uncertainty of the thermometer bridge, and the ± 3.4 mK stability and uniformity of the thermostatic bath. The uncertainty of the pressure measurements included the uncertainty of the absolute digital manometer of ± 30 Pa from (0 to 130) kPa and the uncertainty of the gauge pressure digital manometer (MT 210) of ± 80 Pa up to 3500 kPa after correction for systematic errors. The pressure uncertainty was then estimated to be less than ± 50 Pa from (0 to 130) kPa and ± 100 Pa from (130 to 3000) kPa. Procedure. The Burnett apparatus included two sample cells made of 316 stainless steel. A 500 mL interior volume sample cell was used in this work. About 300 g of HFE 7100 was put into the sample cell to ensure that the HFE 7100 was in the vapor−liquid two phase equilibrium. After the sample cell was filled, the thermostat bath temperature was controlled to the experimental temperature. The vapor pressure and temperature data were measured when thermal equilibrium was achieved between the sample and the bath fluid. The temperature and pressure at each state point was measured three times to reduce the experimental error, with the average value of the three measurements used as the final value. When
U (p) = U (pexp ) + (dp /dT ) U (Texp)
(1)
where U(p) is the vapor pressure uncertainty, U(pexp) is the pressure measurement system uncertainty, dp/dT is the first derivative of the vapor pressure with respect to the temperature, and U(pexp) is the temperature measurement system uncertainty. The total uncertainty of the vapor pressure measurement was ± 300 Pa with a confidence level of 95 % (k = 2). A Wagner-type analytical correlation for the HFE 7100 vapor pressure was used using a least-squares fit of the experiment data in Table 1 based on the following equation:13 5 ⎛ p⎞ T ln⎜⎜ ⎟⎟ = (∑ Ai τ ci) c p T ⎝ c⎠ i=1
(2)
where pc is the critical pressure, Tc is the critical temperature, T is the temperature, Ai and ci are the fitting coefficients, and τ = 1 − T/Tc. Since critical point data for HFE 7100 have not been reported, an estimated value of 468.5 K was used from a previous study.9 The critical pressure was 2325.06 kPa, extrapolated from eq 2 at the critical temperature. The coefficients in eq 2 are listed in Table 2. The absolute and relative deviations of the experimental data vapor pressure for HFE 7100 from the predictions given by eq 2 are shown in Figures 3 and 4. The root-mean-square absolute deviation (RMSa) and rootmean-square relative deviation (RMSb) relative to eq 2 were defined as ⎡ ⎤1/2 N 1 2⎥ ⎢ RMS = ∑ (pj ,exp − pj ,cal ) ⎥ ⎢⎣ N − 1 ⎦ j=1 a
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(3)
DOI: 10.1021/acs.jced.5b00089 J. Chem. Eng. Data 2015, 60, 1206−1210
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Table 1. Experimental Vapor Pressure Data for HFE 7100
a
Ta/K
pb/kPa
Ta/K
pb/kPa
Ta/K
pb/kPa
Ta/K
pb/kPa
305.643 307.087 308.249 308.268 311.228 311.532 312.429 313.474 314.558 314.628 316.794 317.504 318.231 320.872 321.374 321.483 321.569 321.689 322.463 322.52 323.462 324.429 324.435 324.455 325.69 326.345 326.553 327.454 327.519 327.77 328.573 329.521 329.819 330.291 330.427 330.663 331.487 331.557 332.088 333.282 333.525 333.685 334.050 334.067 334.148 335.856 335.879 336.040 336.583 336.710 337.499 338.054 338.957 339.045 339.121 339.719 339.855
36.42 38.62 40.53 40.56 45.68 46.24 47.90 49.94 52.05 52.19 56.73 58.32 59.91 66.13 67.42 67.60 67.85 68.09 70.04 70.23 72.74 75.21 75.32 75.29 78.71 80.53 81.17 83.73 83.98 84.76 87.12 90.03 90.94 92.40 92.92 93.65 96.31 96.47 98.27 102.31 103.05 103.73 105.01 105.13 105.31 111.47 111.58 112.14 114.13 114.54 117.64 119.68 123.42 123.69 123.95 126.29 126.92
341.038 341.557 341.834 341.982 342.509 342.641 342.882 343.040 343.655 345.138 345.786 346.605 346.622 346.764 347.425 348.383 348.686 349.431 350.773 350.778 351.593 351.606 351.662 352.395 353.637 353.884 354.046 354.639 355.056 355.710 356.843 357.508 357.768 358.624 359.189 359.840 360.327 361.627 362.099 362.123 363.198 364.181 365.229 365.338 366.078 366.500 367.489 367.760 369.084 369.146 370.028 370.511 370.707 371.511 372.001 372.097 372.757
131.78 133.95 135.15 135.78 137.99 138.65 139.71 140.41 143.23 149.87 152.85 156.72 156.80 157.50 160.74 165.52 166.94 170.77 177.75 177.73 182.18 182.21 182.34 186.52 193.37 194.70 195.75 199.10 201.62 205.31 211.98 216.06 217.74 223.06 226.65 230.81 233.87 242.47 245.71 246.02 253.18 260.19 267.45 268.20 273.72 277.02 284.52 286.41 296.66 296.98 304.09 307.96 309.61 316.39 319.97 320.91 326.45
373.870 374.151 374.184 375.169 375.533 375.586 375.587 376.163 376.771 377.302 378.139 378.253 378.298 378.928 379.558 380.369 380.931 381.317 382.331 382.337 383.747 383.898 384.301 384.450 385.328 386.343 386.499 387.128 387.347 388.082 388.231 388.380 388.610 389.335 390.211 390.253 390.346 391.339 391.364 392.054 392.382 393.075 393.556 394.434 394.436 395.437 395.568 396.397 396.426 397.542 397.688 397.928 398.531 399.238 399.612 400.484 400.571
335.92 338.45 338.61 347.02 350.37 351.21 350.70 356.03 361.52 366.36 374.54 375.69 375.65 381.71 387.87 395.39 401.26 404.84 414.81 414.88 429.59 431.21 434.82 436.63 446.20 456.90 458.53 465.69 467.56 475.89 477.94 479.36 482.07 490.35 500.51 500.75 501.59 513.55 514.13 522.17 525.77 534.26 540.03 551.49 551.29 563.81 565.75 576.45 576.56 591.39 593.37 596.04 604.29 613.74 618.69 631.09 632.19
401.321 401.722 401.837 402.796 403.065 403.155 403.594 403.697 404.649 404.753 404.895 405.817 405.931 406.007 406.632 406.783 407.376 407.585 407.665 408.583 408.866 409.783 410.611 410.683 411.494 411.534 411.734 413.432 413.583 414.545 414.701 415.147 415.616 416.336 416.342 417.274 417.638 418.852 419.302 419.320 419.341 421.299 421.770 423.158 423.197 424.396 424.662 424.666 427.187 427.212 427.226 429.291 430.117 430.431 431.275
642.55 648.18 649.58 663.64 667.16 669.01 674.80 676.55 690.79 691.97 694.45 707.79 709.87 711.24 720.54 722.52 732.46 734.93 736.17 751.03 755.23 769.76 783.48 784.40 797.57 798.29 802.26 830.33 832.74 849.81 852.49 859.81 867.96 881.07 881.13 897.58 904.49 926.87 934.93 935.53 936.17 972.71 982.15 1009.33 1009.71 1034.37 1039.55 1039.64 1091.68 1092.21 1092.89 1136.85 1154.70 1161.45 1180.31
Uncertainty for temperature measurement is estimated to be ± 5 mK. bUncertainty for pressure is estimated to be ± 300 Pa. 1208
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Figure 4. Relative deviations of the vapor pressure data for HFE7100 from eq 2.
Figure 2. Vapor pressures of HFE 7100: □, experimental data; −, vapor pressure calculated from eq 2.
apparatus. A Wagner-type vapor pressure equation was used for HFE7100 from the experimental data. The correlation contains five coefficients and correlates the measured vapor pressures within 0.11 %. The root-mean-square absolute deviation between the equation and the experimental data is 0.154 kPa, and the root-mean-square relative deviation is 0.04 %. The measured vapor pressures and the equation provide an accurate basis for thermophysical property research of HFE 7100.
Table 2. Values of the Coefficients in Equation 2 i
Ai
ci
1 2 3 4 5
−8.93878 4.60513 −10.13797 8.14194 −45.70926
1.0 1.5 2.5 3.5 7.0
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AUTHOR INFORMATION
Corresponding Author
*Tel.: +86 10 6279 6318. E-mail:
[email protected]. Funding
This work was supported by the National Natural Science Foundation of China (Grant Nos. 51236004 and 51321002) Notes
The authors declare no competing financial interest.
■
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Figure 3. Absolute deviations of the vapor pressure data for HFE7100 from eq 2.
⎡ ⎤1/2 N 1 2⎥ ⎢ RMS = ∑ (pj ,exp /pj ,cal − 1) ⎥ ⎢⎣ N − 1 ⎦ j=1
REFERENCES
b
(4)
where N is the number of experimental points, p j,cal is the vapor pressure calculated from eq 2, and p j,exp is the experimental value of the vapor pressure. The experimental vapor pressures agree well with eq 2. RMSa = 0.154 kPa, and the maximum absolute deviation is 0.531 kPa. RMSb = 0.04 %, and the maximum relative deviation is 0.11 %.
4. CONCLUSION The vapor pressure of HFE 7100 was measured from (306 to 431) K and pressures from (36 to 1180) kPa using a Burnett 1209
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