- Email: [email protected]
Gas phase PVT properties and second virial coefficients of dimethyl ether
Fluid Phase Equilibria 298 (2010) 298–302
Contents lists available at ScienceDirect
Fluid Phase Equilibria journal homepage: www.elsevier.com/locate/fluid
Gas phase PVT properties and second virial coefficients of dimethyl ether Jianguo Yin, Jiangtao Wu ∗ State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, People’s Republic of China
a r t i c l e
i n f o
Article history: Received 22 March 2010 Received in revised form 17 August 2010 Accepted 29 August 2010 Available online 24 September 2010 Keywords: Dimethyl ether (DME) PVT Second virial coefficient
a b s t r a c t Dimethyl ether (DME) is an important chemical material and gets more and more attention as a clean alternative fuel and refrigerant nowadays. The gas phase PVT properties of dimethyl ether were measured using the Burentt-isochoric coupling method in the temperature range of 328–403 K with two Burnett expansions at 383 and 403 K. A total of 126 experimental points have been obtained. The experimental measurement uncertainties were estimated to be within ±10 mK for temperature and ±0.7 kPa for pressure. The second virial coefficients along 16 isotherms were derived using the present data. Crown Copyright © 2010 Published by Elsevier B.V. All rights reserved.
1. Introduction Dimethyl ether (DME) is an important chemical material which has many engineering applications such as aerosol propellant, assistant solvent, vesicant and so on. Furthermore, dimethyl ether is regarded as a promising clean alternative fuel for its lager oxygen content and lower emissions of SOx , NOx or particulates than conventional fuel when burning as well as its high-efficiency and non-petroleum based character [1]. It also has been suggested as an alternative refrigerant named as RE170. In these fields, the thermophysical properties of dimethyl ether are indispensable. A preliminary fundamental equation of state was derived by Ref. [2] and our group has also been done some research on vapor pressure, critical properties, saturation densities, surface tension, liquid viscosity and thermal conductivity of dimethyl ether recently [3–8]. After a literature survey, a very limited data of second virial coefficients and gas phase PVT properties for dimethyl ether were found [9–16]. In this work, a total of 126 experimental data were collected in the gas phase region for the temperature range of 328–403 K including 9 points in the super-critical region. Derived second virial coefficients were compared with the literature data. 2. Experimental The sample of dimethyl ether was provided by Shandong Jiutai Chemical Co. Ltd. of China. The stated mass purity is better than 99.95%. In order to eliminate the effect of gaseous impurity, the
∗ Corresponding author. Tel.: +86 29 82666875; fax: +86 29 82668789. E-mail address: [email protected] (J. Wu).
sample was purified several times by freeze-pump-thaw cycles by using liquid nitrogen and a high vacuum (<0.01 Pa) pump. The experimental apparatus used in this work is illustrated in Fig. 1. It consists of a Burnett apparatus, a thermostatic bath, a temperature measurement system, a pressure measurement system and a vacuum discharge system. The Burnett apparatus consists of two pressure cells: a sample cell (A) and an expansion cell (B). The two cells were all cylinder vessels made of 1Cr18Ni9Ti stainless steel with a thickness of 10 mm. Cell (A), with a volume of about 623 cm3 at room temperature, was 125 mm in outside diameter and the height of the cylinder is 130 mm. Cell (B), with a volume of about 310 cm3 at room temperature, was 80 mm in outside diameter and the height of cylinder is the same as cell (A). The sample valve (V1), expansion valve (V2) and vacuum valve (V3) was non-rotating type valve which could provide excellent seal performance along the whole experimental procedure. The whole apparatus coupled with a diaphragm-type differential pressure transducer was immersed in a thermostatic bath to establish temperature uniformity. Silicone oil was used as a heat transfer medium in the bath and its temperature was controlled by a PID regulator. The temperature measurement system includes a 25 standard platinum resistance thermometer (Model: WZPB, No. 92822, Kunming Temperature Instruments Co. Ltd., China) installed near the cells and a high precision thermometer bridge (Model: F700B, ASL, UK). The thermometer was calibrated on the ITS-90 scale at the National Institute of Metrology of China and the total temperature uncertainty including the temperature fluctuation of the thermostatic bath was estimated to be less than ±10 mK. The pressure was measured with a differential pressure transducer (Model: Rosemount 3051, range: 0–6.0 kPa, accuracy: 0.075% F.S.) and a digital quartz pressure transmitter (Model: Paroscien-
0378-3812/$ – see front matter. Crown Copyright © 2010 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2010.08.023
J. Yin, J. Wu / Fluid Phase Equilibria 298 (2010) 298–302
Fig. 1. Schematic diagram of experimental system: A: sample cell; B: expansion cell; C: differential pressure transducer; D: standard platinum resistance thermometer; E: shield board; F: stirrer; G: heater; H: temperature controller; I: thermometric bridge; J: nitrogen reservoir; K: expansion chamber; L: sample bottle; M: quartz pressure transmitter; N: pressure acquisition system; O: acquisition computer; V1–V3: non-rotating type valve; V4–V11: valve.
tific 31K-101, range: 0–6.9 MPa, accuracy: 0.01% F.S.). Nitrogen gas was used as pressure transfer medium in the differential pressure transducer. The valves used to balance the differential pressure transducer were small needle valves and the size of the connecting tube was small (the outside diameter was 2 mm). When the valves were operated carefully, the nitrogen gas pressure could increase or decrease slowly till the balance was reached. A pressure gauge was used to indicate the pressure change of the nitrogen gas. The differential pressure transducer was carefully calibrated in advance by opening both sides of the diaphragm to the same pressure as a function of temperature. The calibration results were used to modify the pressure measurements and the total uncertainty of pressure measurements was better than ±0.7 kPa. The high vacuum was provided by a turbo-molecular pump (Model: FD110, KYKY, China, the stated ultimate pressure is 1 × 10−6 Pa). High purity helium (99.999 mol%) was used to determine the cell constant N0 , defined as the ratio of the total volume of cell (A) and (B) to the volume of cell (A) at zero pressure. Because the material of cell (A) and (B) are the same, the cell constant is independent of temperature. The pressure distortion of the cell volume is also negligible for the two cells are all thick-walled metal vessels and the maximum pressure was no more than 5 MPa. Two separate Burnett expansions of helium were made at 383 K and two N0 were obtained: N01 = 1.48703, N02 = 1.48695. The Burnett expansion data of helium were listed in Table 1 and the average absolute deviation of experimental densities from the calculated values by the IUPAC equation [17] is 0.005%. Finally the average value of 1.48699 ± 0.00010 was used in this work. The Burnett-isochoric coupling method used in this work was similar to that of Ref. [18]. Before an experiment, all apparatus system was placed under vacuum and rinsed with dimethyl ether
299
for several times, then after the system was discharged to high vacuum again and maintained for at least 4 h, a fitting amount of dimethyl ether was introduced into the sample cell (A). Then the sample valve (V1) and expansion valve (V2) were closed and the thermostatic bath was controlled at the experimental temperature. After the thermal equilibrium between the sample and thermostatic bath was attained and the pressure remained constant, a pressure measurement was done and this formed the first point on the Burnett-isochoric surface. Then the thermostatic bath was cooled to next desired temperature and the pressure measurement was made when the thermal equilibrium was attained again. This sequence of temperature cooling and pressure measurement was repeated until the sample pressure close to vapor pressure value at the corresponding temperature. The thermostatic bath was then heated to the initial temperature and the pressure measurement repeated and compared with the first point value which could indicated any leaks out of cell (A). The first isochore of the maximum sample density was constituted via this sequence of measurements. Next, the first Burnett expansion was made at the base temperature: first, the cell (B) was evacuated by the high vacuum system for 1 h and pressure inside the cell (B) had a conservative value of lower than 0.1 Pa. The vacuum valve (V3) was then closed and expansion valve (V2) was opened quickly by two full turns. After about an hour of equilibration, valve (V2) was closed very slowly, and the pressure of cell (A) was then measured. This procedure made the first Burnett expansion measurement and formed the first point of the second isochore. Then the sequence of temperature cooling and pressure measurement mentioned above was repeated to finish this isochore. The bath was then again heated to the base temperature, the pressure measurement was done and the second Burnett expansion was made to get the third isochore. In this manner, the whole Burnett-isochoric surface was carried out with a single charge of sample. In order to verify the reliability and repeatability of the experimental system, two series Burnett-isochoric experimental procedures were made to cover the entire P-T surface: one process for temperature range from 328 to 383 K with Burnett expansion at 383 K and another process from 388 to 403 K with Burnett expansion at 403 K. 3. Results and discussion A total of 126 gas phase PVT data for dimethyl ether along 16 isotherms in temperature range from 328 to 403 K and for pressures from 183 to 4733 kPa were obtained and the data surface is shown in Fig. 2. All the PVT data were analyzed by Burnett analysis method along each isotherm with the cell constant obtained using helium. The Table 1 Burnett expansion data of helium. T/K
P/kPa
Z
exp /kg m−3
calc from Eq. of IUPAC/kg m−3
Error/%
382.992 382.992 382.992 382.992 382.992 382.992 382.992 382.995 382.995 382.995 382.995 382.995 382.995 382.995
4760.6 3183.9 2133.2 1431.0 960.7 645.4 433.6 4988.6 3335.6 2234.5 1498.8 1006.2 675.8 454.2
1.01690 1.01134 1.00761 1.00512 1.00344 1.00231 1.00155 1.01786 1.01201 1.00808 1.00544 1.00366 1.00246 1.00165
5.88450 3.95723 2.66116 1.78958 1.20343 0.80937 0.54422 6.16044 4.14298 2.78620 1.87381 1.26020 0.84735 0.56998
5.88488 3.95714 2.66103 1.78950 1.20338 0.80935 0.54421 6.16194 4.14349 2.78637 1.87387 1.26022 0.84736 0.56999
−0.006 0.002 0.005 0.005 0.004 0.003 0.002 −0.024 −0.012 −0.006 −0.003 −0.002 −0.001 −0.001
300
J. Yin, J. Wu / Fluid Phase Equilibria 298 (2010) 298–302 Table 2 PVT properties of dimethyl ether.
Fig. 2. Distribution of experimental data for DME: , experimental procedure 1 from 328 to 383 K, , experimental procedure 2 from 388 to 403 K; , critical point [4]; —, vapor pressure line [3].
experimental data along with the calculated compressibility factors and densities are given in Table 2. The density uncertainty was estimated to be within ±0.15%. The Burnett analysis method used in this work was similar to that of Ref. [19]. In the regression, each isotherm was treated separately and the following equation was used: AN0r pr = 1 + Bpr + Cpr
(1)
where A was written for Z0 /p0 , and a least-square routine was used to yield virial coefficients simultaneously. The second virial coefficients, B, and third virial coefficients, C, derived from the present measurements for each isotherm are given in Table 3. The second viral coefficients were fitted to the following temperature relationship: B = B0 + B1 Tr−1 + B2 Tr−2 + B3 Tr−3 + B4 Tr−6
(2)
where the units of T are K, those of B, B0 –B4 are cm3 mol−1 , Tr = T/Tc . The critical temperature used here, Tc = 400.378, was the experimental result obtained by our group in Ref. [4]. The parameters in Eq. (2) are B0 = −2.348816E + 04, B1 = 7.730736E + 04, B2 = −8.821103E + 04, B3 = 3.547363E + 04, and B4 = −1.300762E + 03. All experimental data except two points can be represented by Eq. (2) within ±0.3%. When the experimental data can be expressed by a virial equation having second and third virial terms, the behavior of (Z − 1)/ versus should be a straight line whose intercept also gives the second virial coefficients along each isotherm as shown in Fig. 3. In Table 3, the second virial coefficients obtained in this work are compared with the values calculated by the equation given by Ref. [15], the only source which has made systematically research on second virial coefficients of dimethyl ether in the temperature range of 344–393 K. All data of this work except one point is less than the value calculated by the equation given in Ref. [15] but within the stated uncertainty. Generally, an adsorption effect on the metallic wall of two pressure cells may cause a more negative B value and the dependence of (Z − 1)/ on can be used as a diagnostic. While there is no obvious adsorption feature in Fig. 3, and the base isotherm temperature chosen in the present experimental procedure are relatively high, so the magnitude of error caused by adsorption effect could be neglected. Moreover, the equation given by Ref. [15] only has one item about the reduced temperature and the obvious deviation was found especially in low temperature. The function form used in Ref. [15] may be improved.
T/K
P/kPa
Z
/mol dm−3
403.158 403.158 403.156 403.156 403.158 403.156 403.158 403.157 403.158 398.156 398.159 398.155 398.157 398.156 398.158 398.158 398.156 398.156 393.158 393.155 393.157 393.155 393.154 393.158 393.157 393.157 393.158 388.157 388.156 388.156 388.154 388.159 388.157 388.160 388.158 388.162 382.996 382.996 382.995 382.996 383.000 383.000 382.997 382.992 382.994 378.014 378.013 378.016 378.014 378.012 378.008 378.016 378.014 378.016 373.020 373.021 373.024 373.020 373.022 373.017 373.024 373.022 373.022 368.018 368.022 368.023 368.019 368.019 368.023 368.021 368.019 363.019 363.022 363.026 363.024 363.024
4733.1 3841.3 2927.6 2138.7 1519.6 1059.8 730.6 499.2 339.5 4565.9 3741.7 2867.1 2101.4 1495.8 1044.9 720.6 492.8 335.2 4395.6 3640.7 2806.1 2063.6 1471.9 1029.5 710.6 486.3 330.9 4220.5 3538.7 2744.7 2025.4 1448.0 1014.1 700.6 479.7 326.5 3406.8 2655.8 1965.5 1407.5 986.8 682.1 467.5 318.2 215.8 3303.1 2594.1 1927.6 1383.6 971.3 671.9 460.8 313.8 212.9 3195.6 2531.5 1889.3 1359.6 955.9 662.0 454.2 309.4 209.9 2467.9 1850.7 1335.4 940.4 652.1 447.5 305.0 207.0 2403.4 1811.7 1311.0 924.9 642.0
0.5704 0.6883 0.7801 0.8474 0.8953 0.9286 0.9518 0.9670 0.9780 0.5568 0.6786 0.7732 0.8426 0.8919 0.9265 0.9501 0.9662 0.9773 0.5427 0.6685 0.7661 0.8378 0.8886 0.9242 0.9486 0.9652 0.9766 0.5277 0.6580 0.7589 0.8327 0.8853 0.9219 0.9470 0.9642 0.9760 0.6495 0.7529 0.8286 0.8823 0.9198 0.9454 0.9635 0.9752 0.9834 0.6382 0.7453 0.8235 0.8789 0.9175 0.9437 0.9625 0.9745 0.9831 0.6256 0.7370 0.8179 0.8752 0.9150 0.9422 0.9613 0.9738 0.9824 0.7280 0.8118 0.8710 0.9121 0.9405 0.9598 0.9728 0.9816 0.7187 0.8056 0.8668 0.9093 0.9386
2.476 1.665 1.120 0.7529 0.5063 0.3405 0.2290 0.1540 0.1036 2.477 1.666 1.120 0.7533 0.5066 0.3407 0.2291 0.1541 0.1036 2.478 1.666 1.121 0.7535 0.5068 0.3408 0.2292 0.1541 0.1036 2.478 1.667 1.121 0.7537 0.5068 0.3408 0.2292 0.1541 0.1037 1.647 1.108 0.7449 0.5010 0.3369 0.2266 0.1524 0.1025 0.0689 1.647 1.108 0.7448 0.5009 0.3368 0.2265 0.1523 0.1024 0.0689 1.647 1.108 0.7448 0.5009 0.3369 0.2265 0.1523 0.1025 0.0689 1.108 0.7450 0.5010 0.3370 0.2266 0.1524 0.1025 0.0689 1.108 0.7451 0.5011 0.3370 0.2266
J. Yin, J. Wu / Fluid Phase Equilibria 298 (2010) 298–302
301
Table 2 (Continued) T/K
P/kPa
Z
/mol dm−3
363.025 363.024 363.023 358.023 358.026 358.020 358.025 358.025 358.027 358.026 358.024 353.027 353.029 353.030 353.031 353.030 353.030 353.029 348.028 348.030 348.029 348.030 348.030 348.030 348.030 343.046 343.047 343.044 343.045 343.046 343.045 343.047 338.047 338.042 338.045 338.040 338.045 338.040 333.047 333.039 333.041 333.044 333.041 333.042 328.051 328.044 328.046 328.048 328.042 328.047
440.9 300.7 204.1 2337.4 1772.2 1286.3 909.4 632.0 434.3 296.3 201.2 1732.3 1261.7 893.5 621.8 427.6 291.9 198.3 1691.9 1236.9 877.7 611.6 420.9 287.4 195.3 1650.7 1212.0 861.9 601.4 414.2 283.0 192.3 1186.7 845.9 591.2 407.5 278.6 189.3 1161.0 829.9 580.8 400.9 274.0 186.4 1134.7 813.7 570.5 394.1 269.7 183.5
0.9585 0.9720 0.9810 0.7086 0.7989 0.8622 0.9064 0.9366 0.9572 0.9710 0.9804 0.7918 0.8576 0.9031 0.9345 0.9557 0.9699 0.9798 0.7846 0.8530 0.9000 0.9326 0.9544 0.9690 0.9792 0.7769 0.8482 0.8969 0.9306 0.9531 0.9683 0.9784 0.8430 0.8936 0.9286 0.9518 0.9675 0.9777 0.8373 0.8899 0.9261 0.9505 0.9662 0.9771 0.8304 0.8855 0.9231 0.9484 0.9651 0.9762
0.1524 0.1025 0.0689 1.108 0.7453 0.5012 0.3370 0.2267 0.1524 0.1025 0.0689 0.7453 0.5012 0.3371 0.2267 0.1524 0.1025 0.0689 0.7452 0.5011 0.3370 0.2266 0.1524 0.1025 0.0689 0.7450 0.5010 0.3369 0.2266 0.1524 0.1025 0.0689 0.5009 0.3368 0.2265 0.1523 0.1024 0.0689 0.5008 0.3368 0.2265 0.1523 0.1024 0.0689 0.5010 0.3369 0.2266 0.1524 0.1025 0.0689
Fig. 3. Behavior of (Z − 1)/ versus along each isotherm for DME.
Fig. 4 shows the second virial coefficients against reduced temperature for the present work and values reported in the literature. The figure shows that the second virial coefficients of this work obtained by two separated Burnett-isochoric produces have good consistency. It was found that most literature data were obtained before the 1970s and the investigated temperature range normally below the lowest temperature of the present work. The latest data given by Ref. [15] has a reduced temperature range from 0.86 to 0.98. Compared to the data published in the literature [9,11,13], the tendency of Eq. (2) given by the present work for lower temperature is more reasonable than the equation given by Ref. [15]. Based on 16 sets of the second and third virial coefficients, all experimental data listed in Table 2 can be reproduced by a trun-
Table 3 Second and third virial coefficients of dimethyl ether. T/K
B/cm3 mol−1
C/cm6 mol−2
This work
Calc from Eq. of Ref. [15]
403.157 398.157 393.157 388.158 382.996 378.014 373.021 368.021 363.023 358.025 353.029 348.030 343.046 338.043 333.042 328.046
−215.3 −221.9 −228.7 −235.5 −244.4 −251.3 −258.6 −267.2 −275.5 −284.3 −293.9 −302.5 −310.5 −320.9 −328.0 −342.0
−211.3 −218.4 −225.6 −233.0 −240.9 −248.7 −256.7 −265.0 −273.4 −282.1 −291.1 −300.3 −309.8 −319.5 −329.6 −339.9
16,860 17,374 17,805 18,113 19,194 19,185 19,012 19,565 19,512 19,253 19,614 18,072 14,764 13,552 6441 6366
Fig. 4. Second virial coefficients against reduced temperature: , this work; 夽, Ref. [9]; ×, Ref. [10]; ♦, Ref. [11]; , Ref. [12]; +, Ref. [13]; , Ref. [14]; , Ref. [15]; —, this work; . . ., Ref. [15].
302
J. Yin, J. Wu / Fluid Phase Equilibria 298 (2010) 298–302
of temperature was estimated to be within ±10 mK and that of pressure was less than ±0.7 kPa. Second virial coefficients along 16 isotherms were obtained and a temperature relationship for the calculation of second virial coefficients was also given based on the present work. Acknowledgements This research is supported by the Research Fund for the Doctoral Program of Higher Education (No. 20090201110008) and the Fok Ying Tung Education Foundation Award (No. 111060). References
Fig. 5. Pressure deviation of experimental data of DME from Eq. (3).
cated virial equation of state for each isotherm: p = 1 + B + C2 RT
(3)
where the gas constant R = 8.31447 J mol−1 K−1 . The pressure deviations of experimental data here from Eq. (3) are shown in Fig. 5, and it can be found that all the deviations are within ±0.06%. 4. Conclusions A total of 126 gas phase PVT data for dimethyl ether were obtained using Burnett-isochoric method in the temperature range of 328–403 K, the pressure range of 183–4733 kPa and density range from 0.07 to 2.5 mol dm−3 . The measurement uncertainty
[1] T.A. Semelsberger, R.L. Borup, H.L. Greene, J. Power Sources 156 (2006) 497–511. [2] E.C. Ihmels, E.W. Lemmon, Fluid Phase Equilib. 260 (2007) 36–48. [3] J.T. Wu, J.G. Yin, J. Chem. Eng. Data 53 (2008) 2247–2249. [4] J.T. Wu, Z.G. Liu, B. Wang, J. Pan, J. Chem. Eng. Data 49 (2004) 704–708. [5] J.T. Wu, Z.G. Liu, F.K. Wang, J. Chem. Eng. Data 48 (2003) 1571–1573. [6] J.T. Wu, Z.G. Liu, S.S. Bi, X.Y. Meng, J. Chem. Eng. Data 48 (2003) 426–429. [7] J.T. Wu, X.J. Li, H.F. Zheng, M.J. Assael, J. Chem. Eng. Data 54 (2009) 1720–1723. [8] Y.G. Wang, J.T. Wu, Z.G. Liu, J. Chem. Eng. Data 51 (2006) 164–168. [9] W. Cawood, H.S. Petterson, J. Chem. Soc. 156 (1933) 619–624. [10] R.M. Kennedy, M. Sagenkahn, J.G. Aston, J. Am. Chem. Soc. 63 (1941) 2267–2272. [11] T.B. Tripp, R.D. Dunlap, J. Phys. Chem. 66 (1962) 635–639. [12] B. Osipiuk, R. Stryjek, Bull. Acad. Polon. Sci. Ser. Sci. Chim. 18 (1970) 289–295. [13] W.S. Haworth, L.E. Sutton, Trans. Faraday Soc. 67 (1971) 2907–2914. [14] T.A. Tsujimoto, H. Kubota, Y. Tanaka, S. Matsuo, T.T. Sotani, 13th Japan Symposium on Thermophysical Properties, 1992, pp. 217–220. [15] A. Arteconi, G. Di Nicola, G. Santori, R. Stryjek, J. Chem. Eng. Data 54 (2009) 1840–1843. [16] A. Arteconi, G. Nicola, M. Moglie, G. Santori, R. Stryjek, J. Therm. Anal. Calorim. 97 (2009) 631–636. [17] S. Angus, K.M. de Reuck, R.D. McCarty, International Thermodynamic Tables of the Fluid State Helium-4, Pergamon, Oxford, 1977. [18] D. Gupta, Simulation and Propagation of Random and Systematic Errors in Thermophysical Experiments, Ph.D. thesis, Texas A&M University, 1996. [19] W.C. Pfefferle, J.A. Goff, J.G. Miller, J. Chem. Phys. 23 (1955) 509–513.
Contents lists available at ScienceDirect
Fluid Phase Equilibria journal homepage: www.elsevier.com/locate/fluid
Gas phase PVT properties and second virial coefficients of dimethyl ether Jianguo Yin, Jiangtao Wu ∗ State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, People’s Republic of China
a r t i c l e
i n f o
Article history: Received 22 March 2010 Received in revised form 17 August 2010 Accepted 29 August 2010 Available online 24 September 2010 Keywords: Dimethyl ether (DME) PVT Second virial coefficient
a b s t r a c t Dimethyl ether (DME) is an important chemical material and gets more and more attention as a clean alternative fuel and refrigerant nowadays. The gas phase PVT properties of dimethyl ether were measured using the Burentt-isochoric coupling method in the temperature range of 328–403 K with two Burnett expansions at 383 and 403 K. A total of 126 experimental points have been obtained. The experimental measurement uncertainties were estimated to be within ±10 mK for temperature and ±0.7 kPa for pressure. The second virial coefficients along 16 isotherms were derived using the present data. Crown Copyright © 2010 Published by Elsevier B.V. All rights reserved.
1. Introduction Dimethyl ether (DME) is an important chemical material which has many engineering applications such as aerosol propellant, assistant solvent, vesicant and so on. Furthermore, dimethyl ether is regarded as a promising clean alternative fuel for its lager oxygen content and lower emissions of SOx , NOx or particulates than conventional fuel when burning as well as its high-efficiency and non-petroleum based character [1]. It also has been suggested as an alternative refrigerant named as RE170. In these fields, the thermophysical properties of dimethyl ether are indispensable. A preliminary fundamental equation of state was derived by Ref. [2] and our group has also been done some research on vapor pressure, critical properties, saturation densities, surface tension, liquid viscosity and thermal conductivity of dimethyl ether recently [3–8]. After a literature survey, a very limited data of second virial coefficients and gas phase PVT properties for dimethyl ether were found [9–16]. In this work, a total of 126 experimental data were collected in the gas phase region for the temperature range of 328–403 K including 9 points in the super-critical region. Derived second virial coefficients were compared with the literature data. 2. Experimental The sample of dimethyl ether was provided by Shandong Jiutai Chemical Co. Ltd. of China. The stated mass purity is better than 99.95%. In order to eliminate the effect of gaseous impurity, the
∗ Corresponding author. Tel.: +86 29 82666875; fax: +86 29 82668789. E-mail address: [email protected] (J. Wu).
sample was purified several times by freeze-pump-thaw cycles by using liquid nitrogen and a high vacuum (<0.01 Pa) pump. The experimental apparatus used in this work is illustrated in Fig. 1. It consists of a Burnett apparatus, a thermostatic bath, a temperature measurement system, a pressure measurement system and a vacuum discharge system. The Burnett apparatus consists of two pressure cells: a sample cell (A) and an expansion cell (B). The two cells were all cylinder vessels made of 1Cr18Ni9Ti stainless steel with a thickness of 10 mm. Cell (A), with a volume of about 623 cm3 at room temperature, was 125 mm in outside diameter and the height of the cylinder is 130 mm. Cell (B), with a volume of about 310 cm3 at room temperature, was 80 mm in outside diameter and the height of cylinder is the same as cell (A). The sample valve (V1), expansion valve (V2) and vacuum valve (V3) was non-rotating type valve which could provide excellent seal performance along the whole experimental procedure. The whole apparatus coupled with a diaphragm-type differential pressure transducer was immersed in a thermostatic bath to establish temperature uniformity. Silicone oil was used as a heat transfer medium in the bath and its temperature was controlled by a PID regulator. The temperature measurement system includes a 25 standard platinum resistance thermometer (Model: WZPB, No. 92822, Kunming Temperature Instruments Co. Ltd., China) installed near the cells and a high precision thermometer bridge (Model: F700B, ASL, UK). The thermometer was calibrated on the ITS-90 scale at the National Institute of Metrology of China and the total temperature uncertainty including the temperature fluctuation of the thermostatic bath was estimated to be less than ±10 mK. The pressure was measured with a differential pressure transducer (Model: Rosemount 3051, range: 0–6.0 kPa, accuracy: 0.075% F.S.) and a digital quartz pressure transmitter (Model: Paroscien-
0378-3812/$ – see front matter. Crown Copyright © 2010 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2010.08.023
J. Yin, J. Wu / Fluid Phase Equilibria 298 (2010) 298–302
Fig. 1. Schematic diagram of experimental system: A: sample cell; B: expansion cell; C: differential pressure transducer; D: standard platinum resistance thermometer; E: shield board; F: stirrer; G: heater; H: temperature controller; I: thermometric bridge; J: nitrogen reservoir; K: expansion chamber; L: sample bottle; M: quartz pressure transmitter; N: pressure acquisition system; O: acquisition computer; V1–V3: non-rotating type valve; V4–V11: valve.
tific 31K-101, range: 0–6.9 MPa, accuracy: 0.01% F.S.). Nitrogen gas was used as pressure transfer medium in the differential pressure transducer. The valves used to balance the differential pressure transducer were small needle valves and the size of the connecting tube was small (the outside diameter was 2 mm). When the valves were operated carefully, the nitrogen gas pressure could increase or decrease slowly till the balance was reached. A pressure gauge was used to indicate the pressure change of the nitrogen gas. The differential pressure transducer was carefully calibrated in advance by opening both sides of the diaphragm to the same pressure as a function of temperature. The calibration results were used to modify the pressure measurements and the total uncertainty of pressure measurements was better than ±0.7 kPa. The high vacuum was provided by a turbo-molecular pump (Model: FD110, KYKY, China, the stated ultimate pressure is 1 × 10−6 Pa). High purity helium (99.999 mol%) was used to determine the cell constant N0 , defined as the ratio of the total volume of cell (A) and (B) to the volume of cell (A) at zero pressure. Because the material of cell (A) and (B) are the same, the cell constant is independent of temperature. The pressure distortion of the cell volume is also negligible for the two cells are all thick-walled metal vessels and the maximum pressure was no more than 5 MPa. Two separate Burnett expansions of helium were made at 383 K and two N0 were obtained: N01 = 1.48703, N02 = 1.48695. The Burnett expansion data of helium were listed in Table 1 and the average absolute deviation of experimental densities from the calculated values by the IUPAC equation [17] is 0.005%. Finally the average value of 1.48699 ± 0.00010 was used in this work. The Burnett-isochoric coupling method used in this work was similar to that of Ref. [18]. Before an experiment, all apparatus system was placed under vacuum and rinsed with dimethyl ether
299
for several times, then after the system was discharged to high vacuum again and maintained for at least 4 h, a fitting amount of dimethyl ether was introduced into the sample cell (A). Then the sample valve (V1) and expansion valve (V2) were closed and the thermostatic bath was controlled at the experimental temperature. After the thermal equilibrium between the sample and thermostatic bath was attained and the pressure remained constant, a pressure measurement was done and this formed the first point on the Burnett-isochoric surface. Then the thermostatic bath was cooled to next desired temperature and the pressure measurement was made when the thermal equilibrium was attained again. This sequence of temperature cooling and pressure measurement was repeated until the sample pressure close to vapor pressure value at the corresponding temperature. The thermostatic bath was then heated to the initial temperature and the pressure measurement repeated and compared with the first point value which could indicated any leaks out of cell (A). The first isochore of the maximum sample density was constituted via this sequence of measurements. Next, the first Burnett expansion was made at the base temperature: first, the cell (B) was evacuated by the high vacuum system for 1 h and pressure inside the cell (B) had a conservative value of lower than 0.1 Pa. The vacuum valve (V3) was then closed and expansion valve (V2) was opened quickly by two full turns. After about an hour of equilibration, valve (V2) was closed very slowly, and the pressure of cell (A) was then measured. This procedure made the first Burnett expansion measurement and formed the first point of the second isochore. Then the sequence of temperature cooling and pressure measurement mentioned above was repeated to finish this isochore. The bath was then again heated to the base temperature, the pressure measurement was done and the second Burnett expansion was made to get the third isochore. In this manner, the whole Burnett-isochoric surface was carried out with a single charge of sample. In order to verify the reliability and repeatability of the experimental system, two series Burnett-isochoric experimental procedures were made to cover the entire P-T surface: one process for temperature range from 328 to 383 K with Burnett expansion at 383 K and another process from 388 to 403 K with Burnett expansion at 403 K. 3. Results and discussion A total of 126 gas phase PVT data for dimethyl ether along 16 isotherms in temperature range from 328 to 403 K and for pressures from 183 to 4733 kPa were obtained and the data surface is shown in Fig. 2. All the PVT data were analyzed by Burnett analysis method along each isotherm with the cell constant obtained using helium. The Table 1 Burnett expansion data of helium. T/K
P/kPa
Z
exp /kg m−3
calc from Eq. of IUPAC/kg m−3
Error/%
382.992 382.992 382.992 382.992 382.992 382.992 382.992 382.995 382.995 382.995 382.995 382.995 382.995 382.995
4760.6 3183.9 2133.2 1431.0 960.7 645.4 433.6 4988.6 3335.6 2234.5 1498.8 1006.2 675.8 454.2
1.01690 1.01134 1.00761 1.00512 1.00344 1.00231 1.00155 1.01786 1.01201 1.00808 1.00544 1.00366 1.00246 1.00165
5.88450 3.95723 2.66116 1.78958 1.20343 0.80937 0.54422 6.16044 4.14298 2.78620 1.87381 1.26020 0.84735 0.56998
5.88488 3.95714 2.66103 1.78950 1.20338 0.80935 0.54421 6.16194 4.14349 2.78637 1.87387 1.26022 0.84736 0.56999
−0.006 0.002 0.005 0.005 0.004 0.003 0.002 −0.024 −0.012 −0.006 −0.003 −0.002 −0.001 −0.001
300
J. Yin, J. Wu / Fluid Phase Equilibria 298 (2010) 298–302 Table 2 PVT properties of dimethyl ether.
Fig. 2. Distribution of experimental data for DME: , experimental procedure 1 from 328 to 383 K, , experimental procedure 2 from 388 to 403 K; , critical point [4]; —, vapor pressure line [3].
experimental data along with the calculated compressibility factors and densities are given in Table 2. The density uncertainty was estimated to be within ±0.15%. The Burnett analysis method used in this work was similar to that of Ref. [19]. In the regression, each isotherm was treated separately and the following equation was used: AN0r pr = 1 + Bpr + Cpr
(1)
where A was written for Z0 /p0 , and a least-square routine was used to yield virial coefficients simultaneously. The second virial coefficients, B, and third virial coefficients, C, derived from the present measurements for each isotherm are given in Table 3. The second viral coefficients were fitted to the following temperature relationship: B = B0 + B1 Tr−1 + B2 Tr−2 + B3 Tr−3 + B4 Tr−6
(2)
where the units of T are K, those of B, B0 –B4 are cm3 mol−1 , Tr = T/Tc . The critical temperature used here, Tc = 400.378, was the experimental result obtained by our group in Ref. [4]. The parameters in Eq. (2) are B0 = −2.348816E + 04, B1 = 7.730736E + 04, B2 = −8.821103E + 04, B3 = 3.547363E + 04, and B4 = −1.300762E + 03. All experimental data except two points can be represented by Eq. (2) within ±0.3%. When the experimental data can be expressed by a virial equation having second and third virial terms, the behavior of (Z − 1)/ versus should be a straight line whose intercept also gives the second virial coefficients along each isotherm as shown in Fig. 3. In Table 3, the second virial coefficients obtained in this work are compared with the values calculated by the equation given by Ref. [15], the only source which has made systematically research on second virial coefficients of dimethyl ether in the temperature range of 344–393 K. All data of this work except one point is less than the value calculated by the equation given in Ref. [15] but within the stated uncertainty. Generally, an adsorption effect on the metallic wall of two pressure cells may cause a more negative B value and the dependence of (Z − 1)/ on can be used as a diagnostic. While there is no obvious adsorption feature in Fig. 3, and the base isotherm temperature chosen in the present experimental procedure are relatively high, so the magnitude of error caused by adsorption effect could be neglected. Moreover, the equation given by Ref. [15] only has one item about the reduced temperature and the obvious deviation was found especially in low temperature. The function form used in Ref. [15] may be improved.
T/K
P/kPa
Z
/mol dm−3
403.158 403.158 403.156 403.156 403.158 403.156 403.158 403.157 403.158 398.156 398.159 398.155 398.157 398.156 398.158 398.158 398.156 398.156 393.158 393.155 393.157 393.155 393.154 393.158 393.157 393.157 393.158 388.157 388.156 388.156 388.154 388.159 388.157 388.160 388.158 388.162 382.996 382.996 382.995 382.996 383.000 383.000 382.997 382.992 382.994 378.014 378.013 378.016 378.014 378.012 378.008 378.016 378.014 378.016 373.020 373.021 373.024 373.020 373.022 373.017 373.024 373.022 373.022 368.018 368.022 368.023 368.019 368.019 368.023 368.021 368.019 363.019 363.022 363.026 363.024 363.024
4733.1 3841.3 2927.6 2138.7 1519.6 1059.8 730.6 499.2 339.5 4565.9 3741.7 2867.1 2101.4 1495.8 1044.9 720.6 492.8 335.2 4395.6 3640.7 2806.1 2063.6 1471.9 1029.5 710.6 486.3 330.9 4220.5 3538.7 2744.7 2025.4 1448.0 1014.1 700.6 479.7 326.5 3406.8 2655.8 1965.5 1407.5 986.8 682.1 467.5 318.2 215.8 3303.1 2594.1 1927.6 1383.6 971.3 671.9 460.8 313.8 212.9 3195.6 2531.5 1889.3 1359.6 955.9 662.0 454.2 309.4 209.9 2467.9 1850.7 1335.4 940.4 652.1 447.5 305.0 207.0 2403.4 1811.7 1311.0 924.9 642.0
0.5704 0.6883 0.7801 0.8474 0.8953 0.9286 0.9518 0.9670 0.9780 0.5568 0.6786 0.7732 0.8426 0.8919 0.9265 0.9501 0.9662 0.9773 0.5427 0.6685 0.7661 0.8378 0.8886 0.9242 0.9486 0.9652 0.9766 0.5277 0.6580 0.7589 0.8327 0.8853 0.9219 0.9470 0.9642 0.9760 0.6495 0.7529 0.8286 0.8823 0.9198 0.9454 0.9635 0.9752 0.9834 0.6382 0.7453 0.8235 0.8789 0.9175 0.9437 0.9625 0.9745 0.9831 0.6256 0.7370 0.8179 0.8752 0.9150 0.9422 0.9613 0.9738 0.9824 0.7280 0.8118 0.8710 0.9121 0.9405 0.9598 0.9728 0.9816 0.7187 0.8056 0.8668 0.9093 0.9386
2.476 1.665 1.120 0.7529 0.5063 0.3405 0.2290 0.1540 0.1036 2.477 1.666 1.120 0.7533 0.5066 0.3407 0.2291 0.1541 0.1036 2.478 1.666 1.121 0.7535 0.5068 0.3408 0.2292 0.1541 0.1036 2.478 1.667 1.121 0.7537 0.5068 0.3408 0.2292 0.1541 0.1037 1.647 1.108 0.7449 0.5010 0.3369 0.2266 0.1524 0.1025 0.0689 1.647 1.108 0.7448 0.5009 0.3368 0.2265 0.1523 0.1024 0.0689 1.647 1.108 0.7448 0.5009 0.3369 0.2265 0.1523 0.1025 0.0689 1.108 0.7450 0.5010 0.3370 0.2266 0.1524 0.1025 0.0689 1.108 0.7451 0.5011 0.3370 0.2266
J. Yin, J. Wu / Fluid Phase Equilibria 298 (2010) 298–302
301
Table 2 (Continued) T/K
P/kPa
Z
/mol dm−3
363.025 363.024 363.023 358.023 358.026 358.020 358.025 358.025 358.027 358.026 358.024 353.027 353.029 353.030 353.031 353.030 353.030 353.029 348.028 348.030 348.029 348.030 348.030 348.030 348.030 343.046 343.047 343.044 343.045 343.046 343.045 343.047 338.047 338.042 338.045 338.040 338.045 338.040 333.047 333.039 333.041 333.044 333.041 333.042 328.051 328.044 328.046 328.048 328.042 328.047
440.9 300.7 204.1 2337.4 1772.2 1286.3 909.4 632.0 434.3 296.3 201.2 1732.3 1261.7 893.5 621.8 427.6 291.9 198.3 1691.9 1236.9 877.7 611.6 420.9 287.4 195.3 1650.7 1212.0 861.9 601.4 414.2 283.0 192.3 1186.7 845.9 591.2 407.5 278.6 189.3 1161.0 829.9 580.8 400.9 274.0 186.4 1134.7 813.7 570.5 394.1 269.7 183.5
0.9585 0.9720 0.9810 0.7086 0.7989 0.8622 0.9064 0.9366 0.9572 0.9710 0.9804 0.7918 0.8576 0.9031 0.9345 0.9557 0.9699 0.9798 0.7846 0.8530 0.9000 0.9326 0.9544 0.9690 0.9792 0.7769 0.8482 0.8969 0.9306 0.9531 0.9683 0.9784 0.8430 0.8936 0.9286 0.9518 0.9675 0.9777 0.8373 0.8899 0.9261 0.9505 0.9662 0.9771 0.8304 0.8855 0.9231 0.9484 0.9651 0.9762
0.1524 0.1025 0.0689 1.108 0.7453 0.5012 0.3370 0.2267 0.1524 0.1025 0.0689 0.7453 0.5012 0.3371 0.2267 0.1524 0.1025 0.0689 0.7452 0.5011 0.3370 0.2266 0.1524 0.1025 0.0689 0.7450 0.5010 0.3369 0.2266 0.1524 0.1025 0.0689 0.5009 0.3368 0.2265 0.1523 0.1024 0.0689 0.5008 0.3368 0.2265 0.1523 0.1024 0.0689 0.5010 0.3369 0.2266 0.1524 0.1025 0.0689
Fig. 3. Behavior of (Z − 1)/ versus along each isotherm for DME.
Fig. 4 shows the second virial coefficients against reduced temperature for the present work and values reported in the literature. The figure shows that the second virial coefficients of this work obtained by two separated Burnett-isochoric produces have good consistency. It was found that most literature data were obtained before the 1970s and the investigated temperature range normally below the lowest temperature of the present work. The latest data given by Ref. [15] has a reduced temperature range from 0.86 to 0.98. Compared to the data published in the literature [9,11,13], the tendency of Eq. (2) given by the present work for lower temperature is more reasonable than the equation given by Ref. [15]. Based on 16 sets of the second and third virial coefficients, all experimental data listed in Table 2 can be reproduced by a trun-
Table 3 Second and third virial coefficients of dimethyl ether. T/K
B/cm3 mol−1
C/cm6 mol−2
This work
Calc from Eq. of Ref. [15]
403.157 398.157 393.157 388.158 382.996 378.014 373.021 368.021 363.023 358.025 353.029 348.030 343.046 338.043 333.042 328.046
−215.3 −221.9 −228.7 −235.5 −244.4 −251.3 −258.6 −267.2 −275.5 −284.3 −293.9 −302.5 −310.5 −320.9 −328.0 −342.0
−211.3 −218.4 −225.6 −233.0 −240.9 −248.7 −256.7 −265.0 −273.4 −282.1 −291.1 −300.3 −309.8 −319.5 −329.6 −339.9
16,860 17,374 17,805 18,113 19,194 19,185 19,012 19,565 19,512 19,253 19,614 18,072 14,764 13,552 6441 6366
Fig. 4. Second virial coefficients against reduced temperature: , this work; 夽, Ref. [9]; ×, Ref. [10]; ♦, Ref. [11]; , Ref. [12]; +, Ref. [13]; , Ref. [14]; , Ref. [15]; —, this work; . . ., Ref. [15].
302
J. Yin, J. Wu / Fluid Phase Equilibria 298 (2010) 298–302
of temperature was estimated to be within ±10 mK and that of pressure was less than ±0.7 kPa. Second virial coefficients along 16 isotherms were obtained and a temperature relationship for the calculation of second virial coefficients was also given based on the present work. Acknowledgements This research is supported by the Research Fund for the Doctoral Program of Higher Education (No. 20090201110008) and the Fok Ying Tung Education Foundation Award (No. 111060). References
Fig. 5. Pressure deviation of experimental data of DME from Eq. (3).
cated virial equation of state for each isotherm: p = 1 + B + C2 RT
(3)
where the gas constant R = 8.31447 J mol−1 K−1 . The pressure deviations of experimental data here from Eq. (3) are shown in Fig. 5, and it can be found that all the deviations are within ±0.06%. 4. Conclusions A total of 126 gas phase PVT data for dimethyl ether were obtained using Burnett-isochoric method in the temperature range of 328–403 K, the pressure range of 183–4733 kPa and density range from 0.07 to 2.5 mol dm−3 . The measurement uncertainty
[1] T.A. Semelsberger, R.L. Borup, H.L. Greene, J. Power Sources 156 (2006) 497–511. [2] E.C. Ihmels, E.W. Lemmon, Fluid Phase Equilib. 260 (2007) 36–48. [3] J.T. Wu, J.G. Yin, J. Chem. Eng. Data 53 (2008) 2247–2249. [4] J.T. Wu, Z.G. Liu, B. Wang, J. Pan, J. Chem. Eng. Data 49 (2004) 704–708. [5] J.T. Wu, Z.G. Liu, F.K. Wang, J. Chem. Eng. Data 48 (2003) 1571–1573. [6] J.T. Wu, Z.G. Liu, S.S. Bi, X.Y. Meng, J. Chem. Eng. Data 48 (2003) 426–429. [7] J.T. Wu, X.J. Li, H.F. Zheng, M.J. Assael, J. Chem. Eng. Data 54 (2009) 1720–1723. [8] Y.G. Wang, J.T. Wu, Z.G. Liu, J. Chem. Eng. Data 51 (2006) 164–168. [9] W. Cawood, H.S. Petterson, J. Chem. Soc. 156 (1933) 619–624. [10] R.M. Kennedy, M. Sagenkahn, J.G. Aston, J. Am. Chem. Soc. 63 (1941) 2267–2272. [11] T.B. Tripp, R.D. Dunlap, J. Phys. Chem. 66 (1962) 635–639. [12] B. Osipiuk, R. Stryjek, Bull. Acad. Polon. Sci. Ser. Sci. Chim. 18 (1970) 289–295. [13] W.S. Haworth, L.E. Sutton, Trans. Faraday Soc. 67 (1971) 2907–2914. [14] T.A. Tsujimoto, H. Kubota, Y. Tanaka, S. Matsuo, T.T. Sotani, 13th Japan Symposium on Thermophysical Properties, 1992, pp. 217–220. [15] A. Arteconi, G. Di Nicola, G. Santori, R. Stryjek, J. Chem. Eng. Data 54 (2009) 1840–1843. [16] A. Arteconi, G. Nicola, M. Moglie, G. Santori, R. Stryjek, J. Therm. Anal. Calorim. 97 (2009) 631–636. [17] S. Angus, K.M. de Reuck, R.D. McCarty, International Thermodynamic Tables of the Fluid State Helium-4, Pergamon, Oxford, 1977. [18] D. Gupta, Simulation and Propagation of Random and Systematic Errors in Thermophysical Experiments, Ph.D. thesis, Texas A&M University, 1996. [19] W.C. Pfefferle, J.A. Goff, J.G. Miller, J. Chem. Phys. 23 (1955) 509–513.