Measurements of the Speed of Sound in Propene ... - ACS Publications

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Measurements of the Speed of Sound in Propene in the Liquid and Supercritical Regions K. Meier*,† and S. Kabelac‡ Institut für Thermodynamik, Helmut-Schmidt-Universität/Universität der Bundeswehr Hamburg, Holstenhofweg 85, D-22043 Hamburg, Germany ABSTRACT: This paper reports comprehensive and accurate measurements of the speed of sound in pure propene in the liquid and supercritical regions. The data have been measured by a double-path-length pulse-echo technique and cover the temperature range from 240 K to 420 K with pressures up to 100 MPa. The measurement uncertainties amount to 3 mK for temperature, 0.01 % for pressures below 10 MPa, 0.005 % for pressures between 10 MPa and 100 MPa, and 0.015 % for speed of sound. The high accuracy of the measurements is demonstrated by comparisons with literature data and three fundamental equations of state.

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INTRODUCTION Propene (propylene, C3H6) is one of the most important basic chemicals in the chemical industry. Is is mainly used in the production of the thermoplastic polymer polypropylene, and it also serves as a basic ingredient for the production of important chemicals such as acetone, acrylic acid, acrylonitrile, and many others. For designing and optimizing equipment and production processes for these applications, an accurate fundamental equation of state for propene, from which all thermodynamic properties can be calculated, is desirable. In 2004, when this work was carried out, the fundamental equation of state of Angus et al.1 published in 1980 provided the best representation of the thermodynamic properties of propene. This equation of state was accepted by IUPAC as the international standard. Since then several new and more accurate experimental data for the thermodynamic properties of propene became available, for example the p−ρ−T data of Glos et al.,2 and furthermore, techniques for fitting fundamental equations of state to experimental data have improved, which provides the basis for establishing a new more accurate fundamental equation of state. The development of a new fundamental equation of state requires, among other properties, accurate speed of sound data as part of the experimental data set to which the equation is fitted. For the speed of sound in propene, four rather old data sets are available in the literature, which were published by Blagoi et al.3 in 1968, Dudar and Mikhailenko4 in 1977, Soldatenko and Dregulyas5 in 1970, and Terres et al.6 in 1957. Blagoi et al., Soldatenko and Dregulyas, and Terres et al. applied interferometer techniques to measure the speed of sound, whereas Dudar and Mikhailenko used a pulse method. Blagoi et al. and Dudar and Mikhailenko measured the speed of sound in the saturated liquid. The data of Soldatenko and Dregulyas cover the gas and supercritical regions between 193 K and 473 K with pressures up to 10 MPa. The data of Terres et al. cover the gas and supercritical regions between 293 K and 448 K with pressures up to 10 MPa. A few data were © 2013 American Chemical Society

also measured in the liquid region at low pressures. This work fills a gap by providing speed of sound data in the liquid and supercritical regions at high pressures and thereby contributes to the development of a new fundamental equation of state for propene. It is part of a larger program in our laboratory to measure the speed of sound in several pure fluids.7−9 Parallel, but independent of this work, a new fundamental equation of state for propene was developed by Overhoff14 at the Ruhr-University Bochum without knowing about our speed of sound data. After this work was completed, a new fundamental equation of state for propene was established by Lemmon et al.10 In the optimization process of this equation of state, our speed of sound data were used.

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EXPERIMENTAL PROCEDURE

Our speed of sound instrument has been described in detail in ref 11. The measurement principle of our acoustic sensor is a double-path-length pulse-echo technique, which was first introduced by Muringer et al.12 Our sensor employs a piezoelectric quartz crystal as a sound emitter and receiver, which is operated at its resonance frequency of 8 MHz. The acoustic path length in the sensor and the thermal expansion coefficient of the sensor material were determined by calibration measurements with liquid water at ambient pressure. In the analysis of the measurements, corrections for changes of the distances in the speed of sound sensor with temperature for compression of the sensor with pressure and for diffraction effects are applied. Propene was the first fluid measured with the speed of sound apparatus. The calibration measurements, which were carried out before the propene measurements, showed slightly higher scatter than those achieved in later calibrations. Thus, the Received: December 20, 2012 Accepted: March 19, 2013 Published: April 25, 2013 1621

dx.doi.org/10.1021/je301344y | J. Chem. Eng. Data 2013, 58, 1621−1628

Journal of Chemical & Engineering Data

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MATERIALS The propene sample was purchased from Deutsche Air Liquide with a manufacturer specified volume purity better than 99.95 % (see Table 2). After degassing the sample, its purity was analyzed

uncertainty of the speed of sound measurement is U(c) = (9.0·10−5 + 2.5·10−7·p/MPa)·c, excluding contributions from sample impurities and due to temperature and pressure measurement uncertainties. The second term accounts for the uncertainty of the compression of the sensor with pressure. The uncertainty is 20 ppm higher than that achieved in our studies of propane8 and the refrigerants R-227ea and R-365mfc.9 The speed of sound sensor is mounted in a pressure vessel, which is thermostatted in a circulating liquid-bath thermostat. The temperature inside the pressure vessel is kept constant within 0.5 mK. The temperature was measured by a Pt25 sensor calibrated on ITS-90, which is located in the wall of the pressure vessel, with an estimated uncertainty of 3 mK. The pressure inside the pressure vessel was measured with two nitrogenoperated gas pressure balances with measurement ranges of 5 MPa and 100 MPa. The pressure balances were coupled to the sample liquid via a differential pressure null indicator (Ruska membrane type cell). The uncertainty of the pressure measurement is estimated to be 0.01 % below 10 MPa and 0.005 % between 10 MPa and 100 MPa. All measurement uncertainties refer to a 95 % confidence level. A detailed summary of the contributions to the measurement uncertainties is given in Table 1.

Table 2. Chemical Sample Description chemical name propene

propene a

source of uncertainty

value (confidence level = 95 %)

5·10−6·ΔL 10·10−6·ΔL 10 45·10−6·p 5·10−6·p 2·10−6·p

7 Pa

7 Pa

7 Pa

93·10−6·p

105·10−6·p

53·10−6·p

source

initial purity

purification method

final purity

HSU Sample (Purity in Volume Fractions) Deutsche Air 0.9995 degassing 0.9999 Liquide RUB Sample (Purity in Mole Fractions) Messer 0.9997 none 0.9997 Griesheim

analysis method GCa

none

Gas chromatography.

with a gas chromatograph. Two impurities with 0.008 and 0.002 area % besides the main propene peak were detected, whose nature could not be identified. They are probably other hydrocarbons, which are remains of the production process. No nitrogen, oxygen, or water were detected. Thus, the volume purity of the sample is estimated to be better than 99.990 %. As will be shown below, the impurities have a negligible influence on the speed of sound in propene. The reproducibility of the speed of sound for repeated measurements at the same state point after temperature and pressure cycles was better than 0.002 %. On the subcritical isotherms 340 K and 360 K and on supercritical isotherms, the reproducibility at states with low pressures was somewhat larger, amounting up to 0.005 %. This small scatter of the measured speeds of sound is due to the fact that the uncertainties of the temperature and pressure measurements limit the accuracy within which a state point can be set in the apparatus. Thus, the reproducibility does not contribute to the uncertainty of the speed of sound measurement since it is accounted for in the combined uncertainty by the uncertainty contributions of the temperature and pressure measurements described below. Thermal relaxation phenomena do not significantly influence the propagation of sound waves in propene in the frequency range of our measurements so that no dispersion correction is required.13 The uncertainty contributions due to the uncertainties of the temperature and pressure measurements were estimated by the equation of state of Lemmon et al.10 to be 0.003 % for the temperature measurement and 0.002 % for the pressure measurement. For the lowest measured pressures on the supercritical isotherms, the influence of the pressure measurement is larger, amounting to 0.005 %. When taking these additional contributions into account, the combined uncertainty of the speed of sound becomes Uc(c) = (1.4·10−4 + 2.5·10−7·p/MPa)·c. At the lowest pressures on the subcritical isotherms 340 K and 360 K and on the supercritical isotherms, 1.4 has to be replaced by 1.7. These uncertainty estimates are for a 95 % confidence level.

Table 1. Summary of Uncertainty Budgets determination of acoustic path length: time difference temperature measurement pressure measurement diffraction correction uncertainty of reference data agreement with reference data total uncertainty

Article

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RESULTS The distribution of our measurements and the two literature data sets in the p,T plane are shown in Figure 1. Our data cover the subcritical liquid region from 240 K upward and extend up to 420 K into the supercritical region with pressures up to 100 MPa. At moderate pressures in the supercritical region, they overlap with the data of Soldatenko and Dregulyas.

a

The total uncertainties are upper limits for the lowest pressures of each range. For the measurements at 1.3 MPa on the (240, 260, and 280) K isotherms and at 1.4 MPa on the 300 K isotherm the total uncertainty is 1.2·10−4·p 1622



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Figure 2 shows the speed of sound data for the ten measured isotherms as a function of pressure. In the region of our

Figure 1. Distribution of our measurements and literature data for the speed of sound in propene in the p,T plane. The gray area denotes the region of our measurements. The critical point is at (4.555 MPa, 364.21 K). ×, this work; (△) ref 3; (▽) ref 4; (○) ref 5; (□) ref 6; and () vapor pressure.

Figure 2. Speed of sound in propene as a function of pressure for all measured isotherms. (■) 240 K; (◇) 260 K; (◆) 280 K; (▽) 300 K; (●) 320 K; (△) 340 K; (▼) 360 K; (□) 380 K; (▲) 400 K; (○) 420 K; () speed of sound at the measured isotherms obtained from the fundamental equation of state of Lemmon et al.; and (···) saturated liquid speed of sound obtained from the equation of state of Lemmon et al.

On subcritical isotherms, the lowest pressures, at which measurements were carried out, were chosen close to the vapor pressure. On supercritical isotherms, measurements were started at the lowest pressure where a clear signal cancellation could be observed.11 Below 300 K, a Viton O-ring was used to seal the closure of the pressure vessel, whereas at higher temperatures FEP encapsulated silicone O-rings were used. At the lowest and highest temperatures of 240 K and 420 K, the O-rings did not withstand the highest pressures. Therefore, at 240 K measurements were only taken up to 50 MPa and at 420 K up to 80 MPa. The measurement results are reported in Table 3.

measurements, the speed of sound ranges from about 250 m·s−1 to 1700 m·s−1. After the measurements had been completed, it came to our attention that a new fundamental equation of state for propene had been developed by Overhoff at the Ruhr-Universität Bochum14 without knowing about our speed of sound data.

Table 3. Results for the Speed of Sound in Propenea T

p

c −1

K

MPa

m·s

240.0057 240.0060 240.0060 240.0056 240.0054 240.0052 240.0049 240.0048 240.0050 240.0048 240.0045

1.30295 2.10360 3.10434 4.10503 5.10572 6.10644 7.10733 8.10806 9.10871 10.1093 12.6110

1101.185 1108.727 1117.981 1127.052 1135.947 1144.672 1153.244 1161.649 1169.913 1178.038 1197.777

259.9987 259.9984 259.9984 259.9983 259.9985 259.9979 259.9980 259.9986 259.9983 259.9976 260.0000 259.9999 259.9999

1.30335 2.10391 3.10455 4.10530 5.10605 6.10661 7.10725 8.10779 9.10824 10.1087 12.6127 15.1143 17.6160

970.6167 979.8807 991.1728 1002.157 1012.855 1023.292 1033.466 1043.406 1053.122 1062.635 1085.589 1107.451 1128.358

T

p

c

K

MPa

m·s−1

240.0047 240.0041 240.0042 240.0041 240.0043 240.0043 240.0044 240.0046 240.0048 240.0047

15.1127 17.6138 20.1155 25.1187 30.1221 35.1255 40.1289 45.1323 50.1358 60.1439

1216.761 1235.067 1252.744 1286.456 1318.218 1348.316 1376.953 1404.298 1430.490 1479.896

260.0000 260.0001 260.0000 260.0001 260.0003 260.0001 260.0001 260.0001 259.9999 259.9967 259.9965 259.9967

20.1177 25.1208 30.1242 35.1276 40.1309 45.1343 50.1377 60.1447 70.1517 80.1583 90.1654 100.172

1148.412 1186.290 1221.630 1254.829 1286.199 1315.977 1344.352 1397.522 1446.691 1492.558 1535.614 1576.274

T = 240 K

T = 260 K

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Table 3. continued T

p

c

T

p

c

K

MPa

m·s−1

K

MPa

m·s−1

279.9970 279.9967 279.9970 279.9971 279.9970 279.9966 279.9958 279.9955 279.9955 279.9954 279.9953 279.9954 279.9978

1.30164 2.10240 3.10325 4.10404 5.10491 6.10580 7.10730 8.10806 9.10875 10.1095 12.6112 15.1129 17.6130

836.3895 848.1849 862.3844 876.0391 889.1962 901.9084 914.2260 926.1470 937.7206 948.9727 975.8440 1001.134 1025.030

279.9964 279.9976 279.9967 279.9970 279.9966 279.9966 279.9963 279.9958 279.9959 279.9951 279.9952 279.9954

20.1166 25.1181 30.1221 35.1256 40.1291 45.1326 50.1375 60.1445 70.1514 80.1571 90.1639 100.171

1047.822 1090.299 1129.497 1165.965 1200.175 1232.436 1263.053 1319.965 1372.239 1420.745 1466.060 1508.714

299.9991 299.9996 299.9995 299.9991 299.9989 300.0005 300.0003 299.9980 300.0005 300.0004 300.0006 299.9984 299.9984

1.40274 1.40249 2.10273 3.10319 4.10380 5.10416 6.10472 7.10716 8.10602 9.10668 10.1074 12.6110 15.1128

696.0055 696.0019 709.9808 728.8441 746.5981 763.3956 779.3623 794.6502 809.2137 823.2426 836.7487 868.5757 898.0009

299.9978 299.9977 299.9970 299.9952 299.9950 299.9951 299.9953 299.9953 299.9955 299.9952 299.9948 299.9950 299.9952

17.6129 20.1145 25.1179 30.1210 35.1245 40.1279 45.1313 50.1347 60.1416 70.1486 80.1564 90.1634 100.170

925.4679 951.3014 998.9279 1042.260 1082.142 1119.233 1153.990 1186.769 1247.367 1302.641 1353.625 1401.096 1445.593

319.9995 319.9995 319.9990 319.9989 319.9994 319.9994 319.9995 319.9998 319.9996 320.0000 319.9999 319.9998 319.9999

2.10438 3.10515 4.10582 5.10644 6.10710 7.10777 8.10843 9.10844 10.1090 12.6108 15.1124 17.6142 20.1159

556.1954 584.4265 609.6331 632.5514 653.6827 673.3549 691.8119 709.2415 725.7727 763.8982 798.3686 829.9901 859.3150

319.9919 319.9989 319.9985 319.9987 319.9986 319.9989 319.9993 319.9993 319.9986 319.9990 319.9992 319.9943

22.6161 25.1191 30.1226 35.1261 40.1295 45.1330 50.1364 60.1433 70.1503 80.1573 90.1643 100.172

886.7121 912.5156 960.1770 1003.570 1043.576 1080.799 1115.700 1179.838 1237.921 1291.239 1340.678 1386.918

340.0053 340.0052 340.0052 340.0052 340.0052 340.0055 340.0055 340.0052 340.0052 340.0051 340.0052

4.10499 5.10568 6.10634 7.10701 8.10768 9.10822 10.1092 12.6111 15.1130 17.6149 20.1167

453.1596 489.4936 520.3782 547.5906 572.1165 594.5675 615.3622 661.8283 702.4814 738.9356 772.1799

340.0096 340.0098 340.0097 340.0097 340.0099 340.0100 340.0102 340.0099 340.0159 340.0166 340.0168

25.1187 30.1222 35.1257 40.1292 45.1327 50.1362 60.1432 70.1501 80.1572 90.1641 100.171

831.3877 883.5328 930.4511 973.3167 1012.939 1049.877 1117.334 1178.042 1233.505 1284.765 1332.533

360.0003 360.0008 360.0002 360.0010 360.0009 360.0012 360.0022 360.0026 360.0026

5.10502 6.10574 7.10648 8.10712 9.10783 10.1086 12.6102 15.1120 17.6138

311.2621 370.1493 413.2767 448.5373 478.9194 505.8886 563.3187 611.3697 653.2581

360.0032 360.0030 360.0029 360.0031 360.0031 360.0026 360.0027 360.0026 360.0028

30.1225 35.1266 40.1303 45.1338 50.1372 60.1442 70.1512 80.1582 90.1653

812.7998 863.1282 908.7145 950.5766 989.4131 1059.921 1123.012 1180.418 1233.294

T = 280 K

T = 300 K

T = 320 K

T = 340 K

T = 360 K

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Table 3. continued T

p

c

T

p

c

K

MPa

m·s−1

K

MPa

m·s−1

360.0027 360.0022

20.1155 25.1190

690.7152 756.1986

360.0030

100.172

1282.448

380.0038 380.0019 380.0038 380.0023 380.0035 380.0036 380.0032 380.0033 380.0030 380.0027 380.0026

7.10608 7.35745 7.60654 7.85819 8.10693 9.10764 10.1084 12.6102 15.1120 17.6127 20.1156

268.3329 283.4828 297.2909 310.3168 322.3437 364.5579 399.8405 470.5486 526.7248 574.2551 615.9259

380.0026 380.0025 380.0020 380.0017 380.0022 380.0019 380.0020 380.0019 380.0018 380.0021 380.0020

25.1193 30.1228 35.1264 40.1299 45.1336 50.1372 60.1442 70.1519 80.1590 90.1662 100.173

687.4295 748.2189 801.6801 849.7384 893.6203 934.1499 1007.369 1072.573 1131.680 1185.973 1236.348

400.0020 400.0029 400.0027 400.0029 400.0031 400.0032 400.0041 400.0042 400.0044 400.0043 400.0043 400.0045

10.1084 11.1090 12.1096 13.1102 14.1108 15.1114 16.1112 17.1099 18.1116 19.1123 20.1131 22.6148

309.3001 343.8351 374.7474 402.6829 428.2085 451.7568 473.6279 494.1486 513.4833 531.7898 549.1977 589.4087

400.0045 400.0040 400.0042 400.0043 400.0041 400.0044 400.0042 400.0051 400.0052 400.0052 400.0052

25.1167 30.1207 35.1243 40.1280 45.1317 50.1353 60.1425 70.1484 80.1555 90.1626 100.170

625.8106 690.1602 746.2882 796.4534 842.0517 884.0224 959.5520 1026.538 1087.010 1142.605 1194.015

419.9962 419.9965 419.9963 419.9962 419.9960 419.9963 419.9962 419.9960 419.9961 419.9960

12.1073 13.1082 14.1090 15.1098 16.1105 17.1131 18.1142 19.1149 20.1157 22.6176

315.0009 341.8445 367.2910 391.2481 413.7903 435.0734 455.1739 474.2406 492.3870 534.3180

419.9961 419.9961 419.9960 419.9963 419.9963 419.9968 419.9967 419.9969 419.9969

25.1197 30.1231 35.1268 40.1303 45.1339 50.1375 60.1451 70.1523 80.1594

572.2371 639.0872 697.1889 748.9529 795.8868 838.9913 916.3699 984.8194 1046.574

T = 360 K

T = 380 K

T = 400 K

T = 420 K

a Uncertainty of temperature: U(T) = 3 mK; relative uncertainty of pressure: U(p) = 1·10−4·p for p < 10 MPa, U(p) = 5·10−5·p for p > 10 MPa; and combined uncertainty of speed of sound: Uc(c) = (1.4·10−4 + 2.5·10−7·p/MPa)·c (all uncertainties refer to a level of confidence = 0.95).

Table 4. Additional Results for the Speed of Sound in Liquid Propene Measured with the HSU and RUB Samples at 300 Ka T

p

c m·s

−1

K

MPa

299.9954 299.9952

2.10410 3.10474

710.0426 728.9030

299.9946 299.9960 299.9946 299.9947 299.9950 299.9949 299.9965 299.9955 299.9948 299.9946 299.9939

1.40325 1.40220 2.10374 4.10509 6.10647 8.10782 8.10718 10.1092 15.1126 20.1161 25.1196

696.0529 696.0144 710.0347 746.6577 779.4237 809.2648 809.2459 836.7947 898.0194 951.3293 998.9619

T

p

c

K

MPa

m·s−1

HSU Sample 299.9953 299.9951

3.10509 4.10575

728.9086 746.6704

RUB Sample 299.9949 299.9940 299.9945 299.9938 299.9943 299.9937 299.9938 299.9936 299.9934 299.9933

25.1190 30.1231 35.1259 40.1300 50.1367 60.1436 70.1506 80.1575 90.1645 100.172

998.9331 1042.275 1082.131 1119.259 1186.790 1247.406 1302.674 1353.657 1401.128 1445.648

Uncertainty of temperature: U(T) = 3 mK; relative uncertainty of pressure: U(p) = 1·10−4·p for p < 10 MPa, U(p) = 5·10−5·p for p > 10 MPa; and combined uncertainty of speed of sound: Uc(c) = (9.5·10−5 + 2.5·10−7·p/MPa)·c (all uncertainties refer to a level of confidence = 0.95). a

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within the expected reproducibility of 50 ppm discussed above. One can conclude from this comparison that the impurities in the samples have a negligible influence on the speed of sound in propene.

Since there are differences between our data and speeds of sound calculated from the fundamental equation of state of Overhoff of up to 1.7 % (see discussion below), some additional measurements were carried out with a sample from the same batch that was used at the Ruhr-Universität Bochum to measure the p−ρ−T relationship of propene2 in order to check the influence of the sample purity. This sample was originally purchased from Messer Griesheim GmbH, Germany, and kindly provided to us by Professor Wagner. According to the analysis of the supplier, the purity was as follows: propene: x(C3H6) > 0.9997; impurities: x(N2) < 20·10−6, x(CH4) < 5·10−6, x(C2H6) < 50·10−6, x(C3H8) < 200·10−6, and x(C4H10, C4H8, and C4H6) < 15·10−6, where x(i) denotes the mole fraction of component i. Since these additional measurements were carried out about 2.5 years after the original measurements, the speed of sound sensor was recalibrated with argon at the state point (300 K, 10.1 MPa). As reference for the calibration, the very precise spherical resonator data of Estrada-Alexanders and Trusler,15 which have an uncertainty of 0.001 %, were used. After the calibration, four data at 300 K were measured with a sample from the same batch as was used for the first measurements (HSU sample). The results are reported in Table 4. Then, 21 measurements on the isotherm 300 K were repeated with the sample from the Ruhr-Universität Bochum (RUB sample). The results of these measurements are also reported in Table 4. The combined uncertainty of the additional speed of sound measurements is estimated to be Uc(c) = (9.5·10−5 + 2.5·10−7·p/MPa)·c. Since the temperatures and pressures of the measured state points are not exactly equal to those of the corresponding state points reported in Table 3, the data are best compared by their deviations from an equation of state. Thus, Figure 3

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DISCUSSION Fundamental equations of state in terms of the Helmholtz free energy as a function of density and temperature were developed by Angus et al.,1 Lemmon et al.,10 and Overhoff.14 In this section, our data are compared with these equations of state and the data of Soldatenko and Dregulyas5 and Terres et al.6 The equation of state of Lemmon et al.10 is chosen as the reference for these comparisons because it provides the most accurate representation of the speed of sound in propene. In the optimization process of this equation of state, our speed of sound data were already used. Figures 4, 5, and 6 show percentage deviations of our data from Table 3, the data of

Figure 3. Difference between fractional deviations Δc = c(expt.) − c(calc.) of experimental speeds of sound c(expt.) in propene from Table 4 (HSU/RUB sample) from values obtained from the equation of state of Lemmon et al. and fractional deviations Δc = c(expt.) − c(calc.) of experimental speeds of sound c(expt.) in propene from Table 3 (HSU sample) from values c(calc.) obtained from the equation of state of Lemmon et al. as a function of pressure at 300 K. (○) HSU sample and (×) RUB sample.

depicts differences between fractional deviations of the data reported in Table 4 measured with HSU and RUB samples from speeds of sound obtained from the equation of state of Lemmon et al.10 and fractional deviations of the corresponding speed of sound data from Table 3 from speeds of sound obtained from the equation of state of Lemmon et al. It is evident from Figure 3 that the speeds of sound measured with the two samples agree within about 30 ppm or better. Thus, the agreement is well within the uncertainty contributions of the temperature and pressure measurements and thus

Figure 4. Fractional deviations Δc = c(expt.) − c(calc.) of experimental speeds of sound c(expt.) in propene, literature data, and two equation of state models from values c(calc.) obtained with the equation of state of Lemmon et al. as a function of pressure at 240 K, 260 K, 280 K, and 300 K. (×) This work and (-··-) vapor pressure. Equations of state: (---) ref 1 and (···) ref 14. 1626



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Figure 6. Fractional deviations Δc = c(expt.) − c(calc.) of experimental speeds of sound c(expt.) in propene, literature data at nearby temperatures, and two equation of state models from values c(calc.) obtained with the equation of state of Lemmon et al. as a function of pressure at 380 K, 400 K, and 420 K. Symbols are the same as in figure 5.

Figure 5. Fractional deviations Δc = c(expt.)−c(calc.) of experimental speeds of sound c(expt.) in propene, literature data at nearby temperatures, and two equation of state models from values c(calc.) obtained with the equation of state of Lemmon et al. as a function of pressure at 320 K, 340 K, and 360 K. (×) This work; (□) ref 5; (○) ref 6; and (-··-) vapor pressure. Equations of state: (---) ref 1 and (···) ref 14.

sets are not shown. Between (240 and 280) K the data of Dudar and Mikhailenko agree with the equation of state of Lemmon et al. within about 0.3 %, whereas the data of Blagoi et al. lie up to 1.2 % above the equation of state. Among the two other equations of state, the equation of Overhoff represents our data at subcritical temperatures the best. Below 20 MPa, the equation deviates between up to 0.5 % at 240 K and up to 0.8 % at 340 K from our data. At higher pressures, deviations up to 1.5 % are observed. The deviations of the equation of state of Angus et al. from our data decrease from about 1.5 % at low pressures to 0.7 % at 100 MPa. At supercritical temperatures, the equation of state of Angus et al. yields the best representation of our data. The deviations decrease from 0.9 % at low pressures to 0.3 % at 100 MPa, whereas the deviations of the equation of state of Overhoff are higher. They increase from 0.6 % at low pressures to 1.7 % at 100 MPa.

Soldatenko and Dregulyas and of Terres et al. at nearby temperatures, and the two other equation of state models from the equation of state of Lemmon et al. Our data are represented by the equation of state over almost the entire measured temperature and pressure range within 0.05 % or better. Larger deviations of up to 0.1 % occur only at 360 K and on the supercritical isotherms at low pressures. Generally, the two literature data sets scatter much more than our data and show systematic deviations from our data. The liquid data of Terres et al. at 320 K lie up to 1 % below our data, whereas the data on the two other subcritical isotherms 340 K and 360 K are up to 4 % and 2 % higher than our data. On the supercritical isotherms 400 K and 420 K they agree with our data within 1 % except for one datum at 420 K. The liquid data of Soldatenko and Dregulyas on the subcritical isotherm 360 K and on the three supercritical isotherms 380 K, 400 K, and 420 K agree with our data within 2 %. The best agreement within 1 % is observed at 400 K. Terres et al. report an uncertainty of 5 m/s (∼1 %) for their liquid data, and Soldatenko and Dregulyas state an uncertainty of 0.15 %. The comparison shows that these uncertainty estimates are too optimistic. From the saturated liquid data sets of Blagoi et al.3 and Dudar and Mikhailenko4 only a few data between (240 and 280) K lie in the temperature range of our measurements. Since the vapor pressure in this temperature range is outside the pressure range of Figure 4, the deviations of these two data

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Addresses †

MTU Aero Engines GmbH, Dachauer Str. 665, D-80995 München, Germany. ‡ Institut für Thermodynamik, Leibniz Universität Hannover, Callinstr. 36, D-30167 Hannover, Germany. 1627



Article

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is part of an international collaboration between the National Institute of Standards and Technology in Boulder, Ruhr-Universität Bochum, and the Helmut-Schmidt-University/ Universität der Bundeswehr in Hamburg. Discussions with Dr. Mark McLinden and Dr. Eric Lemmon are gratefully acknowledged. We also thank Prof. Wolfgang Wagner for providing the propene sample and Dr. Arno Laesecke for help with the Russian literature sources. All equation of state calculations were performed with the NIST Standard Reference Database 23 REFPROP Version 9.0.

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REFERENCES

(1) Angus, S.; Armstrong, B.; de Reuck, K. M. International Tables of the Fluid State--7 Propylene (Propene); Pergamon: Oxford, U.K., 1980. (2) Glos, S.; Kleinrahm, R.; Wagner, W. Measurement of the (p,ρ,T) relation of propane, propylene, n-butane, and isobutane in the temperature range from 95 K to 340 K at pressures up to 12 MPa using an accurate two-sinker densimeter. J. Chem. Thermodyn. 2004, 36, 1037−1059. (3) Blagoi, Yu. P.; Blutko, A. E.; Mikhailenko, S. A.; Yakuba, V. V. Velocity of sound in liquid propene, carbon tetraflouride, and ammonia. Russ. J. Phys. Chem. 1968, 42, 564−565. (4) Dudar, B. G.; Mikhailenko, S. A. Possible effect of libration transitions on sound absorption in liquid propylene. Sov. Phys. Acoust. 1977, 23, 25−27. (5) Soldatenko, Y. A.; Dregulyas, E. K. Speed of sound and calculation of the caloric properties of ethylene and propylene in the supercritical region. Proc. 3rd All-Union Scientific-Technical Thermodynamics Conference 1968 1970, 344−352. (6) Terres, E.; Jahn, W.; Reissmann, H. On the knowledge of the determination of adiabatic exponents of low boiling hydrocarbons at different pressures and temperatures by measurements of the ultrasonic velocity. Brennst.-Chem. 1957, 38, 129−160. (7) Meier, K. The pulse-echo method for high-precision measurements of the speed of sound in fluids; Habilitationsschrift, Fachbereich Maschinenbau, Helmut-Schmidt-Universität/Universität der Bundeswehr Hamburg: Hamburg, Germany, 2006. (8) Meier, K.; Kabelac, S. Thermodynamic properties of propane. IV. Speed of sound in the liquid and supercritical regions. J. Chem. Eng. Data 2012, 57, 3391−3398. (9) Meier, K.; Kabelac, S. Measurements of the speed of sound in the refrigerants HFC227ea and HFC365mfc in the liquid region. J. Chem. Eng. Data 2013, 58, 446−454. (10) Lemmon, E. W.; Overhoff, U.; McLinden, M. O.; Wagner, W. A reference equation of state for the thermodynamic properties of propene for temperatures from the melting line to 575 K and pressures up to 1000 MPa. To be submitted to J. Phys. Chem. Ref. Data 2013. (11) Meier, K.; Kabelac, S. Speed of sound instrument for fluids with pressures up to 100 MPa. Rev. Sci. Instrum. 2006, 77, 123903. (12) Muringer, M. J. P.; Trappeniers, N. J.; Biswas, S. N. The effect of pressure on the sound velocity and density of toluene and n-heptane up to 2600 bar. Phys. Chem. Liq. 1985, 14, 273−296. (13) Zuckerwar, A. J. Handbook of the Speed of Sound in Real Gases, Vol. 2: Measurements; Academic: San Diego, CA, 2002. (14) Overhoff, U. Development of a new equation of state for the fluid region of propene for temperatures from the melting line to 575 K with pressures to 1000 MPa as well as software for the computation of thermodynamic properties of fluids; Ph.D. Dissertation; Fachbereich Maschinenbau, Ruhr-Universität Bochum, 2006. (15) Estrada-Alexanders, A. F.; Trusler, J. P. M. The speed of sound in gaseous argon at temperatures between 110 and 450 K and at pressures up to 19 MPa. J. Chem. Thermodyn. 1995, 27, 1075−1089.

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