Measurements of the Speed of Sound in Liquid n-Butane - Journal of

Article pubs.acs.org/jced

Measurements of the Speed of Sound in Liquid n‑Butane Ahmed El Hawary and Karsten Meier* 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 n-butane in the liquid region. The measurements were carried out by a double-path-length pulse-echo technique and cover the temperature range between 200 and 430 K with pressures up to 100 MPa. The expanded uncertainties (at the 95% confidence level) are 2.1 mK for temperature, 0.007% for pressure, and 0.016% for speed of sound. Comparisons with several equations of state and literature data demonstrate that the Helmholtz energy formulation for n-butane can be improved significantly with our accurate data.

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cannot be extracted with high accuracy. Niepmann5,6 measured the speed of sound in the saturated liquid and the homogeneous liquid region with a pulse-echo technique. His data cover the temperature range from 200 to 375 K with pressures up to 60 MPa. The uncertainty of the speed-of-sound data is reported to be 0.2%. Rao7 determined the speed of sound in the saturated liquid between 143 and 258 K with a pulse-echo technique. Rao’s data are by about 2.5% higher than Niepmann’s saturated liquid data, which is much larger than the uncertainties that can be achieved with modern state-of-the-art experimental techniques. The current reference Helmholtz energy formulation for n-butane published by Bücker and Wagner8 was fitted to the two most accurate data sets of Ewing et al. in the gas region and Niepmann in the liquid region. In a previous work,9 we measured the speed of sound in liquid and supercritical propane between 240 and 420 K at pressures up to 100 MPa with an expanded uncertainty of 0.02% (at the 95% confidence level). Niepmann also published speed-of-sound data for liquid propane in refs 5 and 6. In ref 9, we observed that Niepmann’s propane data deviate from our data by up to 1%. It must be assumed that Niepmann’s nbutane data are also in error by a similar amount because they were measured with the same apparatus as the propane data. It is expected that the Helmholtz energy formulation for n-butane can be significantly improved with more accurate speed-ofsound data. Thus, it is the objective of this work to provide accurate speed-of-sound data in liquid n-butane and to extend the measurement range for the speed of sound to higher temperatures up to 420 K and pressures up to 100 MPa.

INTRODUCTION n-Butane is an important fluid with many applications. It occurs as a secondary component in natural gas and is one of the main components of liquefied petroleum gas. Moreover, it is employed as natural working fluid in refrigeration and heat pump cycle processes, as propellant in aerosol cans, or as fuel gas in pocket lighters. In the chemical industry, n-butane serves as a basic ingredient for the production of isobutane and butene isomers as well as for the synthesis of higher alkanes and thiophene. Moreover, in thermophysical property research, it is an important fluid for developing equation of state models for fluids of chain molecules and for natural gas and fuel mixtures. Therefore, the accurate knowledge of the thermodynamic properties of n-butane is of interest to engineers in the chemical and refrigeration industry and to scientists in a wide variety of fields. Thermodynamic properties of fluids are best represented by fundamental equations of state in terms of the Helmholtz energy, from which all thermodynamic properties can be calculated.1 For the development of a Helmholtz energy formulation, accurate speed-of-sound data are required among other properties as part of the experimental data set to which the formulation is fitted. Furthermore, data for other thermodynamic properties such as density or isobaric heat capacity can be derived from accurate speed-of-sound data sets by numerical integration of well-known thermodynamic relations.2 Four investigations of the speed of sound in n-butane are available in the literature. Ewing et al.3 carried out accurate measurements in the gas region between 250 and 320 K at pressures up to 0.11 MPa with a spherical resonator. M’Hirsi4 performed measurements of the speed of sound in the gas, liquid, and supercritical regions between 311 and 511 K up to 90 MPa by an optical technique. Unfortunately, M’Hirsi reported the results only in graphical form, from which they © XXXX American Chemical Society

Received: July 2, 2016 Accepted: September 29, 2016

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DOI: 10.1021/acs.jced.6b00577 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Summary of Uncertainty Budgets source of uncertainty

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expanded uncertainty (confidence level = 95%)

Temperature Measurement SPRT calibration 2.0 mK calibration of reference resistor 0.1 mK ASL F18 bridge 0.1 mK temperature variation in pressure vessel 0.5 mK total 2.1 mK Pressure Measurement: DH 5203 calibration of pressure balance 10−4 MPa+ 4.3 × 10−5p + 2.8 × 10−7p2/MPa differential pressure indicator 5 × 10−6p hydrostatic pressure correction 2 × 10−6p ambient pressure measurement 20 Pa total 72 × 10−6p Pressure Measurement: DH DPG5 calibration of pressure balance [5.6 × 10−10 MPa2+ 1.6 × 10−9p2]1/2 differential pressure indicator 5 × 10−6p hydrostatic pressure correction 2 × 10−6p ambient pressure measurement 20 Pa total p < 0.5 MPa: 130 × 10−6p 0.5 MPa < p < 1 MPa: 65 × 10−6p 1 MPa < p < 5 MPa: 40 × 10−6p Determination of Path Length ΔL with Measurements in Argon time difference 2 × 10−6ΔL temperature measurement 6 × 10−6ΔL pressure measurement 6 × 10−6ΔL correction of ΔL to ambient pressure 3 × 10−6ΔL diffraction correction 2 × 10−6ΔL uncertainty of reference data 20 × 10−6ΔL average deviation of calibration measurements from reference data 10 × 10−6ΔL total 37 × 10−6ΔL Speed-of-Sound Measurement acoustic path length 37 × 10−6c pressure dependence of acoustic path length (25 × 10−8p/MPa)c time difference 2 × 10−6c diffraction correction 7 × 10−6c sample impurities 40 × 10−6c total (84 × 10−6 + 25 × 10−8p/MPa)c

EXPERIMENTAL PROCEDURE The speed-of-sound measurements were carried out with a double-path-length pulse-echo instrument, which has been described in detail in refs 10 and 11. Our sensor employs a piezoelectric quartz crystal as sound emitter and receiver, which is operated at its resonance frequency of 8 MHz. The sensor is enclosed in a pressure vessel, which is mounted in a liquid bath thermostat. The temperature in the pressure vessel was maintained constant within less than 0.5 mK over several hours, which is much longer than the duration of one measurement, which takes about 1 h. The temperature was measured in the wall of the pressure vessel by a 25.5 Ohm standard platinum resistance thermometer with ITS-90 calibration and an ASL-F18 bridge system with an expanded uncertainty (at the 95% confidence level) of 2.1 mK. The pressure inside the pressure vessel was determined with two nitrogen-operated gas pressure balances, a Desgranges & Huot DPG5 (DH DPG5) for the low-pressure range up to 5 MPa and a Desgranges & Huot 5203 (DH 5203) for the highpressure range up to 100 MPa. Both pressure balances were coupled to the sample liquid with a differential pressure indicator (Ruska membrane-type cell). The expanded uncertainty (at the 95% confidence level) of the pressure

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random random random systematic systematic random systematic

random systematic random systematic systematic

measurement with the DH DPG5 is 130 ppm below 0.5 MPa, 65 ppm between 0.5 and 1 MPa, and 40 ppm between 1 and 5 MPa. For pressure measurements with the DH 5203 it is 72 ppm over its whole measurement range. The time difference is determined with a resolution of 2 ppm, whereas the speed of sound was reproducible after temperature and pressure cycles during the measurement campaign within 25 ppm. It is supposed that the uncertainty with which the temperature and pressure of a state point can be set in the pressure vessel limits the reproducibility of the speedof-sound measurement. Before the measurement campaign, the path length at zero pressure and 273.15 K and its temperature dependence were determined by calibration measurements with gaseous argon in the temperature range between 240 and 420 K and pressures between 8 and 13 MPa as described in ref 12. The very accurate speed-of-sound data of Estrada-Alexanders and Trusler13 were used as reference values for the calibration. Argon was used for calibration because it allows calibration of the sensor in a wide temperature range with high accuracy. The path length below 240 K and above 420 K was obtained by extrapolation of the calibrated path length. After the n-butane measurements were completed, a new calibration with argon for a subsequent B



Article

measurement campaign with isobutane over the whole temperature range of our instrument from 200 to 420 K was carried out. The results of this calibration confirmed that the calibration function can safely be extrapolated to 200 K without loss of uncertainty. In the measurement analysis, corrections for changes of the path length with temperature and pressure as well as for diffraction effects are applied. The expanded uncertainty (at the 95% confidence level) of the speed-of-sound measurement is (44 × 10−6 + 25 × 10−8p/MPa)c excluding contributions from temperature and pressure measurements and due to sample impurities. In this equation, p denotes pressure and c is the speed of sound. A detailed summary of the contributions to the measurement uncertainties is given in Table 1.

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MATERIALS The n-butane sample was purchased from Westfalen, Germany. It had a manufacturer specified volume purity better than 99.99% and was used without further purification (see Table 2).

Figure 1. Distribution of our measurements and literature data for the speed of sound in n-butane in the pressure−temperature plane. The gray area denotes the region of our measurements. The critical point is at (425.13 K, 3.796 MPa): × , this work; + , ref 3; ○, ref 6; −, vapor pressure; ············, critical temperature and pressure.

Table 2. Chemical Sample Description

measurement campaign, the measurements below 2.1 MPa and repeated measurements between 2.1 and 5.1 MPa on the isotherms between 200 and 360 K were carried out with the DH DPG5 pressure balance. It was observed that the measured speeds of sound at pressures between 2.1 and 5.1 MPa were systematically lower by up to 0.01% than the speeds of sound measured in the main campaign. During subsequent measurements with isobutane, it was found that the calibration of the differential pressure indicator had shifted by 0.0018 MPa. This difference was measured accurately by applying the two pressure balances on either side of the differential pressure indicator. It is assumed that this shift was caused by an operating error after the main measurement campaign with nbutane was completed. Therefore, the pressures of the additional measurements at low pressures were corrected by this shift. With this correction, the speeds of sound of the repeated measurements between 2.1 and 5.1 MPa agree with the speeds of sound measured during the main campaign within less than 50 ppm. The highest deviation of 50 ppm was found at 320 K, whereas at 240 K, the data agree within 4 ppm. Because the pressure difference corresponding to the shift of the calibration of the differential pressure indicator was determined accurately, no additional contribution to the pressure measurement uncertainty was taken into account. Instead, the largest systematic differences between the speeds of sound from the main campaign and the repeated measurements after application of the correction on each isotherm was added as a systematic contribution to the combined expanded uncertainty (at the 95% confidence level) of the speed of sound. For each measured state point, a detailed analysis of the combined expanded uncertainty (at the 95% confidence level) of the speed-of-sound measurement was carried out. The combined expanded uncertainty includes contributions of the uncertainties of the temperature and pressure measurements and contributions due to sample impurities and due to systematic differences between the measurements with the DH DPG5 and DH 5203 pressure balances at low pressures. The contributions due to the uncertainties of the temperature and pressure measurements were estimated by the Helmholtz energy formulation of Bücker and Wagner.8 The combined expanded uncertainty (at the 95% confidence level) is generally 0.016%. Only at the state points with the lowest measured

chemical name

source

initial volume fraction purity

n-butane

Westfalen

0.9999

purification method

final volume fraction purity

analysis method

none

0.9999

none

According to the specification of the manufacturer, the volume purity is as follows: other hydrocarbons, < 90 ppm; nitrogen, < 20 ppm; oxygen, < 5 ppm; sulfur, < 1 ppm; and water, < 3 ppm. The influence of the sample impurities on the speed-of-sound measurement was estimated by the mixture model implemented in the NIST Standard Reference Database 23 Refprop.14 An additional allowance of 40 ppm was added to the combined expanded uncertainty (at the 95% confidence level) of the speed of sound to account for sample impurities.

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RESULTS A total of 384 speed-of-sound data in n-butane were measured during the course of this work. The distribution of our measurements and the two literature data sets of Ewing et al.3 and Niepmann5,6 is depicted in the pressure−temperature plane in Figure 1. Our data cover the liquid region between 200 and 420 K with pressures up to 100 MPa and were carried out on 12 isotherms in steps of 20 K. Moreover, additional measurements at 430 K were conducted up to 20 MPa in order to provide a few data on a supercritical isotherm. For the first time, measurements at 200 and 220 K were performed with our instrument. Between 200 and 280 K, the lowest pressure was chosen as 0.25 MPa, which is slightly higher than the vapor pressure at ambient temperature of about 0.2 MPa, whereas at higher temperatures, pressures slightly above the vapor pressure at the temperature of the measured isotherm were chosen. Our data set extends the measured region for the speed of sound in n-butane up to 430 K in temperature and up to 100 MPa in pressure. The measurement results are reported in Table 3. Our speed-of-sound data on the 12 completely measured liquid isotherms and the supercritical isotherm are shown in Figure 2 as a function of pressure. In the region of our measurements, the speed of sound ranges from 240 m·s−1 to 1870 m·s−1. Because the DH DPG5 pressure balance was not available in the beginning of this work, the large body of measurements was carried out with the DH 5203 pressure balance. After this main C



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Table 3. Results for the Speed of Sound in n-Butane

a

T/K

p/MPa

c/m·s−1

Uc(c)b/m·s−1

199.9960 199.9961 199.9961 199.9961 199.9960 199.9956 199.9956 199.9956 199.9956 199.9955 199.9956 199.9956 199.9957

1.10143 2.10208 3.10276 4.10347 5.10418 6.10513 7.10588 8.10660 9.10734 10.1080 12.6098 15.1116 17.6134

1447.79 1453.53 1459.25 1464.89 1470.49 1476.03 1481.53 1486.99 1492.39 1497.75 1510.92 1523.84 1536.50

0.14 0.14 0.14 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.15 0.16 0.16

200.9969 200.9967 200.9965 200.9970 200.9970

0.250625 0.600555 1.10047 1.10145 2.10194

1437.19 1439.24 1442.14 1442.16 1447.96

0.14c 0.14c 0.14c 0.14c 0.14c

219.9970 219.9975 219.9973 219.9977 219.9978 219.9973 219.9974 220.0041 219.9977 220.0043 219.9978 220.0042 219.9977 219.9976 219.9979 219.9976 219.9977

0.249978 0.599678 1.10072 1.10082 2.10156 2.10182 2.10210 2.10343 3.10231 3.10410 4.10301 4.10472 5.10360 6.10422 7.10487 8.10549 9.10616

1330.46 1332.78 1336.09 1336.09 1342.65 1342.65 1342.65 1342.64 1349.14 1349.13 1355.55 1355.54 1361.88 1368.15 1374.34 1380.51 1386.56

0.13c 0.13c 0.13c 0.13 0.13 0.13c 0.13c 0.13c 0.13 0.13c 0.13 0.13c 0.13 0.13 0.13 0.13 0.14

240.0016 240.0014 240.0015 240.0016 240.0029 240.0013 240.0032 240.0015 240.0035 240.0014 240.0038 240.0035 240.0037 240.0036 240.0036 240.0034

0.252205 0.602155 1.10302 2.10348 2.10431 3.10405 3.10510 4.10468 4.10589 5.10531 5.10662 6.10733 7.10805 8.10878 9.10952 10.1102

1219.33 1222.00 1225.80 1233.30 1233.30 1240.70 1240.70 1248.00 1248.00 1255.20 1255.20 1262.31 1269.32 1276.24 1283.08 1289.84

0.10c 0.10c 0.10c 0.11c 0.11 0.11c 0.11 0.11c 0.11 0.11c 0.11 0.11 0.11 0.11 0.11 0.11

259.9985 259.9985 259.9987 259.9984 259.9956

0.251449 0.601450 1.10215 2.10277 2.10313

1109.14 1112.23 1116.62 1125.27 1125.31

0.11c 0.11c 0.11c 0.11c 0.11

T/K

T = 200 K 199.9954 199.9955 199.9953 199.9952 199.9948 199.9948 199.9949 199.9951 199.9951 199.9953 199.9954 199.9956 T = 201 K 200.9970 200.9970 200.9971 200.9971

p/MPa

c/m·s−1

Uc(c)b/m·s−1

20.1152 25.1188 30.1226 35.1262 40.1285 45.1321 50.1356 60.1427 70.1498 80.1569 90.1640 100.171

1548.92 1573.08 1596.41 1618.97 1640.80 1662.03 1682.63 1722.21 1759.84 1795.79 1830.15 1863.22

0.16 0.17 0.17 0.18 0.18 0.18 0.19 0.20 0.21 0.22 0.23 0.24

1447.96 1453.68 1459.38 1465.01

0.14c 0.14c 0.15c 0.15c

2.10201 3.10262 4.10338 5.10404

T = 220 K 219.9975 219.9978 219.9978 219.9977 219.9978 219.9977 219.9976 219.9978 219.9975 219.9975 219.9978 219.9977 219.9976 219.9976 219.9978 219.9977

10.1070 12.6088 15.1106 17.6124 20.1142 25.1177 30.1213 35.1249 40.1291 45.1327 50.1364 60.1436 70.1508 80.1579 90.1651 100.172

1392.58 1407.34 1421.75 1435.83 1449.59 1476.25 1501.85 1526.52 1550.28 1573.31 1595.59 1638.17 1678.49 1716.78 1753.24 1788.20

0.14 0.14 0.14 0.14 0.15 0.15 0.16 0.16 0.16 0.17 0.17 0.18 0.19 0.20 0.21 0.22

T = 240 K 240.0033 240.0033 240.0036 240.0036 240.0035 240.0034 240.0036 240.0034 240.0024 240.0025 240.0018 240.0016 240.0021 240.0021 240.0022

12.6120 15.1130 17.6147 20.1164 25.1199 30.1234 35.1268 40.1303 45.1341 50.1376 60.1446 70.1516 80.1585 90.1653 100.172

1306.37 1322.45 1338.08 1353.31 1382.68 1410.72 1437.56 1463.36 1488.20 1512.19 1557.82 1600.75 1641.41 1680.02 1716.86

0.12 0.12 0.12 0.12 0.13 0.13 0.14 0.14 0.15 0.15 0.16 0.17 0.18 0.19 0.20

T = 260 K 259.9948 259.9953 259.9952 259.9957 259.9957

12.6100 15.1117 17.6134 20.1151 25.1186

1208.12 1226.05 1243.41 1260.26 1292.53

0.13 0.13 0.13 0.13 0.14

D



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Table 3. continued T/K

p/MPa

c/m·s−1

Uc(c)b/m·s−1

p/MPa

c/m·s−1

Uc(c)b/m·s−1

259.9986 259.9954 259.9988 259.9957 259.9990 259.9960 259.9957 259.9958 259.9961 259.9957 259.9951

3.10343 3.10382 4.10407 4.10451 5.10472 5.10521 6.10588 7.10652 8.10723 9.10795 10.1083

1133.77 1133.82 1142.13 1142.17 1150.34 1150.38 1158.47 1166.42 1174.26 1181.97 1189.58

0.11c 0.11 0.12c 0.12 0.12c 0.12 0.12 0.12 0.12 0.12 0.12

T = 260 K 259.9961 259.9963 259.9957 259.9956 259.9955 259.9951 259.9950 259.9949 259.9949 259.9963

30.1221 35.1255 40.1290 45.1327 50.1364 60.1436 70.1507 80.1576 90.1646 100.172

1323.15 1352.30 1380.18 1406.90 1432.60 1481.28 1526.84 1569.77 1610.40 1649.05

0.14 0.15 0.15 0.16 0.16 0.17 0.18 0.19 0.20 0.21

280.0034 280.0033 280.0033 280.0032 280.0040 280.0032 280.0041 280.0031 280.0041 280.0028 280.0038 280.0040 280.0042 280.0044 280.0043 280.0043

0.250960 0.601002 1.10174 2.10238 2.10238 3.10303 3.10312 4.10363 4.10390 5.10407 5.10465 6.10539 7.10609 8.10682 9.10755 10.1082

999.470 1003.08 1008.21 1018.28 1018.30 1028.13 1028.15 1037.77 1037.79 1047.20 1047.23 1056.49 1065.56 1074.46 1083.21 1091.80

0.112c 0.11c 0.11c 0.11c 0.11 0.12c 0.12 0.12c 0.12 0.12c 0.12 0.12 0.12 0.12 0.12 0.13

T = 280 K 280.0043 280.0042 280.0041 280.0042 280.0041 280.0040 280.0043 280.0040 280.0040 280.0033 280.0039 280.0039 280.0025 280.0027 280.0026

12.6099 15.1115 17.6133 20.1149 25.1183 30.1217 35.1251 40.1285 45.1320 50.1353 60.1423 70.1493 80.1589 90.1659 100.173

1112.63 1132.65 1151.93 1170.54 1205.97 1239.32 1270.88 1300.89 1329.54 1356.98 1408.68 1456.81 1501.97 1544.56 1584.94

0.13 0.13 0.13 0.14 0.14 0.15 0.16 0.16 0.17 0.17 0.18 0.19 0.20 0.21 0.22

300.0049 300.0055 299.9975 300.0024 299.9976 300.0023 299.9971 300.0024 299.9968 300.0026 300.0026 300.0028 300.0033 300.0035 299.9968

0.599937 1.10040 2.10201 2.10425 3.10280 3.10495 4.10365 4.10567 5.10444 5.10589 6.10651 7.10718 8.10781 9.10838 10.1088

893.833 899.926 911.889 911.909 923.459 923.478 934.713 934.728 945.669 945.676 956.354 966.776 976.954 986.906 996.678

0.092c 0.093c 0.095c 0.095 0.096c 0.096 0.097c 0.097 0.099c 0.099 0.100 0.101 0.103 0.104 0.105

12.6105 15.1122 17.6139 20.1150 25.1185 30.1219 35.1254 40.1289 45.1324 50.1359 60.1430 70.1501 80.1581 90.1652 100.172

1020.17 1042.56 1063.97 1084.50 1123.32 1159.56 1193.62 1225.82 1256.41 1285.58 1340.29 1390.94 1438.22 1482.66 1524.68

0.11 0.11 0.11 0.12 0.12 0.13 0.14 0.14 0.15 0.15 0.16 0.17 0.18 0.19 0.20

320.0016 319.9991 319.9981 319.9953 319.9976 319.9953 319.9976 319.9955 319.9970 319.9956 319.9960 319.9960 319.9962 319.9963 319.9954

0.601275 1.10118 2.10187 2.10408 3.10251 3.10480 4.10320 4.10551 5.10384 5.10614 6.10680 7.10748 8.10817 9.10889 10.1091

783.221 790.665 805.078 805.159 818.927 819.008 832.273 832.354 845.165 845.242 857.711 869.802 881.540 892.953 904.045

0.103c 0.104c 0.105c 0.106 0.107c 0.107 0.109c 0.109 0.111c 0.111 0.113 0.115 0.117 0.118 0.120

12.6113 15.1129 17.6147 20.1164 25.1199 30.1234 35.1269 40.1304 45.1340 50.1373 50.1375 60.1444 70.1516 80.1584 90.1655

930.654 955.743 979.543 1002.21 1044.68 1083.95 1120.58 1155.01 1187.55 1218.44 1218.44 1276.10 1329.16 1378.48 1424.69

0.124 0.128 0.132 0.14 0.14 0.15 0.16 0.16 0.17 0.18 0.18 0.19 0.20 0.21 0.22

T/K

T = 300 K 299.9966 299.9963 299.9964 299.9972 299.9975 299.9972 299.9968 299.9968 299.9966 299.9965 299.9963 299.9962 299.9934 299.9933 299.9929 T = 320 K 319.9964 319.9965 319.9965 319.9966 319.9968 319.9966 319.9971 319.9971 319.9971 319.9956 319.9972 319.9968 319.9968 319.9971 319.9969 E



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p/MPa

c/m·s−1

Uc(c)b/m·s−1

319.9963

10.1096

904.067

0.120

340.0027 340.0029 340.0019 340.0029 340.0023 340.0032 340.0023 340.0032 340.0021 340.0024 340.0022 340.0024 340.0023 340.0035 340.0022

1.10043 2.10109 2.10365 3.10174 3.10431 4.10242 4.10501 5.10292 5.10558 6.10620 7.10682 8.10747 9.10812 10.1065 10.1085

678.122 696.215 696.271 713.300 713.359 729.532 729.589 745.009 745.066 759.882 774.104 787.795 801.008 813.726 813.773

0.070c 0.072c 0.072 0.073c 0.073 0.075c 0.075 0.077c 0.077 0.078 0.080 0.082 0.083 0.085 0.085

359.9977 359.9974 359.9982 359.9978 359.9967 359.9977 359.9976 359.9967 359.9980 359.9969 359.9965 359.9967 359.9967 359.9968 359.9969 359.9967

2.10075 2.10386 3.10139 3.10142 3.10459 4.10200 4.10206 4.10535 5.10259 5.10298 5.10607 6.10686 7.10763 8.10838 9.10909 10.1098

582.292 582.372 604.477 604.479 604.562 625.000 624.999 625.090 644.168 644.182 644.251 662.279 679.330 695.538 711.010 725.827

0.071c 0.071 0.073c 0.073c 0.073 0.076c 0.076c 0.076 0.078c 0.078c 0.078 0.080 0.082 0.084 0.086 0.088

379.9975 379.9976 379.9980 379.9979 379.9980 379.9976 379.9977 379.9979 379.9977 379.9977 379.9973 379.9975

2.10323 3.10416 4.10503 5.10583 6.10671 7.10752 8.10831 9.10912 10.1099 12.6111 15.1128 17.6145

456.129 488.076 515.932 540.877 563.618 584.618 604.199 622.597 639.978 679.849 715.711 748.486

0.042 0.043 0.045 0.046 0.048 0.050 0.051 0.053 0.054 0.058 0.061 0.065

399.9993 399.9992 399.9989 399.9989 399.9989 399.9988 399.9984 399.9985 399.9984 399.9981 399.9983 399.9984

2.70485 3.10508 4.10576 5.10637 6.10701 7.10772 8.10842 9.10939 10.1102 12.6120 15.1139 17.6157

329.550 351.680 396.177 431.840 462.275 489.164 513.443 535.712 556.355 602.563 643.081 679.473

0.039 0.038 0.039 0.040 0.042 0.044 0.045 0.047 0.048 0.052 0.056 0.059

T/K

T = 320 K 319.9953 T = 340 K 340.0022 340.0023 340.0023 340.0022 340.0018 340.0019 340.0021 340.0018 340.0019 340.0016 340.0022 340.0020 340.0022 340.0022 340.0022 T = 360 K 359.9967 359.9967 359.9968 359.9969 359.9967 359.9963 359.9963 359.9966 359.9965 359.9967 359.9966 359.9967 359.9969 359.9968 359.9967 T = 380 K 379.9971 379.9974 379.9974 379.9970 379.9983 379.9986 379.9986 379.9989 379.9989 379.9987 379.9987 379.9986 T = 400 K 399.9989 399.9986 399.9983 399.9986 399.9968 399.9972 399.9969 399.9972 399.9969 399.9970 399.9970 399.9971 F

c/m·s−1

Uc(c)b/m·s−1

100.173

1468.23

0.24

12.6104 15.1122 17.6140 20.1157 25.1192 30.1226 35.1261 40.1296 45.1330 50.1365 60.1447 70.1518 80.1588 90.1658 100.173

844.028 872.222 898.696 923.702 970.085 1012.52 1051.80 1088.46 1122.94 1155.53 1216.04 1271.43 1322.70 1370.55 1415.54

0.088 0.092 0.095 0.099 0.105 0.11 0.12 0.12 0.13 0.13 0.15 0.16 0.17 0.18 0.19

12.6115 15.1133 17.6151 20.1168 25.1204 30.1242 35.1278 40.1312 45.1346 50.1381 60.1451 70.1521 80.1590 90.1661 100.173

760.445 792.205 821.665 849.226 899.751 945.466 987.407 1026.30 1062.68 1096.92 1160.16 1217.74 1270.82 1320.23 1366.55

0.093 0.097 0.102 0.106 0.113 0.120 0.127 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20

20.1162 25.1197 30.1233 35.1268 40.1316 45.1351 50.1387 60.1457 70.1527 80.1597 90.1667 100.174

778.799 833.691 882.725 927.317 968.400 1006.62 1042.44 1108.27 1167.91 1222.69 1273.52 1321.06

0.068 0.074 0.079 0.085 0.090 0.10 0.10 0.11 0.12 0.13 0.14 0.15

20.1175 25.1211 30.1247 35.1283 40.1315 45.1350 50.1384 60.1453 70.1523 80.1592 90.1661 100.173

712.704 772.062 824.409 871.587 914.764 954.727 992.039 1060.28 1121.82 1178.14 1230.27 1278.93

0.063 0.069 0.075 0.080 0.086 0.091 0.096 0.11 0.12 0.12 0.13 0.14

p/MPa



Article


p/MPa

c/m·s−1

Uc(c)b/m·s−1

419.9975 419.9969 419.9972 419.9971 419.9978 419.9969 419.9972 419.9977 419.9974 419.9978 419.9976 419.9976 419.9972 419.9969 419.9972

4.10441 4.45516 4.60499 4.95563 5.10508 5.45611 5.60574 6.10577 6.60648 7.10650 8.10722 9.10796 10.1090 12.6108 15.1125

245.272 271.991 281.850 302.472 310.479 327.761 334.633 355.802 374.829 392.204 423.269 450.696 475.453 529.119 574.769

0.043 0.040 0.039 0.038 0.038 0.037 0.037 0.038 0.038 0.039 0.040 0.042 0.043 0.047 0.051

429.9958 429.9963 429.9959 429.9969 429.9963 429.9976 429.9976 429.9958 429.9972 429.9972 429.9975 429.9979 429.9980

5.10560 5.35526 5.60596 5.85560 6.10629 6.35629 6.35631 6.60663 7.10684 7.10687 7.60719 8.10749 8.60780

240.793 258.169 273.501 287.251 300.071 311.899 311.900 323.008 343.373 343.374 361.852 378.831 394.600

0.040 0.039 0.038 0.037 0.037 0.037 0.037 0.037 0.037 0.037 0.038 0.038 0.039

T/K

T = 420 K 419.9962 419.9961 419.9965 419.9960 419.9963 419.9961 419.9963 419.9962 419.9968 419.9971 419.9973 419.9973 419.9974 419.9976 419.9975 T = 430 K 429.9983 429.9983 429.9975 429.9980 429.9979 429.9983 429.9980 429.9980 429.9973 429.9973 429.9980 429.9973 429.9973

p/MPa

c/m·s−1

Uc(c)b/m·s−1

17.6149 20.1167 25.1202 30.1237 35.1271 40.1306 45.1340 50.1375 50.1380 55.1415 60.1450 70.1521 80.1592 90.1663 100.173

614.982 651.200 714.992 770.535 820.167 865.305 906.887 945.566 945.569 981.829 1016.01 1079.28 1137.01 1190.31 1239.96

0.055 0.058 0.065 0.071 0.076 0.082 0.087 0.092 0.092 0.097 0.10 0.11 0.12 0.13 0.14

409.364 423.279 436.468 461.005 483.546 504.468 524.058 542.492 584.593 622.274 542.492 584.593 622.274

0.040 0.041 0.041 0.043 0.044 0.046 0.048 0.049 0.053 0.056 0.039 0.040 0.041

9.10814 9.60849 10.1088 11.1096 12.1104 13.1114 14.1118 15.1126 17.6140 20.1157 15.1126 17.6140 20.1157

a

Expanded uncertainty (at the 95% confidence level) of temperature: U(T) = 2.1 mK. Expanded uncertainty (at the 95% confidence level) of pressure: DH DPG5, U(p) = 130 × 10−6p below 0.5 MPa, U(p) = 65 × 10−6p between 0.5 and 1 MPa, U(p) = 40 × 10−6p between 1 and 5 MPa; DH 5203, U(p) = 72 × 10−6p; and combined expanded uncertainty (at the 95% confidence level) of speed of sound: Uc(c) = (16 × 10−5 + 25 × 10−8p/MPa)c. bCombined expanded uncertainty (at the 95% confidence level). cMeasured with DH DPG5 pressure balance after the main measurement campaign.

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DISCUSSION In this section, our data are compared with the data of Niepmann and five Helmholtz energy formulations for nbutane. Helmholtz energy formulations for n-butane were developed by Bücker and Wagner,8 Miyamoto and Watanabe,15 Span and Wagner,16 and Kunz and Wagner.17 Polt et al.18 published a thermal Bender-type equation of state while Younglove and Ely19 developed a thermal equation of state of the MBWR-type. Both equations of state combined with an equation for the isochoric ideal gas heat capacity can be formulated as a fundamental equation of state in terms of the Helmholtz energy. The Bücker and Wagner formulation is selected as the basis for the following discussion because it is the current reference formulation for n-butane. In Figures 3 to 6, fractional deviations of our data, Niepmann’s data, and speeds of sound calculated with the formulations of Kunz and Wagner, Miyamoto and Watanabe, and Younglove and Ely from the Bücker and Wagner formulation are plotted for all measured isotherms. The Polt et al. formulation is not considered in the discussion because deviations between speeds of sound calculated with it and with the Bücker and Wagner formulation are so large that they mostly lie outside of the deviation plots. Moreover, because speeds of sound calculated with the Span and Wagner as well as

Figure 2. Speed of sound in n-butane as a function of pressure for all measured isotherms: ○, 200 K; × , 201 K; ●, 220 K; △, 240 K; ▲, 260 K; ◇, 280 K; ◆, 300 K; □, 320 K; ■, 340 K; ▽, 360 K; ▼, 380 K; ⧖, 400 K; black hourglass, 420 K; ⋈, 430 K; , speed of sound calculated with the Helmholtz energy formulation of Bücker and Wagner; -·-·-· speed of sound in the saturated liquid calculated with the Helmholtz energy formulation of Bücker and Wagner; ············, critical pressure.

pressures near the critical point, it increases to 0.018%. The combined expanded uncertainties are also reported in Table 3. G



Article

Figure 3. Fractional deviations Δc = c(expt) − c(calc) of our experimental speeds of sound c(expt) in n-butane, Niepmann’s data at nearby temperatures, and three Helmholtz energy formulations from values c(calc) calculated with the formulation of Bücker and Wagner as a function of pressure at 200, 220, 240, and 260 K. Experimental data: × , this work; ○, ref 6. Helmholtz energy formulations: - - - -, ref 15; , ref 17; ············, ref 19.

Figure 4. Fractional deviations Δc = c(expt) − c(calc) of our experimental speeds of sound c(expt) in liquid n-butane, Niepmann’s data at nearby temperatures, and three Helmholtz energy formulations from values c(calc) calculated with the formulation of Bücker and Wagner as a function of pressure at 280, 300, 320, and 340 K. Experimental data: × , this work; ○, ref 6; -·-·-·, vapor pressure. Helmholtz energy formulations: - - - -, ref 15; , ref 17; ············, ref 19.

the Kunz and Wagner formulations are almost identical, only deviations of the Kunz and Wagner formulation are shown in Figures 3 to 6. Our data are very consistent and are mostly higher than speeds of sound calculated with the Bücker and Wagner formulation. Negative deviations are only observed between 300 and 430 K at pressures below 15 MPa. The largest deviation on an isotherm increases from 0.25% at 200 K up to 1% at 430 K. These deviations are mostly within the uncertainty of the formulation, which was reported by Bücker and Wagner to be 0.5% between 200 and 375 K, where it was fitted to Niepmann’s data, and 2% to 4% at higher temperatures. Only between 320 and 360 K, the deviations at a few state points of up to 0.6% are slightly larger than the uncertainty of the formulation. Niepmann’s data show much higher scatter and agree with the Bücker and Wagner formulation mostly within 0.4%. At low pressures, they agree with our data within 0.2%, but at high pressures, they are systematically lower than our data by up to 1%. These systematic differences are similar to those we observed in ref 9 between our speed-of-sound data and Niepmann’s data for propane as was expected. Furthermore,

the deviations on several isotherms, for example, at 220 K, at 240 K, at 280 K, and at 300 K, show steps of the order of 0.2% at about 20 MPa as was already noticed by Bücker and Wagner.8 Niepmann estimated the uncertainty of his data to be 0.2%. The comparisons in this section show that this estimate is too optimistic. Among the other Helmholtz energy formulations, the formulation of Kunz and Wagner agrees best with our data, whereas the formulations of Miyamoto and Watanabe and of Younglove and Ely show rather large deviations, which in large parts lie outside the scale of the deviations plots. The agreement between our data and the three formulations is best at the highest measured temperatures. At pressures above 10 MPa between 300 and 430 K, our data agree better with the Kunz and Wagner formulation than with the Bücker and Wagner formulation.

■

CONCLUSIONS Comprehensive measurements of the speed of sound in liquid n-butane have been carried out in the temperature range H



■

Article

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We thank Patrick Kraft and Andreas Polster for their assistance during the measurement campaign. All equation of state calculations were performed with the NIST Standard Reference Database 23 Refprop.14

■

REFERENCES

(1) Span, R. Multiparameter equations of state; Springer: Berlin, 2000. (2) Trusler, J. P. M. Physical acoustics and the metrology of fluids; Adam Hilger: Bristol, 1991. (3) Ewing, M. B.; Goodwin, A. R. H.; McGlashan, M. L.; Trusler, J. P. M. Thermophysical properties of alkanes from speeds of sound determined using a spherical resonator 2. n-Butane. J. Chem. Thermodyn. 1988, 20, 243−256. (4) M’Hirsi, A. Variation of the speed of ultrasound in normal butane as a function of temperature and pressure. Comptes Rendus 1958, 246, 2355−2357. (5) Niepmann, R. Measurement of the speed of ultrasound in liquids in a larger temperature and pressure range. Ph.D. Thesis, Abteilung für Maschinenbau, Ruhr-Universtät Bochum, 1983. (6) Niepmann, R. Thermodynamic properties of propane and nbutane. 2. Speeds of sound in the liquid up to 60 MPa. J. Chem. Thermodyn. 1984, 16, 851−860. (7) Rao, M. G. S. Temperature variation of ultrasonic velocity & related thermodynamic parameters in liquid propane & n-butane. Indian J. Pure Appl. Phys. 1971, 9, 169−170. (8) Bücker, D.; Wagner, W. Reference equations of state for the thermodynamic properties of fluid phase n-butane and isobutane. J. Phys. Chem. Ref. Data 2006, 35, 929−1019. (9) 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. (10) Meier, K. The pulse-echo method for high-precision measurements of the speed of sound in fluids. Postdoctoral Thesis, Department of Mechanical Engineering, Helmut-Schmidt-Universität/Universität der Bundeswehr Hamburg, 2006. (11) Meier, K.; Kabelac, S. Speed of sound instrument for fluids with pressures up to 100 MPa. Rev. Sci. Instrum. 2006, 77, 123903. (12) El Hawary, A.; Meier, K. Measurements of the speed of sound in liquid and supercritical ethane. Fluid Phase Equilib. 2016, 418, 125− 132. (13) Estrada-Alexanders, A. F.; Trusler, J. P. M. The speed of sound in gaseous argon at temperatures between 110 K and 450 K and at pressures up to 19 MPa. J. Chem. Thermodyn. 1995, 27, 1075−1089. (14) Lemmon, E. W.; Huber, M. L.; McLinden, M. O. NIST Reference fluid thermodynamic and transport properties database (Refprop version 9.1). NIST Standard Reference Database 23; National Institute of Standards and Technology, Standard Reference Data Program: Gaithersburg, MD, 2013. (15) Miyamoto, H.; Watanabe, K. Thermodynamic property model for fluid-phase n-butane. Int. J. Thermophys. 2001, 22, 459−475. (16) Span, R.; Wagner, W. Equations of state for technical applications. II. Results for nonpolar fluids. Int. J. Thermophys. 2003, 24, 41−109. (17) Kunz, O.; Wagner, W. The GERG-2008 wide-range equation of state for natural gases and other mixtures: an expansion of GERG2004. J. Chem. Eng. Data 2012, 57, 3032−3091. (18) Polt, A.; Platzer, B.; Maurer, G. Parameters of the thermal equation of state of Bender for 14 polyatomic pure substances. Chem. Tech. (Leipzig) 1992, 22, 216−224.

Figure 5. Fractional deviations Δc = c(expt) − c(calc) of our experimental speeds of sound c(expt) in liquid n-butane, Niepmann’s data at nearby temperatures, and three Helmholtz energy formulations from values c(calc) calculated with the formulation of Bücker and Wagner as a function of pressure at 360, 380, 400, and 420 K. Symbols are the same as in Figure 4.

Figure 6. Fractional deviations Δc = c(expt) − c(calc) of our experimental speeds of sound c(expt) in supercritical n-butane and three Helmholtz energy formulations from values c(calc) calculated with the formulation of Bücker and Wagner as a function of pressure at 430 K. Experimental data: × , this work; -·-·-·, critical pressure. Helmholtz energy formulations: - - - -, ref 15; , ref 17; ············, ref 19.

between 200 and 430 K with pressures up to 100 MPa. This range exceeds the previously available speed-of-sound data for n-butane considerably as does the accuracy. With our accurate data, the Helmholtz energy formulation for n-butane can be improved significantly. I



Article

(19) Younglove, B. A.; Ely, J. F. Thermophysical properties of fluids. II. Methane, ethane, propane, isobutane, and normal butane. J. Phys. Chem. Ref. Data 1987, 16, 577−798.

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