Measurements of the Speed of Sound in Liquid and Supercritical n

Article pubs.acs.org/jced

Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Measurements of the Speed of Sound in Liquid and Supercritical n‑Octane and Isooctane Ying Zhang, Yutian Chen, Yu Zheng, Xinxin He, and Maogang He* Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, >P. R. China S Supporting Information *

ABSTRACT: The speed of sound in n-octane and isooctane (2,2,4-trimethylpentane) was measured by the Brillouin light scattering (BLS) method. The examined regions for n-octane are T = (297−580) K along five isobaric lines at p = 0.1, 4.0, 7.0, 10.0, and 12.0 MPa for liquid and T = (573−673) K along ten isobaric lines with p = (3.0−10.0) MPa for supercritical fluid. The examined regions for isooctane are T = (294−525) K along five isobaric lines at p = 0.1, 3.0, 6.0, 10.0, and 12.0 MPa for liquid and T = (543−630) K along six isobaric lines with p = (3.0−10.0) MPa for supercritical fluid. The relative expanded uncertainty of the speed of sound is estimated less than 1.3%. Polynomial representations for the speed of sound in liquid n-octane and isooctane were fitted to the experimental results, respectively. The AADs are 0.27% for n-octane and 0.19% for isooctane. The influence of temperature and pressure on the speed of sound was also analyzed. Moreover, the data were also used to assess the predicted ability of three equations of state for n-octane. T = 253.15−393.15 K and pressures up to 140 MPa.10 Moreover, some researchers have employed the Anton Paar DSA with a sound analyzer to measure the speed of sound in binary/ternary n-octane mixtures at 0.1 MPa: diethyl carbonate + n-octane,11 bis(2-methoxyethyl) ether + n-octane,12 ethanol + n-hexane + n-octane,13 octane +1-butanol,14 and ethanol + n-octane.15 We got only one report on the measurement of the speed of sound in pure isooctane by employing the Anton Paar DSA at T = 293.15−373.15 K and pressures from 0.1 to 150 MPa, which was presented by Plantier et al.16 There are also several reports on the measurement of speed of sound in isooctane binary or ternary mixtures at 0.1 MPa: n-heptane + isooctane,17 isooctane + methylbenzene + butan-1-ol,18 toluene + isooctane and isooctane + methyl t-butyl ether (MTBE),19 ethyl t-butyl ether (ETBE) + isooctane,20 methyl t-butyl ether (MTBE) + isooctane,21 isooctane + sodium bis(2-ethylhexyl) sulfosuccinate (AOT),22 and isooctane + benzene + toluene.23 All of the available experimental speed of sound data of n-octane and isooctane were summarized in Table 1. Meantime,

1. INTRODUCTION Speed of sound is one of the most important thermodynamic properties of fluid. It could be also used to calculate other thermodynamics properties, such as compressibility, bulk modulus, heat capacity, virial coefficient, and so on.1 Moreover, the speed of sound in multicomponent mixtures can be used to study the molecular interactions or intermolecular free length.2,3 n-Octane is a fundamental component of fuels and a product of coal pyrolysis and petroleum cracking.4 Isooctane was considered the standard substance to assess the octane number of gasoline,5 which is also used as organic solvents or diluents, such as in the high-precision measurement of silicon in naphthas.6 The accurate knowledge of sound speed in n-octane and isooctane is essential for different applications in industry. The available experimental speed of sound data for pure n-octane was presented by four researchers. Neruchev et al. measured the speed of sound in n-octane along the saturation curve at T = 233.15−567.15 K.7 Khasanshin et al. carried out an experimental investigation on the speed of sound in liquid n-octane at T = 303−433 K and pressures up to 50 MPa.8 Ding et al. developed a system and measured the speed of sound in n-octane at T = 293.15−363.15 K and pressures up to 100 MPa.9 Boelhouwer measured the speed of sound in liquid n-octane at © XXXX American Chemical Society

Received: August 6, 2017 Accepted: November 27, 2017

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DOI: 10.1021/acs.jced.7b00712 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Literature Reports on the Experimental Speed of Sound in n-Octane and Isooctane author

year

data points

T (K)

p (MPa)

purity

c and uca

0.1 0.1 SLb 0.1 0.1 0.1−49.13 5−90 0.1 0.1−140

>0.995 ≥0.99 − 0.99 >0.995 ≥0.98 − >0.992 >0.996

1064.2−1112 (1) 1168.2 75−1452.2 (0.06%) 1111−1193 (1) 1131−1213 777.4−1432.7 (0.1%) 957.8−1627.4 (0.2%) 1096−1172 (2) 797.3−1899.9 (0.1%)

0.1 0.1 0.1 0.1 0.1 0.1 0.1−150 0.1

≥0.996 ≥0.995 ≥0.995 >0.995 >0.995 ≥0.99 ≥0.99 −

918.5−1102.8 (1.4) 959.4−1082.7 (0.1) 958.4−1082.8 (0.5) 979.25−1124.31 (1) 979.25−1124.31 (1) 979.5−1103.2 (0.07) 899.0−1103.2 (0.3%) 979.2−1082.2 (0.1%)

n-octane 13

a

A. Gayol M. Iglesias15 Y. A. Neruchev7 J. Tojo11 J. L. Legido14 T. S. Khasanshin8 Z. S. Ding9 T. M. Aminabhavi12 J. W. M. Boehouwer10

2012 2007 2005 2003 2002 2001 1997 1994 1967

15 1 41 4 5 48 71 5 64

D. J. L. Prak17 Z. Sedláková18 J. Linek19 R. Gonzalez-Olmos20 R. Gonzalez-Olmos21 ́ 22 D. Gómez-Diaz F. Plantier16 S. V. Subrahmanyam23

2014 2013 2009 2007 2007 2006 2005 1974

11 4 4 3 15 5 144 3

288.15−323.15 298.15 233.15−567.15 293.15−313.15 288.15−308.15 303.15−433.15 293.15−363.15 298.15−318.15 253.15−393.15 isooctane 293.15−343.15 298.15−328.15 298.15−328.15 288.15−323.15 288.15−323.15 293.15−323.15 293.15−343.15 298.15−323.15

The uncertainty of speed of sound (uc) is given in m·s−1 units or percentage. bSL: saturated liquid.

Figure 2. Distribution of our measurements and literature data for the speed of sound in iso-octane in the p and T planes: black diamond, this work; open diamond, Plantier et al.;16 open circle, Subrahmanyam ́ et al.;22 downward triangle, et al.;23 upward triangle, Gómez-Diaz 20,21 left-pointing triangle, Linek et al.;19 rightGonzalez-Olmos et al.; pointing triangle, Sedláková et al.;18 open square, Prak et al.;17 black circle, ref 25; solid line, saturated vapor pressure.

Figure 1. Distribution of our measurements and literature data for the speed of sound in n-octane in the p and T planes: black diamond, this work; downward triangle, data from Gayol et al.;13 times symbol, Iglesias et al.;15 asterisk, Neruchev et al.;7 square, Tojo et al.;11 right-pointing triangle, Legido et al.;14 left-pointing triangle, Boelhouwer;10 open circle, Ding et al.;9 open diamond, Khasanshin et al.;8 upward triangle, Aminabhavi et al.;12 black circle, ref 24; black solid line, vapor pressure calculated from the fundamental equation of state of Span and Wagner.42

Neruchev et al., while the upper limit of measured temperature for isooctane is 373.15 K, presented by Plantier et al. Therefore, to fill the gap by providing new experimental data, we measured the speed of sound in n-octane and isooctane in a wide p−T region by the Brillouin light scattering (BLS) method. The examined regions are T = (297−580) K for liquid n-octane along 5 isobaric lines at p = 0.1, 4.0, 7.0, 10.0, and 12.0 MPa and T = (573−673) K for supercritical n-octane along 10 isobaric lines with p = (3.0−10.0) MPa. The examined regions for isooctane are T = (294−525) K for liquid along five isobaric lines at p = 0.1, 3.0, 6.0, 10.0, and 12.0 MPa and T = (543−630) K for supercritical fluid along 6 isobaric lines with p = (3.0−10.0) MPa.

the distributions of the previous literature reports and our measurements in the p and T planes were shown in Figures 1 and 2. It can be seen that the literature on the measurement of speed of sound in n-octane or isooctane is still very scant. Some measurements of the speed of sound in n-octane and isooctane were carried out at high pressure, such as the upper limit of measured pressures are 140 MPa for n-octane and 150 MPa for isooctane, which were presented by Boehouwer et al. and Plantier et al., respectively. However, most experimental data are available at 0.1 MPa, and almost all of the measurement were carried out in the low-temperature region. The upper limit of measured temperature for n-octane is 567.15 K, presented by B



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2. EXPERIMENTAL SECTION 2.1. Materials. The n-octane and isooctane were supplied by Aladdin Reagent Inc. and had mass purity better than of >0.998

(GC). The samples were not further purified. The sample was filtered through membrane filters with 0.22 mm pure size when filling the sample cell to prevent dust and particles from entering the cell. The basic physical and chemical properties of n-octane and isooctane are listed in Table 2. 2.2. Measurement Principle and Apparatus. There is a classical acoustic method for measuring the speed of sound, which has two types of resonators: one is a spherical resonator, and the other is a cylinder resonator. Many experienced groups researched the speed of sound using the methods.26−30 Besides, the Anton Paar DSA 5000 with a sound analyzer has been widely used to measure the speed of sound of fluids.17−21 Although this method is easy to operate, it limited to the maximum measured temperature. In this work, the Brillouin light scattering method was used to measure the speed of sound. The theory of BLS is based on an

Table 2. Selected Physical and Chemical Properties of n-Octane and Isooctane n-octane

material CAS no. molecular formula molecular weight critical temperature (K) critical pressure (MPa) supplier mass purity purification method

111−65−9 CH3(CH2)6CH3 114.2285 568.725 2.4925 Aladdin Reagent Inc. >0.998 filtered through the membrane filters

isooctane 540−84−1 (CH3)2CHCH2C(CH3)3 114.2285 544.126 2.5726 Aladdin Reagent Inc. >0.998 filtered through the membrane filters

Figure 3. Typical count rate variation with time.

Table 3. Experimental Speed of Sound in Liquid n-Octanea T (K)

p (MPa)

c (m·s−1)

T (K)

p (MPa)

c (m·s−1)

T (K)

p (MPa)

c (m·s−1)

296.97 303.61 318.37 332.50 347.68 362.53 377.50 391.61 297.28 303.53 318.30 332.26 347.40 362.28 377.03 390.80 407.38 412.59 422.73 431.82 442.23 452.55 462.37 472.05 482.98 493.41 502.54 513.00 522.92 532.23

0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0

1173.0 1151.7 1089.5 1029.1 970.1 912.3 855.4 806.4 1196.5 1172.7 1121.2 1066.7 1007.2 955.4 909.7 860.1 802.1 786.2 747.2 720.1 682.1 646.4 614.7 579.7 543.0 503.5 477.8 439.1 407.7 373.2

407.46 412.65 422.88 431.88 442.49 452.64 462.45 472.15 483.04 493.48 502.73 513.26 523.46 532.36 537.75 543.83 547.82 552.01 558.19 561.87 566.82 570.20 573.03 575.57 578.92 297.38 303.38 318.11 332.32 347.37

7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 10.0 10.0 10.0 10.0 10.0

836.9 818.8 784.5 754.2 723.8 689.9 660.1 631.6 599.7 565.4 537.1 506.5 478.6 450.6 436.8 422.0 406.8 398.1 380.2 372.6 356.5 347.6 341.0 332.6 323.1 1242.7 1213.7 1164.8 1108.6 1053.4

532.59 538.10 544.52 548.60 552.52 558.64 562.27 566.96 570.48 573.37 576.28 579.36 297.35 303.42 318.37 332.56 347.46 363.67 379.75 394.67 403.71 414.33 422.69 431.77 442.73 452.88 462.61 472.38 483.14 493.73

10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0

511.4 497.5 483.1 471.5 465.1 448.0 441.3 430.4 424.0 414.0 408.7 400.8 1250.8 1233.0 1184.5 1128.3 1072.7 1027.8 973.9 920.8 896.1 864.0 844.3 815.2 779.7 750.8 724.2 693.8 672.7 645.0

C



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Table 3. continued T (K)

p (MPa)

c (m·s−1)

T (K)

p (MPa)

c (m·s−1)

T (K)

p (MPa)

c (m·s−1)

537.40 542.87 546.68 550.42 557.27 561.20 567.01 570.16 297.34 303.33 318.35 332.33 347.29 362.17 377.33 391.00

4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0

354.7 337.8 325.7 315.2 290.5 276.7 257.3 245.6 1222.0 1199.7 1141.4 1089.1 1031.9 979.6 933.5 892.3

362.12 377.35 391.09 407.45 412.71 422.61 431.92 442.65 452.77 465.54 472.28 483.12 493.62 502.95 513.46 523.60

10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0

1006.2 960.5 917.4 865.2 846.7 818.2 789.8 755.7 728.1 695.8 676.9 646.1 614.7 590.5 563.1 533.3

503.17 513.67 523.17 532.79 538.41 543.27 549.27 552.88 559.37 562.71 567.10 570.75 573.60 576.53 579.57

12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0

616.5 591.5 570.6 545.1 530.4 520.1 505.4 500.8 486.2 477.8 471.0 461.0 454.4 451.3 444.1

a

The expended uncertainties U are U (T) = 0.042 K, U (p) = 0.08 MPa for p = 0 to 20 MPa, and the relative expanded uncertainty Ur is Ur(c) = 0.013. The level of confidence is 0.95 (k = 2).

Table 4. Experimental Speed of Sound in Liquid Isooctanea T (K)

p (MPa)

c (m·s−1)

T (K)

p (MPa)

c (m·s−1)

T (K)

p (MPa)

c (m·s−1)

294.06 304.03 313.81 323.56 333.42 342.88 352.86 363.55 294.37 304.16 313.92 323.61 333.48 343.07 352.89 363.39 373.04 383.18 393.83 402.16 412.57 423.95 434.51 443.70 452.94 462.54 472.45 483.15 493.12 502.80 512.41 523.31 294.65 304.23 313.96

0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 6.0 6.0 6.0

1099.7 1058.5 1017.3 978.2 938.5 898.0 858.9 821.9 1127.4 1088.2 1037.2 999.1 968.0 927.9 891.7 852.2 821.1 783.2 742.3 716.5 677.6 636.8 602.6 569.7 538.4 502.1 464.2 423.5 386.4 350.1 311.4 264.5 1147.6 1109.6 1065.2

323.65 333.50 343.16 352.94 363.49 373.27 383.80 394.00 402.48 412.84 424.32 434.94 444.00 453.22 463.04 472.86 483.63 493.56 503.17 513.04 523.97 294.84 304.27 313.82 323.67 333.46 343.22 353.01 363.54 373.41 384.11 394.15 402.64 413.07 424.49

6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0

1027.4 996.0 954.8 921.1 883.5 843.9 813.8 782.2 750.9 719.3 678.1 647.4 619.6 588.3 558.9 530.7 496.7 464.9 435.4 404.0 371.4 1176.1 1136.9 1100.1 1060.4 1028.0 990.3 961.7 925.7 888.2 855.6 825.8 800.2 766.7 732.1

435.26 444.22 454.37 463.43 473.22 484.05 494.09 503.79 513.78 524.59 294.97 304.27 313.85 323.71 333.40 343.21 353.04 363.58 373.49 384.26 394.19 402.78 413.22 424.59 435.36 444.36 455.24 463.72 473.48 484.30 494.42 504.09 514.01 524.70

10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0

701.0 677.1 648.8 622.7 596.3 569.9 542.2 516.1 491.8 463.0 1181.7 1147.7 1110.8 1075.4 1041.9 1008.5 975.5 943.8 908.6 876.5 848.1 819.5 791.3 756.7 726.5 700.3 671.1 651.6 627.7 598.4 576.5 550.4 526.6 501.3

a

The expended uncertainties U are U (T) = 0.042 K, U (p) = 0.08 MPa for p = 0 to 20 MPa, and the relative expanded uncertainty Ur is Ur(c) = 0.013. The level of confidence is 0.95 (k = 2).

analysis of the Rayleigh and Brillouin light-scattering processes, which were originated from the volume of fluid. As a promising

method, the BLS method has been used to measure the speed of sound of many materials. Leipertz, Fröba, and their group have D



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circuit, and pressure control system. The standard uncertainty in pressure is u (p) = 0.02 MPa for p < 5.0 MPa and u (p) = 0.04 MPa for p > 5.0 MPa. The uncertainty of the speed of sound is estimated less than 1.3%. A detailed summary of the contributions to the measurement uncertainties can be obtained in our previous paper.41

been devoted to the study of this BLS method for many years, and a series of pure substance and mixtures have been measured.31−33 Coakley and co-workers carried out a series of work to investigate the BLS method, and the speeds of sound in many organics were investigated.34,35 Moreover, the BLS method has been developed to measure the sound speed in single crystals.36,37 A brief introduction of the BLS measuring principle and working equations is given as follows: when a coherent laser beam transmits the fluid, the light scattering process would occur. The fluctuating scattered light can be detected in all directions. The macroscopic transport properties of fluid and the corresponding microscopic fluctuation relaxation processes follow the same governing equation. The pressure fluctuations spread at a velocity of local sound speed in the fluid. The mathematical relationship between the scattering characteristic parameters and the speed of sound can be established.38,39 As shown in Figure 3, the spectrum of the scattered light is composed of three peaks; the Brillouin peak and the anti−Brillouin peak are caused by the pressure fluctuation, so we can get the speed of sound by analyzing the BLS frequency spectrogram. Eq 1 shows the relation between the speed of sound and the frequency shift of scattering light: Δω = cq

3. RESULTS AND DISCUSSION 3.1. Liquid. The speeds of sound were measured in liquid n-octane and isooctane, respectively. The speed of sound in liquid n-octane was measured at the temperature ranging from 296.97 to 579.57 K along five isobaric lines at p = 0.1, 4.0, 7.0, 10.0, and 12.0 MPa. The speed of sound in liquid isooctane was measured

(1)

where Δω is the frequency shift of scattering light, q is the modulus of the scattering vector, which is defined as:

q≈

2π sin θex λ0

(2)

where λ0 is the wavelength of the incident light in vacuum, θEx is the incident angle in the air. The experimental setup is similar to our previous paper.40 Here, only a brief depiction about the main equipment was presented. The temperatures were measured with the platinum resistance thermometer (PRT, Fluke Corporation; uncertainties are T = ± 0.01 K). The pressures were measured with the pressure transmitter (Rosemount, 3051S, 0−20 MPa) with an uncertaintiy of ±5 kPa. The uncertainty of pressure is composed of the uncertainties in pressure transmitter, pressure measurement

Figure 4. Experimental speed of sound in n-octane liquid: diamond, p = 0.1 MPa; circle, p = 4.0 MPa; square, p = 7.0 MPa; upward triangle, p = 10.0 MPa; downward triangle, p = 12.0 MPa; solid black line, calculated from eq 3; blue solid line, speed of sound at the measured isobaric lines calculated from the fundamental equation of state of Span and Wagner;42 green solid line, speed of sound at the measured isobaric lines calculated from the volume-translated p−R EOS;43 red solid line, speed of sound at the measured isobaric lines calculated from the modified p−T EOS.44

Table 5. Fitted Coefficients in Eq 3a

a

aij

n-octane

isooctane

a00 a10 a20 a30 a01 a11 a21 a31 a02 a12 a22 a32 a03 a13 a23 a33 AAD (%) MD (%)

3.4410 × 103 −1.2596 × 101 2.2298 × 10−2 −1.8744 × 10−5 −4.3742 × 102 3.3081 × 10° −8.1781 × 10−3 6.8801 × 10−6 6.8735 × 101 −5.0112 × 10−1 1.1931 × 10−3 −9.4140 × 10−7 −3.2527 × 10° 2.3505 × 10−2 −5.5118 × 10−5 4.2436 × 10−8 0.27 0.67

4.0595 × 103 −1.8662 × 101 3.9538 × 10−2 −3.4976 × 10−5 −2.0569 × 102 1.9430 × 10° −5.9233 × 10−3 6.0939 × 10−6 2.0402 × 101 −1.8057 × 10−1 5.3547 × 10−4 −5.3188 × 10−7 −1.0264 × 10° 8.2026 × 10−3 −2.2202 × 10−5 2.0357 × 10−8 0.19 0.54

Figure 5. Experimental speed of sound in liquid isooctane: diamond, p = 0.1 MPa; circle, p = 3.0 MPa; square, p = 6.0 MPa; upward triangle, p = 10.0 MPa; downward triangle, p = 12.0 MPa; solid line, calculated from eq 3.

The coefficients aij are in unit of m·s−1. E



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Figure 6. Fractional deviations Δc = ccalc − cexpt (or cmodel) of the speed of sound calculated from eq 3 (ccalc), the experimental speeds of sound of this work or literature (cexpt.) in liquid octane, the speed of sound (cmodel) calculated from the fundamental equation of state of Span and Wagner, Jorge et al., and Gasem et al. as a function of temperature at 0.1, 4.0, 5.0, 7.0, 10.0, and 12.0 MPa:24 black diamond, this work; downward triangle, Gayol et al.;13 asterisk, Iglesias et al.;15 open square, Tojo et al.;11 right-pointing triangle, Legido et al.;14 left-pointing triangle, Boelhouwer;10 open circle, Ding et al.;9 open diamond, Khasanshin et al.;8 upward triangle, Aminabhavi et al.;12 black solid line, speed of sound at the measured isobaric lines calculated from the fundamental equation of state proposed by Span and Wagner.;42 red solid line, speed of sound at the measured isobaric lines calculated from the modified P−T EOS proposed by Jorge etc.;43 blue solid line, speed of sound at the measured isobaric lines calculated from modified p−R EOS proposed by Gasem etc.44

at the temperature ranging from 294.15 to 524.70 K along five isobaric lines at p = 0.1, 3.0, 6.0, 10.0, and 12.0 MPa. The experimental data were presented in Tables 3 and 4. The experimental data in liquid n-octane and isooctane were fitted into the functions of temperature and pressure as eq 3: 3

c=

3

⎛ T ⎞i ⎛ p ⎞ j ⎜ ⎟⎜ ⎟ K ⎠ ⎝ MPa ⎠

∑ ∑ aij⎝ i=0 j=1

(3)

in which c is the speed of sound in n-octane or isooctane and aij are the fitted coefficients that were listed in Table 5. The absolute average deviations (AAD) and the maximum deviation (MD) are introduced to assess the performances of the polynomial expression, which are defined as: ⎧ N ⎪ AAD (%) = 100 ∑ ⎪ N i ⎪ ⎨ ⎛ ⎪ ⎪ MD (%) = 100max⎜⎜ ⎪ ⎝ ⎩

Figure 7. Deviations of speed of sound between the experimental data of this work (open symbols) and other different authors (black symbols) and the fitting results according to eq 3 for liquid isooctane: open diamond, p = 0.1 MPa; open circle, p = 3.0 MPa; open upward triangle, p = 6.0 MPa; open downward triangle, p = 10.0 MPa; open square, p = 12.0 MPa; black diamond, Subrahmanyam et al.;23 black circle, ́ et al.;22 black upward Plantier et al.;16 black square, Gómez-Diaz 20,21 black left-pointing triangle, Linek triangle, Gonzalez-Olmos et al.; et al.;19 black right-pointing triangle, Sedláková et al.;18 black diamond, Prak et al.17

ccalc, i cexpt, i ccalc, i cexpt, i

−1 ⎞ − 1 ⎟⎟ ⎠

(4)

where cexpt,i is the ith experimental datum of speed of sound in n-octane or isooctane, and ccalc,i is the ith speed of sound calculated from eq 3. Figures 4 and 5 show the experimental speed of sound in liquid n-octane and isooctane, respectively. It can be seen that the F



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in eq 4 are 0.67% for n-octane and 0.54% for isooctane. The available experimental speed of sound in n-octane and isooctane were collected and compared to our correlation. The summary of the literature experimental data was shown in Table 1. The deviations were shown in Figure 6 for n-octane and Figure 7 for isooctane. As shown in Figure 6, it shows a good agreement between the calculated results and literature data proposed by Tojo,11 Gayol,13 Boelhouwer,10 Iglesias,15 Khasanshin,8 Legido,14 and Ding,9 presenting only a maximum deviation of 0.45% at T = 393.15 K and p = 0.1 MPa proposed by Khasanshin,8 which corresponds less than 4.0 m·s−1. The calculated results are slight less than the results from Aminabhavi,12 with a maximum deviation of −0.74% at T = 318.15 K and p = 0.1 MPa, which corresponds less than −8.1 m·s−1. Figure 7 showed the relative deviations between calculated results from eq 3 and the literature experimental data for isooctane. It showed good agreement and most of the relative deviations fall in a

temperature influence the speed of sound more obviously compared to the pressure over the whole investigated p−T region. Moreover, the influences of the pressure on the speed of sound become greater as the temperature rises. For n-octane, a 4 to 12 MPa pressure increase gives an approximately 3.67% increase at T = 297.15 K and a 94.8% increase at T = 570.15 K in the speed of sound. For isooctane, a 3 to 12 MPa pressure increase gives an approximately 4.5% increase at T = 294.97 K and a 67.2% increase at T = 524.70 K in the speed of sound. For both n-octane and isooctane, the speed of sound calculated from eq 3 are compared with the experimental data of this work and literature data, which are shown in Figures 6 and 7. It can be seen that the calculated results from eq 3 agree with all the experimental data obtained in this work. The relative deviations fall in a narrow range (±0.67%) for n-octane and in the range of −0.48% to 0.54% for isooctane. The AADs shown in eq 4 are 0.27% for n-octane and 0.19% for isooctane, and the MDs shown Table 6. Experimental Speed of Sound in Supercritical n-Octanea T (K)

p (MPa)

c (m·s−1)

T (K)

p (MPa)

c (m·s−1)

T (K)

p (MPa)

c (m·s−1)

573.80 577.56 582.19 585.88 589.68 594.90 599.12 605.28 610.17 614.76 619.43 624.89 630.15 635.95 638.90 573.69 577.86 582.61 586.85 591.09 596.02 599.76 605.73 610.28 614.83 619.62 624.55 629.96 635.97 638.73 573.05 575.02 579.05 583.76 588.01 594.05 598.63 602.47 606.87 612.50

3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0

135.4 110.1 86.9 88.4 93.7 102.1 108.9 116.6 124.3 129.2 134.1 139.4 144.3 149.3 152.4 189.0 168.5 144.9 124.2 108.6 100.7 95.6 94.8 103.2 111.5 119.0 124.9 132.1 140.0 142.4 228.1 217.1 198.3 181.0 166.2 140.2 125.5 114.3 111.1 108.7

617.46 622.00 624.66 628.69 632.06 636.07 642.66 573.90 577.56 583.28 587.72 591.69 597.28 601.10 607.11 611.94 616.02 619.76 625.00 630.45 636.31 639.03 584.07 588.39 593.97 599.17 603.01 607.61 613.58 616.33 620.31 623.42 625.29 629.77 633.13 637.58 642.09 584.52 588.83 594.09

4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 6.0 6.0 6.0

110.4 112.6 114.2 120.4 124.2 131.6 142.7 250.4 236.5 215.8 200.5 186.7 170.5 159.7 144.8 133.3 128.5 125.2 125.1 126.6 132.0 134.5 239.2 226.1 206.7 192.7 180.4 169.3 153.7 148.3 144.0 141.6 139.2 137.3 137.6 140.4 144.1 280.5 270.2 255.1

599.18 603.24 607.97 613.80 623.50 633.62 642.28 584.97 589.14 594.28 599.55 603.57 608.40 614.19 623.84 633.94 642.75 585.27 589.41 594.52 599.72 603.85 608.86 614.65 624.50 634.48 643.16 585.51 589.67 594.74 600.00 604.21 609.24 615.18 624.87 585.79 589.93 594.94 601.00 609.54

6.0 6.0 6.0 6.0 6.0 6.0 6.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 9.0 9.0 9.0 9.0 9.0 9.0 9.0 9.0 10.0 10.0 10.0 10.0 10.0

241.2 226.2 215.3 204.8 184.3 169.8 160.5 314.5 302.3 290.8 276.6 254.3 254.8 242.3 224.1 204.8 194.7 351.8 337.0 322.3 309.6 299.0 285.3 273.2 254.1 240.7 229.4 367.9 358.4 346.5 334.0 324.3 312.3 302.0 283.1 392.1 385.1 374.1 358.1 340.1

a

The expended uncertainties U are U(T) = 0.042 K and U(p) = 0.08 MPa for p = 0 to 20 MPa, and the relative expanded uncertainty Ur is Ur(c) = 0.013. The level of confidence is 0.95 (k = 2). G



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narrow range from 0.4% to −0.2% except for two points at T = 363.15 K and p = 0.1 MPa and at T = 373.15 K and p = 0.1 MPa reported by Plantier,16 which correspond the relative deviations of 0.63% and 0.54%, respectively. In this paper, three selected equations of state (EOS) were applied to predict the speed of sound for liquid n-octane: a multiparameter EOS proposed by Span and Wagner,42 a modified p−T EOS proposed by Jorge et al.,43 and a volumetranslated p−R EOS proposed by Gasem et al.44 The EOS proposed by Span and Wagner was used as implemented in REFPROP45 for calculating the density and speed of sound of n-octane. The average deviations with the models proposed by Jorge etc. and Gasem etc. were estimated lower than 1.05% and 1.00% for calculating the density of n-octane, respectively. The three selected EOS were shown as eqs 5−7: o

p=

(1 + δαδr − δταδτr )2 c2 = 1 + 2δαδr + δ 2αδδr − R τ 2(αδδ0 + αδδr )

r

cp (∂T /∂v)p

c=

(∂p /∂ρ) = v 2

ds =

cp cV (∂T /∂p)v dp + (∂T /∂v)p dv T T

s

(8)

cv (∂T /∂p)v

(9)

(10)

For the modified P−T EOS shown in eq 6 and the modified p−R EOS shown as eq 7, the speed of sound can be calculated by combining eqs 9 and 10, which are the general thermodynamic relations. In eqs 9 and 10, cp and cv were specific heat capacity at constant pressure and specific heat capacity at constant volume,

(5)

a(T ) RT − 2 v−b v + (b + c)v − bc

(7)

The EOS proposed by Span and Wagner was formulated in the reduced Helmholtz energy and the function for calculating the speed of sound was also given and shown as eq 8:

a(T , ρ ) a (T , ρ ) a (T , ρ ) = + = α o(τ , δ) + α r(τ , δ) RT RT RT p=

a(T ) RT − v−b v(v + b) + b(v − b)

(6)

Table 7. Experimental Speed of Sound in Supercritical Isooctanea T (K)

p (MPa)

c (m·s−1)

T (K)

p (MPa)

c (m·s−1)

T (K)

p (MPa)

c (m·s−1)

543.28 547.77 552.48 558.01 567.24 570.76 576.9 583.34 586.96 592.79 597.98 602.56 607.97 613.31 618.84 623.75 629.42 633.71 543.47 548.38 553.35 559.18 563.28 568.08 573.32 578.09 582.97 587.1 592.49 597.57 602.34 607.09 612.44 617.81 622.75 628.07 632.19

3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0

159.0 135.2 103.8 97.9 109.9 112.7 117.3 121.9 125.0 130.8 136.1 141.1 145.8 150.4 154.9 159.5 164.0 166.1 233.1 216.1 194.1 172.1 154.4 137.3 122.1 114.9 114.7 116.0 117.9 119.2 121.2 124.3 129.9 134.8 139.0 145.5 148.1

543.63 548.79 553.80 559.16 564.27 569.24 574.23 579.00 584.13 588.18 593.39 598.54 603.22 607.67 612.74 618.08 622.82 627.69 631.25 543.74 548.94 553.96 559.12 564.85 570.06 574.70 579.62 584.82 588.98 594.09 599.18 604.02 608.43 613.49 618.60 623.43 628.11

5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0

282.2 262.4 247.6 232.4 214.5 201.2 187.0 173.2 161.6 151.1 140.6 135.1 132.5 131.0 131.9 135.0 137.2 141.2 143.4 314.4 301.9 286.4 272.8 257.3 244.3 233.0 222.1 208.9 199.3 191.7 184.6 175.1 167.7 164.3 159.9 156.1 153.4

631.51 544.07 549.02 554.27 558.52 564.81 570.54 575.07 580.32 585.35 589.65 595.15 600.35 605.01 609.62 614.69 619.8 624.7 629.13 544.08 548.93 554.24 558.54 564.68 569.81 574.8 580.26 585.19 589.39 594.93 600.58 604.68 609.5 614.9 619.6 624.61 629.2

6.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0 12.0

156.0 409.3 399.6 392.6 386.7 374.5 362.4 354.0 343.6 337.5 331.2 318.7 311.6 304.3 295.9 286.8 281.3 276.4 269.4 448.4 439.8 430.8 426.0 415.3 404.7 398.5 388.5 379.7 374.8 363.8 356.1 350.2 342.6 336.6 329.3 321.5 316.9

a

The expended uncertainties U are U (T) = 0.042 K, U (p) = 0.08 MPa for p = 0 to 20 MPa, and the relative expanded uncertainty Ur is Ur(c) = 0.013. The level of confidence is 0.95 (k = 2). H



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which were estimated using the equation of state by Span and Wagner, which was used as implemented in REFPROP.45 We compared the results from the three models with the results from eq 3 to assess the predictive ability of these models, which were also shown in Figure 6. The calculated results from eq 3 are slightly larger than that of the three models. The AADs between the calculated results from eq 3 and that of the three models are 1.73% for the model proposed by Span and Wagner, 1.30% for the model proposed by Jorge et al., and 1.29% for the model proposed by Gasem et al. As shown in Figure 7, most of the relative deviations between the calculated results from eq 3 and that of the three models are less than 2.0%. Along the isobaric line of 0.1 MPa, the relative deviations between the calculated results from eq 3 and that of the modified p−R EOS proposed by Gasem et al. increase obviously when the temperature rises up to 350 K. Along the isobaric line of 4.0 MPa, the relative deviations between the calculated results from eq 3 and that of the three models increase obviously when the temperature rises up to 550 K. 3.2. Supercritical Fluid. The speed of sound in n-octane was measured along ten isobaric lines from 3 to 10 MPa and in the temperature from 573.15 to 673.15 K in supercritical fluid, while the speed of sound in isooctane was measured along six isobaric lines from 3 to 10 MPa and in the temperature from 543.28 to 629.20 K in supercritical fluid. The literature critical parameters were listed in Table 1 for both for n-octane and isooctane. Each experimental point was independently measured six times at a fixed small scattering angle. The result repeatability was better than 0.5%, and the average value was adopted. The experimental results are summarized in Tables 6 and 7. The variation tendencies of the experimental speeds of sound in n-octane and isooctane with temperature and pressure were shown in Figures 8 and 9. In the low-pressure region (p of less than about 5.0 MPa for n-octane and p of less than about 6.0 MPa for isooctane), the speeds of sound first decrease obviously, exhibit a turning point, and increase slowly with the temperature increase. The temperature dependences of the speeds of sound show

an approximative boomerang-shaped trend along isobaric line. As pressures increase, this trend was gradually not pronounced. Moreover, the temperature of the turning points increase with the increasing pressures. The experimental data of speeds of sound in supercritical n-octane were compared with the speed of sound results calculated from the fundamental equation of state proposed by Span and Wagner along the measured isobaric lines, which were also shown in Figures 8 and 10. It is obvious that the variation trends of our experimental data were similar to that of the calculated values. The AAD between the experimental data and the calculated values is 2.6% at p = 3−5 MPa, while the AAD is 2.0% at p = 6−10 MPa. In the whole supercritical p−T region, the AAD is 2.4%. The maximum deviation of 10.3% occurs at T = 605.73 K along the isobaric line p = 3.5 MPa.

Figure 9. Experimental speed of sound in supercritical isooctane: diamond, p = 3.0 MPa; circle, p = 4.0 MPa; square, p = 5.0 MPa; upward triangle, p = 6.0 MPa; left-pointing triangle, p = 10.0 MPa; right-pointing triangle, p = 12.0 MPa.

Figure 10. Deviations of speed of sound in supercritical n-octane between the experimental data of this work and speed of sound at the measured isobaric lines calculated from the fundamental equation of state of Span, R. and Wagner, W.42 Diamond, p = 3.0 MPa; circle, p = 3.5 MPa; square, p = 4.0 MPa; upward triangle, p = 4.5 MPa; leftpointing triangle, p = 5.0 MPa; right-pointing triangle, p = 6.0 MPa; star, p = 7.0 MPa; downward triangle, p = 8.0 MPa; octagon, p = 9.0 MPa; hexagon, p = 10.0 MPa.

Figure 8. Experimental speed of sound in supercritical n-octane: diamond, p = 3.0 MPa; circle, p = 3.5 MPa; square, p = 4.0 MPa; upward triangle, p = 4.5 MPa; left-pointing triangle, p = 5.0 MPa; right-pointing triangle, p = 6.0 MPa; star, p = 7.0 MPa; downward triangle, p = 8.0 MPa; octagon, p = 9.0 MPa; hexagon, p = 10.0 MPa; black solid line, speed of sound at the measured isobaric lines calculated from the fundamental equation of state of Span and Wagner.42 I



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(6) Gazulla, M. F.; Rodrigo, M.; Orduña, M.; Ventura, M. J.; Andreu, C. High precision measurement of silicon in naphthas by ICP−OES using isooctane as diluent. Talanta 2017, 164, 563−569. (7) Neruchev, Y. A.; Bolotnikov, M. F.; Zotov, V. V. Investigation of ultrasonic velocity in organic liquids on the Saturation Curve. High Temp. 2005, 43, 266−309. (8) Khasanshin, T. S.; Shchemelev, A. P. Sound velocity in liquid n− alkanes. High Temp. 2001, 39, 60−67. (9) Ding, Z. S. Automation of an ultrasound velocity measurement system in high−pressure liquids. Meas. Sci. Technol. 1997, 8, 154−161. (10) Boelhouwer, J. W. M. Sound velocities and adiabatic compressibilities of liquid alkanes at various temperatures and pressures. Physica 1967, 34, 484−492. (11) Rodrıguez, A.; Canosa, J.; Tojo, J. Physical properties of the binary mixtures (diethyl carbonate + hexane, heptane, octane and cyclohexane) from T = 293.15 K to T = 313.15 K. J. Chem. Thermodyn. 2003, 35, 1321−1333. (12) Aminabhavi, M. T.; Aralaguppi, M. I.; Bindu, G.; Khinnavar, R. S. Densities, shear viscosities, refractive indices, and speeds of sound of Bis(2−methoxyethyl) ether with hexane, heptane, octane, and 2, 2, 4− Trimethylpentane in the Temperature Interval 298.15−318.15 K. J. Chem. Eng. Data 1994, 39, 522−528. (13) Blanco, A.; Gayol, A.; Gómez-Díaz, D.; Navaza, J. M. Thermophysical properties of the ternary mixture: ethanol + n−hexane + n-octane in function of the temperature. Phys. Chem. Liq. 2012, 50, 798−811. (14) Cominges, B. E. D.; Piñeiro, M. M. Temperature dependence of thermophysical properties of octane + 1−butanol system. J. Therm. Anal. Calorim. 2002, 70, 217−227. (15) Gayol, A.; Iglesias, M.; Goenaga, J. M.; Concha, R. G.; Resa, J. M. Temperature influence on solution properties of ethanol + n−alkane mixtures. J. Mol. Liq. 2007, 135, 105−114. (16) Plantier, F.; Daridon, J. L. Speed of sound of 2−methylpentane, 2, 3−dimethylpentane, and 2, 2, 4−trimethylpentane from (293.15 to 373.15) K and up to 150 MPa. J. Chem. Eng. Data 2005, 50, 2077−2081. (17) Prak, D. J. L.; Cowart, J. S.; Trulove, P. C. Density, viscosity, speed of sound, bulk modulus, and surface tension of binary mixtures of n− heptane + 2, 2, 4−trimethylpentane at (293.15 to 338.15) K and 0.1 MPa. J. Chem. Eng. Data 2014, 59, 3842−3851. (18) Morávková, L.; Troncoso, J.; Machanová, K.; Sedláková, Z. Volumetric behaviour of the (2, 2, 4− trimethylpentane + methylbenzene + butan−1−ol) ternary system and its binary sub− systems within the temperature range (298.15−328.15) K. J. Chem. Thermodyn. 2013, 64, 137−150. (19) Morávková, L.; Wagner, Z.; Linek, J. Volumetric behaviour of binary liquid systems composed of toluene, isooctane, and methyl tert− butyl ether at temperatures from (298.15 to 328.15) K. J. Chem. Thermodyn. 2009, 41, 591−597. (20) Gonzalez-Olmos, R.; Iglesias, M. Temperature influence on mixing properties of {ethyl tert−butyl ether (ETBE) + gasoline additives}. J. Chem. Thermodyn. 2007, 39, 1557−1564. (21) Gonzalez-Olmos, R.; Iglesias, M.; Goenaga, J. M.; Resa, J. M. Influence of temperature on thermodynamic properties of methyl t − butyl ether (MTBE) + gasoline additives. Int. J. Thermophys. 2007, 28, 1199−1227. (22) Gómez-Díaz, D.; Mejuto, J. C.; Navaza, J. M. Density, viscosity, and speed of sound of solutions of AOT reverse micelles in 2, 2, 4trimethylpentane. J. Chem. Eng. Data 2006, 51, 409−411. (23) Rajagopal, E.; Subrahmanyam, S. V. Excess functions VE, (∂VE/ ∂p)T, and CpE of isooctane + benzene and + toluene. J. Chem. Thermodyn. 1974, 6, 873−876. (24) Ambrose, D.; Tsonopoulos, C. Vapor−liquid critical properties of elements and compounds. 2. normal alkanes. J. Chem. Eng. Data 1995, 40, 531−546. (25) Li, J. F.; Qin, Z. F.; Wang, G. F.; Dong; Wang, J. G. Critical temperatures and pressures of several binary and ternary mixtures concerning the alkylation of 2−methylpropane with 1−butene in the presence of methane or carbon dioxide. J. Chem. Eng. Data 2007, 52, 1736−1740.

4. CONCLUSIONS Experimental data of speed of sound for n-octane and isooctane were measured using the BLS method. The examined region of n-octane is T = 296.97−579.57 K along 5 isobaric lines at p = 0.1, 4, 7, 10, and 12 MPa for liquid and T = 573.15−673.15 K along 10 isobaric lines with p = 3−10 MPa for supercritical fluid. The examined region of isooctane is T = 294.15−524.70 K along five isobaric lines with p = 0.1−12 MPa for liquid and T = 543.28−629.20 K along six isobaric lines with p = 3−10 MPa for supercritical fluid. The change regularities of the speed of sound in n-octane and isooctane with temperature and pressure were analyzed in the investigated p−T region. The function is proposed to fit the data in liquid. The AAD and MD and and bias are 0.27% and 0.67 for n-octane and 0.19% and 0.54% for isooctane. The calculated results in this work were also compared with literature data. It shows that our data agree well with most data in the literature.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.7b00712. The calculated value of the speed of sound from our correlation, the three fundamental equations of state, and the relative deviation between the calculated results from eq 3 with that of three fundamental equations of state. (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +86-29-8266-3863. Fax: +86-29-8266-8789. ORCID

Maogang He: 0000-0002-2364-2140 Funding

This work was supported by the National Nature Science Fund Committee (NSFC no. 51576161) and 111 project (B16038). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The calculations from the equation of state by Span and Wagner were used as implemented in REFPROP.45 REFERENCES

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Measurements of the Speed of Sound in Liquid and Supercritical n

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