Speed of Sound Measurements of 2-Methoxy-2 ... - ACS Publications

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Speed of Sound Measurements of 2‑Methoxy-2-methylpropane in the Temperature Range of 293.15 and 673.15 K and for Pressures up to 10 MPa Ying Zhang, Xiong Zheng, Maogang He,* and Yutian Chen Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, Xi’an Jiaotong University, Xi’an, Shaanxi Province 710049, P. R. China ABSTRACT: Ethers are usually used as gasoline additives, and now 2-methoxy-2-methylpropane (MTBE) is the most widely used fuel additive. The speed of sound in MTBE with a specified mass purity higher than 0.990 (GC) was measured by the Brillouin light scattering method in the temperature range of 293.15−673.15 K and for pressures up to 10 MPa, including saturated liquid/vapor, liquid, and supercritical fluid. The correlations for the speed of sound in saturated liquid/vapor and liquid were proposed by employing the experimental results. Comparing the calculated results with the experimental data, the average absolute deviations are 0.50% for saturated liquid, 0.20% for saturated vapor, and 0.24% for liquid. The tendency of speed of sound to temperature and pressure was also analyzed.

1. INTRODUCTION In order to improve the quality of gasoline, oxygenated compounds are usually added into gasoline as its additives. They can improve engine efficiencies; they can also decrease the emission of NOx, carbon monoxide, and unburned hydrocarbons. In recent years, 2-methoxy-2-methylpropane (MTBE) has become the most widely used gasoline additive because of its high octane number (the octane number of MTBE is 109), low Reid vapor pressure (the Reid vapor pressure of MTBE is 55 kPa), and other advantages.1 Besides, MTBE is also increasingly used as the solvent and chemical intermediate. So in order to get a better understanding of MTBE, it is essential to study its thermophysical properties. Speed of sound is a basic thermophysical property. It could be also used to calculate other thermodynamics properties, such as compressibility, bulk modulus, heat capacity, and virial coefficient, and so forth.2 There are two classic methods for measurement of the speed of sound: acoustic resonator methods and ultrasonic pulse-echo methods. There are some research groups with great experience in investigations of speed of sound by the two methods above.3−7 In particular, Daridon, Dzida, and their co-workers have presented a series of acoustic investigations on fuels and biofuels.8−11 Recently, the Brillouin light scattering (BLS) method has become a promising method for the measurement of the speed of sound. There are some advantages for the BLS method. First, the procedure of the measurement is quick. Second, the BLS method is a noncontact style method, so it could be used in the measurement of the special fluids. Third, it is suitable both for gases and liquids simultaneously. Some researches have used this method to measure solvents, such as R227ea,12 R365mfc,13 toluene,14 hexane, and heptane,15 and so forth. As for the measurement of the speed of sound in MTBE, some researchers have done relative works. Gonzalez-Olmos et al. © XXXX American Chemical Society

measured the ultrasonic velocity in MTBE at T = 278.15− 323.15 K and atmospheric pressure.16 Then they investigated the sound speed in some MTBE binary mixtures at T = 288.15− 323.15 K and atmospheric pressure.17,18 Piňeiro et al. measured the speed of sound in the ternary mixture of MTBE + 1-butanol + n-hexane at T = 288.15−308.15 K and atmospheric pressure.19 Linek et al. measured the speed of sound in binary mixtures of MTBE + toluene or isooctane at T = 298.15−328.15 K and atmospheric pressure.20 Pal et al. measured the speed of sound for the binary liquid mixtures of MTBE with propylamine and dipropylamine at temperatures of 288.15, 293.15, 298.15, 303.15, and 308.15 K and atmospheric pressure.21 Sedlakova et al. measured the speed of sound for the ternary system (MTBE + methylbenzene + butan-1-ol) within the temperature range 298.15− 328.15 K at atmospheric pressure.22 Tojo et al. measured the speed of sound in some MTBE binary mixtures at T = 288.15− 298.15 K and atmospheric pressure.23,24 Arce et al. measured the speed of sound for three ternary systems (ethanol + methanol + MTBE, 1-butanol + methanol + MTBE, and 1-butanol + ethanol + MTBE) and MTBE + 1-propanol binary system at 298.15 K and atmospheric pressure.25−28 Krishnaiah et al. measured the speed of sound for the binary systems of MTBE with hexane, heptane, octane, 2,2,4-trimethylpentane, cyclohexane, and benzene at 303.15 K.29 Legido et al. measured the speed of sound for the ternary mixture MTBE + 1-butanol + decane at 298.15 K.30 The researches mentioned above are mainly focused on the speed of sound measurement of MTBE binary or ternary mixtures. The available speed of sound for pure MTBE was mostly measured Received: March 6, 2016 Accepted: July 11, 2016

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DOI: 10.1021/acs.jced.6b00202 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Equations 1 and 2 implies that we can calculate the speed of sound of the fluids if the frequency shift of the Brillouin peak is measured. The measured scattering light spectrum in our experiment is shown as Figure 1.

at atmospheric pressure. Therefore, we measured the speed of sound in pure MTBE in a wide p−T region using the BLS technique, in order to supply more new experimental data for MTBE.

2. EXPERIMENTAL SECTION 2.1. Materials. The MTBE sample was provided by Aladdin Reagent Inc. with specified mass purity higher than 0.990 (GC). The specimen was not further purified in order to prevent sample alterations. The basic physical and chemical properties of MTBE are listed in Table 1. When filling the sample cell, Table 1. Selected Physical and Chemical Properties of MTBE material

MTBE

CAS number molecular formula critical temperature/K critical pressure/MPa supplier mass purity purification method

1634-04-4 C5H12O 497.037 3.44837 Aladdin Reagent Inc. >0.990 filtered through the membrane filters

Figure 1. Variation of the collected count rate with the scanning of the FPI.

The experimental setup is the same as used in our previous works.15 A continuous wave diode pumped solid state laser (Cobolt Samba, 532 nm, 300 mW) with a single longitudinal mode is used as the light source. A Glan−Taylor prism is adopted to improve the polarization of the laser beam. The laser beam goes through the sample and induces the sample producing the scattering light. Two pinholes with a distance about 1 m are used to limit the scattering light in one coherent area and determine the scattering angle. Fabry−Perot interferometer (FPI, Thorlabs SA200-5B) is used to filter the scattering light. The photon counting head (Hamamatsu H8259−01) is used to detect the scattering light. The data acquisition card (DAQ card, NI-PCI6221) is used to record the single. At last, the spectrum of the scattering light is obtained. The platinum resistance thermometer (PRT, Fluke 5608−12) and the pressure transmitter (Rosemount 3051s) are used to measure the temperature and the pressure, respectively.

the specimens were filtered through the membrane filters with 0.22 μm pore size in order to prevent dusts and particles from entering the cell. The absence of thermal decomposition in the conducted measurements was confirmed by the following evidence. First, the values of speed of sound in saturated vapor at low temperatures measured before and after the high-temperature (673 K) experiments were the same within the uncertainties. Second, the vapor pressures of the sample determined before and after the high-temperature experiments agreed with the data reported in literature.31,32 2.2. Measurement Techniques and Apparatus. In this work, the Brillouin light scattering (BLS) method was used to measure the speed of sound in MTBE. A complete and more detailed description of the measurement principle can be found in our previous works33 and various fundamental studies.34,35 Here the working equations and experimental setups are described briefly. Light scattering is a common phenomenon in nature. When a laser beam transmits a transparent fluid, an obvious scattering phenomenon will occur. The spectrum of the scattering light is composed by three peaks, the central Rayleigh peak, the Brillouin peak, and the anti-Brillouin peak, and the speed of sound of this transparent fluid is related to the frequency shift between the Brillouin peak and the central Rayleigh peak. According to the principle of the scattering light, the microscopic fluctuations of pressure will influence the scattering process. The pressure fluctuations in fluids are moving with the speed of sound. The relationship between the speed of sound and the spectrum of the scattering light is shown as Δω c= q

3. UNCERTAINTY EVALUATION The uncertainty evaluation is analyzed in Table 2. The experimental uncertainties in temperature and pressure can be determined by U = kuc = k

2π sin ΘEx λ0

(3)

Table 2. Experimental Uncertainty of Temperature, Pressure, and Speed of Sound temperature

pressure

(1)

in which c is the speed of sound, Δω is the frequency shift of the Brillouin peak, and q is the modulus of sound wave vector. According to Bragg’s law and refraction law, we can calculate q as q≈

∑ ui 2

speed of sound

(2)

platinum resistance, u1 temperature stability, u2 resistance measurement circuits, u3 combined standard uncertainty, uc pressure transmitter, u1 pressure measurement circuits,u2 pressure control system, u3 combined standard uncertainty, uc wavelength, ur(λ0) incident angle, ur(ΘEx) Brillouin frequency shift, ur(Δω) combined standard uncertainty, ur(c)

in which ΘEx is the incident angle in the air and λ0 is the wavelength of the incident light in vacuum. This equation is valid if only ΘEx is small enough. B

0.005 K 0.020 K 0.001 K 0.021 K 0.001 MPa (5.0 MPa) 0.001 MPa 0.02 MPa (5.0 MPa) 0.02 MPa (5.0 MPa) 3.76 × 10−5 0.001 0.005 0.005



Article

Table 3. Experimental Speed of Sound in MTBE along the Saturation Linea

a

T (K)

c (m·s−1)

T (K)

303.19 308.16 313.08 318.19 323.07 328.21 333.13 338.07 343.12 348.24

1024.7 988.6 960.4 942.7 912.4 904.7 876.8 855.1 826.3 797.5

353.11 358.22 363.16 368.17 373.05 378.05 383.08 388.11 393.16 398.11

378.10 388.20 398.07 408.22

171.6 170.9 170.0 167.8

418.16 428.21 438.17 448.13

c (m·s−1)

T (K)

Saturated Liquid 781.5 403.24 748.6 408.23 727.1 413.20 707.1 418.24 698.9 423.15 668.3 428.24 646.4 433.05 627.5 438.19 609.1 443.09 580.1 448.23 Saturated Vapor 164.7 458.29 161.2 463.17 155.3 468.26 148.4 473.15

c (m·s−1)

T (K)

c (m·s−1)

558.0 537.6 515.8 494.4 476.0 453.8 430.3 405.8 387.3 360.3

453.10 458.19 463.23 468.18 473.17 478.08 483.20 488.11 493.06

339.5 313.6 287.1 265.0 236.5 206.1 177.7 142.8 103.7

139.8 135.7 130.6 124.5

478.08 483.29 488.15 493.15

119.0 111.8 104.9 96.9

The expended uncertainties U are U(T) = 0.042 K, and the relative expanded uncertainty Ur is Ur(c) = 0.01. The level of confidence is 0.95 (k = 2).

Table 4. Fitted Coefficients in eqs 7 to 8 for MTBEa

a

saturated liquid

saturated vapor

a0 a1 a2 a3 a4

1.43806 × 104 −3.55024 × 101 1.34780 × 10−2 −1.10647 × 104 1.12441 × 100

−1.47352 × 103 7.94647 × 100 −9.65554 × 10−3 8.79653 × 103 4.21637 × 100

AAD/% MD/%

0.50 −1.21

0.20 −0.50

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

3.16288 × 103 −1.13841 × 101 2.02937 × 10−2 −2.00715 × 10−5 −7.21842 × 102 5.72783 × 100 −1.50367 × 10−2 1.33498 × 10−5 1.49395 × 102 −1.15694 × 100 2.96163 × 10−3 −2.50941 × 10−6 −8.52028 × 100 6.56082 × 10−2 −1.66793 × 10−4 1.39906 × 10−7 0.24 0.66

The coefficients a0−a3 and aij are in units of m·s−1, while a4 is dimensionless.

Figure 3. Deviations of speed of sound from BLS and the fit according to eq 7 for saturated MTBE: ⧫, saturated-liquid MTBE; ◇, saturatedvapor MTBE.

Figure 2. Experimental speed of sound in saturated MTBE: ■, saturated liquid; ●, saturated vapor; , calculated from eq 7.

in which ui is the uncertainty in each influence factor, uc is the combined standard uncertainty which is composed of uncertainties of all influence factors, and k is the coverage factor,

it equals to 2 when the degree of confidence is 95%. The uncertainty of temperature is contributed by the PRT, the temperature C



Article

Table 5. Experimental Speed of Sound in MTBE Liquida T (K)

p (MPa)

c (m·s−1)

T (K)

p (MPa)

c (m·s−1)

T (K)

p (MPa)

c (m·s−1)

303.13 303.15 303.20 303.20 303.11 303.15 303.12 308.23 308.06 308.12 308.13 308.24 308.13 308.11 313.09 313.10 313.15 313.20 313.13 313.24 313.17 318.07 318.23 318.22 318.24 318.18 318.06 318.25 323.15 323.18 323.25 323.21 323.14 323.12 323.07 328.08 328.11 328.16 328.14 328.06 328.13 328.19 333.08 333.08 333.12 333.20 333.21 333.22 333.18 338.09 338.23 338.22 338.16 338.11 338.11 338.17 343.20 343.22 343.19 343.19 343.15

1.00 2.50 4.00 5.50 7.00 8.50 10.00 1.00 2.50 4.00 5.50 7.00 8.50 10.00 1.00 2.50 4.00 5.50 7.00 8.50 10.00 1.00 2.50 4.00 5.50 7.00 8.50 10.00 1.00 2.50 4.00 5.50 7.00 8.50 10.00 1.00 2.50 4.00 5.50 7.00 8.50 10.00 1.00 2.50 4.00 5.50 7.00 8.50 10.00 1.00 2.50 4.00 5.50 7.00 8.50 10.00 1.00 2.50 4.00 5.50 7.00

1023.2 1035.3 1045.4 1058.1 1078.5 1086.9 1093.4 1003.3 1018.4 1025.3 1037.2 1052.5 1064.6 1080.0 975.0 990.3 1007.0 1018.3 1034.7 1049.0 1051.6 959.3 971.4 985.3 996.7 1012.5 1020.1 1040.0 932.5 947.7 964.9 982.2 987.9 1006.1 1016.8 917.0 926.2 942.5 963.3 971.9 984.6 991.7 893.5 904.6 920.6 941.5 949.1 967.6 978.4 867.8 884.4 898.7 922.2 931.3 941.0 954.4 845.4 868.6 883.2 892.8 911.8

358.15 358.19 358.19 358.09 358.08 358.14 358.18 363.06 363.09 363.23 363.09 363.14 363.18 363.24 368.15 368.25 368.16 368.06 368.13 368.21 368.08 373.07 373.17 373.16 373.12 373.24 373.11 373.07 378.22 378.13 378.06 378.07 378.07 378.13 378.25 383.07 383.12 383.08 383.18 383.13 383.15 383.21 388.22 388.24 388.20 388.09 388.16 388.25 388.24 393.13 393.16 393.13 393.11 393.22 393.13 393.22 398.11 398.18 398.18 398.10 398.25

1.00 2.50 4.00 5.50 7.00 8.50 10.00 1.00 2.50 4.00 5.50 7.00 8.50 10.00 1.00 2.50 4.00 5.50 7.00 8.50 10.00 1.00 2.50 4.00 5.50 7.00 8.50 10.00 1.00 2.50 4.00 5.50 7.00 8.50 10.00 1.00 2.50 4.00 5.50 7.00 8.50 10.00 1.00 2.50 4.00 5.50 7.00 8.50 10.00 1.00 2.50 4.00 5.50 7.00 8.50 10.00 1.00 2.50 4.00 5.50 7.00

779.2 802.1 816.3 835.6 852.1 866.9 883.2 761.1 775.4 796.3 811.7 833.6 844.2 863.5 734.3 754.9 777.0 796.6 813.0 831.5 844.9 713.9 733.6 753.8 770.2 791.5 811.5 828.1 691.3 711.8 732.9 751.9 770.5 791.5 804.0 666.2 690.6 713.0 731.2 753.8 769.5 789.5 646.4 670.7 690.0 711.4 730.1 751.1 768.1 619.0 643.2 669.1 691.8 714.5 736.3 753.4 594.9 624.4 647.1 671.4 692.8

413.08 413.16 413.24 413.14 413.06 418.19 418.07 418.23 418.07 418.11 418.08 423.06 423.06 423.19 423.05 423.11 423.12 428.11 428.18 428.14 428.15 428.19 428.20 433.05 433.18 433.22 433.05 433.22 433.08 438.11 438.24 438.14 438.13 438.16 438.13 443.18 443.06 443.08 443.23 443.14 443.12 448.06 448.16 448.07 448.22 448.23 448.23 453.20 453.18 453.07 453.24 453.21 453.18 458.18 458.06 458.24 458.08 458.22 458.12 463.13 463.23

4.00 5.50 7.00 8.50 10.00 2.50 4.00 5.50 7.00 8.50 10.00 2.50 4.00 5.50 7.00 8.50 10.00 2.50 4.00 5.50 7.00 8.50 10.00 2.50 4.00 5.50 7.00 8.50 10.00 2.50 4.00 5.50 7.00 8.50 10.00 2.50 4.00 5.50 7.00 8.50 10.00 2.50 4.00 5.50 7.00 8.50 10.00 2.50 4.00 5.50 7.00 8.50 10.00 2.50 4.00 5.50 7.00 8.50 10.00 2.50 4.00

585.4 612.9 638.1 661.5 682.3 535.7 565.2 588.6 617.5 639.1 661.5 511.7 541.9 571.4 595.1 624.1 647.8 485.7 520.9 549.7 575.1 605.5 625.5 463.5 498.5 530.9 560.1 586.5 610.8 443.0 477.2 507.9 540.4 569.0 590.9 418.1 454.3 487.7 519.9 548.7 575.0 394.3 435.5 467.5 500.2 529.7 557.1 372.4 411.5 448.8 483.8 515.2 544.0 350.8 389.5 426.1 464.6 497.9 524.8 326.7 368.2

D



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Table 5. 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)

343.18 343.24 348.22 348.22 348.16 348.10 348.12 348.16 348.17 353.25 353.20 353.22 353.05 353.10 353.23 353.11

8.50 10.00 1.00 2.50 4.00 5.50 7.00 8.50 10.00 1.00 2.50 4.00 5.50 7.00 8.50 10.00

926.4 941.0 829.7 844.7 858.5 874.9 890.7 907.4 915.3 800.0 825.4 841.4 858.5 868.9 889.4 903.3

398.20 398.24 403.12 403.11 403.12 403.14 403.07 403.16 403.14 408.23 408.16 408.19 408.09 408.21 408.24 413.19

8.50 10.00 1.00 2.50 4.00 5.50 7.00 8.50 10.00 2.50 4.00 5.50 7.00 8.50 10.00 2.50

715.9 733.5 574.7 602.6 627.2 649.2 672.1 697.5 716.1 576.4 605.6 631.8 657.5 679.5 697.8 557.9

463.16 463.25 463.14 463.10 468.19 468.22 468.06 468.15 468.10 473.07 473.22 473.15 473.12 473.11

5.50 7.00 8.50 10.00 4.00 5.50 7.00 8.50 10.00 4.00 5.50 7.00 8.50 10.00

409.6 445.2 480.9 507.9 347.2 389.7 427.3 459.5 491.9 324.5 366.0 408.5 443.1 479.0

a The expended uncertainties U are U(T) = 0.042 K, U(p) = 0.04 MPa for p = 0−5.0 MPa, and U(p) = 0.08 MPa for p = 5.0−20 MPa, and the relative expanded uncertainty Ur is Ur(c) = 0.01. The level of confidence is 0.95 (k = 2).

The uncertainty of pressure is composed of the uncertainties in pressure transmitter, pressure measurement 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 speed of sound is composed of uncertainties in Brillouin frequency shift, the wavelength of the incident light, and the incident angle. The standard uncertainty in speed of sound is estimated by u r (c ) =

0.00152 + ur2(Δω) + ur2(λ 0) + ur2(ΘEx )

(4)

in which ur(Δω), ur(λ0), and ur(ΘEx) are the standard uncertainties in the Brillouin frequency shift, the wavelength of the incident light and the incident angle, respectively. A constant 0.0015 results from the approximate calculation of the scattering vector modulus as shown in eq 1. So the relative expanded uncertainty in the speed of sound is 1.0% when the coverage factor k equals 2 with 0.95 level of confidence.

Figure 4. Experimental speed of sound in MTBE liquid: □, p = 1.0 MPa; ○, p = 2.5 MPa; △, p = 4.0 MPa; ▽, p = 5.5 MPa; ◇ with ×, p = 7.0 MPa; ⬡ with ×, p = 8.5 MPa; ☆, p = 10.0 MPa; , calculated from eq 8.

4. RESULTS AND DISCUSSION The speed of sound in MTBE was measured in saturated liquid/vapor, liquid, and supercritical fluid. The data in saturated liquid/vapor and liquid were fitted into the functions of temperature and pressure. The absolute average of the deviations (AAD) and maximum deviation (MD) are introduced to assess the performances of the correlations expressions, which are defined as eqs 5 and 6. AAD/% =

100 N

N

∑ i

c Exp, i cCal, i

−1 (5)

⎛ c ⎞ Exp, i MD/% = 100Max⎜⎜ − 1 ⎟⎟ ⎝ cCal, i ⎠

Figure 5. Deviations of speed of sound between the experimental data of this work and other different authors and the fit according to eq 8 for MTBE liquid: □, p = 1.0 MPa; ○, p = 2.5 MPa; △, p = 4.0 MPa; ▽, p = 5.5 MPa; ◇ with ×, p = 7.0 MPa; ⬡ with ×, p = 8.5 MPa; ☆, p = 10.0 MPa; ■, Gonzalez-Olmos et al.;16−18 ●, Pineiro et al.;19 ▲, Linek et al.;20 ▼, Pal et al.;21 ⧫, Sedlakova et al.;22 ◀, Tojo et al.;23,24 ▶, Arce et al.;25−28 ⬢, Krishnaiah et al.;29 ★, Legido et al.30

(6)

where cExp,i is the ith experimental datum of speed of sound and cCal,i is the ith speed of sound calculated from the polynomial expression. 4.1. Saturated State. The speed of sound was measured along the saturation line at the temperature from 303.15 to 493.15 K in saturated liquid and from 378.15 to 493.15 K in

stability of the system, and the PRT measurement circuit. The standard uncertainty in temperature is u(T) = 0.021 K. E



Article

Table 6. Experimental Speed of Sound in Supercritical-Fluid MTBEa T (K)

p (MPa)

c (m·s−1)

T (K)

p (MPa)

c (m·s−1)

T (K)

p (MPa)

c (m·s−1)

498.62 502.11 505.00 507.99 512.91 515.53 518.50 521.86 526.73 530.79 537.44 541.71 545.24 552.84 557.56 563.20 569.34 575.71 588.01 596.89 608.35 617.43 628.64 639.24 650.27 660.50 669.73 498.01 501.63 505.25 508.05 512.33 515.16 517.76 521.36 526.25 529.66 536.98 539.71 544.59 551.57 556.47 562.05 567.57 574.47

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 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 4.5 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 4.5 4.5 4.5

125.15 98.76 116.56 128.60 138.66 144.35 147.40 151.91 157.17 161.36 168.97 172.58 175.38 182.02 186.80 192.68 196.16 200.36 208.48 214.92 221.02 226.37 232.98 238.53 244.26 248.39 252.60 188.01 162.12 149.84 132.82 114.98 111.73 113.48 119.65 126.95 133.34 142.70 151.24 155.00 163.47 167.49 176.77 178.14 187.18

586.07 595.50 605.92 615.70 626.25 637.75 648.88 659.72 673.26 498.34 501.60 505.30 508.23 512.54 515.36 517.95 521.33 526.41 529.48 534.41 539.92 543.87 550.93 555.98 561.06 566.91 574.09 585.36 594.61 605.09 614.85 625.53 637.41 648.33 663.94 673.34 498.46 501.30 505.57 508.29 512.45 515.47 517.76 521.49 526.31

4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5

196.07 204.51 211.41 216.92 225.99 232.99 237.06 241.59 245.13 233.54 226.48 216.55 208.97 188.37 170.70 159.05 149.71 138.30 133.37 131.22 137.46 143.11 149.03 155.52 161.69 168.39 176.06 186.29 196.71 205.90 210.59 219.99 225.47 229.50 234.53 237.56 283.90 275.57 265.86 255.55 235.82 225.15 217.13 202.98 188.10

529.36 537.57 539.69 543.98 550.63 555.57 560.71 566.50 573.90 584.83 593.71 604.60 614.48 625.36 636.99 651.36 663.48 673.69 498.81 501.77 505.49 508.20 512.21 515.42 517.60 521.44 526.12 529.30 537.55 539.68 544.05 550.55 555.38 560.63 566.54 573.78 584.63 593.62 604.78 614.44 628.15 641.39 653.40 663.56 673.63

6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 6.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5

178.55 157.47 155.58 152.48 152.53 155.29 159.18 164.78 170.52 180.06 190.33 199.54 204.70 213.06 219.71 224.36 227.01 230.65 319.08 309.61 302.13 292.25 274.26 265.71 256.78 243.52 230.08 219.02 196.82 191.93 184.44 178.82 174.10 174.01 172.90 174.43 181.82 189.40 197.42 201.42 207.42 213.43 217.43 220.43 224.43

a The expended uncertainties U are U(T) = 0.042 K, U(p) = 0.04 MPa for p = 0−5.0 MPa, and U(p) = 0.08 MPa for p = 5.0−20 MPa, and the relative expanded uncertainty Ur is Ur(c) = 0.01. The level of confidence is 0.95 (k = 2).

temperature of MTBE is taken as Tc = 497.0 K, which was measured by Xia et al.37 in 2013. The coefficients are listed in Table 4. Comparing the experimental data with the calculating results from the correlation in the measured range, the AAD and MD are 0.50% and −1.21% for the saturated liquid and 0.20% and −0.50% for the saturated vapor, respectively. The experimental results of the speed of sound in saturated MTBE are shown in Figure 2. The deviations between the experimental results and the calculated results according to the correlation are shown in Figure 3. It shows that the experimental results can be well-represented by the polynomial expression of eq 7 with the fitted coefficients in Table 4.

saturated vapor. The data are presented in Table 3. The experimental data in saturated state are represented by eq 7, which included an additional term that explicitly takes into account the curvature toward the critical point for a good representation of the speed of sound in the vicinity of the critical point. ⎛ TC − T ⎞a4 ⎛ T ⎞i ⎜ ⎟ + a3⎜ c = ∑ ai ⎟ ⎝K ⎠ ⎝ TC ⎠ i=0 2

(7)

−1

where c is in m·s , T is the temperature in kelvin, Tc is the critical temperature in kelvin, and ai are the fitted coefficients. This function was suggested by Fröba et al.36 to fit the speed of sound data in saturated state, and it performed well. The critical F



Article

4.2. Liquid. The speed of sound in MTBE liquid was measured in the temperature from 303.15 to 473.15 K along seven isobaric lines (from 1.0 to 10.0 MPa). The results are presented in Table 5. The three-degree polynomial has been used to describe the speed of sound data in liquid phase by Lago et al.,38 which perform well. So the three-degree polynomial was also used in this paper, the equation is shown as 3

c=

3

⎛ T ⎞i ⎛ p ⎞ j ⎜ ⎟⎜ ⎟ K ⎠ ⎝ MPa ⎠

∑ ∑ aij⎝ i=0 j=0

increase of the speed of sound, while it will induce the decrease of the speed of sound when the temperature is higher.

5. CONCLUSIONS This work determined the speed of sound in MTBE using the Brillouin light scattering method. The examined region is at the temperature from 303.15 to 673.15 K and at the pressure from 0.1 to 10.0 MPa, including saturated liquid/vapor, liquid, and supercritical fluid. The experimental data in saturated liquid/ vapor and liquid were fitted to the functions of temperature and pressure. Comparing the calculating results with the experimental data, the AADs of MTBE are 0.50% for saturated liquid, 0.20% for saturated vapor, and 0.24% for liquid, respectively. The influence of temperature and pressure on the speed of sound was also analyzed; it shows that the tendency of the speed of sound to temperature and pressure is significantly different at different regions.

(8)

in which aij are the fitted coefficients which were also listed in Table 4. The AAD and MD of the experimental data with the functions in the measured range are 0.24% and 0.60%. The speed of sound in the liquid MTBE is shown in Figure 4. It shows that the impact of the temperature to the speed of sound is stronger than the impact of the pressure to the speed of sound. The impact of the pressure to the speed of sound becomes stronger as temperature rises. In literature, some researchers16−30 have measured the speed of sound in liquid MTBE at 0.101 MPa. In this paper, the speed of sound at 0.101 MPa were not measured, so we used eq 8 to calculate the data at 0.101 MPa and compared with the literature data. The deviations among the experimental data, literature data, and the calculated results according to the correlation are shown in Figure 5. It shows that our data are relatively smaller in low temperature region, while relatively larger in high temperature region. The AAD between experimental data and all literature data is 0.11%. The MD occurs at the temperature of 318.15 K for the data of Pal and Kumar et al.,21 which is −0.42% and corresponds to less than 4.5 m/s. It shows that our data agree well with the literature data. 4.3. Supercritical Fluid. The speed of sound in supercritical fluid was measured along five isobaric lines (from 3.5 to 7.5 MPa) and in the temperature from 498.15 to 673.15 K. The experimental results are summarized in Table 6 and Figure 6.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +86-29-8266-3863. Fax: +86-29-8266-8789. E-mail address: [email protected] (Maogang He). Funding

This work was supported by the National Nature Science Fund Committee (NSFC No. 51576161). Notes

The authors declare no competing financial interest.

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REFERENCES

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Figure 6. Experimental speed of sound in supercritical-fluid MTBE: −□−, p = 3.5 MPa; −○−, p = 4.5 MPa; −△−, p = 5.5 MPa; −▽−, p = 6.5 MPa; −◇−, p = 7.5 MPa.

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