Speed of Sound in Methyl Caprate, Methyl Laurate, and Methyl

Article pubs.acs.org/EF

Speed of Sound in Methyl Caprate, Methyl Laurate, and Methyl Myristate: Measurement by Brillouin Light Scattering and Prediction by Wada’s Group Contribution Method Ying Zhang, Xiong Zheng, Mao-Gang He,* and Yutian Chen Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, People’s Republic of China ABSTRACT: The speed of sound related with the isentropic bulk modulus has a significant effect on fuel injection and NOx emissions in diesel engines. Nevertheless, the speed of sound in pure fatty acid (methyl and ethyl) esters, which were widely used and investigated as the main components of biodiesel, is scarce in the literature. Most of the experimental data are available only at atmospheric pressure or in a narrow range of temperatures. In this work, the speed of sound in three fatty acid methyl esters [FAMEs = caprate (MeC10:0), laurate (MeC12:0), myristate (MeC14:0)] was measured by the Brillouin light scattering method. The measurements were carried out at temperatures ranging from 288 to 498 K along four isobaric lines of 0.1, 4.0, 7.0, and 10.0 MPa. The relative expanded uncertainty in the speed of sound was estimated to be less than 1.0%. A rational function that correlates 1/c2 as a function of the pressure and temperature was used to correlate the experimental speed of sound in liquid MeC10:0, MeC12:0, and MeC14:0, respectively. In comparison of the experimental speed of sound to the correlation results in the measured range, the absolute average deviations (AADs) are 0.15% for MeC10:0, 0.10% for MeC12:0, and 0.17% for Mec14:0. Moreover, the data were also used to assess the predicted ability of Wada’s model.

1. INTRODUCTION Currently, the potential of biodiesel fuels has been frequently highlighted as an alternative to diesel fuel. Biodiesel comprises the alkyl monoesters of fatty acids from vegetable oils, animal fats, or mixtures of them. It can be produced by the transesterification of triglycerides with a short-chain alcohol, such as methanol or ethanol, which results in the formation of fatty acid methyl esters (FAMEs) or fatty acid ethyl esters (FAEEs), respectively.1 Biodiesel as a renewable fuel has offered some significant benefits, such as reduction of greenhouse emissions, biodegradability, and nontoxicity. Tests showed that biodiesels also have total miscibility with petrodiesel and compatibility with modern engines.2,3 Biodiesels can be directly applied in existing diesel engines without modifications. However, thermophysical properties of bio- and petroleum-based diesels, such as the speed of sound, density, surface tension, and compressibility, are different as a result of the differences in the chemical structure. The changes of thermophysical properties may influence combustion and exhaust emission as well as alter the injection timing of the engine.4−6 The injection process is of great importance for optimizing the combustion and reducing the fuel consumption and emissions. The properties of major influence in the injection time are surface tension, viscosity, and isentropic compressibility determined by the speed of sound.7,8 Therefore, the accurate knowledge of biodiesel speed of sound plays an important role for the accurate design and improvement of the injection system. There are two classic methods for the speed of sound measurement: acoustic resonator methods and ultrasonic pulse-echo methods. There are some research groups with great experience in investigations of the speed of sound by the two methods above.9−12 Especially, Daridon, Dzida, and their co-workers have presented a series of acoustic investigations on fuels and biofuels.8,13−18 © 2016 American Chemical Society

The previous literature reports on the speed of sound in three widely used FAMEs, methyl caprate (MeC10:0), methyl laurate (MeC12:0), and methyl myristate (MeC14:0), are summarized in Table 1. It shows that the literature on the speed of sound data for FAMEs is still very scant. The oldest experimental speeds of sound for MeC10:0, MeC12:0, and MeC14:0 were reported by Gouw et al. at 293.15 and 313.15 K in 1964. Tat et al. measured the speed of sound for MeC12:0 at temperatures from 293.15 to 373.15 K and at pressures from atmospheric to 34.5 MPa in 2003. Recently, some experimental data were reported by Paredes et al. for MeC10:0 and Coutinho et al. and Ferreira et al. for MeC12:0 and MeC14:0. Daridon, Dzida, and their co-workers have presented a series of significant investigations on the speed of sound for pure FAMEs. Especially, the high-pressure speeds of sound for liquid-phase MeC10:0, MeC12:0, and MeC14:0 were presented with the pressure upper limit of 210 MPa. However, most experimental data are available at atmospheric pressure, in large pressure steps, or in a narrow range of temperatures, in which the upper limit temperature is 403.15 K for MeC10:0 reported by Daridon et al. It is obvious that the available experimental speed of sound in MeC10:0, MeC12:0, and MeC14:0 is not sufficient to develop novel accurate estimation models or improve the existing models for speed of sound calculation. In present work, which focuses on pure liquid FAMEs most frequently found in biodiesel and aims to fill the gap of the speed of sound by providing new experimental data, the speed of sound was investigated for MeC10:0, MeC12:0, and MeC14:0 by the Brillouin light scattering (BLS) method. The temperatures ranged from 288 to 498 K and at pressures p = 0.1, 4.0, 7.0, and Received: August 5, 2016 Revised: October 21, 2016 Published: October 31, 2016 9502

DOI: 10.1021/acs.energyfuels.6b01959 Energy Fuels 2016, 30, 9502−9509

Article

Energy & Fuels Table 1. Literature Reports on the Experimental Speed of Sound in MeC10:0, MeC12:0, and MeC14:0 author(s)

year

number of points

Gouw et al.7 Daridon et al.8 Daridon et al.15 Paredes et al.17 Dzida et al.18

1964 2012 2013 2013 2014

2 126 7 12 48

Gouw et al.7 Tat et al.4 Coutinho et al.19 Dzida et al.18 Ferreira et al.20

1964 2003 2013 2014 2014

2 30 12 47 12

Gouw et al.7 Daridon et al.15 Coutinho et al.19 Dzida et al.18 Ferreira et al.20 Daridon et al.21

1964 2013 2013 2014 2014 2013

2 8 10 28 12 53

T (K)

p (MPa)

MeC10:0 293.15, 313.15 0.1 283.15−403.15 0.1−210 283.15−343.15 0.1 288.15−343.15 0.1 292.89−318.26 0.1−101 MeC12:0 293.15, 313.15 0.1 293.15−373.15 0.1−34.5 288.15−343.15 0.1 292.87−318.36 0.1−101 298.25−353.15 0.1 MeC14:0 293.15, 313.15 0.1 303.15−373.15 0.1 288.15−343.15 0.1 298.13−318.34 0.1−91 298.25−353.15 0.1 303.15−393.15 0.1−80

purity

c and uca

methodb

>0.997 0.990 0.990 0.990 0.996

(1324, 1252) (0.08%) (1018−1958) (0.2−0.3%) (1364−1142) (0.1%) (1344−1143) (0.02) (1230−1698) (0.5−1)

interf PE PE DAS5000 PEO

>0.997 0.970 0.996 >0.970

(1351, 1278) (0.08%) (1080−1498) (0.1−0.7%) (1171−1370) (0.23) (1258−1691) (0.5−1) (1138−1332) (1)

interf PE PE PEO NIU

>0.997 0.990 0.980 0.995 >0.980 0.99

(1372, 1299) (0.08%) (1335−1098) (0.1%) (1194−1353) (0.23) (1281−1654) (0.5−1) (1162−1351) (1) (1036−1614) (0.2%)

interf PE PE PEO NIU PE

a

The uncertainty of the speed of sound (uc) is given in meters per second or percentage. bInterf, interferometer; PE, pulse-echo; PEO, pulse-echo overlap; and NIU, non-intrusive ultrasonic. in which kI is wave vectors of incident light, n is the refractive index of the fluid, λ0 is the wavelength of the incident light in vacuum, ΘS is the scattering angle in the sample, and ΘEx is the incident angle in the air. When a beam transmits the fluid, it will induce the sample, radiating the scattered light. The scattered light spectrum is composed of three peaks, which are the central Rayleigh peak, symmetrical Brillouin peak, and anti-Brillouin peak. According to Doppler frequency shift laws, the frequency shift of the scattered light can be determined by the speed components of the sound wave in the direction of the scattered light and incident light as eq 2

10.0 MPa. Moreover, the experimental results were used to assess Wada’s model.

2. EXPERIMENTAL SECTION 2.1. FAME Sample. Purities, CAS Registry Numbers, and suppliers of MeC10:0, MeC12:0, and MeC14:0 are shown in Table 2. The

Table 2. Specification of FAME Samples sample

CAS Registry Number

supplier

mass fraction purity (%)

MeC10:0 MeC12:0 MeC14:0

110-42-9 111-82-0 124-10-7

Sigma-Aldrich Sigma-Aldrich Sigma-Aldrich

>0.990 0.995 >0.990

⎛ Δω ⎞ ⎛ c ⎞ ⎛Θ ⎞ ⎜ ⎟ = ± 2n⎜ ⎟sin⎜ S ⎟ ⎝ ω0 ⎠ ⎝ c0 ⎠ ⎝ 2 ⎠

in which Δω is the frequency shift of scattered light, ω0 is the frequency of incident light, c is the speed of sound in the sample, and c0 is the light speed in vacuum. When eqs 1 and 2 are combined, the relation between the speed of sound and the frequency shift of scattered light can be obtained as eq 3.

samples were provided by Sigma-Aldrich, Inc. The manufacturer-specified mass fraction is higher than 0.990 (GC) for each sample. The samples were not further purified to prevent sample alterations. When the sample cell was filled, the samples were filtered through the membrane filters with 0.22 μm pore size to prevent particles from entering the cell because impurities, such as particles and undissolved substances, can induce stronger scattered light and make the measurements unfeasible. 2.2. Measurement Method and Apparatus. The speed of sound was measured by the BLS technique. BLS is an effective method to investigate the speed of sound in fluids and has been widely used.22−24 Moreover, some other light scattering methods related to BLS have been used to investigate other thermophysical properties, such as thermal diffusivity, viscosity, mutual diffusion coefficient, and Soret coefficient.25−28 A complete and more detailed description of the measurement principle can be found in our previous paper29 and fundamental studies.30,31 Here, only the working equations are depicted briefly. The thermal motion of fluid molecules induces thermal excited waves, which can be considered as the mixing of a myriad of sound waves. These sound waves modulate the scattered light periodically as a diffraction grating. According to Bragg’s law, we can calculate the modulus of the sound wave vector as eq 1 4nπ sin ⎛Θ ⎞ q = 2|kI|sin⎜ S ⎟ = ⎝ 2 ⎠ λ0

ΘS 2

( ) ≈ 2π sin Θ λ0

(2)

Δω = cq

(3)

Equation 3 implies that we can calculate the speed of sound in the sample when the frequency shift of the Brillouin peak is measured. The photon counting head in conjunction with the Fabry−Perot interferometer was applied to measure the frequency shift of the Brillouin peak. Figure 1 shows a typical count rate variation with time. It is regarded as the scattered light spectrum. The optical setup and temperature and pressure control and measure units in this work are shown in Figures 2 and 3. Both the optical setup and temperature and pressure control and measure units are the same as that presented in our previous paper29 and similar to that employed by Kraft et al.31 Here, only the main equipment is depicted briefly. A laser (Cobolt Samba, 532 nm, 300 mW) with a single longitudinal mode is adopted as the light source. A Fabry−Perot interferometer (Thorlabs SA200-5B), photon counting head (Hamamatsu H8259-01), and a DAQ card (NI-PCI6221) are used to acquire the scattered light spectrum. The temperatures were measured with the platinum resistance thermometer (PRT, Fluke Corporation; uncertainties are T = 0.01 K), which were inserted into the sample cell. The pressures were measured with the pressure transmitter (Rosemount, 3051S, 0−20 MPa) with uncertainties of 5 kPa. The uncertainty of the speed of sound is composed of uncertainties in the Brillouin frequency shift,

Ex

(1) 9503


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Energy & Fuels

Figure 1. Typical count rate variation with time.

Figure 2. BLS experimental setup for the sound speed measurement.

Figure 3. Temperature and pressure control and measurement units. wavelength of incident light, and incident angle. The relative expanded uncertainty of the speed of sound is estimated less than 1% (coverage factor k = 2; the level of confidence is 0.95).

15% increase at a high temperature in the speed of sound for MeC10:0, MeC12:0, and MeC14:0. From Figures 4−6, we also find that the temperature has a small influence on the slope of the speed of sound versus pressure. Approximately, the speed of sound in liquid MeC10:0, MeC12:0, and MeC14:0 can be considered to increase linearly with the temperature at a constant pressure. Several different models for estimating the speed of sound in FAMEs and FAEEs have been proposed in the literature, such as Wada’s group contribution model,32 Auerbach’s model,33 etc. For all of these models mentioned above, the densities of FAMEs and FAEEs are needed. Unfortunately, the density of methyl caprate, methyl laurate, and methyl myristate are not available for the investigated p−T region in this work. Therefore, a rational function, which correlates 1/c2 as a function of the pressure and temperature by considering nine adjustable parameters, was used to correlate the experimental speeds of sound in liquid MeC10:0, MeC12:0, and MeC14:0, respectively, which is shown as follows:

3. RESULTS AND DISCUSSION 3.1. Experimental Measurements. In this work, the measurement of the speed of sound at temperatures from 288 to 498 K with 15 K steps and pressures p = 0.1, 4.0, 7.0, and 10.0 MPa was carried out for three FAMEs: MeC10:0, MeC12:0, and MeC14:0. Each experimental point was independently measured 6 times at three different scattering angles. The result repeatabilities were better than 0.5%, and the average value was adopted. The obtained experimental data are presented in Table 3. Figures 4, 5, and 6 show the experimental speed of sound in liquid MeC10:0, MeC12:0, and MeC14:0, respectively. It can be seen that the speed of sound increases slightly with the pressure increase and decreases obviously with the temperature increase over the whole examined p−T region. Moreover, the influences of the pressure on the speed of sound become greater as the temperature rises. About a 10 MPa rise in pressure gives an approximately 3.5% increase at a low temperature and a

A + Bp + Cp2 + Dp3 1 = E + Fp c2 9504

(4) DOI: 10.1021/acs.energyfuels.6b01959 Energy Fuels 2016, 30, 9502−9509

Article

Energy & Fuels

Table 3. Experimental Speed of Sound in Liquid MeC10:0, MeC12:0, and MeC14:0 Measured at Pressures 0.1, 4.0, 7.0, and 10.0 MPa and Temperatures Ranging from 288 to 498 K with 15 K Steps 0.1 MPa

4.0 MPa

7.0 MPa

T (K)

c (m s−1)

T (K)

c (m s−1)

288.24 303.14 318.06 333.15 348.06 363.19 378.14 393.18 408.15 423.20 438.13 453.07 468.23 483.21 498.24

1343 1290 1232 1179 1127 1075 1024 974 931 884 836 791 744 699 649

288.22 303.11 318.10 333.18 348.22 363.22 378.18 393.06 408.24 423.17 438.24 453.08 468.12 483.18 498.17

1364 1307 1252 1203 1151 1097 1053 1003 962 913 873 828 788 740 698

288.19 303.15 318.22 333.08 348.12 363.08 378.10 393.21 408.12 423.15 438.20 453.19 468.10 483.10 498.13

1366 1313 1261 1209 1158 1108 1059 1010 963 916 870 825 781 737 693

288.18 303.17 318.06 333.21 348.20 363.10 378.10 393.18 408.15 423.24 438.15 453.20 468.25 483.14 498.22

1386 1333 1282 1230 1180 1132 1085 1038 993 949 906 864 824 784 743

288.25 303.24 318.22 333.17 348.24 363.15 378.19 393.18 408.06 423.21 438.17 453.07 468.12 483.16 498.12

1386 1333 1282 1229 1178 1131 1085 1037 991 945 899 855 814 774 736

288.07 303.23 318.09 333.25 348.20 363.17 378.21 393.08 408.13 423.14 438.24 453.06 468.09 483.13 498.12

1411 1357 1311 1258 1210 1162 1116 1071 1027 984 939 897 855 817 775

10.0 MPa

T (K)

c (m s−1)

T (K)

c (m s−1)

288.09 303.20 318.12 333.20 348.21 363.09 378.22 393.24 408.19 423.07 438.22 453.20 468.20 483.08 498.19

1375 1324 1268 1218 1169 1116 1072 1023 984 937 898 853 812 773 731

288.19 303.25 318.10 333.11 348.22 363.07 378.07 393.18 408.19 423.09 438.13 453.21 468.06 483.19 498.12

1394 1342 1286 1238 1189 1136 1094 1046 1007 960 923 883 842 800 763

288.15 303.14 318.07 333.23 348.24 363.05 378.09 393.18 408.17 423.20 438.23 453.21 468.05 483.24 498.24

1400 1348 1297 1246 1198 1151 1104 1059 1015 972 931 891 852 813 775

288.17 303.07 318.10 333.16 348.17 363.19 378.19 393.09 408.22 423.18 438.06 453.21 468.06 483.20 498.20

1414 1363 1313 1264 1216 1170 1124 1080 1037 995 955 915 877 839 801

288.25 303.19 318.20 333.11 348.22 363.23 378.16 393.11 408.24 423.17 438.12 453.15 468.15 483.15 498.11

1426 1372 1326 1275 1226 1184 1136 1095 1044 1007 964 922 887 847 808

288.23 303.18 318.07 333.11 348.10 363.24 378.17 393.16 408.15 423.08 438.20 453.21 468.16 483.15 498.19

1435 1383 1338 1288 1240 1197 1149 1107 1059 1023 976 937 903 871 834

MeC10:0

MeC12:0

MeC14:0

results from eq 4 with the parameters listed in Table 4 and the experimental data were calculated as

in which A = A 0 + A1T + A 2 T 2 + A3T 3

and

E = 1 + E1T

⎧ N ⎪ AAD (%) = 100 ∑ ⎪ N i ⎪ ⎪ ⎛ ⎪ ⎨ MD (%) = 100max⎜⎜ ⎪ ⎝ ⎪ N ⎪ ⎪ bias (%) = 100 ∑ ⎪ N i ⎩

in eq 4, and the adjustable parameters A0−A3, B, C, D, E1, and F were listed in Table 4. This function was initially proposed by Daridon et al.34 and improved by Queimada et al.,35 which has been demonstrated to provide an adequate correlation of speed of sound data for n-alkanes ranging from ethane up to n-hexatriacontane with an average deviation of less than 1%.8,34−37 The absolute average deviation (AAD), maximum deviation (MD), and average deviation (bias) between the calculated 9505

ccal, i cexp, i ccal, i cexp, i ccal, i cexp, i

−1

⎞ − 1 ⎟⎟ ⎠ −1

(5) DOI: 10.1021/acs.energyfuels.6b01959 Energy Fuels 2016, 30, 9502−9509

Article

Energy & Fuels

The available literature experimental data of the speed of sound in MeC10:0, MeC12:0, and MeC14:0 were collected and compared to our correlation in the investigated p−T region. The summary of the literature experimental data was shown in Table 1. The deviations were shown in Figures 7−9. It can be affirmed that the calculated results are in agreement with all experimental data obtained in this work, presenting relative deviations less than 0.3%, which correspond to ca. 2.0 m s−1. As shown in Figure 7 for MeC10:0, it is obvious that the calculated results are slightly larger than the literature data proposed by Gouw et al., Daridon et al., and Paredes et al. and slightly less than that proposed by Dzida et al. The AAD between the calculated results and literature data is 0.08%, presenting only a maximum deviation of 0.27% at T = 283.15 K and p = 10.0 MPa proposed by Daridon, which corresponds to less than 3.79 m s−1. As shown in Figure 8 for MeC12:0, it shows a good agreement between the calculated results and literature data proposed by Gouw et al., Dzida et al., Coutinho et al., and Ferreira et al., presenting only a maximum deviation of 0.23% at T = 338.15 K and p = 0.1 MPa proposed by Ferreira et al., except for the data reported by Tat et al. Figure 9 show the relative deviations between calculated results and literature data for C14:0. They fall in a narrow range of ±0.4%, which corresponds less than ±4 m s−1, except for data at T = 323.15 K reported by Ferreira et al. Above all, the comparison of the literature data to the calculated results from eq 4 shows good agreement with satisfactory deviations. 3.2. Wada’s Model. In this paper, Wada’s model15−17 was applied to predict the speed of sound for three FAMEs at atmosphere pressure. We compared the results from Wada’s model to our experimental data to assess the predictive ability of Wada’s model. Wada’s constant, Km, is described as

Figure 4. Experimental speed of sound in MeC10:0: (solid squares) 0.1 MPa, (solid circles) 4.0 MPa, (solid diamonds) 7.0 MPa, and (solid triangles) 10.0 MPa. The full line corresponds to the calculations with eq 4.

⎛ c ⎞2/7 Km = ⎜ 3 ⎟ Mw ⎝ρ ⎠


(6)

where ρ is the density at atmosphere pressure and Mw is the molar mass. Km can be estimated by an additive group contribution method, which is nj

K m(T ) =

∑ NK j m, j(1 − χ (T − T0)) j=1

(7)

where Km,j is the contribution of the group type j to Km, which occurs Nj times in molecule j, χ is a constant parameter used to take into account the influence of the temperature, T is the absolute temperature, and T0 is 298.15 K in this work. In this paper, the parameters Km,j reported by Daridon et al.15 were used directly. According to the definition of Wada’s constant, the speed of sound could be calculated as ⎛ K m ⎞7/2 c=ρ⎜ ⎟ ⎝ Mw ⎠ 3


(8)

In eq 8, it is obvious that the prediction needs the density at atmospheric pressure first. Therefore, an approach proposed by Coutinho et al.38 was used to estimate the density. The equation is shown as ρs Mw = ρc = V (1 + Ep) (1 + Ep) (9)

in which cexp,i is the ith experimental speed of sound and ccal,i is the ith calculated speed of sound (eq 4). In comparison of the experimental speed of sound to the correlation results in the measured range, the AAD, MD, and bias are 0.15, 0.38, and 0.0003% for MeC10:0, 0.10, 0.46, and 0.0004% for MeC12:0, and 0.17, 0.62, and 0.0008% for Mec14:0.

where ρc is the density of compressed liquid, p is the absolute pressure, ρs is the saturated density, and E is a fitting parameter. 9506


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Table 4. Parameters of eq 4 for MeC10:0, MeC12:0, and MeC14:0 over the Range of T = 288−498 K and p = 0.1−10.0 MPa parameter

MeC10:0

MeC12:0

MeC14:0

A0 A1 A2 A3 B C D E1 F AAD (%) DM (%) bias (%)

3.48863 × 10−7 −1.89079 × 10−9 8.37517 × 10−12 −9.09119 × 10−15 1.15901 × 10−9 1.61017 × 10−10 −1.31860 × 10−11 1.70225 × 10−3 6.68867 × 10−3 0.15 0.38 0.0003

4.34853 × 10−7 −2.47597 × 10−9 9.51149 × 10−12 −9.68897 × 10−15 1.67762 × 10−9 3.69815 × 10−11 −2.50261 × 10−12 1.65748 × 10−3 7.20775 × 10−3 0.10 0.46 0.0004

4.67750 × 10−7 −2.57098 × 10−9 9.22473 × 10−12 −8.65278 × 10−15 1.06752 × 10−9 −1.83344 × 10−11 9.95523 × 10−12 1.57100 × 10−3 7.70390 × 10−3 0.17 0.62 0.0008

Figure 7. Deviation of the sound speed in MeC10:0 from different authors compared to eq 4: (crossed upward-facing triangles) this work at 0.1 MPa, (crossed circles) this work at 4.0 MPa, (crossed downwardfacing triangles) this work at 7.0 MPa, (crossed diamonds) this work at 10.0 MPa, (solid squares) Gouw at 0.1 MPa, (solid circles) Daridon at 0.1 MPa, (solid diamonds) Paredes at 0.1 MPa, (solid pentagons) Dzida at 0.1 MPa, and (solid triangles) Daridon at 10.0 MPa.

Figure 9. Deviation of the sound speed in MeC14:0 from different authors compared to eq 4: (crossed upward-facing triangles) this work at 0.1 MPa, (crossed circles) this work at 4.0 MPa, (crossed downwardfacing triangles) this work at 7.0 MPa, (crossed diamonds) this work at 10.0 MPa, (solid squares) Gouw at 0.1 MPa, (solid circles) Daridon at 0.1 MPa, (solid diamonds) Dzida at 0.1 MPa, (solid pentagons) Coutinho at 0.1 MPa, (solid triangles) Ferreira at 0.1 MPa, and (solid stars) Daridon at 10.0 MPa.

−5.7 × 10−4 MPa−1, with an overall average relative deviation (OARD) of 0.37%. Because the density has a significant effect on the speed of sound, a little deviation of the density would cause a large deviation of the speed of sound. Therefore, in this paper, we used literature data1,8,21 to fit E in eq 9. The value of E is −5.61 × 10−2 MPa−1 for MeC10:0, −2.46 × 10−2 MPa−1 for MeC12:0, and −9.5 × 10−3 MPa−1 for MeC14:0. The deviations between literature data and calculated data using the value of this work and Coutinho et al. are shown in Figure 10. It shows that the prediction is much better using the value of E is this work than using that of Coutinho et al. The maximum deviation between literature data and estimated data using the value of E in this work is less than 0.15%. Moreover, it also shows a regular phenomenon, which is that most of the calculated data for three FAMEs below 350 K are larger than literature data and smaller above 350 K. The comparisons of the speed of sound between the results from Wada’s model and our data are shown in Figure 11. The AAD is 0.45% for MeC10:0, 1.05% for MeC12:0, and 1.56% for MeC14:0. Figure 11 shows that Wada’s model fits well with our data within the low temperature region, and the predicted values are a little larger than our experimental results at the temperature of about 283−350 K. The deviations become larger with the increase of the temperature, and the predicted values are a little

Figure 8. Deviation of the sound speed in MeC12:0 from different authors compared to eq 4: (crossed upward-facing triangles) this work at 0.1 MPa, (crossed circles) this work at 4.0 MPa, (crossed downwardfacing triangles) this work at 7.0 MPa, (crossed diamonds) this work at 10.0 MPa, (solid squares) Gouw at 0.1 MPa, (solid circles) Dzida at 0.1 MPa, (solid diamonds) Coutinho at 0.1 MPa, (solid pentagons) Ferreira at 0.1 MPa, (solid triangles) Tat at 0.1 MPa, and (solid stars) Tat at 6.89 MPa.

We used the GCVOL method to predict the saturated density, ρs. The detailed information on this method could be found in ref 39. Coutinho et al.38 suggested that the value E is equals to 9507


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The AAD is 0.15% for MeC10:0, 0.10% for MeC12:0, and 0.17% MeC14:0. The calculated results in this work were also compared to literature data. It shows that our data agree well with most data in the literature. The experimental data were also used to assess the predicted ability of Wada’s model. It shows that the predicted data by Wada’s model at a low temperature is relatively larger than our experimental data and smaller at a high temperature. The regular deviation distribution of the density was doubted to lead to a regular deviation distribution of the speed of sound.

■

AUTHOR INFORMATION

Corresponding Author

*Telephone/Fax: +86-29-8266-3863. E-mail: [email protected]. edu.cn.

Figure 10. Deviation of the density at 0.1 MPa between the calculated values and literature experimental results using the value of E of this work and Coutinho et al.:38 for this work, (solid squares) MeC10:0, (solid circles) MeC12:0, and (solid triangles) MeC14:0 and for Coutinho et al., (crossed squares) MeC10:0, (crossed circles) MeC12:0, and (crossed triangles) MeC14:0.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Natural Science Fund Committee (NSFC 51576161). REFERENCES

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Figure 11. Deviation of the speed of sound between the results from Wada’s model and our experimental results at 0.1 MPa: (solid squares) MeC10:0, (solid circles) MeC12:0, and (solid diamonds) MeC14:0.

lower than our experimental results in the high-temperature region, while the deviations are within 2.0% at the temperature below 400 K. While at the temperature above 400 K, the deviations are relatively large and the maximum deviation is 3.25%, which occurs at the temperature of 498.12 K. This deviation distribution is very similar to the deviation distribution of the density. As shown in eq 8, the speed of sound is particularly sensitive to the density; therefore, we doubt that the regular deviation distribution of the density may lead to a regular deviation distribution of the speed of sound.

4. CONCLUSION This work aims at the investigation of the speed of sound in three FAMEs, methyl caprate (MeC10:0), methyl laurate (MeC12:0), and methyl myristate (MeC14:0), in a large temperature and pressure region. The change regularities of the speed of sound in MeC10:0, MeC12:0, and MeC14:0 with temperature and pressure were analyzed in the investigated p−T region. The speed of sound in MeC10:0, MeC12:0, and MeC14:0 increases slightly with increasing pressure and decreases obviously with increasing temperature. Moreover, the influences of the pressure on the speed of sound become greater as the temperature rises. The experimental sound speed data were fitted to a nine parameter rational function as functions of the temperature and pressure. 9508


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Speed of Sound in Methyl Caprate, Methyl Laurate, and Methyl

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