Speed of Sound, Density, and Derivative Properties of Fatty Acid

Article pubs.acs.org/jced

Speed of Sound, Density, and Derivative Properties of Fatty Acid Methyl and Ethyl Esters under High Pressure: Methyl Caprate and Ethyl Caprate El Hadji Ibrahima Ndiaye, Djamel Nasri, and Jean Luc Daridon* Laboratoire des Fluides Complexes et leurs Réservoirs, Faculté des Sciences et Techniques, UMR 5150, Université de Pau, BP 1155, 64013 Pau Cedex, France ABSTRACT: The speed of sound in methyl caprate (C11H22O2) and ethyl caprate (C12H24O2) was measured using a pulse echo technique operating at 3 MHz. The measurements were carried out at pressures up to 210 MPa in the temperature range (283.15 to 403.15) K. Additional density measurements were performed up to 100 MPa from (293 to 393) K. From these measurements, the density was evaluated up to 210 MPa, and the isentropic and isothermal compressibilities were determined in the same P−T domain.

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INTRODUCTION

introduce the appropriate quantity of fuel into the engine cylinder and to mix properly it with air to achieve a complete combustion. This process, carried out under pressure, is strongly affected by the density of fuel and by its derivative with respect to pressure. Density influences the conversion of volume flow rate into mass flow rate,1 whereas the compressibility (or bulk modulus) acts on the fuel injection timing.2 Therefore, the adaptation of injection systems to biodiesels requires an accurate knowledge of the volumetric properties of biodiesels over a wide range of pressure. With this aim in mind, a volumetric and an ultrasonic investigation of pure compounds coming from the esterification of fatty acids of chain length ranging from 10 to 20 has been initiated. In this work, which focuses on methyl caprate and ethyl caprate, speed of sound and density measurements were carried out in an extended range of pressure and temperature. These measurements were used to determine the derivatives properties, that is, the isentropic compressibility and isothermal compressibility of these components under high pressure.

The growth in gasoline demand leads to the development of alternatives to conventional fuels. Among those alternatives, biodiesels along with bioethanol appear as the main resources to substitute to fossil fuels in the short run because they can be produced from agricultural resources of most of the countries. Moreover their properties allow an easy blending with conventional gasolines, and the diesel engine can run with various mixtures of biodiesels and petroleum fuel ranging from 2 % (B2) to 100 % (B100). Finally, only minor changes in diesel engine technologies as well as in the production and distribution channels are needed to use biodiesels instead of conventional gasoline. Biodiesels are produced from the transesterification of any vegetable or animal lipids with a short chain alcohol such as methanol or ethanol which results in the formation of fatty acid methyl esters or fatty acid ethyl esters, respectively. Naturally occurring fatty acids are straight chain aliphatic carboxylic acids with an even number of carbon atoms. The chain differs in length as well as in its degree of unsaturation. The most common plants used in the production of biodiesels contain fatty acids with 16 and 18 carbons such as rapeseed, soybean, sunflower, and palm. However, some tropical oils such as palm kernel and coconut oils have shorter length chains (10 to 14 carbon atoms). Finally, some rape species and animals fats contain fatty acids with 20 and 22 carbon atoms. Consequently, biodiesels coming from varying sources may have a significantly different fatty acid methyl esters structure. The difference in ester profile between biodiesels can change their physical properties and affect the engine efficiency and emissions. In diesel engine, one of the most important operation that influences performances is the injection. Its purpose is to © 2012 American Chemical Society

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EXPERIMENTAL SECTION Materials. Table 1 shows the sample descriptions of methyl caprate (decanoic acid methyl ester, CAS No.: 110-42-9, molar mass: 186.2912 g·mol−1) and ethyl caprate (decanoic acid ethyl ester, CAS No.: 110-38-3, molar mass: 200.3178 g·mol−1) used in the present work. Speed of Sound Measurement. The method deployed to carry out measurements of ultrasonic velocity in compressed Received: April 6, 2012 Accepted: August 28, 2012 Published: September 10, 2012 2667

dx.doi.org/10.1021/je300405a | J. Chem. Eng. Data 2012, 57, 2667−2676

Journal of Chemical & Engineering Data

Article

the same time increase the volume of liquid needed. The piezoelectric elements are held on their housing by a damper mechanism made up of a Teflon layer screwed on the probe. The high pressure cell is made up of a cylinder closed at one end by a plug in which three electric connections were located. These electrical connections are used to wire the acoustic sensor to an ultrasonic emission/reception device (Olympus) installed outside the cell. Three holes were machined in the lateral face of the cell. One at the top is connected thanks to an outlet valve to a vacuum pump. The second, at the bottom, is linked thanks to an inlet valve to a volumetric pump whereby pressure can be transmitted to the cell by the liquid itself. Two pressure gauges (HBM) are fixed on the circuit linking the pump to the measurement cell. One is calibrated in the full high pressure scale (0.1 to 210) MPa, whereas the other is only calibrated between (0.1 and 100) MPa to achieve a better accuracy in this range. Finally, the last hole is positioned at the middle of the cell. It allows the passage of a Pt 100 type temperature probe housed in a metal finger (1.2 mm diameter) used to isolate it from the pressure. To ensure satisfactory thermal uniformity within the fluid, the cell is fully immersed in a thermo-regulated bath of stability 0.02 K in the temperature range (283 to 403) K. The ultrasonic velocity was measured by a time-of-flight method using two successive echoes. In this method, the pulses produced by the generator are supplied to one of the transducers so as to generate an ultrasonic wave that travel into the fluid sample. The first and the second echoes received by the other transducer are then displayed on a digital oscilloscope with memory storage and the time-of-flight for a round trip into the sample is deduced from the measurement of the time interval between these echoes using the base time of the oscilloscope. The path length was determined at different temperatures and pressures by measuring the time-of-flight of the wave into a liquid of known speed of sound. Water4,5 and heptane6 were used for this calibration. This calibration leads to an uncertainty in the speed of sound of about 0.06 %. However, the ultimate precision depends also on the temperature measurement which leads an additional uncertainty of 0.04 % and in the measurement pressure which involve an error less than 0.1 % up to 100 MPa and 0.2 % between (100 and 210) MPa. Consequently the overall experimental uncertainty in the reported speed of sound values is estimated to be 0.2 % between (0.1 and 100) MPa and 0.3 % between (100 and 210 MPa). Density Measurement. Density was measured between (0.1 and 100) MPa in the temperature interval (293 to 393) K by means of an ANTON-PAAR densimeter connected to a high pressure cell (DMA HPM). The principle of this apparatus is to measure the period of oscillation of a U-shape tube and to deduce the density which is related to the square of the period by a linear law. The parameters of this linear function are calibrated by the method proposed by Comuñas et al.7 using vacuum and a liquid of known densities. Water8 and decane9 are used as reference fluid depending on the P,T domain investigated. The temperature of the densimeter is regulated by an external circulating fluid and is measured with a Pt100 with an uncertainty of ± 0.1 K in the temperature range investigated. The pressure is transmitted to the cell by the liquid itself using a volumetric pump and measured thanks to a HBM pressure gauge (0.1 % of uncertainty) fixed on the circuit linking the pump to the U-tube cell. Taking into account the uncertainty of the temperature, the pressure, and the density of the reference fluid as well as the error in the measurements of the period of oscillation for the vacuum and for both the reference and the

Table 1. Sample Description chemical name methyl caprate ethyl caprate

shorthand designation MeC10:0 EeC10:0

source SigmaAldrich SigmaAldrich

initial mole fraction purity

purification method

0.99

none

0.99

none

liquids is based on a pulse echo technique working in transmission mode.3 In this technique, the speed of sound is determined by direct chronometry of the time-of-flight of an ultrasonic wave through the sample located between two transducers. To achieve satisfactory measurements using this technique, it is essential to known the length of passage L with accuracy. With the aim to reduce the influence of pressure on this quantity that can be significant on the pressure range investigated (0 to 210) MPa, a new apparatus was designed and used in this work. It consists in an acoustic sensor fully immersed in an autoclave cell (Figure 1). The acoustic sensor is made up of two piezoelectric

Figure 1. High pressure cell. (1) Plug with electric connections; (2) autoclave cylinder; (3) temperature probe; (4) electric wire; (5) inlet connection; (6) acoustic sensor immersed in the compressed fluid; (7) internal electric pin; (8) outlet connection; (9) external electric pin connected to the ultrasonic pulse emission/reception device.

transducers (12 mm in diameter) whose resonant frequency is 3 MHz, one of them acting as a transmitter, the other as a receiver. They are fixed parallel to the ends of a stainless steel cylindrical support (30 mm in length). This length represents an acceptable trade-off between shorter distances which would reduce the amount of sample required but would also reduce measuring accuracy and longer trajectories which would have the advantage of increasing the accuracy of the measurements but would at 2668



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Table 2. Experimental Values of Speed of Sound c at Temperatures T and Pressures p for the Liquid Methyl Caprate and Ethyl Capratea p/MPa

T/K

c/m·s−1

T/K

0.1013 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 170 190 210 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 170 190 210

283.15 283.15 283.15 283.15 283.15 283.15 283.15 283.15 283.15 283.15 283.15 283.15 283.15 283.15 283.15

1362.6 1408.9 1452.2 1493.2 1531.7 1568.0 1602.6 1634.5 1666.4 1696.9 1726.9 1755.2 1783.4 1809.5 1835.9

363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15

1138.5 1195.9 1247.9 1296.3 1341.1 1382.7 1421.6 1458.4 1493.8 1527.4 1559.7 1590.9 1620.7 1649.4 1677.2 1730.6 1780.4 1827.2

303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15

0.1013 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 170 190 210 0.1013 10

283.15 283.15 283.15 283.15 283.15 283.15 283.15 283.15 283.15 283.15 283.15 283.15 283.15 283.15 283.15 283.15 283.15 283.15 283.15 363.15 363.15

1352.7 1398.5 1442.3 1483.7 1522.5 1558.3 1593.9 1627.0 1658.8 1689.9 1720.7 1753.7 1781.4 1808.5 1834.6 1860.3 1908.7 1951.8 1998.0 1065.9 1130.1

303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 383.15 383.15

c/m·s−1 Methyl Caprate 1287.7 1339.2 1385.8 1429.6 1470.3 1508.7 1544.9 1580.2 1614.1 1646.1 1676.9 1706.8 1735.1 1762.8 1789.2 1815.2 1864.9 1912.7 1957.6 1077.4 1138.6 1193.5 1244.5 1291.3 1334.9 1375.4 1414.2 1450.6 1485.3 1518.9 1550.9 1581.2 1610.8 1641.0 1692.7 1743.0 1791.1 Ethyl Caprate 1275.0 1325.7 1373.2 1416.8 1458.3 1498.0 1535.5 1569.9 1603.2 1635.3 1666.2 1696.2 1724.8 1752.9 1779.2 1805.4 1854.6 1902.4 1947.7 1001.3 1071.1 2669

T/K

c/m·s−1

T/K

c/m·s−1

323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 403.15 403.15 403.15 403.15 403.15 403.15 403.15 403.15 403.15 403.15 403.15 403.15 403.15 403.15 403.15 403.15 403.15 403.15

1214.8 1269.1 1319.3 1365.7 1409.0 1449.5 1487.8 1524.0 1558.3 1591.2 1623.3 1653.9 1684.6 1711.9 1739.6 1765.9 1817.0 1864.8 1910.9 1017.7 1083.2 1141.7 1194.7 1242.9 1288.1 1330.6 1370.3 1407.7 1442.8 1476.6 1509.7 1541.7 1571.6 1600.1 1655.5 1706.6 1754.5

343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15

1142.8 1202.4 1255.9 1304.9 1350.5 1393.5 1433.7 1471.7 1508.2 1541.7 1574.1 1606.0 1636.2 1665.9 1694.0 1721.2 1773.2 1822.0 1868.7

323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 403.15 403.15

1203.1 1258.2 1309.5 1355.9 1399.1 1439.4 1478.4 1515.1 1550.3 1583.7 1615.7 1645.8 1676.7 1705.7 1733.7 1760.3 1811.6 1861.2 1909.8 937.8 1013.4

343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15

1133.3 1192.8 1247.0 1297.2 1343.0 1385.7 1425.7 1463.9 1500.3 1535.3 1568.4 1600.4 1631.5 1661.5 1690.0 1717.3 1769.7 1818.5 1865.0



Article

Table 2. continued p/MPa 20 30 40 50 60 70 80 90 100 110 120 130 140 150 170 190 210

T/K

c/m·s−1

T/K

363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15

1188.5 1241.2 1289.6 1334.7 1376.5 1415.4 1452.8 1488.9 1522.8 1556.0 1586.9 1617.1 1646.6 1675.1 1727.6 1777.0 1824.5

383.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15

c/m·s−1 Ethyl Caprate 1132.9 1188.3 1239.3 1286.4 1329.7 1370.2 1408.3 1445.0 1480.0 1513.4 1545.8 1576.6 1606.2 1634.6 1687.7 1740.7 1786.8

T/K

c/m·s−1

403.15 403.15 403.15 403.15 403.15 403.15 403.15 403.15 403.15 403.15 403.15 403.15 403.15 403.15 403.15 403.15 403.15

1080.3 1138.6 1191.3 1240.5 1285.9 1328.1 1367.6 1404.6 1439.8 1473.4 1506.4 1537.5 1567.3 1596.2 1650.9 1702.8 1751.8

c/m·s−1

T/K

a

Standard uncertainties u are u(T) = 0.1 K, u(p) = 0.01 MPa up to 100 MPa, u(p) = 0.1 MPa between (100 and 210) MPa and the combined expanded uncertainties Uc (level of confidence = 0.95) are Uc(c) = 0.002 c up to 100 MPa, Uc(c) = 0.003 c between (100 and 210) MPa.

Table 3. Parameters of eqs 1 to 3 for Methyl Caprate and Ethyl Caprate from (283 to 403) K and for Two Pressure Ranges: (0.1 to 100) MPa and (100 to 210) MPa methyl caprate parameter A0 A1 A2 A3 B C D E1 F Deviationsa AD% AAD% MD% a

(0.1 to 100) MPa −7

3.42537·10 −1.77630·10−9 7.87806·10−12 −8.38330·10−15 1.66854·10−9 −5.81710·10−12 1.58346·10−14 −1.68981·10−3 6.86460·10−3 1.5·10−3 3.9·10−2 1.7·10−1

ethyl caprate (100 to 210) MPa

(0.1 to 100) MPa

−7

−7

3.87612·10 −2.11160·10−9 9.20025·10−12 −9.40860·10−15 1.59075·10−9 −3.02990·10−12 3.58933·10−15 −1.58702·10−3 7.80614·10−3

1.21721·10 1.01178·10−10 2.75100·10−12 −3.70220·10−15 1.82184·10−9 −6.17670·10−12 1.46201·10−14 −1.67973·10−3 7.21167·10−3

2.5·10−4 5.3·10−2 1.9·10−1

1.6·10−3 4.2·10−2 1.5·10−1

(100 to 210) MPa −4.64070·10−7 5.11296·10−9 −1.03630·10−11 9.78021·10−15 2.69448·10−9 −4.50250·10−12 3.65473·10−15 −1.41573·10−3 1.18977·10−2 8.4·10−4 4.7·10−2 1.4·10−1

AD = average deviation. AAD = absolute average deviation. MD = maximum deviation.

studied liquid, the overall experimental uncertainty in the reported density values is estimated to be ± 0.5 kg·m−3 (0.06 %) between (0.1 and 100) MPa.

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

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(2)

and

RESULTS AND DISCUSSION Speeds of sound c were measured along isotherms spaced at 20 K intervals from (283.15 to 403.15) K in the pressure range from atmospheric pressure to 210 MPa using 10 MPa steps up to 150 MPa and 20 MPa steps beyond. At lower temperature measurements in methyl caprate were limited by the appearance of solid at pressure higher than 140 MPa. Table 2 lists the measured values of methyl caprate and ethyl caprate respectively. These data were correlated using a rational function which correlates 1/c2 as a function of pressure and temperature by considering nine adjustable parameters: 1 A + BP + CP 2 + DP 3 = 2 E + FP c

E = 1 + E1T

(3)

As the uncertainty in measurement is higher between (100 and 210) MPa than below 100 MPa, the parameters were evaluated by a least-squares fit in two different pressure ranges: (0.1013 to 100) MPa and (100 to 210) MPa. The results for both compounds are given in Table 3 along with the average and maximum deviations. The observation of these deviations reveals that the correlation leads to a good interpolation of the speed of sound data of both methyl caprate and ethyl caprate within the estimated uncertainty. Moreover, this expression leads to a simple analytical form of the integral of 1/c2 with respect to pressure which represents the main contribution of the change of density with pressure. The speed of sound in methyl caprate was measured previously at atmospheric

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Table 4. Values of Densities ρ at Temperatures T and Pressures p Measured in Liquid Methyl Caprate and Ethyl Caprate by Using a U-Tube Densimetera p/MPa

T/K

ρ/kg·m−3

T/K

ρ/kg·m−3

T/K

0.1013 10 20 30 40 50 60 70 80 90 100 0.1013 10 20 30 40 50 60 70 80 90 100

293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15

872.1 878.9 885.0 890.9 896.5 901.7 906.6 911.3 915.5 920.1 924.3 822.4 831.4 839.8 847.4 854.3 860.8 867.0 872.6 878.1 883.3 888.2

303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15

863.6 871.0 877.4 883.5 889.3 894.6 899.6 904.5 909.1 913.6 917.9 814.5 823.7 832.4 840.3 847.7 854.4 860.7 866.5 872.0 877.3 882.5

313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15

0.1013 10 20 30 40 50 60 70 80 90 100 0.1013 10 20 30 40 50 60 70 80 90 100

293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15

863.8 870.8 877.1 883.0 888.6 893.8 898.8 903.5 907.7 912.2 916.4 814.4 823.6 832.1 839.6 846.7 853.2 859.3 865.2 870.6 875.8 880.8

303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15

855.5 863.2 869.7 875.8 881.5 887.0 892.1 897.1 901.7 906.3 910.6 806.4 815.9 824.7 832.7 840.1 846.8 853.1 859.3 864.8 870.1 875.1

313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15

ρ/kg·m−3

T/K

Methyl Caprate 855.9 323.15 863.1 323.15 869.9 323.15 876.2 323.15 882.2 323.15 887.8 323.15 893.0 323.15 898.1 323.15 902.9 323.15 907.5 323.15 911.9 323.15 805.4 383.15 816.0 383.15 825.2 383.15 833.4 383.15 841.1 383.15 848.0 383.15 854.8 383.15 860.9 383.15 866.9 383.15 872.3 383.15 877.6 383.15 Ethyl Caprate 848.0 323.15 855.2 323.15 862.0 323.15 868.5 323.15 874.4 323.15 880.0 323.15 885.4 323.15 890.5 323.15 895.4 323.15 900.0 323.15 904.4 323.15 797.3 383.15 807.9 383.15 817.1 383.15 825.5 383.15 833.4 383.15 840.5 383.15 847.1 383.15 853.1 383.15 859.2 383.15 864.7 383.15 869.8 383.15

ρ/kg·m−3

T/K

ρ/kg·m−3

T/K

ρ/kg·m−3

847.7 855.4 862.5 869.0 875.0 880.8 886.5 891.7 896.7 901.4 905.8 797.5 808.4 818.1 826.7 834.6 841.7 848.6 855.1 861.1 866.7 872.1

333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15

839.4 847.3 854.4 861.5 867.9 874.0 879.6 885.0 890.1 894.9 899.6 788.7 800.1 810.1 819.2 827.5 835.0 842.0 848.6 854.7 860.6 866.1

343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15

830.8 839.5 847.6 854.6 861.4 867.6 873.4 879.0 884.3 889.4 894.3

839.7 847.5 854.8 861.5 867.5 873.2 879.1 884.3 889.3 894.1 898.4 789.4 800.6 810.4 819.1 827.0 834.3 841.2 847.6 853.6 859.3 864.9

333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15

831.2 839.4 846.9 854.0 860.4 866.4 872.2 877.5 882.6 887.5 892.2 780.8 792.2 802.3 811.5 819.8 827.4 834.4 841.0 847.2 853.0 858.4

343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15

822.9 831.4 839.6 846.9 853.8 860.0 865.9 871.5 876.8 881.9 886.7

a

Standard uncertainties u are u(T) = 0.1 K, u(p) = 0.01 MPa and the combined expanded uncertainties Uc (level of confidence = 0.95) is Uc(ρ) = 0.5 kg·m−3.

pressure by Gouw and Vlugter10 for two temperatures, (293 and 413) K. A comparison (Table 4) of these measurements with our interpolation function shows good agreement with a deviation less than the estimated error. The volumetric properties of both components were measured with the U-tube densimeter from atmospheric pressure to 100 MPa along 11 isotherms ranging from (293.15 to 393.15) K. The experimental data obtained by this method are reported in Table 4 for both methyl caprate and ethyl caprate. Densities in methyl and ethyl caprate were measured previously at

atmospheric pressure by several authors.11−14 The measurements reported by Pratas et al.11 represent the majority of the available data as a function of temperature. The other references provide only one or two temperatures conditions. A comparison between the present measurements and literature data (Table 5) shows a good agreement with an absolute average deviation of 0.04 % for methyl caprate and 0.07 % for ethyl caprate. No literature values are available under pressure. In addition, density was determined in the full pressure range (0.1 to 210) MPa from speed of sound data by using a 2671



Article

Table 5. Literature Data and Deviations with the Reported Measurements at Atmospheric Pressure methyl caprate T/K

c/m·s−1

ethyl caprate

ρ/kg·m−3

a

b

293.15 1324.7 (0.03 %) 872.3 (−0.03 %); 872.4c (−0.04 %) 298.15 868.2b (−0.03 %); 868.8d (−0.1 %) 303.15 864.1b (−0.06 %) 313.15 1251.8a (0.01 %) 856.0b (−0.02 %); 855.8c (0.01 %) 323.15 847.8b (0.02 %) 333.15 839.5b (−0.02 %) 343.15 831.2b (−0.05 %) 353.15 363.15 368.15

822.9b (−0.07 %) 81x4.5b (0.001 %)

ρ/kg·m−3 864.3b (−0.06 %) 856.2b (−0.08 %) 848.0b (−0.00 %) 839.8b (−0.01 %); 839.9e (−0.02 %) 831.6b (−0.05 %) 823.4b (−0.06 %) 815.1b (−0.09 %); 815.3e (−0.1 %) 808.6b (−0.03 %) 864.3b (−0.06 %) 802.6e (−0.09 %)

Figure 3. Compressibility of methyl caprate as a function of pressure along various isotherms. ●, ○, 303 K; ▲, △, 383 K. Full line: isentropic compressibility κS; dashed line: isothermal compressibility κT.

a

Gouw and Vlugter.10 bPratas et al.11 cGouw and Vlugter.12 dKrop et al.13 eShigley et al.14

Figure 4. Relative deviations ΔκT/κT = {κT(exp) − κT(calc)}/κT(exp) between calculated and experimental isothermal compressibility of methyl caprate. ●, rational function eq 13 at 303.15 K; ○, Tait-like equation eq 16 at 303.15 K; ■, rational function at 343.15 K; □, Taitlike equation at 343.15 K; ▲, rational function at 383.15 K; △, Taitlike eq 383.15 K. The dashed lines at ± 2 and ± 3 are the expanded uncertainties in the determination of isothermal compressibility from the speed of sound integration method.

Figure 2. Relative deviations Δρ/ρ = {ρ(exp U-tube) − ρ(exp c)}/ ρ(exp U-tube) between density data measured by U-tube densimeter and determined from speed of sound measurements in compressed liquid ethyl caprate. ●, 303.15 K; ■, 343.15 K; △, 383.15 K. The dashed lines at ± 0.1 are the expanded uncertainties in the speed of sound integration method. 15

analytical integration of the rational function eqs 1 to3 with the fitted parameters of Table 3. The second integral, that can be regarded as perturbation of the first one, is evaluated iteratively using a predictor−corrector procedure.16,17 The heat capacities required to initiate this iterative procedure were taken at atmospheric pressure18,19 and were expressed as a cubic function of temperature in the range investigated:

16

modification of Davis and Gordon’s procedure. This method rests on the Newton−Laplace relationships which related the isothermal compressibility κT to the isentropic compressibility κS and itself to speed of sound:

κT = κS + TαP2/ρcp

(4)

cP,ref (MeC10:0)/J·K−1·kg −1

1 κS = 2 ρc

= 2.026·103 − 2.433T + 7.981·10−3T 2

(5)

where αP represents the isobaric thermal expansion and cp the isobaric heat capacity. The combination and integration of these relations lead to express the change in density with respect to pressure: ρ(P , T ) = ρ(Pref , T ) +

∫P

P

ref

1 dP + T c2

∫P

P

ref

αP2 dP CP

(7)

cP,ref (EeC10:0)/J·K−1·kg −1 = 1.541·103 + 4.280· 10−1T + 3.838· 10−3T 2

(8)

The data obtained by this second method are reported in Table 6. A comparison of the densities determined from speed of sound measurements with those measured using a U-tube densimeter for ethyl caprate at three temperatures of (303.15, 343.15, and 383.15) K shows (Figure 2) a satisfactory agreement with a maximum deviation that does not exceed 0.1 %. The absence of systematic deviation is also observed with methyl caprate. This good agreement between both techniques indicates

(6)

where Pref is a reference pressure where density is known. In this work it corresponds to the atmospheric pressure. The first integral represents the main contribution to the change of density with pressure. It is evaluated with a good accuracy by 2672



Article

Table 6. Values of Densities ρ at Temperatures T and Pressures p Determined from Integration of Speed of Sound Measurements in Liquid Methyl Caprate and Ethyl Capratea p/MPa

T/K

ρ/kg·m−3

T/K

ρ/kg·m−3

T/K

0.1013 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 170 190 210 0.1013 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 170 190 210

293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15

872.2 878.9 885.1 891.0 896.5 901.7 906.7 911.4 915.9 920.3 924.5 928.5 932.4 936.2 939.8 943.3 950.1 956.5 962.7 822.6 831.7 840.1 847.7 854.7 861.3 867.4 873.2 878.7 883.9 888.8 893.6 898.1 902.5 906.8 910.8 918.6 925.9 932.8

303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15

864.0 871.0 877.6 883.7 889.5 894.9 900.0 904.9 909.6 914.1 918.4 922.5 926.5 930.4 934.2 937.8 944.7 951.3 957.5 814.2 823.9 832.6 840.6 847.9 854.7 861.0 867.0 872.6 878.0 883.1 888.0 892.6 897.1 901.5 905.6 913.6 921.0 928.1

313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15

0.1013 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 170 190 210 0.1013

293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 353.15

863.7 870.4 876.6 882.4 887.8 893.0 897.9 902.5 907.0 911.2 915.3 919.3 923.0 926.7 930.2 933.6 940.1 946.3 952.1 814.5

303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 363.15

855.8 862.9 869.5 875.6 881.3 886.7 891.8 896.7 901.3 905.7 910.0 914.1 918.0 921.8 925.4 928.9 935.7 942.0 948.1 806.1

313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 373.15

ρ/kg·m−3

T/K

Methyl Caprate 855.8 323.15 863.2 323.15 870.1 323.15 876.5 323.15 882.4 323.15 888.1 323.15 893.4 323.15 898.5 323.15 903.3 323.15 907.9 323.15 912.4 323.15 916.6 323.15 920.8 323.15 924.7 323.15 928.6 323.15 932.3 323.15 939.4 323.15 946.1 323.15 952.5 323.15 805.8 383.15 816.0 383.15 825.2 383.15 833.5 383.15 841.1 383.15 848.1 383.15 854.7 383.15 860.8 383.15 866.6 383.15 872.2 383.15 877.4 383.15 882.4 383.15 887.2 383.15 891.8 383.15 896.2 383.15 900.5 383.15 908.6 383.15 916.2 383.15 923.4 383.15 Ethyl Caprate 847.8 323.15 855.3 323.15 862.2 323.15 868.6 323.15 874.6 323.15 880.3 323.15 885.6 323.15 890.7 323.15 895.5 323.15 900.1 323.15 904.5 323.15 908.7 323.15 912.8 323.15 916.7 323.15 920.5 323.15 924.1 323.15 931.1 323.15 937.7 323.15 943.9 323.15 797.6 383.15 2673

ρ/kg·m−3

T/K

ρ/kg·m−3

T/K

ρ/kg·m−3

847.5 855.3 862.6 869.2 875.5 881.3 886.8 892.1 897.1 901.8 906.4 910.8 915.0 919.1 923.0 926.8 934.1 940.9 947.5 797.3 808.2 817.8 826.5 834.4 841.6 848.4 854.8 860.7 866.4 871.8 876.9 881.8 886.5 891.0 895.4 903.6 911.4 918.7

333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15

839.2 847.5 855.0 862.0 868.5 874.6 880.3 885.7 890.9 895.8 900.5 905.0 909.3 913.5 917.5 921.4 928.9 935.9 942.5 788.9 800.3 810.4 819.5 827.7 835.2 842.2 848.7 854.9 860.7 866.2 871.4 876.5 881.3 885.9 890.3 898.8 906.7 914.1

343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15

830.9 839.6 847.6 854.8 861.6 867.9 873.8 879.4 884.7 889.8 894.6 899.3 903.7 908.0 912.1 916.1 923.7 930.9 937.6

839.6 847.5 854.8 861.6 867.9 873.8 879.3 884.6 889.6 894.4 898.9 903.3 907.5 911.5 915.4 919.2 926.4 933.2 939.6 789.2

333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 393.15

831.3 839.7 847.4 854.5 861.0 867.2 873.0 878.4 883.6 888.5 893.3 897.8 902.1 906.3 910.3 914.2 921.6 928.6 935.1 780.9

343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15 343.15

822.9 831.8 839.9 847.3 854.2 860.5 866.5 872.2 877.6 882.7 887.5 892.2 896.7 901.0 905.1 909.1 916.7 923.9 930.6



Article

Table 6. continued p/MPa 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 170 190 210

T/K

ρ/kg·m−3

T/K

ρ/kg·m−3

T/K

353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15

823.9 832.4 840.1 847.2 853.9 860.1 865.9 871.5 876.8 881.8 886.6 891.2 895.6 899.8 903.9 911.7 919.1 926.0

363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15

815.9 824.8 832.9 840.3 847.2 853.6 859.7 865.4 870.8 876.0 880.9 885.6 890.2 894.5 898.7 906.7 914.3 921.3

373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15

ρ/kg·m−3

T/K

Ethyl Caprate 808.0 383.15 817.4 383.15 825.8 383.15 833.5 383.15 840.6 383.15 847.2 383.15 853.5 383.15 859.3 383.15 864.9 383.15 870.2 383.15 875.3 383.15 880.1 383.15 884.8 383.15 889.2 383.15 893.5 383.15 901.7 383.15 909.4 383.15 916.6 383.15

ρ/kg·m−3

T/K

ρ/kg·m−3

800.2 809.9 818.7 826.7 834.0 840.9 847.3 853.3 859.0 864.5 869.7 874.6 879.4 883.9 888.3 896.7 904.5 911.9

393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15

792.4 802.6 811.7 820.0 827.5 834.6 841.2 847.4 853.2 858.8 864.1 869.1 874.0 878.7 883.2 891.7 899.7 907.2

T/K

ρ/kg·m−3

a Standard uncertainties u are u(T) = 0.1 K, u(p) = 0.01 MPa up to 100 MPa, u(p) = 0.1 MPa between (100 and 210) MPa and the combined expanded uncertainties Uc (level of confidence = 0.95) are Uc(ρ) = 0.001 ρ up to 100 MPa and Uc(ρ) = 0.002 ρ between (100 and 210) MPa.

Table 7. Values of Isothermal Compressibility κT in Liquid Methyl Caprate and Ethyl Caprate at Temperatures T and Pressures pa p/MPa

T/K

κT/GPa−1

T/K

κT/GPa−1

0.1013 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 170 190 210

303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15

0.855 0.781 0.720 0.670 0.627 0.590 0.557 0.529 0.503 0.481 0.461 0.441 0.424 0.408 0.394 0.381 0.357 0.336 0.318

323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15

0.976 0.880 0.804 0.741 0.689 0.645 0.606 0.573 0.543 0.517 0.494 0.472 0.453 0.435 0.419 0.404 0.378 0.355 0.335

0.1013 10 20 30 40 50 60 70 80 90 100 110 120 130

303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15 303.15

0.870 0.792 0.728 0.675 0.630 0.592 0.558 0.529 0.502 0.479 0.457 0.437 0.419 0.403

323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15

1.003 0.901 0.820 0.755 0.700 0.654 0.614 0.579 0.549 0.521 0.497 0.474 0.454 0.436

T/K

κT/GPa−1

Methyl Caprate 343.15 1.116 343.15 0.993 343.15 0.897 343.15 0.820 343.15 0.757 343.15 0.704 343.15 0.658 343.15 0.619 343.15 0.585 343.15 0.555 343.15 0.529 343.15 0.504 343.15 0.483 343.15 0.463 343.15 0.445 343.15 0.428 343.15 0.399 343.15 0.374 343.15 0.352 Ethyl Caprate 343.15 1.151 343.15 1.020 343.15 0.920 343.15 0.839 343.15 0.774 343.15 0.719 343.15 0.672 343.15 0.631 343.15 0.596 343.15 0.565 343.15 0.537 343.15 0.511 343.15 0.489 343.15 0.468 2674

T/K

κT/GPa−1

T/K

κT/GPa−1

363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15

1.120 1.000 0.905 0.829 0.767 0.714 0.668 0.629 0.595 0.565 0.538 0.513 0.491 0.471 0.453 0.421 0.393 0.369

383.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15

1.264 1.114 0.998 0.907 0.833 0.772 0.719 0.675 0.636 0.602 0.572 0.544 0.520 0.498 0.478 0.443 0.413 0.387

363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15 363.15

1.317 1.150 1.025 0.927 0.849 0.784 0.730 0.683 0.643 0.607 0.576 0.548 0.522 0.499

383.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15 383.15

1.505 1.291 1.136 1.018 0.925 0.850 0.787 0.734 0.688 0.648 0.614 0.583 0.555 0.530



Article

Table 7. continued T/K

κT/GPa−1

T/K

κT/GPa−1

303.15 303.15 303.15 303.15 303.15

0.388 0.374 0.350 0.328 0.310

323.15 323.15 323.15 323.15 323.15

0.419 0.403 0.376 0.352 0.332

p/MPa 140 150 170 190 210

κT/GPa−1

T/K

Ethyl Caprate 343.15 0.449 343.15 0.432 343.15 0.402 343.15 0.376 343.15 0.353

T/K

κT/GPa−1

T/K

κT/GPa−1

363.15 363.15 363.15 363.15 363.15

0.479 0.460 0.427 0.399 0.374

383.15 383.15 383.15 383.15 383.15

0.507 0.487 0.451 0.420 0.393

a

Standard uncertainties u are u(T) = 0.1 K, u(p) =0.01 MPa up to 100 MPa, u(p) = 0.1 MPa between (100 and 210) MPa and the combined expanded uncertainties Uc (level of confidence = 0.95) are Uc(κT) = 0.02 κT up to 100 MPa, Uc(κT) = 0.03 κT between (100 and 210) MPa.

Table 8. Parameters and Deviations of Density Correlations for Methyl Caprate and Ethyl Caprate from (283 to 403) K methyl caprate parameters v0 v1 v2 v3 A0 A1 A2 B C D E1 F Deviationsa AD% for ρ AAD% for ρ MD% for ρ AD% for κT AAD% for κT MD% for κT a

rational equation, eqs 1 to 3

ethyl caprate Tait equation

rational equation, eqs 1 to 3

9.48917·10−4 3.43632·10−7 9.60682·10−10 5.81370·10−13

Tait equation

1.18373·10−3 −1.65510·10−6 6.83198·10−9 −5.07610·10−12

2.17298·10−7 −2.91950·10−9 2.60262·10−12 −1.24580·10−9 5.23126·10−12 −1.00700·10−14 −1.87691·10−3 5.90566·10−3

4.44330·102 −1.57890 1.50864·10−3 8.85320·10−2

5.33110·10−7 −4.55370·10−9 4.08975·10−12 −1.71780·10−9 7.88028·10−12 −1.54350·10−14 −1.77477·10−3 6.93344·10−3

5.26686·102 −2.06086 2.19389·10−3 8.85435·10−2

−8.6·10−3 1.5·10−2 7.9·10−2 2.4·10−2 1.8·10−1 7.0·10−1

1.2·10−2 2.1·10−2 5.1·10−2 −1.5·10−1 8.1·10−1 2.7

2.8·10−5 6.6·10−3 2.8·10−02 2.3·10−2 1.0·10−1 4.9·10−1

2.1·10−2 2.8·10−2 1.2·10−1 1.8·10−3 9.0·10−1 3.4

AD = average deviation. AAD = absolute average deviation. MD = maximum deviation.

the overall consistency between the speed of sound and the density measurements and confirms the ability to measure density under high pressure by the acoustic technique. Combining, according to eq 5, speed of sound and density data given in Tables 2 and 6 makes it possible to evaluate isentropic compressibility with an uncertainty of 0.5 % up to 100 MPa and 0.9 % between (100 and 210) MPa. Ultimately, the knowledge of both density and speed of sound yields to isothermal compressibility using Newton Laplace relationships as in eq 4. The values determined in this way are listed in Table 7. The uncertainty of this determination can be considered better than 2 % below 100 MPa and 3 % beyond. Both isentropic and isothermal compressibilities of methyl caprate were plotted as a function of pressure at (303.15 and 383.15) K in Figure 3. It can be observed in this figure that the general shapes of the curves are identical. The curves are simply translated by the term Tα2/Cp whose contribution decreases as the pressure rises. The volumetric behavior of these compressed liquids was represented by a rational function that correlates the change in volume with respect to pressure instead of the volume itself: ⎛ ∂v ⎞ A + BP + CP 2 + DP 3 ⎜ ⎟ = ⎝ ∂P ⎠T E + FP

and Ev = 1 + E1T

as this function correlate with a good accuracy the quantity 1/c2 that represents the most contribution of the change in density. Parameters of eqs 9 to 11 were adjusted by minimizing the following objective function: ⎛⎛ ∂v ⎞cal ⎞2 exp exp OF = ∑ ⎜⎜⎜ ⎟ − vi κT , i ⎟⎟ ⎝ ∂P ⎠T ⎠ i ⎝ Nexp

(12)

The results are given in Table 8. Integration of this equation leads to the volume and consequently to the density and to the compressibility: ⎛B ⎛C CE DE2 ⎞ DE ⎞ v = vref + ⎜ − 2 + 3 ⎟(P − Pref ) + ⎜ − 2 ⎟ ⎝ F ⎝F F F ⎠ F ⎠ 2 3 P 2 − Pref ⎛ D ⎞ P 3 − Pref +⎜ ⎟ ⎝F⎠ 2 3 2 ⎛A BE CE DE3 ⎞ ⎛ E + FP ⎞ + ⎜ − 2 + 3 − 4 ⎟ln⎜ ⎟ ⎝F F ⎠ ⎝ E + FPref ⎠ F F

×

(9)

with A = A 0 + A1T + A 2 T 2

(11)

(13)

where vref is the volume at the reference pressure (Pref = 0.1013 MPa). It is expressed as a third-order polynomial function of temperature.

(10) 2675


Journal of Chemical & Engineering Data vref = v0 + v1T + v2T 2 + v3T 3

Article

Normandie” and the “Conseil Général des Yvelines” is gratefully acknowledged.

(14)

Figure 4 show the deviations observed between the experimental and the calculated values of compressibility. It can be noted that the correlation leads to a good representation of both the density and its derivative. To compare these results to those obtained with a Tait equation that is usually considered for representing volumetric behavior of compressed liquids, the parameter of a Tait-like equation were adjusted by using the same objective function. The Tait equation considered takes the following form: Bvref ⎛ ∂v ⎞ ⎜ ⎟ = − ⎝ ∂P ⎠T P+A

Notes

The authors declare no competing financial interest.

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(1) Boudy, F.; Seers, P. Impact of physical properties of biodiesel on the injection process in a common-rail direct injection system. Energy Convers. Manage. 2009, 50, 2905−2912. (2) Boehman, A. L.; Morris, D.; Szybist, J. The Impact of the Bulk Modulus of Diesel Fuels on Fuel Injection Timing. Energy Fuels 2004, 18, 1877−1882. (3) Dutour, S.; Daridon, J. L.; Lagourette, B. Pressure and temperature dependence of the speed of sound and related properties in normal octadecane and nonadecane. Int. J. Thermophys. 2000, 21, 173−184. (4) Wilson, W. D. Speed of sound in distilled water as a function of temperature and pressure. J. Acoust. Soc. Am. 1959, 31, 1067−1072. (5) Baltasar, E. H.; Taravillo, M.; Baonza, V. G.; Sanz, P. D.; Guignon, B. Speed of Sound in Liquid Water from (253.15 to 348.15) K and Pressures from (0.1 to 700) MPa. J. Chem. Eng. Data 2011, 56, 4800−4807. (6) Daridon, J. L.; Lagrabette, A.; Lagourette, B. Speed of sound, density, and compressibilities of heavy synthetic cuts from ultrasonic measurements under pressure. J. Chem. Thermodyn. 1998, 30, 607− 623. (7) Comuñas, M. J. P.; Bazil, J. P.; Baylaucq, A.; Boned, C. Density of Diethyl Adipate using a Vibrating Densimeter from 293.15 to 403.15 K and up to 140 MPa. Densimeter calibration and measurements. J. Chem. Eng. Data 2008, 53, 986−994. (8) Wagner, W.; Pruß, A. The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use. J. Phys. Chem. Ref. Data 2002, 31, 387−535. (9) TRC Thermodynamic Tables; Texas A&M University: College Station, TX, 1996. (10) Gouw, T. H.; Vlugter, J. C. Physical properties of fatty acid methyl esters: IV Ultrasonic sound velocity. J. Am. Oil Chem. Soc. 1964, 41, 524−526. (11) Pratas, M. J.; Freitas, S.; Oliveira, M. B.; Monteiro, S. C.; Lima, A. S.; Coutinho, J. A. P. Densities and Viscosities of Fatty Acid Methyl and Ethyl Esters. J. Chem. Eng. Data 2010, 55, 3983−3990. (12) Gouw, T. H.; Vlugter, J. C. Physical Properties of Fatty Acid Methyl Esters. I. Density and Molar Volume. J. Am. Oil Chem. Soc. 1964, 41, 142−145. (13) Krop, H. B.; Velzen, M. J. M.; Parsons, J. R.; Govers, H. A. J. Determination of Environmentally Relevant Physical-Chemical Properties of Some Fatty Acid Esters. J. Am. Oil Chem. Soc. 1997, 74, 309− 315. (14) Shigley, J. W.; Bonhorst, C. W.; Liang, P. M.; Althouse, P. M.; Triebold, H. O. Physical Characterization of a) a Series of Ethyl Esters and b) a Series of Ethanoate Esters. J. Am. Oil Chem. Soc. 1955, 32, 213−215. (15) Davis, L. A.; Gordon, R. B. Compression of mercury at high pressure. J. Chem. Phys. 1967, 46, 2650−2660. (16) Daridon, J. L.; Lagourette, B.; Grolier, J. P. Measure and exploitation of ultrasonic speed in n-hexane up to 150 MPa. Int. J. Thermophys. 1998, 19, 145−160. (17) Daridon, J. L.; Lagourette, B.; Lagrabette, A. Acoustic determination of thermodynamic properties of ternary mixtures up to 150 MPa. Phys. Chem. Liq. 1999, 37, 137−160. (18) van Bommel, M. J.; Oonk, H. A. J.; van Miltenburg, J. C. Heat capacity measurements of 13 methyl esters of n-carboxylic acids from methyl octanoate to methyl icosanoate between 5 and 350 K. J. Chem. Eng. Data 2004, 49, 1036−1042. (19) Zaitsau, D. H.; Paulechka, Y. U.; Blokhin, A. V.; Yermalayeu, A. V.; Kabo, A. G.; Ivanets, M. R. Thermodynamics of Ethyl Decanoate. J. Chem. Eng. Data 2009, 54, 3026−3033.

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with A = A 0 + A1T + A 2 T 2

that leads by integration to the volume: ⎡ ⎛ P + A ⎞⎤ v = vref ⎢1 − B ln⎜ ⎟⎥ ⎢⎣ ⎝ Pref + A ⎠⎥⎦

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The density and compressibility calculated with this equation using parameters listed in Table 8 were compared with experimental data of methyl caprate, and deviations for compressibility were plotted in Figure 4. It can be noted from this table that both the rational function and Tait equation lead to deviations lower than the experimental uncertainty of density whereas it is not the case for compressibility. The Tait-like equation leads to maximum deviation of 5 %, whereas the rational function exhibits a maximum deviation inferior to percent (Figure4). Consequently, this formulation can be used to represent both the density and its first derivative versus pressure within their experimental uncertainties.

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CONCLUSIONS The speed of sound was measured in methyl caprate and ethyl caprate over a temperature range between (283.15 to 403.15) K with pressure ranging from atmosphere to 210 MPa. Density was measured in the same liquids by using a U-tube densimeter up to 100 MPa and was determined between atmospheric pressure and 210 MPa by the integration of speed of sound measurements. A very satisfactory agreement has been observed between both sets of density data with a maximum deviation that do not exceed the experimental uncertainty of both methods (0.1 %). These measurements were used to determine the volumetric derivative properties, that is, isentropic compressibility and isothermal compressibility of these components in an extended range of pressure. Finally a correlation was proposed to correlate within the experimental uncertainty of both the density and its derivative with respect to pressure.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Funding

The work was carried out in the frame of the project NADIAbio (New Advance Diesel Injection Diagnosis for bio fuels) supported by Mov’eo the French Automotive Cluster. Financial support of this research by the DGCIS (Directorate General for Competitiveness, Industry and Services), the “Région Haute 2676


Speed of Sound, Density, and Derivative Properties of Fatty Acid

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