- Email: [email protected]
The effect of temperature and pressure on the physicochemical properties of petroleum diesel oil and biodiesel fuel
Available online at www.sciencedirect.com
Fuel 87 (2008) 1941–1948 www.fuelfirst.com
The effect of temperature and pressure on the physicochemical properties of petroleum diesel oil and biodiesel fuel Marzena Dzida a
a,*
, Piotr Prusakiewicz
b
University of Silesia, Institute of Chemistry, Szkolna 9, 40-006 Katowice, Poland b Rafineria Trzebinia S.A., Fabryczna 22, 32-540 Trzebinia, Poland
Received 10 July 2007; received in revised form 13 October 2007; accepted 16 October 2007 Available online 3 December 2007
Abstract Three commercial fuels were studied: biodiesel (based mainly of the fatty acids methyl esters of rapeseed oil), diesel oil Ekodiesel Ultra (standard petroleum diesel oil with sulphur content less than 10 mg/kg), and ON BIO 10 (blend of 20 vol.% of biodiesel with 80 vol.% of standard petroleum diesel oil with sulphur content less than 10 mg/kg). The speeds of sound were measured within the temperatures from 293 to 318 K and at pressures from 0.1 to 101 MPa. The densities and heat capacities were measured under atmospheric pressure in the temperature range from 273 to 363 K and 283 to 359 K, respectively. Using the experimental results, the physicochemical properties such as: density, isentropic bulk modulus, heat capacity, and isobaric thermal expansion were calculated in the same temperature and pressure range as the speed of sound was measured. The results obtained show that although the bulk modulus of ON BIO 10 is higher than that of diesel oil Ekodiesel Ultra over the whole pressure range, the difference is rather small and can be compensated by temperature. Isobaric thermal expansivity of biodiesel decreases with pressure slightly less than that of the diesel oil Ekodiesel Ultra. It is approximately independent of temperature and composition of the fuel at pressures 40 ± 5 MPa. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Physicochemical properties; Diesel; Biodiesel
1. Introduction In the petrochemical and automotive industries, an important point of interest is the influence of ‘‘bio-component’’ additives, such as alcohols or esters, on the properties of fuels and greases. Biodiesel is an alternative diesel fuel consisting of alkyl monoesters of fatty acids obtained from vegetable oils or animal fats. Mixtures of biodiesel and petroleum-based diesel fuel can be used in diesel engines. Physicochemical properties of bio- and petroleum-based diesels, such as density, bulk modulus, and heat capacity, are different due to dissimilar chemical composition of the fuels. That may influence combustion and
*
Corresponding author. Tel.: +48 032 359 1612; fax: +48 032 259 9978. E-mail address: [email protected] (M. Dzida).
0016-2361/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.fuel.2007.10.010
exhaust emission. Density is one of the most important properties of fuels, because injection systems, pumps and injectors must deliver the amount of fuel precisely adjusted to provide proper combustion. Isobaric thermal expansion and bulk modulus, or its reciprocal, i.e. compressibility, characterize how temperature and pressure affect density. The bulk modulus of biodiesels is higher than that of petroleum diesels. Since the modulus determines the spray characteristics upon injection, it has been closely related to NOx content in the exhausts [1–5]. That content depends also on the temperature of exhausts, thereby on the heat capacity of fuel [6]. As the fuel injection in an engine is approximately an adiabatic process, the adiabatic bulk modulus seems to be more useful than the isothermal one in estimation of the fuel injection timing. That is particularly important for modern common rail systems where the pressure can reach 250 MPa
1942
M. Dzida, P. Prusakiewicz / Fuel 87 (2008) 1941–1948
instead of ca. 35 MPa. The only experimental method that leads directly to adiabatic modulus is the acoustic one, based on the measurement of the speed of sound. The method has found wide acceptance as a relatively simple tool for determination of thermodynamic properties, especially at high-pressures. Apart from the adiabatic modulus and compressibility, the isothermal compressibility, density, isobaric thermal expansion, and heat capacities of compressed liquids obtained by that method have been reported [7–12]. Sun et al. [7] even claimed that at elevated pressures, density determined by the acoustic method is more nearly accurate than that measured in a direct way. In the present paper, we report experimental speeds of sound in a standard petroleum diesel oil, as well as in a biodiesel and in ON BIO 10, being a blend of 20 vol.% of biodiesel with 80 vol.% of standard petroleum diesel oil. The data cover the pressure range from 0.1 to 101 MPa and the temperature interval from 293 to 318 K. The speeds are completed with densities and heat capacities measured at atmospheric pressure and temperatures 273–363 K and 283–359 K, respectively. The densities and isobaric heat capacities at pressures up to 100 MPa were calculated from experimental data according to the suggestion of Davis and Gordon [8]. To this end, a slightly modified procedure of Sun et al. was applied [7,9]. From the relationships between pressure, temperature and density, the material constants were determined: adiabatic bulk moduli and isobaric thermal expansions of the three fuels studied. We aimed this work mainly at comparison of effects of pressure and temperature on density, heat capacity, adiabatic bulk modulus, and isobaric thermal expansion of three commercial fuels. Furthermore, we tried to find out whether the differences in the physicochemical properties
of the studied fuels are significant from the practical point of view. Data similar to those reported in this work have been used in calculations of other thermodynamic parameters, in simulations, and as a reference material for tests of performance characteristics of diesel engines [5,13,14]. 2. Experimental section 2.1. Samples Three commercial fuels were studied: (i) Ekodiesel Ultra, a standard petroleum diesel oil with sulphur content less than 10 mg/kg, which fulfilled norm EN 590, manufactured by PKN Orlen S.A., (ii) Biodiesel, based mainly of fatty acids methyl esters of rapeseed oil, which fulfilled norm EN 14214, manufactured by Rafineria Trzebinia S.A., and (iii) ON BIO 10, blend of 20 vol.% of biodiesel with 80 vol.% of standard petroleum diesel oil with sulphur content less than 10 mg/kg, also made by Rafineria Trzebinia S.A. Properties of diesel and biodiesel fuels are given in Table 1. 2.2. Ultrasonic speed measurements The speed of sound in liquids under test has been measured at atmospheric and higher pressures using two apparatus designed and constructed in our laboratory [15,16]. Two measuring vessels of the same acoustic path and construction have been used, one of them designed for measurements under atmospheric pressure, the other one for measurements under elevated pressures. A single transmitting–receiving ceramic transducer operating at 2 MHz and an acoustic mirror have been applied. The measuring sets
Table 1 Physical and chemical properties of diesel oil Ekodiesel Ultra, ON BIO10, and biodiesel Property Cetane number Cloud point Flash point Kinematic viscosity at 40 °C Water content Sulfur content Carbon residue on 10% distillation residue FAME content Oxidation stability at 110 °C Acid value Iodine value Linoleic acid methyl ester Methanol content Distillation at 101.3 kPa: 95% recovered up to Up to 250 °C recovered Up to 350 °C recovered
Units
Ekodiesel Ultra from PKN Orlen SA
ON BIO10 from RT SA
European standard for diesel EN 590
Biodiesel from RT SA
European standard for biodiesel-FAME EN 14214
°C °C mm2/s
54.1 14 65 2.7
51 10 68 2.88
>51 <0 >56 2.0–4.5
51.7 – >130 4.5
>51 – 120 3.5–5.0
mg/kg mg/kg % m/m
64 8.8 0.02
110 9.9 0.03
<200 <10 <0.3
88 9.7 0.04
<500 <10 <0.3
% m/m
–
17.7
5.0
97.5
>96.5
h mg of KOH/g g of I2/ 100g % m/m % m/m
– –
– –
<25 –
8.1 0.33
>6.0 <0.50
–
–
–
115
<120
– –
– –
– –
8.7 <0.05
<12 <0.20
°C vol.% vol.%
330 40 98
339 30 98
<360 <65 >85
– – –
– – –
M. Dzida, P. Prusakiewicz / Fuel 87 (2008) 1941–1948
operate on the principle of the pulse-echo-overlap method. The pressure was provided by a hand operated hydraulic press and was measured with a strain gauge measuring system (Hottinger Baldwin System P3MD) with accuracy better than 0.15%. The temperature was measured using an Ertco Hart 850 platinum resistance thermometer (traceable to a NIST standard) with an uncertainty of ±0.05 K and resolution of 0.001 K. The uncertainty of the speed of sound measurements was estimated to be 0.03% at atmospheric pressure, 0.04% under pressures up to 60 MPa and 0.05% under pressures from 60 MPa to 101 MPa.
1943
Other details of the high-pressure device and the method of the speed of sound measurements can be found in the previous papers [15,16]. 2.3. Density measurements The densities at atmospheric pressure were measured using a vibrating tube densimeter Anton Paar DMA 5000. The uncertainty of the density measurements was 0.05 kg m3, whereas the repeatability was estimated to be better than 0.005 kg m3.
Table 2 Speed of sound in diesel oil Ekodiesel Ultra, ON BIO10, and biodiesel measured at pressures up to 101 MPa within the temperature range 293–318 K Ekodiesel Ultra
ON BIO10
Biodiesel
T (K)
p (MPa)
u (m s1)
T (K)
p (MPa)
u (m s1)
T (K)
p (MPa)
u (m s1)
292.88 292.87 292.86 292.86 292.87 292.86 292.86 292.86 298.16 298.15 298.15 298.15 298.15 298.16 298.15 298.15 303.14 303.14 303.14 303.13 303.14 303.13 303.14 303.14 308.10 308.13 308.13 308.13 308.13 308.13 308.13 308.13 313.11 313.11 313.11 313.11 313.11 313.10 313.10 313.10 318.28 318.30 318.29 318.29 318.29 318.29 318.29 318.29
0.10 15.20 30.40 45.60 60.79 75.99 91.18 101.32 0.10 15.20 30.39 45.59 60.79 75.99 91.18 101.32 0.10 15.20 30.39 45.59 60.79 75.99 91.18 101.32 0.10 15.20 30.39 45.59 60.79 75.99 91.18 101.32 0.10 15.20 30.39 45.59 60.79 75.99 91.18 101.32 0.10 15.20 30.39 45.59 60.79 75.99 91.18 101.32
1370.76 1446.68 1513.41 1574.04 1630.60 1682.79 1731.94 1763.07 1350.67 1427.29 1494.57 1555.73 1613.02 1665.71 1715.26 1746.72 1331.91 1408.42 1477.07 1539.25 1597.12 1650.84 1700.62 1732.67 1313.30 1390.52 1460.51 1523.58 1581.90 1636.44 1686.91 1718.90 1294.68 1373.44 1444.26 1508.45 1567.18 1622.22 1673.14 1705.42 1275.61 1356.21 1428.16 1493.14 1552.45 1608.16 1659.76 1692.19
292.91 292.86 292.86 292.86 292.86 292.86 292.86 292.86 298.17 298.15 298.15 298.15 298.15 298.15 298.15 298.15 303.16 303.14 303.14 303.14 303.13 303.13 303.13 303.13 308.13 308.13 308.13 308.13 308.13 308.13 308.13 308.12 313.12 313.10 313.10 313.11 313.10 313.10 313.10 313.10 318.30 318.30 318.30 318.30 318.30 318.30 318.30 318.29
0.10 15.20 30.39 45.59 60.79 75.99 91.18 101.32 0.10 15.20 30.39 45.59 60.79 75.99 91.18 101.32 0.10 15.20 30.39 45.59 60.79 75.99 91.18 101.32 0.10 15.20 30.39 45.59 60.79 75.99 91.18 101.32 0.10 15.20 30.39 45.59 60.79 75.99 91.18 101.32 0.10 15.20 30.39 45.59 60.79 75.99 91.18 101.32
1379.57 1453.58 1518.94 1578.62 1634.08 1685.40 1733.72 1764.43 1359.69 1434.72 1500.96 1561.16 1617.66 1669.47 1717.81 1749.44 1341.03 1416.90 1484.09 1545.04 1602.03 1654.76 1703.72 1735.30 1322.58 1399.36 1467.83 1529.71 1586.94 1640.55 1690.06 1721.65 1304.19 1382.43 1451.79 1514.65 1572.56 1626.52 1676.69 1708.53 1285.28 1365.24 1435.71 1499.39 1557.67 1612.63 1663.24 1695.25
292.92 292.86 292.86 292.86 292.86 292.86 292.86 292.86 298.20 298.15 298.15 298.15 298.15 298.15 298.15 298.14 303.18 303.14 303.14 303.13 303.13 303.13 303.13 303.13 308.16 308.13 308.13 308.13 308.13 308.12 308.12 308.12 313.14 313.10 313.10 313.10 313.10 313.10 313.10 313.10 318.31 318.29 318.28 318.30 318.30 318.29 318.29 318.30
0.10 15.20 30.39 45.59 60.79 75.99 91.18 101.32 0.10 15.20 30.39 45.59 60.79 75.99 91.18 101.32 0.10 15.20 30.39 45.59 60.79 75.99 91.18 101.32 0.10 15.20 30.39 45.59 60.79 75.99 91.18 101.32 0.10 15.20 30.39 45.59 60.79 75.99 91.18 101.32 0.10 15.20 30.39 45.59 60.79 75.99 91.18 101.32
1414.95 1482.08 1541.36 1596.67 1647.96 1695.54 1741.08 1769.94 1395.70 1463.92 1524.19 1580.09 1632.20 1680.47 1726.16 1755.32 1377.71 1446.76 1508.29 1564.48 1617.60 1666.26 1712.43 1741.88 1359.86 1430.19 1492.54 1549.56 1602.96 1652.55 1698.72 1728.68 1342.10 1413.95 1477.24 1534.76 1588.66 1639.09 1685.83 1715.79 1323.81 1397.11 1461.47 1519.87 1574.29 1625.11 1672.44 1702.47
1944
M. Dzida, P. Prusakiewicz / Fuel 87 (2008) 1941–1948
Table 3 Densities and specific heat capacities of diesel oil Ekodiesel Ultra, ON BIO10, and biodiesel measured at atmospheric pressure Ekodiesel Ultra
ON BIO10
Biodiesel
T (K)
q (kg m )
T (K)
q (kg m )
T (K)
q (kg m3)
273.15 278.15 283.16 288.15 293.16 298.16 303.16 308.16 313.15 318.16 323.15 328.16 333.16 338.16 343.15 348.16 353.15 358.15 363.15
845.882 842.363 838.845 835.331 831.816 828.303 824.789 821.277 817.760 814.242 810.719 807.191 803.660 800.127 796.584 793.038 789.482 785.919 782.350
273.15 278.15 283.16 288.16 293.15 298.16 303.16 308.16 313.16 318.16 323.15 328.16 333.16 338.16 343.15 348.16 353.15 358.15 363.15
855.514 851.980 848.449 844.923 841.398 837.874 834.348 830.825 827.301 823.776 820.248 816.715 813.178 809.643 806.099 802.550 798.996 795.433 791.865
273.15 278.15 283.16 288.16 293.15 298.16 303.16 308.16 313.16 318.16 323.15 328.15 333.15 338.16 343.15 348.15 353.16 358.15 363.15
894.390 890.731 887.086 883.445 879.814 876.185 872.563 868.942 865.325 861.709 858.096 854.483 850.871 847.261 843.648 840.034 836.416 832.796 829.181
T (K) 282.60 283.14 288.14 293.15 298.14 303.15 308.14 313.16 318.15 323.14 328.15 333.14 338.15 343.14 348.16 353.15 358.14 358.97
3
Cp (J kg1 K1) 1895.2 1897.8 1916.5 1935.0 1952.7 1971.4 1990.5 2009.9 2028.7 2049.1 2068.6 2089.3 2109.0 2128.7 2147.4 2166.7 2186.0 2188.8
T (K) 282.67 283.14 288.14 293.15 298.14 303.15 308.14 313.14 318.15 323.14 328.15 333.14 338.15 343.14 348.16 353.15 358.14 358.97
3
Cp (J kg1 K1) 1899.1 1901.2 1919.2 1937.2 1954.6 1971.8 1990.2 2008.5 2026.3 2045.4 2064.6 2083.6 2102.5 2121.2 2139.7 2157.6 2175.4 2178.6
T (K) 282.51 283.14 288.14 293.15 298.16 303.15 308.14 313.16 318.15 323.16 328.15 333.14 338.15 343.14 348.16 353.15 358.14 358.97
Cp (J kg1 K1) 1942.7 1945.6 1959.4 1971.9 1985.2 1998.5 2013.1 2028.1 2042.3 2057.6 2073.1 2088.9 2104.6 2119.6 2134.5 2148.5 2163.7 2165.9
Table 4 Coefficients of polynomial Eq. (1) for the speed of sound, density, and specific isobaric heat capacity, respectively and mean deviations from the regression line Fuel
c0 (m s1)
c1 (m s1 K1)
Ekodiesel Ultra ON BIO10 Biodiesel
2727.370 2749.493 2717.464
5.446246 5.564141 5.234999
Ekodiesel Ultra ON BIO10 Biodiesel
q0 (kg m3) 1032.289 1044.171 1095.576
q1 (kg m3 K1) 0.6653943 0.6788419 0.7461680
q2 Æ 105 (kg m3 K2) 6.27435 4.36606 3.48745
Ekodiesel Ultra ON BIO10 Biodiesel
h0 (J kg1 K1) 1035.764 1033.153 1547.327
h1 (J kg1 K2) 2.388477 2.573437 –
h2 Æ 103 (J kg1 K3) 2.31209 1.73489 5.47687
2.4. Specific heat capacity measurements The specific isobaric heat capacity was measured by a high sensitivity differential scanning calorimeter Micro DSC III,
c2 Æ 103 (m s1 K2)
du0 (m s1)
2.78037 3.02869 2.69146
0.009 0.002 0.004 dq (kg m3) 0.016 0.016 0.015 h2 Æ 106 (J kg1 K4) – – 1.82282
dCp (J kg1 K1) 0.8 0.8 1.0
manufactured by Setaram and based on the Tian-Calvet principle. The uncertainty of the measurements was estimated to be ± 0.15%. More details of the measuring set, calibration and measurement procedure can be found in [17].
M. Dzida, P. Prusakiewicz / Fuel 87 (2008) 1941–1948 Table 5 Coefficients of Eq. (2) and mean deviations from the regression line du Fuel
j
a1j (Kj MPa s m1)
Ekodiesel Ultra
0 1 2
0.2620890650
ON BIO10
Biodiesel
– 8.70894267Æ107
a2j (Kj MPa s2 m2) 2.67267574Æ104
du (m s1) 0.51
– 1.00348744Æ109
0 1 2
0.2822989252
2.48484590Æ104
– 1.05453199Æ106
– 7.36412361Æ1010
0 1 2
0.3301165804 – 1.34877055Æ106
2.56840831Æ104 1.95352490Æ107 –
0.26
0.26
1945
3. Measurement results The ultrasonic speeds in diesel oil Ekodiesel Ultra, ON BIO10, and biodiesel were measured at temperatures from 293 to 318 K in about 5 K steps and under pressures 0.1, 15, 30, 45, 60, 75, 90, and 101 MPa. The experimental values are listed in Table 2. The densities of the fuels and biofuels were measured under atmospheric pressure in the temperature range from 273 to 363 K in 5 K steps. The experimental values are collected in Table 3. The specific isobaric heat capacities were measured at atmospheric pressure and at temperatures from 283 to 359 K in about 0.02 K steps. Thus it has given ca. 3400 experimental points
Table 6 The calculated densities of diesel oil Ekodiesel Ultra, ON BIO10, and biodiesel at pressures up to 100 MPa and within the temperature limits 293 and 318 K
Table 7 The calculated isobaric specific heat capacities of diesel oil Ekodiesel Ultra, ON BIO10, and biodiesel at pressures up to 100 MPa and within the temperature limits 293 and 318 K
q (kg m3)
Cp (J kg1 K1)
p (MPa)
T (K) 293.15
p (MPa) 298.15
303.15
308.15
313.15
298.15
303.15
308.15
313.15
318.15
814.24 821.17 827.61 833.59 839.18 844.44 849.41 854.13 858.63 862.93 867.05
Ekodiesel Ultra 0.1a 1935 10 1930 20 1926 30 1923 40 1921 50 1919 60 1918 70 1917 80 1916 90 1916 100 1915
1953 1948 1945 1942 1940 1938 1937 1936 1935 1934 1934
1972 1967 1963 1960 1958 1956 1955 1954 1953 1953 1952
1991 1986 1982 1979 1977 1975 1974 1973 1972 1971 1971
2010 2005 2001 1998 1995 1994 1992 1991 1990 1990 1989
2030 2024 2020 2017 2014 2012 2011 2010 2009 2009 2008
827.31 833.97 840.18 845.97 851.40 856.52 861.38 866.00 870.41 874.63 878.69
823.78 830.60 836.96 842.87 848.41 853.62 858.56 863.26 867.74 872.03 876.14
ON BIO10 0.1a 10 20 30 40 50 60 70 80 90 100
1937 1932 1929 1926 1924 1922 1920 1919 1918 1917 1917
1955 1950 1946 1943 1941 1939 1938 1937 1936 1935 1934
1973 1968 1964 1961 1959 1957 1956 1954 1953 1953 1952
1991 1986 1982 1979 1977 1975 1973 1972 1971 1970 1970
2009 2004 2000 1997 1995 1993 1991 1990 1989 1988 1987
2028 2022 2018 2015 2013 2011 2009 2008 2007 2006 2005
865.33 871.66 877.61 883.20 888.48 893.48 898.25 902.80 907.16 911.35 915.39
861.71 868.19 874.28 879.98 885.35 890.45 895.29 899.91 904.34 908.59 912.68
Biodiesel 0.1a 10 20 30 40 50 60 70 80 90 100
1972 1968 1965 1963 1961 1960 1958 1957 1956 1956 1955
1986 1982 1979 1977 1975 1973 1972 1971 1970 1969 1968
2000 1996 1993 1990 1988 1987 1986 1984 1984 1983 1982
2014 2010 2007 2004 2002 2001 1999 1998 1997 1997 1996
2028 2024 2021 2018 2016 2015 2013 2012 2011 2011 2010
2043 2039 2035 2033 2031 2029 2028 2027 2026 2025 2024
Ekodiesel Ultra 0.1a 831.84 10 837.94 20 843.67 30 849.04 40 854.09 50 858.88 60 863.43 70 867.77 80 871.92 90 875.91 100 879.74
828.32 834.58 840.45 845.93 851.09 855.97 860.60 865.02 869.24 873.29 877.18
824.81 831.23 837.23 842.83 848.10 853.07 857.79 862.28 866.57 870.68 874.63
821.29 827.87 834.02 839.74 845.12 850.18 854.98 859.55 863.91 868.08 872.09
817.77 824.52 830.81 836.66 842.14 847.30 852.19 856.84 861.27 865.50 869.57
ON BIO10 0.1a 10 20 30 40 50 60 70 80 90 100
841.42 847.44 853.12 858.43 863.45 868.21 872.73 877.05 881.19 885.17 888.99
837.89 844.07 849.87 855.31 860.42 865.27 869.88 874.27 878.48 882.52 886.40
834.37 840.70 846.64 852.19 857.41 862.34 867.03 871.51 875.78 879.88 883.82
830.84 837.33 843.41 849.07 854.40 859.43 864.20 868.75 873.09 877.25 881.25
Biodiesel 0.1a 10 20 30 40 50 60 70 80 90 100
879.83 885.59 891.05 896.21 901.10 905.76 910.21 914.47 918.57 922.52 926.33
876.21 882.10 887.68 892.94 897.93 902.67 907.20 911.54 915.70 919.71 923.57
872.58 878.61 884.32 889.69 894.77 899.60 904.21 908.61 912.84 916.91 920.83
868.96 875.13 880.96 886.44 891.62 896.54 901.22 905.70 910.00 914.13 918.10
a
Calculated from Eq. (1).
318.15
T (K) 293.15
a
Calculated from Eq. (1).
1946
M. Dzida, P. Prusakiewicz / Fuel 87 (2008) 1941–1948
for each liquid. Therefore the values of isobaric specific heat capacity every 5 K are collected in Table 3. The dependencies of the speed of sound, density, and isobaric specific heat capacity on temperature at atmospheric pressure were approximated by second-order polynomials of the type: y¼
2 X
bj T j ;
ð1Þ
In order to calculate the density at p2, q, ap and Cp at p1 should be known beside the speed of the ultrasound as a function of pressure. The change of the heat capacity within the pressure limits Dp is given by: " # T 2 oap DC p ap þ Dp: ð5Þ q oT p
j¼0
where y is the speed of sound, u0, density, q, or isobaric specific heat capacity, Cp, at atmospheric pressure p0; bj are the polynomial coefficients bj = cj for the speed of sound, bj = qj for the density, and bj = hj for the isobaric specific heat capacity) calculated by the least squares method. The backward stepwise rejection procedure was used to reduce the number of non-zero coefficients. The coefficients and standard deviations from the regression lines are given in Table 4. The standard deviations are much smaller than the measurements accuracy. Since the sensitivity of the pressure gauge is lower than that of both the ultrasonic apparatus and the thermometer, the equation suggested by Sun et al. [7] was chosen in this work for smoothing out the speed of sound, pressure and temperature: p p0 ¼
m X n X i¼1
A numerical procedure proposed by Sun et al. [7] slightly modified by Marczak et al. [9] was applied. Details of the algorithm were discussed in previous work [9]. The densities and isobaric heat capacities of the fuels under test were calculated for temperatures from 293.15 to 318.15 K and for pressures up to 100 MPa. The calculated density and isobaric specific heat capacity are listed in Tables 6 and 7, respectively. From the densities and Table 8 The isentropic bulk modulus of diesel oil Ekodiesel Ultra, ON BIO10, and biodiesel at pressures up to 100 MPa and within the temperature limits 293 and 318 K bS Æ 106 (Pa) p (MPa)
T (K) 293.15
i
aij ðu u0 Þ T j ;
ð2Þ
j¼0
where aij are the polynomial coefficients calculated by the least squares method, u is the speed of sound at p > 0.1 MPa, u0 is the speed calculated from Eq. (1). The coefficients aij and the mean deviations from the regression lines are given in Table 5. The stepwise rejection procedure was used to reduce the number of the non-zero coefficients. 4. Physicochemical properties at elevated pressures The pressure dependence of the density is given by the following thermodynamic relationship: oq 1 T a2p ¼ 2þ ; ð3Þ op T u Cp where ap is the isobaric thermal expansion calculated from definition: ap ¼ ð1=qÞðoq=oT Þp . The change of the density of the liquid Dq, caused by a pressure increase from p1 to p2 at constant temperature, can be calculated by integration: ! Z p2 Z p2 a2p T 1 a2p T 1 Dq ¼ þ dp þ Dp: ð4Þ dp 2 u2 C p Cp p1 p1 u The approximate relationship Eq. (4) is sufficiently accurate, provided Dp is small enough, because the heat capacity depends rather slightly on pressure. Moreover, the first term on the right hand side of Eq. (4) is significantly larger than the second one since the latter results from the difference between the isentropic and isothermal compressibility that is small in comparison with both the compressibilities.
298.15
303.15
308.15
313.15
318.15
Ekodiesel Ultra 0.1 1561 10 1690 20 1815 30 1937 40 2055 50 2170 60 2283 70 2394 80 2504 90 2611 100 2718
1511 1640 1765 1886 2004 2119 2231 2342 2451 2559 2665
1463 1591 1716 1836 1954 2068 2181 2292 2401 2508 2615
1416 1544 1668 1788 1905 2020 2132 2243 2352 2459 2565
1370 1498 1622 1742 1858 1973 2085 2195 2304 2411 2518
1326 1453 1576 1696 1813 1927 2039 2149 2258 2366 2472
ON BIO10 0.1 10 20 30 40 50 60 70 80 90 100
1599 1728 1853 1974 2091 2206 2319 2430 2539 2646 2752
1549 1678 1802 1923 2040 2155 2267 2378 2487 2594 2700
1501 1629 1753 1874 1991 2105 2217 2328 2436 2543 2649
1453 1581 1706 1826 1943 2057 2169 2279 2387 2494 2600
1407 1535 1659 1779 1896 2010 2122 2232 2340 2447 2553
1362 1490 1614 1734 1851 1965 2076 2186 2295 2402 2507
Biodiesel 0.1 10 20 30 40 50 60 70 80 90 100
1759 1884 2005 2123 2238 2351 2461 2570 2677 2783 2887
1707 1832 1953 2071 2186 2298 2408 2517 2624 2729 2834
1656 1781 1903 2020 2135 2247 2357 2466 2572 2678 2782
1607 1732 1853 1971 2086 2198 2308 2416 2522 2627 2731
1559 1684 1805 1923 2038 2150 2259 2367 2474 2579 2682
1511 1637 1759 1876 1991 2103 2213 2321 2427 2532 2635
M. Dzida, P. Prusakiewicz / Fuel 87 (2008) 1941–1948
5. Discussion The densities of the fuels and biofuels increase monotonically with increasing pressure and decreasing temperature. Temperature dependence of densities of the fuels and biofuels is described by the second-order polynomials (Table 4) while pressure dependence is described by the thirdorder polynomial. Respective slopes of the curves are practically the same. Nevertheless, densities of ON BIO 10 and diesel oil Ekodiesel Ultra are lower than densities of biodiesel, over the whole temperature and pressure range, by about 4.6–4.2% and 5.8–5.3%, respectively. The isobaric specific heat capacity of the fuels decreases with increasing pressure and decreasing temperature. However, the effect of pressure is smaller than that of temperature (Table 7). Difference between isobaric specific heat capacities of diesel oil Ekodiesel Ultra and ON BIO 10 are negligible over the whole temperature and pressure range. The heat capacity of biodiesel is higher than that of diesel oil Ekodiesel Ultra and ON BIO 10 by 2% at the most (Tables 3 and 7). Isobaric thermal expansivity of biodiesel decreases with pressure slightly less than that of the diesel oil Ekodiesel Ultra. It is approximately independent of temperature and composition of the fuel at pressures 40 ± 5 MPa (Fig. 1). The crossing point of isobaric thermal expansion is characteristic for simple liquids. For example, the isotherms of ap of hexane cross each other at 65 ± 2 MPa [18]. However, taking into account the uncertainty of the thermal expansion coefficient equals ± 1%, there is not sig-
nificant difference between ap of all the tested fuels. At temperatures from 293.15 to 318.15 K and pressures from atmospheric one to 100 MPa, the bulk moduli of biodiesel and ON BIO 10 were higher than that of diesel oil Ekodiesel Ultra by 6.2–14.0% and 1.3–2.7%, respectively (Fig. 2 a). Temperature change by 5 K changes the bulk modulus by 1.9–3.1% and by 1.8–3.3% for biodiesel and ON BIO 10, respectively. Thus, the effect of addition of biodiesel to the petroleum fuel on the bulk modulus is of the same order as that resulting from the slight change of temperature (Fig. 2b). With temperature increasing from 293.15 to 318.15 K, at atmospheric pressure, the bulk moduli decrease in a similar way for the diesel oil Ekodiesel Ultra and ON BIO 10: from 1561 to 1325 MPa and from 1599 to 1361 MPa, respectively. These ranges almost overlap each other. Thus, although the bulk modulus of ON BIO 10 is indeed higher than that of diesel oil Ekodiesel Ultra, the difference is rather small and can be compensated by temperature. Similar conclusion is valid for pressures up to100 MPa. These results show that effect of temperature on the bulk modulus should be taken into account over the whole pressure range.
3000
2500
Β S / MPa
speeds of sound, the adiabatic bulk modulus (the reciprocal of adiabatic compressibility jS) were calculated by the 2 1 Laplace formula: B1 S ¼ jS ¼ ðqu Þ . Results of the calculations are given in Table 8. The isothermal compressibility ðjT ¼ jS þ a2p T =qC p Þ and isothermal bulk modulus ðjT ¼ B1 T Þ can be also calculated from the above data.
1947
2000
1500
1000
0
20
40
60
80
100
60
80
100
p / MPa 0.9
3000
293.15 K
2500
Β S / MPa
α p · 10 3/ K -1
0.8
0.7
2000
1500 318.15 K
0.6
0
20
40
60
80
100
p / MPa
Fig. 1. Isobaric thermal expansion of: diesel oil Ekodiesel Ultra: (d) 293.15 K, (s) 318.15 K; ON BIO 10: (j) 293.15 K, (h) 318.15 K; Biodiesel (m) 293.15 K, (4) 318.15 K, lines calculated from empirical P function: ap ¼ 3i¼0 ai pi .
1000 0
20
40
p / MPa
Fig. 2. Isentropic bulk modulus of : a) diesel oil Ekodiesel Ultra: (d) 293.15 K, (s) 318.15 K; ON BIO 10: (j) 293.15 K, (h) 318.15 K; Biodiesel (m) 293.15 K, (4) 318.15 K; b) (s) diesel oil Ekodiesel P Ultra; (h) ON BIO 10; lines calculated from empirical function: Bs ¼ 3i¼0 ai pi .
1948
M. Dzida, P. Prusakiewicz / Fuel 87 (2008) 1941–1948
6. Conclusions 1. Investigated fuels and biofuels differ in density. That facilitates telling one fuel from another. 2. Isobaric specific heat capacity of biodiesel is higher than those of diesel oil Ekodiesel Ultra and ON BIO 10 that are approximately the same in the temperature range from 293.15 to 318.15 K and pressures up to 100 MPa. 3. Isobaric thermal expansions of the three investigated fuels are approximately equal to each other and independent of temperature at pressures 40 ± 5 MPa. 4. Increase of bulk modulus of petrodiesel due to addition of 20 vol.% of biodiesel is small. It is approximately the same as that caused by decrease of temperature by ca. 5 K. That probably holds even for pressures much higher than 100 MPa attained in this experiment. Acknowledgements The authors are profoundly indebted to Dr. W. Marczak for critical reading of the manuscript and Ms. M. Bucek for the participation in the density measurements. References [1] Tat ME, Van Gerpen JH, Soylu S, Canakci M, Monyem A, Wormley SJ. The speed of sound and isentropic bulk modulus of biodiesel at 21 °C from atmospheric to 35 MPa. Am Oil Chem Soc 2000;77:285–9. [2] Tat ME, Van Gerpen JH. Effect of temperature and pressure on the speed of sound and isentropic bulk modulus of mixtures of biodiesel and diesel fuel. J Am Oil Chem Soc 2003;80:1127–30. [3] Szybist JP, Boehman AL, Taylor JD, McCormick RL. Evaluation of formulation strategies to eliminate the biodiesel NOx effect. Fuel Proc Technol 2005;86:1109–26. [4] Boehman AL, Morris D, Szybist JP. The impact of the bulk modulus of diesel fuels on fuel injection timing. Energ Fuels 2003;18:1877–82. [5] Kegl B. Numerical analysis of injection characteristics using biodiesel fuel. Fuel 2006;85:2377–87.
[6] Forson FK, Oduro EK, Hammond-Donkoh E. Performance of jatropha oil blends in a diesel engine. Renew Energ 2004;29:1135–45. [7] Sun TF, Ten Seldam CA, Kortbeek PJ, Trappeniers NJ, Biswas SN. Acoustic and thermodynamic properties of ethanol from 273.15 to 333.15 K and up to 280 MPa. Phys Chem Liq 1988;18:107–16. [8] Davis LA, Gordon RB. Compression of mercury at high pressure. J Chem Phys 1967;46:2650–60. [9] Marczak W, Dzida M, Ernst S. Determination of the thermodynamic properties of 1-propanol and 1-hexanol from speed of sound measurements under elevated pressures. High Temp – High Press 2000;32:283–92. [10] Plantier F, Daridon JL, Lagourette B. Nonlinear parameter (B/A) measurements in methanol, 1-butanol and 1-octanol for different pressures and temperatures. J Phys D: Appl Phys 2002;35:1063–7. _ [11] Dzida M, Zak A, Ernst S. Thermodynamic and acoustic properties of binary mixtures of alcohols and alkanes. I. Speed of sound in (ethanol + n-heptane) under elevated pressures. J Chem Thermodyn 2005;37:405–14. [12] Dzida M, Marczak W. Thermodynamic and acoustic properties of binary mixtures of alcohols and alkanes. II. Density and heat capacity of (ethanol + n-heptane) under elevated pressures. J Chem Thermodyn 2005;37:826–36. [13] Tate RE, Watts KC, Allen CAW, Wilkie KI. The densities of three biodiesel fuels at temperatures up to 300 °C. Fuel 2006;85:1004–9. [14] Yamate K, Ueta A, Shimamoto Y. Influence of physical and chemical properties of biodiesel fuel on injection, combustion and exhaust emission characteristics in a DI-CI Engine. In: The fifth international symposium on diagnostics and modeling of combustion in internal combustion engines (COMODIA 2001), July 1–4, 2001, Nagoya; p. 402–9. _ [15] Zak A, Dzida M, Zore˛bski M, Ernst S. A high pressure system for measurements of the speed of sound in liquids. Rev Sci Instrum 2000;71:1756–65. [16] Dzida M, Chora˛z_ ewski M, Zore˛bski M, Man´ka R. Modification of a high pressure device for speed of sound measurements in liquids. J Phys IV 2006;137:203–7. [17] Go´ralski P, Tkaczyk M, Chora˛z_ ewski M. Heat capacities of a,xdichloroalkanes at temperatures from 28415 K to 353.15 K and a group additivity analysis. J Chem Eng Data 2003;48:492–6. [18] Randzio SL, Grolier J-PE, Quint JR, Eatough DJ, Lewis EA, Hansen LD. n-hexane as a model for compressed simple liquids. Int J Thermophys 1994;15:415–41.
Fuel 87 (2008) 1941–1948 www.fuelfirst.com
The effect of temperature and pressure on the physicochemical properties of petroleum diesel oil and biodiesel fuel Marzena Dzida a
a,*
, Piotr Prusakiewicz
b
University of Silesia, Institute of Chemistry, Szkolna 9, 40-006 Katowice, Poland b Rafineria Trzebinia S.A., Fabryczna 22, 32-540 Trzebinia, Poland
Received 10 July 2007; received in revised form 13 October 2007; accepted 16 October 2007 Available online 3 December 2007
Abstract Three commercial fuels were studied: biodiesel (based mainly of the fatty acids methyl esters of rapeseed oil), diesel oil Ekodiesel Ultra (standard petroleum diesel oil with sulphur content less than 10 mg/kg), and ON BIO 10 (blend of 20 vol.% of biodiesel with 80 vol.% of standard petroleum diesel oil with sulphur content less than 10 mg/kg). The speeds of sound were measured within the temperatures from 293 to 318 K and at pressures from 0.1 to 101 MPa. The densities and heat capacities were measured under atmospheric pressure in the temperature range from 273 to 363 K and 283 to 359 K, respectively. Using the experimental results, the physicochemical properties such as: density, isentropic bulk modulus, heat capacity, and isobaric thermal expansion were calculated in the same temperature and pressure range as the speed of sound was measured. The results obtained show that although the bulk modulus of ON BIO 10 is higher than that of diesel oil Ekodiesel Ultra over the whole pressure range, the difference is rather small and can be compensated by temperature. Isobaric thermal expansivity of biodiesel decreases with pressure slightly less than that of the diesel oil Ekodiesel Ultra. It is approximately independent of temperature and composition of the fuel at pressures 40 ± 5 MPa. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Physicochemical properties; Diesel; Biodiesel
1. Introduction In the petrochemical and automotive industries, an important point of interest is the influence of ‘‘bio-component’’ additives, such as alcohols or esters, on the properties of fuels and greases. Biodiesel is an alternative diesel fuel consisting of alkyl monoesters of fatty acids obtained from vegetable oils or animal fats. Mixtures of biodiesel and petroleum-based diesel fuel can be used in diesel engines. Physicochemical properties of bio- and petroleum-based diesels, such as density, bulk modulus, and heat capacity, are different due to dissimilar chemical composition of the fuels. That may influence combustion and
*
Corresponding author. Tel.: +48 032 359 1612; fax: +48 032 259 9978. E-mail address: [email protected] (M. Dzida).
0016-2361/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.fuel.2007.10.010
exhaust emission. Density is one of the most important properties of fuels, because injection systems, pumps and injectors must deliver the amount of fuel precisely adjusted to provide proper combustion. Isobaric thermal expansion and bulk modulus, or its reciprocal, i.e. compressibility, characterize how temperature and pressure affect density. The bulk modulus of biodiesels is higher than that of petroleum diesels. Since the modulus determines the spray characteristics upon injection, it has been closely related to NOx content in the exhausts [1–5]. That content depends also on the temperature of exhausts, thereby on the heat capacity of fuel [6]. As the fuel injection in an engine is approximately an adiabatic process, the adiabatic bulk modulus seems to be more useful than the isothermal one in estimation of the fuel injection timing. That is particularly important for modern common rail systems where the pressure can reach 250 MPa
1942
M. Dzida, P. Prusakiewicz / Fuel 87 (2008) 1941–1948
instead of ca. 35 MPa. The only experimental method that leads directly to adiabatic modulus is the acoustic one, based on the measurement of the speed of sound. The method has found wide acceptance as a relatively simple tool for determination of thermodynamic properties, especially at high-pressures. Apart from the adiabatic modulus and compressibility, the isothermal compressibility, density, isobaric thermal expansion, and heat capacities of compressed liquids obtained by that method have been reported [7–12]. Sun et al. [7] even claimed that at elevated pressures, density determined by the acoustic method is more nearly accurate than that measured in a direct way. In the present paper, we report experimental speeds of sound in a standard petroleum diesel oil, as well as in a biodiesel and in ON BIO 10, being a blend of 20 vol.% of biodiesel with 80 vol.% of standard petroleum diesel oil. The data cover the pressure range from 0.1 to 101 MPa and the temperature interval from 293 to 318 K. The speeds are completed with densities and heat capacities measured at atmospheric pressure and temperatures 273–363 K and 283–359 K, respectively. The densities and isobaric heat capacities at pressures up to 100 MPa were calculated from experimental data according to the suggestion of Davis and Gordon [8]. To this end, a slightly modified procedure of Sun et al. was applied [7,9]. From the relationships between pressure, temperature and density, the material constants were determined: adiabatic bulk moduli and isobaric thermal expansions of the three fuels studied. We aimed this work mainly at comparison of effects of pressure and temperature on density, heat capacity, adiabatic bulk modulus, and isobaric thermal expansion of three commercial fuels. Furthermore, we tried to find out whether the differences in the physicochemical properties
of the studied fuels are significant from the practical point of view. Data similar to those reported in this work have been used in calculations of other thermodynamic parameters, in simulations, and as a reference material for tests of performance characteristics of diesel engines [5,13,14]. 2. Experimental section 2.1. Samples Three commercial fuels were studied: (i) Ekodiesel Ultra, a standard petroleum diesel oil with sulphur content less than 10 mg/kg, which fulfilled norm EN 590, manufactured by PKN Orlen S.A., (ii) Biodiesel, based mainly of fatty acids methyl esters of rapeseed oil, which fulfilled norm EN 14214, manufactured by Rafineria Trzebinia S.A., and (iii) ON BIO 10, blend of 20 vol.% of biodiesel with 80 vol.% of standard petroleum diesel oil with sulphur content less than 10 mg/kg, also made by Rafineria Trzebinia S.A. Properties of diesel and biodiesel fuels are given in Table 1. 2.2. Ultrasonic speed measurements The speed of sound in liquids under test has been measured at atmospheric and higher pressures using two apparatus designed and constructed in our laboratory [15,16]. Two measuring vessels of the same acoustic path and construction have been used, one of them designed for measurements under atmospheric pressure, the other one for measurements under elevated pressures. A single transmitting–receiving ceramic transducer operating at 2 MHz and an acoustic mirror have been applied. The measuring sets
Table 1 Physical and chemical properties of diesel oil Ekodiesel Ultra, ON BIO10, and biodiesel Property Cetane number Cloud point Flash point Kinematic viscosity at 40 °C Water content Sulfur content Carbon residue on 10% distillation residue FAME content Oxidation stability at 110 °C Acid value Iodine value Linoleic acid methyl ester Methanol content Distillation at 101.3 kPa: 95% recovered up to Up to 250 °C recovered Up to 350 °C recovered
Units
Ekodiesel Ultra from PKN Orlen SA
ON BIO10 from RT SA
European standard for diesel EN 590
Biodiesel from RT SA
European standard for biodiesel-FAME EN 14214
°C °C mm2/s
54.1 14 65 2.7
51 10 68 2.88
>51 <0 >56 2.0–4.5
51.7 – >130 4.5
>51 – 120 3.5–5.0
mg/kg mg/kg % m/m
64 8.8 0.02
110 9.9 0.03
<200 <10 <0.3
88 9.7 0.04
<500 <10 <0.3
% m/m
–
17.7
5.0
97.5
>96.5
h mg of KOH/g g of I2/ 100g % m/m % m/m
– –
– –
<25 –
8.1 0.33
>6.0 <0.50
–
–
–
115
<120
– –
– –
– –
8.7 <0.05
<12 <0.20
°C vol.% vol.%
330 40 98
339 30 98
<360 <65 >85
– – –
– – –
M. Dzida, P. Prusakiewicz / Fuel 87 (2008) 1941–1948
operate on the principle of the pulse-echo-overlap method. The pressure was provided by a hand operated hydraulic press and was measured with a strain gauge measuring system (Hottinger Baldwin System P3MD) with accuracy better than 0.15%. The temperature was measured using an Ertco Hart 850 platinum resistance thermometer (traceable to a NIST standard) with an uncertainty of ±0.05 K and resolution of 0.001 K. The uncertainty of the speed of sound measurements was estimated to be 0.03% at atmospheric pressure, 0.04% under pressures up to 60 MPa and 0.05% under pressures from 60 MPa to 101 MPa.
1943
Other details of the high-pressure device and the method of the speed of sound measurements can be found in the previous papers [15,16]. 2.3. Density measurements The densities at atmospheric pressure were measured using a vibrating tube densimeter Anton Paar DMA 5000. The uncertainty of the density measurements was 0.05 kg m3, whereas the repeatability was estimated to be better than 0.005 kg m3.
Table 2 Speed of sound in diesel oil Ekodiesel Ultra, ON BIO10, and biodiesel measured at pressures up to 101 MPa within the temperature range 293–318 K Ekodiesel Ultra
ON BIO10
Biodiesel
T (K)
p (MPa)
u (m s1)
T (K)
p (MPa)
u (m s1)
T (K)
p (MPa)
u (m s1)
292.88 292.87 292.86 292.86 292.87 292.86 292.86 292.86 298.16 298.15 298.15 298.15 298.15 298.16 298.15 298.15 303.14 303.14 303.14 303.13 303.14 303.13 303.14 303.14 308.10 308.13 308.13 308.13 308.13 308.13 308.13 308.13 313.11 313.11 313.11 313.11 313.11 313.10 313.10 313.10 318.28 318.30 318.29 318.29 318.29 318.29 318.29 318.29
0.10 15.20 30.40 45.60 60.79 75.99 91.18 101.32 0.10 15.20 30.39 45.59 60.79 75.99 91.18 101.32 0.10 15.20 30.39 45.59 60.79 75.99 91.18 101.32 0.10 15.20 30.39 45.59 60.79 75.99 91.18 101.32 0.10 15.20 30.39 45.59 60.79 75.99 91.18 101.32 0.10 15.20 30.39 45.59 60.79 75.99 91.18 101.32
1370.76 1446.68 1513.41 1574.04 1630.60 1682.79 1731.94 1763.07 1350.67 1427.29 1494.57 1555.73 1613.02 1665.71 1715.26 1746.72 1331.91 1408.42 1477.07 1539.25 1597.12 1650.84 1700.62 1732.67 1313.30 1390.52 1460.51 1523.58 1581.90 1636.44 1686.91 1718.90 1294.68 1373.44 1444.26 1508.45 1567.18 1622.22 1673.14 1705.42 1275.61 1356.21 1428.16 1493.14 1552.45 1608.16 1659.76 1692.19
292.91 292.86 292.86 292.86 292.86 292.86 292.86 292.86 298.17 298.15 298.15 298.15 298.15 298.15 298.15 298.15 303.16 303.14 303.14 303.14 303.13 303.13 303.13 303.13 308.13 308.13 308.13 308.13 308.13 308.13 308.13 308.12 313.12 313.10 313.10 313.11 313.10 313.10 313.10 313.10 318.30 318.30 318.30 318.30 318.30 318.30 318.30 318.29
0.10 15.20 30.39 45.59 60.79 75.99 91.18 101.32 0.10 15.20 30.39 45.59 60.79 75.99 91.18 101.32 0.10 15.20 30.39 45.59 60.79 75.99 91.18 101.32 0.10 15.20 30.39 45.59 60.79 75.99 91.18 101.32 0.10 15.20 30.39 45.59 60.79 75.99 91.18 101.32 0.10 15.20 30.39 45.59 60.79 75.99 91.18 101.32
1379.57 1453.58 1518.94 1578.62 1634.08 1685.40 1733.72 1764.43 1359.69 1434.72 1500.96 1561.16 1617.66 1669.47 1717.81 1749.44 1341.03 1416.90 1484.09 1545.04 1602.03 1654.76 1703.72 1735.30 1322.58 1399.36 1467.83 1529.71 1586.94 1640.55 1690.06 1721.65 1304.19 1382.43 1451.79 1514.65 1572.56 1626.52 1676.69 1708.53 1285.28 1365.24 1435.71 1499.39 1557.67 1612.63 1663.24 1695.25
292.92 292.86 292.86 292.86 292.86 292.86 292.86 292.86 298.20 298.15 298.15 298.15 298.15 298.15 298.15 298.14 303.18 303.14 303.14 303.13 303.13 303.13 303.13 303.13 308.16 308.13 308.13 308.13 308.13 308.12 308.12 308.12 313.14 313.10 313.10 313.10 313.10 313.10 313.10 313.10 318.31 318.29 318.28 318.30 318.30 318.29 318.29 318.30
0.10 15.20 30.39 45.59 60.79 75.99 91.18 101.32 0.10 15.20 30.39 45.59 60.79 75.99 91.18 101.32 0.10 15.20 30.39 45.59 60.79 75.99 91.18 101.32 0.10 15.20 30.39 45.59 60.79 75.99 91.18 101.32 0.10 15.20 30.39 45.59 60.79 75.99 91.18 101.32 0.10 15.20 30.39 45.59 60.79 75.99 91.18 101.32
1414.95 1482.08 1541.36 1596.67 1647.96 1695.54 1741.08 1769.94 1395.70 1463.92 1524.19 1580.09 1632.20 1680.47 1726.16 1755.32 1377.71 1446.76 1508.29 1564.48 1617.60 1666.26 1712.43 1741.88 1359.86 1430.19 1492.54 1549.56 1602.96 1652.55 1698.72 1728.68 1342.10 1413.95 1477.24 1534.76 1588.66 1639.09 1685.83 1715.79 1323.81 1397.11 1461.47 1519.87 1574.29 1625.11 1672.44 1702.47
1944
M. Dzida, P. Prusakiewicz / Fuel 87 (2008) 1941–1948
Table 3 Densities and specific heat capacities of diesel oil Ekodiesel Ultra, ON BIO10, and biodiesel measured at atmospheric pressure Ekodiesel Ultra
ON BIO10
Biodiesel
T (K)
q (kg m )
T (K)
q (kg m )
T (K)
q (kg m3)
273.15 278.15 283.16 288.15 293.16 298.16 303.16 308.16 313.15 318.16 323.15 328.16 333.16 338.16 343.15 348.16 353.15 358.15 363.15
845.882 842.363 838.845 835.331 831.816 828.303 824.789 821.277 817.760 814.242 810.719 807.191 803.660 800.127 796.584 793.038 789.482 785.919 782.350
273.15 278.15 283.16 288.16 293.15 298.16 303.16 308.16 313.16 318.16 323.15 328.16 333.16 338.16 343.15 348.16 353.15 358.15 363.15
855.514 851.980 848.449 844.923 841.398 837.874 834.348 830.825 827.301 823.776 820.248 816.715 813.178 809.643 806.099 802.550 798.996 795.433 791.865
273.15 278.15 283.16 288.16 293.15 298.16 303.16 308.16 313.16 318.16 323.15 328.15 333.15 338.16 343.15 348.15 353.16 358.15 363.15
894.390 890.731 887.086 883.445 879.814 876.185 872.563 868.942 865.325 861.709 858.096 854.483 850.871 847.261 843.648 840.034 836.416 832.796 829.181
T (K) 282.60 283.14 288.14 293.15 298.14 303.15 308.14 313.16 318.15 323.14 328.15 333.14 338.15 343.14 348.16 353.15 358.14 358.97
3
Cp (J kg1 K1) 1895.2 1897.8 1916.5 1935.0 1952.7 1971.4 1990.5 2009.9 2028.7 2049.1 2068.6 2089.3 2109.0 2128.7 2147.4 2166.7 2186.0 2188.8
T (K) 282.67 283.14 288.14 293.15 298.14 303.15 308.14 313.14 318.15 323.14 328.15 333.14 338.15 343.14 348.16 353.15 358.14 358.97
3
Cp (J kg1 K1) 1899.1 1901.2 1919.2 1937.2 1954.6 1971.8 1990.2 2008.5 2026.3 2045.4 2064.6 2083.6 2102.5 2121.2 2139.7 2157.6 2175.4 2178.6
T (K) 282.51 283.14 288.14 293.15 298.16 303.15 308.14 313.16 318.15 323.16 328.15 333.14 338.15 343.14 348.16 353.15 358.14 358.97
Cp (J kg1 K1) 1942.7 1945.6 1959.4 1971.9 1985.2 1998.5 2013.1 2028.1 2042.3 2057.6 2073.1 2088.9 2104.6 2119.6 2134.5 2148.5 2163.7 2165.9
Table 4 Coefficients of polynomial Eq. (1) for the speed of sound, density, and specific isobaric heat capacity, respectively and mean deviations from the regression line Fuel
c0 (m s1)
c1 (m s1 K1)
Ekodiesel Ultra ON BIO10 Biodiesel
2727.370 2749.493 2717.464
5.446246 5.564141 5.234999
Ekodiesel Ultra ON BIO10 Biodiesel
q0 (kg m3) 1032.289 1044.171 1095.576
q1 (kg m3 K1) 0.6653943 0.6788419 0.7461680
q2 Æ 105 (kg m3 K2) 6.27435 4.36606 3.48745
Ekodiesel Ultra ON BIO10 Biodiesel
h0 (J kg1 K1) 1035.764 1033.153 1547.327
h1 (J kg1 K2) 2.388477 2.573437 –
h2 Æ 103 (J kg1 K3) 2.31209 1.73489 5.47687
2.4. Specific heat capacity measurements The specific isobaric heat capacity was measured by a high sensitivity differential scanning calorimeter Micro DSC III,
c2 Æ 103 (m s1 K2)
du0 (m s1)
2.78037 3.02869 2.69146
0.009 0.002 0.004 dq (kg m3) 0.016 0.016 0.015 h2 Æ 106 (J kg1 K4) – – 1.82282
dCp (J kg1 K1) 0.8 0.8 1.0
manufactured by Setaram and based on the Tian-Calvet principle. The uncertainty of the measurements was estimated to be ± 0.15%. More details of the measuring set, calibration and measurement procedure can be found in [17].
M. Dzida, P. Prusakiewicz / Fuel 87 (2008) 1941–1948 Table 5 Coefficients of Eq. (2) and mean deviations from the regression line du Fuel
j
a1j (Kj MPa s m1)
Ekodiesel Ultra
0 1 2
0.2620890650
ON BIO10
Biodiesel
– 8.70894267Æ107
a2j (Kj MPa s2 m2) 2.67267574Æ104
du (m s1) 0.51
– 1.00348744Æ109
0 1 2
0.2822989252
2.48484590Æ104
– 1.05453199Æ106
– 7.36412361Æ1010
0 1 2
0.3301165804 – 1.34877055Æ106
2.56840831Æ104 1.95352490Æ107 –
0.26
0.26
1945
3. Measurement results The ultrasonic speeds in diesel oil Ekodiesel Ultra, ON BIO10, and biodiesel were measured at temperatures from 293 to 318 K in about 5 K steps and under pressures 0.1, 15, 30, 45, 60, 75, 90, and 101 MPa. The experimental values are listed in Table 2. The densities of the fuels and biofuels were measured under atmospheric pressure in the temperature range from 273 to 363 K in 5 K steps. The experimental values are collected in Table 3. The specific isobaric heat capacities were measured at atmospheric pressure and at temperatures from 283 to 359 K in about 0.02 K steps. Thus it has given ca. 3400 experimental points
Table 6 The calculated densities of diesel oil Ekodiesel Ultra, ON BIO10, and biodiesel at pressures up to 100 MPa and within the temperature limits 293 and 318 K
Table 7 The calculated isobaric specific heat capacities of diesel oil Ekodiesel Ultra, ON BIO10, and biodiesel at pressures up to 100 MPa and within the temperature limits 293 and 318 K
q (kg m3)
Cp (J kg1 K1)
p (MPa)
T (K) 293.15
p (MPa) 298.15
303.15
308.15
313.15
298.15
303.15
308.15
313.15
318.15
814.24 821.17 827.61 833.59 839.18 844.44 849.41 854.13 858.63 862.93 867.05
Ekodiesel Ultra 0.1a 1935 10 1930 20 1926 30 1923 40 1921 50 1919 60 1918 70 1917 80 1916 90 1916 100 1915
1953 1948 1945 1942 1940 1938 1937 1936 1935 1934 1934
1972 1967 1963 1960 1958 1956 1955 1954 1953 1953 1952
1991 1986 1982 1979 1977 1975 1974 1973 1972 1971 1971
2010 2005 2001 1998 1995 1994 1992 1991 1990 1990 1989
2030 2024 2020 2017 2014 2012 2011 2010 2009 2009 2008
827.31 833.97 840.18 845.97 851.40 856.52 861.38 866.00 870.41 874.63 878.69
823.78 830.60 836.96 842.87 848.41 853.62 858.56 863.26 867.74 872.03 876.14
ON BIO10 0.1a 10 20 30 40 50 60 70 80 90 100
1937 1932 1929 1926 1924 1922 1920 1919 1918 1917 1917
1955 1950 1946 1943 1941 1939 1938 1937 1936 1935 1934
1973 1968 1964 1961 1959 1957 1956 1954 1953 1953 1952
1991 1986 1982 1979 1977 1975 1973 1972 1971 1970 1970
2009 2004 2000 1997 1995 1993 1991 1990 1989 1988 1987
2028 2022 2018 2015 2013 2011 2009 2008 2007 2006 2005
865.33 871.66 877.61 883.20 888.48 893.48 898.25 902.80 907.16 911.35 915.39
861.71 868.19 874.28 879.98 885.35 890.45 895.29 899.91 904.34 908.59 912.68
Biodiesel 0.1a 10 20 30 40 50 60 70 80 90 100
1972 1968 1965 1963 1961 1960 1958 1957 1956 1956 1955
1986 1982 1979 1977 1975 1973 1972 1971 1970 1969 1968
2000 1996 1993 1990 1988 1987 1986 1984 1984 1983 1982
2014 2010 2007 2004 2002 2001 1999 1998 1997 1997 1996
2028 2024 2021 2018 2016 2015 2013 2012 2011 2011 2010
2043 2039 2035 2033 2031 2029 2028 2027 2026 2025 2024
Ekodiesel Ultra 0.1a 831.84 10 837.94 20 843.67 30 849.04 40 854.09 50 858.88 60 863.43 70 867.77 80 871.92 90 875.91 100 879.74
828.32 834.58 840.45 845.93 851.09 855.97 860.60 865.02 869.24 873.29 877.18
824.81 831.23 837.23 842.83 848.10 853.07 857.79 862.28 866.57 870.68 874.63
821.29 827.87 834.02 839.74 845.12 850.18 854.98 859.55 863.91 868.08 872.09
817.77 824.52 830.81 836.66 842.14 847.30 852.19 856.84 861.27 865.50 869.57
ON BIO10 0.1a 10 20 30 40 50 60 70 80 90 100
841.42 847.44 853.12 858.43 863.45 868.21 872.73 877.05 881.19 885.17 888.99
837.89 844.07 849.87 855.31 860.42 865.27 869.88 874.27 878.48 882.52 886.40
834.37 840.70 846.64 852.19 857.41 862.34 867.03 871.51 875.78 879.88 883.82
830.84 837.33 843.41 849.07 854.40 859.43 864.20 868.75 873.09 877.25 881.25
Biodiesel 0.1a 10 20 30 40 50 60 70 80 90 100
879.83 885.59 891.05 896.21 901.10 905.76 910.21 914.47 918.57 922.52 926.33
876.21 882.10 887.68 892.94 897.93 902.67 907.20 911.54 915.70 919.71 923.57
872.58 878.61 884.32 889.69 894.77 899.60 904.21 908.61 912.84 916.91 920.83
868.96 875.13 880.96 886.44 891.62 896.54 901.22 905.70 910.00 914.13 918.10
a
Calculated from Eq. (1).
318.15
T (K) 293.15
a
Calculated from Eq. (1).
1946
M. Dzida, P. Prusakiewicz / Fuel 87 (2008) 1941–1948
for each liquid. Therefore the values of isobaric specific heat capacity every 5 K are collected in Table 3. The dependencies of the speed of sound, density, and isobaric specific heat capacity on temperature at atmospheric pressure were approximated by second-order polynomials of the type: y¼
2 X
bj T j ;
ð1Þ
In order to calculate the density at p2, q, ap and Cp at p1 should be known beside the speed of the ultrasound as a function of pressure. The change of the heat capacity within the pressure limits Dp is given by: " # T 2 oap DC p ap þ Dp: ð5Þ q oT p
j¼0
where y is the speed of sound, u0, density, q, or isobaric specific heat capacity, Cp, at atmospheric pressure p0; bj are the polynomial coefficients bj = cj for the speed of sound, bj = qj for the density, and bj = hj for the isobaric specific heat capacity) calculated by the least squares method. The backward stepwise rejection procedure was used to reduce the number of non-zero coefficients. The coefficients and standard deviations from the regression lines are given in Table 4. The standard deviations are much smaller than the measurements accuracy. Since the sensitivity of the pressure gauge is lower than that of both the ultrasonic apparatus and the thermometer, the equation suggested by Sun et al. [7] was chosen in this work for smoothing out the speed of sound, pressure and temperature: p p0 ¼
m X n X i¼1
A numerical procedure proposed by Sun et al. [7] slightly modified by Marczak et al. [9] was applied. Details of the algorithm were discussed in previous work [9]. The densities and isobaric heat capacities of the fuels under test were calculated for temperatures from 293.15 to 318.15 K and for pressures up to 100 MPa. The calculated density and isobaric specific heat capacity are listed in Tables 6 and 7, respectively. From the densities and Table 8 The isentropic bulk modulus of diesel oil Ekodiesel Ultra, ON BIO10, and biodiesel at pressures up to 100 MPa and within the temperature limits 293 and 318 K bS Æ 106 (Pa) p (MPa)
T (K) 293.15
i
aij ðu u0 Þ T j ;
ð2Þ
j¼0
where aij are the polynomial coefficients calculated by the least squares method, u is the speed of sound at p > 0.1 MPa, u0 is the speed calculated from Eq. (1). The coefficients aij and the mean deviations from the regression lines are given in Table 5. The stepwise rejection procedure was used to reduce the number of the non-zero coefficients. 4. Physicochemical properties at elevated pressures The pressure dependence of the density is given by the following thermodynamic relationship: oq 1 T a2p ¼ 2þ ; ð3Þ op T u Cp where ap is the isobaric thermal expansion calculated from definition: ap ¼ ð1=qÞðoq=oT Þp . The change of the density of the liquid Dq, caused by a pressure increase from p1 to p2 at constant temperature, can be calculated by integration: ! Z p2 Z p2 a2p T 1 a2p T 1 Dq ¼ þ dp þ Dp: ð4Þ dp 2 u2 C p Cp p1 p1 u The approximate relationship Eq. (4) is sufficiently accurate, provided Dp is small enough, because the heat capacity depends rather slightly on pressure. Moreover, the first term on the right hand side of Eq. (4) is significantly larger than the second one since the latter results from the difference between the isentropic and isothermal compressibility that is small in comparison with both the compressibilities.
298.15
303.15
308.15
313.15
318.15
Ekodiesel Ultra 0.1 1561 10 1690 20 1815 30 1937 40 2055 50 2170 60 2283 70 2394 80 2504 90 2611 100 2718
1511 1640 1765 1886 2004 2119 2231 2342 2451 2559 2665
1463 1591 1716 1836 1954 2068 2181 2292 2401 2508 2615
1416 1544 1668 1788 1905 2020 2132 2243 2352 2459 2565
1370 1498 1622 1742 1858 1973 2085 2195 2304 2411 2518
1326 1453 1576 1696 1813 1927 2039 2149 2258 2366 2472
ON BIO10 0.1 10 20 30 40 50 60 70 80 90 100
1599 1728 1853 1974 2091 2206 2319 2430 2539 2646 2752
1549 1678 1802 1923 2040 2155 2267 2378 2487 2594 2700
1501 1629 1753 1874 1991 2105 2217 2328 2436 2543 2649
1453 1581 1706 1826 1943 2057 2169 2279 2387 2494 2600
1407 1535 1659 1779 1896 2010 2122 2232 2340 2447 2553
1362 1490 1614 1734 1851 1965 2076 2186 2295 2402 2507
Biodiesel 0.1 10 20 30 40 50 60 70 80 90 100
1759 1884 2005 2123 2238 2351 2461 2570 2677 2783 2887
1707 1832 1953 2071 2186 2298 2408 2517 2624 2729 2834
1656 1781 1903 2020 2135 2247 2357 2466 2572 2678 2782
1607 1732 1853 1971 2086 2198 2308 2416 2522 2627 2731
1559 1684 1805 1923 2038 2150 2259 2367 2474 2579 2682
1511 1637 1759 1876 1991 2103 2213 2321 2427 2532 2635
M. Dzida, P. Prusakiewicz / Fuel 87 (2008) 1941–1948
5. Discussion The densities of the fuels and biofuels increase monotonically with increasing pressure and decreasing temperature. Temperature dependence of densities of the fuels and biofuels is described by the second-order polynomials (Table 4) while pressure dependence is described by the thirdorder polynomial. Respective slopes of the curves are practically the same. Nevertheless, densities of ON BIO 10 and diesel oil Ekodiesel Ultra are lower than densities of biodiesel, over the whole temperature and pressure range, by about 4.6–4.2% and 5.8–5.3%, respectively. The isobaric specific heat capacity of the fuels decreases with increasing pressure and decreasing temperature. However, the effect of pressure is smaller than that of temperature (Table 7). Difference between isobaric specific heat capacities of diesel oil Ekodiesel Ultra and ON BIO 10 are negligible over the whole temperature and pressure range. The heat capacity of biodiesel is higher than that of diesel oil Ekodiesel Ultra and ON BIO 10 by 2% at the most (Tables 3 and 7). Isobaric thermal expansivity of biodiesel decreases with pressure slightly less than that of the diesel oil Ekodiesel Ultra. It is approximately independent of temperature and composition of the fuel at pressures 40 ± 5 MPa (Fig. 1). The crossing point of isobaric thermal expansion is characteristic for simple liquids. For example, the isotherms of ap of hexane cross each other at 65 ± 2 MPa [18]. However, taking into account the uncertainty of the thermal expansion coefficient equals ± 1%, there is not sig-
nificant difference between ap of all the tested fuels. At temperatures from 293.15 to 318.15 K and pressures from atmospheric one to 100 MPa, the bulk moduli of biodiesel and ON BIO 10 were higher than that of diesel oil Ekodiesel Ultra by 6.2–14.0% and 1.3–2.7%, respectively (Fig. 2 a). Temperature change by 5 K changes the bulk modulus by 1.9–3.1% and by 1.8–3.3% for biodiesel and ON BIO 10, respectively. Thus, the effect of addition of biodiesel to the petroleum fuel on the bulk modulus is of the same order as that resulting from the slight change of temperature (Fig. 2b). With temperature increasing from 293.15 to 318.15 K, at atmospheric pressure, the bulk moduli decrease in a similar way for the diesel oil Ekodiesel Ultra and ON BIO 10: from 1561 to 1325 MPa and from 1599 to 1361 MPa, respectively. These ranges almost overlap each other. Thus, although the bulk modulus of ON BIO 10 is indeed higher than that of diesel oil Ekodiesel Ultra, the difference is rather small and can be compensated by temperature. Similar conclusion is valid for pressures up to100 MPa. These results show that effect of temperature on the bulk modulus should be taken into account over the whole pressure range.
3000
2500
Β S / MPa
speeds of sound, the adiabatic bulk modulus (the reciprocal of adiabatic compressibility jS) were calculated by the 2 1 Laplace formula: B1 S ¼ jS ¼ ðqu Þ . Results of the calculations are given in Table 8. The isothermal compressibility ðjT ¼ jS þ a2p T =qC p Þ and isothermal bulk modulus ðjT ¼ B1 T Þ can be also calculated from the above data.
1947
2000
1500
1000
0
20
40
60
80
100
60
80
100
p / MPa 0.9
3000
293.15 K
2500
Β S / MPa
α p · 10 3/ K -1
0.8
0.7
2000
1500 318.15 K
0.6
0
20
40
60
80
100
p / MPa
Fig. 1. Isobaric thermal expansion of: diesel oil Ekodiesel Ultra: (d) 293.15 K, (s) 318.15 K; ON BIO 10: (j) 293.15 K, (h) 318.15 K; Biodiesel (m) 293.15 K, (4) 318.15 K, lines calculated from empirical P function: ap ¼ 3i¼0 ai pi .
1000 0
20
40
p / MPa
Fig. 2. Isentropic bulk modulus of : a) diesel oil Ekodiesel Ultra: (d) 293.15 K, (s) 318.15 K; ON BIO 10: (j) 293.15 K, (h) 318.15 K; Biodiesel (m) 293.15 K, (4) 318.15 K; b) (s) diesel oil Ekodiesel P Ultra; (h) ON BIO 10; lines calculated from empirical function: Bs ¼ 3i¼0 ai pi .
1948
M. Dzida, P. Prusakiewicz / Fuel 87 (2008) 1941–1948
6. Conclusions 1. Investigated fuels and biofuels differ in density. That facilitates telling one fuel from another. 2. Isobaric specific heat capacity of biodiesel is higher than those of diesel oil Ekodiesel Ultra and ON BIO 10 that are approximately the same in the temperature range from 293.15 to 318.15 K and pressures up to 100 MPa. 3. Isobaric thermal expansions of the three investigated fuels are approximately equal to each other and independent of temperature at pressures 40 ± 5 MPa. 4. Increase of bulk modulus of petrodiesel due to addition of 20 vol.% of biodiesel is small. It is approximately the same as that caused by decrease of temperature by ca. 5 K. That probably holds even for pressures much higher than 100 MPa attained in this experiment. Acknowledgements The authors are profoundly indebted to Dr. W. Marczak for critical reading of the manuscript and Ms. M. Bucek for the participation in the density measurements. References [1] Tat ME, Van Gerpen JH, Soylu S, Canakci M, Monyem A, Wormley SJ. The speed of sound and isentropic bulk modulus of biodiesel at 21 °C from atmospheric to 35 MPa. Am Oil Chem Soc 2000;77:285–9. [2] Tat ME, Van Gerpen JH. Effect of temperature and pressure on the speed of sound and isentropic bulk modulus of mixtures of biodiesel and diesel fuel. J Am Oil Chem Soc 2003;80:1127–30. [3] Szybist JP, Boehman AL, Taylor JD, McCormick RL. Evaluation of formulation strategies to eliminate the biodiesel NOx effect. Fuel Proc Technol 2005;86:1109–26. [4] Boehman AL, Morris D, Szybist JP. The impact of the bulk modulus of diesel fuels on fuel injection timing. Energ Fuels 2003;18:1877–82. [5] Kegl B. Numerical analysis of injection characteristics using biodiesel fuel. Fuel 2006;85:2377–87.
[6] Forson FK, Oduro EK, Hammond-Donkoh E. Performance of jatropha oil blends in a diesel engine. Renew Energ 2004;29:1135–45. [7] Sun TF, Ten Seldam CA, Kortbeek PJ, Trappeniers NJ, Biswas SN. Acoustic and thermodynamic properties of ethanol from 273.15 to 333.15 K and up to 280 MPa. Phys Chem Liq 1988;18:107–16. [8] Davis LA, Gordon RB. Compression of mercury at high pressure. J Chem Phys 1967;46:2650–60. [9] Marczak W, Dzida M, Ernst S. Determination of the thermodynamic properties of 1-propanol and 1-hexanol from speed of sound measurements under elevated pressures. High Temp – High Press 2000;32:283–92. [10] Plantier F, Daridon JL, Lagourette B. Nonlinear parameter (B/A) measurements in methanol, 1-butanol and 1-octanol for different pressures and temperatures. J Phys D: Appl Phys 2002;35:1063–7. _ [11] Dzida M, Zak A, Ernst S. Thermodynamic and acoustic properties of binary mixtures of alcohols and alkanes. I. Speed of sound in (ethanol + n-heptane) under elevated pressures. J Chem Thermodyn 2005;37:405–14. [12] Dzida M, Marczak W. Thermodynamic and acoustic properties of binary mixtures of alcohols and alkanes. II. Density and heat capacity of (ethanol + n-heptane) under elevated pressures. J Chem Thermodyn 2005;37:826–36. [13] Tate RE, Watts KC, Allen CAW, Wilkie KI. The densities of three biodiesel fuels at temperatures up to 300 °C. Fuel 2006;85:1004–9. [14] Yamate K, Ueta A, Shimamoto Y. Influence of physical and chemical properties of biodiesel fuel on injection, combustion and exhaust emission characteristics in a DI-CI Engine. In: The fifth international symposium on diagnostics and modeling of combustion in internal combustion engines (COMODIA 2001), July 1–4, 2001, Nagoya; p. 402–9. _ [15] Zak A, Dzida M, Zore˛bski M, Ernst S. A high pressure system for measurements of the speed of sound in liquids. Rev Sci Instrum 2000;71:1756–65. [16] Dzida M, Chora˛z_ ewski M, Zore˛bski M, Man´ka R. Modification of a high pressure device for speed of sound measurements in liquids. J Phys IV 2006;137:203–7. [17] Go´ralski P, Tkaczyk M, Chora˛z_ ewski M. Heat capacities of a,xdichloroalkanes at temperatures from 28415 K to 353.15 K and a group additivity analysis. J Chem Eng Data 2003;48:492–6. [18] Randzio SL, Grolier J-PE, Quint JR, Eatough DJ, Lewis EA, Hansen LD. n-hexane as a model for compressed simple liquids. Int J Thermophys 1994;15:415–41.