Reference correlations for the density and viscosity of squalane from 273 to 473 K at pressures to 200 MPa

Reference Correlations for the Density and Viscosity of Squalane from 273 to 473 K at pressures to 200 MPa Sofia K. Mylona, Marc J. Assael Laboratory of Thermophysical Properties and Environmental Processes, Chemical Engineering Department, Aristotle University, Thessaloniki 54124, Greece María J. P. Comuñas, Xavier Paredes, Félix M. Gaciño, Josefa Fernándeza) Laboratorio de Propiedades Termofísicas, Departamento de Física Aplicada, Universidade de Santiago de Compostela, E-15782 Santiago de Compostela, Spain Jean Patrick Bazile, Christian Boned,a) Jean Luc Daridon, Guillaume Galliero, Jêrome Pauly Laboratoire des Fluides Complexes et leurs Reservoirs (UMR-5150 with CNRS and TOTAL), Université de Pau et des Pays de l'Adour, BP 1155, F-64013 Pau Cedex, France Kenneth R. Harris School of Physical, Environmental and Mathematical Sciences, University College, University of New South Wales, P.O. Box 7916, Canberra BC, ACT 2610, Australia This paper presents new reference correlations for both the density and viscosity of squalane at high pressure. These correlations are based on critically evaluated experimental data taken from the literature. In the case of the density, the correlation, based on the Tait equation, is valid from 273 to 473 K at pressures to 200 MPa. At 0.1 MPa, it has an average absolute deviation of 0.03%, a bias of -0.01%, and an expanded uncertainty (at the 95% confidence level) of 0.06%. Over the whole range of pressures, the density correlation has an average absolute deviation of 0.05%, a bias of -0.004%, and an expanded uncertainty (at the 95% confidence level) of 0.18%. In the case of the viscosity, two correlations are presented, one a function of density and temperature, based on the Assael-Dymond model, and the other a function of temperature and pressure, based on a modified Vogel-Fulcher-Tammann equation. The former is slightly superior to the latter at high temperatures (above 410 K), whereas the reverse is true at low temperatures, where the viscosity is strongly temperature dependent. In the temperature range from 320 to 473 K at pressures to 200 MPa, the first correlation has an average absolute deviation of 1.41%, a bias of -0.09%, and an expanded uncertainty (at the 95% confidence level) of 3%. Below 320 K, deviations from the present scheme rise to a maximum of 20%. In the temperature range from 278 to 473 K at pressures to 200 MPa the second viscosity correlation has an average absolute deviation of 1.7%, a bias of -0.04%, and an expanded uncertainty (at the 95% confidence level) of 4.75%. Key words: density; reference correlation; squalane; transport properties; viscosity; pressure. a)Authors to whom correspondence should be addressed electronic addresses: [email protected] and [email protected]. CONTENTS 1. Introduction 2. The Density Correlation 2.1. The Density Correlation for 0.1 MPa 2.2. The Density Correlation for High Pressure 3. The High Pressure Viscosity Correlation 3.1. Viscosity Correlation as a Function of Density and Temperature 3.2. Viscosity Correlation as a Function of Temperature and Pressure 4. Conclusion Acknowledgments 5. References List of Tables 1. Density measurements for squalane at 0.1 MPa. 2. Evaluation of the squalane density correlation for the primary data at 0.1 MPa. 3. Density measurements for squalane at high pressures. 4. Evaluation of the squalane density correlation for the primary data at high pressures. 5. Viscosity measurements for squalane at high pressures. 6. Evaluation of the squalane viscosity correlation as a function of density and temperature for the primary data in the temperature range 320 to 473 K at pressures to 200 MPa. 7. Parameters and relative deviations for the VFT model, Eq. (7). 8. Evaluation of the squalane viscosity correlation as a function of pressure and temperature for the primary data in the temperature range 278 to 473 K at pressures to 200 MPa. 9. Some selected reference values List of Figures 1. Percentage deviations for the primary density data as a function of temperature at 0.1 MPa, from the values calculated from Eq. (1). 2. Percentage deviations for the secondary density data as a function of temperature at 0.1 MPa, from the values calculated from Eq. (1). 3. Percentage deviations for the primary density data at high pressures, as a function of density, from the values calculated from Eqs. (1) – (3). 4. Percentage deviations for the primary density data at high pressures, as a function of temperature, from the values calculated from Eqs. (1) – (3). 5. Percentage deviations for the primary density data at high pressures, as a function of pressure, from the values calculated from Eqs. (1) – (3). 6. Temperature and pressure coordinates of data points retained for the primary viscosity correlations 7. Percentage deviations for the primary viscosity data in the temperature range 320 to 473 K and up to 200 MPa, as a function of density, from the values calculated from Eqs. (1) – (6). 8. Percentage deviations for the primary viscosity data in the temperature range 320 to 473 K and up to 200 MPa, as a function of temperature, from the values calculated from Eqs. (1) – (6). 9. Percentage deviations for the primary viscosity data in the temperature range 320 to 473 K and up to 200 MPa, as a function of pressure, from the values calculated from Eqs. (1) – (6). 10. Percentage deviations for the primary viscosity data in the temperature range 278 to 473 K and up to 200 MPa, as a function of temperature, from the values calculated from Eqs. (1) – (6). 11. Percentage deviations for the secondary viscosity data in the temperature range 278 to 473 K and up to 200 MPa, as a function of temperature, from the values calculated from Eqs. (1) – (6). 12. Percentage deviations for the primary viscosity data in the temperature range 278 to 473 K and up to 200 MPa, as a function of density, from the values calculated from Eq. (7). 13. Percentage deviations for the primary viscosity data in the temperature range 278 to 473 K and up to 200 MPa, as a function of temperature, from the values calculated from Eq. (7). 14. Percentage deviations for the primary viscosity data in the temperature range 278 to 473 K and up to 200 MPa, as a function of pressure, from the values calculated from Eq. (7). 15. Percentage deviations for the secondary viscosity data in the temperature range 278 to 473 K and up to 200 MPa, as a function of temperature, from the values calculated from Eq. (7). 1. Introduction Most of the instruments for the measurement of viscosity require calibration and, for that purpose, certified reference liquids can be obtained commercially covering wide ranges of viscosity. Unfortunately, these viscosity standards are certified only for use at standard atmospheric pressure and their viscosities at high pressures are not generally available. There is therefore a need for fluids that can serve as viscosity reference standards at high pressures. In the oil industry, the viscosities of petroleum fluids are often measured under conditions of reservoir temperatures and pressures and, with ever deeper reservoirs being exploited, this necessitates calibration under similar conditions. The present work is aimed at establishing squalane as a viscosity reference material applicable at pressure - to 200 MPa and at temperature to 473 K. The choice of a reference liquid involves several considerations. Ideally, it should be a single substance available commercially, with high chemical purity and at a reasonable cost. It should be chemically stable at the maximum working temperature, and should not be hygroscopic, toxic, nor excessively volatile. These requirements are difficult to satisfy even for a single area of application. However, for work on petroleum oils and similar applications, squalane appears to be a good choice as it satisfies all of the above criteria and has a viscosity of the order of 1 mPa∙s at T = 473 K. Recently, a correlation for the viscosity of squalane (C30H62, 2,6,10,15,19,23hexamethyltetracosane, CAS No. 111-01-3) at standard atmospheric pressure was reported by our group.1 This extends over the temperature range 273 to 373 K. Since then, new data have been published2, 3 and, in any event, there is a need to extend the correlation to high pressures and higher temperatures. Accordingly, in this work two new correlations are proposed that extend the temperature range to 473 K and that are applicable at pressures from 0.1 to 200 MPa. One is a function of density and temperature, based on the Assael-Dymond model, and the other a function of temperature and pressure, and is based on a modified Vogel-Fulcher-Tammann equation (VFT). As the first correlation is based on density, we have also critically examined high pressure density data in the literature and correlated the density over the same range of temperature and pressure as the viscosity, using the Tait equation. TABLE 1. Density measurements for squalane at 0.1 MPa 1st author Year published Technique employeda Purity (%) Uncertainty (%) No. of points used Temperature Range (K) Primary Data Fernández4 2013 OT 99.0 0.06 19 278-373 Fandiño5 2010 VT 99.0 0.1 3 298-348 Trusler3 2010 VW 99.0 0.2 2+6b 338-473 Harris6 2009 VT 99.0 0.006 12 273-363 Fandiño7 2005 VT 99.0 0.01 9 278-353 Tripathi8 2005 PC > 99.0 0.07 1 298 Fermeglia9 1999 VT 99.0 0.004 1 298 Kumagai10 1995 PC >99.0 0.04 3 293-333 Korosi11 1981 PC na 0.04-0.08 4 293-473 Secondary Data Korotkovskii12 2012 QD 99.5 0.01 28 298-413 Hata13 2010 na na na 1 288 Dubey14 2008 VT 99.0 0.25 3 298-308 Kumagai15 2006 GP na 0.4 3 293-333 Graaf16 1992 WB 99.0 0.5 9 293-473 Kuss17 1970 GP na 4.0 4 298-353 Sax18 1957 na 99.9 0.004 1 293 aVW, Vibrating-Wire Densimeter; VT, Vibrating-Tube Densimeter; GP, Glass Piezometer; na, not given; PC, Pycnometer; OT, Oscillating-Tube Viscometer; QD, Quartz Densimeter; WB, Westphal balance. bThese data have been extrapolated from high pressure density values. 2. The Density Correlation 2.1. The Density Correlation for 0.1 MPa Table 1 lists, to the best of our knowledge, all the investigators who have measured the density of squalane at 0.1 MPa. We note the following points about the various sets of data in the table. The measurements of Tomida et al.19 are excluded from the correlation as these are values interpolated from the 2006 measurements of Kumagai et al.15 These latter authors15 re-measured densities in 2006 as a function of pressure, but the values quoted are of inferior uncertainty to those determined in 1995 by this group.10 Therefore we have only used the 1995 measurements for the primary data set at 0.1 MPa with the exception of one density value at 273 K that is inconsistent with the rest of the data. We consider a datum to be inconsistent with the primary database when the residual is more than twice the standard deviation of the fit. The single measurement of Lal et al.20 has been excluded, as this value was republished by Tripathi.8 The data of Ciotta et al.21 were also excluded as the measurements were made at much higher pressures and could not be safely extrapolated to 0.1 MPa. The measurements of Dubey and Sharma,14 Kuss and Taslimi,17 and Graaf et al.16 were excluded from the primary data set as they were of inferior uncertainties, 0.25, 4.0, 0.5% respectively. The measurements of the first authors were re-published by Dubey et al.22 Hata and Tamoto13 quote no uncertainty for their single measurement, and this was placed in the secondary data set. The data of Korotkovskii et al.12 show a distinctively different dependence on temperature to those of all other investigators, and thus these have also been considered as secondary data. The single measurement of Sax and Stross,18 was also excluded as insufficient information was given about the technique employed. The remaining data3-11 listed in Table 1, all obtained with very low uncertainties, form the primary data set. We note that the measurements of Trusler3 are extrapolated from high pressure isotherms to 0.1 MPa, though without any apparent increase of uncertainty. Temperatures for all the data were converted to the ITS-90 temperature scale.23 The primary data were fitted to an equation for the density, ρo in kg/m3, as a function of the absolute temperature, T in K, as 0996.28-0.6402 T  = . (1) This equation represents the selected primary data at 0.1 MPa from 273 K to 473 K. The percentage deviations of the experimental values from the values calculated by Eq.(1) are shown in Figure 1. Table 2 summarizes comparisons of the primary data with the correlation. We have defined the percent deviation as PCTDEV = 100(ρο,exp− ρο,fit)/ ρο,fit, where ρο,exp is the experimental value of the density and ρο,fit is the value calculated from the correlation. Thus, the average absolute percent deviation (AAD) is found with the expression AAD = (∑│PCTDEV│)/n, where the summation is over all n points, and the bias, as a percentage, is found with the expression bias = (∑PCTDEV)/n. The average absolute deviation of the fit is 0.03%, the bias -0.01%, and the expanded uncertainty at the 95% confidence level is 0.06%. The maximum deviation is 0.08% for a data point from Korosi and Kovats11 at 293.15 K. Figure 2 shows the percentage deviations of the secondary density data as a function of the temperature at 0.1 MPa, from the values calculated from Eq. (1). The same figure also includes the recommended values for the density of squalane from the American Petroleum Institute (API),24 as well as the densities reported in the US National Institute of Science and Technology (NIST) Thermodynamic Research Center (TRC)25 correlation tables. It is worthwhile noting that the recommended values from API24 agree with the proposed correlation within 0.2%, and that the values reported in the NIST/TRC25 tables agree within 0.5%. Figure 1. Percentage deviations for the primary density data as a function of temperature at 0.1 MPa, from the values calculated from Eq. (1): () Fernández et al.,4 (+), Fandiño et al.,5 (◼) Trusler et al.,3 (▲) Harris.6 (⚫) Fandiño et al.,7 () Tripathi,8 () Fermeglia and Torriano,9 () Kumagai and Takahashi,10 and ( ) Korosi and Kovats.11 TABLE 2. Evaluation of the squalane density correlation for the primary data at 0.1 MPa 1st Author Year Publ. AAD (%) Bias (%) Fernández4 2013 0.02 0.02 Fandiño5 2010 0.05 -0.05 Trusler3 2010 0.04 0.00 Harris6 2009 0.02 0.02 Fandiño7 2005 0.03 -0.03 Tripathi8 2005 0.00 0.00 Fermeglia9 1999 0.03 -0.03 Kumagai10 1995 0.04 -0.04 Korosi11 1981 0.05 -0.01 Entire data set 0.03 -0.01 Figure 2. Percentage deviations for the secondary density data as a function of temperature at 0.1 MPa, from the values calculated from Eq. (1). () Korotkovskii et al.,12 (⚫) Hata and Tamoto,13 (+) Dubey and Sharma,14 () Kumagai et al.,15 () Graaf et al.,16 () Kuss and Taslimi,17 (◼) Sax and Stross,18 () API,24 and ( ___ ) NIST/TRC.25 2.2. Density Correlation for High Pressure Table 3 indicates all the investigators who have measured the density of squalane above atmospheric pressure. The investigations3, 5, 7, 15, 21 that contributed to the primary data for the 0.1 MPa correlation,1 also make up the primary data set here. In addition, the data of Kuss and Taslimi,17 are included as primary values as they cover a very wide pressure range. The densities from Trusler et al.3 at pressures lower than 2 MPa were also not considered as they are inconsistent with the remaining points on the corresponding isotherms. In the case of the measurements by Ciotta et al.,21 the densities at 303.18 K and 15.58, 35.79, 45.77 and 55.77 MPa, as well as at 348.13 K and 115.8, 145.9 and 175.12 MPa, were excluded, as they are inconsistent with the rest of that data set. TABLE 3. Density measurements for squalane at high pressures 1st author Year published Technique employeda Purity (%) Uncertainty (%) No. of data used Temperature Range (K) Pressure Range (MPa) Fandiño5 2010 VT 99.0 0.7-1.0 50 298-398 1-60 Trusler3 2010 VW 99.0 0.2-0.6 70 338-473 21-202 Ciotta21 2009 VW 99.0 0.2-0.6 25 303-448 1-176 Kumagai15 2006 GP na 0.4 12 273-333 10-30 Fandiño7 2005 VT 99.0 0.01 90 278-353 1-45 Kuss17 1970 GP na 0.4 20 298-353 39-196 aGP, Glass Piezometer; VT, Vibrating-Tube Densimeter; VW, Vibrating-Wire Densimeter; na, not given. Temperatures for all data were converted to the ITS-90 temperature scale.23 The primary data were fitted to a Tait equation for the density, ρ in kg/m3, as a function of the absolute temperature, T in K, and the pressure, p in MPa, as o10 0.20log 0.1 Bp B   −+  = +  , (2) where -4 2 398.314-1.25406 10.652510B T T=+ (3) In Eq. (2), the density at 0.1 MPa, ρo, is obtained from Eq. (1). We note that the coefficient of 0.20 in Eq.(2) is in full agreement with previous correlations of the densities of n-alkanes.26 The equations above represent all the primary data from 273 K to 473 K and up to 200 MPa. Table 4 summarizes comparisons of the primary data with the correlation. The average absolute deviation of the fit is 0.05%, the bias -0.004% and the expanded uncertainty at the 95% confidence level is 0.18%. Figures 3 to 5 show the percentage deviations of the primary density data as a function of the density, temperature, and pressure, from the values calculated from Eqs. (1) – (3). TABLE 4. Evaluation of the squalane density correlation for the primary data at high pressures 1st Author Year Publ. AAD (%) Bias (%) Fandiño5 2010 0.03 0.01 Trusler3 2010 0.07 -0.05 Ciotta21 2009 0.15 0.09 Kumagai15 2006 0.12 -0.11 Fandiño7 2005 0.02 0.00 Kuss17 1970 0.05 0.04 Entire data set 0.05 -0.004 Figure 8. Percentage deviations for the primary viscosity data in the temperature range 320 to 473 K and up to 200 MPa, as a function of temperature, from the values calculated from Eqs. (1) – (6). () Comuñas et al.2 (UNSW); (◧) Comuñas et al.2 (UPPA-FB); (◨) Comuñas et al.2 (UPPA-QCR); (+) Mylona et al.27; () Trusler et al.3; (⚫) Ciotta et al.21; () Harris6; () Tomida et al.19; (◐) Kumagai et al.15; () Pensado et al.28; (__) Comuñas et al.1 Figure 9. Percentage deviations for the primary viscosity data in the temperature range 320 to 473 K and up to 200 MPa, as a function of pressure, from the values calculated from Eqs. (1) – (6). () Comuñas et al.2 (UNSW); (◧) Comuñas et al.2 (UPPA-FB); (◨) Comuñas et al.2 (UPPA-QCR); (+) Mylona et al.27; () Trusler et al.3; (⚫) Ciotta et al.21; () Harris6; () Tomida et al.19; (◐) Kumagai et al.15; () Pensado et al.28 TABLE 6. Evaluation of the squalane viscosity correlation as a function of density and temperature for the primary data in the temperature range 320 to 473 K at pressures up to 200 MPa 1st Author Year Publ. AAD (%) Bias (%) Comuñas2 (UNSW) 2013 1.34 -0.91 Comuñas2 (UPPA) 2013 2.79 2.71 Comuñas2 (UPPA) 2013 1.32 -0.17 Mylona27 2013 1.16 1.16 Trusler3 2010 1.45 -0.40 Ciotta21 2009 2.25 -2.11 Harris6 2009 1.21 0.39 Tomida19 2007 1.51 -0.51 Kumagai15 2006 0.46 -0.09 Pensado28 2006 0.86 0.08 Entire data set 1.41 -0.09 Figure 10. Percentage deviations for the primary viscosity data in the temperature range 278 to 473 K at pressures to 200 MPa as a function of temperature from the values calculated from Eqs. (1) – (6). () Comuñas et al.2 (UNSW); (◧) Comuñas et al.2 (UPPA-FB); (◨) Comuñas et al.2 (UPPA-QCR); (+) Mylona et al.27; () Trusler et al.3; ( ) Ciotta et al.21; () Harris6; () Tomida et al.19; (◐) Kumagai et al.15; () Pensado et al.28 (___) Comuñas et al.1 Figure 11. Percentage deviations for the secondary viscosity data in the temperature range 278 to 473 K at pressures to 200 MPa, as a function of temperature from the values calculated from Eqs. (1) – (6). () Comuñas et al.2 (USC); () Hata and Tamoto13; () Bair29; () Bair30; () Krahn and Luft31; (⚫) Kuss and Golly.32 3.2 Viscosity Correlation as a Function of Pressure and Temperature The viscosity data for squalane were also correlated as a function of pressure and temperature, by employing a modified VFT equation, which is known to be suitable at high viscosities.2, 6 This also has eight parameters and employs a third degree polynomial in the pressure as follows:         − +++ ++= CT pbpbpbB papaA 3 3 2 21 2 21 exp   (7) where Δp = p - pref. Comuñas et al.2 have used this correlation equation (7) very recently and Ducoulombier et al.38 and Paredes et al.39, 40 have used very similar equations in the past. In equation (7) we use 0.1 MPa as reference pressure. Thus, when p is also equal to 0.1 MPa this equation collapses to:       − =CT B Aexp  (8) The VFT form, equation (8), has been used by Comuñas et al.1 in proposing a reference correlation for the viscosity of squalane at 0.1 MPa, but is valid only over the temperature interval 273 to 373 K. As in this work the maximum temperature is extended to 473 K. Instead of using the previously obtained A, B and C regression parameters,1 we have performed a new fit for Eq. (7), considering all the primary viscosity data in the 278-473 K interval and up to 200 MPa. In Table 7, the parameter values are given to six significant figures in order to not introduce changes in calculated viscosities linked to rounding of the parameters in the calculations. The AAD obtained is 1.69%, the bias is -0.04% and the maximum absolute deviation is 9.1%. The expanded uncertainty at the 95% confidence level is just under 4.75%. Note that for viscosity values at 0.1 MPa with the new A, B and C values we obtain an AAD of 1.2% and bias 0.48%, close to the previous results.1 TABLE 7. Parameters and relative deviations for VFT model, equation (7) Parameters Values A (mPa·s) 0.0831311 B (K) 727.325 C (K) 172.993 a1·103 (MPa-1) 2.06832 a2 ·106 (MPa-2) 1.31522 b1 (MPa-1· K) 2.60294 b2·103 (MPa-2· K) -4.19779 b3·106 (MPa-3· K) 6.10051 AAD (%) 1.69 Bias (%) -0.04 In the previous subsection, 3.1, the density correlation is limited to 200 MPa as there are reliable direct experimental data for the density only below that pressure. Above 200 MPa, when needed, the density can be generally indirectly evaluated (see, for instance, the extrapolation method used by Harris6). In practice, the working equations of most experimental viscosity methods require the density as an inputbut fortunately the viscosity value isnot very sensitive to the accuracy of the density in most of these methods,. For instance, for the falling body method,2 an uncertainty of 1% in the density (which is a big uncertainty) implies a relative uncertainty of less than 0.2% in the viscosity due the large difference between the density of the sinker and that of squalane. Nevertheless, the uncertainty in the viscosity is probably larger at high pressures than at low pressures. Consequently, we have limited the viscosity correlation to pressures below 200 MPa as the viscosity values are then linked to reliable direct density measurements. Note that, in theory, the proposed viscosity (T, p) correlation, Eq.(7), could have been applied to pressures higher than 200 MPa because it is independent of the density. For pressures higher than 200 MPa the reader can use the correlation proposed by Comuñas et al.2 to 350 MPa, though this may be a less accurate correlation, being obtained with a smaller data set over a smaller temperature interval (below 363.15 K. Figures 12, 13 and 14 show all the primary data in the temperature range 278 to 473 K at pressures up to 200 MPa as a function of the density, temperature and pressure. Table 8 summarizes the comparison of the primary data with the scheme of Eq. (7). Finally, by examining Figure 13, it can be seen that our previous reference correlation1 for the viscosity of squalane (which has an expanded uncertainty of 1.5%, at 0.1 MPa and in the temperature range 273 to 373 K), agrees very well with the present correlation. Figure 15 shows the percentage deviations for the secondary viscosity data in the temperature range 278 to 473 K at pressures to 200 MPa, as a function of the temperature for the values calculated from Eq. (7). A comparison of Figures (10) and (13) shows that this model gives a better fit to the data at low temperatures than the Assael-Dymond model, Eq. (4) to (6), at the cost of a poorer fit at higher temperatures. TABLE 8. Evaluation of the squalane viscosity correlation as a function of pressure and temperature for the primary data in the temperature range 278 to 473 K and up to 200 MPa 1st Author Year Publ. AAD (%) Bias (%) Comuñas2 (UNSWd) 2013 2.28 -2.17 Comuñas2 (UPPAd) 2013 1.88 1.59 Comuñas2 (UPPAd) 2013 1.45 0.33 Mylona27 2013 1.23 1.23 Trusler3 2010 2.98 0.39 Ciotta21 2009 2.98 -2.37 Harris6 2009 1.13 0.16 Tomida19 2007 2.02 -1.66 Kumagai15 2006 1.93 -0.29 Pensado28 2006 0.75 -0.41 Entire data set 1.69 -0.04 Figure 12. Percentage deviations for the primary viscosity data in the temperature range 278 to 473 K and up to 200 MPa, as a function of density, from the values calculated from Eq. (7). () Comuñas et al.2 (UNSW); (◧) Comuñas et al.2 (UPPA-FB); (◨) Comuñas et al.2 (UPPA-QCR); (+) Mylona et al.27; () Trusler et al.3; () Ciotta et al.21; () Harris6; () Tomida et al.19; (◐) Kumagai et al.15; () Pensado et al.28; (____) Comuñas et al.1 Figure 13. Percentage deviations for the primary viscosity data in the temperature range 278 to 473 K and up to 200 MPa, as a function of temperature, from the values calculated from Eq. (7). () Comuñas et al.2 (UNSW); (◧) Comuñas et al.2 (UPPA-FB); (◨) Comuñas et al.2 (UPPA-QCR); (+) Mylona et al.27; () Trusler et al.3; (⚫) Ciotta et al.21; () Harris6; () Tomida et al.19; (◐) Kumagai et al.15; () Pensado et al.28; (____) Comuñas et al.1 Figure 14. Percentage deviations for the primary viscosity data in the temperature range 278 to 473 K and up to 200 MPa, as a function of pressure, from the values calculated from Eq. (7). () Comuñas et al.2 (UNSW); (◧) Comuñas et al.2 (UPPA-FB); (◨) Comuñas et al.2 (UPPA-QCR); (+) Mylona et al.27; () Trusler et al.3; (⚫) Ciotta et al.21; () Harris6; () Tomida et al.19; (◐) Kumagai et al.15; () Pensado et al.28 Figure 15. Percentage deviations for the secondary viscosity data in the temperature range 278 to 473 K at pressures to 200 MPa, as a function of temperature from the values calculated from Eq. (7). ()Comuñas et al.2 (USC); () Hata and Tamoto13; () Bair29; () Bair30; () Krahn and Luft31; (⚫) Kuss and Golly.32 4. Conclusion New reference correlations for the density and viscosity of squalane are presented. These correlations are based on critically evaluated experimental data taken from the literature. In the case of the density, the correlation, employing the Tait equation, is valid from 273 to 473 K at pressures to 200 MPa. At 0.1 MPa, it shows an average absolute deviation of 0.03%, a bias of - 0.01%, and an expanded uncertainty (at the 95% confidence level) of 0.06%. Over the whole range of pressure, the density correlation shows an average absolute deviation of 0.05%, a bias of -0.004%, and an expanded uncertainty (at the 95% confidence level) of 0.18%. The first viscosity correlation expresses the viscosity as a function of density and temperature, and is based on the Assael-Dymond model, Eq. (4) to (6). It is slightly superior at higher temperatures, the region of primary interest in applications, but gives a poorer fit at low temperatures when the viscosity is strongly temperature dependent. This correlation covers the temperature range from 320 to 473 K at pressures to 200 MPa, and has an average absolute deviation of 1.41%, a bias of -0.09%, and an expanded uncertainty (at the 95% confidence level) of 3%. Below 320 K, the deviations from the present scheme rise to a maximum of 20%. The second correlation is based on a modified Vogel-Fulcher-Tammann equation, with the viscosity expressed as a function of pressure and temperature, Eq. (7). It is superior to the first at low temperatures, but inferior at higher temperatures. This correlation covers a broader temperature range from 278 to 473 K at pressures to 200 MPa, and has an average absolute deviation of 1.69%, a bias of - 0.04%, and an expanded uncertainty (at the 95% confidence level) of 4.75%. Finally, Table 9 gives some selected reference values for density and viscosity calculated from Eq.(1) to (3) (density), and Eq.(5) to (6) or Eq. (7) (viscosity). TABLE 9: Some selected reference values T (K) p (MPa)  corr (kg.m-3)  (mPa.s)  (mPa.s) Eq (1)-(3) Corr Eq. (4)-(6) Corr Eq. (7) 333.15 0.1 783.0 7.86 7.80 353.15 0.1 770.2 4.65 4.71 373.15 0.1 757.4 3.08 3.15 393.15 0.1 744.6 2.21 2.26 413.15 0.1 731.8 1.68 1.72 433.15 0.1 719.0 1.33 1.36 453.15 0.1 706.2 1.06 1.11 473.15 0.1 693.4 0.85 0.94 333.15 100 833.6 37.57 38.38 353.15 100 824.3 19.35 19.84 373.15 100 815.4 11.43 11.71 393.15 100 806.7 7.50 7.60 413.15 100 798.2 5.33 5.30 433.15 100 790.0 4.02 3.91 453.15 100 781.8 3.17 3.01 473.15 100 773.5 2.58 2.40 333.15 200 866.2 137.42 137.09 353.15 200 858.3 63.16 62.70 373.15 200 850.7 33.80 33.53 393.15 200 843.4 20.35 20.09 413.15 200 836.3 13.42 13.11 433.15 200 829.4 9.47 9.13 453.15 200 822.4 7.04 6.70 473.15 200 815.3 5.42 5.12 Acknowledgments M.J.P.C, X.P., F.M.G. and J.F. acknowledge the support of the Project CTQ2011-2395 granted by the Spanish Ministry of Economy and Competitiveness. The authors are indebted to Prof. J.P. Martin Trusler for providing his measurements, and giving very valuable advice and consultation during this work.