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Energy & Fuels 2004, 18, 968-975
Transport Properties of n-Dodecane Marcia L. Huber,* Arno Laesecke, and Richard Perkins Physical and Chemical Properties Division, National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305-3328 Received December 30, 2003. Revised Manuscript Received April 9, 2004
We have surveyed literature data and developed correlations for the viscosity and thermal conductivity of n-dodecane that are valid over a wide range of fluid states. The new correlations are applicable from the triple point (263.59 K) to 800 K, and at pressures up to 200 MPa. The viscosity correlation has an estimated uncertainty of 0.5% along the saturation boundary in the liquid phase, 3% in the compressed liquid region, and 3% in the vapor (where the uncertainties can be considered as estimates of a combined expanded uncertainty with a coverage factor of 2). The thermal conductivity correlation has an estimated uncertainty of 4% along the liquid saturation boundary and in the compressed liquid, and ∼5% in the vapor region.
Introduction Jet fuels are mixtures of many components, and it is often desirable to model the thermodynamic and transport properties of such complex fuels using a surrogate mixture. The surrogate models contain a variety of fluids, depending on which particular jet fuel or propellant is the target mixture, and on the specific purpose for which the surrogate is constructed. However, ndodecane is often an important component in surrogate mixtures for many jet fuels, including JP-4, JP-5, JP-7, JP-8, and RP-1,1-3 because it has, as a first approximation, physical properties that are similar to those of some of these fuels. Recently, a reliable equation of state (EOS) has been developed for the thermodynamic properties of n-dodecane on the entire fluid region,4 as well as a new algorithm for the computation of liquid thermodynamic properties.5 In this manuscript, we survey the available data for viscosity and thermal conductivity and provide wide-ranging correlations for both transport properties. Viscosity Viscosity Data. There are several major compilations of data that we have used to aid in the collection of experimental data.6-10 In addition, in 1979, Stephan and Lucas11 provided graphs and recommended values for the viscosity of n-dodecane in the dense-fluid phase, * Author to whom correspondence should be addressed. E-mail address:
[email protected]. (1) Edwards, T.; Maurice, L. Q. J. Propul. Power 2001, 17, 461466. (2) Violi, A.; Yan, S.; Eddings, E. G.; Sarofim, A. F.; Granata, S.; Faravelli, T.; Ranzi, E. Combust. Sci. Technol. 2002, 174, 399-417. (3) Wood, C. P.; McDonell, V. G.; Smith, R. A.; Samuelson, G. S. J. Propul. Power 1989, 5, 399-405. (4) Lemmon, E. W.; Huber, M. L. Energy Fuels 2004, 18, 960-967. (5) Khasanshin, T. S.; Shchemelev, A. P. High Temp. 2001, 39, 6067. (6) Wohlfarth, C.; Wohlfarth, B. Viscosity of Pure Organic Liquids and Binary Liquid Mixtures, Subvolume B: Pure Organic Liquids. In Landolt-Bo¨ rnstein-Numerical Data and Functional Relationships in Science and Technology; Lechner, M. D., Ed.; Springer-Verlag: Berlin, Heidelberg, New York, 2001; Vol. IV/18, p 389.
10.1021/ef034109e
based on the measurements of Keramidi and Rastorguev,12 who reported an experimental uncertainty of 1.2% using a capillary viscometer. Since that time, much more information has become available. In 1994, Dymond and Øye13 made a comprehensive critical assessment of the experimental viscosity data for several alkanes, including n-dodecane, along the liquid saturation boundary. They recommended the data sets of Dymond and Young14 and Knapstad et al.15 as primary data sets, which they defined as data resulting from measurements that are performed with an instrument of high precision and for which a complete set of working equations and a detailed knowledge of all corrections are available. The data of Dymond and Young14 were measured with a suspended level viscometer at saturation pressure over 283-393 K, and the data of Knapstad et al.15 were measured with an oscillating cylinder viscometer at atmospheric pressure over 293-425 K. Both sets have an estimated uncertainty of 0.5% but are limited to the region near the saturation boundary. Knapstad et al.16 later reported measurements on dodecane and its mixtures with hexane, benzene, and cyclohexane at atmospheric pressure from 289 K to 343 K, with estimated uncertainties of 0.4%-0.6%, with the (7) Vargaftik, N. B.; Vinogradov, Y. K.; Yargin, V. S. Handbook of Physical Properties of Liquids and Gases, Third ed.; Begell House: New York, 1996. (8) Viswanath, D. S.; Natarjan, G. Data Book on the Viscosity of Liquids; Hemisphere Publishing Corporation: New York, 1989. (9) Rowley, J. R.; Wilding, W. V.; Oscarson, J. L.; Rowley, R. L. DIADEM, DIPPR Information and Data Evaluation Manager; 2.0 ed.; Brigham Young University: Provo, UT, 2002. (10) Frenkel, M.; Dong, Q.; Wilhoit, R. C.; Hall, K. R. Int. J. Thermophys. 2001, 22, 215-226. (11) Stephan, K.; Lucas, L. Viscosity of Dense Fluids; Plenum Press: New York, 1979. (12) Keramidi, A. S.; Rastorguev, Ya. L. Izv. Vyssh. Uchebn. Zaved., Neft Gaz 1970, 13, 113-114. (13) Dymond, J. H.; Oye, H. A. J. Phys. Chem. Ref. Data 1994, 23, 41-53. (14) Dymond, J. H.; Young, K. J. Int. J. Thermophys. 1981, 2, 237247. (15) Knapstad, B.; Skjølsvik, P. A.; Øye, H. A. J. Chem. Eng. Data 1989, 34, 37-43. (16) Knapstad, B.; Skjølsvik, P. A.; Øye, H. A. J. Chem. Eng. Data 1991, 36, 84-88.
This article not subject to U.S. Copyright. Published 2004 by the American Chemical Society Published on Web 07/03/2004
Transport Properties of n-Dodecane
uncertainties lower at the lower temperatures. There have been many other studies17-44 that provide data over a limited temperature range at or near saturation conditions. The measurements of Giller and Drickamer22 were performed with a Cannon-Fenske modified Ostwald viscometer from near the freezing point up to 293 K, with an estimated uncertainty of 0.5%. We include them in our primary data set to extend the temperature range of the measurements to near freezing. The only other data we include in our primary data set near the saturated liquid region are those of Dymond and Young45 and Knapstad and co-workers,15,16 in accordance with the recommendation of Dymond and Øye.13 In addition to the many studies that provide data over a limited temperature range, usually at atmospheric or saturation pressure, several authors have studied liquid n-dodecane over a wider range of temperature and pressure. These more-comprehensive studies include those of Dymond et al.,46 Kashiwagi and Makita,47 Ducoulombier et al.,48 Gouel,49 Tanaka et al.,50 Hogen(17) Aminabhavi, T. M.; Banerjee, K. Indian J. Chem. 2001, 40A, 53-64. (18) Shepard, A. F.; Henne, A. L.; Midgley, T. J. Am. Chem. Soc. 1931, 53, 1948-1958. (19) Burgdorf, R.; Zocholl, A.; Arlt, W.; Knapp, H. Fluid Phase Equilib. 1999, 164, 225-255. (20) Aucejo, A.; Cruz Burguet, M.; Mun˜oz, R.; Marques, J. L. J. Chem. Eng. Data 1995, 40, 141-147. (21) Aucejo, A.; Part, E.; Medina, P.; Sancho-Tello, M. J. Chem. Eng. Data 1986, 31, 143-145. (22) Giller, E. B.; Drickamer, H. G. Ind. Eng. Chem. 1949, 41, 20672069. (23) Aminabhavi, T. M.; Patil, V. B. J. Chem. Eng. Data 1997, 42, 641-646. (24) Aminabhavi, T. M.; Gopalkrishma, B. J. Chem. Eng. Data 1994, 39, 529-534. (25) Awwad, A. M.; Salman, M. A. Fluid Phase Equilib. 1986, 25, 195-208. (26) Awwad, A. M.; Allos, E. I. Fluid Phase Equilib. 1985, 22, 353365. (27) Bidlack, D. L.; Anderson, D. K. J. Phys. Chem. 1964, 68, 37903794. (28) DeLorenzi, L.; Fermeglia, M.; Torriano, G. J. Chem. Eng. Data 1994, 39, 483-487. (29) Cooper, E. F.; Asfour, A. A. J. Chem. Eng. Data 1991, 36, 285288. (30) Aralaguppi, M. I.; Aminabhavi, T. M.; Balundgi, R. H.; Joshi, S. S. J. Phys. Chem. 1991, 95, 5299-5308. (31) Chevalier, J. L. E.; Petrino, P. J.; Gaston-Bonhomme, Y. H. J. Chem. Eng. Data 1990, 35, 206-212. (32) Awwad, A. M.; Al-Azzawi, S. F.; Salman, M. A. Fluid Phase Equilib. 1986, 31, 171-182. (33) Wakefield, D. L.; Marsh, K. N. Int. J. Thermophys. 1987, 8, 649-662. (34) Wakefield, D. L. Int. J. Thermophys. 1988, 9, 365-381. (35) Wu, J.; Shan, Z.; Asfour, A. A. Fluid Phase Equilib. 1998, 143, 263-274. (36) Cutler, W. G.; McMickle, R. H.; Webb, W.; Schiessler, R. W. J. Chem. Phys. 1958, 29, 727-740. (37) Iwahashi, M.; Yamaguchi, Y.; Ogura, Y.; Suzuki, M. Bull. Chem. Soc. Jpn. 1990, 63, 2154-2158. (38) Bingham, E. C.; Fornwalt, H. J. J. Rheol. 1930, 1, 372-417. (39) Trenzado, J. L.; Matos, J. S.; Segade, L.; Carballo, E. J. Chem. Eng. Data 2001, 46, 974-983. (40) Nayak, J. N.; Aralaguppi, M. I.; Aminabhavi, T. M. J. Chem. Eng. Data 2001, 46, 891-896. (41) Moreiras, A. F.; Garcia, J.; Lugo, L.; Comunas, M. J. P.; Lopez, E. R.; Fernandez, J. Fluid Phase Equilib. 2003, 204, 233-243. (42) Celda, B.; Gavara, R.; Tejero, R.; Figueruelo, J. E. J. Chem. Eng. Data 1987, 32, 31-33. (43) Aralaguppi, M. I.; Jadar, C. V.; Aminabhavi, T. M. J. Chem. Eng. Data 1999, 44, 435-440. (44) Garcia, B.; Alcalde, R.; Aparicio, S.; Leal, J. M. Ind. Eng. Chem. Res. 2002, 41, 4399-4408. (45) Dymond, J. H.; Young, K. J. Int. J. Thermophys. 1980, 1, 331344. (46) Dymond, J. H.; Robertson, J.; Isdale, J. D. Int. J. Thermophys. 1981, 2, 133-154. (47) Kashiwagi, H.; Makita, T. Int. J. Thermophys. 1982, 3, 289305.
Energy & Fuels, Vol. 18, No. 4, 2004 969
Figure 1. Plot showing the distribution of primary viscosity data for n-dodecane.
boom et al.,51 and Caudwell et al.52 Caudwell et al. have reported the most-recent measurements, which were made with a vibrating-wire instrument that measured both viscosity and density, operating between 298 and 473 K at pressures up to 200 MPa, with a reported uncertainty of 2%. We selected this work as our primary basis for the behavior of dodecane at high pressures. Caudwell et al. 52 compare their data with the earlier studies of Ducoulombier et al.,48 Dymond et al.,46 Kashiwagi and Makita,47 Tanaka et al.,50 Hogenboom et al.,51 and Stephan and Lucas11 (which was based on the data of Keramidi and Rastorguev12). At pressures up to 200 MPa, the data of Dymond et al.46 and Tanaka et al.50 show deviations of as much as 4%; however, this is considered to be within the mutual uncertainty of these sets. The data of Hogenboom et al.51 agree with those of Caudwell et al.52 at low pressures; however, at higher pressures, the two sets exhibit differences of up to 6%. Duculombier et al.48 agree with the results of Caudwell,52 to within 3%. We found only two sets of data in the gaseous region. The experimental data of Lyusternik and Zhdanov,53 using a capillary viscometer with an uncertainty of 1.3%, cover a temperature range of 503-681 K. An earlier publication by these authors54 reported no experimental data, but only an empirical correlation. Figure 1 shows the temperature and pressure range of the data sets selected for use in the development of our viscosity correlation, along with the saturation boundary computed from the EOS for dodecane.4 Viscosity Correlation. We represent the viscosity η of a pure fluid as the sum of a dilute gas contribution and a residual term,55
η(F,T) ) η(0)(T)[1 + Bη(T)F] + ∆Hη(F,T)
(1)
where the term η(0)(T) represents the viscosity in the (48) Ducoulombier, D.; Zhou, H.; Boned, C.; Peyrelasse, J.; SaintGuirons, H.; Xans, P. J. Phys. Chem. 1986, 90, 1692-1700. (49) Gouel, P. Bull. Cent. Rech. Explor.-Prod. Alf-Aquitaine 1978, 2, 419-467. (50) Tanaka, Y.; Hosokawa, H.; Kubota, H.; Makita, T. Int. J. Thermophys. 1991, 12, 245-264. (51) Hogenboom, D. L.; Webb, W.; Dixon, J. A. J. Chem. Phys. 1967, 46, 2586-2598. (52) Caudwell, D. R.; Trusler, J. P. M.; Vesovic, V.; Wakeham, W. A. Presented at the 15th International Symposium on Thermophysical Properties, Boulder CO, 2003.
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limit of zero density, Bη(T) is the second virial coefficient for viscosity based on Rainwater-Friend theory,56 and ∆Hη(F, T) is the residual contribution that represents the higher-order density terms as a function of the absolute temperature T and density F. We have chosen to omit a term for the critical enhancement of the viscosity, ∆cη(F,T), because it is restricted to a region very close to the critical region,57 for which we have no experimental data. This formulation of the viscosity (eq 1) is expressed in terms of density and temperature and requires that the density be available. In this work, we use the recent EOS of Lemmon and Huber4 for ndodecane to obtain density values. Dilute Region. An expression for the viscosity in the limit of zero density58 is Figure 2. Plot showing the dilute-gas viscosity.
η(0)(T) )
0.021357xMT σ2S*η(T*)
(2)
where η is the viscosity (given in µPa s), M the relative molar mass (given in g/mol), T the temperature (given in Kelvin), and σ the length scaling parameter (given in nanometers). Empirical correlations of the logarithm of the reduced effective collision cross section S/η are written as polynomials of the logarithm of the reduced temperature T* ) kBT/: 2
ln S*η )
ai(ln T*)i ∑ i)0
(3)
where /kB is the energy scaling parameter and kB is the Boltzmann constant. Unfortunately, there are very few data for the viscosity of n-dodecane in the dilutegas region; because of the lack of experimental data, we determined the values of the scaling parameters σ and /kB, using a predictive method developed by Chung et al.59 This method provides an estimate of the energy and length scaling parameters, in terms of the critical temperature (Tc) and critical volume (Vc):
Tc ) kB 1.2593
(4)
σ ) 0.0809V1/3 c
(5)
where Vc is given in cm3‚mol-1 and σ is given in nanometers. The critical parameters are from the EOS:4 Tc ) 658.1 K, Pc ) 1.817 MPa, and Fc ) 1.33 mol/L, with a molar mass of M ) 170.33 g/mol. Also, throughout this (53) Lyusternik, V. E.; Zhdanov, A. G. Teplofiz. Svoistva Veshchestv Mater. 1973, 7. (54) Zhdanov, A. G.; Lyusternik, V. E. Russ. J. Phys. Chem. 1971, 45, 113. (55) Vogel, E.; Ku¨chenmeister, C.; Bich, E.; Laesecke, A. J. Phys. Chem. Ref. Data 1998, 27, 947-970. (56) Rainwater, J. C.; Friend, D. G. Phys. Rev. A 1987, 36, 40624066. (57) Olchowy, G. A.; Sengers, J. V. Int. J. Thermophys. 1989, 10, 417-426. (58) Millat, J.; Vesovic, V.; Wakeham, W. A. Transport Properties of Dilute Gases and Gaseous Mixtures. In Transport Properties of Fluids: Their Correlation, Prediction and Estimation; Millat, J., Dymond, J. H., Nieto de Castro, C. A., Eds.; Cambridge University Press: Cambridge, 1996; pp 29-65. (59) Chung, T. H.; Ajlan, L.; Lee, L. L.; Starling, K. E. Ind. Eng. Chem. Res. 1988, 27, 671-679.
Table 1. Parameters Used in the Representation of the Dilute Gas Viscosity in eqs 1-3 a0
a1
a2
σ (nm)
/kB (K)
0.382987
-0.561050
0.313962 × 10-1
0.735639
522.592
work, we use the CODATA value60 of the molar gas constant, R ) 8.314472 J mol-1 K-1. The experimental viscosity data of Lyusternik and Zhdanov,53 which cover the range of 503-681 K, along with several points generated from the equation presented by Zhdanov and Lyusternik,54 were used to obtain the parameters ai in eq 3, which are reported in Table 1, along with the estimated length and energy scaling parameters. Figure 2 compares the present correlation with the experimental data, a correlation presented by Vargaftik et al.61 that has been attributed to Tarzimanov et al.,62 and the correlation of Zhdanov and Lyusternik.54 They are all in excellent agreement. The correlation of Vargaftik et al.61 reports an estimated uncertainty of 1%-3%. We estimate that the uncertainty of our dilute-gas correlation is 3%. At very low densities, the density dependence of the viscosity is initially linear, and the temperature variation is represented by the second viscosity virial coefficient Bη(T). Rainwater and Friend56,63 calculated the second viscosity virial coefficient of the Lennard-Jones fluid theoretically. For this two-parameter force field model, Bη(T) is obtained from its dimensionless form, according to
Bη(T) ) NAσ3B*η(T*)
(6)
where NA is the Avogadro constant. The results of Rainwater and Friend were later adjusted by Bich and Vogel64 for better agreement with experimental data, and tabulated revised values of B/η(T*) were given in the range of 0.5 e T* e 100. We use the correla(60) Mohr, P. J.; Taylor, B. N. J. Phys. Chem. Ref. Data 1999, 28, 1713-1852. (61) Vargaftik, N. B. Tables on the Thermophysical Properties of Liquids and Gases in Normal and Dissociated States; Hemisphere Publishing Corporation: Washington, DC, 1975. (62) Tarzimanov, A. A.; Lyusternik, V. E.; Arslanov, V. A. Review Series on Thermophysical Properties of Substances; Institute of High Temperatures Academy of Sciences: Moscow, 1987; Vol. 1, p 63. (63) Friend, D. G.; Rainwater, J. C. Chem. Phys. Lett. 1984, 107, 590-594. (64) Bich, E.; Vogel, E. Initial Density Dependence. In Transport Properties of Fluids. Their Correlation, Prediction and Estimation; Millat, J., Dymond, J. H., Nieto de Castro, C. A., Ed.; Cambridge University Press: Cambridge, 1996; pp 72-82.
Transport Properties of n-Dodecane
Energy & Fuels, Vol. 18, No. 4, 2004 971
Table 2: Parameters for the Second Viscosity Virial Coefficient in eq 7a
a
i
bi
ti
0 1 2 3 4 5 6 7 8
-19.572 881 219.739 99 -1015.322 6 2471.012 5 -3375.171 7 2491.659 7 -787.260 86 14.085 455 -0.346 641 58
0 -0.25 -0.50 -0.75 -1.00 -1.25 -1.50 -2.50 -5.50
From ref 55.
tion proposed by Vogel, Ku¨chenmeister, Bich, and Laesecke:55 8
B*η(T*) )
bi(T*)t ∑ i)0
(7)
i
with the parameters bi and the exponents ti taken from ref 55; these values are given in Table 2. Equation 7 may be safely extrapolated to temperatures as low as T* ≈ 0.3, which corresponds to a point well below the triple point of n-dodecane. However, this relation must be used with caution, because the correlation was developed for spherical molecules and n-dodecane is ellipsoidal. Residual Contribution. We expressed the higher density terms ∆Hη(F,T) of eq 1 in terms of the reduced density δ ) F/Fc and the reduced temperature τ ) T/Tc. After systematic consideration of the alternative structures, the final correlation contains the following combination of polynomial and free-volume terms:
[ ∑∑ 3
∆Hη(F,T) ) 1000
2
j)2k)1
δj
(
1
1
)]
Rjk + c1δ δ0 - δ δ0 τk
(8)
In this equation, the term ∆Hη(F,T) is given in units of µPa s, the individual terms are constrained to be zero at F ) 0, and its leading-order density dependence is of higher order (higher than linear). The free-volume term is one used successfully for other fluids.55,65,66 A term, which is called linear-in-density, which results from a Taylor-series expansion of the free-volume term about zero density, is subtracted, because the linear-in-density term has already been taken into consideration in the second viscosity virial coefficient term that was discussed earlier. No linear-in-density polynomial terms were permitted for this reason as well. The reduced close-packed density δ0(τ) is written as
Figure 3. Plot showing the viscosity deviations of selected data, as a function of (a) temperature and (b) density. Table 3: Parameters for the Residual Viscosity Contribution, from eqs 8 and 9 j
k
Rjk
2 3 2 3
1 1 2 2
-0.471703 × 10-1 0.827816 × 10-2 0.298429 × 10-1 -0.134156 × 10-1
j
cj
1 2 3
0.503109 2.32661 2.23089
A total of eight adjustable parameters were used in the determination of the dense-fluid contributions in eqs 8 and 9. These parameters were determined by fitting experimental data. The primary data were used to establish the coefficients of the high-density contribution (eqs 8 and 9), which are presented in Table 3. We also added two
points at 800 K and a pressure (P) of 20 and 100 MPa, and two at 1000 K and P ) 20 and 100 MPa, obtained from the estimation method of Lee and Thodos,67 so that the correlation will extrapolate reasonably to 1000 K. The fitting was performed with the statistical package ODRPACK.68 Additional polynomial terms were included in the initial fitting procedure but were discarded because of a lack of statistical significance. Figure 3a and b show the percentage deviations (100(ηcalc - ηexp)/ ηexp) of the primary data and selected secondary data from the correlation, as a function of temperature and density. The data of Dymond and Young14 and Knapstad et al.15,16 are represented to within their estimated uncertainty of 0.5%. The data of Caudwell et al.52 are represented with an average absolute deviation of 1.1%
(65) Vogel, E.; Ku¨chenmeister, C.; Bich, E. Int. J. Thermophys. 2000, 21, 343-356. (66) Vogel, E.; Ku¨chenmeister, C.; Bich, E. High Temp.-High Pressures 1999, 31, 173-186.
(67) Lee, H.; Thodos, G. Ind. Eng. Chem. Res. 1988, 27, 2377-2384. (68) Boggs, P. T.; Byrd, R. H.; Rogers, J. E.; Schnabel, R. B. ODRPACK, Software for Orthogonal Distance Regression; National Institute of Standards and Technology: Gaithersburg, MD, 1992.
δ0 ) c2 + c3xτ
(9)
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Table 4. Summary of Viscosity Results first author
reference number
Aminabhavi Aminabhavi Aminabhavi Aralaguppi Aralaguppi Aucejo Aucejo Awwad Awwad Awwad Bidlack Bingham Burgdorf Caudwell Celda Chevalier Cooper Cutler De Lorenzi Ducoulombier Dymond Dymond Garcia Giller Gonzalez Gouel Hogenboom Iwahashi Kashiwagi Keramidi Knapstad Knapstad Lyusternik Moreiras Nayak Shephard Tanaka Trenzado Wakefield Wakefield Wu
17 24 23 30 43 20 21 25 26 32 27 38 19 52 42 31 29 36 28 48 45 46 44 22 86 49 51 37 47 12 15 16 53 41 40 18 50 39 33 34 35
temp, T (K)
F (mol/L)
pressure, P (MPa)
number of points
AAD
RMS
Max
298-308 298-318 298-308 298-308 298-308 298 298 298 298 298 298 273-373 298-323 298-473 293 298 293 372 298 293-373 283-393 298-373 278-318 263-293 293-303 293-393 311-408 298-323 298-348 303-518 294-425 289-343 503-681 298 298-308 298 298-348 283-313 318-338 303-308 293-313
4.33-4.38 4.29-4.38 4.33-4.38 4.33-4.38 4.33-4.38 4.38 4.38 4.38 4.38 4.38 4.38 4.05-4.49 4.27-4.38 3.58-4.80 4.40 4.38 4.40 4.05 4.38 4.04-4.70 3.96-4.44 4.04-5.10 4.29-4.47 4.40-4.53 4.36-4.40 3.96-4.55 3.88-4.98 4.27-4.38 4.16-4.71 3.50-4.53 3.81-4.40 4.19-4.42 0.01-0.01 4.38 4.33-4.38 4.38 4.16-4.72 4.31-4.44 4.20-4.29 4.33-4.35 4.31-4.40
0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1-192 0.1 0.1 0.1 0.1 0.1 0.1-100 sat 0.1-502 0.1 0.1 0.1 0.1-40.1 0.1-360 0.1 0.1-111 0.1-49 0.1 0.1 0.05 0.1 0.1 0.1 0.1-151 0.1 0.1 0.1 0.1
3 3 3 3 3 1 1 1 1 1 1 8 2 85 1 1 1 1 1 30 8 32 5 8 3 54 55 2 71 41 11 7 8 1 3 1 21 5 3 2 4
6.80 3.89 2.26 1.09 0.30 1.47 0.37 0.58 0.44 0.86 1.59 1.27 0.94 1.11 2.67 1.05 0.60 0.60 0.45 1.36 0.29 3.32 0.98 0.70 0.75 4.19 4.15 2.80 0.88 2.22 0.35 0.29 0.92 2.63 2.85 0.46 1.62 0.19 1.52 0.87 0.24
1.62 1.08 0.06 0.11 0.15 0 0 0 0 0 0 0.71 0.21 1.19 0 0 0 0 0 1.57 0.20 4.47 1.26 0.42 0.08 5.68 4.02 0.08 0.96 2.82 0.24 0.34 1.12 0 0.49 0 1.60 0.22 0.12 0.00 0.31
9.06 5.27 2.32 1.22 0.50 -1.47 -0.37 -0.58 0.44 -0.86 1.59 -2.72 -1.15 3.44 2.67 1.05 0.60 -0.60 0.45 4.05 -0.49 16.18 -2.03 1.17 0.85 -18.69 -10.98 2.88 2.33 -12.03 -0.66 -0.73 2.14 2.63 3.30 0.46 -4.36 -0.35 -1.68 -0.88 0.58
for all 85 points, although some individual points have deviations of >2% (the experimental uncertainty). The data of Tanaka et al.,50 and of Kashiwagi and Makita,47 with estimated uncertainties of 2%, are represented to within their uncertainty values. The data of Dymond, Robertson, and Isdale,46 with an estimated uncertainty of 2%, are not represented to within their experimental uncertainty and have large deviations of 10% or more at the highest densities. The EOS that we used4 is valid for temperatures up to 800 K, pressures up to 700 MPa, and a maximum density of 4.53 mol/L. Some of the points in the data of Caudwell et al.,52 and especially those of Dymond et al.46 and Hogenboom et al.,51 exceeded this maximum density. At higher densities, particularly above the recommended limit for the EOS, the deviations increase; however, it is not known whether this is due to inadequacies in the EOS or whether additional terms in the correlation are necessary to fit the data for very high densities. To address the highest density data, we added exponential terms to the viscosity correlation but were unable to obtain statistical significance for these terms; therefore, they were not included in the final correlation. The data of Keramidi and Rastorguev12 report an uncertainty of 1.3%; we show an overall average absolute deviation of 2.2%. Table 4 presents a tabular summary of the results of comparisons of the correlation with available experi-
mental data, using the following definitions for average absolute deviation (AAD) and root-mean-square (RMS) deviation:
AAD )
∑ | i)1
100 n
n
ηcal i
ηexp i
|
-1
(10)
and
2
RMS )
[ ( ) ] [ ( )]
100 n
n
∑ i)1
ηcal i
ηexp i
2
-1
-
100 n
n
∑ i)1
ηcal i
ηexp i
2
-1
(11)
Finally, test points for validating computer calculations are obtained under the following conditions: T ) 300 K, F ) 4.4115 mol/L, and η ) 1484.8 µPa s (corresponds to P ) 10 MPa); and T ) 500 K, F ) 3.4447 mol/L, η ) 183.76 µPa s (corresponds to P ) 1 MPa). Thermal Conductivity Thermal Conductivity Data. We used several large data compilations to aid in collecting thermal conductiv-
Transport Properties of n-Dodecane
Energy & Fuels, Vol. 18, No. 4, 2004 973
Figure 4. Plot showing the distribution of primary thermal conductivity data for n-dodecane.
ity data for n-dodecane.7,9,69,70 In 1975, Jamieson et al.70 comprehensively surveyed liquid thermal conductivity data, including that for n-dodecane. The data were grouped by estimated accuracy level, and no data sets were found that had an estimated accuracy of 2% or better. Since that time, measurements have been made with estimated uncertainties of
