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Thermodynamic Properties of n-Dodecane

ARTICLE in ENERGY & FUELS JULY 2004

Impact Factor: 2.79 DOI: 10.1021/ef0341062

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Marcia L Huber

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Thermodynamic Properties of n-Dodecane

Er ic W. Lemmon* a nd Ma rcia L. Hu ber

P h ysi ca l a n d Ch emi ca l P r o p er t i es Di vi si on , N a ti o n a l I n st i tu te of S ta n d a r d s a n d Tech n o l o gy,

325 Broadway, Boulder, Colorado 80305-3328

Recei ved D ecem ber 23, 2 003

An equation of state has been developed to represent the thermodynamic properties of all liquid,vapor, and supercrit ical sta tes of n-dodecane. Experimenta l da ta used to develop t he equa tionincluded pressure-density-temperature state points, vapor pressures, isobaric and saturat ionheat capacit ies, heats of vaporizat ion, and speeds of sound. The uncertaint ies of propert iescalculated using the equa tion are as follows: 0.2%in density a t pressures up to 200 MPa , and0.5%at higher pressures up t o 500 MPa ; 1%in h eat capacity; 0.5%in the speed of sound; a nd0.2%in vapor pressure. Deviations of calculated properties from available experimental data inthe critical region are higher for all properties except vapor pressure.

Introduction

The modeling of petroleum based rocket and jet fuelso f t e n re q u ire s t h e u s e o f s u rro g a t e mix t u re s wit h alimited number of components to represent the ther-m od y n a m ic a n d t r a n s por t p rop er t i es of t h e a c t ua lmixture (see, for example, Edwards and Maurice 1). Thethermophysical propert ies of dodecane are similar tothose of a viat ion kerosene, a nd accurate knowledge ofits chara cterist ics is a precursor t o modeling rocketfuels. Khasanshin et al .2 reported equations for calcu-lat ing the t hermodyna mic properties of dodeca ne in theliquid phase based primarily on their own speed-of-s o u n d me a s u re me n t s a n d, t o a le s s e r de g re e , o n t h emeasurements of others.

Equations of state for pure fluid properties are often

e xp res s ed a s f u n da men t a l e q u a t ion s e xp lici t in t h eHelmholtz energy, with the density a nd t emperature a sin dep en de n t v a r ia bles . F rom t h e s e e q u a t ion s , mos tsingle-phase thermodynamic propert ies can be calcu-lated using density or temperature derivat ives of theHelmholtz energy. The location of the saturation bound-aries requires an iterat ive solution using t he so-calledMaxw ell criterion, i.e. , equa l pressures and G ibbs ener-gies at constant temperature during phase changes. Ane q u a t i o n o f s t a t e t h a t c a n b e u s e d t o c a l c u l a t e t h etherm odyna mic properties of dodecane at liquid, vapor,a n d s u p e rc ri t ic a l s t a t e s is g iv e n h e re , a n d t ra n s p o rtequations are given in a companion paper (Huber eta l. 3).

Equation of State

The genera lized functional form developed in th e workof Span an d Wagner 4 wa s used here as a sta rt ing point

t o f it a n e q ua t i on t o r ep re se nt t h e t h er m od y n a m ic

properties of dodecane. They developed a single equationfor nonpolar fluids by fitting multiple properties overall liquid a nd va por sta tes, including the critical region.Their technical equations were developed with muchinsight into the proper behavior of an equation of state.The number of terms in their equation was kept to aminimum, th us decreasing the intercorrelat ion betw eenterms and the possibility of overfitting. The objectiveo f Sp a n a n d W a g n e r wa s n o t t h e de t e rmin a t io n o f afunctional form that described the data sets as well aspossible, but rather the development of the best func-t io n a l f o rm t h a t c o n s ide re d t h e da t a f o r a l l t h e s u b-sta nces simultaneously.

To describe the properties of n-dodecane more ac-

curately, the temperature exponents reported in thework of Span and Wagner 4 were fit ted as variables inaddition to the coefficients of the equation. This allowedfor greater flexibility, especially because dodecane hasa longer saturation boundary (greater range of temper-a t u re bet we e n t h e t r iple p oin t a n d t h e c r i t ica l p oin t )than that of many of the f luids f it ted in their work. Inaddit ion, because t here is a l imited a mount of experi-me n t a l da t a in t h e v a p o r p h a s e a n d a t h ig h t e mp e ra -tures, the shorter functional form with fixed exponentson density a ids the ability of the equa tion to extrapolatein t o t h e s e a re a s . G ra p h ic a l t e c h n iq u e s we re u s e d t oensure that the behavior in the vapor phase was similarto that of other f luids (such as propane, where vapor

phase data are available). Nonlinear techniques usedin t he development of the R-125 equa tion of sta te (fromLemmon a nd J acobsen 5) were a lso used to improve thebehavior outside the regions characterized by experi-m en t a l d a t a .

The values of tempera ture a nd density a t the crit icalpoint a re tw o of the most importa nt properties requiredin t h e de ve lop men t of e q u a t ion s of s t a t e . H o we ve r ,

* Author t o whom correspondence should be addressed. Fa x: 303-497-5224. E-Mail: [email protected] t.gov.

(1) Edw ar ds, T.; Ma urice, L. Q.J . Propul. Power2001, 1 7(2), 461-466.

(2 ) Khasa nshi n, T. S . ; Sh c hami al i ou, A. P . ; P oddubskij , O . G . I n t .J. Thermophys. 2003, 24(5), 1277-1289.

(3) Huber, M. L.; La esecke, A.; Perkins, R. A. Energy Fuels2004,18, 968-975.

(4) Spa n, R.; Wagn er, W. I n t . J . T h e r m o ph y s. 2003, 24 (1), 1-39.(5) Lemmon, E. W.; J acobsen, R. T J . Ph y s. C h em . R ef . D a t a , in

press, 2004.

960 E n er g y & Fu el s 2004, 18 , 9 60-967

10.1021/ef0341062 This ar ticle not subject to U.S . Copyright. P ublished 2004 by the American Ch emical SocietyP ubl ish ed on Web 07/03/2004

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measurements of the critical point are often scarce andv a r y w i d el y f or t h e h ea v i er h y d roca r b on s s u ch a sdodecane. In addit ion, the number of measurements ofthe crit ical density are substantially fewer than thosef or t h e cr i t ica l t e mpe ra t u re . Th e cr i t ica l de n si t y isdifficult to determine accurately by experiment, becauseof the infinite compressibility at the crit ical point andt h e a s s ocia t e d di ff icu l t y of re a ch in g t h e rmody n a micequilibrium. For dodeca ne, the critical tempera ture liesin the same region as the limits of dissociat ion, thusincreasing the uncertaint ies in experimenta l tempera-

t u r e v a l ue s. H ow e ve r , s ev er a l m et h od s h a v e b ee nproposed tha t f it temperatur e, pressure, or density asa function of the carbon number t o best represent th ecri t ica l v a lu es . Th e on e s u s ed h e re f o r t h e cr i t ica ltempera ture a nd pressure were published by Lemmona n d G o o dwin .6 Th e cri t ica l de n si t y wa s t a k e n f romAnselme et al.7 These values are

The published values of critical pa ra meters a nd sourcesfor dodecane are listed in Table 1. The selected triplepoint temperature of Finke et al .16 is 263.60 K and isu s e d a s t h e lo we r l imit o f t h e e q u a t io n o f s t a t e . A naddit ional va lue of 263.51 K wa s reported by Huffmane t a l .17

The equation of state expressed in its fundamentalform, explicit in the Helmholtz energy, is widely usedf or c a lcu la t in g t h e rmody n a mic p rop ert ies wit h h ig haccura cy for ma ny fluids. The independent var iables in

the functional form are density and temperature:

where ais the molar H elmholtz energy,a0(F,T) the idealgas contribution to the Helmholtz energy, and ar(F,T)the residual H elmholtz energy tha t corresponds t o theinfluence of intermolecular forces. In many applications,the functional form is explicit in the dimensionlessHelmholtz energy R, using independent variables ofdimensionless density a nd t emperat ure. The form of this

equation is

wh e re ) F/Fc, ) Tc/T, a n d Tc a n d Fc are the crit icalpara meters given a bove and in Table 1.

The dimensionless Helmholtz energy of the idea l ga scan be represented by

wh e re 0 ) F0/Fca n d 0 ) Tc/T0. T0a n d p0a re a rbi t ra rycon s t a n t s , a n d F0 i s t h e idea l g a s de ns i t y a t T0 a n d p0(F0 ) p0/(T0R)). The a rbitra ry da tum sta te va lues for h0

0

a nd s00 are chosen based on common conventions in a

part icular industr y. For hydrocarbons, the entha lpy andentropy ar e often set to zero for th e liquid at the norma lboiling point.

The calculation of thermodynamic properties from theideal gas H elmholtz energy requires an equa tion for the

ide a l g a s h e a t c a p a c i t y , cp0. These values can be ob-

tained from heat capacity measurements extrapolatedto zero pressur e, ga seous speed-of-sound m easu rement s,or calculat ions from stat ist ical methods using funda-menta l frequencies. Values calculated from st at ist ical

t e ch n iq u es a re a v a i la ble f rom t h e Th e rmody n a micsResear ch Center (TRC; see Ma rsh et a l .18) for temper-at ures in the ra nge of 200-1000 K. Their values werefitted to the expression

wh e re t h e ide a l g a s c o n s t a n t , R, is 8.314472 J mol-1

K -1. The Einstein functions containing the terms uk

(6) Lemmon, E. W.; Goodwin, A. R. H. J. Phys. Chem. Ref. Data2000, 29(1), 1-39.

(7) Anselme, M. J .; G ude, M.; Teja, A. S. F l u i d Ph a s e Eq u i l i b . 1990,57(3), 317-326.

(8) Allema nd, N.; J ose, J .; Merlin, J . C. Thermochim. Acta 1986,105, 79-90.(9) Ambrose, D.; Town send, R. T rans. Faraday Soc. 1968,6 4, 2622-

2631.(10) Ambrose, D.; Cox, J . D.; Townsend, R. T r a n s. F a r a d a y Soc.

1960, 56, 1452-1459.(11) Gomez-Nieto, M.; Thodos, G . I n d . En g . C h em . F u n d a m . 1977,

16, 254-259.(12) Mogollon, E.; K a y, W. B.; Teja , A. S. I n d . En g . C h em . F u n d a m .

1982, 21(2), 173-175.(13) Pak, S. C.; Kay, W. B. I n d . En g . C h em . F u n d a m . 1972, 1 1(2),

255-267.(14) Rosenthal, D. J .; Teja, A. S. A I C h E J . 1989, 35, 1829-1834.(15) Teja, A. S.; Gude, M.; Rosenthal, D. J . F l u i d Ph a s e Eq u i l i b .

1989, 52, 193-200.(16) Finke, H. L.; Gross, M. E.; Waddington, G.; Huffman, H. M. J .

Am. Chem. Soc. 1954, 76, 333-341.(1 7) Huffman, H. M.; P arks, G . S. ; B armore , M.J . Am. Chem. Soc.

1931, 53, 3876-3886.

(1 8) M a r s h , K . N . ; Wi lh oi t , R . C . ; F r e nk el , M . ; Y in , D . T RCT h er m o d y n a m i c Pr o p er t i es of Su b st a n ces i n t h e I d ea l G a s St a t e ;Thermodyna mics Resear ch Center: 1994.

Table 1. Summary of Critical Points for n-Dodecane

sourcecritical

temperature (K)critical

pressure (MPa )critical

den sit y (mol/dm 3)

Allemand et a l .8 (1986) 658.154 1.8239Ambrose and Town send 9 (1968) 658.281 1.824Ambrose et al. 10 (1960) 658.281Anselme et al.7 (1990) 658.154 1.3268Gomez-Nieto an d Thodos11 (1977) 653.855 1.8066Mogollon et al.12 (1982) 657.655P a k a n d K a y 13 (1972) 658.904 1.8602

Rosenthal and Teja14

(1989) 658.754 1.810Teja et al.15 (1989) 658.154t h is w or k 658.1 1.817 1.33

Tc ) 658.1 K (1)

pc ) 1.817 MP a (2)

Fc ) 1.33 m ol/dm3

(3)

a(F,T) ) a0(F,T) + a

r(F,T) (4)

a(F,T)

R T ) R(,) ) R

0(,) + R

r(,) (5)

R0

)h0

0

R Tc-

s00

R - 1 + ln (

0

0) - R0

cp0

2

d +1

R

0

cp0

d

(6)

cp0

R) c0 +

k)1

4

ck(uk

T)

2 exp(uk/T)

[exp(uk/T) - 1]2

(7)

T her mod yn am ic Pr oper ti es of n -D od ecan e E n er gy & F u el s, V ol . 18, N o. 4, 2004 961

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we re u s e d s o t h a t t h e be h a v io r o f t h e ide a l g a s h e a t

capacity as a function of temperature w ould be similarto tha t derived from sta tistical methods. However, theseare empirical coefficients and should not be confusedwith the fundamental frequencies.

The ideal gas Helmholtz energy equation, derivedfrom eqs 6 and 7, is

wh e re a1 a n d a2ca n be a n y a rbi t ra ry v a lu e s se t by t h ed ef in i t ion of t h e r e fe re nce s t a t e f or e nt h a l py a n d

entropy. The coefficients of these equations are givenin Table 2.

The functional form used for t he H elmholtz energyequation of state is given as

The coefficients nkof the residua l port ion of the equa tionof state are given in Table 3. The functions used forcalculat ing pressure (p), entha lpy (h), entropy (s), iso-choric heat ca pacity (cv), isobar ic heat ca pacity (cp), an dthe speed of sound (w) from eq 5 a re given in eqs 10-15. The molar mass (M) is 170.33484 g /mol .

Equa tions for additional thermodynamic properties suchas the isotherma l compressibility a nd t he J oule-Thom-son coefficient can be found in Lemmon and J acobsen. 19

The derivatives of the ideal gas Helmholtz energy (given

in eq 8) and the residual Helmholtz energy required byt h e e q u a t io n s f o r t h e t h e rmo dy n a mic p ro p e rt ie s a regiven in Span and Wagner.4

Experimental Data and Comparisons to theEquation of State

The units adopted for this work were kelvins (Inter-national Temperature Scale of 1990, ITS-90) for tem-perature, megapascals for pressure, and moles per cubicdecimeter for density. Units of the experimental datawere converted as necessary from those of the originalpublications to these units. Where necessary, temper-a tur es reported on IP TS-68 and I P TS-48 were convert edto ITS-90 (see P rest on-Thoma s20).

Multiple da ta types over much of the fluid surface ar eoften used in th e development of equa tions of sta te. Notall da ta are used in the fit t ing of the equa tion, althoughcomparisons are ma de to all ava ilable experimental da tato estimate the uncertainties. These uncertainty valuesar e determined by sta t ist ical comparisons of propertyvalues calculated using the equa tion of sta te to th e ex-perimental dat a. These stat ist ics a re based on the per-cent deviat ion in any property, X, which is defined as

Using this definit ion, the avera ge absolute deviat ion isdefined a s

wh e re n i s t h e n u mber of da t a p oin t s . Th e a v era g eabsolute deviat ions between experimental da ta and thee q u a t ion of s t a t e a re g iv en in Ta ble 4. D a t a s et s t h a tconta in only one or t wo da ta points for vapor pressure

(19) Lemmon, E . W.; J acobsen, R. T J. Phys. Chem. Ref. Data2000,29(4), 521-552.

(20) Preston-Thomas, H. M etrologia1990, 27, 3-10.(2 1) Ai cart , E . ; Tardajos, G . ; D i az Pe na, M. J . C h e m . En g . D a t a

1981, 26(1), 22-26.(22) Amina bha vi, T. M.; Ba nerjee, K. I n d i a n J . C h em . 2001, 40 A ,53-64.

(23) Aminabh avi, T. M.; G opalkrishna , B . J . Chem. Eng. Data1994,39, 529-534.

(24) Amina bha vi, T. M.; P at il , V. B. J . C h em . En g . D a t a 1997, 42,641-646.

(25) Aralaguppi, M. I .; J adar, C. V.; Aminabhavi, T. M. J . C h e m .En g . D a t a 1999, 44, 435-440.

(26) Asfour, A.-F. A.; Siddique, M. H.; Vava nellos, T. D. J . C h em .En g . D a t a 1990, 35(2), 192-198.

(27) Beale, E. S. L.; Docksey, P. J. Inst. Pet. Technol. 1935, 2 1, 860-870.

(28) Bessieres, D.; S aint -Guirons, H.; D ar idon, J .-L. High PressureRes. 2000, 18, 279-284.

(2 9) Bi ng ham, E . C . ; Fornwa l t , H . J . J. Rheol. 1930, 1 (4), 372-417.

(30) B oelhouwer, J . W. M . Physica1960, 26(11), 1021-1028.(31) B oelhouwer, J . W. M . Physica1967, 34(3), 484-492.

Table 2. Coefficients of the Ideal-Gas Heat-CapacityEquations

k ck uk

0 23.0851 37.776 12802 29.369 23993 12.461 57004 7.7733 13869

Table 3. Coefficients of the Equation of State

k nk k nk

1 1.38031 7 0.9566272 -2.85352 8 0.03530763 0.288897 9 -0.4450084 -0.165993 10 -0.1189115 0.0923993 11 -0.03664756 0.000282772 12 0.0184223

%X ) (Xd a t a - Xcalc

Xd a t a ) 100 (16)

AAD )1

ni)1

n

||%Xi

|| (17)

R0

) a1 + a2+ ln + (c0 - 1) ln +

k)1

5

ck ln [1 - exp(-uk

Tc)] (8)

Rr(,) ) n1

0.32+ n2

1.23+ n3

1.5+ n4

2

1.4+

n53

0.07+ n6

7

0.8+ n7

2

2.16exp

-+

n85

1.1ex p

-+ n9

4.1exp

-2+ n10

4

5.6exp

-2+

n113

14.5exp-

3

+ n124

12.0ex p-

3

(9)

p ) FR T[1 + (Rr

)

] (10)

h

R T ) [(R

0

)

+ (R

r

)

] + (R

r

)

+ 1 (11)

s

R ) [(R

0

)

+ (R

r

)

] - R0 - Rr (12)

cv

R

) -2

[(

2

R0

2

)

+

(

2

Rr

2

)

] (13)

cp

R )

cv

R +

[1 + (Rr/) - (

2R

r/)]

2

1 + 2(Rr/) +

2(

2R

r/

2)

(14)

w2

M

R T ) 1 + 2(R

r

) + 2(

2R

r

2)

-

[1 + (Rr/)

- (

2R

r/)]2

2[(

2R

0/

2)

+ (2

Rr/

2)]

(15)

962 E n er gy & F u el s, V ol . 18, N o. 4, 2004 L em m on an d H u ber

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Table 4. Summary and Comparisons of Experimental Data for n-Dodecane

referencenumberof points

temperatureran ge (K)

pressurer a n g e (M P a )

densityra nge (mol/dm 3) AAD (%)

Pressure -Density -Temperature, p-F-TBoelhouwer 30 (1960) 28 303-393 0-118 3.96-4.7 0.107Ca u d w e ll e t a l .32 (2003) 85 298-473 0.1-192 3.57-4.81 0.038Cutler et a l .34 (1958) 78 311-408 0.1-689 3.89-5.13 0.953Dymond et a l .38 (1981) 32 298-373 0.1-502 4.05-5.17 0.139Dymond et a l .39 (1982) 35 298-373 0.1-442 4.05-5.1 0.071Gouel47 (1978) 90 298-394 5.17-40.6 3.98-4.52 0.492Lan dau a nd Wuerflinger53 (1980) 88 268-313 10-250 4.35-4.94 0.124

Rousseaux et a l . 67 (1983) 18 323-423 0-30.6 3.82-4.4 0.046Snyder a nd Winnick71 (1970) 96 298-358 0.101-417 4.11-5.04 0.169Taka gi a nd Teran ishi72 (1985) 3 298 0.1-100 4.37-4.69 0.061Tanaka et a l . 73 (1991) 21 298-348 0.1-151 4.16-4.72 0.056

Vapor P ressureAllemand et a l .8 (1986) 19 298-390 0-0.004 1.17Bea le and D ocksey27 (1935) 21 300-658 0-1.77 1.9Dejoz et al.35 (1996) 38 344-502 0-0.134 0.15Gierycz et a l .44 (1985) 13 378-418 0.003-0.013 0.84Houser and Van Winkle48 (1957) 5 401-441 0.007-0.027 0.055Keist ler and Van Winkle49 (1952) 8 363-486 0.001-0.101 1.59K r a f f t 51 (1882) 6 364-488 0.001-0.101 5.49Maia de Oliveira et a l . 54 (2002) 10 432-489 0.02-0.102 0.063M or g a n a n d K ob a y a s h i60 (1994) 13 353-588 0.001-0.671 0.261Sasse et a l .68 (1988) 37 264-371 0-0.002 1.65Viton et al.76 (1996) 35 264-468 0-0.058 0.871Willingham et a l .78 (1945) 20 400-491 0.006-0.104 0.057

S a t u r a t e d L iq u id D e n s it yAicart et a l .21 (1981) 4 298-333 4.23-4.37 0.035Aminabhavi and Gopalkrishna 23 (1994) 3 298-318 4.29-4.38 0.06Aminabhavi and Banerjee22 (2001) 3 298-308 4.33-4.38 0.11Am in a b h a v i a n d P a t i l24 (1997) 3 298-308 4.33-4.38 0.057Arala guppi et a l .25 (1999) 4 298-308 4.34-4.38 0.087Asfour et al.26 (1990) 4 293-313 4.31-4.39 0.106B in g h a m a n d F or n w a lt 29 (1930) 8 273-373 4.04-4.48 0.183Boelhouwer 30 (1960) 4 303-393 3.96-4.35 0.026Cutler et a l .34 (1958) 6 311-408 3.89-4.32 0.045Diaz Pena and Tardajos 36 (1978) 4 298-333 4.22-4.37 0.04D or n t e a n d S m y t h 37 (1930) 12 263-483 3.51-4.53 0.062Dymond and Young40 (1980) 9 283-393 3.97-4.44 0.059Findenegg41 (1970) 6 286-333 4.22-4.43 0.054Francis 42 (1957) 28 373-643 2.2-4.05 0.181G a r c ia e t a l .43 (2002) 5 278-318 4.29-4.46 0.073Gomez-Ibanez a nd Liu 46 (1961) 3 288-308 4.33-4.42 0.04Lan dau a nd Wuerflinger53 (1980) 7 268-313 4.3-4.5 0.183

Mansker et a l .55 (1987) 3 298-338 4.19-4.38 0.12Meeussen et al. 56 (1967) 3 298-328 4.24-4.37 0.079N a y a k e t a l .61 (2001) 3 298-308 4.33-4.37 0.111Ortega et a l .63 (1988) 4 288-318 4.29-4.43 0.05Quayle et a l .66 (1944) 3 293-313 4.31-4.4 0.04Schiessler et al.69 (1946) 5 273-372 4.05-4.48 0.054Schmidt et a l .70 (1966) 4 298-313 4.31-4.37 0.037Trenzado et al.75 (2001) 5 283-313 4.31-4.44 0.019Vogel77 (1946) 4 293-359 4.12-4.4 0.175Wu et al.79 (1998) 4 293-313 4.31-4.4 0.03

Heat of Vaporizat ionMelaugh et a l .57 (1976) 1 298 0.343M or a w e t z58 (1968) 8 298 1.84M or a w e t z59 (1972) 1 298 0.445

Isobaric Heat CapacityBessieres et a l .28 (2000) 77 313-373 0.1-100 0.59Cos t a s a n d P a t t e r s on 33 (1985) 3 283-313 S a t . L iq . 0.22

Lainez et a l . 52 (1989) 1 298 S a t . L iq . 1.27Tardajos et al.74 (1986) 1 298 S a t . L iq . 0.224

S a t u r a t ion H e a t Ca p a ci t yFinke et a l . 16 (1954) 80 11.8-317 0.302H u f f m a n e t a l . 17 (1931) 19 93.3-298 0.843

Isochoric Heat C apa cityPolikhronidi et a l .65 (2002) 55 324-377 4.05-4.27 4.16

Speed of SoundAminabhavi and Gopalkrishna 23 (1994) 3 298-318 S a t . L iq . 0.194Boelhouwer 31 (1967) 85 273-473 10-140 0.349Golik and Ivanova 45 (1962) 6 293-343 S a t . L iq . 0.09Khasanshin and Shchemelev 50 (2001) 30 303-433 0.1-49.1 0.161Neruchev et a l .62 (1969) 19 293-653 S a t . L iq . 0.94P la n t ie r e t a l .64 (2000) 9 293-373 S a t . L iq . 0.145Taka gi a nd Teran ishi72 (1985) 3 298 0.1-100 0.454Tardajos et al.74 (1986) 1 298 S a t . L iq . 0.138


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o r s a t u ra t e d l iq u id de n s i t y a re n o t s h o wn . T h e c o m-parisons given below for the various data sets compare

values from the equation of state to the experimentaldata using the average absolute deviat ion as given by

(32) Ca udw ell, D . R.; Trusler, J . P . M.; Vesovic, V.; Wakeha m, W.A. In Pr oceedi ngs of t he 15th Sym posiu m on Th erm ophysical Properti es,Boulder, CO, J une 2003.

(33) Costas, M.; P at terson, D. J. Chem. Soc., Faraday Trans. 11985,81, 635-654.

(34) Cutler, W. G.; McMickle, R. H.; Webb, W.; Schlessler, R. W. J .Chem. Phys. 1958, 29(4), 727-740.

(35) Dejoz, A.; Gonzalez-Alfaro, V.; Miguel, P. J .; Vazquez, M. I. J .Chem. Eng. Data1996, 41, 93-96.

(36) Dia z P ena, M.; Tarda jos, G . J. Ch em. Th erm odyn. 1978,1 0(1),19-24.

(37) Dornte, R. W.; Smyt h, C. P. J. Am. Chem. Soc. 1930, 5 2, 3546-3552.(38) Dymond, J . H.; Robertson, J .; Isda le, J . D . Int. J. Thermophys.

1981, 2(2), 133-154.(39) Dymond, J . H.; R obertson, J .; Isda le, J . D.J. Chem. Thermodyn.

1982, 14(1), 51-59.(40) Dymond, J . H.; Young, K. J . I n t . J . T h er m o p h y s. 1980, 1 (4),

331-344.(41) Findenegg, G . H . M onatsh. Chem. 1970, 101, 1081-1088.(42) Fra ncis, A. W. I n d . En g . C h em . 1957, 10, 1779-1786.(43) G ar cia, B .; Alcald e, R.; Aparicio, S.; Lea l, J . M.In d. Eng. Chem.

Res. 2002, 41, 4399-4408.(44) Gierycz, P.; Rogalski, M.; Ma lanows ki, S. F l u i d Ph a s e Eq u i l i b .

1985, 22, 107-122.(45) Golik, O. Z.; Ivanova, I. I. Z h . F i z . Kh i m . 1962, 3 6, 1768-1770.(46) G omez-Iba nez, J .; Liu, C.-T. J. Phys. Chem. 1961, 65, 2148-

2151.(47) Gouel, P . Bu ll . Cent. Rech. Explor.sPr o d . El f -Aq u i t a i n e 1978,

2, 211-225.

(48) Houser, H. F.; Van Winkle, M. Chem. Eng. Data Ser. 1957, 2,12-16.

(49) Keistler, J . R.; Van Winkle, M. I n d . En g . C h em . 1952, 44 (3),622-624.

(50) Kha san shin, T. S.; S hchemelev, A. P . H i g h T em p .2001, 3 9(1),60-67.

(51) Krafft , F . Ber. Dtsch. Chem. Ges. 1882, 15, 1687-1712.(52) Lain ez, A.; Rodrigo, M.-M.; Wilhelm, E.; Gr olier, J .-P . E. J .

Chem. Eng. Data1989, 34(3), 332-335.(53) Lan dau , R.; Wuerflinger, A. Ber. BunsensGes. Phys. Chem.

1980, 84, 895-902.

(5 4) M a i a d e O li ve ir a , H . N . ; B e ze r r a L op es , F . W. ; D a n t a sNeto, A. A.; Chiavone-Filho, O. J . C h em . En g . D a t a 2002, 47, 1384-1387.

(55) Mansker, L. D.; C riser, A. C.; J angka molkulcha i, A.; Luks, K.D . Chem. Eng. Commun. 1987, 57, 87-93.

(56) Meeussen, E .; Debeuf, C.; H uyskens, P . Bull. Soc. Chim. Belg.1967, 76, 145-156.

(57) Melaugh , R. A.; Ma nsson, M.; R ossini, F. D. J . Chem. Th erm o-d y n .1976, 8, 623-626.

(58) Morawetz, E. Acta Chem. Scand. 1968, 22, 1509-1531.(59) Morawetz, E. J. Chem. Thermodyn. 1972, 4, 145-151.(60) Morgan, D. L.; Kobayashi, R. F l u i d Ph a s e Eq u i l i b . 1994, 97,

211-242.(61) Nayak, J . N.; Aralaguppi, M. I .; Aminabhavi, T. M. J . C h em .

En g . D a t a 2001, 46, 891-896.(62) Neruchev, Yu. A.; Zotov, V. V.; Otpushchennikov, N. F. Russ.

J. Phys. Chem. 1969, 43(11), 1597-1599.(63) Ortega , J .; Ma tos, J . S.; P ena, J . A.; Pa z-Andrade, M. I .; P ias,

L . ; Fe rnan de z, J . Thermochim. Acta1988, 131, 57-64.

Figure 1. Comparison of densities calculated with the equation of state to the experimental data for n-dodecane.

964 E n er gy & F u el s, V ol . 18, N o. 4, 2004 L em m on an d H u ber

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eq 17. In t he figures, dat a of a given ty pe are generallys e p a ra t e d in t o t e mp e ra t u re in c re me n t s o f 10 K ; t h etemperat ures listed at t he top of each sma ll plot are the

lo we r bo u n ds o f t h e da t a in t h e p lo t . D a t a p o in t s o f fscale a re shown a t the top or bottom of each plot .

Experimental measurements for dodecane and devia-tions of properties ca lculat ed using the equa tion of stat ef r om t h es e d a t a a r e g iv en i n Ta b l e 4 a n d s h ow n i nFigures 1 thr ough 4. Figure 1 compa res the equa tion ofstate to experimental pressure-density-temperature(p-F-T) dat a in t he liquid phase (no data ar e availablein the vapor phase or at supercrit ical temperatures).The equation wa s f it ted prima rily to the data of Ca ud-well et al.32 in the liquid phase. The equation representst h e d a t a o f C a u d w e l l e t a l . , 32 Dymond and co-work-ers,39,40 Rousseaux et al. ,67 Takagi and Teranishi,72 a ndTanaka et al .73 genera lly all w ithin 0.1%, wit h several

(6 4) Pl a nt i e r, F. ; Da ri don, J .-L . ; L ag ouret te , B. ; Bone d, C . H i g h Temp.sH igh Pressures2000, 32(3), 305-310.

(65) Polikhronidi, N. G.; Abdulagatov, I . M.; Batyrova, R. G. F l u i d Ph a se Eq u i l i b . 2002, 201, 269-286.

(66) Quayle, O. R.; Day, R. A.; Brown, G. M. J. Am. Chem. Soc. 1944,

66, 938-941.(67) Rousseaux, P .; Richon, D.; Renon, H. F l u i d Ph a s e Eq u i l i b . 1983,11, 169-177.

(68) Sa sse, K .; J ose, J .; Merlin, J .-C. F l u i d P h a se E q u i l i b .1988, 4 2,287-304.

(69) Schiessler, R. W.; Herr, C. H.; Rytina, A. W.; Weisel, C. A.;Fischl, F.; McLaugh lin, R. L.; Kuehner, H. H. Pr oc. Am . Pet. In st., Sect.31946, 26, 254-302.

(70) Schmidt, R. L.; Ra nda ll, J . C.; Clever, H . L. J . Phys. Chem. 1966,70, 3912-3916.

(71) Snyder, P. S.; Winnick, J . In Proceedi ngs of the 5th Sym posiu mon Thermophysical Properties; B onilla, C. F., E d.; American S ociety ofMecha nical En gineers: New York, 1970; pp 115-129.

(72) Takagi, T.; Teranishi, H. F l u i d Ph a s e Eq u i l i b .1985, 20, 315-320.

(7 3) Ta n a k a , Y . ; H o s ok a w a , H . ; K u b ot a , H . ; M a k i t a , T. I n t . J .Thermophys. 1991, 12(2), 245-264.

(74) Tarda jos, G .; Aicart, E .; Costas, M.; P at terson, D. J. Chem. Soc.,F a r a d a y T r a n s. 1 1986, 82(9), 2977-2987.

(75) Trenzado, J . L.; Ma tos, J . S.; Sega de, L.; Ca rbalo, E. J. Chem.En g . D a t a 2001, 46, 974-983.

(7 6) Viton, C . ; C ha vre t , M.; Be har , E . ; J ose, J . I n t . El e c t r o n . J .Phys.sChem. Data1996, 2, 215-224.

(77) Vogel, A. I. J . Chem. Soc. 1946, 1946, 133-139.(78) Willingha m, C. B.; Tay lor, W. J .; P ignocco, J . M.; Rossini, F.

D . J . R es . N a t l . Bu r . St a n d . 1945, 35, 219-232.(79) Wu, J .; Shan, Z.; Asfour, A.-F. A. F l u i d Ph a s e Eq u i l i b . 1998,

143, 263-274.

Figure 2. C o mp a r is on of s a t u r a t e d l iq u id d en s it i es ca l cu la t e d w i t h t h e e q ua t i on of s t a t e t o t h e e xp er i me n t a l d a t a f orn-dodecane.


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outliers at 340 K. The data of Snyder and Winnick 71

are consistently 0.1%-0.2% lower tha n tha t given by

t h e e q u a t ion o f s t a t e . Th e da t a of L a n da u a n d Wu e r-flinger53 ar e generally w ithin 0.2% of the equa tion ofs t a t e , wi t h s o me o f t h e da t a a bo v e a n d s o me be lo w.Differences are up to 2%for the data of Cutler et al .34

a n d 1. 5% f or t h e da t a of G o u el ;47 t h e s e da t a o v e rla pother high-accuracy da ta in the liquid pha se. Of the 150da t a p oin t s a v a i la ble f or t h e s a t u ra t e d l iq u id de n si t y(see Figure 2), th e deviat ions of 122 of these points a rewit hin 0.15%. However, the tempera tur es for a ll but tw oof t h e da t a s e t s a re 350 K . T h e a v e ra g e a bs o lu t e e rro rs a t t h e s ehigher temperatures are 0.06%for the data of Dejoz etal. ,35 0.16% f or t h e da t a of M org a n a n d K o ba y a s h i ,60

0.04%for the data of Willingham et al. ,78 and 0.3%fort h e d a t a of Vi ton et a l .76 Th e s c a t t er i n t h e d a t aincreases substantially as the temperature decreases,approaching 5%at 300 K. However, the vapor pressurei s 2 1 P a a t t h is t em per a t u re, a n d s ma l l a b sol ut edifferences r epresent significan t percenta ges of thevalues at these low pressures.

The isobar ic hea t capa city of dodeca ne wa s meas uredby Bessieres et al .28 from 313 K to 373 K at pressuresup to 100 MPa. There are also f ive data points in theliquid phase a t

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uncertainties (where the uncertainties can be consideredt o be e s t ima t e s of a combin ed e xp a n ded u n ce rt a in t ywit h a covera ge factor of 2) of density values calculat edusing the equa tion of sta te in t he liquid phase (includingat saturation) are 0.2%for pressures of 350 K a n d a p pr oa ch 5% a s t h etempera ture decreases to the triple point temperature.These estima ted uncerta inties for calculated propertiesare consistent w ith t he experimenta l a ccuracies of th evarious available experimental data. I f addit ional data

are measured in the future, i t is reasonable to expectt h a t t h e ov er a l l a c cu r a cy of t h e cor r el a t i on ca n b eimproved, consistent with the accuracy of the new data.As a n a id to those using computer programs to calcula tethe properties of dodecan e, calculated va lues of proper-ties from the equa tion of sta te a re given in Table 5. Thenumber of digits displa yed in the ta ble does not indicat ethe a ccuracy in the va lues but is given only for valida-tion of computer code.

Acknowledgment. We gra tefully acknowledge pa r-tia l finan cia l support for t his project t hrough th e NASAJ ohn H. G lenn Research Center.

EF0341062

Figure 4. C omparison of speed-of-sound values calculat ed with the equa tion of stat e to the experimenta l dat a for n-dodecane.

Table 5. Calculated Property Values for Algorithm Verification

temperature(K )

pressure( M P a )

density(mo l/dm 3)

cv(J mol-1 K -1)

cp(J mol-1 K -1)

speed ofsoun d (m/s)

300.0 0.0 0.0 271.3952 279.7096 122.8511

300.0 7.161946 4.4 311.1937 377.1307 1316.614600.0 0.7228018 0.2 488.1173 526.2322 123.5851600.0 120.2532 4.0 499.9857 539.3864 1255.247658.2 1.820055 1.33 547.6852 128753.9 49.76424


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