William G. Lloyd Institute for Mining and Minerals Research University of Kentucky Lexington, KY 40506 and Derek A. Davenport Purdue Universitv West Lafayene. IN 47907
Applying Thermodynamics to Fossil Fuels
I
Heats of combustion from elemental compositions
In a famous passage in the Preface of their classic 1923 text, Lewis and Randall liken thermodynamics to a partially completed cathedral: Science has its cathedrals, built by the efforts of a few architects and of many workers. In these loftier monuments of scientificthought a tradition has arisen wherehy the friendly usages of colloquial speech give way to a certain severity and formality. While this may sometimes promote precise thinking, it more often results in the intimidation of the neophyte. Therefore we have attempted, while conducting the reader through the classic edifice of thermodyamics into the workshops where construction is now in progress, to temper the customary severity of the science in so far as is compatible with clarity of thought. In the eyes of many teachers of physical chemistry that cathedral is now largely completed:
What can be done, however, to estimate heats of formation and b ~ a t of s cwnbu~fion o i the mixtures encotmrered in fossil fuels? As part of a larger study of a coal liquvfaction process being examined in 11 600 ton day pilot plant' we have been intrrested in predicting the heating valttes of various coalderived liauid fractions and uf other fosstl fuel liuuids. These are extremely complex mixtures for which detail& molecular composition is unavailable. indeed for which some comoonenis remain unanalyzed and even uncharacterized. F O ~a liquid fuel composed principally of carbon and hydrogen it might he hoped that a determination of carbon and hydrogen contents would permit a rough prediction of the heating value of the mixture. This approach has not received much recent attention for the good reason that values of AHcofor common organic compounds are found to be quite variable, even when reduced to a per cm? or per gram basis. Figure 1illustrates the scatter obtained for a number of commonoreanic comoounds when AH,' is plotted against the atomic ratio. ~ ~ d r o carbons as a group typically have enthalpies of combustion in the range -38 to -48 kJ1g. If we examine some members of the small subgroup of hydrocarbons of formula C,H,, it is evident that these are spread across the entire range of values, e.g., tetrametbylphenanthrene, 40.1; cubane, 45.5; benzene, 38.5; and acetylene, 48.3 kJlg. This scatter has not encouraged efforts to seek a good predictive correlation between elemental composition and enthalpy of combustion. Fossil fuel liquids do not, however, contain significant auantities of manv imnortant classes of oreanic comnounds. whether formed by siow geochemical processes or Gy hightemperature hydroliquefaction technology, these liquids are
HY/c
centuries. Seeing only the perfection of the completed whole, we are impressed as by some superhuman agency. T o the average student the achievement does indeed verge on the superhuman and the edifice is one of almost paralyzing perfection. But one can't (or a t least chemists usually don't) live in such a place. The real world obtrudes and Euclidean abstractions must give way to quantity-surveying. In view of the amount of time devoted to chemical thermodynamics in both the undergraduate and graduate curriculum it is surnrisine how rarelv one hears strictlv thermodynamic arguments in academic discussions: structural and even kinetic arguments tend to predominate. In the industrial world, however, thermodynamics comes into its own, though it is often a work-a-day variety only distantly related to the ex cathedra statements of the schoolmen. Fossil fuel research provides a number of o~portunities for such amlied ther.. .. modynamics. Heats of combustion of pure comnounds are easilv calculated when heats of formation are available. For a hydrocarbon underpoinz - ..complete combustion ( e m . (1)) the standard enthalpy of combukon, AHCo,is
-
-
+
The coal liquefaction plant in Catlettsburg, Kentucky, is operated by Ashland Oil Company using the H-Coal Process developed by Hydrocarbon Research, Ine., Trenton, New Jersey.
+
C,H, + ( m 0.25n)Os mC02 0.5nH20 (1) obtained from the heats of formation of COa (-393.5 kJ/mole) and of Hz0 (-241.8 kJ/mole) ( I ) AHCo(kJ/mole)= -393.5m
- 120.9n - AHP(C,H,)
(2)
For compounds containing heteroatoms it is necessary to make some assumptions concerning the products of combustion. For a compound of formula C,H,O,N,S,, for example, we may assume that the nitrogen is substantially converted to Np and the sulfur to SO2 (AH," = -296.8 kJ1 mole). The heat of combustion is then calculated by eqn. (3): AH,'(k.Jlmale)
=
-393.5m
- 120.9n - 296.8y
- AHP(C,H,O,N,S,) (3) When the structure of a pure compound is known hut the standard heat of formation has not been measured there exist several means of estimating AHIo by summing partial molal quantities. 56 / Journal of Chemical Education
Figure 1. Enthaipiesof combuslion of various organic compounds.Ordinate: Enthalpy in kJlg Abscissa: Hydrogenlcarban atomic ratio. A-acetylene. B--anthraquinone,C-benzene, Lbenroic acid, E-benzoquinone, Fbenzyl ethyl sulfide. Gbiacetyl. kbutadiene. Lbutanone. J-l-butanoi. K-tert-b~tyl hydmpemxide. L-eubane, kcumene. N--cumyl hydropsroxide. &cydarctanone, P-cydopropane, 0-cyclohexane. Rdi-tert-butyl peroxide. S-ethyl acetate. T-indene, &isabutme. V-naphthalene. W-l-oclanol, X-perylena, Y-phenyl acetate, Z-spiropentane.
substantially free of reactive olefins, diolefins, acetylenes, and strained small-ring structures. The functional group spread among heteroatom compounds is similarly limited. Oxygenated comoounds. for examnle. . . include ohenolic and ether functions and some alcohol functions but no significant levels of carbonyl or peroxidic functions. This proves to be a very important limitation, and makes possible the following treatment,
the low value of MCofor ethanediol reflects that comnound's hieh .. oxveen content (52% bv . weight). .. All 138 compounds, of whirh only selecled exnmples are given in'l'al)le I , have been subjected t o a multiple regresiun an;d)sis of enthalpy of n~mbustionas a functi~moi~lt.~nental composirion, using a standard program (31 and forcing the for thr(,ugh the origin. Coef'iicie~~ts for the leait squared i i t i m these data are given in eqn. (4).
Procedure and Calculations Selections taken from a compilation of 138 compounds representative of those found in fossil fuel liquids, for which gaseous state enthalpies of formation are known (2),are listed in Tahle The corresoondinz enthaloies of combustion calculated hy cqn. (31areuhulnied m a perpram basis under s listed in order thr headinr 411. O uwtual). H s d r w ~ r h o n nre of increasing atomic H/C ratio. These compounds show a regular increase in enthalpy of comhustion per gram as the hydrogen content increases. On casual inspection the remaining compounds, all containing 0 , N o r S, do not follow this trend very closely, since the heteroatom content on a weight fraction basis varies almost randomly. For example,
AHCo(kJ/g)= -0.35777[%C] 0.91758[%H]+ 0.08451[%01 - 0.05938[%N]- 0.11187[%S] (4) The goodness of this fit is indicated by the following. For a n average value of iW,' of 36.6 kJ/g the average predictive error is 0.16 kJIg, less than 0.5%. A plot of the predicted values of Ah'," (using eqn. (4)) versus the actual values (using eqn. (3)) for all of the compounds in Table 1 is shown in Figure 2. Hingrn, 1.nnum and Miknih have recently rcported the elemental analyses and the experimentally determined heats o-~~~ f comhustion of 2h ioreien shale oils (41. Anr>licatiunof can. (4) to their data res& in"estimates whici A o n s i s t e n t l y low bv 5-7%. Most of this error mav he attributed to the heat of vaporization of the water formed in the oxygen bomb calorimeter. For a typical shale oil containing 12% hydrogen, condensation of the water of reaction a t 25°C provides an additional 2.63 kJ/e. For each incremental 1%of hvdroeen. the heat of condensation of the water formed increases-thd observed heat of comhustion hy 0.22 kJ per gram of sample. When the coefficient of [%HI is corrected for this heat of condensation the predictive regression of eqn. (4) becomes
Table 1. Heats of Combustion of Selected Organic Compounds -AkO,m,,,, Compound
HIC ratio
C
H
perylene tetracene anlhracene naphthalene
20 18 14 10
12 12 10 8
0.600 ,667 ,714 ,800
benzene indane telralin cumene
6 9 10 9
6 10 12 12
1.000 1.111 1.200 1.333
9 6 8 5
16 12 18 12
1.778 2.000 2.250 2.400
ciShexahvdroindane methyicyclopentane 2,3,6trimelhylpenlane
X
kJ/ gram actuals estimatedb
X = Oxygen 12 10 6 7
8 8 8 8
o-ethylphenol mmelhylani~ole 1,d-dioxane cyclopentanol
8 8 4 5
10 10 8 10
2 1
1.250 1.250 2.000 2.000
tehahvhofurhrrvl alcohol cb3-methyicyclohexanol lrans9-methyicyclohexanol ethanediol
5
10
2
2.000
dibenzofuran 1-naphthol 1.4-dioxatetralin benzyl alcohol
1 1
2 I
1
I
0.667 800 1000 1.143
-
~~~~
Table 2 shows the compositions and heating values of selected shale oils from the data of Ringen and coworkers (4), along with the heating values predicted by eqn. (5). These predictions are fairly good. The average error for the set of 28 shale oils is 0.75% relative. By comparison, the average error using the Boie equation (5) is 0.94%,and that using the Dulong equation (discussed below) is 3.6%. Francis and Thomas (6)have examined the heating values of a number of coal- and petroleum-derived fuel oil fractions, for which they have also determined elemental compositions by microcombustion train analysis. Recent data are shown in Tahle 3, along with predicted heating values using eqn. (5). Predictions for these liquid fuels covering a wide range of properties are again in reasonable agreement with measured heats of comhustion. Data for the entire sets of analyses abstracted in Tables 1 , 2 and 4 may be obtained by writing to W.G.L.
carbazole indole diphenylamine pyridine 3-picoline pyrrole N-elhyianiiine pyrrolidlne diphenyl sulfide lhiophene thiophenoi n-toluenelhiol benryl ethyl sulfide tetrahydrothiophene cyciohexanethiol
20 Calculated from megas mstandard emhalpiesdfarmation(datad Coxand ~ilcher. ref. 2).using eqn. 13). aCafcufated bom elemental composition by eqn. 14).
30
40
Figure 2. Enthalpiesof combustion of various organic compounds. Ordinale: Enmaipy predicted by eqn. (4). in kJlg. Abscissa: Enthaipy from heat of fwmation data (Cox and Pilchar, ref. in kJ/g.
a,
Volume 57. Number 1. January 1980 / 57
Table 2.
Heats of Combustion of Selected Foreign Shale Oils heating value, kJ/gram actuals estimateda
Australia Australia Brazil Brazil
43.70 44.35 43.84 43.93 43.19 43.10 42.40 43.33 40.58 41.79 42.70 43.10
France France Manchuria New Zealand Sweden Sweden South Africa South Abica
43.16 44.21 42.90 43.73 43.34 42.95 42.17 43.02 40.55 41.80 43.30 4334
oafaandaccerrionnumbers tromRingen. Lanvmand Miknir, re,. (4, %~alcvlafed tram elemental compositionby egn. (5).
Table 3. no.
1 2 3 4 5 6
source H-Coal Oil, ASOr H-Coal Oil. ASBE H-Coal Oil. ASB ( S y n c r ~ d e ) ~ KCaal VSBC (22.5% ash) NO. 2 fuel oil NO. 4 fuel oil
Heating Values for Coal- and Petroleum-Derived Fuel Oils' %C
%H
%N
%S
87.15 87.78 87.76 69.17 85.63 87.53
10.53 1001 10.17 4.35 13.28 11.00
0.38 0.44 0.34 1.29
0.33 0.16 0.12 2.25 0.29 0.74
. . .d . . .d
~ a t provided a by H E. ranc cis and G, A, momao, institute for ~iningam ~inerslr~esearch. eqn. (5). s i m c ~ e kindly s omuided by Hydrocarbon Research. ~nc..rento on. N.J. ASO = atornospheric still overhead fraction: ASB d L e s ~than 0 05%
heating values, kJ/gram actual calcd4
42.50 42.66 42.54 28.75 45.58 43.54
43.06 42.68 42.85 28.08 45.68 43.83
%Y
Coal is one of the more difficult materials to work with in a rigorous manner. A crosslinked and substantially insoluble "organic rock", its composition is markedly variable from seam to seam and even from one location to another within a seam. Coals commonly contain 5-15% inorganic constituents. 70-90% carbon. 4-20s oxvaen. a HIC atomic ratio between 0.4 and 1.0, and up to sevkra~percent sulfur and nitroEen. Eauation (5)was tested (7) as a ~redictorfor the heatina ialues bf a group of 196 coals, for which elemental analyses, experimental heating values, and many other characteristics have been tabulated in the Pennsylvania State University coal database (8).Application of eqn. (5) to this body of data (7) shows a good correlation (r = 0.995) hut with a systematic offset of about 1kJ/g: the calculated heating values are higher than those actually found. With the addition of an intercept term, this correlation can he applied to coals Qo(kJ/g)= -0 3578[%C]- 1.1357[%H]+ 0.0845[%0] -0.05941%Nl . . - 0.11191%SI . . + 0.974 ( 6 ) Equation (6) yields an average error (196 coals) of 0.26 kJ/g (0.79% relative), au~roximatelvthat associated with the expected analytical variations (7). The coals in this group come from many locations and include all ranks from anthracites to lignites. Some representative coals are shown in Table 4. Figure 3 shows the correlation of estimated versus actual heating values for these coals. The intercept term in eqn. ( 6 ) measures a systematic difference between an "average" coal and an "average" fossil fuel liquid. The magnitude of this term, -0.97 kJ/g, can he interpreted as an estimate of the average investment in energy required to disrupt the network structure of a coal. Discussion
P. L. Dulong is credited with formulation of the idea" that heats of combustion of materials can he estimated by summing "is idea is part ot the substantialM y of thoughts, formulations and experimental measurements which Dulong shared with contemporary scientists but did not formally publish. Most later workers refer to the "Dulong equation" without citation (4, 10-14); the Jarrier citation (9) is in error. 58 1 Journal of Chemical Education
= atmmpheric still bomms: VSB =vacuum still bottoms.
. 24
28
32
Figure 3. Heah of combustion of selected coals. Ordinate: Heat of combustion predicted by eqn. (€4,in kJIg. Abscissa: Observed heat of combustion. Pennsylvania State University coal database (Spackman, et al.. ref. 8). in kJ/g.
the weighted heats of combustion of the constituent elements (4, $14). When oxygen is present, it is assumed to be present effectively as H20, and the hydrogen fraction is corrected accordingly (9,12,13). Hence the "Dulong formula" given by Jarrier (9) is: Qo(kJ/g)= -0.3389[%C] - 1.433[%H]- 0.094[%S]+ 0.179[%0] (7) [Note that the coefficient of the oxygen term is one-eighth that of the hydrogen term.] This formulation has proven to he extraordinarily durable. It has been used, often without attribution, in applied, technical and trade publications related to fossil fuel use. Heats of formation of compounds were not available to Dulong, and have been ignored by subsequent generations of users. Furthermore, as others have noted, (10-12) the assumption that all oxygen present is bound as H z 0 is obviously not valid; the true coefficient for oxygen "dipend du mode de ripartition (supposi) de 1'oxygPne de
pretation can be tested by measuring departures from the exoectations of ean. (4). usine the data of Cox and Pilcher (2). The actual and pk,dicted valk\uf for ~ndetware- 1 i 2 5 and -:I968 kd/& indicating a derxxture of ahout -66 k.1 mole. The departuredfrom eqn.74) o i trans-2-hutene, styrene, and ethyl vinyl ether are -69, -87 and -78 kJ/mole; that for l&butadiene is -134.8 kJImole or -67 kJ per double bond. These five markedly different compounds share the structural feature of non-aromatic C=C unsaturation, and all show departures of about 73 f 8 kJ/mole. A similar examination of cyclopropane, spiropentane, hicyclopropyl and bicyclo [3.1.0]hexane shows departures of 115,116,98 and 104 kJ/ mole Der rine. e r o u. ~ e daround 108 8 kJ/mole. . cvclo~roaane . . . ...,. The rmsisrenry of these estimates suggest.? that njn. 1.4, may afford 11uuirk roueh estimate u i the c n t h a l ~ vn,utrihutimi of high-energy st6ctural or functional wherever heat of combustion data are obtained. As a practical matter the use of elemental compositional information to predict heating values has not been seen to he very attractiv;, owing to thk "congenital and prohibitive weakness" (10) that the required elemental analyses have entailed considerably more time and effort than direct bomb calorimetric measurements. With the recent availability of several fast and reliable instrumental packages for CHNS analysis these time requirements have been reversed. Furthermore. a aood correlatine eauation ~ e r m i t both s current and retr~$~e;tivemonitoring 01fuel analysis data and thus provides an additional quality control tool.
constitution entre le carbone et l'hydropthe: dlQment de doute qui, en multipliant les solutions, prouue assez qu'aucune n'est satisfaisante" (10). Actually, the situation is not that serious. Standard enthalpies of formation of the compoundsin Table 1areseldom asmuch as 5% of their enthalpies of combustion. Values of AH," for benzene and tetralin, for instance, are 2.6% and 0.6% of the corresponding values of AHCo.Furthermore, the impact of C-0 versus C-H bonding upon AHco is quite small. If we consider the four hutaools, their three isomeric ethers and the four butene isomers (these latter calculated as butene water = CaHloO), the average enthalpy of combustion is 34.0 kJ/g and the standard deviation for these eleven cases--covering all possible combinations of C-O-H, C-O-C and H-O-H-is 0.30 kJ/g, less than 1%of the average AHc'. A comparison of our eqns. (5) and (6) with eqn. (7) which was proposed approximately 150 years ago shows the modest progress we have made since Dulong. Jarrier (9) and Selvig and Gibson (12) have reviewed a number of similar formulas for the prediction of heats of combustion from elemental composition. The best of these and of several newer formulas, in terms of the data we have examined, is that of Boie (5).Equations (5) and (6), from our present work, afford somewhat better fits than any of these, including the Boie equation, to the data of Tables 1-4. Given the compositional correlation of eqn. (4), it is possible to estimate enthalpies of formation for "average" members of each of the several atomic species. For example, from the coefficient of [%C] in eqn. (4) it is evident that the value of AHC0for an "average" carbon atom in a fossil fuel liquid is -35.8 kJ/g or -430 kJImole. Then from eqn. (2) the value of AH,' of this "average" carbon can he estimated to he +36.5 kJ/mole or +3.04 kJ/g. By similar reasoning the values of AHc' and A H f o for "average" H, 0 , N, and S atoms can be estimated. These estimates are given in Table 5. In the scatter plot of Figure 1the hydrocarbons of Table 1 fall close to a line running from perylene and naphthalene (X and V) on the left through cyclohexane and isobutane (Q and U) on the right. Compounds falling below this line are heteroatom compounds, in which the hydrogen and carbon are partially replaced by elements providing smaller per-gram heats of combustion ( N or S) or none a t all (oxygen). When these heteroatoms are taken into account by eqn. (4), all of these compounds fall into line (Fig. 2). Compounds in Figure 1 falling above this line are characterized by high-energy functional groups or highly strained structures. This inter-
+
Table 4. PSU
no.*
apparent rank
"
*
Acknowledgment
We are indebted to Henry E. Francis and Gerald A. Thomas of the Institute for Minine and Minerals Research for the elemental and calorimetricdata presented in Table 3 Table 5.
Carbon in fuel Hydrogen in fuel Oxygen in fuel Nitrogen in fuel Sulfur in fuel
AH,', kJ/g
+301 -28.20 (-810-12)4 +5.94 t1.93
-35.78 -91.76 +8.4Sh -5.94= -11.19"
mcrerat and toluene: AH,'
Heats of Combustion of Selected United States Coals
state
seam
an
130 236 5 163 70 272 305 105A
mvb mvb hvAb hvAb
MO
Baxter
hvBb hvBb hvBb
WA KY OH
Big Seam #2 Kentucky #9 Ohio # I I
hvcb
IN
Indiana Block 1
243 309 022 230 242 87 92 141
hvCb hvCb SU~A
IA NM IL
Iowa Bottom NO. 8 Seam Illinois #6
sub8
MT
Rosebud
subs SU~C lig lig
WY
Dietz
ND
Zap Lower Lignite Lignite
lvb lvb
AH,', kJlg
Estimated from the coefficients of eqn. (41. "AH,' estimated from differences between pairs, eg., calculated from the oxygen coeflicient in eqn. 141. Assuming N2 to be the praduct of combustion. dAssumi"g SOz to be the woductof combusfim.
80 85 145 147
an
'Average' Enthalpies of Formatlon and Combustiona
PA PA OK AR
Buck Mountain Seam 8 Hartshorne Lower Spadra
WV CO
Pocahontas #3 Coal Basin B Elkharn #3
KY
MT
TX
heating value, kJlgram actuals estimated
29.30 32.83 34.43 29.36 33.78 33.99 33.28 29.89 24.25 30.56 25.18 31.50 26.72 25.53 29.46 27.18 28.28 25.95 25.52 26.32
29.28 32.91 34.40 29.23 33.78 33.85 33.31 30.03 24.04 30.66 25.48 31.43 27.60 25.38 29.82 27.56 28.44 26.28 25.29 26.35
Accession numbers, m k and hesting values are hom medata base esublishedby meCast Research Secfion.Pennsylvania StateUnivemity(Spackman.et ai., ref. 1 8 ) . Rank abbreviations: an-amhracite. Ivb-low volatile bituminous. mvb-medium volatile bituminalu, hvb-high volstile bituminous, sub-sub-bituminous, iig-lignite: A, e and C denote subgroups within the hvb and rub ranks. %~aiculated from elemental composition by eqn. (6).
Volume 57, Number 1. January 1980 1 59
Literature Cited ill Stull. D. R.. and Pmphct, H.."JANAFThem~hhhical TabI11"2nd ed., Nat'l. RUB*" of Standards NSRDS-NBS 37, U.S. Gov't. Plinting Office. Washington, DC., 8971
(2) Cox, J. D., and Pibher, G., "Thermahemistry of O~ganicand Organumetallic C m poundr.)'Aeademie Press, N.Y., 1971. (3) Slstisticd AnalysisSystem, SAS76edition. General Linear Models (GLM) pracedure, SAS Institute, he.. Raleigh. N.C. (4) Ringen, S., Lanum, J., sndhlik6n, F. P., Fuel, 58.63 11979). (5) Roie, W., Wisr~nscholLlich~ Zeitschriji dsr Terhnirehpn Hochschul~Drsrd~n, 2,687 11952mi. . . ~ ~ , ~ (6) Francis. H. E, and Thmru, G. A. (Institute far Mining and MinerabRereareh), private ~ornmunleati~~.~ ~~
60 I Journal of Chemical Education
(71 L I O Y ~ W. . G., and ~ ~H E., submitted ~ ~ to F U~ ~ . i ~ . (81 Spaekman, W., Dsvis.A., Wa1ker.P. L.,Lovell. H.L..Stefanko,R.,Essenhigh,R.H., Vastola, F. L a n d Given, P. H. "Evaluation and Development of Special Purp-e Coalr,"U.S. Energy Research and Develupment Administration Rept. FE-0390.2.
..."
".
q a n h m b . 707n
(9) Jarrier. P., C h o l ~ u r elnduslrie. t 10,107 11929). 110) Veron, M.. Chalmr et Induslrie. 10,433 (19291. (11) Fiddner. A. C., and Selvig, W. A,, U.S. Rureau of Minea Teehnicvl Paper586 (1938). p. 29. 1121 Sdvig, W. A,. and Gihmn. F. H., "Calorific Value of Coal': in H. H. Lowry (Editor) "Chemistry of Coal Utilization", Wiley & Sons, New York, 1915. Voi. 1. pp 13%
...
A,
(13) Schuyler, J., and Van Krevelen. D. W., &el, 31. L 8 (1954) 114) Suhramanian,T. K.,CoolAze, 82.no. 12,163 (1977).
