combustion of coal chars- a review

8/12/2019 Combustion of Coal Chars- A Review

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Nineteenth Symposium (International) on Com bustion/The Comb ustion Institute, 1982/pp. 1045-1065

T H E C O M B U S T I O N R A T E S O F C O A L C H A R S A R E V I E W

I . W . S MITHCSIRO Division of Fossil FuelsP.O. Box 136North Ryde NS W 2113 Australia

A brief description is given of devolati lization of raw coal and com bus tion of the residualchar. M ajor achiev em ents in the study of devolati lization and imp ortan t areas for fur therexperimentat ion are noted; how ever, a t tent ion is focussed on the ra te processe s involved inchar combustion.Means o f calculating re act ion rates are shown w hich acco unt for tem per ature s of partic les,mass t ransfe r and d if fus ion of oxygen in to the pa r t ic le s po re s t ruc ture , and reac t ion on thepor e walls . Theoretical consid erat ion is then given to the changes in the size, de nsi ty, andpore s t ruc ture of chars a s they burn .Exp erimen tal data are show n for obs erved react ivi ties of coal chars correc ted for externalmass transfer effects , an d intrinsic react ivi t ies are re po rted for various coal chars an d oth ercarbons corrected for por e diffusion effects . M easur ed data on mass-transfer ra tes andchanges in part ic le structure during combustion are given.Recommendat ions a re mad e for fur the r resea rch on char react iv i ty and th e m anne r inwhich pore s t ruc ture deve lops du r ing combust ion . Th e nee d for com bust ion-or ien ted k ine ticsstudies o f coal devolatilization is outlin ed.

ntroductionSolid fuels have a major and increasingly impor-tant role to play in combustion: pulverized fuel (pf)(coa l groun d to


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1 04 6 C O A L C O M B U S T I O N K I N E T I C S A N D M E C H A N I S M Scombustion of coal chars and re la ted sol ids . Th enext section describes the beha viour o f part ic lesdurin g combustion, including devolat il izat ion. Sub-sequent sect ions deal with: Calculat ion of Part ic leCombust ion Ra tes , Theore t ica l Re la t ionships forCalculat ing Burning Rates, Experimental Data onBurning Rates, and Changes in Part ic le StructureDu ring Combust ion . In the C onc luding Remarksemphasis is given to some key areas for further re-search.Reliance is placed on earl ier reviews to coverestablished ground: emphasis here is placed on newwork and its consequences. The review deals mainlywith th e m ajor sol id fuel----coal . Ho w ever the the-ory outl ined below is applicable to the com bustio nof other sol id fuels. Experimental data on masstransfer rates are applicable to any solid fuels.

Pa r t ic le Combust ionHistorical aspects of coal and carbon combustionhave been out l ined by Essenhigh 1 and Mulcahy. 2Field e t a l 3 a nd S m oo t a nd P ra tt4 have g iven com-prehen sive accoun ts of pulverized-coal combustion.Essenhigh and his col leagues published a numberof reviews on coal combustion5-9 and specific re-views on the mechanisms involved in coal-oxygenand rela ted react ions have been given by Wendt,10Mulcahy and Smith, 11 H edle y and Leesley, 12 and

3 2Laurendeau. Mulcahy highligh ted som e of themore notable aspects of the carbon-oxygen react iona nd S mi t h 14,15 r e v i e w e d fa c t o rs c on t ro l l i ng t hereactivity of pulverized-coal chars. T he m echanism sof coa l pyrolys i s have been reviewed by J i ingtenand van H eek, 1~ An thony an d How ard, 17 and Ho w-ard . 18A9 At the mo me nt the re i s mu ch in te res t inthe mechanist ic and technical aspects of coal pyrol-ysis as a step in the production of l iquid fuels fromcoal, Is '2~ how ever, there is a notab le lack of kinet icdata re levant to combustion condit ions.The processes involved in the pyrolysis and com-bustion o f partic les are complex. D epe nd ing on thetype of coal , the part ic le size , the re la t ive ra tes ofheating, decom position, a nd oxygen transfer, vo la-t i le evolut ion and combustion of the sol id may oc-cur in separate stages or simultaneously.Recent photographic s tudies of the behaviour ofdi lute suspensions of pulverized coals in the post-flame gases of small-scale gas bu rners 21'2z show edthat volat i les issue from bituminous coal part ic les(80 to 100 Ixm in size) in jets o r trails, no t alwaysas spherically-uniform clouds (see Fig. 1). It is pos-sible that, in regions o f the particle surface w he re

there are no volat i le je ts , oxygen can at tack thepart ic le direct ly. No tra i ls were shown for anthra-ci tes, l ignites, or 40 ~m part ic les of a bi tuminouscoal. 22 Particles (1 mm ) of an Australian br ow n coal( l igni te ) showed he te rogeneous combust ion be forethe ons et of volatile evolution, z3 Leslie e t a l z 4working on the com bus tion of - 6 0 VLm partic lesof Montana sub-bi tuminous coa l a t -7 % v/ v oxy-gen, indicated that a t gas temperatures about 1100K part ic les burn by direct oxygen at tack with l i t t leseparate evolut ion of volat iles. Ho we ver a t 160 0 Kvolat i le evolut ion appears to precede the combus-tion of the solid particles.The behaviour of coa ls dur ing pyrolys i s dependson the fac tors a l ready out l ined , and on o the r con-di t ions spec i f ic to pa r t icula r combustors . In pfflames, coal is injected in a dense stream conveyedin a je t o f a ir . Ini t ial heat ing is mainly b y ho t gasesrecirculated into the je t . Part ic les in the centre ofthe je t a re hea ted re la t ive ly s lowly; those on theedge a re hea ted rapid ly and in the presence ofhigh levels of oxygen. The amount of volat i le mat-te r produced, the na ture of the pore s t ruc ture , andthe s ize of the resul t ing char pa r t ic les depend onthe ra te of hea t ingz5 26 and on the level o f oxy-ge n. 27 Dur i ng f l u i d i z e d -be d c omb us t i on t he i n -jected fuel part ic les are heated rapidly, with muchof the heating taking place by direct particle-to-par-ticle contact. Tylerzs,29 injec ted fine particles (~ 10 0pLm) of a w ide ra nge of coals into fluid ized bedsof sand. Over the tempera ture range 400 to 1000~ C,in the absence of oxygen, coking and non -cokin gbituminous coals, sub-b itumin ous coals, and l ignitesal l showed some degree of plast ic behaviour andadhesion to other particles.Useful studies have been made on the kinet icso f p y r o l y s i s o f p u l v e r i z e d c o a l i n e n t r a i n -ment , ~ -33 bu t l it tl e work has been done on coalbehaviour under combustion condit ions. Lit t le a t-tent ion has been given to the effects of the a tmo-sphere (especially oxidizing) on pyrolysis, nor hasthe re been adequa te de te rmina t ion of the na tureof the volat i le products. Very few studies havebeen done on coa l pyrolys i s dur ing f lu id ized-bedc o m b u s t i o n . S o m e u s e f u l st u d i es h a v e b e e ndone34-36 bu t few d ata are available un der the re l-evant chemical and physical conditions.

alculations of Particle omb ustion RatesUsua l ly ca lcula t ions a re made of the burningrates of a single particle or an assembly of parti-c les, of the temperature of the part ic les by simul-

FIG. 1. Co m bus tion o f high-volatile bitu m ino us coals: (a) Pittsburgh Seam, 65 ~m , a t ignition; 2~ (b) Pitts-bur gh Seam, 65 p~m, after ignit ion; z~ (c) Fo ur Co rners, 80 txm, ~1 0 ms react ion t ime ; 2~ (d) Utah, 90 ~Lm,--5 ms reaction time. 21


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COMBUST ION RATES OF COAL CHARS: REVI EW 1 47


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1 04 8 C O A L C O M B U S T I O N K I N E T I C S A N D M E C H A N I S M Staneous heat balance, and of the effect the com-bustion process has on the surroundings, e .g. o nt he t e mpe ra t u re a nd oxyge n con t e n t o f t he a mb i e n tgas.Th ere are man y mathematical models of varioustype s of particle com bu stio n systems. 3a'37~39 Basedon F ie ld e t a l . , ~ McKenzie e t al . 4~ mo delled thecombustion of a polydisperse suspension of pf par-t ic les in plug flow. Their t reatment showed frac-t ional burn-o ff (extent o f combustion), u, to be re-lated to time, t, by:

du 6y l V ~ ~ p 1 / s 1 )d t d o

wh ere y = 1 - u, a and 13 are coeffic ients in theexpress ions re la t ing respec t ive ly the changes inpartic le size (d) and den si ty ((r) to bu rno ff (seeEqs. (27) and (28)), sub scrip t o refers to initial c on -ditions (u = o) and p is the actual (observed) rateof combustion of carbon per unit external surfacearea of the particle.The change of pa r t ic le tempera ture , To, wi tht ime is given by:

1 2 [ d . _d--~ = C-~ [ d t y - *l( Tp - Tg)

- 6 ~ ( ~ - ~ ) ] K / s ( 2 )w here C~ is the specific heat o f the part ic le, Tgand T s a re the tempera tures of the surrounding gasand radiating surfaces respectively, D 1 and 42 in-volve convective and radiative heat transfer coeffi-c ients respectively and depend on part ic le size anddensi ty. H is the heat of react ion which dependsstrongly on the nature of the combustion process.At f l a me t e mpe ra t u re s c a rbon bu rns t o p roduc ecarbon m onoxide, i .e . C + 1/ 2 0 2 ---> CO in whic hcase H -2300 ca l /g . However , i f the ca rbon mon-oxide oxid izes with suffic ient spe ed to be c om -pletely burned before leaving the part ic le the heatof react ion is that ap prop riate to the step C + O zC O 2, i.e, H - 7900 cal /g.Equations (1) and (2) can be used to calculate thebehaviour of polyd isperse suspensions w hen th eequations are evaluated simultaneously for each sizefraction, as well as using ot he r relationships to cal-culate the corre spo ndin g changes in the pro pert iesof the ambient gas. The equations can also be usedto calculate the beh aviou r of monodisperse susp en-sions, or the behaviour of a single part ic le .Th e situation in fluidized -bed combustors, andconsequently the e quations for calculat ing co m bus-t i on be ha v i ou r , a re more c ompl e x424w t ha n fo rplug-flow entrainment systems. This is because of

the need to account for the behaviour of gas bub-bles passing through a dense phase, and the trans-por t of oxygen through the dense phase which con-tains most of the burning part ic les.Avedesian and Davidsona~ developed a simplemode l for f lu id ized-bed combustors , ex tended byLeung and Smith 46 to incorporate the effects offuel reactivity, which allows the effects of key vari-ables, e.g. fluid izing velocity, particle size, bub blesize, to be stu died. Figu re 2 i l lustra tes the si tua-t ion: a well-mixed dense phase of inert materia lwith fuel part ic les dispersed in i t and gas flowingthroug h at the min imu m fluidizing velocity, Urn.Gas in excess of th is passes up through the bed inspherical bubbles of diameter, db, a t veloci ty Ub.The burning ra te i s cont ro l led by the e ffec t s ofoxygen exchange through the dense phase to theburn ing part ic les, and th e reaction of oxygen withthe pa rt ic les . The p a r t ic les a re assum ed to bespheres of d iamete r , d , a t the same tempera tu reas the gas and the inert materia l of the bed. Thefrac t iona l consumpt ion of oxygen fed to the com-bustor, Ao, is calculated from:

Ao = 1 - % - (1 - ) Z / ( k ' - 1 - % ) (3)where % = [ (Z - I ) /Z ] exp ( -X ) (4)

6 34h~ [ I ' 3e (DP ~ 1 76 ]x - d~ a~g)O.-- Um+ 1 u ~ S J 5)

k, =z = U b / U , . o )6Vcho(1 - e ) O9 - ( 7 )du~z c~

X is the number of t imes the bubble i s f lushed outas i t r i ses through the bed, k ' i s a measure of thepart ic le combustion rate , h o is the ini t ia l height ofthe bed, e is the voidage of the dense phase, Dis the diffusion coeffic ient of oxygen in ni trogen at

BUBBLE RISfNG T U b

FIG. 2. Fluidized-b ed com bustion model .


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C O M B U S T I O N R A T ES O F C O A L C H A R S : R E V I E W 1049c o m b u s t i o n t e m p e r a t u r e a n d r e f e r e n c e p r e s s u r e P o ,a n d P i s t h e c o m b u s t i o n p r e s s u r e . V c i s t h e v o l u m ef r a c t io n o f c a r b o n a n d C ' i s t h e o x y g e n c o n c e n t r a -t i o n i n t h e d e n s e p h a s e , gF o r t h e c a l c u l a t i o n s i t i s n e c e s s a r y t o k n o w ,a m o n g s t o t h e r t h i n g s , t h e v a l u e o f p a n d i t s r e -s p o n s e t o t e m p e r a t u r e a n d o x y g e n c o n c e n t r a t i o n ,t h e m a n n e r b y w h i c h p a r t ic l e s i z e a n d d e n s i t yc h a n g e d u r i n g c o m b u s t i o n , a n d t h e a p p r o p r i a t e v a l u ef o r t h e h e a t o f r e a c t i o n , H .

T h e o r e t i c a l R e l a t i o n s h i p s f o r C a l c u l a t i n gB u r n i n g R a t e s

O b s e r v e d K i n e t i c sF i g u r e 3 i l l u s t r a t e s t h e c i r c u m s t a n c e s c l o s e t o ab u r n i n g p a r ti c le . F r o m m a s s - b a l a n c e c o n s i d e r a ti o n st h e b u r n i n g r a t e , p , c a n b e e x p r e s s e d a s :

p = hm(C ~ - C~ ) = Rc(C S g / cm Z s (8 )w h e r e C s i s t h e o x y g e n c o n c e n t r a t i o n a t t h e o u t e rs u r f a c e o f t h e p a r t i c l e , C g i s t h e o x y g e n c o n c e n -t r a t io n i n t h e b u l k g a s , R c is a c h e m i c a l r a t e c o e f -f i c ie n t o f a p p a r e n t o r d e r n i n C s , a n d h m is t h em a s s t r a n s f e r c o e f f i c i e n t d i s c u s s e d b e l o w .M a n i p u l a t i o n o f E q . ( 8 ) t o e l i m i n a t e t h e g e n e r -a l ly u n k n o w n C ~ g i v e s a r e l a t i o n s h i p f o r c a l c u l a ti n gp :

O = C~ (1 - X) '* Rc g / c m 2s (9 )w h e r e = P / P r o ( 1 0)P m i s t h e p r o d u c t h m C ~ , th e m a x i m u m p o s s i b l e

XYGEN:ONCENTRATION

0 ~F IG . 3 . D i a g r a m m a t i c x e p r e s e n t a t i o n o f a c a r b o np a r t ic l e b u r n i n g i n o x y g e n .

g

c o m b u s t i o n r a t e , f o u n d w h e n c h e m i c a l r e a c t i o n sa r e s o f a st t h a t C s ~ O , a n d t h e b u r n i n g r a t e i sc o n t r o l l e d s o l e l y b y m a s s t r a n s f e r o f o x y g e n t o t h ep a r t i c le . N o t e t h a t X c a n n e v e r b e g r e a t e r t h a n 1 .A f u r t h e r u s e f u l e q u a t i o n in v o l v i n g d e r i v e da n a l y t i c a l l y ,47 i s :

X/ (1 - X)n = R c C ~ / p m = R c C ~ - l / h m (11)E q u a t i o n ( 11 ) s h o w s t h a t d e p e n d s o n t h e o r d e rn . B e c a u s e c a n b e d e t e r m i n e d e x p e r i m e n t a l l yw i t h o u t a n y k n o w l e d g e o f n , E q . ( 1 1 ) c a n b e u s e di n t h e d e t e r m i n a t i o n o f n . 4 7-4 9

E q u a t i o n ( 8 ) c a n b e m a n i p u l a t e d t o g i v e r e l a -t i o n s h i p s f o r s p e c i f i c v a l u e s o f n . F o r n = 1 t h ef a m i l i a r r e s u l t i s :

p = C g / 1 / h m + 1 / R e ) g / c m Z s ( 12 )F or n -= 06 :

P - Pro)(P - Re) = 0 g2 /cm 4s2 (13)w h i c h s h o w s t h a t f o r z e r o o r d e r r e a c t i o n s t h a t p= Rc w h e n t h e r e i s a f i n i te c o n c e n t r a t i o n o f o x y g e na t t h e p a r t i c l e ' s s u r f a c e (C ~ > 0 ) , a n d t h a t t h e r a t ec h a n g e s a b r u p t l y t o g i v e p = p ,,, w h e n C ~ = 0 .

P a r t i c l e R e a c t i v i tyT h e c o e f f i c i e n t R c i s r e f e r r e d t o a b o v e a s ac h e m i c a l r a t e c o e f fi c i e n t, b u t i t s r e s p o n s e t o t e m -p e r a t u r e a n d o x y g e n c o n c e n t r a ti o n , i ts d e p e n d e n c e

o n p a r t i c l e s i z e a n d i t s v a r i a t i o n d u r i n g t h e c o m -b u s t i o n o f t h e p a r t i c l e , a r e t h e r e s u l t s o f t h r e e i n -t e r a c t i n g f a c t o r s : ( i) t h e i n t r i n s i c r a t e o f c h e m i c a lr e a c t i o n o f o x y g e n w i t h t h e i n t e r n a l s u r f a c e o f t h ep a r t i c l e , ( ii ) t h e e x t e n t o f t h i s s u r f a c e , a n d ( ii i) t h ee x t e n t t o w h i c h o x y g e n d i f f u s io n t h r o u g h t h e p o r e s( w h i c h f o r m t h e i n t e r n a l s u r f a c e ) r e s t r i c t s t h e r e -a c t i o n r a t e . T h e r e l a t i o n s h i p b e t w e e n p (a n d h e n c eR e) a n d t h e c o e f f ic i e n t o f i n t r i n s i c c h e m i c a l r e a c -t i v it y , R ( t h e r a t e o f r e a c t i o n p e r u n i t a r e a o f p o r ew a l l p e r [ u n i t c o n c e n t r a t io n o f o x y g e n ] m i n t h e a b -s e n c e o f a n y m a s s t r a n s f e r o r p o r e d i f fu s i o n a l l i m -i t a t i o n ) i s g i v e n b y :

P = rl~/CrAgRi[Cg( - X)]m g / c m Z s ( 14 )w h e r e ~/ i s t h e c h a r a c t e r i s t i c s i z e o f t h e p a r t i c l e

5( r a ti o o f t h e v o l u m e t o e x t e r n a l s u r f a c e a r e a ) A _i s t h e p a r t i c l e s s p e c if i c a r e a , m i s t h e t r u e o r d e ro f r e a c t i o n i n t h e c o n c e n t r a t i o n o f o x y g e n a n d x li s t h e e f f e c t i v e n e s s f a c t o r , t h e r a t i o o f t h e a c t u a lc o m b u s t i o n r a t e t o t h e r a t e a t t a i n a b l e ( a l l e l s e b e i n ge q u a l ) i f n o p o r e - d i f f u s i o n r e s i s t a n c e ' e x i s t e d . ~q i s


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1 5 C O A L C O M B U S T IO N K I N E T IC S A N D M E C H A N I S M Sa func t ion of the Thie le mo dulus , 51 6 , and can b ecalculated from:*[ n 4 ,~ m + 1 ) / 2 ]

= ~ p m + 1 ) / [ 8 D ~ C g 1 - X ) ] 1 5 )wh ere D e is th e e f fec t ive coef f ic ient for d i f fus ionth r ough the p o r e s t r uc tu r e , c a l c u l a t e d a s show nbe low . T he t e r m s on the r i gh t ha nd s ide o f E q .(15) can a l l be me asure d , thus a l lowing ~ lqb (m+ 1 ) /2 t o be c a l c u l a t e d f r om e xp e r im e n ta l da t a.T he n q ( and he nc e R i by E q . ( 14 )) c a n be d e t e r -min ed us ing the re la t io ns be tw een -q and qd~ (m+ 1 ) /2 g ive n by M e h ta a nd A r i s.~zW hen chem ica l r eac t ions a re suf f ic ient ly s low,pore d i f fus ion h as no ra te - l im i t ing e f fec t , the oxy -ge n c onc e n t r a t i on t h r oughou t t he po r e i s C , a ndq = 1 . Equ a t ion (14) then becom es:

p = ~/trAgRi[Cg(1 _ g/cm 2s (16)Fo r thes e c i rcu mstan ces (k ine t ic r eg ime 15a '54) pva r ie s w i th pa r t i c l e si z e , a nd show s the t r ue o r d e ro f re a c t ion , m , a nd the t r ue a c t iva t i on e ne r gy w h e nR~ is expresse d in Ar rhen ius form. Du r ing co m-bus t ion the pa r t i c l e de ns i ty de c r e a se s bu t t he s i z er e m a ins c ons ta n t . W he n po r e d i f fu s ion a s w e l l a schemica l r eac t ion has a s t rong ra te - l im i t ing e f fec t52(kine t ic r eg im e I I , 5a '54) the te rm ~ (m + 1) /2 - -~ 1 / r l , 52 then Eqs . (14) and (15) g ive :p = 2 {2 AgtrDeRi[Cg(1 - 1)}~

g /c m 2s ( 17 )E qua t ion ( 17 ) i s t he f a m i l i a r r e l a t i onsh ip de r ive d ,f or exa m ple , by F r a nk - K a m e n e t sk i i5s spec if ically forr e g im e I I c ond i t i ons . I n t he se c i r c um s ta nc e s p i si nde pe nde n t o f pa r t i c l e s i z e , show s a n a ppa r e n torder , n , g iven by:

n = (m + 1) /2 (18)a nd ha s a n a ppa r e n t a c t i va t i on e ne r gy a bou t ha l ftha t found for R . As comb ust ion p roceed s , la rgepa r t i c l e s sh r ink a s t he y bu r n a t c ons t a n t de ns i ty .

*Jamaluddin et aL~2~ e c e n t l y p o i n t e d o u t t h a t t h eequa t ions used ea r l ie r to ca lcula te R~9 inc o r r e c t l yused / /2 ra the r than ~ / a s the charac te r is t ic s ize .H e nc e E qs . ( 15 ) a nd ( 17 ) a r e i nc o r r e c t a nd th e r ea re e r ror s in the repor ted va lues of R~9 o f up toa fac tor of 4 when pore d i f fus ion has a s t rong e f -fect . The e r ro r does no t s igni f icant ly change thekine t ic conclusions of r e fe renc e 59 . H ow ever , i fuse i s made of th e rep or t ed v a lues of R~ to ca l -cula te Rc o r p t he c o r r e c t r e su l t w i l l be g a ine d u s -ing , / /2 ra the r than 3 ' .

F o r p f -s i ze pa r t i c le s , w he r e t he de p t h o f pe ne t r a -t i on o f oxyge n in to t he po r e s i s o f t he o r de r o fpa r t i c le s iz e , u bo th de ns i ty a n d s i z e o f t he pa r t i -c les r educe wi th burn-of f .N um e r i c a l va lue s o f Rc and R , and func t ions ofthe se t e r m s , a r e g ive n f o r va r ious c a r bons i n t hese c t ion on E xpe r im e n ta l D a ta on B ur n ing R a te s .The da ta a re shown in Ar rhenius form:R ~ (o r R i) = A e xp [ - E / ( R T ) p ] ~

g/cm2s(a tm) ~ (19)w he r e A i s t he f r e que nc y f a c to r , E i s t he a ppa r e n to r t r ue a c t iva t i on e ne r gy a s a pp r op r i a t e a nd K i sthe c o r r e spond ing a ppa r e n t o r t r ue o r de r . F o r c on -ve n ie nc e , r a t e s a r e r e l a t e d t o t he pa r t i a l p r e s su r eof oxygen.Effective Po re Dif fusion Coeff ic ient , De, andMode ls o f Pore S t ruc ture

The e f fec t ive por e d i f fus ion coef f ic ient , D e , i sr e l a t e d t o un i t c r o s s - se c tiona l a r e a o f po r ous m a -t e r i a l a nd thus i nc o r po r a t e s t he e f f e c t o f t he num -be r a nd s i z e o f t he po r e s i n t he un i t c r o s s - se c t iona nd the t o r tuos i t y ( z ) o f t he se po r e s . S a t t e r f i e ld56g ive s a u se f u l r e v i e w o f t he o r e t i c a l a nd m e a su r e dva lues of De . F rom the s imple pore - s t ruc ture mode lo f W he e le r , 57 D e c a n be c a l c u l a t e d by :D e = D p 0 /z c m e / s (20)

wh ere 0 i s the l~orosi ty of the so l id and Dp is thedi ffusion coef f ic ient throu gh the p ore . Fo r la rgepores (>1 I~m in s ize when bulk d i f fus ion occurs) ,Dp is equa l to the molecula r d i f fus ion coef f ic ient .F o r po r e s


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C O M B U S T I O N R A T ES O F C O A L C H A R S : R E V I E W 1051they d i f fe r f rom measured va lues-- fac tors of morethan 10 a re no t unknown. 56 Ind eed these factorsare mainly for the correct ion of simplified modelsof pore structure and diffusion processes. W heeler ' smod el, giving rise to Eqs. (20) to (22), assumes tha tthe pores can be adequately represented as a mono-disperse system. It is well know n, how ever, th atchars have a wide distribution of pore sizes, andthat the size distributions are often polymodal. Smitha nd Ty l e r5s deve loped a res t r ic ted mode l for re -action in semi-anthracite particles w ith a po lym od aldistribution of pore sizes. Th ey fou nd the intrinsicreactivity was essentially the same calculated bytheir bimodal and unimodal models. Other modelsare available for react ions in bimodal systems ofporous sol ids6~ and for sol ids with Gaussian andMaxw ellian distributions of po re siz es Y

The second point on pore d i ffusion an d s t ruc tureconcern s the no n-steady sta te o f the si tuation. D ueto reac tion, pores op en up, changing in s ize andshape. P ore surface areas increase an d ma y ulti-mately decrease due to coalescence. The refore un-der reg ime I conditions ra tes vary with the frac-t ional degree of burn-off, increasing as pore areaincreases and ul t imately decreasing as pores co-a lesce or a s expanding macropores engu l f mic ro-pores. It is difficult, however, to make a generallyuseful model for such a situation. Som e carbons(though not many) show rates that increase steadilywith burn-off, othe r de crease steadily, e4 N oneth e-l e s s t he re ha ve be e n a numbe r o f a t t e mp t s t omod e l evolving pore s t ruc tures . S imons and co-workers , ~ -c 's extending the t rea tm ent by Cho rne tet al . , 69 model led the engul f ing macrop ore sys-tem. Bha tia and Per lmu t te r 7~ deve lop ed a random -pore mo del for fluid-solid react ions, and Srinivasa nd Amundson71 modelled the gasificat ion of characcounting for progressive pore growth. Gavalas7z'r3se t up a mode l o f spa t i a l l y - ra ndom c y l i nd r i c a lpores. SimonsT and Gavalas75 compared some ofthe meri t s of the i r re spec t ive mode ls .Under regime II condi t ions an inc rease in poresize leads to an increase in pore diffusion rates andchanges in the amount of pore surface available forreac t ion . There have been few a t tempts to deve loptheoretical models for such circumstances. Pe ter-sen76 treated reactions in a single p ore and in anarray of pores which were ini t ia l ly uniform in size;Hashimoto and Silveston ~a'77 rela ted chang es in th eeffect iveness factor, r I , with bu rn- off du ring gasi-ficat ion of carbon with a polydisperse pore system;Ramachandran and Smith 7s exam ined the effect ondi f fus ion when a pore changed s ize due to the de -posi tion or removal of sol id. Gavalas 73 dev elope dhis earlier model72 to a l low for the effect of porediffusion, as well as external m ass transfer, du ringthe com bust ion of char par ticles . Kriegbaum andLau rende au 79 mo delled th e gasification o f char co n-taining conical pores, having a polymodal distribu-

t ion of sizes. Smith and Tyler5a showed tha t wherei t is appropriate to t reat the pores as mono-sizedand where Knudsen d i f fus ion i s occurr ing , the ob-served rate in regime II can be calculated from aknowledge of the intrinsic react ivi ty and the po-rosi ty of the carbon alone. Holves~ extended thetreatment by S mith and Tyler to acco unt for changesi n p o r o s i t y d u r i n g c o m b u s t i o n . S r i n i v as a o dA m u n d s o n81 dealt w ith the effects o f po re diffusionin evolving bimodal po re structures .M a s s T r a n s f e r C o e f f i c ie n t , h m

In pract ical combustion systems the transfer ofoxygen to the burning pa r t ic le of ten cont r ibutesnotably to ra te l imitat ion. Indeed in the case offluidized -bed co mb ustion li tt le, i f any, l imitat ionis imp osed b y chemical ra tes. 45'~ Th erefo re in or -der to calculate p i t is usually necessary to knowthe mass transfer coefficient, h m.For gas-solid systems, in fixed or fluidized bedsor in entrainm ent, th e re la t ionship betw een h m andthe na ture and s ta te of f low of the ambient gas i sgiven by equations of the form:36'82'8~

Sh = h ' d / D = 2 (1 + B Rel/Z Sc 1/3) (23)where Sh, Re , and Sc a re the Sherwoo d, Rey-hold's , an d Schmidt nu m bers respectively , B is aconstant and h is the mass transfer coeffic ientwith respect to the flux of oxygen. To calculate Re,and hence .h~ , a knowledge of the gas ve loc i typast the part ic le is required. In fluidized beds thisis difficul t to define. La Nau ze and Jung , s4 for ex-ample, used th e superfic ia l gas veloci ty thro ug h thecombustion vessel , modified to take account of theaverage voidage of the bed (see below).In pf combustion, re lat ive veloci ties be twe en gasand particle are usually sufficiently small that Recan be se t equa l to ze ro . .11 There i s l i t t l e e r rorif the part ic les are t re ated as spheres. 3a Th en Sh= 2, the result obtained analyt ical ly for a spherein a stat ionary gas , wh ence:

hm = 0.75 D o ( P o / / P ) ~ m / / T o ) 1 7 5 / d cm//s (24)where T,~ i s the mean tempera ture of the boundarylayer arou nd the partic le and subscrip t o deno tesreference condit ions. The factor 0.75 is the con-vers ion involved in chan ging f rom h~ ( for oxygenflux) to hm (for carb on e=ide flux) an d assumes thepr imary produc t of reac t ion to be CO, i .e . com-bus tion i s by C + 1 / 2 0 2 ~ CO , as noted above .In the case of f lu id ized-bed combust ion the ap-propriate value of h m for the f lux of gases throughthe dense phase of ine r t pa r t ic les a round the burn-ing part ic le is less well def ined . 83'sS-Ss Re cen two rk 4 suggests a modification of Eq . (23) to ac-count for the voidage, ~, of the dense phase:


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1052 C O A L C O M B U S T I O N K I N E T I C S A N D M E C H A N I S M SS h = 2 e + 2 B R e / e ) I / Z S c 1 /3 (2 5) E x p e r i m e n t a l D a t a o n B u r n i n g R a t e s

T h e s u i t a b i l i t y o f E q . ( 2 5) i s d i s c u s s e d i n t h e s e c -t i o n s o n e x p e r i m e n t a l v a l u e s o f t h e m a s s t r a n s f e rc o e f f i c i e n t .

C l ~ a n ge s i n P a r t i c l e S i z e a n d D e n s i t yT h e w e i g h t ( W ) o f a p a r t i c l e i s r e l a t e d t o i t s i n i -t ia l w e i g h t ( W o ) a n d t h e f r a c ti o n a l d e g r e e o f b u r n -of f ( n ) by :

W = W o ( 1 - u ) g (26)w h e n c e ( fo r s p h e r e s o r c u b e s ) :

d = d o (1 - u) ~ cm (27)an d ( r = ( r ( 1 - u ) I~ g / c m 3 (28)w h e r e 3 a + 13 = 1 . F o r p a r t ic l e s t h a t b u r n w i t hs t e a d i l y r e d u c i n g s i z e a n d c o n s t a n t d e n s i t y a =1 / 3 a n d 13 = 0 . H o w e v e r i f s i z e r e m a i n s c o n s t a n tw h i l s t d e n s i t y d e c r e a s e s a - - 0 a n d 13 = 1 .E q u a t i o n s ( 27 ) a n d ( 28 ) a p p l y f o r p a r t i c l e s w i t ha h o m o g e n e o u s s t r u c t u r e o f p o r e s th a t a r e s m a l lc o m p a r e d w i t h p a r t i c l e s i z e . I n f a c t w h i l s t c o a lc h a r s a r e p o r o u s t h e y d o n o t h a v e a s i m p l e p o r es t r u c t u r e : c h a r s o f t e n c o n t a i n l a r g e i n t e r n a l v o i d s( o f d i m e n s i o n s o f t h e o r d e r o f p a r t i c l e s i z e ) s u r -r o u n d e d b y m i c r o p o r o u s m a t e r ia l 9 -9 1 . I n p f f l a m e s ,b i t u m i n o u s c o a l s o f t e n f o rm t h i n - w a l l e d c e n o -s p h e r e s . 92 I n t h e s e c i r c u m s t a n c e s a b e t t e r , t h o u g hs t il l a p p r o x i m a t e , m o d e l i s t h a t o f a h o l lo w s p h e r ew i t h a w a l l o f h o m o g e n e o u s l y - m i c r o p o r o u s m a t e -r ia l . s 9 F o r c o m p l e t e p e n e t r a t i o n o f o x y g e n i n t os u c h a p a r t i c l e a = 0 a n d 1 3 = 1 , i . e . t h e p a r t i c l ew o u l d b u r n w i t h a s t e a d y r e d u c t i o n i n d e n s i t y b u ta t c o n s t a n t s i z e. F o r r e a c t i o n c o n f i n e d t o t h e o u t e rs u r f a c e o f s u c h a p a r t i c l e i t c a n b e s h o w n t h a t :

d = d o (1 - u + u x3 ) 1 /3 cm (29)a n d

(r = ( ro (1 - u ) / ( 1 - u + u x 3 ) g / c m 3 ( 30 )w h e r e x i s t h e r a d i u s o f t h e i n s i d e t o t h e i n i t i a lo u t s i d e d i a m e t e r o f t h e p a r t i c l e . F o r t h e c a s e o fn o in t e r n a l v o i d s , x = 0 , t h e n w i t h c t = 1 / 3 a n d13 = 0 , E q s . ( 2 9) a n d ( 30 ) r e d u c e t o E q s . ( 27 ) a n d( 28 ) r e s p e c t i v e l y . A t t h e o t h e r e x t r e m e , a s x ~ 1 ,i . e . f o r a t h i n - w a l l e d c e n o s p h e r e , E q s . ( 29 ) a n d ( 30 )s h o w t h a t t h e p a r t i c l e s b u r n a t c o n s t a n t s i z e a n dw i t h s t e a d i l y r e d u c i n g d e n s i t y , e v e n i f r e a c ti o n s a r ec o n f i n e d t o t h e o u t e r s u r f a c e .

R a t e C o e f f i c i e n t , R cI n o r d e r t o d e t e r m i n e R c , i t i s n e c e s s a r y t o c a r r y

o u t e x p e r i m e n t s t h a t s a t is f y a n u m b e r o f c o n d i -t io n s : m e a s u r e m e n t s m u s t b e m a d e w i t h s i n g le p a r -t i c l e s o r c l o s e l y - s i z e d m a t e r i a l s 93 i n o r d e r t o r e l a t er a t e s t o p a r t i c l e s i z e , t o c o r r e c t f o r e x t e r n a l m a s st r a n s f e r e f f e c t s ( i . e . c o r r e c t f o r t h e e x t e n t t h a t C ~d i f fe r s f r o m C ~ ) a n d t o a l lo w t h e d e t e r m i n a t i o n o ft h e c h a n g es i n p a r t i c l e s i ze a n d d e n s i ty w i th b u r n -o f f . T h e e f f e c t s o f c h a n g e s i n o x y g e n c o n c e n t r a t i o na n d p a rt ic l e t e m p e r a t u r e n e e d t o b e d e t e r m i n e ds e p a r a t e l y . B e c a u s e o f t h e n e e d t o k n o w t h e i n i t i a lp r o p e r t i e s o f t h e m a t e r i a l s t u d i e d a n d b e c a u s e m a -j o r c h a n g e s o c c u r i n c o a l s t r u c t u r e ( c h e m i c a l a n dp h y s i c a l ) d u r i n g d e v o l a t i l i z a t i o n , i t i s n e c e s s a r y t ou s e c h a r s p r e p a r e d s e p a r a t e l y u n d e r c o n d i t i o n s f o u n di n t h e i n i t i a l s t a g e o f t h e r e l e v a n t c o a l c o m b u s t i o ns y s t e m .F e w e x p e r i m e n t a l s t u d i e s s a t is fy th e a b o v e c r i-t e r ia . T h e d a t a g i v e n h e r e a r i s e m a i n l y fr o m t w os u i t a b l e s e r i e s o f e x p e r i m e n t s . O n e s e r i e s , d u e t oF i e l d a n d c o - w o r k e r s 9 1 9 4 9 5 o f t h e B r i t is h C o a lU t i l iz a t i o n R e s e a r c h A s s o c i a t io n w a s p e r f o r m e d u s -i n g d i r e c t m e a s u r e m e n t o f t h e w e i g h t l o ss o f p a r -t ic l e s c a r r i e d i n l a m i n a r f l o w t h r o u g h a r e a c t o r f o ra k n o w n r e a c t i o n t i m e . T h e s e c o n d s e r i e s w a s c a r -r i e d o u t b y C S I R O w o r k e r s , 9 w 98 w h o m e a s u r e dt h e p r o g r e s s i v e b u r n - a w a y o f p a r t i c l e s i n a p l u g -f l o w r e a c t o r u s i n g g a s a n a l y s i s t e c h n i q u e s .T h e p u r p o s e h e r e i s t o r e p o r t a n d c o m p a r e v a l -u e s o f r e a c t i v i t y f o r v a r i o u s c h a r s . H o w e v e r a d i f -f i c u lt y a r i s e s b e c a u s e n o t a l l c h a r s s h o w t h e s a m ed e p e n d e n c e o f r e a c t iv i t y o n o x y g e n c o n c e n t r a t i o n ,i .e . n c a n c h a n g e f r o m C h ar to c h a r . I n o r d e r t oc o m p a r e r e a c ti v i ti e s o n a c o m m o n b a s is th e d a t aa r e g i v e n , w h e r e n e c e s s a r y , i n t h e f o r m o f a r a t e ,P c , d e f i n e d b y :

P c = R c (P o2) n g / c m 2s (31)F i r s tl y v a lu e s o f R c a r e c o n s i d e r e d f o r p e t r o l e u mc o k e . F i g u r e 4 s h o w s t h e r e l a t i o n b e t w e e n R c a n dT ~ i n A r r h e n i u s f o r m f o r f o u r s i z e d f r a c t i o n s o fc o k e , o f m e d i a n s i z e s 1 8 , 7 7 , 8 5 , a n d 8 8 I xm . 9 s 4 9

I t h a s p r e v i o u s l y b e e n s h o w n 1 1 9 5- 9s t h a t t h e i n -d e p e n d e n c e o f R c o n p a r t i c le s i z e , a n d t h e a p p a r -e n t a c ti v a ti o n e n e r g y o f - 2 0 k c a l / m o l ( a b o u t h a l ft h e v a l u e s h o w n b y i m p u r e c a r b o n s b u r n i n g u n d e r

9r e g i m e I c o n d i t io n s ) a r e c o n s i s t e n t w i t h r e a c t i o nu n d e r r e g i m e I I c o n d i ti o n s . W h a t h a s b e e n l es sc l e a r i s t h e a p p r o p r i a t e v a l u e o f t h e o b s e r v e d r e -a c t io n o r d e r , n .S m i t h 9 s r e p o r t e d r a t e d a t a f o r p e t r o l e u m c o k eb u r n i n g a t o x y g e n p a r t i a l p r e s s u r e s c l o s e t o 0 . 2a t m , a s s u m i n g n = 1 . Y o u n g 4 9 9 9 b u r n e d p e t r o l e u m


9/21

C O M B U S T I O N R A TE S O F C O A L C H A R S : R E V I E W 1 05 3

E

T p ~ZOO0 160 0 400 1200 1000 900 800 700 600

}O'2 ~ A =

~ f10"3 & l~ I t ~ A

I 0 4 I i i I& 5 6 7 8 9 10 It 12t 0 6 ] T p K "11

FIG. 4 . Ef fec t of te mp era tu re on Pc for pe t ro le umcoke (V] 18 Ixm,~ 9 77 Ixm,~ 9 85 and 88 ~m49).

c oke a t oxyge n p r e s su r e s ove r t h e r a nge 0 . 05 to 0 . 3a tm a nd u se d s t a ti s ti c a l t e c hn ique s t o a na ly se h i sr e su l t s . H e f ound l e a s t s c a t t e r i n A r r he n iu s p lo t so f da t a ( t he sum o f t he squa r e s o f t he r e s idua l s a ta minimum) a t n c lose to 0 .5 ( see F ig . 5) . F romthe e v ide nc e a l r e a dy no te d t h e r e a c t ion is p r oba b lyunde r r e g im e I I c ond i ti ons , w he n Eq . ( 18 ) show stha t th e t ru e order , m , i s c lose to ze ro . Young 1~176

4 " 8 ,

4'6

4 " 4_ww 4 " 2

u .04 " 0n*

0" ' 3 . 80~ 3 " 6

, . . /3-/~ # # I I0 "2 0 "4 0 "6 08 1 "0

A P P A RE N T RE A CTIO N O RDE R (n )FIG. 5 . Sum o f the sq uare of the res idua ls ve r susthe a ppa r e n t r e a c t ion o r de r .

a lso found a va lue of n ~ 0 .5 for a char produ cedby the f la sh pyro lys is of an Au st ra l ian ~oituminouscoal . I~ Likew ise a va lue of n ~ 0 .5 was de te r -m i n e d b y H a m o r a n d c o - w o r k e r s47'4s for an Aus-t ra l ian brown coa l char .I t i s know n tha t t he t r ue o r de r o f r e a c t ion de -p e n d s o n t e m p e r a t u r e a n d o n t h e c o n c e n t r a t i o n o foxygen. 11'1~ I t i s m ore than l ike ly , a l l e lse be in ge qua l , t ha t t he o r de r w i l l a l so de p e nd on the na -t u r e o f t h e c a r b o n b e i n g o x i d i z e d . 99 T h e r e a r ep r a c t i c al d i f fi c u l ti e s i n de t e r m in ing th e t r ue o r de ri n t h e p r e s e n c e o f p o r e d i f f u s i o n l i m i t a t i o n s - - ac ha nge in t he t r ue o r de r f r om z e r o t o un i ty w ou ldon ly r e su l t i n a n a ppa r e n t c ha nge f r om 0 . 5 t o 1(Eq. (1) ) . Few exper iments have used a suf f ic ient lyw ide r a nge o f oxyge n c onc e n t r a t i ons f o r a de qua tede t e r m ina t ion o f m . Th i s i s i l l u s t r a t e d by the c a r e -f u l e xpe r im e n t s o f F i e ld91 on the c om bus t ion o fs ized f rac t ions of pf char (median s izes 28 , 38 , 82 ,and 105 I~m) a t 0 .05 an d 0 .1 a tm oxygen . F ie ld ' sda t a ha ve be e n r e a na ly se d49 and a re shown in Ar -r he n iu s f o r m in F ig . 6 . The uppe r pa r t o f t he d i a -gram shows resul ts f rom n = 1 , the low er for n= 0 .5. Ap pl ica t ion of the s ta t i s t ica l ana lys is r e -fe r red to above shows no s igni f icant d i f fe rence us-ing e i t he r o f t he o r de r s . F i e ld ' s r e su l t s show a na c ti v at io n e n e r g y o f - 2 0 k c a l / m o l , a n d a n i n d e -p e n d e n c e o f R c on p a r t ic le s ize , i . e . h is char wasp r oba b ly bu r n ing unde r r e g im e I I c ond i t i ons .Enc ou r a g ing a g r e e m e n t i s f ound in va lue s o f Rcde te r m ine d f o r s im i l a r m a te r i a l s by w or ke r s u s ingvar ious techniques . F igure 7 shows resul ts for an-th r a c i t e s a nd se m i - a n th r a c i t e s de t e r m ine d on s i z e df rac t ions of ma te r ia ls by F ie ld , 95 F i e ld a nd R ob-e r ts , 94 and Smith , 97 toge the r w i th resul ts for f lamesof poly dispe rse mater ia ls (M arsden, ]~ He in, 1~ Be6rt a / .l~ W i th t he e xc e p t ion o f t he p ione e r ingwork of B e6r , th e resul ts a re a l l wi th in a fac tor of2 a bove o r be low the m e d ia n l e ve l . The da t a i nF ig . 7 for s ized mate r ia ls show Rc to be i nde pe n -dent of pa r t ic le s ize ; th is f ac t toge the r wi th thea ppa r e n t a c t i va t i on e ne r gy o f a bou t 20 kc a l /m o l ,

suppo r t e d by the obse r ve d c ha nge s i n pa r t i c l e s i z eand den s i ty d ur ing com bust ion , 95,97 shows th e re -a c t i on t o be unde r r e g im e I I c ond i t i ons . S im i l a rc onc lu s ions w e r e m a de f o r t he c om bus t ion o f 89and 49 }xm fractions of a bro wn coal c har . 47'4sHow ever 22 Ixm part ic les of th is char showed low erva lues of Rc (and poss ib ly a h igh er va lu e of ac t i -va t ion e ne r gy ) t ha n the l a r ge r pa r t i c l e s . L ike w iseva lues of Rc for 4 I~m pe t ro leum coke pa r t ic les9sand 6 txm semi-anthrac t ive pa r t ic les97 were foundto be lower than the cor responding va lues for la rge rpa r t i c l e s . The f i ne pa r t i c l e s w e r e show n by m e a -su r e m e n t , c a l c u l a t i on , o r bo th , t o be r e a c t ing un -de r r e g im e I c ond i t i ons , o r i n t he t r a ns i t i on be -tw e e n r e g im e s I a nd I I .F igu r e 81~ show s the r e l a t i onsh ip be tw e e n P c


10/21

1054 C O A L C O M B U S T IO N K I N E T IC S A N D M E C H A N I S M ST p ( ' C )

- 1 0 2 ( X ) O 1 6 0 0 1 / - ,0 0 1 2 0 0i 9 i , i 9 i i

010- 2 . 0I/1

EU0 1,3

- 1 . 0 :o roi/1

~.~E -2 .0 i0

t3t ~ J

- 3 0

n = 1 = = \ ~ v

2 0 0 0 1 8 0 0 16001000 100 ~ ~! !

v0 5 0 6 0 - 7 0 8I I I I1 0 3 / T p ( K 1 )

0 &a 9

r = O . S o

o , tv

i i i i i i i t i2 0 0 0 1 6 0 0 1 4 0 0 1 20 0T p ( * C I

0 9I

F ie . 6. A r r he n iu s d i a g r a m r e l a t i ng R~ to t e m p e r -a tu r e r e p lo t t e d f r om F ie ld ' s da t a89 for a low rankchar . Init ia l pa r tic le s ize: 28 p,m (F 'I , I I ) , 28 Ixm(O, O), 38 Ixm (A, 9 82 p,m (V), 105 Ixm (Q0). Po2 in a tm = 0.05 (open symbols) , 0.10 (clos edsymbols),a nd T o fo r n ine c ha r s a nd pe t r o l e um c oke . O r ig ina lda t a on Rc a nd n ha ve be e n u se d to c a l c u la t e Pca t a c om m on oxyge n p r e s su r e o f 1 a tm , by E q .( 31 ) . T he A r r he n iu s pa r a m e te r s a nd o the r r e l e va n tda ta for the ca rbons in F ig , 8 a re shown in TableI. A t 2000 K the h ighe s t r e a c t iv i t ie s a r e show n bychars f rom US coals (Pit tsburg h and I l linois)1~ whicha r e a f a c to r o f 10 h ighe r t ha n pe t r o l e um c oke : A tthe s a m e t e m pe r a tu r e t he r e a c t iv i t i e s o f a num be rof chars ( f rom Mil lmer ran sub-bi tuminous and Ya l-lourn brown coa ls , Aust ra l ia ; an thrac i te s and semi-a n th r a c i t e s , U K a nd w e s t e r n E u r ope ; F e r r ym oorand Brodswor th b i tuminous coa ls , UK) a re about

lo 1E

~ u 1 0 . 2

1 0 - 3~ 4

r p ( ' C )1400 1200 lOOOi

- ' . . , , , : ~ = z 0 . 4 = x p [ - e 0 0 0 / ( e T ~ ]/='~'~ '~k '~..- ' - /

; s ~ , ' ~ , . . o oo

I I I I0 0 0 0 5 0 . 0 0 0 6 0 0 0 0 7 0 . 0 0 0 8I / T p ( K - 1)

FIG. 7 . Com bust io n ra te da ta for an thrac i te s andsemi-anth rac i te s (0 78 , 49 , 22 p ,m;~ O 72, 42 txm;9rx 28 , 25 p,m;95 9 31, 2 4, 23 Ix m;~ A p o l y d i s p e r s es ingle Va lue ; ~ [ ] po lyd isp ers ey poly dispers e l~) .

a fa c to r o f t h r e e h ighe r t ha n pe t r o l e um c oke . H ow -e ve r bo th t he U S m a te r i a l s , l i ke t he E a s t H e t tonc ha r, show a s t e e p de c l ine i n r e a c t iv i t y w i th t e m -pe r a tu r e ( E ~ 34 kc a l /m o l ) . A t 1430 K the r a t e f o rthe E a s t H e t ton c ha r f a l l s be low tha t o f pe t r o l e umc oke , w h i l s t a t t he s a m e t e m pe r a tu r e ( a s sum ingextrapola t ion i s jus t i f ied) the US coa ls would showreac t iv i t ie s s imi la r to the ch ars f rom th e A ust ra l iancoa ls , the anthrac i te s and semi-anthrac i te s , and soo n .

1.0

0.1

0 0 1

0 ' 0 0 1

Tp,~2 0 0 0 1 6 0 0 1 4 0 0 1 2 0 0 1 0 0 0 8 0 0

, , 3 X -

\ \

i / i i i4 5 6 7 8 9 1 010t ' / Tp , K - I

FIG. 8 . Burnin g ra tes of co ke a nd chars , Po2 =1 atm (see Table I for key) .


11/21

C O M B U S T I O N R A T E S O F C O A L C H A R S : R E V I E WT A B L E IData for coa l chars in F ig . 8

1055

L i n eno. Pa rent coa l

A ppa r -P r e - e xpone n t i a l A c t iva t ion e n tf a c to r e ne r g y o r de r o f(g /cm2s (atm) ) (kca l /m ol) r eac t ionP a r t i c l es ize~m) R e f e r e nc e

1 P e t r o l e um c oke 7 . 02 Ea s t H e t ton , sw e l l ing b i t um ino us 635. 8coal, UK3 Brodsw or th , swe l l ing b i tum inou s 111.3coal, UK4 An thrac i te s and sem i-anthrac i te s , 20 .4U K a n d w e s t e r n E u r o p e5 M il lmer ran , non-sw el l ing , sub-b i - 15 .6tuminous coa l , Aust ra l ia6 Ya l lourn brow n coa l , Au st ra l ia 9 .37 F e r r ym oor , non - sw e l l i ng b i t um i - 70 .3nous c oal , U K8 W h i t w i c k , n o n - s w e l l i n g b i t u m i - 5 0 .4nous coal, UK9 P i t t sbu r gh se a m , sw e l l i ng b i t u - 4187 .0minous coa l , USA10 I l l inois No. 6 , sw e l l ing b i t um i- 6337.0nous coa l , USA

19.7 0.5 18,77,85,88 49,9834.0 1.0 72 9524.1 1.0 31 9519.0 1 .0 78 ,49 ,22 ,72 ,42 95 ,9717.5 0.5 85 10016.2 0.5 89,49 4721.5 1.0 34 9517.7 1.0 27 9534.0 0,17 16 10734.1 O. 17 13 107

I n m a k i n g t h e f o r e g o i n g c o m p a r i s o n t h e d a t aw e r e b r ough t t oge the r on a c om m on ba s i s by e x -t rapola t ing , in many cases by a fac tor of 10 orm or e , t he e f f e c t o f oxyge n p r e s su r e a bove tha tu se d e xpe r im e n ta l l y . H ow e ve r , t he pa r a m e te r u se din m a k ing th i s e x t r a po la t i on - - the a ppa r e n t r e a c t iono r d e r - - i s o ft e n unc e rt a in . M uc h o f t he i n f o r m a t iongiven in F ig . 8 appl ies to a s ingle s ize of a g ivenc ha r . C oa l i s no t a hom o ge ne ous m a te r i a l : d i ff e r e n ts ize f rac t ions g iv e r i se to ch ars of d i f fe rent po res t r uc tu re s a nd c he m ic a l p r ope r t i e s , t h us g iv ing r i s eto d i f fe r ing reac t iv i t ie s . Pa r t ic le s ize a lso has ane f f e c t on t he r a t e - c on t r o l r e g im e unde r w h ic h pa r -t ic les burn . Al l e lse be ing equa l , f ine pa r t ic les canbu r n und e r r e g im e I a nd c oa r se pa r t ic l e s und e rr e g im e I I c ond i t i ons . Thus t he e f f e c t s o f t e m pe r -a tu r e a nd oxyge n c onc e n t r a t i on , a nd the m ode o fc ha nge o f pa r t i c l e s i z e a nd de ns i ty w i th bu r n - o f f ,a l l depend on pa r t ic le s ize .The da ta for the US coa ls show ac t iva t ion ener -g i e s o f a bou t 34 kc a l /m o l a nd r e a c t ion o r de r s o fabo ut 0 .2. These fac ts , tog e the r wi th the smal l s izeof the pa r t ic les (13 and 16 Ixm ) sugg es t tha t com -bus t ion w a s unde r r e g im e I c ond i t i ons o r i n t het r a ns i t i on be tw e e n r e g im e s I a nd I I .

I n t r i n s i c C h e m i c a l R e a c t i v i t y C o e f f i c i e n t I~ .T h e p r e c e d i n g d i s c u s s i o n s h o w s t h a t t h e o b -se r ve d r e a c t iv i t y o f c oa l c ha rs , a s m a n i f e s t by t he

ra te coef f ic ient , Rc, and the rate , Pc, diffe r for dif-fe rent types of coa l . I t i s a lso shown tha t the va lueo f Rc c om bine s t he s e pa r a t e e f f e ct s o f t he i n t r i n s icr e a c t iv i ty o f t he c a r bon a nd the e x t e n t a nd a c c e s -s ib i l it y o f t he i n t e r na l po r e su r f a ce o f t he c ha r .Spec i f ic sur face a reas va ry f rom about 1 mZ/g forpe t r o l e um c oke to ne a r ly 1000 m 2 /g f o r b r ow n c oa l59c ha r . S o , t o w ha t e x t e n t do c he m ic a l o r phys i c a ld i f f e r e nc e s i n va r ious c a r bons a f f e c t t he obse r ve dd i f f e re nc e s i n r e a c t iv i t i e s? To a nsw e r t h i s que s t i oni t i s necessa ry to know the coef f ic ient of in t r ins icchem ica l r eac t iv i ty , R , de f ine d by Eq. (14).S m i th59 has used publ ished da ta to ca lcula te R / .f o r a w ide r a nge o f po r ous c a r bons , i nc lud ing m a nyc h a r s, m e t a l l u rg i c a l c o k e , p e t r o l e u m c o k e , p i t c hc oke , nuc l e a r g r a ph i t e , c a r bon l a id dow n on c r a c k -ing c a t a ly s t a nd va r ious h igh ly - pu r i f i e d c a r bons .R e f e r e nc e 59 g ive s t he da t a sou r c e s a nd e s se n t i a li n f o r m a t ion on the c a r bons c onc e r ne d .The resul ts a re shown in F ig . 9 , where the in-t r ins ic reac t ion r a t e p ~ i s a t a n oxyge n p r e s su r eof 1 a tm. P l i s ca lcula ted f rom:

Pi = ~ (Po~)m g/cm 2s (32)an equ a t ion ana logous to Eq . (31) , and used for thesa m e r e a son , na m e ly t o a l l ow c om pa r i son o f m a -te r ia ls which show di f fe rent va lues of r eac t ion or -de r m . P i show s a n a c t iva t ion e ne r gy o f - 4 0 ' kc a l /m o l , t he va lue p r e v ious ly no t e d t o be e xpe c t e d f o r


12/21

1056 C O A L C O M B U S T I O N K I N E T I C S A N D M E C H A N I S M ST p ( ~ I

Z O O 0 1 6 0 0 1 2 0 0 1 0 0 0 8 0 0 6 0 0 4 0 0 3 0 01 0 1 1 I I t I I I I

lO 2 ~ | ' e~ o . ' . .1 0 ~ ~ ~ .,.

~ ~ x Pi=305 exp. Rip

v1 0 -6 ~ '~ /z z ~ 9

~ o t L v v~ . . 1 0 7

l 0 - g

1 0 - 1 1 o) \-l g f I I I ~ ] o

6 8 1 0 l Z 1 4 1 6 l f l1 0 4 l p ( k 1 )

FIG. 9. Intr ins ic react ivi ty of various carbons w he nPo2 = 1 atm.

' t P e t r o l e u m c o k eA Brown-coa l cha rC) L ign i t e cha r~ t A n t h r a c i t e( I ) Semi -anthrac i t eB i t u m i n o u s - c o a l c h a r[ ] M e t a l l u r g i c a l c o k ex Soot17;1: P it c h c o k eO P i t ch res in~ f N u c l e a r g r a p h i t e+ Crac ker ca rb on (uncata lysed)_L Cr ack er car bo n (eatalysed)~ I A G K S P g r a p h it e

A G K S P g r a p h i t eA U F] S P IS P I

f S p e c t r o s c o p i c g r a p h i t e

t h e r e a c ti o n o f i m p u r e c a r b o n s w i th o x y g e n . F i g u r e9 s h o w s t h a t t h e r e a r e l a r g e d i f f e r e n c e s i n r e a c t i v -i t y b e t w e e n d i f f e r e n t c a r b o n s , e v e n t h o u g h e f f e c t sd u e t o d i f f e r e n t p o r e s i z e s a n d s u r f a c e a r e a s h a v eb e e n e l i m i n a t e d . F o r e x a m p l e a t 7 7 5 K t h e i n t r i n -s i c r e a c t i v i t y o f p e t r o l e u m c o k e i s f o u r o r d e r s o fm a g n i t u d e h i g h e r t h a n t h a t o f g ra p h 0 n , a n d t w oo r d e r s o f m a g n i t u d e h i g h e r t h a n t h a t o f n u c l e a rg r a p h i t e . A t 1 2 5 0 K t h e r e a c t i v i t y o f p e t r o l e u mc o k e is 1 0 0 0 t i m e s h i g h e r t h a n t h a t o f c h a r s f r o mb r o w n c o al a n d l ig n i t e . I t i s s t r ik i n g t h a t p e t r o l e u mcoke shows the h ighes t in t r ins i c reac t iv i ty (as d i s -t i n c t f r o m t h e n e t r e a c t i v i t y p e r p a r t i c l e ) o f a l l b u tt w o o f t h e c a r b o n s s h o w n i n F i g . 9 .T h e w i d e r a n g e o f r e a c t i v i t i e s p r e s u m a b l y r e -f l e c t s t h e e f f e c t s o f t h e a t o m i c s t r u c t u r e o f t h e c a r -bons , a s we l l a s the e f fec t s of impur i t i e s in thesol id and gaseous reac tant s . Inc luded in F ig . 9 a red a t a f r o m e x p e r i m e n t s w i t h h i g h l y - p u r i f i e d c a r b o n sa n d o x y g en , w h e r e d i f f e r e n c e s in a t o m i c s t r u c t u r eo f th e c a r b o n s m a y b e a t a m i n i m u m . T h e s e d a t aa r e s h o w n s e p a r a t e l y i n F i g . 1 0 . T h e r e s u l t s f r o ms i x s e p a r a t e s e r i e s o f e x p e r i m e n t s s h o w s i m i l a r i n -t r ins i c reac t iv i t i e s . The resu l t s of Lang e t a l l ~ a r ee s p e c ia l ly n o ta b l e . T h e y m e a s u r e d t h e i n t r i n s icr e a c t i v i t y o f 1 5 c a r b o n s , r a n g i n g f r o m n u c l e a r a n ds p e c t r o s c o p i c g r a p h i t e s t o s u g a r a n d w o o d c h a r -c o a l s . T h e s e m a t e r i a l s , b e f o r e f u r t h e r t r e a t m e n t ,s h o w e d w i d e l y d i f f e r e n t i n t r i n s ic r e a c t iv i t ie s . H o w -e v e r , a f t er t h e c a r b o n h a d b e e n h e a t t r e a t e d a t2 9 7 3 K o r a b o v e , a n d a f t e r s e v e r a l o f t h e c a r b o n sh a d b e e n e x p o s e d t o c h l o r i n e a t h i g h t e m p e r a t u r e s ,a l l t he mate r i a l s show s imi la r reac t iv i t i e s . At 893K the h ighes t and lowes t va lues of P i ( shown inF igs . 9 and 10) d i f fe red only by a fac tor of three .T h e p r e l i m i n a r y h e a t t r e a t m e n t g i v e n t o t h e c a r -b o n s w o u l d h a v e r e d u c e d t h e i m p u r i t y l e v e l s s u b -s tan t ia l ly , bu t wou ld a l so hav e cau sed a rea r ra ng e-m e n t o f t h e c a r b o n a t o m s t o a m o r e o r d e r e ds t r u c t u r e . I t i s n o t y e t c l e a r w h i c h c h a n g e w o u l dh a v e t h e m o s t e f f e c t .Th e d i scuss ion of R~ and Rc s h o w l i m i t e d a r e a sw h e r e c o m m o n d a t a e x i s t : s i m i l a r i n t r i n s i c r e a c t i v -i ti es a r e f o u n d f o r t h e p u r i f i e d c a r b o n s j u s t m e n -t i o n e d , a n d o b s e r v e d r e a c t i v i t i e s ( R e ) o f s i m i l a rm a g n i t u d e a r e f o u n d f o r a n t h r a c i t e s a n d s e m i - a n -thrac i t es (F ig . 7) . The wide va r i a t ions found for Rca n d R a n d t h e u n c e r t a i n t i e s i n n a n d m s h o w t h a tthe re i s s t i l l a s t rong need to ga in a uni fy ing un-d e r s t a n d i n g o f c a r b o n r e a c t i v i t y . M o r e p r a g m a t i -c a l l y t h e r e i s a n e e d t o d e t e r m i n e R c f o r e n g i -

~ ] ' f G r a p h o nP u r i f i e d c a r b o n s- O S t e r l in g F T17 Ach eson NC~ ' A c h e s o n A F C 4


13/21

C O M B U S T I O N R A T E S O F C O A L C H A R S : R E V I E W 1057to 7

I0-8 ~ c ~ E = 6 0 k c o l l m o tcl /~ 1 0 - 9 t :ll~ [ :I o I ~ _

6 ~ ~ 11 o 1 2 I 1

t0 t l t? 13 141 0 4 / T p ( K -I)

FIG. 10. Oxidation rate o f highly p urified c arbonswhen Po2 = 1 atm (see Fig. 9 for key).

neering purposes for each char considered at relevanttempera tures and oxygen concent ra t ions , and in-dee d for a range o f part ic le sizes for a given char.M a s s T r a n s f e r C o e f f i c i e n t , h m

The first data on the mass transfer coeffic ient ,hm, consid ered here are for pf-sized part icles. Ithas been asserted th at E q. (24) is sat isfactory forcalculating mass transfer rates in pf flames. Fig ure11 show s the calculated variation of Pm (the pro d-uc t h m C g with tempera ture for 82 and 105 Ixmchar part ic les burning at 0.1 a tm of oxygen for car-

0"03

0'020"01

Eu"--- 0v

82 .#am PARTICLESmCOos s ) 9t o s s

. 9 I I I I I

q O'O2 j 105/urn PARTICLES?m (CO t o ~ s L % . - - - - - ' -0.01 ~ r 9I ~e~ee,, . . . . . . . .

~ - - - - X ~ c o , t os s)O: I I I r n l I1200 1400 1600 1800 2 000 2200 2400T p { K )

FIG. 11.Comparison of measured and theore t i -cal maximum bur ning rates wh en Po~ = 1 atm. 91

bon loss as CO and CO 2. Th e data p oints (valuesof p re po rted by Field 91) rise to, and l ie c loselyabout , the CO-loss l ine . The fact that some of themeasured values of p l ie sl ightly above the calcu-la ted maximum possible value of Om arises fromexperimental erro r and b ecaus e Pm was calculatedfor the init ial part ic le size, a d ime nsion that de-creases as particles burn, with corresponding highervalues for Pro Eq uation (24) shows h, , , and h enc ePro, vary inversely with part ic le size .A number of o the r k ine t ic s exper iments wi thvarious pf chars 47~49'91'9s sho w values of p tha t riseto, but do not significantly exceed, the correspond-ing values of Pm calculated for carbo n loss as CO .Larger-scale experiments in which polydisperse pfsuspensions have been burned at high intensi t iesalso support the val idi ty of calculat ing h m by Eq.(24). Hoy e t a l } ~ ope ra t e d an M H D c ombu s t o r a t~ 2600 K a nd up t o 6 a t m p re s su re . The me a su re dcomb ustion efficiencies and he at release rates agreedwell with those calculated assuming the variously-sized partic les bu rne d away with p = Pm and car-bon rem oved f rom the par ticles a s CO. M or e re -cent ly Farzan and Essenhigh 11~ bur ned pf a t a t -mospher ic pressure but a t t empera tures above 2000K. The measured combustion behaviour agreed withthat calculated with p set equal to pro.Th ere is amp le evidence tha t for partic les largerthan pf, i .e . >0.1 in size , in isolat ion or in packedbeds, the mass transfer ra tes can be calculated withconf idenc e by Eq. (23). 36 ,82 '83 Fo r exam ple thebur nin g times o f larger partic les, calculated set t ingP = Pro, agree well with ex perim ent. 11 Rob erts andS mi t h i n showe d t ha t t he me a su re d bu rn i ng r at esfor 6 mm spheres of graphite imm ersed in f lowingstreams of cold, dry , oxyg en agre ed with the cal-culated mass transfer rates.Roberts and Smith 111 also show ed that the mea-su re d t empe ra t u re s o f the bu rn i ng sphe res we reclose to thos e calculated assum ing car bon l os s asCO . Likewise Ayl ing and Sm i th 1Iz found agree -ment be tween measured and ca lcula ted va lues ofTp for pu lver ized semi-anthracite particles, for car-bon loss as CO . Recen tly wo rkers a t Sandia 113 re-po r t e d good a g re e me n t be t we e n me a su re d a nd c a l-culated values of Tp, assuming carbon loss as CO,for petro leum coke and Millmerran coal char. I t hasbe e n no t e d t ha t C O is t he p r i ma ry p roduc t o f theoxygen-carbon react ion at flam e tem pera tures, bu tthe locat ion of the subsequent CO-oxidation zonecan affect bo th h m and T~. Ear ly est imates 3e of thelocation of this zon e shoew it to b e sufficiently faraway from pf-sized part ic les not to have a notablee ffec t on the i r burning. Ho we ver for pa rt ic les >1mm CO-oxidation was est imated to take place onthe particle surface, with the carbon loss effectivelyas COz. Recent , and more complex, calculat ions byAm und son and co-workers 114'115 sup po rt this con-clusion.


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1058 C O A L C O M B U S T I O N K I N E T I C S A N D M E C H A N I S M SThe matters deal t with so far in this sect ion areconcerned with small part ic les in entrainment andlarger particles (singly or in beds) fixed in relationto a known f low of gas . I t has a l ready been notedthat the si tuat ion in fluidized-bed combustion ismore complex and le ss we l l unders tood. Cons id-e r ing only the s tep of oxygen t ranspor t through thede nse , i ne r t pha se o f t he f l u i d i z e d be d t o t heburning part ic le (see Fig. 2 and the re levant dis-cuss ion) the problem i s to de te rmine the appropr i -a te coefficient for mass transfer. M as s transfer inthe dense phase of f lu id ized beds i s not ye t we l lunderstood, and ind eed ther e are confl ic t ing inter-pretat ions of th e re levan t data . s3 s5 s~ Ho we ver, forthe s i tua t ion in f lu id ized-bed combust ion , wherethe active particles are dispersed and well-dilutedin a bed o f inert part icles, re la t ionships of the fo rm

of Eq. (23), modified along the l ines used in E q.(25), can be used with some success. Avedesian andDavidson 45 a rgued tha t in the dense phase of f lu id-ized beds, wh ere th e gas veloci ty is low, the Sher-wood number (Sh) i s c lose to 2 . However morerecen t studies 34,s4A16 show values of Sh of 4 ormore under f lu id ized-bed combust ion condi t ions .For these c ircumstances there are difficul t ies ingaining adequate knowledge of Sh. Sat isfactory de-termina tions requi re a measu rem ent o f the pa r t i -c le s bur ning rate , mea ns o f accounting for the ex-tent that chemical ra te control affects this ra te , aknowledge of pa r ticle temp era ture and an under -standing o f w het her the O z diffusing to the part ic leleaves i t a s C O or CO 2. Recent ly L a N auze andJungs4 made ca re ful measurements of the burningrates of single petro leum coke sph eres (in a ir) im-mersed in a fluidized sand bed (so avoiding raterestric t ions due to bubble-to-bed transfer). The ap-propriate values of RC a nd n w e re a l r e ady knownfrom the me asure me nts on the same materia l , a9He nce Pm and Sh co uld be calculated, given thatthe va lue of T_ was known and the manner of lossof carbon as ~O or as CO ~. Reliable calculat ionsof T_ by Eq. (2) are no t possible , the k now ledgeyof hea t transfer betw een bur nin g part ic les a nd flu-idized beds is at least as uncertain as the masstransfer process. La Nau ze and Jung , s4 on th e basisof visual estimates o f part ic le temp erature , giveweight to carbon leaving the part ic le as CO2, cal-culating Rc, h m and Sh on this basis . More re-cent ly these workers have measured pa r t ic le tem-p e r a t u r e s u si n g e m b e d d e d t h e r m o c o u p l e s ; t h emeasured temperatures are c lose to those calcu-lated for COz loss . F igure 12 comp ares the m ea-sured rela t ion between Sh and part ic le size withthe value calculated by E q. (25) for carbon loss asC O2 . The a g re e me n t be t we e n t he o ry a nd e xpe r i -ment i s good. None the less more ins ight i s neededinto mass (and heat) t ransfer in fluidized-bed com-bustion and into sui table means of determining Tp.

1

2

o o o0 oO_ o o o

O ~ 7 60 O

0 0

I I I I0 2 / * 6 8 10 12

P a r t i c l e d i a m e t e r m i n iFIC. 12. M easure d and calculated values of th eS h e r w o o d n u m b e r i n a f l u i d i z e d - b e d c o m b u s t o r(from La N auze and Jung). ~

C h a n g e s i n P a r t i c le S t r u c t u r e D u r i n gC ombus t i onIt has a lready been pointed out that the size ,density, porosity, pore size, and pore surface areahave important e f fec t s on the combust ion behav-iour of par ticles . In sum mary, w here com bust ion

is l imited to the outer surface of the part ic le or toa shal low zone below the outer surface, part ic leswil l burn with constant densi ty but with a steadyreduc t ion in s ize . W hen oxygen pen e t ra tes com -pletely within a part ic le s pore structure , com bus-t ion occurs a t constant size but with decreasingdensi ty. For pf-sized part ic les burning in regime IIcondit ions the penetrat ion depth of oxygen is ofthe order o f pa r tic le radius, consequen t ly thesepart ic les burn with reduction in both size and den-si ty. Thin-walled cenospheres burn with reducingdens i ty but a t cons tant s ize whe ther oxygen pen-etrates the pores or not .In regim e II conditions, as por e diffusion playsa major role , i t is important to have data on theopening of pores and changes in pore surface. Inregime I i t i s important to unders tand the deve l -opment of pore surface a rea dur ing combust ion .Changes in Part ic le S ize and Densi ty

Figure 13 shows the change in s ize and dens i tywith burn-off for a sphere of petroleum coke burnedin a fluidized bed. The burning rate was control ledmainly b y oxygen diffusion t o th e particle. 84 Th echange in size with bur n-o ff decreases steadily inthe manner shown by Eq. (29) wi th a = 1 /3 ,whilst there is little change in particle density, as


15/21

C O M B U S T I O N R A T E S O F C O A L C H A R S : R E V I E W 1059

d 1 o

5

3 " 0 9 9 9 m e 9 e ) ~ o. . . . . . . ;0 8 ~ - ~ -

0"6

( 9 0 . 4 d ~ = ( 1 - U lV a ' ~

0 ' 2I ) I I

0 0 2 0 . 4 0 ' 6 0 ' 8 1 '0UFIG. 13. Changes in particle size and d ensity w ithbu rn -o f f i n a f l u i d i z e d -be d c ombus t o r ( f rom LaNauze and Jung). ~4

1 ' 0

0 ' 8bo~ " 0 6

0 ' 4

0 ' 2

9 , : : ,/ . o : ( '1o / % = ( ~ - u ) ' / ' - , , , , ' \ 0 1

(a )/ ,

e r i c ~( l t - U ) l ' ~ % % 1 " }

~ ' 0 D m ~

0 ' 6 , / b ) d / d o = ( 1 - u ) ' " ~ % \ ~0 - 4 | ~ i l I \0 0 . 2 0 . 4 0 -6 0 8 1 .0F R A C T IO N A L B U R N O F F , u

FIC. 14. Relation betw een bu rn-o ff an d (a) par-ticle density and (b) particle size, for semi-anthrac-cite (particle size: 9 78 Izm , O 49 I~m , 9 22 Izm,9 6 p .m) .

should be the case when external mass-transfer inthe main limitation of the rate.F igure 14 shows changes in s ize and dens i ty wi thbu rn-o ff for size graded particles of pulverized semi-anthracite, g7 Th e d ata, thou gh scattered, show steadyreduc t ions in both s ize and dens i ty and can be rep-resen ted by Eqs. (29) and (30), with e t = 13 =1/4 . This i s the expec ted resul t for regime II con-d i ti o n s w h i c h , f r o m o t h e r m e a s u r e m e n t s , w e r es h o w n t o a p p l y d u r i n g t h e e x p e r i m e n t s c o n s i d -ered.g7The d a ta in F ig . 15 show the changes in s ize anddensi ty with burn-off for 89, 49, and 22 p,m par-t ic les of brown coal char47. With the exception ofthe 22 txm fract ion there is li tt le chan ge in densi ty(13 = 0 in Eq. (30)), bu t the size redu ces steadily(or = 1/3 in Eq . (29)). In fact diffusion of oxygento the part ic les had a major ra te-control l ing effectfor the 89 an d 49 ixm partic les 47, and th e obse rvedchanges in size and densi ty are consistent with thisfact . However, the densi ty of the 22 p,m fract ionred uced steadily with bu rn- off (13 = 1 in Eq . (30))in a manner consistent with regime I condit ions,which in fac t were shown to apply for these pa r-ticl es. 47,r

Data are a lso available on the varia t ion of sizeand dens i ty dur ing the combust ion of chars f rom

1 ' 0

~- - 0 . 5

o1 . 0

o 0 . 5" o

, = ~ _ _ ' ' / ~ [ r '= ': J n . , = - , , - - , - q - - . . - ~ - o_ _ _ - - 0 - _ _

+x~ '~ " ~ . .+ +( o ) r : (1 - u ) ~ ' . ~ - .

1 I L I. . . . ~__~ ~o ol

d / d o = ( 1 -u .) ~1 ~ ' ~b )I I I I

0 2 0 4 , 0 6 0 8 1 0F R A C T I O N A L B U R N - O F F , U

F I X E D - B E DE N T R A I N M E N T R E A C TO R R E A C TO Rp 9 a r m : 0 " 2 0 " 1 0 ' 1

8 9 9 o dd o , p m 4 g 9 ~ - x2 2 9 n

FIc. 15. Relation b etw een bu rn- off and (a) par-ticle density and (b) particle size, for a brown coalc h a t ' .


16/21

1 06 0 C O A L C O M B U S T I O N K I N E T I C S A N D M E C H A N I S M SPO

5 [ . ~ . , , ~ ' ~ ' ~ 0 0 B 6 a im 0 '4

% ~ s ~ ~ .3 ~ l i e9 " .~ 0 3

E

o~ ,; ~ 3'o ~ 0. 28 u r n - o f f , % tE

F I c . 16 . V a r i a ti on o f o bse r ve d r e a c t ion r a t e w i thburn_ off, zl7 nn 0 l

a sw e l l i ng b i t um inous c oa l f r om N e w Z e a la nd89 an da num ber of B r i t i sh b i tum inou s coa ls. 95Changes in Pore Sur face Area

The e f fec ts of changes in pore sur face a rea canbe s igni f icant for combust ion in regimes I I and I ,bu t e spe c i a ll y so i n t he l a t t e r a s t he r a t e i s d i r e c t l yp r opo r t i ona l t o t he su r f a ce a r e a o f t he po r e s ( Eq .(16) ) . The we l l -known fac t tha t r a tes can changew i th bu r n - o f f unde r r e g im e I c ond i t i ons i s i l l u s -t r a t e d i n F ig . 16 , a da p te d f r om the s tudy o f g r a ph -i t e ox ida tion by Ty le r et al 117 The spe c if i c r a t e o fox ida t ion ( pe r un i t w e igh t o f c a r bon bu r n ing ) i n -c r e a se d un t i l a bou t 25% bu r n - o f f , a nd the n s t a r t e dto de c l ine . Tha t spe c i f i c su r f a c e a r e a s c a n pa s sth r ough a m a x im um du r ing c om bus t ion i s show nin F ig . 17 , us ing da ta on the o xida t ion of an thra -c i te . u s The d i r e c t r e l a t i on be tw e e n r e a c t iv i ty a nd

2 0 0

NE

1 0 0Uf f l

Offl

0 0 7/

0 I I I20 40 60B u r n - o f f , %

FIG. 17 . Var ia t ion o f spec i f ic sur face a rea wi thbu rn- of f. 118

00 8

z 35/~//6 5 6 / .

/// In i t ia l/ su r fac e a reat f L

0 -2 0 4 0 ' 6Sur face a rea , m 2 (B.E.T . )F IG . 18. R e la t i onsh ip be tw e e n bu r n ing r a t e a ndpore sur face a rea u9 ( num be r s de no te % bu r n - o f f ) .

pore sur face a rea i s shown in F ig . 18 , for theox ida tion o f spe c t r o sc op ic g r a ph i t e , u9 The num -be r s on the l i ne de no te pe r c e n t bu r n - o f f a nd theda t a show the l i ne a r va r i a t i on o f r a t e w i th t he de -ve lopm e n t o f su r f a c e a r e a du r ing r e a c t ion .S om e da t a ha ve be e n pub l i sh e d on the de ve l -opm e n t o f po r e su r f a c e a r e a du r ing the c om bus t ionof p f chars , a s 'Ss In the case of sem i-anthrac i te pa r -t ic les5s a r e as r e du c e d s t e e p ly w i th i nc r e a s ing bu r n -of f . I t was shown, however , tha t the reduc t ionc ou ld w e l l be due t o a nne a l ing a w a y o f t he f i nepo r e s , a s t he da t a a t h igh l e ve l s o f bu r n - o f f w e r ep r o d u c e d a t h i g h c o m b u s ti o n t e m p e r a t u r e s ( - 2 0 0 0K .In the ea r l ie r sec t ion on pore d i f fus ion coef f i -c i e n ts a num be r o f r e f e r e nc e s a r e g ive n to m ode l so f t he de ve lopm e n t o f po r e s t r uc tu r e s du r ing thecombu st ion and gas i f ica tion of ca rbon. Mo st of thepa pe r s c on tain e xpe r im e n ta l da t a on po r e s t r uc tu r e so r r e l a t e d m a t t e r s w h ic h a r e c om pa r e d w i th t hec o r r e spond ing the o r e t i c a l p r e d i c t i ons .

C o n c l u d i n g R e m a r k sI t ha s be e n show n tha t t he r e a r e r e l a t i onsh ip sby w h ic h the bu r n ing r a t e s o f c oa l c ha r s a nd pa r -t ic le tempera tures can be ca lcula ted , account ing formass t r ansfe r of oxygen to the pa r t ic les , d i f fus ionin to t he po r e s t r uc tu r e a nd c he m ic a l r e a c t ion onthe pore walls.There a re many da ta on the ra te coef f ic ient , Rc ,for pf chars and s imi la r ma te r ia ls . However Re ,w h ic h c om bine s t he e f f e c t s o f po r e d i f f u s ion a ndin t r ins ic chemica l r eac t iv i ty , va r ies notably in ab-


17/21

C O M B U S T I O N R A T E S O F C O A L C H A R S : R E V I E W 1 61solu te va lue and in tempera ture dependence f romchar to char, only showing similar values for similartype s of material, i .e. anthracites an d semi-anthra-c i te s . Fur the rmore , Rc can v ary with partic le sizefor a given char. T he effect of oxy gen pressure onRe, i.e. the observed reaction order n, is uncertain.Given adequa te informat ion on the pore s t ruc -ture of carbons i t is possible to separate the chem-ical and physical contributions to the value o f Rc.The intrinsic chemical reactivity coefficient, R (orrate , Pi) so deter m ined varies wid ely with th e typeof carbon. At a given temperature for different car-bons, differences of react ivi ty of up to four ordersof magni tude a re found.It is possible to calculate Rc (and hence the re-act ion rate , p) from a knowledge of R and data onthe pore s t ruc ture , a ssuming the la t te r i s in asteady sta te . M athematical mo dels are now beingdevelo ped tha t a l low, in principle , the calculationof the way pore s t ruc ture deve lops dur ing com-bus t ion f rom some in i t i a l va lue . However , themodels do not yet ful ly account for the complexnature of the pore structure of coal chars.In general , then, there is as yet no unifying ap-proach to unders tanding the reac t iv i ty of impurecarbons (i .e . coal chars) to oxygen. Where requiredfor engineering purposes i t is necessary to deter-mine Re for chars m ade from coals un de r condit ionsappropr ia te to the type of com bust ion sys tem ofinterest. Th e response of R~ to tem pera ture , oxy-gen concent ra t ion and pa r t ic le s ize needs to beknown for each type of char.To ga in a deeper ins ight in to the combust ionprocess it is necessary to have better experimentalinformation on the pore stru cture of part ic les, es-pecial ly on th e po re diffusion coefficient, coup ledwi th improved mode ls of deve loping pore sys tems.Re lated exper iments a re needed to unders tan d wh y1~. varies so wide ly for differen t carbons. Th e rolesof impuri t ies and the a tom ic structu res o f carbonsneed further invest igat ion.The mass transfer of oxygen to part ic les is wellunders tood for pf sys tems and for l a rge burningparticles in gases of well-defined flow properties.The s ituat ion for f lu id ized-bed com bust ion i s muchless well understood, as are the re la ted matters ofpart ic le temperature and whether carbon is lostfrom the partic le as CO or CO 2.To sat isfy the needs outl ined above, experimentsare required that include the fol lowing; the use ofmodern optical techniques to give information onpar t ic le tempera ture and ve loc i ty , toge the r wi thdetai led descriptions of the beh aviou r of pf charsburning in laboratory flames, coupled with accurateme a su re me n t s o f c ombus t i on r a t e s i n t he s a meflames; the deve lopment of t echniques to de te r-mine the pore structure propert ies of chars (espe-cial ly the pore diffusion coeffic ient) a t temperaturesapproaching those found in flames; the determ i-

nation of R/where pore diffusion effects are absent(e.g. for very fine particles at flame temperatures);the m easurem ent of m ass t ransfe r ra tes to fue l pa r-t ic les burning in fluidized beds, coupled with tem-pera ture measurements on the burning pa r t ic les .In addit ion to those matters direct ly re la ted tochar combust ion the re i s a need to have muchm ore information on the devolatilization process ofcoal, particularly on the devolatilization kinetics ofmateria ls a t s izes appropriate to pf and fluidized-bed combustion. The kinet ic experiments shouldinvolve a tmospheres and hea t ing envi ronments ap-propr ia te to the combustors cons ide red . Da ta a realso required on the chemical and physical prop-erties of the chars pro duc ed d uring devolat il izat ion.

Nome nc l a t u reA pre-exponential factorAg specific pore-surface areaAo fract io nal consumption ofoxygenB cons tantCg oxygen concen trat ion inbulk gastCg oxygen conce ntrat ion indense phaseCp specific hea t of particleC s oxygen concentration o n

particle s ou ter surfaceD bulk gas diffusion coeffi-c ientD e effective diffusion coeffi-c ient in porous sol idp po re diffusion coefficientparticle sizedb bubb le d iamete rE activation ener gyg gravitational accelerationH heat of reactionm m a s s t r a n s f e r c o e f f i -

c i e n t - c a r b o n o x i d efluxh ,~ m a s s t r a n s f e r c o e f f i -c ient - -oxygen f luxo ini t ia l height of fluidizedbe dk function of partic le com -bustion rate (Eq. (7))M molecular weig htm true ord er of react ionn apparent orde r of reac -t iono (subscript) den otes initial

o r r e f e r e n c e c o n d i -tionsP com busto r pressurePo referenc e pressure

g/cmZs(atm) ~e m 2 / g

g / c m 3g / c m 3c a l / g t oo l Kg / c mc m 2 s

c m 2 / scmZ/sc mc mkc a l / mo le m s 2c a l / ge m / s

c m s

em

g / g m o l

a tm, kPaatm, kPa


18/21

1062 C O A L C O M B U S T IO N K I N E T IC S A N D M E C H A N I S M SPO ~ p a r t i a l p r e s s u r e o f o x y - a t m , k P ag e nR g a s c o n s t a n t c m a a t m / g m o l K1 ~ r a t e c o e f f i c i e n t p e r u n i t g / c m 2 s ( a t m )e x t e r n a l s u r f a c e a r e aR . i n t r in s i c r a t e c o e f f i c i e n t g / c m 2 s ( a tm ) mR e R e y n o l d ' s n u m b e rm e a n p o r e r a d i u s c m~ S c h m i d t n u m b e rS h S h e r w o o d n u m b e rTgm g a s t e m p e r a t u r e Km e a n t e m p e r a t u r e i n K

b o u n d a r y l a y e rT p p a r t ic l e t e m p e r a t u r e KT , r a d ia t io n t e m p e r a t u r e Kt t i m e sU b b u b b l e v e l o c i ty c m / sU m m i n i m u m f l u i d iz i n g v e - c m / sl o c i t yu f r a c ti o n a l b u r n - o f fVc v o l u m e f r a c t io n o f c a r -b o n i n f l u i d i z e d b e dW w e i g h t o f p a r t i c l e gX n u m b e r o f t i m e s a b u b -b l e is f l u s h e d o u t ( E q .~ ) )x r a t io o f i n i t ia l o u t s i d e t oi n s id e d i a m e t e r o f

h o l l o w p a r t i c l ey 1 - uZ Ub U ma c o e f f i c i e n t f o r p a r t i c l es i z e c h a n g e ( E q . ( 27 ) )13 c o e f f i c i e n t f o r p a r t i c l ed e n s i t y c h a n g e ( E q .

(28))- / c h a r a c t e r i s t i c s i z e o f p a r - c mt i c l e% f u n c t i o n o f Z ( E q . ( 4 ))

e v o i d a g e-q e f f e c t i v e n e s s f a c t o r0 p o r o s i t y o f p a r t i c l eK r e a c t i o n o r d e r ( E q . ( 1 9) )p a c t u a l ( o b s e r v e d ) r a t e o f g / c m 2 s

c o m b u s t i o n o f c a r b o np e r u n i t e x t e r n a l s u r -f a c e a r e a o f t h e p a r t i -c l eP c r e a c t i o n r a t e g / c m 2 sP i i n t r i n s i c r e a c t i o n r a t e g / c m 2 s(Eq. (32))Pm m a x i m u m r e a c t i o n r a t e g / c m Z s( r p a r t ic l e d e n s i t y g / c m 3

t o r t u o s i t y o f p o r e sT h i e l e m o d u l u sd~l t e r m i n v o l v i n g c o n d u c - c a l / g s Kt i v e h e a t t r a n s f e r ( E q .2 ) )

4 2 t e r m i n v o l v in g r a d i a t iv eh e a t t r a n s f e r ( E q . ( 2 ) )X r a t i o P/Pm

c a l / g s K 4

Ac k now l e dgme n t sT h e a u t h o r i s i n d e b t e d t o m a n y p e o p l e f o r t h e i rc o n t r i b u t i o n s t o th i s r e v i e w . P a r t i c u l a r t h a n k s a r ed u e t o R . H . E s s e n h i g h a n d J . B . H o w a r d f o r p r o -v i d i n g t h e o p p o r t u n i t y t o g i v e t h i s re v i e w , a n d t oR . H . E s s e n h i g h f o r h i s g u i d a n c e i n i ts p r e p a r a t i o n .

W . J. M c L e a n a n d W . R . S e e k e r k i n d l y s u p p l i e dt h e p h o t o g r a p h s f o r F i g . 1 . U n p u b l i s h e d d a t a h a v eb e e n p r o v i d e d b y R . H . E s s e n h i g h , H . F a r z a n , K .J u n g , G . K o t h a n d a r a m a n , R . D . L a N a u z e , W . J .M c L e a n , R . E . M i t c h e l l a n d G . A . S i m o n s .

R E F E R E N C E S1. ESSENHIGH, R . H . : J . I n s t . F u e l 3 4 , 1 6 (1 9 6 1 ).2. MULCAHY, M . F . R . : Ox y ge n i n M e t a l andGaseous Fuel Industries, p . 1 7 5 , T h e C h e m -i c a l S o c i e t y , L o n d o n , 1 9 7 8.3 . F I E L D , M . A . , G m L , D . W . , M O R G A N , B . B .AND HAWKSLEY, P. G . W .: Combust ion o f Pul -verized Coal, T h e B r i t i s h C o a l U t i l i z a t i o n R e -s e a r c h A s s o c i a ti o n , L e a t h e r h e a d , 1 9 6 7 (a ) p .216 , ( b ) p . 301 , ( c ) p . 189 , ( d ) p . 3 05 , ( e ) p .201.4 . S M OOT , L . D . ANO P R ay , D . T . (E ds ) : Pulver-ized-coal Com bustion an d Gasifwation, P l e n u m

P r e s s , N e w Y o r k , 1 9 7 9 .5. THRING, M . W . AND ESSENHIGH, R. H . : C h e m -istry of Coal Utilization ( H . H . L o w r y , E d . ) ,S u p p l . V o l . , C h . 1 7 , J o h n W i l e y , N e w Y o r k ,1963.6. ESSENHIGH, Ft. J . , FROBERG, R. AND HOWARD,J . B . : I n d . E n g . C h e m . 5 7 , 3 2 ( 19 6 5 ).7. GraY, D . , COGO LI, J . G . AND ESSENHIGH, R .H . : i n Coal Gasification ( L . G . M o s s e y , E d . ) ,p . 7 2 , A d v a n c e s i n C h e m i s t r y S e r i e s 1 3 1 ,A m e r i c a n C h e m i c a l S o c i e t y , 1 9 7 4 .8. ESSENHIGH, R. H . : Six teenth Sym posium In-t e r n a t i o n a l ) o n C o m b u s t i o n , p . 3 5 3 , T h eC o m b u s t i o n I n s t i t u t e , P i t t s b u r g h , 1 9 7 7.

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21. SEEKER, W. R., SAMUELSEN, G. S., HEAP , M .P. AND TROLINGER, J. D .: Eigh te e n th Sy m po-s ium I n t e rna t iona l ) on C om bus t ion , p. 1213,T h e C o m b u s t i o n I n s t i t u t e , P i t t s b u r g h , 1 98 1.

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27. STREET, P. J ., WE IGH T, R. P. AND LIGHTMAN,P. : Fuel 48, 343 (1969) .28. TYLER, R. J. : Fu el 58, 680 (1979).29. TYLER, R. J . : F ue l 59, 218 (1980) .30. BADZlOCH, S. AND HAWKSLEY, P. G . W .: I n d .Eng . Chem. , Proc . Des . Dev . 9 , 521 (1970) .31. NSAKALA, N. YA, ESSENHIGH , R. H . ANDW ALKER, P . L . : Com bu s t . Sc i .T echn o l . 16 ,

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tu te , Pi t t sburgh, 1977.33. SCARONI, A. W ., WALKER, P. L. AND ESSEN-

HIGH, R. H. : Fu el 60, 71 (1981).34. PILLAI, K. K. : J . Inst . En er gy 54, 143 (1981).35. LA NAUZE, R. D , : in Fluid iza t ion ( J . F . Dav id -

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ESSENHIGH, R H : Eigh te e n th Sy m pos

combustion of coal chars- a review

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