chapter 6 fluidisation

8/13/2019 Chapter 6 Fluidisation

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Chapter six

Fluidisation6.1.CHARACTERISTICSOF FLUIDISEDYSTEMS

6.1.1. eneral behaviour l gas solidsand iquidsolidssystems

r**l*n:ult"ffie***H*ffi*Hi+rfr,#:Jfim*w*$**Emgf;*f,rJ:t".:,i-H*t'*******t*":**ff'i,,"*i*fl,jJ

*NruN*rum'*p*


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179Chemical n9ineeing rocesses

the Lean or bubble phase. The ffuidisation s then sald ro be aggrceatiie. At much highervelocities. the bubbles tend to break down a feature hat leads o a much more chaoticstructure. When gas bubbles pass hrcugh a relalively high-densily luidised bed the systemclosely esembles boiling iquid, with the ean phase oncsponding o the vapour andthe dense or continuous phase conesponding o th liquid. The bed is then often referedto as a boilinq bed, as oppose.d o ti,e quiescent bed usually formed at low flowrates.As the gas flowrate is increased, he velocity relative to the particles n the dense phasedoes noi change appreciably, and streanline flow may persist even at very high overallrates of flow because a high proportion of the total flow is then in the form of bubbles.At high flowrates n deep beds, coalescence f rhe bubbles akes place, and n nanowvesscls, lugs of gas occupying he whole cross-section ay be produced. hese slugsof gas altematc with slugs of iluidisedsolids hat are carried upwards nd subsequentlycollapse, eleasing he solids which all back.

In an early attempt to differendare between the condiaions eading to particqlate oraggregative fuidisation, WTLHELM nd KwAUK(rr uggested sing the value of the Froudenumber ri,/gd) as a criterion, wherel

,,r is tbe minimum velocityof ltow, calculated ver he whole cross-sectionof the bed. al which fluidisarionakes lace,

/ i . lhc diameler l f ie part i , e ' . an,I is the accelenlion ue o gravity.

At values of a Froude group of less han unity, particulate luidisation normaliy occurs and,al higher values, ggregative luidisation akes place. Much lower values of the Froudenumber are encountered with liquids because he ninimum velocity required to producefluidisation is less. A theoretical ustification for using lhe Froude group as a meansof distinguishing between paticuiate and aggregative luidisation has been provided byJAcKsoNe) nd MuRRAy(r)_

Although he possibjlityof fonning fluidised beds had been known for many years,the subject remained of academic nrerest until the adoption of fluidised catalysts by thepefoleum ndustry or the cracking f heavy hydroca$ons nd or the synlhesis f fue]sfrom natural ar or from carbon monoxide nd hydrogen. n many ways, he fluidised edbehavcs s a single luid of a density qual o that ofthe mixture of solids and luid. Sucha bed will flow, it is capable of tansmilting hyd.ostatic forces, and solid objects withdensitles ess than that of the bed will float at the surface. ntimate mixing occurs withinthe bed and heat tansfer rutes are very high with the result that uniform temperatures requicHy attained 0roughout the system. The easy conlrol of temperature s fte feature hathas ed to the use of fluidised solids for highly exothermic processes, where unifonnityof temperaturc s imporlant.

In order to understand he propeties of .r fluidised system, t is necessary o study theflow patiems of both the solids and tbe fluid. Thc mode of formation and behaviour oIfluid bubbles s of particular mportance ecause hese sually account or the low of ahigh proportion f the lujd in a gas solids system.

In any study of the properties f a fluidised ystem, t is necessary 0 selecl condi-tions whicb are reproducible nd the lack of agrcement etween he resulls of manyworkers, paticularly those elating to heat transfer. s largely alldbulable to the exislenceof widely different uncontrolled onditions wirhin the bed. The fluidisation hould be of


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good qudiiry, hat s ro say, hat he bcd should e ree rom ffegu]ariries nd channellins.Many solids, parricularly hose of appreciably on_isometric hape nrt hose hat havia tendency o form agglomerates ill never lLridise eadily n a gas. Furrtrermore, hefluid nust be evenly disrribured t rhe botrom of the bcti and t;i**ffy

"";""raryt"providc dirr ib or Jcro. , $hict- he pre . .u re rop . cqLal o ar te, . r tur acro. . ' r t re

Deo. nrc onJrt ,on - ,nuch . lore eJdil) che\cJ i r a .mi l iboraloryppar.rar. harrn trrge-scctendu\if l t equlDmenr

. As already ndicated, ben a liquid s the iuidising agenr, ubstanrially niformcondi_lion5 e^ade n lhe bed. l though ' th g. . . buDbtc ormJliun end, ,o o, . r,"r. .or u, ery ow Jlurd.5inpelocir 'e ' . n dn renpl o rplore Lhe ef , ,oducrbil iDf cordirjon.wrlnrn ocd. much ot thc earl ier e.earch orl $i .1 gJ. Jl . r iJi ,eo.y. tems J . ( r l r iedout at gas velocities ufficienrlyow for bubbje omation ro be abse;a. recent earshowever, r has bcen ecognised hat brbbles normally end o form n such y,t".., tfruitney exct an mponanL nfluence n the low patrem f both gas and solids,aDd har hebehaviour f individualbubbles an often be predictecl ith rcasonable ccuracv.

6.1.2.Effect ol fluid velocity on pressure gradient and pressure drop\ \hcn a FLrid_Jlou,r, ,ou,ypsnrJ. r t roJgh d bed or \ery t rnepa icles he lo$ i .slrcamli le nda ine]J , r on e\i ,1 . betheen rc. , r e grudren tno Uoqrate . . . . . . .. r a l j - . , . , .

S e . t o n 1 . 2 . a f r t e p r e - I c C r J d , e n r , p i , r . p l o n e dg n n , r h e . L r p e f _n c r 0 r e , u c | | ) , . ' r . r n d o g d n r h r nc u _ o r o i l J r e , .r r r i g t r t i n e , u n i r t o p e , o b L a i ; e d ,d. .how1 n l- igrrre . l . A, rnc uperficiJt c L,cy rDpfodc.e. t . . i , ; -r. | ] , id ; . ; ;'clociD rr. r l . thc beo un5 ro c\pa10 nd uhen te pfirctcj are no ongcr n phl . icjcontact wrth one aDorher he bed s uidiseLt..lhe |]essweercdient rt,"n e"o.is io*"rbeczuse l lhc n. ed.ed o idage nd. on.eqr r l) . rhe$ eigt . o . panicle. er ni lheiphLot bed . qmallerThi , ta | conrinue. r t hc\etoci ) i . t - ighenolgh or ri . r, r.pon tinenilericl . lo alc placc. rd |nc pre,sure radie. l the : larts o inc,eE.c ga.n ecduse heIncl ,onll rcg f t l -e uid J, lhe wall . ot rhe rbe Llj- . o be.one ignificarr.When hebed s composed f lare parlicles, he flow witt be larninar nly ar

-verylow veloclties

and he slope of rhe ower par of rhe curve wilt be $eater ti . ". il _a _"u

"oi

I{ :t-1-

-9

Figure 6.1, Presure gradienr ithioa bed as f0nction oi nujd velocfu


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181Chem lEngineering rocesses

Ia1

,1.----( :"*.)"" '" ,"" , , ' : :"**^

(bedol narimum porosily)

Figue 6,2, Pfe$ur drcp oler lixed and Ruidised eds

be constant, arlicularly f there s a prog.essive hange n ffow regime as thc velocity

If the prcssure cross he whole bed nstead f the pressure radicnt s plolted againstvelocily, also using ogarirhnic coordinates s shown n Figure 6.2, a linear relation sagain oblained up to the point where expansion f thc bcd starts o take place (A),although he slope of the curve hen gradually iminishes s the bed expands nd tsporosity ncredses. s the velocity s further ncreased, he pressurc rop passes hrougha maximrm value B) and hen alls slightly and attains n approximately onstant aluethat s independent f the fiuid velocity CD). i lhc lluid velocity s reduced gain, hebed contracts ntil ir reaches he condition where hc parlicles are ust resting on oneanother E). The porosiry hen has he naxilnum lable alue which can occur or a fixedbed of the particles. l the velocity s further decreased, he struclure f the bed thenremains naffecled rovided hat he bed s not subjecied o vibration.The pressure rop(EF) across his reformed ixed bed al any lluid velocity s then ess han tha belorefluidisation. f the velocity s now inueased again, t might be expected hat the curve(FE) would be retraced nd that the slope would suddenly hange rom I to 0 at thefluidisingpoinl. This condition s difficult o reproduce, owever. ecause he bed endsto bccomc onsolidated gainunless t is complereLy ree rom vibration. n thc absenceof channclling, t is the shape nd size of rhe pafticles hat determinc oth the naximumporosity and he pressure rop across given height of fluidisedbed of a given depth.In an idedl fluidised bed thc pressure drop corresponding o ECD is equal to the buoyantweight of particles er unit area. n praclice, l may deviale appreciably rom this valueas a result of channelling nd the effecl oI particlewall frictlon. Point B lies aboveCD because he liiclional forces between he particles ave o be overcome efore bedrearrangement an take place.

The minimum luidising elocity, L./, may be deterrnined xperinentally y neasuringthe pressure rop across bc bed or both ncreasing nd decreasing elocities nd plottingthe esults s shown D Figurc 6.2.The wo 'best' straight ines are hen &awn through heexpedmental ointsand he vclocilyal their point ofintersection s taken as he minlmumfluidisingvelocity.Linear ather han ogarithnic plots are generally scd, although t isnecessary o use ogarithmic lots f the plot of pressure radient gainst elocily n thefixedbed s no linear.

los ,J -


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The heoreticat alueof the minimum luidising elociry uy be calculaled ionr hecqurlr)nssi\crr l {-tllLir.ft tor rhe elationU"**" p.".** a-f";;;i";i;; t; ;frxeddckeded. i,h he rcs,ureroph,uushr, . a p"i.q,1ii"l. ,pffi i.l;ri

fl ix;.lli::,"',-"". and he orosirler , he 1\ mum rrrc harun e:.rainer

tn a fiuidised bed, rhc total frictional orce on rhe panicles nrusr equal he effectiveweishr f rhebed . -15 . in r beo L, r n i r ,^.* .cc, i*"i""" .

a"pii i" ia-; ; ; ;" . ; ; ; ' ' ; ; :iddironal pre. . rre rop cju, . the bed arlr ibluble o rhc aloui *. igt , ,

" ,,h . p_.1. .r . e : \ e n t :

( 6 . 1 )

(6.2)

whcre: I is rhe acceleration ue ro gravity andp" and p are he densities f rhe particles nd he luid fespectively.

,Thi .rcluIol apptie. rom ne niriatrpan, ior o t rhcbed LI{- t ran.por f .orid , uie\phce. There miJ be ,omc d. .crepa1() crwecn tc cd,c,r ta.ed rd mer \uredminirnu. l1veiocilies-fbr luidisatjon. his may be arlributable 0channelting, s

",.r"f, "i v-fr.ihe drag orce.acting n rhe bed s rccluced, o the acrionof elecirosiarj" "r"., i" ;;;;ol .Ba-eou. lu ,disadon- sfl i . tJrJ) ,npondnr n rhe. .eo, *"a, _:"' ' "

, ' - 'h :ch i . oJtel con. iJeruble rh nal t pui . r e5. r to t r icr.on er*een ne nt , iaana ne$ d ' 1 , l r h e . o n . d , n i n ge s e t . T l r ; . a . r : t r u r , , o r g r c J r e . t N n a i c e r i r hb e d . rsmall diameiers. EvA ral.ra) ntroduced tenn. (GF _ Gl)/Gr,'wh.ch s" rl"ri""l""efficiency, n which cF is the minimum iowri,5 ,hc e,equi ,ed ,o proJuce he " , , , ,

" , , r, ; : i l : ' ' : ro . . | . : loouce

Iruid. ' ion cnd c/l , f lo$ condit iol . \ r 'h in hc bed re. lrciml.ne. he e.?. ion cl{ecnpLidve,ocrt \ . .pre . su rerop , ap , Jnd o id r se . g iven .o r

" , , , . a o" a . r9 i . " . , i o " , f r J ." i' dmerer.1 . ) rhe Carnan-K1, , ,e1)qJarion,a. t2dl hrch arc , h; Io; l' - --""

- ^ P = ( I - e ) ( p : - p ) t s

," o 05.Jr) (:eI4)

ffiiffi1lfji'_'t?i:il:fiil:ffffi";i,,"i,"#ilio li;::o' .'n"u*'

(6.3.)

rq::, Jili.:,:;:t"i:'l,liliH1.,:Jil,,:ili;"il::i:.i.":illiT:fffhe iuid.as n sedimertarion nd luidisarion,hc equarions oriressure drop " n}r.a r.i.o.r'erestimatehe valueswhe.e he parricles an choose.tncir orieltat;on. i;;t;";;;.;;rd lher ' \ an for rheCcin xn-Ko,/en) onnsnr s In cto. . r * ,o ,a"i . f , . ' .p . . t lni" ," t "u, , .he oethcienrn equcrion .J Lnea Jk. . on he higher JtLcot0.00xq ;"; ;p; ; ; ; ; ievidence s limiied ro a few measurenents

rnaccurucies.s used hereer and equation .3, wirh its possible


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183Chemical ngineerins rc@sses

6,1"3,Minimum luidising velocityAs the upward velocity of flow of ffuid through a packed bed of uniform spheres sincreased, he point ofir?cipkntfu lisation isrc ched when he particles arejusr supportedin.he fluid. The corresponding alu.e f the nititnun fuidisin| .relocirJ (",,,r) is $enobtained y substituting ,,t into equalion .3 o give:

(6.4)

Since equation .4 s based n the Carman-Kozeny quation, t applies niy to condi-tions of laminar low, and hence 1o ow values of the Reynolds umber or flow in thebed. n practice, this restricrs ts appiication to fine particles.

The value ofzar will be a function of the shape, size distribution and surface proF,ertiesof the particles. Substituting a typical value of 0.4 for enf in equation 6.4 gives:

/ . 1 \ - r , ^r,-, o.oos: ''"' lu :-tE

\ t- e l t l

(,.r)",/:0.4o.ooose4+^) (6.5)

# :,, q#)#).,,,+) (+)

When the flow regime at the point of incipient fluidisation is oulside the range overwhich the Carman-Kozeny equation s applicable, t is necessary o use one of the moregeneral equations or the pressure gradient n the bed, such as the Ergun equation givenin equation .20 as:

where d is the diameter of the sphere with the same volume:surface area fttio as theparlicles.Substituting = ?nf at the ncipient iuidisadon oint and or -AP from equation .1,equation .6 s then applicable t the minimum luidisalion elocity ldt, and gives:

/ , ) \ / . , \ / _ . . 2 \t t - c " . t t p , p r 3 - l s O f

' r - " 4 f rl { i r " l ' r ) + t . 7 s ( " . " ' " 1 [ ' " " ' I

\ . i _ , / \ d . \ e i , , t / \ d I(6.1)

MuLtipiying oth srdes y -, i:- gjves: ' t I en , i

:''(?)(n.(+-)('f) (6.8)

(6.6)

(6.e)

ln equation .8:d3p(p" - p)e

where Gd is the Calileo number'.

and: 'f =*"''''' (6.10)


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Ftuidi2ation 184

where Re,,f is the Reynolds umber t rhe minimum iuidising elocityand equarion .8

",- ,ro t ' - ; , , .1o / r '7), ",,, |

.,.,\a:,

rn,,,Fora typical alue f ,rit= 0.4:

Ga = 1406Re;f 27 3Re':rThus: Re':J +51.4Re:,J o.O366Ga:0

and: 8e',1)s"o:6 = 25.7 J(t +5.53 x l0-5cd) _ l}and, imilarlyor r,n, = 0 45:

(6 .1l)

By definirion:

(6.12)

(6.13)

(6.14)

(6.14a)

(6.15)

It is probable hat the Ergun equation, ike the Carman_Kozeny quaaion. tso overpredictspressure rop fof fluidised ysrems, rthough o expenmentar vidence s avairabre nrhe,ba\ is f wh;c-hhe vrtues t rhccoetficinr. may be amendcd.wE\ lnd yu" ha\e e\amined he ret . r ion.hip er$een oiJcgc t lhe minimumfluidi ' ing elocl) . p . , , . and anicte hape.d. . whi.r, , a.nn.a,r. r"?urio i i ;_; j ; . ; . ;

;1,il:ii,T:,:'.f;::T:'nH:'[,]#':fl Jj:[;.*u,e,""q,,"-1.'.

(Re:,)",r=a45:23.61J(1+ 9.39 r0 5Gd)_rl

w:fia"-r

d :6v,/At, and4 : 6vt,/1t)1/3

\+)i:"(#;):',

Thus:(6.16)

Ij"':it:i i{5hlTi"':ili:,H"flil:.",T:1.'i,ffiiJ;T"1"*t""J:[ff::;ffH:ill :*:':i?';:t:.il::T;*: -***'r'"p*i"i"'".i";;";;;;

::$:& il t,l *'iu*J';:J,J#?:"ffi:,i'Jl#l#l#:;fiili#*::l,.ji. jj';,T :Tl1"l{n:H:i:ftil:,3t,ififir.,:}:it#it',?r.iltl;i';:":'$"i:*::J#lin:':ii1l"**1"13::'rp*r"r""i*'""'lia''*e"coneralons etween u| -o a", ^ *"*. * l*,#l 6expresslons

give reasonablv ood

(6.17)

(6.18)


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185Chemical ngineenns rcesses

1 , 0:. g0

oi

0 0.2 0,4 0.6 0.3 1,0

Figue 6.3. Relation betwn ,,/ ffd 4i

NrveNo) iscusses he significance f &e two dimensionless roups n oquations .17and 6.18, and also suggests hat d and. -t in equations .8, 6.9 and 6.10 are moreappropriately eplaced by a mean inear dimersion of the pores ard the mean pore velocityat the poini of incipient fiuidisation.

U.ingequalion . lo ro sunrrirure or d; for i rn equalron .6 Sives:ap

, . cd l , ( r, . r l 8 - r so 1 r-

" ' r " \( u" t \

* , r ,(

- " - \*" i -

\ " i , / J \o:d , 'zI - \ , ) , , )o .a ,Thus:t+4 =""+)he?).,,'#)W)Substituting rom equations .1? and 6.18:

Glp: (150 11)Re^Jt+ O.75 x lqR;:Jl

\vhere Gar and Renfr are the calileo number and the particle Reynolds number at rhepoint of incipient fluidisation, in both cases with the linear dimensior of the particlesexpressed as d,,.

Thus: Re':tu + 67 3Re^Jp o.0408cap O

0.2

sivins: Re^Jp 33.651J0 6.18 to-5cl]p) 1l (6.19)

(6.20)

Example .1A bed consists of unifom spherical panicles of diameter 3 Im and densiry 4200 kg/nr. What willbe the minimum fluidisjng velocity in a liquid of viscosity 3 rnNvn'? and densiry 1i00 kg/ ?

,,=l;r";,


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Solution

By definirion:

catiteo amtf,r, Ga = dt p(p, _ p\e /p2= (3 x rO{f x lt00 x (4200 I00) x 9.81)/(3 l0-3),= 1.003 10r

Assuming vrlue 10.4 or,r" , . qualion. l4gi\er: .R4,r = 2s.j JO + 6.53 x t0-)(1.003 x t0)) _ tl = 40

and: 4-l :(40x3x 10-r)/(3 l0 3x lt00)= 0.0364 rls r 36 :1 , ry4

Example 6.2

Oil, of densiry 00 Shl and iccosiry rNvmr. is p6sed venicr ] Lp$dd\ throlsh a bed ofcatal) rconsisrin8 fappro\imlety sphericatpaJticle\ f dmeler 0. nu mddensiru oOO "i JAr approxrmaret) har mass mte oi flow per Lnirarea f bed wi ra, ffuidjsrlioD.nAO, *iponof particles occur?

Solution

(a) Equations 4.9 and 6.1 nlay be used o determiDe he fluidising vetociry, ,,r.

"= (1 K')(e3(st r _ ortl /p)t_ p / t)

-^P = (1 - e)(p, - p)t8 (equarion .t )

wnere s = surface arca/volume, which, for a sphere, = n .t, / (r d316) = 6/d.Substituting " = 5, S:6 /d and -Lp /t fiom e,ln^rion _t nto equation .9 Sives:

u,, : o.$5s(e3 /(1 _ e))(d, p" , d0 / pHenc: G_r: pu = (0.0o5sei/(t _ e))(tt2(p, Ddlp

In fiis problem,A = 2600 kg/m1p = 900 kgmr, p = 3_0 10 r NVm,and = 0.1 nnn = L0 x 10-4 m

.As no valu of the voidage s availabte. e wilt be estinated by considding eight closety packedspheres of dianeter d in a cube of side 2d. Thus:

volufte of sphers 8(r/6U3

volun of the enclosure = (2d)r = 8dr

and hence: voidase, = I8l3 _ s(z/6)d3ll8tr = 0.478, say, 0.48.rhus I c;r : 0.0055(0.4s)3 0+),((900 x 1700) 9.81)/(t _0.48) x 3 x l0 r

= 0.059 kg/m,s


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i87 chemical nglneering rocesses

(b) Tnnsport of the particls will occur when the fluid velocjly js equal to the terminal falingvelociiy of the paficle.

Using Stokes aw: uo= d1eb, d/18tt (equation z)

= ( (10-4) '1 9.81 1?00) / (18 3 x l0-3)

:0 .0031 n ts

The Reynolds umber: ((10 a x 0.0031 900)/(3 x 10 i) :0 093 and hence Stokes' lawappltes.

The required mass low: (0.003t x 900) = 2.?8 kg/m'zsAn altemative aplmach is to lnalG use of Figure 3.6 and equation 3.35,

(R / puz) Re'z 2d1 s(p" - p) /3 px

- (2 x ( l0r ) r x (900 9.81) 1700) / (3(3 l0r )1 : 1 .11

From FiguE 3.6, Re = 0.09

uo ReQtl d = (O.$ x 3 x l0-r)/(900 x l0+) = 0.003m/s

G' : (0.003 900)= 2.7 kg/m'?s

Hence:

6.1.4. Minimum luidising velocity n terms of terminal ailing velocity

The minimum fluidising velocity, u,,r, may be expressed n tems of rhe free-fallingvelocity uo of the parlicles n the fluid. The Ergun equation equalion .11) elates heCalileo number Gd to the Reynolds number R4l jn lerms of the voidage s,t at theincipienr fl uidisation point.

In Chrplcr4, elations re givcn hat permit he calculation f Re6(xodp/p), he particleRoynolds umber or a sphere l its terminal alling velocity uo, also as a function ofGalileo number. Thus, t is possible o express Rs;/ in terms of ReiJ nd r,J in terms

For a sphencal particle the Reynolds numbcr R6 s expressed n terms of the Galileonumber G/' by equation 3.40 which covers he whole range of values of R?' of itterest.This takes the fbrm:

Rei, : Q.33caa0t3 1.53cd-0 '0r6)3 6.21)

Equation .21 applies when hc partlclemolion s not significantly ffected y the wallsof the container, hat is when d/4 tends o zero.

Thus, or any value of Ga, Re6 may be calculaled rom equation .21 and R;f fromequation .11 for a given vdrc of e./. The ratio ReLlRe'-re uo/u-I) may then beplotted against Gd with ,rf as the parameter. Such a plot is given in Figure 6.4 whichincludes some experimental data- Some scatter s ovident, largely attdbutable to the factthat the diameter of the vessel 4) was not always arge compared with that of the particle.Nevertheless, t is seen hat the expenmental esults straddle he curves covering a range

1 0


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FiguF 6.4. Rario of iominat riiting votocily o nininum fluidisins etocity, s a fu.ction of Catilm nunber

of_values of e,t from abour 0_38 o 0.42. The agreemenl berween he experimental andcrlculaled.vxl es s quire ood. spec.a in viewot Lhe ncenainry

"f ,+; ; ;" i ; t r ; :or ?,r / n heerpenmental ork. nd he acl hal he Ergun quadon ocs o tnecesranlv

fiffi*],|il:1f;.l*tt"tonorpressureropn a fixed ed' speciallvear h";;ip#

^.1'"1 :,1 lia, . ,ol: , ,rhar.ir \dsopossibte o \press co n rerns tGd by meansor rnfte srmpte quatrons.ach overinS lirniledangc f value\ t Oa

124

1 1 0

100

201 00tor rtr1 1o2 103 1d

Galileo umber Ga)los

C a : 1 8 R e ' (Ga < 3.6) (6.22)

(6.23)

(6.24)

It is convenienr o use equarions .22 and 6.24 as hesc nable ery simple elations orR6lRe;f to be obtained t borh ow and high vatues f ca.Taling

-a_typical vaiue of s,/ of 0.4, the relarion beNeen Re; and Ga is given byequaaion .13.For ow va.lues f Rz;J(


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189 Chemil Engiree.ing Pro@sses

Combining quarions .25 and 6.26:

R, ; l = r rR". , ,

Again, or high values of Re',,y'>- 2OO) nd Ga(>los). cquation .13 gives:

Re' , , , 0 . l9lGat/z

Re'o: ; l32catt2

n"'on"',,5

This shows hat o/r,if is much larger or low values of Ga, generally obtainedwith small particles, han with high values. or particulale luidisationwith liquids, tetheoretical ange of fiuidisingvelocities s fron a minimum ol t/,,,/ o a maximum of tlo.It is thus sen hat there s a far greater ange of velocities ossible n the streamlineffow region. n praclice, t is possible o achieve low velocities reatly n excess f u0for gases, ecause high proportion l the gas can pass hrough he bed as bubbles ndeffectively y-pass he particles.

6.2, LIQUID-SOLIDS YSTEMS

6.2.1.Bed expansion

Liquid-fluidised ystems re generally haracterised y the rcgular expansion f the bedthat lakes place as the velocity increases rom the minimum fluidisation elocity tothe terminal falling velocjly of the particles. The general relation between velocily andvolumetric concentration or voidage s found to be similar to that belween sedimentationvelocity and concentralion or particles n a suspension. he two systems re hydrody-namically imilar n lha n the fluidised ed rhe particles ndergo o net movement ndare maintained n suspension y the upward iow of liquid, whereas n the sedimentingsuspension he paticles move downwards nd he only flow of liquid s the upward low

or har quid $ hi , h i \ d r.p .aced ) rhe errl ing $Licles . .hARD.oNndZqxtrlrr ho*edthat, or sedimentation r fiuidisalion f uniform panicles:

= (1 - c ) . (6.3

(6.2:7)

Equation .24 gives:

Thus : lL :g . t

(6.28)

(6.29)

(6.30)

where: 2.. s the obseNed edimentation elocityor the empty ube luidisation

,i is the conesponding elocityat infinite dilution,e is the voidagc of lhe system,C is the volumetric fractional concentrution of solids, andn is an ndex,


13/50

The existence f a rclationship f rhe orm ofequarion .31 had been stabtished ix yearsearlier by WTLHELMnd KwAUK(rr ho fiuidised parricles f glass, and and ead shotwjth water. On plottingparticleReynolds umber gainst ed voidage sing ogarithmicscales, ood slraight incs were obtained ver rhe ange of conditions or which he bedwas lxidised.

index l, range from 2.4 ro 4_8 and are the sane for sedimentarion and for ffuidisation ata given vaiue of the calileo number cd. These may be calcuiated ron equation .32.

(4.8,)

@ 2.4)

RrcfiARDsoNnd Zaxlrl) found rhali cofiespondcd losely o u0, rhe free settlinsveloc;r) r r pir. ice in an nfir i te ncdjr m, tor ,ork on .edimcnLalion ' r , -- , -Chxf[r 5. although &j wassomewhat ess han u0 n fluidisalion. he o]lowins eouationfbr tluidisationwas presented:

log,oe tog,o ;+f

(6.33)

The differcnce s likely to be aftribuled o the facr lhat Ll/.l, \|as \efl small n rheicJimenta. iol ^perinenr. . 4o ie ccently. l]A\ ar, l R.H^pDs. a 'have propo.e.dt-cl b l l u $ i n pe l d r t o no r c . o d l t u i l h e e f e ( l o f . n e w a t . u f l h e v e " s c l n f l u i a c r i o n :

(6.34)

- If logarithnic co-ordinales re used o plot hc voidage ol the bed against he supeFficial velocity '," (Figure6.5), he resulring urve can be represcnted pproxinarely ytwo straight ines oined by a shorr ransitional urve. Ar low velociries he voidaseremuin\ on\rr1l orre\pondingo rhdr flhe h\ed bcJ, d "or he l . rd:seJ lale.he;cis a linear elation berween og ,. and og ?. The curvc shown efcrs o rhe fluidisarionof stel spheres n water- 11 houldbe noted har whercas. n rhe absence f channellins.the pie.sure roparrc5c bed ot a g i en erprn. ion . direcrly roporLiondto i ls depr; ,

rhe luid. inp elocir) . indeperdenl tdeprh .An altemative way of calculating hl3 ndex n in equation .31 for rhe cxDansion fpaniculatety luidised ystems s now considered. eglccting ffects ue ro rhe conrainerwall lhen:

:r.*,",' '[ '- 'r(f)""]

11= , _, , , ( ; ) . .

u, _ Re',,uo Rei)

(6.32)

(6.35)

where R4 is the Reynolds umbcr .lplrr.

log(n. /f tu) -tog(Rel , /R. l l

roge loga(6.36)

1 3

Taking ogarilhms:


14/50

191ChemicalEnginee g Prosses

In dis way: Re;J = Q.33Gatrotg 1.53cata01113 er

FiguE 6.5. Relarion between duid velocity (,.) fld voidage (z) for the duidharion of 6.4 nn steet spheresi. water

On h assumption hat equation .31may be applied t the point ofincipient fuidisaiion:

nloe(u.r ud _

-tog(ieL/Re;r)(6.37)

-0.36 -0.28 o,2 0.12 -0.04

)ogc.J loq e..f

For a t'?ical value_oJ 4J of 0.4, Re;, is given by equarion .14. Fudremore, R?6 sgiven by equa.ion .21. Subsriturionnro equarion .37 hen gjves:

- - . . l 1 l . 8 J G a 0 0 - l . 2 c l ? - 0 0 l d r 1 3 1 |' - " ' 'oel -? - - 55 . rc : r6 , , r iEquation 6.38 which applies o low values of d/4 is ploned n Figure 6.6, togerier withexpenmental points from the liiemture, annotated according to tho

d/4 range which isapplicable(ra) The scatter and the low experimental valuei of n, are aitribuitable oartlvro rhe widef fi:e ot l/4 values covered anJ rto inaccuracirs n rle exoerimenralmeaeuremenLs hich are obtatned rom lhe resulls of a number l workers. For r., _0.43, the calculated values of, are virtually unchanged over the range l0 < c/' < 1b5.

An altemative method of calculating the value of R?; , (and hence ,, /) is to substitutefbr R6 tom equation .21 nto equation .35,and o put rhe voidage equal o its valuenJ at the minimum fuidising etocity.

(6.38)

where is given by equation .J2.

(6.39)


15/50

Gallleo umber(6a)

Fienre 6.6. Conpuho. of lalues of the ndex n calculated rom equalion .37 with exp.rimenLll at a

The same procedure may be adopte.d or calcularing the minimum fluidising for ashcar-thinDing non-Newtonian fluid whicb extnbirs po\rer-tot behaviour, atthough r isnecessary o use he nodilicd Reylrokls umiler r?.,r.1,i oxtlorl 60),equation .28.

For neiastic luidsexhibiting owerlaw behaviour, he bed expansion hich occurs sthe velocjly is increased above he minimum fluidising velocily follows a sjmilar panemto that obtainedwith a Newlonian iquid, with the exponent n equarion .31differingbyno more than abour 10 per cent. There is some evidencc, however, rhat with viscoelasticpolymer solutions he exponentmay be considerably igher Reference ay be made owork by SRrNrvAs nd CHHABRA(15)or fufher details.

Example 6.3

Glass panicles of 4 mm diameter arc fluidised by wlrer at a velocity of 0.25 nts. What will be ihe

'lhe dens; ) ol Ela$ 2500 k8/m'. ,he den.iry ot r'rer t000 k8/n, Jnd rhe vi\co.jb of

Solutiont ' t p - o t eCalileo number or pJrri.le. n wdrer C4 - :--I:/]

(4x 10-r ) r x 1000x 1500 9.81( 1 x i 0 ) ,

(equation .9 )

o


16/50

193Chemical ngireering focesses

Reynolds umber qei at teminal falling velociry s given by equation .211

Re; = (.2.33Ga0013 l.53ca 0016)rr'r

Thus:

The value of n in equation .31 s given by equation .32 or smal values f d/4 as:( 4 8 - n '" -- o o.r.lcnu' 0s 5\ 4 - 2 . 4 t

. . n = 2 . 4 2

Thevoidage at a velocity f 0.25 ts is rhen iven y equarion .31 sl0.25

e = 0.784

6.2.2. Non-uniform luidisation

Regular nd cven expansion fthc bed does not always ocur when particles re luidisedby a liquid- This js pafticularlyso for solids of high densiries, nd non-unifomiriesare most marked with deep beds of small parricles. n such cases, here are significantdeviations rom rhe elation berween ed voidage nd velociry redided by equation .31.

SrEwARrreferred o n SrDwARrnd DAvrDsoN(r6))as shown hat well-deined bubblesof liquid and slugs are ormed when ungsrcn eads densiry 19,300 g/m3, and parriclesizes 776 and 930 pm) are fluidised with water. SrMpsoN nd RoocER(17), ,*nrsoNdtcl.(13), AWTHERnd BERCLTN(|9)nd RJcHARDsoNnd SMnH(2o)ave observed hat eadshot luidisedby water gives ise o non-uniform uidised eds. NDERSoNndJAcKsoN@r)hav shown hat his syslemwouldbe expecled o be ransitional n behaviour_ AssErr(22)and LAwsoN nd HassErr(23) ave also noed instabilities nd non-uniformitiesn liouid-.olrds:) iem\. pJniculir l ) r beJs . narro$ diameler. mitrr obsenations ave lsobeen made by CARNs nd PR^usNrrz(24),y Kmvrrs et a1.t25) nd by ReurmG6). whohave published hotographs l bubbles n liquid solids systems. rsrr-,\Ro r at.Pl havemade experimentalmeasurements f one dimcnsjonal aves n tiquid-soiids fluidisedbeds. qrrrv 23 hr. , rudied le t luidisdrion fteadrhor i rhqarerind has eporred heoccurrence

f non-uniformities,hough ot of welldefined bubbles. e has shown hat helogarithmic lots of voidage gairst velocityare no longer inear and hat he deviationsfrom the ine given by equation .31 ncrease ith:

(a) increase n bed weight per unit area,(b) decrcase n particlesize.

The deviation passes hrough a ma\irnum as lhc velociry s incrcased, s shown nFigure 6.7.

The mportance fpanicle densiry n delermining he nature f fluidised ystems s wellestablished, nd ncrease n density generally esults n a less uniform luidised ystem.

0 3-

l(uu : 1800 000) = oo, r.,


17/50

Applyingequation .31 o each fuidised ed givesl

L=": i ^"a lL=i1u0L

Noting hat the superficial elocity . is lhe same n each case, nd assuming hat/t,Ir

e ' l u ' " '_=r_q l (6 . 43 )e H \ u o L

As the iuidisingvelocity s progressively ncrcased, he voidages f both beds ncreases,althougb not generally at the same ate Two cases are considered:

From equation .43, ?n < z, and herefore, rom cquations 424 nd 6.42b' pbh > phtat all fluidising veloc;lies ., and he heavy parlicleswill always orm the boltom ayer.

tf, with increase n velocity, the density of the upper zone decreases more rapidly thanrha oI the bottom zone, lhe two beds will maintain the samc relative orientation ll thereverse ituationapplies, herc may be a velocity /rNvwhere he densities f the twolayen become equa1,with virtually complele mixing of the two species aking place.Any fudher increase n velocity above rNv then causes he bcds o invert' as showndiagrammaiicallyn Fig re 6.8(d).

Increaslngluld elocily

Figue 6.8. Bed invesion t conPlete sgEgation (l) Conplele md pafiial sccFgation('?e)

The elative ates t which he bed densities hange s he luidising elocity s ncreasedmay be obtained y difterentiating quations 424 and 6'12, wilh respect o u.' anddividing o give:

l p , u / a p , t J t r r , . p , n - r t I i d \ " t o H p t c H| _ : t - t | - - ( o . l g 1

d t . / d 4 t l q ( P t P \ \ u o l tI t P t - P t ? L

. o

i:o{

i.'.'.1'..:lii;:...:i.o^oou^

x^'o


18/50

195Chemical ngineedng rcesses

As e t > e utd p"a > pr, then from equation 6.44, r, which is independent f fluidisingvelociry, must be greater han unity. It is thus the bed of heavy particles which expandsmore rapidly as the velocify is increased, nd which must therefore be foming the bottomlayer at low velocities if inveIsion is possible. That is, it is the small heavy panicleswhich move from the lower to the upper ayer, and vice versa, as he veloity is increasedbeyond the inversion velocity &tw. RTcHARDsoN nd Ad,fnr(3o) have analysed he rangeof conditions over which segregation of spherical pa{icles can occur, and have shownthese dia$ammatically in Figure 6.9 for the Stokes' aw region (a) and for tbe Newton'sla\r reg.ion r) .

It has been observed by seveml workers, ncluding by MoRntiMr er dl.(ze) and EpsrEINald PnuoeN(3|), hat a sharp transition between two mono-compbnent ayers does not

always occur and that, on each side of the ransition point, there may be a conditionwhere the lower zone consists of a mixtwe of both species of pa$icles, the Foportion ofheavy particles becoming pro$essively smaller as he velocity is increased. This situation,depicted n Figure 6.80, can adse when, at a given fluidising velocity, there is a stabletwo-component bed which has a higher density than a bed composed of either of the twospecies on its owlt. Figure 6.10, taken ftom the work of EpsrEIN and PRUDEN(3j), howshow tlrc bed densities or the two mono-componeni ayels change as te liquid velocity isinffeased, with point C then defining the inversion point when complete segregation antake placo. Between points A and D (conesponding o velocities ,.A and r.B), however,a two-component bed (represented y curve ABD) nay be formed which has a density$eater than that of eilhr mono-component ed over this velocity range. n moving alongthis cwve ftom A to D, the proportior of light particles in the lower layer decroasesprogressively

tom unity tozero, as shown on the top scale of the diagram. This proportion

0.75

: 0.50

o.25

0.000.00 0.25 0.50 0.75 1,00

(prpYlpu-p)lncreasing luid veloclt

0.00 0.25 0.50 0.75 1.00(prdtba-p)

Incrcasing luid vel@ity

(D)a)

I

6

.9

Figue 6.9. The posibility ot invesioi (a) Sotes law Eeio. (r) Nevton s lav Esion(r)


19/50

cLKcL+ H)0 0.2 0,4 0.6 0.8

(ks/m9

FLuldisingelocity c nts)

Fieurc 6,10, Bed densities s a funciion ofnuidising velocity, howing he mixed plrlicle reionl)

is equal o that n the otal mix ofsolids al poiniB, where he whole bed s rhe of uniformcomposition, nd he velocityxrB tbcrefore eprescnts he effective nversion elocitv.

l f lhe lo$ of nLidising rquid oa comptclely egregarcd ed s.urtJenll ropped .the particleswill all then start o settle at a velocity equal o that at which they havebeen luidised, ecause quaiion .31 s equaity applicabte () edimenrarion nd luidis-

Thus, since he voidages f rhe wo beds wilt borh be greatcr at higher Uuidisationvelocilics, he subsequenr edimenlalion elocity will then also be grearer. articles inboth beds will setrle r he same elocity and se$egarion ill be mairtained. ventually,two packed eds will be formed, one above he other. Thus, f the Ituidisins velocitv s

le. . l fan he rJn. i on reloci l) .a pc(ked ed ot l1lge igl t par cle. ui torm aboiebed of small dense articles, nd conversely, f rhe luidisingvelocity s greater han heinversion elociry.Thus. luidisaiion ollowedby sedimenrarion an provide a means florming qo complelei) egrcg ed nono ornpo-rented. . he eldt ive onfiAural ionluhich depend. lel , on r l-e iquid e.ocir) l shich he p l icle. arc beeq Rurdi .ed.

6-2,4. iquid and solids mixingKa*nns etal.(25)have rudied ongirudinal ispersior n the tiquid in a fluidised bedc o m p o s e d o l g l a s . . p h e r e . o f 0 . 5 m m a r d l n x n d r a n c l e r . A - e p ( h r n g e w a \ i n r r o d u c e d

Smallhea$/ adicles copperrH=8800 gr'm3 =0.135mm)Large ghloanclesz, ronra . -300k9m' . d-0.7 rm)Fu,dis q qud warer = lood ,9 /n3 =r mNs/m1VoLme hc l ron r- Ce Cd -Cr r-O.a i rL CLl rC Cr 0 .6


20/50

197Chemica Enginee inq foesse s

by feeding a nornal solution of potassium chloride into the system. The concentration atthe top of the bed was measured s a function of tirneby means f a small conductivitycell. On the assunplion hat he flow pattern ould be regarded s ongitudinal iffusionsupedmposed n piston low, an eddy ongiludjnaldiffusivily$,as calculated. his wasfound o range rom l0 4 to 10 3 m2ls, ndeasing with both voidage nd particlesize.

The movement findividual paficles n a iquid-solid fluidised ed has been measuredby HANDLEY/ zl.(32) ARLos(33.31),nd LArrFFt. In all cases, he mcthod nvolvedfluidising ransparent arficles n a liquid of the same efradive ndex so that he wholesystem became ransparent- he movemenl of coloured racer particles, whose otherphysical properlieswere dentical o those of lhe bed particles, ould hen be follolvedphorographically.

Handley luidised soda glass particles using methyl benzoare, nd obtained ata onthe flow pattern of lhe solids and the distibution of vertical velocity components fthe particles. t was found hat a bulk cnculation of solids was superimposed n theirrandom movement. articles ormally ended o move upwards n lhe cenhe of the bedand downwards t the walls, ollowing a circulation atten which was ess marked nregions remotc from the distribulor.

Carlos and Latif both fluidised glass particles n dimclhyl phlhalale. Dala on themo\,ement f tbe facel particle. n the form of spatial co-ordinates s a function oftime, were used as dircct nput o a computer rcgnmmed o calculate ertical,ndial,tangential nd radial velocities f the particle as a function of location. When plottedas a histogram, ie tolal velocitydistribulionwas found o bc of the samc o.m as thatpredicted y the kinetic lheory or lbe molecules n a ges. A lypical rcsull s shownin FiglLrc .11(33). ffective diffusionor mixing coefficients or the particles were hencalculated rom the product of the mean velocny and mean ree path of the particles,using he simple kinetic heoly.

0.03EE

e o.o2

.9

6

0,001

Panicle peed mnvs)

FiCuF 6.11. Distribution i p:trlicle peeds n nuidised ed(]|)

Solidsnixing was also studied y CaRl-os(rarn the same pparatus, taningwlth abedcomposed frransparent afiicles nd a ayer of tracer articles t he base f the bed.Theconcentration f particles n a control one was hen determined t various ntervals f time


21/50

ailer he commencemenr f liuidisation. hetypequation.hiswashen"""0,";r";,#iiljo"ilii'r':.ilf"#fll,.Xrlllt:lT;the values fmixing coefficienr blained v 1lfl'r,i,:$ff;T[1rr*;:i,3::#;'':ii: i:.ii::'"1;1"*"i

erocrry.t a vclocitv of lwice he minimum luidising

LArrF(rs) epresenred he circulation currersmt:#*[:ti:#?fu:1":":r;r.i$r'6"Hi:ff:''il::trI,",fjjjrTi'fi'}ffr:':; ?xd$[ii]:'1,,'lii Hi;:i:xF:'1,ffi,'ll"Tpa.ernver

nry adia,";. * *.*". ,,.ilTJ*iJ';'"1#;:i::*::f ;'"",,}i:l:ff "H:'""Xfl1il:#:jfl'#f:t$H$i;Xt"ly;:n:":tr;:**;*tffi':'af*".'.'J:#fi,,il";,"j1X5:i".J,;TJi;i:i:j#;; ;;"d;;;

0.000 0.800 i.000

E

3

I

0.400 0,600


22/50

199Chemiel Enqineenng rocesses

Later wo* on axial dispersion of particles has been carried oRt by DoRcELo er al (36)who used an random-walk apFoach.

6.3. GAS-SOLTDS SYSTEMS

6-3,1,General behaviour

In general, he behaviour of gas-fluidised systems s considerably more complex than tiatof liquid-fluidised systems which exhibit a gradual transition from fixed bed ro fluidisedbed followed by paflicle transport, without a series of transition regions, and with bed

expansior and pressure drop coniorming reasonably losely to values calculated or idealsystems.Pafi of the complication with gas-solid systems arises from the fact that the purely

hydrodynamic orces acting on the particles are relatively small compared with frictionalforces between pafticles, electrostatic orces and surfac orces which play a much moredominant role when the particles are vcry fine. As the gas velocity in a fluidised bed isincreased, he system ends 10 go through adous stages:

(a) Fixed bed ]n which thc pa(icles rcmain n contact with one another and he stnrctureof the bed remains stable unail the velocity is increased o the point lrhere thepressure drcp is equal to the weight per unit area of the particles.

(b) Pa,liculate ^nd rcgrlar predictable expansion over a limited range of gas velocities.(c) A babbling region characterised y a high proportion of th gas passing hrough

the bed as bubbles which cause apid mixing in the dense particulate phase.(d) A turbulent chaoldc cgion in which the gas bubbles end to coalesce and ose their

identity-(e) A region where the dominant pattem is one of .refticallJ upwa l tmnsport of

par"ticler, essentially gas-solids transporl or pneumatic conveying. This condition,sometimes eferred o as tst fuidisation, lies o\ttside he range of Fue fluidisation.

6.3.2.Particulate luidisation

Although fine particles generaliy form ffuidised beds more readily than coarse particles,surface-related orces tend to predominate with very fine particles. It is very difficuh rofluidise

somevery fine partjcles

as they tend to form large stable conglommerates hatare almost enthely by-passed by the gas. In some extreme cases, particularly with smalldiameter eds, he whole of the particulatemass may be lifted as a solid 'piston'. Theuniformity of the fluidised bed is often critically inlluenced by the characteristics of thegas distributor or bed suppo.t. Fine mesh distributors are generally to be prefered ro aseries of nozzles at the base of lhe bed, although the former fie generally more dilficultto install in larger beds because hey are less robust.

Good distribution of gas over the whole cross-section f the bed may often be dilficultto achieve, although this is enhanced by ensuring that the pressure drop across thedistributor is large compared with that across he bed of parricles- n general, he qualityof gas distribution improves with increased lowmte because he pressure drop across he


23/50

bed when it is ltuidised is, theoreticalty, ndependenr of the flowrare. The Dressure rcDacros. hedislr ibulor i l l increa\c. owerer. pp1sr,rnr, .1 , n pjoporl iono de .quxr;of lhe floumre. and rherelore he jrclion of the oralpresruie trop nar occr,. ,.ro.i ih;disriburor ncrea.e. apidl] a, the lourdle ncrease..

Apart rom the non-uniformiries hichcharacterise any gas solid luidised eds, tisin the low fiuidising-vetociry region thar rhe behavjour of itri gas sotid and iquirt_solidbeds dre most similar. At low gas rates the bed may exhibir ; regular expunrion u, tt,"l lo\ rare ncjease\ . Li rhe et ron berwecn uid.si , rg ro. iD nnJ,oi , jagi oflo" ne .lo rmol equarion .JL atrhough.n genera' . he atui , o f rh." . rpo"."r -*. hieh;; :h; ;those for liquid-solids systems partiy because particles have a tendency to fo"nn smallagglomerates hereby increasing he effective particle size. The range oi velocities overwhich paniculaie

xpansion ccurs s, bowever, uire narrow n moit cases.

6,3.3.Bubbling luidisation

The egion f paniculate uidisdtn u ,ua come\ o ar abrup t nd a5 he sa5 elocihr jncrea.ed. ai t l . rhe ormarion fga. bLrbbler.hese ubbti . are usur

' re ,ponv teror he no \ ol atmollal t o f lhe gds n e\ce. . ol thalUoning l rhe minimum luidi . inA

velocity. f bcd expansion ar occurred eforebubbling ommerces, he e*c."" gas nuiiibe transferred o rhe bubbles whilst the conmuous pnase reverrs to rrs voidaAe at rheminimrm luid,singeloci . ] and. n rhi"sa) . i rconirdcri hu. . lhe \prnded c; aDoears{o be In a meta-rable ondil ion hich . rnalogoL\ o rnzr t a .upir.aruraret otu |onrevertmg o rts sarurated oncenrration hen ed with small seed rystals,with rhe excesssolute being deposited n to rhe seed rystals which hcn ndcase n size as a result.

. J l : ,pp. , l imir of ga5 eloci ' ) to r panrculare \pan. ion s r. tmed he nininunbubbttnq etoc|y. u rb . Determrninghis rn prc\ent i l f icul t .cs\ ,1 \ \alur ma) dependon the nature of th distribuaor, on the presence f even tiny obskuctions n tfr"i.O,

""aven on the mmediate re-history f the bed. The latlo uftb/ui, whjch Eives measureof the degre of expansion which may bc effected, usuatty has trign vatue for fine liqhrparticles nd a low valuc or large dense arricies.F9r crac^ker aTllsl (d:55 p.m,densiry 950 ks/m3) fluidised by air, vatues ofarl ,7 , , , r ofup lo 2.8 have ecn ornd b) D{vrfsand R, FqRDsoJ\ ' , - , .u ;ng rte cour,e

ol f i rs \ oik ir uas ound har here a minimurn /e ol bubbte hich . ;ble. Smattbubtles injected into a non-bubbling bed tend ro become assimilated n the a"nr" of,*".whilst, on the other hand, larger bubbles end to grow ar theexpense of the gas fl'ow inthe dense hase. f a bubble arger han he cdtical size s injected nto an exp;ded bed,the bed_will niriallyexpand by an amount equal o the voiume of rhe ";"i"a U"U-Uf"l

men, however, the bubble breaks rhe surface, the bed will faI back biow the tevelexisting efore njeciion and will therefore ave acquired reduced oidage.Thus, the bubbling egion, which is an importanr eature of beds op-erating t gas

velocities n excess f rhc minimum fuidisingvetociry, s usually chara;erisdby ;; ;phases-a conrinuous mulsion hase wirh a voidage pproximatety quat o tfraiof abed l i t . minimum luidr\ ingetociL). nda d;sconrinou. r brbble t ,o . . t rcr" .counr.o"rmort ol lhe e\cc.5 flo\^ol ga.. Tht .r sometimec eterred o as hi rlra- hrs" thco\

23


24/50

201 Chemil Engineering roesses

The bubbles exert a very strong influence on the flow pattem in the bed and providethe mechanisim or the high degree of mixing of solials which occurs. The pmperties andbehaviour of the bubbles are describe ater n this Section.

When rhe gas flowrate is increased o a level at which the bubbles berome very largeand unstable, the bubbles tend to lose their identity and the flow pattem changes o achaotic form without well-defined regions of high and low concentraiions of particles.This is commonly described. s the turbulent rcgion which has, until fairly recently, beenthe subiect of relativelv few studies.

Catego isati n of Sol ds

The ease with which a powder can be fluidised by a gas s highly dependent n theploperlies f the parlicles.Whilst l is not possible o forecasr ust how a given powderwill fluidisewilhout carrying out ests on a sample, t is possible o indicate ome rends.ln general, ire low density particles fluidise more evenly than arge dense ones, providedthat they are not so small that the London-van der Waals ailractive forces are greatenough or the particles o adhere ogether strongly. For very fine particles, hese altractiveforces can be dree or more orders of magnitude greater han their weight. cenerally, $emore nearly spherical he particles then the beller they will fluidise. In this respect, ongneedle-shaped articles are lhe most difficult to fiuidise. Particles of mixed sizes willusually ffuidise more evenly than those of a uniform size. Furthermore, he presence f asmall proportion of fines will frequently aid the fluidisation of coarse particles by coatingthem with a 'lubricating' Iayer.

In classifying articlesnto four

groups,GELDART(a6)as used he ollowing criteda:

(a) Whether or not, as the gas flowrate is increase4 the fluidised bed will expandsignificantly before bubbling takes place. This property may be quantified by theratlo unh/u,nJ, vherc uh, is the minimum velocityat which bubblingoccurs. hisassessment an only be qualitative as the value of Il,, is very c.itically dependenton the conditions under which it is measured.

(b) Whether he ising velocityof the majorityof the bubbles, s grearer r ess han heinterstitial as velocity.The significance fthis factor s discussed n Seclion6.3.5.

(c) Whether the adhesive forces between particles are so $eat that the bed tendsto channel rather than to fluidise. Channolling depends on a number of factors,including the degree o which rhe bed has consolidated and the condition of thesurface of the particles at the time. With powders hat channel badly, t is sometimespossible o initiate fluidisation by mechaoical tirring, as discussed n Section 6.3.4.

The classes nto which powders are grcuped are given in Table 6.1, which is ta*enfrom the work of GELDART(33),nd in Figure 6.13. In they are located apFoximately ona particle density particle size chart.

The Effect of Prcssure

The effect of pressure on the behaviour of the bed is impotant because nany industrialprocesses, ncluding luidised bed combustion hich s discussed n Section .8.4.,arc


25/50

ftble 6.1. Cltegonsadon of Powders l Relation b Fluidisarion Cbaacteristica{33)

30 100 P liculate dlansion of bed

sienincdt velocity range.Snall padicle sir rd

Bnbbling occus a vebcny>r l, Most blbbleshave velociries grearer

velocity. No evidence ofnaxinum bubble size.

diffcuh to fluidne andHdily forn chahnels.

All but ldgst bubbles rise

interstirial g6 vetocity.

spouEd bds, Panjcles

GrcUp B t00 800

20

r000

7000600050004000

3000

i

3 1 o o oI6

E soo

20 50 100 200 500 10 0Meai padicle siz6 (pm)

l-rguF 6.lJ Poqdd ( a\ihcarion diogro tor fludFadon b) air ar rnoienr condrliotu s,


26/50

203 Chemical ngineering foesses

crmied out at elevated pressures, Several workers have reported measurements f bed

:I'#':ilfr :,'l#'ff ,aiii,'.'i138.fff"n**"*shenerv uchisherarues

Because minimum fluidising velocity is not very sensitive to the pressure n the bed,much geater mass lowrates of gas may be obtained by increasing he operating pressurc.

The influence of pressure, over rhe range 100-1600 kN/m2, on the fluidisation of threegrades of sand in rhe particle size range 0.3 to I mm has been studied by OLowsoN ndAI-MsrEDr(421nd t was showed hat the minimum fluidising velocity becane less as thepressure was ncreased. The effect, most marked with tbe coarse soliis, was n asreementvr'ith haLpredicled y slandard elanons uch as equirion 0.14. For frne pard:les. heminimum luidisingvelocir) s independenL f ga5 deDsity equadon .5 uirh p" > > p1.

and honce of pressule,


27/50

6.4. MASSANDHEATTRANSFER ETWEEN LUIDAND PARTICLES

6,4.1.ntroduction

The calculation of coeflicients for the rransfer of heai or nass bctween the particles andthe fuid_stream equires knowledge fthe hear rmass fow,lhe nrertacial rca, and hedriving force expressed ither as a temperature or a concentralion lifference. Many earlyinvestigations re unsatisfactoryn thar onc or mo.e pf rhese ariableswas nacclratel;determired. his applies articularly o the driving orce, which was requently ased ncomplelely roneous assunptions bour he nature of the flow in the bed.

One difficulty n m.Lkingmeasuremenrs t transfe. oefficients s thar equilibrium srapidty attained elween arricles nd fluidising mcdium.This ha.s n some cases eenobviated y rhe use of very shallow beds. r addirion. n measwements f mass ransfer,lhe methods fanalysis have been naccurale, nd he particles sed have requently eenof such a nature hat t has not been possible o obtaii Ruidisation f good quality.

6.4.2.Mass ransfer between luid and particles

BAKHIARIaS)dsorbed oluene nd so,octanc apours rom a vapour-laden ir stream nto- hc surface fsynthcticalumjnamicrospheres nd ollowed htchange f concentrationof the outlergas wiih Lime, sjng a sonic gas analyser. t was bund h;r equitibriumwasattained etween utlelgas and solids n all cascs, nd hcrefore ransfer oefficicnrs ouldnotbe clculdred heproSrcs,ot he adrorption roci* $a. n: l l to , .o$eo, o$ever.

5 , , xrL\ " ' modjfied he y. lem o lharequil ibr, rm a, nol Jcl cved t .ne outlel .Thin beds and ow concenrralions f vapourwere used, o hat he slope of the adsorDtionrsothermwas 8]eater_ arlicles f charcoai f different orc structures, nd of sjlc; gel,were luidised by means f air or hydrogen ontaining known concenrration f cariorr e i u c h l o r e o r w a l e r a p o u f . n n J l g ' a , , J p p d a l u " w : . . e d . o l h a . c u u , d c r e a d i l \dFrnan. led. nd ne od.orpdon roce. . "c, fo osed b) $eigh,rg he oed a. i rrervats.The inle concenlration as known and the ouilet concertration was deiermined s alunctionof time iom a matcrial alance, sjng he nformation btained iom the pcriodicweighings. he driving o.ce was hen obrained t lhe nlet and he outlet of the bed, onine assumption hat he solids were completlymixed and rhat the partial pressure fvapour at their sur{accwas given by the adsorption sotherm.At any heighr above he boltom of the bed, he mass ransfcr are per unit time, onthe assumption f pirr.rrlJ4ri, ofgas, is given by:

dNs:11o66o'6 '

whcrc r' is the ransfer reaper unit height of bed.Integrating ver he whole depth of rhe bed grves:

(6.4s)

N^ hDa'Jracd: (6.46)


28/50

205 Chemical ngineer g Processes

The integraion may be canied out only if thc varialion f driving force hroughout hedepth of the bed may be estimaled. 1 was nol possible o nake measurements f rheconcentration rofileswithin the bed, although s he valuc of AC did not vary greatlyfrom he nlet 1{) he outle . no scious error was ntroduced y using he oga.ifimic meanvalue ACh.

Values of mass ransfer oefficients ere calculated sing equation .47, and t wasfound hat the coefficient rogressively ecamc ess a cach expciment prcceeded ndas the solids became aturated. his effect was attributed o the gradudl build up ofthe resistance o lransfer n the solids. n al1 cases he transfer oefficient was plottedagainst he relative saturatron of the bed, and the values were extrapola.ed back to zerorelative saturation, coffesponding to the commencement of the test. These mr\imumextrapolated alues were then coffelated by plotting the co esponding alue of theSherwoodnunber Sn' = /rDdlD) asainst he particleReynolds umber R?: = ltdplp)to give two lines as shown n Figure 6.i4, which could be represented y the followjngequalions:

Thus: (.6.4',7)

l : 51, 6.31p"".,D '

These corelalions are applicable 0 all the syslems mployed, rovided hai the initialmaximum values of thc transfer ocfficicnls re uscd. Tbis suggcsts hai the extrapo-lalion givcs he rue gas-fi]m oefficienl. his s bome oul by the act thtr he coefficientremained nchanged or a considerablc criod whcn he pores werc arge. hough t fe11off extremely apidly wirh solids with a fine pore structure- t was not possible, o .eiatl3the behaviour f ihe system uantitativelyo the pofe size distribuiion owever.

The values oI Sherwood umber all below the theoretical minimum value of 2 formass ransfer o a spherical articleand his ndicaLcs hal thc assumption f piston lowof gases s not valid at low values of the Reynolds umber- n order o obtain calisticvalues n this region, nformation n the axial disperslon oefficient s required.

A study of mass ransfer etween liquid and a panicle orming part of an assemblageof particles was nade by MULLN and TRTLEAVEN(45, who subjected a sphere of benzoicacid o the action of a stream f water. For a 6xed sphere, r a sphe.e ree o circulale

in the iquid, the mass ransler oefficient was given. or 50 < Re| < 700, by:

(0 .1 < R"; < 15)

h " dLr5 R. ' 50 r 1{a - s l - : . 0 n

'

sh' : o.g4Re',|12st1/3

(6.48)

(6.49)

(6.s0)

The presence f adjacent pheres aused n ncrease r the coefficient ecause he urbu-lencewas hereby ncreased. he effectbecame rogressively reater s he concentrationincreased, lthough he results were not influenced y whether or not the suroundingpafticles were free to move. This suggesls hat the transfer coefficient was the sane in afixedor a fluidised bed.


29/50

1 0

0.1

t

E

-o charcoall2s Air-CC[o Charcoa't56-AirCCt4

' chafoatJS6-H, CCt40_01

o 0.1 r ro --lid----libo

""t."****""; {=f )Figure 6.14. Sheqood nunber as a functior of Reynotds number or adsorption experimenB(q )

The resulrs of earlier work by CHU.KALTL,nd WEmrnonr(46 suggested hat transfercoelficienrs ere imitar n fi\ed and luidised eds.Apparen( i|fercn;s al to$ Revnotd\numben were probabt) due ro rhe facr rhar here ouja be"pp,..trbi;

;;_.i;1;;';fluid n the fluidisedbed.

Example 6.4In a fluidised bed, riftr'ocrane vapour is adsorbed rom d air srream on ro the surface of aruminamicrospheres. he nole fncrjon of do octane n rhe nlet gas s 1.442 t0_, and h.n;;;";iD the outlet gas s found to vary wit| rime as fo ows:

(s )Mole ftaction n outler

sas x10,)

250500750

1000

1250150017502000

F: tq'r"r##iti:i$"fif;:Ir,TridilI:::*F;:'#ffi:'J#::"';::i;#:*: l"-J?oretheidsorytion

isothdma'r'* ru"'* a" i" *'"r* q.;"lii

0.2230.6010.8571.04

1 .20 /1.287r.3381.373


30/50

207 Chemiel Engineedng rocesses

SolutionA rnass balance over a bed of particles at dy time ,

G-Oo )) =

after the stan of the experiment, givesr

d(vF)

G," is lhe molai ffowrate of gas, W is the mass of solids in the bed, F is the nurnber of nolesof vapour a&orbed on unit nass of soiid. and )0. ) is the mole fmdion of lapour in the inlet andourle,"tream espe.rirely.

r the adsorption sotherm s linear. and if equilibriun is r;ched between he outlet gas and thesolids ard if none of the gas bypasses he bed, then a is Biven by:

F = J + h

where / and , de the iniercept md slope of the jsotherm respectively.Combining these equations and iniegrating gives:

tn(1 r/ri = -Gn/wb)t

If the ssumptions outlinedpreviously re valid, a plot of ln(l -:y//o) againsr should ield ash'aight ine of slole -G,,,/ WD.As )o : 0-01442, he ollowirg lable may be producedl

rime G) I - (r/)o) lntl - 0/)tur)250500750

1000t250150017502000

o.002230.006010.008570.01060.01210.01290.01340.0137

0 .1550.41'10.5940.'7360.8370.893o928o952

0.8450.5830.406o.2630 .163o.107o.0720.048

-0.r68-0.539-0.902-1.33

l . 8 l-2.23-2.63-3.04

500 1000 1500

Y

s -2.0

-3.0

sror".ol**'ption.\

FiSure .15. Adsorption sorherm or Exnple 64


31/50

Thse data are plotted- n Figore 6.tS ard a shaighr ine is obtained, with a slope of _0.00r67/sIf G,, = 0.679 x t0 6 kmoys and W = 4.66 e.-the,:

-0.001 7= (-0.61 x tO-\ /4.66bb = a7 x 10 6kmoy8or 0.0873 nol/kg

dQ = h\Ia 'dz

6.4.3. Heat ransler between luid and particlesIn meas-uring eat rransfer coefficients, many *o.k k fuil"d fo measue any temper-aturc djtfcrence er\^een as dnd otid in a Jiuidised ed. F*qr.",ty, r" i;;";.,;;^for transfer asassumed, ince r was not appreciaredhar h;"r irqriirii". *ri#elerlwheie n a f luidised ed. excepr i rhin c ,hr" r"y. , i , ;Ji" ;-] ;

""b*; ' je; ; .isrdbutor, uTTr\RING. oNor-nqtro. nd Svnn,?,and H"ERTJ.rna V.f ,"" ,nr, f l ,measured eat transfer coefficients or the evaporation ot water from panicte" .f A_rrfr"or silica gel ffuidised by heared air. In rhe former in"""ttg"ti.", it i, piJ"ti" tf,"t""""ia-rable erors arose from the conaluction ofusedormeasurins,he4\,empera,ure...,l;1#:"$,,[ri";i$,n*.ilT":i*T

a{ure rrdienl aar onfined o lhe bolom pan ot lhe brd . A ,r. , i"" ,h"; ; ; ; i ; ; ; .useo or measunng cs temperdlures. llhough hi. probably cauced ome a;surtanc"to the flow pattern r fte bed. FRANz(4e has reviewed many .f ft" ;;;Jil;;-;;this field.

1**'l. ]used a sready-state ystem n which spherical particles were fluidised in arectangllar bed by means

of hot air. A continuous low of solids was mai"trt; ;;;;i1".'i:#"*:Tff"fi;i'1ffi'f,JT"y*'were cooredirdhen"tu,n"ao '"asseTbrv;p ";i*'r.,

i",,".JJf ,J;ff :r:;:%1r:""?5,11""t""'#::"#;constantan. he rhermo-junctioneads werehJd in un opp.iiro:t"ry t"oi}t;;_;il;;;minimise he eflectof heat onduction. fteli, ,a. ound,r.",,r,.,".p.oi,,.-,uil;i;:'::lr'""Jj:-Ij;l"ij:";T*,1lhan .5 mm decp t he borom ot ine UeO ,newhere. he emperatur. r , ; ; , ;" ; ; ;i"o;t'lo#11fl'"u

o"*een heeas ndhe olidsl tvpicat".p",utr'."p.o;i; ;"ffi;

At any height z above he bottom of rhe bed, the heat rransfer ate between he particres

l* t"rl,lt'"*"

""umPtionor complete ixineor the solids nd ,r ,;";,";;l;;

Integrating gives:(6.s1)

(6.s2)t Z

Q = ha'Jo^rdz

In equation .52, C may be obtained rom ri r

***n*;ti;#**ret*t


32/50

209 Chemiel Engineenng ro@sses

o.o2

Seed luidised llh ai r

Lsad luidised lthai td 0.96 mm

Glass luidised ith CO,

+ 0.37 mm

0 1.0 2.O 3-0Heighi bove ed uppod rnm)

Figure 6.16. vertical temperatute gradient n fllidised bed(50

if the solids were completely mixed, their temperature would be the sane as that of thegas n the upper portion of the bed.

The results or the heat ransfer coefficient were satisfactorily correlated by equation 6.53as shown n Figure 6.17.Sinc he esistance o heat ransfer n ihe solid couldbe neglectedcompared wilh thai in the gas, he coefficients which were calculated were gas-film coef6_cients, conelated by:

, r, , -11 .o .oso l t ln1-ooro1n"

1r" (o . s J J| \ ( t ' / \ , /

1 0

Glass luidised ilhai r

. 0 . 11 4v0.137o 0.165. 0.231o0.838o 1.55

0.1 1.0 10 100l do\Feynordsumbre;/el=fr-l

FiguE 6.1?. Coffelation of erperinental @sllts for bear transfer to particles n Rui.tised bed($ )

340

338

336p

EF

: - 1 ,0

E

3 0.1


33/50

this equation may be

(6.54)

Taking an average vatue of 0.57 for the voidage of the bed.

?.r '2r, 0 . l lRe:rr3

Distance above be.d suppor Temlerature(lml (K)

Th: e.qua,tion ds ound o be appticabtc or \atuer ot R?; trom 0.25 ro t8.As In (l lecaie of ma\. ran\[er. he a5\umption f pi . t ;n flo\a s not val id , enainl \notat ow values.ofheReynotds umber < a) at *r,iir, m" "*J""_t".ii

i"""lr,.ithefheorerical inimum value of 2. This question s discussed urrherat th; ;;J;;;

Example 6.5Cold panicles of gtass balotini are flui.lised with heated air in a bed in which a constant low ofptrticles is mainiai'ed in a horizontat direcrion. when s,"dy

"..,litt.,,;;;; ;""d.';;tebpelatu.es recorded by a bare rhermocouple mmerxed n the bed are as foltows

0o.64| .27l . 9 l

3.81

339.5337.7335.0333.6333.3

333.2Calculate the coefficient for hear ftnsfer blween the gas and the particles. and the corre_sponding values of the particle Reynotds and Nussett n"*t"". C..rn*, i" J" ,..rr, ;";;

The ga\ frowrate \ 0.2 kg/r',. rhe specific ear or iir n 0.88 UAg K. rhe i,co.iry ot air L0.0t5 n\s/m,. rhe pd.jcje djdeltr i,0.25 mm and he *_"r*"0*f,,i,y"i,ir;_

O.ol wi. ri .

SolutionForrhe system desoibed in rhis p.oblem, the rate of heat rransfer between he particles dd thenuid s given by:

d Q : h a ' ^ T d z (equatron.51)

(equalion 6.52)

where 0 is tbe hear transferred, l is the tEat hansfer coefncient. z, is the area for rransfer/unitheighr l bed. and A? rs rhe erperdrLre ,fference rhei8hr .,

r rom me data r len. Ar ma) be plo ed agl insr. a . shoun n f igu_e t8 wheF ge dea underthe curve gives he value ofrhe integralas 8.82 mm K

Heut t raosfemd:0.2 0.881i39.5 3i22)

a: ha la^r dz

Thus:

= Ll1 kwn'zof bed ross-secrion.


34/50

211 Chemil Ensineeins rocesses

,.of

g 4 0

- 3 0

5.0

2 ,0

6.0

1 . 0

Height bove ed suppo {mm)

Fieue 6.18.'remp.raturc iseas a function f bed eight or Eranple -5

If the bed voidage = 0.57, and a bed I m'z x I m high, is considered with a volBne = 1 nr,

then: Volune of particles = (l - 0 57) x 1 : 0.43 mr.

volune of I panicle = (r/6)(0.25 x l0 1tr = 8.18 x 10-''z mr.

Thus umber of padicles = 0.43l(8.18 x 10-'1 : 5.26 x l0r0 per m3.

Aea of particles ' =5.:26x l]to x (1t/4)\O.X x 10 )'z= 1.032 lO4m?/mr.

Substituting n equation 6.52 gives:

11tJ0 i1 x (1.03 loa x 8.82 10-r)

h = r2.2w/m'K

Fron equation .69:Nr:0.11Rer'3

Re = G'd/p = (O.2 O.25 10-)/@.015 10-) = 3.33

Thus: lra = 0.11 (3.33)r'z3 0.513

3.0

, (0 5iJ . 0 .01V{0.25 l0 ) = 6l .o $/m7 K

1 .0 2_O 4.0

Example 6.6

Ballotini particles, 0.25 lM jn diameter, are fluidised by hor an flowing at r]le raie of 0.2 kg/n, sto give a bed of voidage 0.5 and a cross-flow of parricles is mairrained ro rmove the heat.Under steady state conditions, a small bd thermocouple mmersed n the hd gives the following

Area ndercurve=8,82 mK


35/50

Distance above bed support(K) Cc)

00-625L251.8752.53.75

339.5337.7335.0333.6

66.364.56 1 . 860.460.60.0

Assuming plug flow of the gas and comtrlete mixir

tllxi:if;r'T,tr;lffT:,.#mirud:l;fuH*n::rii**F:H; '."1ii",?jil":fi ,:'*:,1,n';:ll"+::l*rn';*ji:Hilt,?fu"Hfiiillr:il}ifif t;""', T"irTT;Iffi::fi$,;mm:*,krnil* ;ffiaporisation of water is 2.6 MJ/kg.Solution

ffil:t"ili Hffii:$tedwithvoidaee ano mass owrate', rhen heat arancever

G', FT = hS t - e.) z (TP_ TJ

wherq Cp : specific heat (Jftg K)4 = parricle ienperature, (K)

s(l - ) = surface aiervolune of bed (mrlm,ltr = hear transfer coefficient (w/m, K)

hs(l- e)zG'CO

c'c,u = nsg 4 l" 170 711"

U,{(l,,*tro.nay be fourd from a plo of the experinental data shown n FisuE 6.19 as

i,' e) - 6(1 o.s) (0.2s x t0-) = 1.2x 104/mG, = 0.2kglm,s, p = 850rkCK

Hence: (0.2 850x 6.3):11 (12x loax6.31 x l0-3)atrd: h=14.1W/m,K


36/50

213 Chemicl ngineeing ro@sses

2 3Hoighiabove bd support z {mm)

Figurc .19. AZ as a function f bedheieht. n Exanple .6

lf the evaporation ate is 0.1 kg/s at a temperature difference, AZ = 50 deC Kthe heat low: (0.1 x 2.6 x 106) = 2.6 x ld w

If the etrective dea of th bed is ,4 thenl

(14.1 x ,4 x 50) = 2.6 x 105 and A = 369 m'z

The surface ea of the bed = (1.2 x loa x 0.1) = 1200n'?Hence, he ractionof bed which s used: (369/1200) 0.31 or 3l ler cent

6.4.4.Analysis of results or heat and mass ransfer o particles

A comparison of equations 6.48 and 6.54 shows hai similar forms of equations describethe prccesses fheat and mass ransfer. The values of the coefficients arc however differentin the two cases, argely to the fact that the average value or lhe Prandtl number, Pr", inthe heat transfer work was ower than the value of the Schmidt number, 'S., in the masstransfor tests.

It is convenient o exprcss esults or tests on heat ransfer and mass ransfer o Partilesin the form of j-factors. If the concentration of the diffusing component s snall, thenthe l-factor for mass ransfer may be defined by:

i ' , 25,oat

E

EE

E

(6.s5)


37/50

where: r is the mdss ransfer coefficienr,t. is the fluidisingvelocity,Sd s the Schmidr umber ,/pD),p is the luid viscosiry,p is the fluid densiry, andD is the diffusivity of the transfered component n rhe fluid.

The corresponding clilion for hear ransfer ,:

where: , is the heat transfer coefficient,Cp is rhe specific heat of rbe ffuid at consrant pressure,P/ is the prandrlnumber Ct,tr/k), andi is the thermal conduclivity of the flujd.

Thc sisrili..ntce of I,facto's s dtscusle(l n dc]ail Coutson(j9)Reaffanging quarions _49,6.50, nd6.55 n rhe orm of6.55, and 6.56and subsriruring

mean values of 2.0 and 0.7 respecrivety or Sc and pr, gives:

( 0 . 1 R " : < 1 5 )

i l : =L p,oui

/: fif sco':o.:7Re',02sc-otz6.2sp"'oz( 1 5 < R e ' , < 2 5 O )

ii,:ffis'""'

=z.olRrf 5sc 33 159p"'-os( 0 . 2 5 < R e t , < 1 8 )

_ _ ' ' " . p " u d _ 0 I t R p . o 2 3 p r 0 1 , _ 0 _ t . t R p . o . 2 3' ' f t R. .

(6.56)

(6.s7)

(6.58)

(6.s9)

These elations are plotted in Figure 6.20 as lines A, B and C resDectivelv.

.tu (\rcK and whrrrrT2 fluid,sed Ephrhalenerysrat \ t f iv; . Iffe;r

si , ,e anger(1elween.1000 nd 250 pm) in air, hydrogen, nd carbon dioxide at u temp".arure-of298 K. Th_gas was passed hrcugh a sinrered disc, which seNed as rhe bid support,at rates of between 0.01 and 1.5 kg/m, s. Because f the nature of the surface'aniof the shape of the particles, uneven fluialisarion would have been oblained. The ftteof vaporisation was determined by a gravimerric analysis of rhe outlet gas, and masstransfer coefficierts were calculared. These were expressed s ;_facrors and lotted againstReynolds urnber Re:(: u,tlp/tt) in Fievre 6.21.Ir may be seen t,ut,wt it"t sei*atecuNes were obtained for each size fraction of particles, each curve was of the samegeneml shape, showing a maximum in rhe fluidisation regjon, roughly at the iransitionbetwen bubbling and slugging con{]itions.


38/50

215 Chemical ngineering rocesses

0.02

0.01 0.1 1 r0 100 1000nevnorosumoerd- = @ I - \ 4 I

Figurc 6.20, Hat od mas tRnsfer resllrs expsed as j-tacios

o 500v 250

-+-g -e't

'-"."--.%-.-4-'

v-Fixed d i

'Bubbling Slugglngreqon L luldisation luidisallon

.E

E

0 . 5 1 2 5 1 0 2 0RCL

Figure 6.2l. .r, lor tbe lransfer of naphtbalene apour to an in fi xed and fluidis.d bedsFr )

CHU,KALTL, nd wETrERorn(46 obrained an improved quality offfujdisation by coatingspherical parlicles with naphthalene, lthough t is probable hat some attrition occured.Tests were carried out with particles ranging n size from 0.75 to 12.5 mm ard voidagesfrom 0.25 to 0.97. Fixed beds were also used. Again, it was found thal particle size was animportant parameter n the relation beiwen -factor and Reynolds number. When plottedas shown n Figure 6.22 against modifiedRelrolds number Reil: (u.Ap/0 - e)LL)1,however, a single correlation was obtained. n addition, it was possible to represent witha single curve the results of a number of workers, obtained n fixed and fluidised bedswith both iquids and gases s he luidising media. A range o10.6-1400 or the Scbmidt


39/50

6

g

=

Figurc 6.22. j factor Ji, for ffxed and nuidjsed beds(46

number was covered. t may be noted thar rhe resutts for fiuidiseal systems are confinealto value.s obtained at relarively high vatues of rhe Reynolds number: The .".""_;t-;;represented pproximately by the equarions:

( l < R e i < 3 0 ) j i t : s.1Rei-ot3 (6.60)

(6.61)30< Rri < 5000) j 'a:l . ' | tnei oAa

@ Naphthalene-ano 2-naphtbol waler. Isoburyt atcohol rarer@ Methyl ethyt kelo.e-warer+ Salicyliclcid-benzenex Succinic cid-, butyl alcoholA Succinic id acetone

2.570.601400866176368690

l 1 7t23t24125t25t26t26126

These wo relations are atso shown as curve D in Figurc 6.20 for a voidage of 0.5.A numter of other workers have measured mass tmnsfer rates, McCuNE andWr. HerNrr5rstudjed rrnster bc(ween aphlhol drlicle. and u ar., i" r,^"t u"j noiai..jDeos, sJ and Mor(rAD')o, b.orbcd drbon etrachtorideapour n act i \ared arbonparticles in very shaltow beds which were somerimes ess than one parricle aiameter


40/50


41/50

r

E

- - Ayreoabisind

r00Fenoro, u.bqFe:

{,fLl

Figure 6.23. Recalcuiar,ed atues oI NNselt nunher, tatine i.to account rhe ellecls of bac nin.gl4r )

Conusn(57 considered he ninimum possi

r,*::"'"'".TJil:n'ffi:it[i{#:t*tt,";ifrdj'fH:J*'"kili*:"[;ifff"?J::1.[""XJii;lill$iilT1il'"'' '**nv..e*aJ*'r"',i*l#zABRoDsKy(5shas lso iscussedhe a,,""r"ii[ii;[r1i;;X".yse]t

number pplies.

6.5. SUMMARYOF THE PROPERTIES F FLUIDISED EDS

:1t: -lr:_ii. i: ":.".:iandins of, fluidised ystems.arc ncreasrns r a very high ra.e,",I i . '*.") a\ a hunJred ape,s ppeanngn anJ i\en)car.

",';:'Hx.i::'fiifi:;f:fl: ;:*;:i,*f:,"j;::JlT,f,1,.T$l::;*il,.'flJ:ir-r#*:ti;ft#jbiql:;ff{ ff;J"TsT:$i;1gpxi1r"rur.*fu#.:,:riiT1li*"r$'*iree alling vetociries. n partjcut;re luidisaricr,T,'.?:ffr'""Hfi'j",:#*:*f:;l'i"lJlt:ls*HtT:,:.1'}:.}3tilf''"'.s"jf'"i:'"T"::l'li,,i,"li;l,,iijiii,,iiji:iiimt*lr"m+i:


42/50

219Chemical n9ineering roesses

is the pattem normally encountere.d with gas-solids systems. Bubbles tend to form atgas rates above he minimum fluidising rate and grow as hey rise through the bed. Thebubbles grow because he hydrostaiic pless re is falling, as a result of coalescence withother bubbles, and by flow of gas from the continuous o the bubbie phase. The rate ofrise of the bubble is approximately Foportional to the one-sixth power of ils volume. Ifthe rising velocity of the bubble exceds he free-falling velocity of the palticles, it q,illtend 10 draw in particles at its wake and to deslroy itsell There is therefore a maximumstable bubble size in a given system. If this exceeds about l0 particle diameters, hebobble will be obvious and aggregative luidisation ill exist; his s the usual conditionwith a gas-solids system. Otherwise, he bubble will'not be observable nd paniculatefluidisationwill occur. n aggregative fuidisation,he flow of the luid in the continuous

phase s predominantly treamline.In a gas solids syslem, the gas distnbutes ilself between the bubble phase and thecontinuous phase which generally has a voidage a lilde grealer than at the point ofincipienr fluidisation. lf tbe rising velocity of the bubbles s less than that of the gas nthe continuous phase, t behaves as a ris;ng void through which the gas will tend to flowFeferentially. lf the rising velocity exceeds he velocity h the continuous phase-andthis is the usual case the gas n the bubbte s continuously ecycled hrough a cloudsurrounding he bubble.Partial y-passing herefbe occurs nd he gas comes nto contactwith only a imiled quantity of solids. The gas cloud surrounding he bubble detaches tselffrom time to time, howcvcr.

The bubbles appear o be rcsponsible for a large amount of mixing of the solids. Adsing bubble draws up a spout of panicles ehind t and carries wake of particles qualto aboui one-third of the volume of the bubble and wake together. This wal(e deiachesitself at intervals. The pattem n a bed containing a large number of bubbles s, of coune,very much more complex.

One of the most important properties of fte fluidised bed is its good heat transfercharacteristics. For a liquid solids system, he presence f thc particles may increase hecoefficient by a factor of 2 or 3. In a gas-solids syslem, the factor may be about twoorders of magnitude, with the coefficient being raised by the presenc of the particles,from a value for the gas to one normally associate.d ith a liquid. The improved heattransfer s associated with the movemeDt of the particles between he main body of thebed and the heat ransfer surface. The particles act as healtransfeffing elements and bringmaterial at the bulk temperatue in close proximity to the heat transfer surface, A rapidcirculation therelore gives a high heat lransfer coefficient. In a gas-solids system, theamount of bubbling within the bed should be sufficient 0 give adequate ixing, and atthe same ime should not be sufficient o cause an appreciable lanketing f tho heattransfer suface by gas.


43/50


44/50

221 Chemical ngineering roesses

10. PINCMECK, . H. md PoppF, F.: Cheh. EE. Sci. 6 (1956) 57. Cntical and terninal velocnies n

I r. RrcHARDsoN.. F. rnd zA(t, w. N.. Ttuns, nst Cheti Ens. 12 ( 1954) 5 Sedinenration nd luidisation.

12. CoD^RD. K E. and RrctsARDsoN. . l.: Clen, E B. S.i 2,1 | qi9) 363. Codelation of data for mininunRuidising elociry nd bed exprnsion n pa.ricnldtely uidised eds.

13. LEw6, E, W. and BowERMN,E. W -.Chn. Ens. Pros. 48 (1952) 03. Fluidizalion f solid parlicles n

14. KH^N, A. R. a.d RrcHARDsoN, . F,: Cli.,r, E g, C.'iz r.78 {1989) 1l. Fluid pariicle nrerrctions ndRo* chracle.istics fnnidized beds nnd settling uspetrsions f spheical paniclcs,

15. SRtNIvAs, . K. and CHSABRA, .P.: Crcn. En8 .t Ptucessing 9 11991) 2l l3l. A. experime.talsludy of non-Nellonian luid flow in fluidised eds ninnnun fluidhation elocity and bed expansio..

16. SlEwARr, . S. B. and DAvrDsoN, . F.: P,"dcr ftcn. I (1967)61. Slug now in fluidised eds.l?. SrMpsoN, . C. lnd RoDcER. . W.: Clcu. t B. S.i t6 (1961) 153. The nuidization f liehl solidsby

gases nder pressure nd heavy olids y qlter,

I 8. HARRrsoN. ,, DAvJDsoN, , F. and DEKoc(, J, w.: Ifdnr, Inst, Chen, Ens. 9 (.1961) O2.On he naturcof agercgalive nd pariicularc lnidhation19. LAWTHER,. P. and BERGLTN, L. W.: United Kingdom Atomic Encrey AutnorityReport, A.E,R.E.,

CE,R 2360 al95?). Fhidisation l lead shot wnh warer.20 .RrcHARDsoN,J .F.andSMtrH, l .W. :Trans . l ns r.Che t lEnB.40(1962) l3Hedransfe r to l i qu id f lu idkcd

systens |d $ suspensions l coa6e pafiicles n vefiical iansport,21. ANDERSoN,. B. and JAcKsoN, .:Cle,,. Ens. S.': 19 (196.1) 09. Tbe nlture of aggEgative nd pafiic-

22. HAssm. N. J.: a/r, Che,,, E?rs. (1961) 777. The nechanGn of flui{iizarion.23. LAwsoN, . md HAssEn,N. l.: Pra.. tki. Stftp. an Fbi.lr.dri,,, Nethedands niv. Press, indhoven.

(1967) 113. Disconrinuities nd low pattems n liquid fluidized eds.24. CAros, E. J. and PRAlsNm, LM.: A.l.Ch.E. l.61.1960) 00. Lonsitudinal iing in fluidization.25. Kn^MERs, ., WESTERM^\N, . D., DE CRoor, J, H. and Dr.rfr:)Nr. . A. A,: Thnd Congress i the

Eurcpean ederation f Chenical EDgineering 1962). t, /,n.ractioh betwen Fluith ah.l Pdni.let 114,The ongnudinal ispe$ion fliquid in a fruidised ed.

26. REmR. H.: Cnen '],g. PDg 8,,/. Sulirs No.62 (1966)92. On thc naturc f bubbles . gas and iquid

27. CrBrLARo.. G., d F LrcE.R.. HossArN,I. nd FoscoLo,P, V.: Chan. Ens. Sci.44\ 1989) 0l. Theexpernncntal etdmination f onc dimcnsional ave velocities n liquid nlidized beds.

24. BatLE\. C.t Pnvak Colununicatiot.29, MotrrJDM,H,, YAMAcrsHr,, and CHTBA, .: Chem. EnE. Sci. 41 (1986) 297. Prediction f conplete

nixing ofliquid fluidized inary solid inicles.30. RrcHAnDso"_, , F. and Ant an;t, E.: T & S 9th Intematio4al Ca feren.e an Solirt Pa icles 2 5 September,

1997, Crakow, Poland) 86. Fluidisation nd sedimentltion f ni{tuFs of prrricles.31. EpsrElN, . and PRUDEN, .B: ChenL Et1E. ci. 54 (1999) 401. Liquid fluidkalion of binary pliricle

nixtures IIL Strddficatim v size and Elated oDic..32. HANDr..v, ., DoRArsAMy, ,, BlrcHrR, K. L., and FRANnTN, . L.: Traa .1,r. Cr.rn. D1s.44 (1966)

T260. A studyof the luid and paiticlenechanics n Iiquid luidised eds,33. CARLos, . R and RrcH^RDsoN.l. .r cheht. Ehg. Sci.22 (.1961) 05. Pdticle speed isdburion n a

34. CARLos, . R.: Univehi , ofwlles, Ph.D, iesis (i96?). Solids ixins in fluidised eds.35. LArrF,B, A, J. a.d RrcHARDsoN.. F.: Cr.?n, Eig. ,5.i 27 (1972) 1933,Cnculalion altems nd velocitt

dhiributions or padiclcs nr a liqnid duidised ed .36, DoRaELo, . ,\, H,, vAN DERMEER, , P , and wEssELlNoH,. A.: Chen. Ens. S.i 40 (1985) 2105.

Mersure eni oi tbe axialdispesion f pafticlesn a i quid nuidized ed apllling a mndoD walk netlod,37. DAvrs, L. and RrcHARDso\,1. .: Tmns. nst. Chen. Ens. 44 (1966) T293. CN interchange etwecn

bubbles nd &e continuous hase n liuidhed bed.38. CELDART, .: Povdcr t.nnobsr 7 (19?3) 285. Types f fluidization.


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Ftuidization 222

,""9rTiT;5J.1,:5,*ft::DsoN.

r F.: c,rc'. e ,ivp,ri - s,ri.r No.30 re68) 26.hebehaviour40 . L | \ a , ,L S . Uni \ r r " rqo , C1mb. :dge . h .D r t e . r. , oo t , gLDbte .i n RJrd , , ed eds .' # " H l ; ; i I " J ; T * 3r i / : 4 / " E J t r i ' r q 8 7' r o q 8 H i e hp F " r c p d r n l ur s , c e \ p b i . i o na n d

tf f i l ' ; r ? , f , . i l X * J ; i ; " '

a E ' ( " " . r , s r ' i 4 0 ' r q o r ' b 1 / n ' u p n leo re s .u ro n r i e

*iiii'1ff,i,,);,ii.i,lli"l^kHraR' A o:rroB /nrr c'?u d's 36 ie5s) 8i.Ma$ amrd between

44, RTGARDSoN,, F. and Szrcd, .1 TruN. r6t. Chen_ Eng, 19 (t96i) 212, Ma$ ransfer n a nuidised

" )1*ii.i");,::.1j:t;"'iT.;?,1,,'ll,'ijtiil%,i:5ih':iff,j:::,.;:::liff:i46. CH ,J C-J


46/50

223 Chmical ngineering roesses

A

c

CoAC

NOTATION

Afta of heat tmsfd surface

AEa for hadfer per unit vobme of bedArea for mnsfer pr unii highi of bedFrrctional yolunetric concentraaon of

Driving force expressed as a nolar. concentrationdifference

Loeditbnic nean value of CSpecinc heat of gas at constmt pBsureSpeific het of solid particle

tangitudinal diff usieiryPsrticle didnerer or diameter of spheE

with sane sudeeiwaas particle

Dianeter of spheF of same volune as

F&tor /d2lr for cenEifugal fluidised bed

Voidag coftsponding to mininun

Fr&tion of nuid passing hrough chmhels

Mass noarate of nBidMss noqrate of ffuid 10 cause nilial

Mass nowrate of duid to initiatefluidisarion

Mass flowr.te of iuid pe. nnir reaAcceldalion due rl) gravirtHeat tonsfer coeincienrMass t msfer coefncientHeat transfe. c@fficient lbr liquid alone a1

sane nte as in bedj-facro. for nrss fansfer to paniclesj-facror for h* tansfer to paniclsDistance navelled by bubble lo incrase

its volDme by a facror eThemal conduclivity of fluidDepth of nuidised bed

constmt in equanon 6.53lndex or (L - r) in equation .55

Molf rale of trdsfer of diftusing

Index of, i equation .31

Prssurc drcp acrcss bed due to the

Rare of tmsfer of near

Ratio of mles of change of bed densirywith velocity for two species

Sl Systen

t/^

JeEKJ&gK

-

M , \ L , T , d , AL2L2L- lL

;- ,

Nl-lL2'r to I

L2.t-20-1Lz"t I

L2"t-lL

LL

LL

MT-lM T t

Mr- l

i tr--2T 1

ul-zMt-rd-r T-rMr3o-t

L

MLT 3o-rL

N'I-r

Ntr-rT-2

lff-zT 3If-2T rA

DDL

E

G

8

I

ots


47/50

sTTSTEr"

vvr

z

Specinc surface of panict$

TmperatuE dnviog fore

Velociry of rise of bubbleSlpericial velocilyof nuid (open ube)Value of rc ar infnile dilur'onMininum valle of,c a which bubbli.g

Mininlm value of 4 ar whicn

F.e-falling velociry of panicte in injiniie

voitase apdied ro ehment

VolMe lilction of spheEsMol. fncrion of vapour n gas sllenMole fiaction of vapour n inlet sa sMole fmction of vapou. in qliti'briun

Height above bottom of bdRatio of gas velocides n bubbte and

Particle stiean fDndionRatio of diaheter of rhe sane spcifc

sn.r&e ss panicles to ihar of samevolumc equation .16)

Angular sped of olltionGalil@ nunbe. [lrr(p" p)8/r1]

Galileo number at oioinun fluidisirg

Nuselr nunher t4lt)Nu$eit nnnber (rlln)Prandd number (crplt)

ftbe Reynolds Mbn (r.4pl/.)Panicle Rey.olds number ( c&/&)Particle Reynolds nuDber al ninimun

nuidisine elocity an.plll )Panicle Reynoids nlnbei Rcl ar

niniDun nuidising elociqtBed Reynolds unber .r/Jr.(l e) )Pailicle Reynolds nunber with I, as

[email protected] irmererl?"r for po*erlav nuidParticle Reynolds number (ro4lp)?anicle Reynolds numbef

scnnidt numls (//rD)sheryood numbr (rDllD)

KKKKdeg K

Y.

Fluidjzarion 224

L l

TI]T ILr lLrrL T '

LI-I

t fl,2T_rA-LiLrM

Y''

i

LL

ML-IT-IM L 3t&-:ML-J

Ltr-3

' r r

R"'"

Rlo

R" aR.i


48/50


49/50

6.6. .obrain a ehdonship for rhe ratio of rbc ,.nninlt fahrs"",""," ", " r".r.,"

," .n"

t;::::,t::;,:'-:"-

velcny for a bed of sinile parlictcs, t nay be assuned hat Stokes; Laq ;nd lhe Carnln i";;;;;;;;;are appli.able. har is the vat@ or rhc 6rio if rhe bcd oidag""

,r," ,i"i.". n.i,i"i,g""i."rl,;";-,

6 . 7 . A b c d c , n . . o r t r , t J a . p h e r n r , o : " h e r o . m e l , r , , f a n J a . r . r J . 4 . O l ] t e , m , . w h : r q , o rr h e . n i q , L 1 f l u i d . n , 6 \ . . o . , , \ i , a . , q t r d o r\ . \ o r D . n u . . . , _ o , o a . . . i . y i . o o i - ; ; ,

* ' "

6,8. Ballodri prticles,0.25Dm in diameter. re Rridised by hot an flowine at the rare of 0.2 kg/n2crc$-scrion or bed o gile a bed of voidage .5 and a cros,-lrow"f

p*i.hs i; .ai;;i;;,;_;;;"heat. Under $eady srare condirions. a smait bde rhcmocoupte imme$; ii rhe bed eives ttr. r.,rJ"g J"i",Dislance bove

bcd suppon Tempemtue(nn, Cc) (K)0 66.3 339.50 . 0 2 ) J ' - . /1 .25 6 t . l j 335 .0t.875

6A.4 333.62.5 60.1 133.33.15 60.0 333.2

Assunins phg now .f the gas and conpkrc frixing of lhc sotids, alcutare e coetficienr or hear ransfermr \Tn rhe . c l e \ d r t ? 9d . .T, . pec i t c ea r apd r J or d . r 08 . i J h J ( .b , l v o l ' 0 . , ' ' c , r a i r n B r p . J m p r . r . , , i ? d r i To J r J 1 p p , . \ r d r c t yu'rom tempeturur of 42J K bv exremar heding. dnd a dflute aqueous sorution ar 375 K i, rii to tr," r,"i

at ir iare of 0.1 kg6 $ that the ,ar* is .omplccty evapo.ated ar ahnospberic p.essure. f the heat ransfcr

o i | h e c \ l p o r o n . T ' r t J r e n , n . d r o : o o . . . . . r o r , o tb 1 . . 2 . ^ V, t E .

6.9, An etedicalt hated elc,Ent of surfacc er 12 cmz s inrmcned o rhai t is in direct cotrtact irh anuidised cd. Tne resisiance f rhc etemenl mcasuredrolowing darar

Las a tunclion f the oltase applied o it 8iling the

Potential V) 1 2 I + 5 6Resisrance oh,is) t5.47 15.63 15.91 t6.32 1683 17.48

Tl . r eh . i onDc n re 11 ,ce F. ano enpe . . r / , r .

+ =0.00ar" 0.0e2Bhere n0. the resisunce f tbe wie at 273 K, k t4 ohLhe^ \ J l l r r r l . l ? r u . , I e r ro . r L r , r { n t r , q h ) r r c . e d : i p , . o r . < t o , D o t t r , . o n , c ^ . . " p , , t r c . . , r J . , . p c n . r n r r e . , . , . e . " r h e. m . e n i o r r m . T . a t d e n r i r )" r o , u r p , . p o . . U t . . o . o , , , , ( b . 4 u . t i i , . i n o t v e d .. r r t " n e . " nJ d . ffc . e r- . , I r \ - , y, Iod j _n . o t . \ d .mer np .u . f (n . i onof , r r ro r,p , i c l e . , r d r_ r f l en l n jd d d oed , r t e d r p r, f t e " r r he bq r ._ r ' ' A h q r i d n ' i d i l e J b e o . o 1 . i . r , " t e d - J . \ o t , r r . " o r p r c r p d r , e . 0 r r , , " n J O I n i r . l . n e t e r .Thc bd s fluidised nd conplcte sesrceadon t$e rwo sFecies ;cus. when rhc iquid no; t, il;:;drrcres eule o iomr a sgregared wolayer bed. The iqlid no* s rr,en r.tea

"ga'"Wr,e" ;. ffi;;,such ha de larger par{icics re at rheir nciDiert ini.ti\

"i,r" n"iai,"o ".p*"i;iil;"iiilil"]::;'""""pornr hat' pffoximaterv'irr e he oidage

wh{e.R0, tic ristmce of ihe wne 1273 K, is t4 ohms nd 4, ts n K. Esrinrare tre red efrpemture nde yalue

chapter 6 fluidisation

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