Chapter 6 Fluidisation [PDF]

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Chapter six

Fluidisation 6.1.CHARACTERISTICS OF FLUIDISED SYSTEMS 6.1.1.ceneralbehaviourol gassolidsandliquid solidssystems

r**l*n:ult"ffieg

***H*ffi*Hi+rfr,#:Ja

fim*w*$**Emgff {'i,,"*i*fl,jJ ;*f i,rJ:t".:,i-H*t'*******t*":**ffi

*NruN*rum'*p*$

En9ineeingProcesses 179Chemical

the Leanor bubble phase.The ffuidisation is then sald ro be aggrceatiie. At much higher velocities. the bubbles tend to break down a feature that leads to a much more chaotic structure.When gasbubblespassthrcugha relalively high-densily fluidised bed the system closelyresemblesa boiling liquid, with the lean phaseconcspondingto the vapourand the denseor continuousphaseconespondingto th€ liquid. The bed is then often refered to as a boilinq bed, as oppose.dto ti,e quiescentbed usually formed at low flowrates. As the gas flowrate is increased,the velocity relative to the particles in the densephase does noi change appreciably, and streanline flow may persist even at very high overall rates of flow becausea high proportion of the total flow is then in the form of bubbles. At high flowratesin deepbeds,coalescence of rhe bubblestakesplace,and in nanow gas may be produced.Theseslugs vesscls,slugsof occupyingthe whole cross-section of gasaltematcwith slugsof iluidisedsolidsthat are carriedupwardsand subsequently collapse,releasingthe solidswhich fall back. In an early attempt to differendare between the condiaionsleading to particqlate or aggregativeffuidisation, WTLHELM and KwAUK(rrsuggestedusing the value of the Froude number(ri,/gd) as a criterion,wherel !,,r is tbe minimum velocityof ltow, calculatedover the whole cross-section of the bed.al which fluidisarionrakesplace, / i. lhc diameler ol fie parti,e'. an, is the accelenlion due to gravity. I At valuesof a Froude group of lessthan unity, particulatefluidisation normaliy occursand, fluidisationtakesplace.Much lower valuesof the Froude al highervalues,aggregative number are encounteredwith liquids becausethe ninimum velocity required to produce fluidisation is less. A theoretical justification for using lhe Froude group as a means of distinguishing betweenpaticuiate and aggregativefluidisation has been provided by JAcKsoNe) and MuRRAy(r)_ Although the possibjlityof fonning fluidisedbedshad beenknown for many years, the subject remainedof academicinrerestuntil the adoption of fluidised catalystsby the pefoleumindustryfor the crackingof heavyhydroca$onsand for the synlhesisof fue]s from naturalgar or from carbonmonoxideandhydrogen.In manyways,lhe fluidisedbed behavcsas a singlefluid of a densityequalto thatofthe mixtureof solidsandfluid. Such a bed will flow, it is capableof tansmilting hyd.ostatic forces, and solid objects with densitlesless than that of the bed will float at the surface.Intimate mixing occurs within the bed and heat tansfer rutes are very high with the result that uniform temperaturesare quicHy attained0roughout the system.The easyconlrol of temperatureis fte featurefhat has led to the use of fluidised solids for highly exothermic processes,where unifonnity of temperaturcis imporlant. In order to understandthe propeties of .r fluidised system,it is necessaryto study the flow patiems of both the solids and tbe fluid. Thc mode of formation and behaviour oI fluid bubblesis of particularimportancebecausetheseusuallyaccountfor the flow of a high proportionof the ilujd in a gas solidssystem. In any study of the propertiesof a fluidisedsystem,it is necessary10 seleclconditions whicb are reproducibleand the lack of agrcementbetweenthe resullsof many workers, paticularly thoserelating to heat transfer.is largely alldbulable to the exislence of widely differentuncontrolledconditionswirhin the bed.The fluidisationshouldbe of

goodqudiiry,rhatis ro say,rhatthebcd shouldbe treefrom iffegu]ariries andchannellins. Many solids,parricularlythoseof appreciablynon_isometric shapeanrtthosethat havi a tendencyto form agglomerates will neverflLridisereadily in a gas.Furrtrermore, rhe fluid nust be evenlydisrriburedat rhe botromof the bcti and ;t;i**ffy t" providca dirrib or Jcro., $hict-rhepre..uredrop r. cqLalro ar te,.r itur "";""rary acro..'rtre Deo.t nrcconJrt,on r- -,nuchr.lorereJdil)Jche\cJ ir a .mi liboraloryippar.rar. lhar rn trrge-sccte lndu\iflat equlDmenr As alreadyindicated,wbena liquid is thefiuidisingagenr,substanrially uniformcondi_ . lion5pe^ade n lhe bed.although w'th r g... buDbtcformJliun.end,,oo,.r,"r..or u, !ery low Jlurd.5inp \elocir'e'.In dn renpl ro irplore Lheref,,oducrbiliD of cordirjon. wrlnrnd ocd.muchot thc earlierre.earch worl $i.1 gJ. Jl.riJi,eo.y.tems $J. (rlried out at gas velocitiessufficienrlylow for bubbjefomation ro be abse;a.h recentyears! however,ir hasbcenrecognised thatbrbblesnormallytendro form in such.y,t".., tfrui tneyexct an imponanLinfluenceon the flow patremof both gasand solids,aDdrhar rhe behaviourof individualbubblescanoften be predictecl with rcasonable accuracv.

6.1.2.Effect ol fluid velocityon pressuregradientand pressuredrop \\hcn a FLrid_Jlou,r,,ou,y I psnrJ. rtroJghd bed or \ery trnepa iclesrhe flo$ i. slrcamlileanda line]Jr, ,r on e\i,1.betheen prc.,rfe grudrent rno Uoqrate. .. . . .. . S e . t o n 1 . 2 . Iaf r t e p r e - I c C r J d , e n r ,A p i , r . p l o n e rdg n n , r he.Lrpef_ .nrcarl0j v-r.e, ,. u, .c | |r), . ' r . r n dt o g d n r hcr nc u _ o r o i l J r er ,r.r r i g t r t i noe, u n i r, t o p ei , o b L a i ; e d , d. .how1 in l-igrrre b.l. A, rnc .uperficiJt \c L,cy rDpfodc.e.,t. .i,;-r. |],id;.;; 'clociD rr.r l. thc beo.un5 ro c\pa10lnd uhen rte pfirctcj areno longcrin phl.icj contactwrth one aDorherthebed is fuidiseLt..lher|]esswe ercdient rt,"n te"o.is io*"r beczuse ol lhc in.red.ed\ oidageand.con.eqr errl). rhe$ eigt. o. panicle.DerunilheiphL ot bedr. qmallerThi, ta| conrinue. u rt ,hc\etoci) i.t-ighenolghtor ri.r,r.pon otine nilericl.loralc placc.rrd |ncpre,sure pradie.lt rhe :lartsto inc,eE.c aga.nbecduse .he Incl,onlldrcgof tl-eluid J, lhe wall. ot rhetrbe .Llj-. to be.one,ignificarr.When lhe -very bed is composedof lar€eparlicles,the flow witt be larninaronly ar low veloclties and the sloper of rhe lower par of rhe curve wilt be . il _a _"u $eater ti . " "oi

I {: t-1-9

Figure6.1, Presuregradienrwithio a bed as r f0nctionoi nujd velocfu

181Chem€lEngineeringProcesses

I a 1

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

los(,J Figue 6,2, Pfe$ur! drcp oler lixed andRuidisedbeds

be constant,parlicularlyjf thereis a prog.essivechangein ffow regimeas thc velocity If the prcssureacrossthe wholebed insteadof the pressuregradicntis ploltedagainst velocily,also using logarirhnic coordinates as shownin Figure6.2, a linear relationis again oblainedup to the point where expansionof thc bcd startsto take place (A), althoughthe slope of the curve then graduallydiminishesas the bed expandsand its porosityincredses. the pressurcdrop passesthrough As the velocityis furtherincreased, constantvalue a maximrm value(B) andthenfalls slightlyand attainsan approximately that is independent of the fiuid velocity(CD). Ii lhc lluid velocityis reducedagain,the bed contractsuntil ir reachesthe conditionwhere thc parliclesare just restingon one another(E). The porosirythenhasthe lnaxilnumslablevaluewhich canoccurfor a fixed lhe struclureof the bed then bed of the particles.ll the velocity is further decreased, remainsunaffecledprovidedthat the bed is not subjeciedto vibration.The pressuredrop (EF) acrossthis reformedfixed bed al any lluid velocityis then less than tha! belore fluidisation.If the velocityis now inueasedagain,it might be expectedthat the curve (FE) would be retracedand that the slope would suddenlychangefrom I to 0 at the however.because the bed tends fluidisingpoinl. This conditionis difficult to reproduce, againunlessit is complereLy free from vibration.In thc absence to bccomcconsolidated of channclling,it is the shapeandsizeof rhe pafticlesthat determincboth the naximum porosityand the pressuredrop acrossa given heightof fluidisedbed of a given depth. In an idedl fluidised bed thc pressuredrop correspondingto ECD is equal to the buoyant weight of particlesper unit area.In praclice,il may devialeappreciablyfrom this value as a result of channellingand the effecl oI particlewall frictlon. Point B lies above CD becausethe liiclional forcesbetweenthe particleshave to be overcomebeforebed rearrangementcan take place. experinentallyby neasuring Theminimumfluidisingvelocity,L./, maybe deterrnined velocitiesandplotting the pressuredropacrosslbc bedfor bothincreasinganddecreasing the resultsasshowniDFigurc6.2.The two 'best'straightlinesarethen&awn throughthe pointsandthe vclocilyal theirpoint ofintersectionis takenas the minlmum expedmental fluidisingvelocity.Linearratherthanlogarithnicplots are generallyuscd,althoughit is necessary to uselogarithmicplots if the plot of pressuregradientagainstvelocily in the fixed bed is no! linear.

Thetheoreticat valueof theminimumfluidisingvelocirynuy tionrrhe cqurlr)nssi\crr il {-tllLir.f,t tor rherelationU"**" p.".** be calculaled a-f t;; frxed pdcked bed. $i,hrheprcs,ure drop rh,uush rr,.ua p"i.q,1ii"l.";;;i";i;; ,pffi i.l;ri

fl ix;.lli::,"',

-"". andrheporosirl .era,rhen1\mumrrrrcrhar funbe:.rainer

tn a fiuidisedbed, rhc total frictionalforce on rhe panicles nrusrequalthe effective weishrof rhebed.l-15. in r beoL,runirc,^.*.cc,i*"i a"pii i ;'';;: iddironalpre..rredroprcju,. the bedarlribluble """. "ia-;;;;".;; ro rhc laloui *.igt,, p_.1.. ,h. r . e : \ e nb t : ", -^P=(I-e)(p:-p)ts (6.1) whcre: I is rhe acceleration due ro gravity and p" and p are rhe densitiesof rheparticlesand the lluid

fespectively.

Thi.rcluIol apptie.tromIneiniriatirpan,ior ot rhc bedLI{-trran.porof.orid, uie\ , phce. TheremiJ be ,omcd..crepa1()bcrwecn rtc cd,c,rta.ed ard mer\uredminirnu.l1 veiocilies-fbrfluidisatjon.This may be arlributable10 channelting,as the drag force.actingon rhe bed is rccluced, ",.r"f, ro the acrionof elecirosiarj" f"r"., ''""i!v-fr.i i" ;;;; ol.Ba-eou.flu,disadon-psfli.LtJrJ)i,npondnr in rhe.!.eo, *"a, _:" ,'-' qh:ch i. oJtelcon.iJeruble $ irh .nalt pui.rte5.or to tricr.onUer*een rne nt,ia ana rne $ d ' 1 ,o l r h e . o n . d , n i nr e g s e t .T l r ; .t a . rf : t r u r , , o r g r c J r e . t n N n a i c e\ r i r hb e d .o r smalldiameiers. LEvA€ral.ra)introducedatenn. (GF _ Gl)/Gr,'wh.ch s" rl"ri""l"" efficiency,in which cF is the minimumtiowri Iruid.'ion cndc/ ,5,hc 'e,equi,ed ,o proJuce Lhe,",,,, ",,r,;:il:'':ro..|.:loouce l, flo$ conditiol.l\r'hin hc bedcre.lrciml.ne. lhere.?.ion bcl{ecnpLid ve,ocrt\/.. p r e . s udrreo p -, a p , J n d\ o i d r s e i . g i v e nf o. r o"a.r9i.".,i o rJ. '- " , f--"" d'dmerer.1. " ,$hrch , , . a rarc, b) rheCarnan-K1,,,e1) eqJarion,a.t2dl "i rh; Io;l

,": o!05. (Jr)

(:eI4)

(6.2)

o'*.'n"u*' ffii!ffi1lfiji'_'t?i:il:fi :il:ffiffi ";i,,"i,"#ilio!li;::o (6.3.)

ft"i:'l,liliH1. :,:Jil,,:il ;i;"il::i:.i." ;:illiT:fff rq::,!Jili.:,:;:

ihe fiuid. asin sedimertarion andfluidisarion, rhcequarions foriressuredropi" n}r.a fr.i. o.r'erestimate the valueswhe.eihe parriclescan .choose.tncir orieltat;on. ,i;;t;";;;.;; rdlher'\an5 for rheCcinxn-Ko,/en) connsnris In cto..r *,o,a The(oethcienr "i.f,.'.p..tlni","t "u,,. :n equcrion h.JLneatJk.. on .hehigher\JtLcot0.00xq i;";;p;;;;;i evidenceis limiied ro a few measurenents h er and equation6.3, wirh its possible rnaccurucies. is usedhere

183ChemicalEngineerins Prc@sses

6,1"3,Minimumtluidisingvelocity As the upward velocity of flow of ffuid through a packed bed of uniform spheresis increased,the point ofir?cipkntfu lisation isrc chedwhen the particlesarejusr supported in.he fluid. The corresponding valu.eof the nititnun fuidisin| .relocirJ(",,,r) is $en obtainedby substitutinge,,t into equalion6.3 to give: / . 1''"' \ - r , ^

r,-,- o.oos: I \t

-eltl

lu !:-tE

(6.4)

Sinceequation6.4 is basedon the Carman-Kozenyequation,it appliesoniy to conditions of laminarflow, and hence1olow valuesof the Reynoldsnumberfor flow in the bed. ln practice, this restricrs its appiication to fine particles. The value ofzar will be a function of the shape,size distribution and surfaceproF,erties of the particles. Substituting a typical value of 0.4 for enf in equation 6.4 gives:

(,.r)",/:0.4 : o.ooose ( 4+^)

(6.5)

When the flow regime at the point of incipient fluidisation is oulside the range over which the Carman-Kozenyequationis applicable,it is necessaryto use one of the more generalequationsfor the pressuregradient in the bed, such as the Ergun equation given in equation4.20 as:

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

(6.6)

where d is the diameter of the sphere with the same volume:surfacearea fttio as the parlicles. Substituting€ = ?nf at the incipientfiuidisadonpoint and for -AP from equation6.1, equation6.6 is thenapplicableat the minimumfluidisalionvelocitylldt, and gives: /

t t - c " . t' t p ,

pr3-lsOf

' r, - " 4 f r .i_, \

MuLtipiyingboth srdesby -, i:!'t I

)\

/.,

\

/_..2 \

l{ir"l'r )+ t.7s(" ."'"1['""'I ei,,t /\d /\d. \

I (6.1)

gjves: e n , iI

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

(6.8)

ln equation6.8: d3p(p" - p)e whereGd is the 'Calileonumber'. and:

'f =*"'''''

(6.e)

(6.10)

Ftuidi2ation 184

whereRe,,f is the Reynoldsnumberat rheminimum fiuidisingvelocityandequarion6.8

- ,ro1t'-;,,.1o .,.,, / r'7)\ rn,,, , ", \a:,) ",,, |

(6.1l)

Fora typicalvalueof €,rit= 0.4:

Thus:

Ga = 1406Re;f+27 3Re':r

(6.12)

Re':J+51.4Re:,J_ o.O366Ga:0

(6.13)

and:

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

(6.14)

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

(6.14a)

w:fia"-r

(6.15)

By definirion:

It is probablethat the Ergun equation,like the Carman_Kozeny equaaion.atso overpredicts pressuredrop fof fluidisedsysrems,arthough no expenmentar evidenceis avairabreon rhe,ba\is of wh;c-h rhevrtuesot rhccoetficinr.maybe amendcd. wE\ lnd yu" ha\e e\aminedlhe ret.rion.hip ber$eenvoiJcgcat lhe minimum fluidi'ingvelocl).p.,,.andpanicte\hape. whi.r,i, a.nn.a,r.rr"?uriooii;_;j;.;.; d..

i. ;1,il: :ii,T:,:'.f;::T: ;'nH:'[,]#':ffl;tJj:[';.*u,e," "q,,"-1.' Thus:

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

jt""J:[ff Ij"':it:i!i{5hlTi"':ili:,H"flil:.",T:1.'i,ffiiJ;T"1"* : - -***'r'"p*i"i"'".i";;";;;; j:*:':i?';:

:;ffH:ill

t:.il::T;*:

Hfiili#*:: ::$:&!il!t,l!*'iu*J';:J,J#?:"ffi:,i'Jl#l#l#:; }ifif;ir.,:}:it#it',?r.iltl; ,til:,3t, l,.ji.!jj';,T!:Tl1"l{n:H:i:f p*r"r" *ia''*e"

i';:":'$"i:*::J#lin "r "i*'""'l H:':ii1l"**1"13::' give reasonablv good coneralons between ?u | -o a", ^ *"*.

* l*,#l

6expresslons

\+)i:"

(#;):',

(6.17) (6.18)

185Chemical Engineenns Prcesses

1,0 :.

g0

oi

0.2

0

0.2

0,4

0.6

0.3

1,0

Figue 6.3. Relation betw€n €,,/ ffd 4i

NrveNo)discusses the significance groupsin oquations6.17 of &e two dimensionless and 6.18, and also suggeststhat d and.u-t in equations6.8, 6.9 and 6.10 are more appropriatelyreplacedby a meanlinear dimersion of the poresard the meanpore velocity at the poini of incipient fiuidisation. d; U.ingequalion b.lo ro sunrrirure lor for /i rn equalron 6.6 Sives: ap

, l . c d l , ( r -, . r l 8 - r s o/ 1 r " ' r " \ ( u " t \

\

Thus:

, ( !- "-\ *"i* , r -\,),,

"i,/ J\o:d,'zI

)o.a,

t+4 =""(+)he?).,,' (#)W)

Substitutingfrom equations6.1?and 6.18:

(150x 11)Re^Jt+O.75 x lqR;:Jl \vhere Gar and Renfr are the calileo number and the particle Reynolds number at rhe point of incipient fluidisation, in both caseswith the linear dimensior of the particles expressedas d,,. Glp:

Thus:

sivins:

Re':tu+ 67.3Re^Jp- o.0408cap: O

Re^Jp= 33.651J0+ 6.18x to-5cl]p)- 1l

,,=l;r";,

(6.19) (6.20)

Example6.1 A bed consistsof unifom sphericalpanicles of diameter3 Im and densiry 4200 kg/nr. What will be the minimum fluidisjng velocity in a liquid of viscosity 3 rnNvn'? and densiry 1i00 kg/ ?

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)/(3x l0-3), = 1.003x 10r Assuming a vrlueo10.4tor,r",.equalion o.l4gi\er: . R4,r = 2s.jIJO + 6.53 x t0-)(1.003 x t0)) _ tl = 40 and: 4-l:(40x3x 10-r)/(3xl0 3x lt00)= 0.0364 nrlsor 36:1,ry4

Example6.2 Oil, of densiry900 lShl and \ iccosiryJ rNvmr. is p6sed venicr Lp$dd\ throlsh a bed of ] catal)srconsisrin8 ofappro\imlety sphericatpaJticle\ of dmeler 0. I nu mddensiruioOOi"iJ Ar approxrmaret) wharmassmteoi flow per Lnir areaof bedwi ra, ffuidjsrlioD.anA O, *ipon of particles occur?

Solution (a) Equations 4.9 and 6.1 nlay be used to determiDethe

-^P

"

fluidising vetociry, ,,r.

= (1/ K')(e3 / (st(r _ ortl / p)t_^p / t) = (1 - e)(p, - p)t8

(equarion6.t)

wnere s = surfacearca/volume,which, for a sphere,= n .t, (r d3 / 16) = 6/d. Substitutingr" = 5, S:6 /d and -Lp /t fiom e,ln^rion6_t into equation 4.9 Sives: Henc€:

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

In fiis problem,A = 2600kg/m1p = 900 kgmr, p = 3_0x 10 r NVm, and I = 0.1 nnn = L0 x 10-4m no valu€ of the voidage is availabte.e wilt be estinated by considding eight closety packed .As spheresof dianeter d in a cube of side 2d. Thus: volufte of spher€s: 8(r/6U3 volun€ of the enclosure= (2d)r = 8dr and hence: rhus I

voidase,e = I8l3 _ s(z/6)d3ll8tr = 0.478, say,0.48. c;r : 0.0055(0.4s)3 0 0+),((900 x 1700)x 9.81)/(t _0.48) x 3 x l0 r = 0.059kg/m,s

i87 chemicalEnglneering Processes

(b) Tnnsport of the particl€s will occur when the fluid velocjly js equal to the terminal faling velociiy of the paficle. UsingStokes law:

uo= d1eb,

d/18tt

(equation3 z)

= ( ( 1 0 - 4 ) 'x1 9 . 8 1x 1 ? 0 0 ) / ( 1 8 x 3 x l0-3) :0.0031 nts The Reynoldsiumber: ((10 a x 0.0031x 900)/(3 x 10 i) :0 093 and hence Stokes' law appltes. The requiredmassflow:

(0.003t x 900)= 2.?8 kg/m'zs

An altemative aplmach is to lnalG use of Figure 3.6 and equation 3.35, (R/ puz) Re'z= 2d1p s(p" - p) /3 px - ( 2 x ( l 0 r ) r x ( 9 0 0x 9 . 8 1 )x 1 7 0 0 ) / ( 3 (x3 l 0 r ) 1 : 1 . 1 1 From FiguE 3.6, ,Re= 0.09 Hence:

uo: ReQtlpd = (O.$ x 3 x l0-r)/(900x l0+) = 0.003m/s G' : (0.003x 900)= 2.7kg/m'?s

6.1.4.Minimumlluidising velocityin terms of terminalfailing velocity The minimum fluidising velocity, u,,r, may be expressedin tems of rhe free-falling velocityuo of the parliclesin the fluid. The Ergun equation(equalion6.11)relatesthe Calileo number Gd to the Reynolds number R4l jn lerms of the voidage s,t at the incipienr fl uidisation point. In Chrplcr4,relationsaregivcnthatpermitthecalculationof Re6(xodp/p),theparticle Roynoldsnumberfor a sphereal its terminalfalling velocity uo, also as a functionof Galileonumber.Thus, it is possibleto expressRs;/ in termsof ReiJand r,J in terms For a sphencalparticle the Reynolds numbcr R€6 is expressedin terms of the Galileo number G/' by equation 3.40 which covers the whole range of values of R?' of itterest. This takes the fbrm: 13I - 1.53cd-0'0r6) Rei,: Q.33caa0t3

6.21)

Equation6.21 applieswhen thc partlclemolion is not significantlyaffectedby the walls of the container,that is when d/4 tendsto zero. Thus,for any valueof Ga, Re6may be calculaledfrom equation6.21and R€;f from equation6.11 for a given vdrc of e./. The ratio ReLlRe'-re uo/u-I) may then be plotted against Gd with €,rf as the parameter.Such a plot is given in Figure 6.4 which includes some experimentaldata- Somescatteris ovident, largely attdbutable to the fact that the diameterof the vessel(4) was not alwayslarge comparedwith that of the particle. Nevertheless,it is seenthat the expenmentalresults straddlethe curves covering a range

10

124 110

ud, tor spherestrom

100

o o o 6 e

t \^'

Fow€(8) Roweand Parrddgs(e) Pinchb€lckand Popper(1o) B.chardson and Zakitjl) W l h o l ma n dK w a u k ( l )

I codad andHichadson(1r)

20 10 0

tor

rtr1

1o2 103 1d Galileo (Ga) number

los

FiguF 6.4. Rarioof iominat riiting votocilyto nininum fluidisinsvetocity, asa fu.ction of Catilm nunber

of_valuesof e,t from abour 0_38ro 0.42. The agreemenlberweenthe experimentaland crlculaled vxlues is quiregood.cspec.a) in viewot Lheuncenainry ;;;"i ;tr;: . or ?,r/ In the erpenmental work.andthefaclthaltheErguncquadon "f,+ notnecesranlv docs

fiffi*],|il:1f;.l*tt"ton

or pressure dropin a fixedbed'especiallv nearth";;ip#

,rhar.iri\dsopossibte Loe\press Rcoin rernsotGd by means ^.1'"1 lia,.,ol:, or rnfte:,1 srmpte equatrons. eachcoverinS a lirniledrangcof value\ot Oa Ca:18Re'

(Ga < 3.6)

(6.22)

G a : r BR e '+o z _ R i ;;637 (3.6=Ga=105)

(6.23)

c" = :R"?

(6.24)

(cd > ca.105)

It is convenienrto useequarions 6.22and 6.24 as thescenablevery simplerelationsfor R€6lRe;f to be obtainedat borh Iow andhigh vatuesof ca. Taling vaiue of s,/ of 0.4, the relarion beNeen Re; and Ga is given -a_typical by equaaion 6.13. For low va.lues of Rz;J( pht at all fluidisingveloc;liesd., and the heavyparlicleswill alwaysform the boltomlayer. tf, with increasein velocity, the density of the upper zone decreasesmore rapidly than rha! oI the bottom zone, lhe two beds will maintain the samc relative orientation ll the reversesituationapplies,therc may be a velocity i/rNv wherelhe densitiesof the two layen becomeequa1,with virtually complelemixing of the two speciestaking place. Any fudher increasein velocityabove,rNv then causesthe bcds to invert' as shown in Fig re 6.8(d). diagrammaiically

i.'.'.1'..

.o

:lii; :...:i. o^o ou^

i:o{

x^'o

iluldvelocily Increaslng

Figue 6.8. Bed invesion t

conPlete sgEgation (l) Conplele md pafiial sccFgation('?e)

changeasthefluidisingvelocityis increased Therelativeratesat which thebeddensities may be obtainedby difterentiatingequations6 424 and 6'12, wilh respectto u.' and dividing to give: |

lp,u /

_:t

dt./

ap,t d4

Jtrr,

.p,n-rt

tlq

(Pt

-t

Iid

P\\uolt

\| " I

-

toH

ptcH

tPt-Pt?L

-

(o.lg1

Engineedng Prcesses 195Chemical

As ett > et utd p"a > pr, then from equation 6.44, r, which is independentof fluidising velociry, must be greaterthan unity. It is thus the bed of heavy particles which expands more rapidly as the velocify is increased,and which must thereforebe foming the bottom layer at low velocities if inveIsion is possible. That is, it is the small heavy panicles which move from the lower to the upper layer, and vice versa,as the velo€ity is increased and Ad,fnr(3o) have analysedthe range beyond the inversion velocity &tw. RTcHARDsoN of conditions over which segregationof spherical pa{icles can occur, and have shown thesedia$ammatically in Figure 6.9 for the Stokes' law region (a) and for tbe Newton's la\r reg.ionfr). It has been observedby seveml workers, including by MoRntiMr er dl.(ze)and EpsrEIN ald PnuoeN(3|),ihat a sharp transition between two mono-compbnentlayers does not always occur and that, on each side of the ransition point, there may be a condition where the lower zone consistsof a mixtwe of both speciesof pa$icles, the Foportion of heavy particlesbecomingpro$essively smaller as the velocity is increased.This situation, depicted in Figure 6.80, can adse when, at a given fluidising velocity, there is a stable two-componentbed which has a higher density than a bed composedof either of the two shows specieson its owlt. Figure 6.10, taken ftom the work of EpsrEINand PRUDEN(3j), how tlrc bed densitiesfor the two mono-componenilayels changeas fte liquid velocity is inffeased, with point C then defining the inversion point when complete segregationcan take placo. Between points A and D (conespondingto velocities ,.A and r.B), however, a two-componentbed (representedby curve ABD) nay be formed which has a density $eater than that of eilh€r mono-componentbed over this velocity range.In moving along this cwve ftom A to D, the proportior of light particles in the lower layer decroases progressivelyftom unity to zero, as shown on the top scaleof the diagram.This proportion

0.75

:

0.50

I 6

o.25 .9

0.00 0.00 0.25 0.50 0.75 1,00 (prpYlpu-p) lncreasingiluid veloclt

ta)

0.00 0.25 0.50 0.75 1.00 (prdtba-p) Incrcasingfluid vel@ity (D)

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

cLKcL+cH) 0 0.2 0,4 0.6 0.8

padicles (copperrH=8800 Smallhea$/ kgr'm3d=0.135mm) L a r g ei g h l o a n c l e( zs , r o n roa. - 3 € 0 0 k 9m ' . d - 0 . 7 r m ) F u , d ins q i q u d( w a r e/ = r l o o dr , 9 / n 3/ = r m N s / m 1

V o L m eh c l r o n r r - C e ' C d - C r r - O . a i r L

CLlrC! Cr 0.6

(ks/m9

FLuldising velocityuc(nts) Fieurc6,10, Bed densitiesas a funciionofnuidisingvelocity,showingthe mixed plrlicle reion€l)

is equalto thatin the total mix ofsolids al poini B, wherethe wholebedis rheof uniform composition,and the velocityxrB tbcreforereprescnts the effectiveinversionvelocitv. lf lhe llo$ of nLidisinglrquidLo a comptclely segregarcd bed is.urtJenll .ropped. the particleswill all then start to settleat a velocityequalto that at which they have beenlluidised,becauseequaiion6.31 is equaityapplicabte1()sedimenrarion and fluidisThus, sincethe voidagesof rhe lwo bedswilt borh be greatcrat higher Uuidisation velocilics,the subsequenr sedimenlalion velocity will then also be grearer.particlesin both bedswill setrlear the samevelocityandse$egarionwill be mairtained.Eventually, two packedbedswill be formed,one abovethe other.Thus,if the Ituidisinsvelocitvis le.. lfan lhe rrJn.i on relocil).a pc(kedbedot l1lgeliglt par cle. ui tormaboier bed of smalldenseparticles,and conversely, if rhe fluidisingvelocityis greaterthanthe inversionvelociry.Thus.fluidisaiionfollowedby sedimenrarion can providea meansof lormingrqo complelei)\egrcg ed Inonocornpo-rent bed..lhe reldtiveconfiAuralion ol uhich depend.$lel, on rl-eliquid\e.ocir)cl shich he p licle.farc beeqRurdi.ed.

6-2,4.Liquid and solids mixing Ka*nns etal.(25)havesrudiedlongirudinaldispersiorin the tiquid in a fluidisedbed composedolglas..phere.of0.5mmardlnxndrancler.A-ep(hrngewa\inrroduced

1 9 7C h e m i c aE n g i n e e i n qP f o e s s e s

by feeding a nornal solution of potassiumchloride into the system.The concentrationat the top of the bed was measured as a functionof tirneby meansof a smallconductivity cell. On the assunplionthat the flow patterncould be regardedas longitudinaldiffusion on piston flow, an eddy longiludjnaldiffusivily $,ascalculated.This was supedmposed found to rangefrom l0 4 to 10 3 m2ls,indeasingwith both voidageand particlesize. The movementofindividual paficlesin a liquid-solid fluidisedbedhasbeenmeasured and LArrFFt. In all cases,the mcthod involved by HANDLEY e/ !zl.(32)CARLos(33.31), parficlesin a liquid of the samerefradiveindex so that the whole fluidisingtransparent The movemenlof colouredtracer particles,whose other systembecametransparentphysicalproperlieswere identicalto thoseof lhe bed particles,could then be follolved phorographically. Handleyfluidisedsodaglassparticlesusing methyl benzoare,and obtaineddata on the flow patternof lhe solids and the distibution of vertical velocity componentsof on their the particles.lt was found that a bulk cnculationof solids was superimposed randommovement.Particlesnormallylendedto move upwardsin lhe cenheof the bed and downwardsat the walls, following a circulationpatten which was less markedin regions remotc from the distribulor. Carlos and Latif both fluidisedglass particlesin dimclhyl phlhalale.Dala on the mo\,ementof tbe facel particle.in the form of spatialco-ordinatesas a function of time, were usedas dircct input !o a computerprcgnmmedto calculatevertical,ndial, tangentialand radial velocitiesof the particleas a functionof location.When plotted as a histogram,fie tolal velocitydistribulionwas found to bc of the samcfo.m as that predictedby the kinetic lheory Ior lbe moleculesin a ges. A lypical rcsull is shown in FiglLrc6.11(33). Effectivediffusionor mixing coefficientsfor the particleswere then calculatedfrom the productof the mean velocnyand meanfree path of the particles, usingthe simplekinetic lheoly.

0.03 E E

e o.o2 .9 6 0,001 Paniclespeed(mnvs) FiCuF 6.11. Distributionoi p:trliclespeedsin nuidisedbed(]|)

Solidsnixing wasalsostudiedby CaRl-os(rar in the sameapparatus, staningwlth abed pafiiclesanda layerof tracerparticlesat ihe baseof the bed.The composed ofrransparent concentration of particlesin a controlzonewasthendetermined at variousintervalsof time

ailer thecommencemenr of liuidisation.Ther

type equation. rhiswas then """0,";r";,#iiljo"ilii'r':.ilf"#f ll,.Xrlllt:lT;

the valuesofmixing coefficienroblainedbv 1l

fl\'r,i,:$ff;;T[1rr*;:i,3::#;'':ii:!i:.ii::'"1;1"*"i:" t a vclocitvof lwice the minimumfluidising verocrry. LArrF(rs)represenredthe circulation currer

j:''il: smt:#*[:ti:#?fu:1":":r;r.i$r'6"Hi:ff ','ll"T :trI,",fj ijjrTi'fi'}ffr:': :;;?xd$[ii]:'1,,'l "ii!Hi;:i:xF:'1,ffi ;'"",,}i:l:

pa.ern over onry aradia, * *.*". ,,.ilTJ*iJ';'"1#;:i::*::f ";.

ff:"H:'""X Jfl1il:#:jfl :'#f:t$H$i;Xt"ly;:n:":tr;: :**;*t ",,il";,"j1 ffi':'af i*".'.'J:#fi TX5:i".J,;TJi;i:i:j# m;; ;;"d;;; 3

I

E

0.000

0.400

0,600

0.800 i.000

199ChemielEnqineenng Processes

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

6.3. GAS-SOLTDSSYSTEMS 6-3,1,Generalbehaviour In general,the behaviour of gas-fluidisedsystemsis considerablymore complex than tiat of liquid-fluidised systemswhich exhibit a gradual transition from fixed bed ro fluidised bed followed by paflicle transport, without a series of transition regions, and with bed expansior and pressuredrop coniorming reasonablyclosely to valuescalculatedfor ideal systems. Pafi of the complication with gas-solid systemsarises from the fact that the purely hydrodynamicforces acting on the particles are relatively small comparedwith frictional forces betweenpafticles, electrostaticforces and surfac€forces which play a much more dominant role when the particles are vcry fine. As the gas velocity in a fluidised bed is increased, the systemlends10go throughvadousstages: (a) Fixed bed ]n which thc pa(icles rcmain in contactwith one anotherand the stnrcture of the bed remains stable unail the velocity is increased to the point lrhere the pressuredrcp is equal to the weight per unit areaof the particles. (b) Pa,liculate ^nd rcgrlar predictableexpansionover a limited rangeof gasvelocities. (c) A babbling region characterisedby a high proportion of th€ gas passingthrough the bed as bubbles which causerapid mixing in the denseparticulate phase. (d) A turbulent chaoldcrcgion in which the gasbubblestend to coalesceand lose their identity(e) A region where the dominant pattem is one of .refticallJ upwa l tmnsport of par"ticler, essentiallygas-solids transporl or pneumaticconveying. This condition, sometimesreferred !o asjtst fuidisation, lies o\ttside the range of Fue fluidisation.

6.3.2.Particulatelluidisation Although fine particles generaliy form ffuidised beds more readily than coarseparticles, surface-relatedforces tend to predominatewith very fine particles. It is very difficuh ro fluidise some very fine partjcles as they tend to form large stable conglommeratesthat are almost enthely by-passedby the gas. In some extremecases,particularly with small diameterbeds,the whole of the particulatemassmay be lifted as a solid 'piston'.The uniformity of the fluidised bed is often critically inlluenced by the characteristicsof the gas distributor or bed suppo.t. Fine mesh distributors are generally to be prefered ro a seriesof nozzles at the base of lhe bed, although the former fie generally more dilficult to install in larger beds becausethey are less robust. Good distribution of gasover the whole cross-sectionof the bed may often be dilficult to achieve, although this is enhancedby ensuring that the pressure drop across the distributor is large comparedwith that acrossthe bed of parricles-In general,the quality of gas distribution improves with increasedflowmte becausethe pressuredrop acrossthe

bed when it is ltuidised is, theoreticalty, independenrof the flowrare. The DressuredrcD acros.rhedislribulorwill increa\c. howerer.app1sr,rnr,.1, In pjoporlion io de .quxr; of lhe floumre.and rherelorelhe ljrclion of the roralpresruiertropinaroccr,. ,.ro.i ih; disriburor increa.e.rapidl] a, the flourdle increase.. Apartfrom the non-uniformiries whichcharacterise manygas solid fluidisedbeds,itis in the low fiuidising-vetociry region thar rhe behavjourof itri gas sotid and liquirt_solid beds dre most similar. At low gas rates the bed may exhibir ; regular expunrion u, tt," llo\ rareincjease\. $ iLi rheret ronberwecn Uuid.si,rg wro.iD nnJ,oi,jagitoflo"ine;. lormol equarion o.JL atrhough. ,n genera'. Lhevatui,of rh.".rpo"."r ,-*. hieh;;:h;; those for liquid-solids systemspartiy becauseparticles have a tendency to fo"nn small agglomeratesthereby increasing the effective particle size. The range oi velocities over which paniculaieexpansionoccursis, bowever,quirenarrowin moit cases.

6,3.3.Bubblingfluidisation The regionof paniculate Uuidisdt on u,ua ] come\lo ar abruptcnd a5 lhe're, sa5\elocih r jncrea.ed. \aitl.rhetormarion ofga. bLrbbler. Thesebubbti.are usur l ponvtte ror the no!\ ol atmollalt of lhe gdsin e\ce.. ol thalUoningal rheminimumfluidi.inA velocity.If bcd expansionhar occurredbeforebubblingcommerces,the e*c."" gas nuiii be transferredto rhe bubbles whilst the conmuous pnase reverrs to rrs voidaAe at rhe minimrmfluid,sing !eloci.]and.in rhi"sa). ir conirdcriThu..lhee\prndedbc; aDoears {o be In a meta-rable condilionuhich i. rnalogoL\ro rnzrot a .upir.aruraret .otu|on revertmgto rts sarurated concenrration whenfed with smallseedcrystals,with rheexcess solutebeingdepositedon to rhe seedcrystalswhich thcn indcasein size as a result. ,pp., limir of ga5 !eloci') tor panrculare e\pan.ionis r.tmedhe nininun . Jl: bubbttnq\etoc|y.urb. Determrning thiscrn prc\entdilficult.cs r\,1\ \alur ma) depend on the nature of th€ distribuaor,on the presenceof even tiny obskuctions in tfr"i.O, evenon the immediatepre-historyof the bed.The latlo uftb/ui, whjch ""a Eivesa measure of the degre€of expansionwhich may bc effected,usuatty has i trign vatue for fine liqhr particlesand a low valucfor largedenseparricies. F9r crac^ker caTllsl (d:55 p.m,densiry= 950 ks/m3) fluidisedby air, vatuesof arl,7,,,r ofup lo 2.8havebecnforndb) D{vrfsandR, FqRDsoJ\',-,. Ou;ng rte cour,e ol firs \ oik ir uas loundlharrheret a minimurn!/e ol bubbtewhichi.;ble. Smatt bubtles injected into a non-bubbling bed tend ro becomeassimilatedin the a"nr" of,*". whilst, on the other hand, larger bubbles tend to grow ar the expenseof the gas fl'ow in the densephase.If a bubblelargerthanthe cdtical sizejs injectedinto an exp;ded bed, the bed_willinirially expandby an amountequalto the voiumeof rhe i";"i"a U"U-Uf"l men, however, the bubble breaks rhe surface, the bed will faI back biow the tevel existingbeforeinjeciionandwill thereforehaveacquireda reducedvoidage. Thus, the bubblingregion,which is an importanrfeatureof beds op-erating at gas velocitiesin excessof rhc minimumffuidisingvetociry,is usuallychara;erisdby ;;; phases-a conrinuousemulsionphasewirh a voidageapproximatety equatto tfraiof a bedal it. minimumfluidr\ing!etociL).anda d;sconrinou. or brbblept,o.. rtrcr lo"rmort ol lhe e\cc.5 flo\^ ol ga.. Tht .r sometimec ".counr. reterredlo as .hi rlra-phrs" thco\

23

201Chemi€lEngineering Proesses

The bubbles exert a very strong influence on the flow pattem in the bed and provide the mechanisimfor the high degreeof mixing of solialswhich occurs.The pmpertiesand behaviourof the bubbles are describeIater in this Section. When rhe gas flowrate is increasedto a level at which the bubbles berome very large and unstable, the bubbles tend to lose their identity and the flow pattem changesto a chaotic form without well-defined regions of high and low concentraiionsof particles. This is commonly described.as the turbulent rcgion which has, until fairly recently, been the subiect of relativelv few studies.

Categorisation of Solids The easewith which a powder can be fluidisedby a gas is highly dependenton the ploperliesof the parlicles.Whilst il is not possibleto forecasrjust how a givenpowder will fluidisewilhout carryingout testson a sample,it is possibleto indicatesometrends. ln general,fire low density particles fluidise more evenly than large denseones,provided that they are not so small that the London-van der Waals ailractive forces are great enoughfor the particlesto adheretogetherstrongly. For very fine particles, thesealtractive forces can be dree or more orders of magnitudegreaterthan their weight. cenerally, $e more nearly spherical the particles then the beller they will fluidise. In this respect,long needle-shapedparticles are lhe most difficult to fiuidise. Particles of mixed sizes will usually ffuidise more evenly than those of a uniform size. Furthermore,the presenceof a small proportion of fines will frequently aid the fluidisation of coarseparticles by coating them with a 'lubricating'Iayer. In classifyingparticlesinto four groups,GELDART(a6) hasusedthe lollowing criteda: (a) Whether or not, as the gas flowrate is increase4 the fluidised bed will expand significantly before bubbling takes place. This property may be quantified by the ratlo unh/u,nJ,\vhercuh, is the minimumvelocityat which bubblingoccurs.This assessmentcan only be qualitative as the value of Il,, is very c.itically dependent on the conditions under which it is measured. (b) Whetherthe risingvelocityof the majorityof thebubbles,is greareror lessrhanthe interstitialgasvelocity.The significance ofthis factoris discussed in Seclion6.3.5. (c) Whether the adhesive forces between particles are so $eat that the bed tends to channel rather than to fluidise. Channolling dependson a number of factors, including the degree to which rhe bed has consolidatedand the condition of the surfaceof the particlesat the time. With powdersthat channelbadly, it is sometimes possibleto initiate fluidisation by mechaoicalstirring, as discussedin Section 6.3.4. The classesinto which powders are grcuped are given in Table 6.1, which is ta*en from the work of GELDART(33), and in Figure 6.13. In they are located apFoximately on a particle density particle size chart.

TheEffect of Prcssure The effect of pressureon the behaviour of the bed is impotant becausenany industrial processes, includingfluidisedbed combustionwhich is discussed in Section6.8.4.,arc

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

30 100

P liculate dlansion of bed sienincdt velocity range. Snall padicle sir rd

t00 800

GrcUp B

Bnbbling occus a! vebcny >r l, Most blbbles have velociries grearer velocity. No evidenceof naxinum bubble size.

20

diffcuh to fluidne and Hdily forn chahnels. All but ldgst bubbles rise

r000

interstirial g6 vetocity. spouEd b€ds, Panjcles

7000 6000 5000 4000 3000

i 31ooo I

6

E soo

20

50

100

200

Meai padicle siz6 (pm) l-rguF 6.lJ

500

10!0

Poqdd ( a\ihcarion diogro tor fludFadon b) air ar rnoienr condrlioturs,

203Chemical Engineering Pfoesses

crmied out at elevated pressures,Several workers have reported measurementsof bed

when verv much hisher varues :I'#':ilfr :,'l#'ff ,aiii,'.'i138.fff"n**"*s

Becauseminimum fluidising velocity is not very sensitive to the pressurein the bed, much geater massflowrates of gas may be obtainedby increasingrhe operatingpressurc. The influence of pressure,over rhe range 100-1600 kN/m2, on the fluidisation of three gradesof sand in rhe particle size range 0.3 to I mm has been studied by OLowsoNand AI-MsrEDr(421 and it was showedthat the minimum fluidising velocity becane less as the pressurewas increased.The effect, most markedwith tbe coarsesoliis, was in asreement vr'ithrhaLpredicledby slandardrelanonssuch as equirion0.14. For frne pard:les.the minimumfluidisingvelocir) is independenL of ga5deDsitytequadon6.5 uirh p" > > p1. and honceof pressule,

6.4. MASSAND HEATTRANSFERBETWEENFLUID AND PARTICLES 6,4.1. Introduction The calculation of coeflicients for the rransferof heai or nass bctween the particles and theffuid_stream requiresa knowledgeofthe hearormassffow,lhe inrertacial;rca, andthe driving force expressedeither as a temperatureor a concentralionilifference. Many early investigations are unsatisfactory in tharonc or mo.e pf rhesevariableswas inacclratel; determired.This appliesparticularlyto the driving force,which wasfrequentlybased on complelelyeroneousassunptionsabourrhenatureof the flow in the bed. One difficulty in m.Lkingmeasuremenrs ot transfe.coefficientsis thar equilibriumis rapidty attainedbelweenparriclesand fluidisingmcdium.This ha.sin somecases been obviatedby rhe useof very shallowbeds.tr addirion.in measwements of massrransfer, lhe methodsofanalysishavebeeninaccurale, andthe particlesusedhavefrequentlybeen of sucha naturethat it hasnot beenpossibleto obtaii Ruidisationof good quality.

6.4.2.Mass transfer betweenfluid and particles BAKHIARIaS) adsorbed rolueneandiso,octancvapoursfrom a vapour-laden air streamon to-thc surfaceofsynthcticalumjnamicrospheres andfollowedrhtchangeof concentration of the outlergaswiih Lime,usjnga sonicgasanalyser.It wasfbundrh;r equitibriumwas attainedbetweenoutlelgasandsolidsin all cascs,andthcreforetransfercoefficicnrs could notbe (clculdredlheproSrcs,otlhe adrorption proci* $a. n:ll to,.o$eo,ho$ever. 5,, xrL\ "' modjfiedlhe .y.lem .o lharequilibr,rm$a, nol Jcl icveddt .ne outlel. Thin bedsandlow concenrralions of vapourwereused,so thatrheslopeof theadsorDtion rsothermwas 8]eater_ Parliclesof charcoaiof differentporc structures, and of sjlc; gel, werelluidisedby meansof air or hydrogencontaininga known concenrration of carior r e i u c h l odre o r w a l e!ra p o u fA. n n J l g ' a , , J p p d a l u " w u : .. e d . o l h a .r c u u , do c r e a d i l \ dFrnan.led. Jnd Ine od.orpdon proce..\"c, fo osed b) $eigh,rg-he oeda. irrervats. The inle! concenlrationwas known and the ouilet concertrationwas deiermined as a lunctionof time liom a matcrialbalance,usjngtheinformationobtainedfiom thepcriodic weighings.The driving fo.ce was thenobrainedat lhe inlet and the outletof the bed,on ine assumptionrhat ihe solids were complet€lymixed and rhat the partial pressure of vapourat their sur{accwasgiven by the adsorptionisotherm. At any heighr. abovelhe boltom of the bed,lhe masstransfcrrareper unit time, on the assumption of pirr.rrlJ4ri,ofgas, is givenby: dNs:11o66o'6'

(6.4s)

whcrc.r' is the rransferareaper unit heightof bed. Integratingover the wholedepthof rhebed grves:

N^ hDa'Jra cd:

(6.46)

205Chemical Engineer ig Processes

The integraionmay be canied out only if thc varialionof driving force throughoutthe depthof the bed may be estimaled.I1 was nol possibleto nake measurements of rhe profileswithin the bed,althoughas the valuc of AC did not vary greatly concentration from the inlet 1{)ihe outle!.no scious errorwasintroducedby usingthe loga.ifimic mean value ACh.

(.6.4',7)

Thus:

Valuesof masstransfercoefficientswere calculatedusing equation6.47, and it was found that the coefficientprogressively becamcless a! cachexpciment prcceededand as the solids becamesaturated.This effect was attributedto the gradudlbuild up of the resistanceto lransferin the solids.In al1casesthe transfercoefficientwas plotted against the relative saturatronof the bed, and the values were extrapola.edback to zero relative saturation, coffesponding to the commencementof the test. These mr\imum extrapolatedvalues were then coffelatedby plotting the co espondingvalue of the Sherwoodnunber(Sn' = /rDdlD) asainsttheparticleReynoldsnumber(R?: = ltdplp) to give two lines as shownin Figure6.i4, which could be represented by the followjng equalions: (0.1< R"; < 15)

Lr5 R.

'50r

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

h"d 1 {a sl -:.0 n

'

(6.48) (6.49)

Thesecorelalionsare applicable10 all the syslemscmployed,providedthai the initial maximum valuesof thc transfercocfficicnlsare uscd.Tbis suggcstsihai the extrapolalion givcsthe lrue gas-fi]mcoefficienl.This is bomeoul by the fact thtr!the coefficient pcriod whcn lhe poreswerc large.thoughit fe11 remainedunchangedfor a considerablc off extremelyrapidly wirh solidswith a fine porestructure-lt was not possible,to .eiatl3 the behaviourof ihe systemquantitatively to the pofe sizedistribuiionhowever. The valuesoI Sherwoodnumberfall below the theoreticalminimum value of 2 for masstransferIo a sphericalparticleandthis indicaLcs lhal thc assumption of pistonflow of gasesis not valid at low valuesof the Reynoldsnumber-In orderto obtainrcalistic valuesin this region,informationon the axial dispersloncoefficientis required. A studyof masstransferbetweena liquid anda panicleformingpart of an assemblage ), who subjecteda sphereof benzoic of particles was nade by MULLN and TRTLEAVEN(45 acid to the actionof a streamof water.For a 6xed sphere,or a sphe.efree to circulale in the liquid, the masstranslercoefficientwasgiven.for 50 < Re| < 700, by: sh' : o.g4Re',|12st1/3

(6.s0)

The presence of adjacentspherescausedan increaseir the coefficientbecausethe turbugreaterasthe concentration lencewastherebyincreased. The effectbecameprogressively increased,althoughthe resultswere not influencedby whetheror not the surounding pafticles were free to move. This suggeslsihat the transfer coefficient was the sane in a fixed or a fluidisedbed.

t 10

E

-

o charcoall2sAir-CC[ o Charcoa't 156-AirCCt4

0.1

' chafoatJS6-H, CCt4 0_01

o

0.1

r

ro

--lid----libo

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

The resulrs of earlier work by CHU.KALTL,and WEmrnonr(46) suggestedthat transfer coelficienrs uere \imitar in fi\ed andfluidisedbeds.Apparen(di|fercn;s al to$ Revnotd\ numben were probabt)due ro rhe facr rharrherecouja be ;;_.i;1;;'; fluid in the fluidisedbed. "pp,..trbi;

Example6.4 In a fluidised bed, riftr'ocranevapour is adsorbedfrom d air srreamon ro the surface of arumina microspheres. The nole fncrjon of do octanein rheinlet gasis 1.442x t0_, andth.n;;;"; iD the outlet gas is found to vary wit| rime as fo ows:

(s)

Mole ftactionin outler s a s( x 1 0 , )

250 500 750 1000 1250 1500 1750 2000

0.223 0.601 0.857 1.04 1.20/ 1.287 r.338 1.373

*;:Ir,TridilI:::*F;:'#ffi:'J# F:!tq'r"r##iti:i$"fif

::"';::i;#:*:

isothdm ta'r'**ru"'* a" ii" *'"r* q.;"lii l"-J?oretheidsorytion

207ChemielEngineedng Processes

Solution A rnassbalanceover a bed of particles at dy time , after the stan of the experiment,givesr

G-Oo - )) =

d(vF)

G," is lhe molai ffowrate of gas, W is the massof solids in the bed, F is the nurnberof noles of vapour a&orbed on unit nass of soiid. and )0. ) is the mole fmdion of lapour in the inlet and ourle, respe.rirely. "tream r the adsorptionisotherm is linear. and if equilibriun is r;ched betweenthe outlet gas and the solids ard if none of the gas bypassesthe bed, then a is Biven by: F=J+h! where / and , de the iniercept md slope of the jsotherm respectively. Combining theseequationsand iniegrating gives:

tn(1- r/ri = -Gn/wb)t If the ssumptionsoutlinedpreviouslyare valid, a plot of ln(l -:y//o) againsrI shouldyield a sh'aightline of slole -G,,,/ WD.As )o : 0-01442,the followirg lablemay be producedl

I - (r/)o)

rime G) 250 500 750 1000 t250 1500 1750 2000

o.00223 0.00601 0.00857 0.0106 0.0121 0.0129 0.0134 0.0137

0.155 0.41'1 0.594 0.'736 0.837 0.893 o928 o952

500

lntl - 0/)tur)

0.845 0.583 0.406 o.263 0.163 o.107 o.072 0.048

1000

1500

sror".ol **'ption.\

Y s -2.0

-3.0 FiSure6.15. Adsorptionisorhermfor Exnple 64

-0.r68 -0.539 -0.902 -1.33 l.8l -2.23 -2.63 -3.04

Thse data are plotted-in Figore 6.tS ard a shaighrtine is obtained, with a slope of _0.00r67/s If G,, = 0.679x t0 6 kmoysand W = 4.66 e.-the,:

-0.00167= (-0.619 x tO-\ 4.66b / 6kmoy8 = b a73 x 10 or 0.0873knol/kg

6.4.3.Heattransler betweenlluid and particles In meas-uringheat rransfer coefficients, many *o.k k fuil"d fo measue any temperaturc djtfcrenceber\^eengas dnd .otid in a Jiuidisedbed. F*qr.",ty, r" i;;";.,;;^

for transferwasassumed, sinceir wasnotappreciared rharrh;"r irqriirii".

*ri# elerlwheiein a fluidisedbed.exceprwirhinc ,hr" r"y., i,;Ji";-]; disrdbutor, fuTTr\RING. MoNor-nqtro. and Svnn,?,and H"ERTJ. ""b*;'je;;. s rna V.f,"",nr,fl, measuredheat transfercoefficients for the evaporationot water from panicte" .f A_rrfr" or silica gel ffuidised by hearedair. In rhe former in"""ttg"ti.", it i, piJ"ti" tf,"t erable erors arose from the conaluctionof """"ia-

used formeasurins,he r..,l;1#:"$,,[ri";i$,n*.ilT":i*T s4\,empera,ure.

a{uregrrdienl\aarconfinedto lhe bolom pan ot lhe brd. A ,r.,i"" ,h";;;;i;;;. useoror measunnggcs temperdlures. cllhoughthi. probablycaucedtome a;surtanc" to the flow pattern r fte bed. FRANz(4e) has reviewed many .f ft" ;;;Jil;;-;; this field. used a sready-statesystem in which spherical particles were fluidised in a 1**'l. ] rectangllar bed by meansof hot air. A continuousflow of solids was mai"trt; ;;;;

coored aird then '"tu,n"a to*'" i1".'i:#"*:Tff"fi;i'1ffi'f,JT"y*'were -i",,".J

asseTbrv; yp " ;i*'r.,

Jf.,J;ff::r:;:%1r:""?5 ;,11""t""'#::"#;

constantan. Therhermo-junction leadswerehJd in unopp.iiro:t"ry t"oi}t;;_;il;;; minimisetheeflectof heatconduction. Aftel

i, !,a.found,r.",,r,.,".p.oi,,.g,uil;i;:'::lr'""Jij:-Ij;l"ij:";T*,1 lhan2.5 mm decpat lhe boromot ine UeOt,newhere. rhelemperatur. *r, ;;,;";;;

i"o;t'lo#11ffl'"u

o"*eentheeasandthesolids'l tvpicat t".p",utr'."p.o;i; j;"ffi;

At any height z abovethe bottom of rhe bed, the heatrransfer rate betweenthe particres

l* t"rl,lt'"

*"

or complete mixineor thesolidsand/,r ,;";,i";;l;; ""umPtion dQ = h\Ia'dz

(6.s1)

Integrating gives: tZ

Q = ha' ^rdz Jo In equation6.52, C may be obtainedfrom rir

(6.s2)

***n*;ti;#**ret*t1

Pro@sses 209ChemielEngineenng

340 338 p

336

! E

F 2.O 3-0 1.0 Heighiabovebedsuppod(rnm)

0

Figure 6.16. vertical temperatutegradient in fllidised bed(50)

if the solids were completely mixed, their temperaturewould be the sane as that of the gas in the upper portion of the bed. The resultsfor the heattransfercoefficientwere satisfactorilycorrelatedby equation6.53 to heattransferin ihe solidcouldbe neglected asshownin Figure6.17.Sinc€theresistance comparedwilh thai in the gas,the coefficientswhich were calculatedwere gas-film coef6_ cients, conelated by:

dn1 '-ooro1n" , r , ,- - 1 1 . o . o s o l t l 1r" |

\(t'/

\,

(o.sJJ

/

10 Glasslluidisedwilhair

:- 1,0 E 3

.0.114 v0.137 o 0.165 . 0.231 o0.838 o 1.55

Seedlluidisedwllhair Lsadfluidisedwlthait d 0.96mm withCO, Glassfluidised

0.1

+ 0.37mm

o.o2 0.1

1.0

100

10 l

do\ Feynords numb€r Fe;/el=fr-l FiguE 6.1?. Coffelation of erperinental @sllts for bear transfer to particles in ! Rui.tisedbed($ )

Taking an average vatue of 0.57 for the voidage of the bed. this equation may be = 0.llRe:rr3 ?.r'2r,

(6.54)

Th: e.qua,tion wds found to be appticabtctor \atuer ot R?; trom 0.25 ro t8. As In (llecaie of ma\. ran\[er.thea5\umption of pi.t;n flo\ais not valid,cenainl\

notat lowvalues.of theReynotds number(< a) at*r,iir, m" l"*J

i"""lr,.i

thefheorericalminimum valueof 2. This questionis discussed ""_t".ii furrher at th; ;;J;;;

Example6.5 Cold panicles of gtass balotini are flui.lised with heatedair in a bed in which a constantflow of ptrticles is mainiai'ed in a horizontat direcrion. when s,"dy ;;;; ;""d.';; tebpelatu.es recorded by a bare rhermocoupleimmerxedin the"..,litt.,, bed are as foltows Distance abovebe.dsuppor (lml

Temlerature (K)

0 o.64 |.27 l.9l

339.5 337.7 335.0 333.6 333.3 333.2

3.81

Calculate the coefficient for hear ftnsfer b€lween the gas and the particles. and the corre_ spondingvaluesof the particle Reynotdsand Nussettn"*t"". C..rn*, i" J" ,..rr, ;";; The ga\ frowratei\ 0.2 kg/r',. rhe specifichearor iir n 0.88 UAg K. rhe \i,co.iry ot air L 0.0t5 n\s/m,. rhepd.jcje djdeltr i,0.25 mm andrher*_"r*"0*f,,i,y O.ol wi. ri. "i,ir;_

Solution Forrhe system desoibed in rhis p.oblem, the rate of heat rransferbetween lhe particles dd the nuid js given by: d Q : h a ' ^ Td z

a: ha ^r dz la

(equatron 6.51) (equalion 6.52)

where 0 is tbe hear transferred,ll is the tEat hansfer coefncient. z, is the area for rransfer/unit heighrol bed.and A? rs rhe rerperdrLred,fferencear hei8hr z. r r o m m ed a t ag r l e n .A r m a ) b ep l o e d a g l i n s r . a . s h o u n i n f i g u _ eO t 8 w h e Fg e d e a u n d e r , the curvegivesrhe valueofrhe integralas 8.82mm K

Thus:

H e u t t r a o s f e m d : 0 . 2. 0 . 8 8 1 i 3 9 . 5 3 i 2 2 )

= Ll1 kwn'zof bedcross-secrion.

211Chemi€lEnsineeinsProcesses

,.of 6.0 5.0 g 40

Areaundercurve=8,82 mmK

- 30 2,0 1.0 1.0

2_O

3.0

4.0

Heightabovebed suppo {mm) Fieue6.18.'remp.raturc riseasa function of bedheightfor Eranple6-5

If the bed voidage = 0.57, and a bed I m'zx I m high, is consideredwith 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 = 8.18x 10-''zmr. Thusjumber of padicles = 0.43l(8.18x 10-'1 : 5.26 x l0r0 per m3. Aea of particlesa' =5.:26x l]to x (1t/4)\O.X x 10 )'z= 1.032x lO4m?/mr. Substituting in equation 6.52 gives:

= i1x (1.03x loa x 8.82x 10-r) 11tJ0 h = r2.2w/m'K Fron equation 6.69:Nr:0.11Rer'3 Re= G'd/p = (O.2x O.25x 10-)/@.015x 10-) = 3.33 Thus:

: 0.513 lra = 0.11x (3.33)r'z3 ,

( 0 5 i J . 0 . 0 1 V { 0 . 2 y5 l 0 ) = 6 l . o $ / m 7 K

Example6.6 Ballotini particles, 0.25 lM jn diameter, are fluidised by hor an flowing at r]le raie of 0.2 kg/n, s to give a bed of voidage 0.5 and a cross-flow of parricles is mairrained ro r€move the heat. Under steady stateconditions, a small bd€ thermocoupleimmersedin the h€d gives the following

Distance above bed support

(K) 0 0-625 L25 1.875 2.5 3.75

339.5 337.7 335.0 333.6

Cc) 66.3 64.5 61.8 60.4 60.! 60.0

tllxi:if;r'T,tr;lff T:,.#mirud:l;fuH*n::rii**F Assuming plug flow of the gas and comtrletemixir

:H;!'."1ii",?jil":f fif,:'*:,1,n';:l ll"+::l*rn';*j ii:Hilt,?fu"Hfi ff:t;""',!T"irT [T;Iffi::f :i$,;mm:*,krnil*!;ffi iillr:il}ifi vaporisationof water is 2.6 MJ/kg.

Solution ffil:t"ili

Hffii:$ted

withvoidaee e anoa mass nowrate c', rhena heat6arance over G',CFT = hS(t - e.)dz (TP_ TJ

wherq

: specific heat (Jftg K) parricle ienperature, (K) = 4 s(l - €) = surface aiervolune of bed (mrlm,l = hear transfer coefficient (w/m, K) tr Cp

hs(l- e)z G'CO

c'c,u = nsg- 4 170 ' 711" l" U,{(l,,*tro.

nay be fourd from a plo! of the experinental data shownin FisuE 6.19 as

i,'

- e) - 6(1- o.s) /(0.2sx t0-) = 1.2x 104/m

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

213Chemic€l EngineeingPro@sses

E E E E

23 Hoighiaboveb€d supportz {mm) Figurc6.19. AZ asa function of bedheieht.in Exanple6.6 lf the evaporationrate is 0.1 kg/s at a temperaturedifference, AZ = 50 deCK the heatflow: (0.1 x 2.6 x 106)= 2.6 x ld w If the etrective dea of th€ bed is ,4 thenl (14.1x ,4 x 50) = 2.6 x 105and A = 369m'z The surfacedea of the bed = (1.2 x loa x 0.1) = 1200n'? Hence,the fractionof bed which is used: (369/1200)= 0.31or 3l ler cent

6.4.4.Analysisof resultsfor heat and masstransferto particles A comparisonof equations6.48 and 6.54 showsthai similar forms of equationsdescribe the prccessesofheat and masstransfer.The valuesof the coefficientsarc howeverdifferent in the two cases,largely to the fact that the averagevalue lor lhe Prandtl number, Pr", in the heat transfer work was lower than the value of the Schmidt number, 'S., in the mass transfor tests. It is convenientto exprcssresultsfor testson heattransferand masstransferto Parti€les in the form of j-factors. If the concentrationof the diffusing componentis snall, then the l-factor for masstransfer may be defined by:

i', : !25,oat

(6.s5)

where: ir is the mdsstransfer coefficienr, t. is the fluidisingvelocity, Sd is the Schmidrnumber(!,/pD), p is the fluid viscosiry, p is the fluid densiry, and D is the diffusivity of the transfered componentin rhe fluid. The corresponding rclilion for heartransferi,:

il: =L p,oui

(6.56)

where: , is the heat transfer coefficient, Cp is rhe specific heat of rbe ffuid at consrantpressure, P/ is the prandrlnumber(Ct,tr/k), and i is the thermal conduclivity of the flujd. Thc sisrili..ntceof I,facto's is dtscusle(lin dc]ail Coutson(j9) Reaffanging equarions6_49,6.50, and6.55in rheform of6.55,and6.56andsubsriruring meanvaluesof 2.0 and 0.7 respecrivety for Sc and pr, gives: ( 0 . 1< R " :