Effect of particle size on solids mixing in bubbling fluidized beds

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I)~wdcr "rcchn~,h~gy 97 i 1991',;) 171)- 177

Effect of particle size on solids mixing in bubbling fluidized beds Laihong Shen * Mingyao Zhang In~tilllt~' ~!/"lh~'l~llnt'll{'r.k,y I"nt~incvri, tl R r w , r { h. SOlll/IroW I 'tllvl'l'~ltv. NI/II/HIt~ 2 ltlllJ,%'. ("/lill~/ Received 7 Augu'q It~'gt~: t¢¢¢i~.t'd in re'~,ed h v m 2 .hll'~t' [{)tr,7

Ahstraet Experinlental and the~retical qtrdie.~ ~t ht~lh ~erlical and lateral mixing i~l s:~litt~, in a I~t~-dinlel~,it,lal I~ul~hling tluidi/ed bed I 13(~1 .~ 9211 × 611 mm ' ) are COlltlucled by u,,ing heaJed particlc~ a~, Jhe tracer. The el'ft.,el ol parlicle ni/e tm ,,olitl,, mixing i,, ,,ludied. l:hlcltr|ti~nl,. in the concentration respt)n,,es along holh vemcal and laler:d direcli~m~, h:~ve i~erl ~l~,er~ed experimentally. "lhe,,e fhtctu.'lti~ms become mcrea,,ingly nmre pr,~minenl as tile bed parlicle q / e inrrea.,,e',. The ctm~ ¢clit~ll- diffu,,i~ul rlmdcl o1 ,,olitlr, mixing I1.. Siren, M. Zhaug, Y. Xtt. I)t~wder "rechn~d. 84 ( 1905 ) 2(17-2121 i, w,ed to ilrl~.rlv/e tile e\periJlJental tibia. The tl.~namtc,, of ~,olid~, exchange beh~een tile bubble ~ ake and the ernul,,ion pha,,e in buhhling lluidi/ed bed,, i~ irl~ e,,tigated, and a Ile~.t.' nl~)del l'or exch:lnge coetticienl i,, prop, v,ett. In the nl~tlel, particle ,,ize dr. parJicle derl,,ity Pv. ga,, vi,,coqJ),/a~, ga,, tiell,,il.~, p~. mininmrn Ih|idi/ation veh~.'it~ I ',,,, anti huhl~le ,,i/e I)~. eh.'.. ;li'C taken into acct}ltnt:

h',,- ,~ Iv,. ~,, ~,,.,z,.t,',,,,// v,here A-; I.I)~ II1'. The exchat~ge c{~cllicient K~ ~alttc,, I{~r Jilt" m~del th~ II~l comp:tre fa'~orabh ~viJh the prcdiclion'~ ~1 Iwtl available Ihet)t'cJi¢;d nlt}tlcl.~ ill Jhc Iiler;.ttt|re I K. Ytv, hitla. I). Kunii..I. ('hem. I-ng. Jpn. I I 19(~NI I I 16: T. ('hd'~a. II. Kol~:lxa,,ili..I. Cheln. |'.'n~. Jpn. I1) ( 19771 2()h 2 I()1 These ilmdeb, predict Jh;.ll the ~ :lke excll:tn~2e c~wllicwnJ ,,houhl incle:l,,c ~Aith inclc;t~e Ill ltlinill|un| iluidi/ation ~ch~'il.x I.!,l,, (i.e.. parlicle si/c dv j l Itl~Wevcr. our nmdcl sllo~ s thai tire ~ ake cxcllarrge c o c l ' | i c l e l l l ~'~.,. decreases ~ iih mininuml Ihlltli/alit~n ~.eloeil~ I

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Jrcnd ~, rcas~,l:ihlv ~.ell. The model I'~l ,,tditb, exchange I~eJ~ccn Ihe btnl~l~lc ~;ikc alrd Jhe cn|tllxitm pha,,c i01 a L,a,, Iluidi/ctl I~ctl i~ needed inl Ilh~tlelilL', ',t~litl~, nuxin,~ ~.lntl ~c~rc~:alit)n pattern,,. , It)tiN I'l~e~ ier Science N.A..All righl,, re~er~ed. K~'vuord~ Ilubhhn].' Ihlldi/t'tl I~t.tl: S~did,, illlxlnt_,: ~,Vakt. t.xt.h.lll~,.t., t ~'~t'lll...V,'lll ...................................................................................

ennpiel I I I I. and Frever and l)otter 112 I. I.aknhm;umn and

I. l n t r l ~ u c l i o n F.arly stLklics ~ff.,,olids mixing in th~idi/ed I~ed,, ~ e r e iehrted Io axial iir radial .~olids di.~persit,I. ~.rJltl tile vast nlajt~rity t)l' Ihe solitl~, mixin~ ~ltJdic~ J'eporlcd ill literature deal ~ i t h ~),~erall mixing rate~, ill tall. narrow beds o f ,,mall particle',. "rile diffusion c~leI'licient,, t~l' paJ'licle~ alorl~ lilt_' axial direction I 1-31 and the lateral direction 14-71 o f the bed ha~ e I~een cstinlaled mainly by restlrlin~ to a tlelerlnini~,tic apl~roacrl, t~r by lilting a FickiaJl-type tlilfu,,ion (ir tli~persitm equation to the data obtaineti e x p e r i m e n t a l l y . I-tt~wevcr. thene diffusion coeflicienls m a k e ;i great differellce; and .~ome ~1 tile ntmlerical results were lllll in satisli.icttlrv a~reenlenl with experimental data I I.~1. Sitnai I t~l propt).~ed a COll~ection model for vertical solids mixin,, in (,~e-dimensitlnal Iluidizcd beds. Sitnai's model bears close similarities, with the c o u n t e r c u r r e n t b a c k m i x i n g nmdel o f Stephcns et al. I101. Kunii and l.c~''

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I}{~ller 113l t,~ed .%illl;li '~, limited d~ll;I for model ~isSCSM|IeIII. de~eh)ped a n,,}llinlrLlM%C i111;.l~e analysis metlmd Ibr ,,{did,,inixmg in l~Ao-dinl~.'ll~,itlllill huhhlhlg llttidi/ed hed,,, and discussed the ¢OlllllerCtll'rellt backmixing model, l h ~ ever, the countercu~ent backmixing model did nol I;Ik¢ into ;lCCOLIIIItile lateral~,t~lid~, llli'dI|g,;.Illdcould l|l.lt Mudv tileeIl~'ctsof the di.,,tnbutionel I~'edcr.,,on the dynanfic and ,,lead)-,,talccharacteriMicx of lluidi/edbed~. l,;.itCl', ,~Ilell ct al. I 151 combined ~ erticalmixing ~vithhtleralmixing, and dc~ehlped a convedhm-difI'ush)n model of .,,oIidsmixing in twt)-dhnen,,ional lhIidi~edbeds,,in ~IIicll?ropertie~,of bubhies, and solids convection-dil't'u~ion coefticient.~ are variable ah)nu bed hei-ht Information on vertical and latend mixing of solids in a gas-.~olid bed is of ~r¢{ll importance for its performance as a J.inl el ill. II41

reactor, t t o w e v e r , little research has been d o n e t o w a r d s both v e a i c a l and lateral mixing o f solids in Iluidized beds. As a result this aspect is less ~ e l l understuod. For this objective.

!. Slwn. M. "/Jrmt: / Pot~dcr T~'~hnolocx 97 t 199,~ 1711 177

an experimental and analytical study of both vertical and lateral solids mixing in a freely bubbling two-dimensional fluidized bed ( 1300 x 920 x 60 mm ~) is performed. The effect of panicle size on both vertical and lateral mixin,,~, of solids is studied. The convection--diffusion mo'dcl of solids mixing 1151 is used to characterize the solids mixing. The dynamics of solids exchange between the bubble wake and the emulsion phase in bubbling Iluidized beds is investigated. and a new mt~el for exchange coeflicient K~v is proposed. In the model, particle size dp. panicle density I~,. minimum fluidization velocity U,,,, and bubble size l)~. etc.. are taken into account. The mtvdel for solids exchange between the bubble wake and the emulsion phase in a ..-as. fluidized bed in needed in modeling solids mixing and segregation patterns.

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The present experimental technique uses heated particles as the tracer, and tracer concentration is inferred from the temperature pruliles in the bed. The tracer is identical to the bed panicles, There is thus no tendency for segregation due to differences in size. shape, or density. Also. within minutes after injection, the tracers are indistinguishable from the rest of the bed. Thus. several tests can be run in a short period. To study the solids mixing i,a lluidized beds. an experimental technique is required which possesses the following characteristics: (a) fa.sl resl-amse: I b) ability to measure the tracer concentration while the bed is Iluidized: and ( c I ability to measure, instantaneously, the mixing behavior at different locations in the bed. Also. the technique must be such that the tracer dries not accumulate in the bed. in this way. experiments can be repeated a number tff times and meaningful average values are obtained. Since bubbling and panicle motion are quite random. numerous repetitions of a test are needed to achieve an accurate representation of the average rate of mixing. Because of the high particle-to-gas heat transfer rate and the low air heat capacity, the gas and the particles at any h)calio,) are approxinmtely at the same temperature. Moreover. the solid-to-air heat capacity ratio is so high that sensible enlhalpy transport in the bed results primarily from the nfixing of the heated particles 1161. The time constant of solids mixing in the vertical and lateral direction is much shorter than that of temperature decrease of the heated particles due to heat transfer to the fluidized medium (air). Fan et al. 1171 assumed that the temperature of the heated p a n t i e s does no'. oh:rage during each experimental run. Therefore. the local temperatare rise is proportional to the It~al tracer concentration. A schematic diagram of the experimental facilities employed is illustrated in Fig. I. Solids mixing experiments are conducted in a two-dimensional Iluidized bed of glass particle,,;, l'he bed ~ 1301)x 920 × 60 mm ~l is fabricated from transparent Plexiglas to permit visual observation. A porous plate serves as the distributor for dry air. In order to ensure uniform gas flow with fine bed panicles, a layer of cotton is

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mocL,uple proN.'. padded under the perflmlted plate distributar t,.I,, -= 1.0× 10 ~ m" I. and the perforated plate distributor has enough pressure dn~p. Minimum fluidization veh~ities of the bed panicles are determined u xperimentally. Panicles heatedoutside the bed are pneumatically injected into the bed by discharging a solenoid val~e through the feed tube. The duration of the injection process is of the order of 0.1 s. without disturbing the flow pattern. Eight miniature thermocouples fur measuring temperature are Ioca:ed at vertical and lateral directions. The probes each have a 0.5 mm thermocouple bead placed at tl,e end of a I mm hyl~'v,lernlic needle. The measurements of the solids mixin-~, behavior are pcrli~rmed for the bed Iluidized at various superlicial gas vehx:ities. More than 211 sets of identical experiments of sol!ds mixing are dtme under xarious ~peration conditions.

3. Solids mixing model In a bubbling lluidized bed. each bubble carries a wake of particles which is ultimately deposited on the bed surface. and complete mixing of solids occurs in the wake where movement is generated. This contributes partiall,~ to the lateral mixing of solids. 1ii addition, a bubble causes u drift of particle,. It) be dnl~vn up as a spout below it. Panicles appe;lr to be pulled into the x~ake and drift, carried up the bed fi~r a di,;~unce, and then shed. Thus. panicles travel upwards where It.ere are bubble.,. There is a primary downflow of solids in the bed where there are no bubbles. The descending stream corresponds to the surrounding re,_,ions, of risin,,~., bubbles, so that overall convective circulation is set up. At the bed surface. the bubble eruption induces lateral dispersion of part of the wake's panicles over a certain area. and the remainder of these particles are ejucted into the freeboard. Solids mixing in a freely bubbling fluidized bed is caused not only by the vertical movement of bubbles and bursting of bubbles at the bed surface, but also by the lateral motion of bubbles as a result of the interaction and coalescence of

1.. Shell M. Zha,'Ll;I Pnli'tk,r Tech,,,I,tt,'yq7 (Iqq,~l 1711 -I 77

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neighboring bubbles. The lateral mixing o1 solids is augmented by the hlteral motion of bubbles. Shen el al. 115] proposed a convection-diffusion model of solids mixing in bubbling fluidized bed. The differential equations describing the vertical anti lateral movelnenl of the lr-:cer solids are then: iff.'w -;~t

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Hath huhhle carries wilh il a wake ofcirculalin; ixirticle~. and it sheds ~(llllC pih ,ions ill' Ihis wake eli route. Models for exl.'h;lll~7 ill'solids helweCII itle huhhle waki." and the elllU Hills phase have been proposed hy Yoshida and Kunii II ~ll and ('hiha iilld Koha)'ashi [ItJl. "['h¢ inlerchanTe of ~.lid~ between Ih0 ph;.l~eS i~ uS~ilili~d Ill io~iill frtun lhe Ilow of solids inlll and Ollt (if Ihe w:ike with the slllid~ inll,¢in; dllx~'n in Ihe Ihin cloud regilui leaving Ih; wake al the ~allle ral¢ they ellh.'r. The lllod¢l i-:rllpo.~ed b) Yo~llJda and Kunii I I~il ix: #,'~ :--

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Chiba and KohayashJ I It~l propused a Miuple rehllilln Illr ihe cxchall~e coel'lJcienl. ~lS~UlllJll~ ih;il lluidi/ed pariicle~ Ihl~ around a hl.lhhle ~is ++illinviscid Iluid. alid that the particle Ihix inl(i and Olll of the wake is proporlional to both Ihe v, ake v(ihllne lnlClion alld ~olid~ Ihix Jlll(1 Ihe 7~is chllld ~lirlac¢ ill l'rlliil ill' Ihe buhhle. "l'his yielded Ihe folhlwin 7 e(itlalilln Ior

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"l'J'l)II ll: lill II should he noted thai huth exchange cuellicient~ sara direclly with U,,,, and inversely with huhhle ~ize D.. Bolh Ihexe lllodel~ are very similar, and Ihere is lilile diHerence hetween both exchange cllel'licienls ( ;l~ ~hown ill t:i#~. 3-6 ). Koealulum el al. 1201 llSl.'~.] i.ln invi,~,id Jrrotational Ilo~v model, and obtained Iwu dimen.~ional linile element xoluiions for the velocity lield in lhe wake regiun for variou.~ hubhle wake Irac'tillns. They Ihen tl~etl these xolulillns Ill conlpute the vohil~elric llow rate of emulsion pllase material across Ihe circuhir path ciiclosing the bubble and wake. They presented the nlodel for exchange cilellJcJeni A'~v: Kw = 0.807 U,,, I).

(5 )

To study the effect of particle size on solids mixing in bubbling Iluidized beds. a series of exl~rimentations are carried out. Fluctuations in the concentration responses ahmg holh vertical and hiteral directions have heen observed experimentally. These Iluctuations hecoine increasingly more prominent as the bed particle size increases. Hov,ever. these phenomena cannot he exphiined by the exchange coeflicienl models already described. In these models, the influences of particle size and parlicle density are not taken into account, and the Ihm: of bed particles around a buhhle is assumed to he ideal, inviscid, incompressible and irrotalional. Consider Ihe movenlenl of solids around a clouded bubble shown in Fig. 2. Kunii and I.evenspiel I I I I assumed that all Ihe particles from Ihe lower part of Ille cloud are swept into the wake, mix wilh the parlicle~, already there, and e~,emuall,, leak back into the emulsion. By this process, slowly downIh>wing emulsion solids are suept into the rising hubhle wake alld Ihen relurn lo Ihe downlh~wing emulnion. Based on Ihix inechanism, the influences are laken inlo account of particle size dr. particle demdty IJ~,. gas viscosity Ix,, gas density Pl. and gas ~elocity relative to particles in the emulsion I,/li,l / ~,ll,,I on the exchange coeflicienl model K~. With increase in particle densit) PE,alld parlicle size d,,, Ihe particle nlonlent of inertia increa,+e,,. It i'., difficult for Ihe parlicles h) the emulxiol) pha.~e tu he ,,~vepl into tile wake at Ihe lower part of the cloud. Thus. the Ih)w rale of emulsion pha~e p-trticle,, swepl inlo the wake hecomcs smaller, and the Ixirticle exchange cueflicient Ku het~veen Ihe buhble w:ike and the enlulnion phase decreases corre,,imndingly. The larger gas viscosity Ix, and gas density Pl, the more inlen~ive Ihe h)drod)'nainic force which affects the particles. The Ilow iale I~ecome~ larTer ill eniulkJon phase parlicle,~ ~vepl iilio ~ake al lhe lower lXirl of tile <.'loud. ~o. A'~ illClea~c~, The 7a~ in Ihe enlul~Jlln pha~e inove~ up~;'rtls rehiti~e Ill IxiriJcl¢~ of the c'lniilkiOll pilate, The hitter the gas vehlcily rehdi~c to IXlrlicle~ Jn the elnulxion U,,,I/~.',,,~, the ,~lnailer the llou nile o1 einul~Jlln pha~e ixinicle~ s~vepl into wake at the ll)t~t,i part of the cloud. Thll.~. K~v decleaxi2,~. ii i. ~l~lillic'tl thai these varhibles are either direcily pror-wtiotlal or inversely prllpl~rlit,lal to #~'~. hi liondhnensional ft.'rillS, dl,. ll~. ill . - tJ~. pi,, #.it l.llld [,711,, ! ti~'ll,i are expressed as:

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I;ig. 2. Schemali¢~;:the intetcllan~eol,,ulid,, hetu ten upllo'~,ing wakesolids and dov..nlh~.mg elnul,,i(m ,,~lid,,.

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To take into account the Ilow of bed particles around a bubble as that of a viscid, compressible, and rotational 11o~,,,. combine Eq. 16 ) with Eq. ( 5 ) with Ut,, ¢x ~ . a new model lbr wake exchange coeflicient Kw is proposed:

In tile absence or' a more detailed model. A in F.q. ¢71 is assumed to be a constant, and to bc determined from experimental data. This :~ssumption is further supported by Baseme and I.c~,~ 121 I. while the effect of particle size on Kxv in their model ix not ,st) prominent. Tile) assuincd th;'t the flow of bed particles around a bubble to be an ideal tlt:~,~,. ;|nd the ~akc be well mixed, which are apparently diffcrcm from the actual llow. To lake into account the inlluence of solids drill induced by bubble motion, wc lump ,solids motion through wake transport as well as drift in the wake fraction. The combined meclumi`sm of solids transport are responsible for higher ~,'altics t)l" the wake I'ractioll. The wake fraction.l;.x is treated as an ;,djustablc parameter. Glicksman and McAndrews 1221 measured bubble voida~c and ~isible bubble lit),,,, to ivcrmit an estimate of 1;.~ from a one-dimensional Ih|idizcd bed. and I'ound.l:,~ to ~ary between 0.55 and I. 10 ( A. = 2. I x 10 ' 1 1 1 : . U,,,,=67X I0 " m/s, U , , = 8 0 X I0 " m / s ) . Bac)cns and 30 I.

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Geldarl 1231 ,,tudicd the I'ractio,!/~.~ of tile solid,, in huhhling lluidized beds. and I'~mnd that this decreases ~ ith increasing particle ,;lee. A bubble of a given ~ d u m c prtvJucc~, a much greater degree of .,olids tno~ement in a bed of cracking catal~st tha,1 in a bed of coal a,,h. The larger the lluidi/atitm number ( / . / , , / ( r ) . the inore intensive the ,,olids mixing in ;he beds. and then the larger I;,~. Thus. ¢kv may ~a~ between O. I0 and 1.50 accordi,g to the experimental conditions. S~. xvith the model ol'x~ake exchange toe flicicn;, the con~ cottondiffusion model liar solids mixing does pro~ide reasonably g~n)d aereenlent x,,ith experi,'netllall,, obscr~ed solids mixin,, trends. Other CoiTelatitms used in simulation of solid,, mlxillg of a gas--,,olids Iluidi/cd bed are described in earlier paper 115 I.

-~ Results and discu~,;ion

[-xperinlental measurements, are presented in Figs. 3-5 h)r particle density of 281X; k g / m ~, particle si/es of O.45 ---O.58, 0.5h -- 0.70 and 0.70 -,- 1.0 ram, respecti,, ely. First, the ¢xperiilqeilt;ll measurements of tracer concentration as function of time are used to obtain the parameter A in Eq. (7). The theorettcal predictions arc compared with experimental data using hod parlicies of size d,,=(t).45"--0.561 × 10 ~ Ill. U,,, = 17.5 >< I0 "m/,, lluidized at U./U,,,, = 2.0 in Fig. 3. A pulse of hot particles is injected at the bed centerline. 0.21 m aboxc the distributor. In order to proxide an oxcrall picture

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21ill -kml~elalule re,p.m,e. ~ t ; • " tin ,,olid line ~ Ih,, ~ r k . ( ' , / t " 14 - 1.11 .. I l l 1: (ill buoken lille) Y~,,hida and Ktmli I I~1, (',,/C.: L3 I~ i i ( ill I~~kcll line I ('liib;i ;l/Ill Kol~ay;I,,hl I It) J. C . , / ( ' ( I~) ('~Unl~artx~ul,d CXl~¢rlll|Cnh, I tl;ln'.,icIII lempe~;iture re',p~u~',e x~Itil numclic~fl tracer ¢ollt'elltr;llloll,, h~, x;Jri~u. /Xv, lUl~ulcls,llt,ll~ I~qh xerllc;ll and I;ller+ll tlll'¢Clilltls II1,,--~h(ll} k l~/lll +. dp tl)4S-(|.~fl) "g Ill ' m: I'.,,, = 17 S× I11 ' Ill/n; I',,/I/,,,, =2.11: IIo " d~ , Ill $11~ ('~or¢lill;qC ol lilieCliOII plqlll luml: Ilillll: Ill Ill. 211)1. • leUlll~..r;ilur¢I¢',.]ltlllx¢. ~1"; " ' " 1'11 ,,~flld lineP till,, ~ork. C J { ' . i,.t • I.() , Ill l: ¢111btoke0l lin.' I Y~r,lml;z ,lnd KUllll I IN I. ('.,/1". ; ' l'. J (Ill luoken hn¢) (.'hfl~a mid Kol~as,r, hz I I~bl. ('.p"(

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oblaincd ai dilTerenl vellical and laleral posilions in the bed. Fluulualiolzs hi tilL" COllCcnlratiOll responses along both vertical and I:llcra] directioas have been observed experimentally. These Iluctuations in the tracer concentration b¢con)e increasingly more prominen! a:; the bed panicle sizes increases in Fi,,s ~ . . 3-5. For vertical s:)lids mixing. Figs. 3-5 show that the hot particles propagate faster in the upward direction than in the downward direction owing It) the upward moving wake velocity being larger Ihall the downllowing emulsion velocity. N o t e that l a r g e - s c a l e t l u c t u a t i o n s e x i s t in the c o n c e n t r a -

O. 1.01 x 10 ' m for Ihe s a m e U , , / U , , , . = 2 . 0 , lb, = 2 6 0 0 k g / m ~ at d i f f e r e n t v e r t i c a l a n d l a t e r a l p o s i t i o n s in F i g s . 4 a n d 5, respeclively. As may be seen. reasonable agreement can be

l i o n r e s p o n s e s , s u g g e s t i n g t h a i c o n v e c t i o n is the m a i n p r o c e s s in v e r t i c a l s o l i d s m i x i n g . F o r l a t e r a l s o l i d s m i x i n g , t h e t e m p e r a t u r e r e s p o n s e s at f o u r po.~itions e q u i d i s t a n t f r o m t h e

d i f f e r e m p o s i t i o n ' , in tile b e d ;ire n l c a s u r e d Sil]ltlllallL'Otlnls. T h e d a t a s h o w s p r o m i s e s ) I l u c t u a ) i o n n ;llld r e c y c l i n , J o f Ihe I r a e e r in Ihe b e d . T h e c o m p a r i s o n o1,,i = 1.1)× Ill 7 ill Eq. t 7 I will] e x l ~ e r i m e n l a l d a l a in F i g . 3 ( a l s o in F i g s . 4 a a d 5 ) i n d i c a t e s thai t h e y ,igre¢ ~ e l l . A l s o . l h e I ~ o Ihc~)ries f o r x~ a k e e x c h a n g e c(~eflicienl Kx~ ( I/.qs. ( 3 ) a n d ( J, ) ) a r c i n c l u d e d in F i g . 3 ( a n d in F i g s . 4 a n d 51. T o .study Ihe el'feel o f p a r l i c l e s i z e s on solid,, m i x i n g in Iluidized beds. experiment;tl are ploued

data and model calculalions

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Fig. 5. ( ' o l n p a r l , , O u ol exr~2rilltental IrallMCill t e n l [ ~ r a l U l ¢ i-c.',[~rl',¢ ~.~.ith ntltllcrlcal t r a c e r c*.lllCentratiotP, b~, ~ariou,, K ~ nwxl¢ls a l o n g h o l h ~ e n i c a l a n d lateral di[cctiou,,, liq. -- "(-dill k g i m ' , d , , = ll).Tt} ~ I.OI x It) ' 111; t',,.~ = 4 7 -. Ill : ,11/,,. I',,/I',,., = 2.11. t l l - 5 0 ,, lit ' m I. t ' ~ , r d i t l a t e o f injecll~t~n ~ U l , t I unit: m m I. In t II. 2 lit I. -. . . . . . . tet11perature rcr, l~m~,e...~T: • °°lu:,,t~lidhnellhi,,v,l~rk.('r:('. I..l = I . t l ,. I I ) i . - . Iitlbrokenline) ~l o,,hida a n d Ktlnii ] I ,~ I. 1"",~.'(" . ? i [ ?..] t Ul b r o k d l liue : (.'hiba a n d K o b a ) -

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injection point are shown in Fig. 3b. The figure clearly ilh,strates the asymmetry in the vertical particle translm~rt. The temperature responses in lateral direction are much slower than in vertical direction in Figs. 3-5 and the rate of vertical convective solids mixing is much faster than the rate of lateral diffusive solids mixing. This indicates that lateral solids mixing is composed of two components, the primary component is the diffusion generated by the random movement of solids. and the supplement~:ry one is the convective component imparted by rising bubbles. As a result, the exchange coefti-

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cienl K~ model may hase little inlluence on lateral solids mixin,, as shov,n in the comp,..,ison of model calculations with experimental data m Figs. 3-5. The present model for K..~ is able to lollow the fluctuations in the concentration respolse, resulting from lhe gross circulation of solids, along broth vertical and lateral directions, as shown in Figs. 3-5. The se fluctuations appear to become ih~creasingly more prominent with increase in bed particle size. The reason is that ~,olids mixing depends mainly upon bubble size and vekx:ity in fluidi.,.ed beds. At the same con-

176

L Shen, M. ZJumg / Pow~h,r Technology 97 (1998) 1 7 0 - 1 7 7

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l:l~d. {'1. ('l~lllllilri,,i)ll of t'~,l~¢lhllt.nl.'ll Irill|',iciiI I¢llll'~t'lilD, llt' rcsl~Oll',t" ~,~,llh illuiii¢lil.;ll llilvt'l t'l,lll.'t'lllrillitHl~ 11) ~,;.Iril|ll'~ K,q, IllOt|t'l ~. ,Ih~llg ~erlical dire~lion. 14, - 13111) k~,./in'; tip 1 I).48 -- (1 :'2 1 ..: II) ' m; I ',,,, - I(11) x II) : rn/'-.: I',,/I,',,,, -- 2.0: ltl 45 ,~. I(1 : In |. ('t.brtlill,att" o f irljcction i'Joinl I unit: iiiiii): hi 11), 2 I(11. -. . . . tcmpcr:JttJrc r¢,,l)t)rP, c. )tT. • . . (ill ,,tdid line) thi,, ~,~,tlrk, (',l/( '. (,.! .- 1.11 x II)'); 1ill brt,ke,I l i n e ) Yo,,hida a,ld Kunii I 18 I. C,,IC. ; L_q E] L:J I i , hrokcr~ line I ( ' h i b a and Kot~iLva~,lti I I tj I. f ' , , / ( ' . .

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dition U,,/II,,,, :: 2.0. with increase in bed panicle size. huhbles hccolllC larger and rise fasler, especially the x~ake excllange coel'licien! Kv,. hccomcn increasingly smaller (as shown in Eq. ( 7 ) ) . In view of convection in the vertical direction, the Iluctuations arc mainly deternlincd by bubble velocity and wake exchange cueflicienl; and becume more prominem with increase in bed particles site. The Iluctualions along the lateral direction are mainly due to ones in the vertical direction. To examine the inlluence of panicle density I',, o n wake exchange coeflicient K~v (Eq. ( 7 ) ) . other experimental measurements are presented in Fig. 0 fi)r particle density {4,= 13(X) k g / m ~, particle size 0.48-0.52 ram. Compared with Fig. 3a. solids mixing is faster as the bed particle density decreases, at the same liuidization number U . / U . , , bed height/-It.. The reason is that the particles in the emulsion

phase can be easily to .,,wept inlo lhe wake will) decrease in panicle density 14,. and wake exchange coeflicienl Kw im.'reasen correspondingly. The comparisons of model calculations and eXl~dmenlal dala show thai the previous models for the wake exchange coeflicient available in the literature 118,191 agree wilh cxwrimenlal data only over very narrow ranges. In contrast to our model, the models predict thai the wake exchange coefficient should increase with increase in minimum fluidiz~,lion vel(~:ily U,,,,. The differences are very likely due to the assumption of an ideal, inviscid, incompressible, irroultional flow in the previous models. Also, the previous models consider the wake to be contained within a circle enclosing the bubble ( or within a sphere in the case o f a three-dimensional bubble ). In addition, we do not know what the effective outer boundary o f the wake really is, It is likely that this boundary

L. Shen, M. Zhang t Powder l'echnnh~gy 971 tt,a?Sj 171/- 177

is not the circle or sphere as is often assumed. The present model for wake exchange coefficient interprets successfully experimental data, and may have a signiiicant beating on modeling solids mixing and segregation in bubbling fluidized beds.

t T U Uh, U. x

6. Conclusions v The experimental results obtained from this investigation indicate that the convection-diffusion model is adequate tot both vertical and lateral mixing of solids in bubbling fluidized beds. The effect of particle sizes on solias m~xing is studied. Fluctuations in the concentration responses along both verlical and lateral directions have been observed experimentally. These fluctuations become increasingly more prominent as the bed particle size increases. The experimental data have been interpreted using the convection-diffusion model for solids mixing. The dynamics of solids exchange between the bubble wake and the emulsion phase in bubbling Iluidized beds is investigated, and a new m(v,lel fi~rexchange coefficient is proposed, in the model, particle size de. particle density bh,. gas viscosity/.t~, gas density p~, minimum fluidization velocity U,,,t and bubble size Dn are taken into account. The values for the exchange coefficient Kw for the model do not compare fi~vorably with the predictions of two available theoretical models in the literature I Ig,191. These models predict that the wake exchange coefficient should increase with increase in minimum Iluidization velocity U,,.. However. our model shows that the wake exchange coefficient Kw decreases with minimum lluidization velocity Urn,. With the model of wake exchange coeflicient, the convectiondiffusion model of solids mixing is lbund to predict the experimental trends reasonably well. The model for solids exchange between the bubble wake and the emulsion phase in a gas Iluidized bed is needed in modeling solids mixing and segregation paltems.

7. List of symbols A

Parameter in Eq. ( 7 ) Area of distributor plane per orilice ( m z) Solid tracer concentration ( kg/m 3) C Equilibrium concentration of solid tracer after total C~ mixing with the bed material at time t --- x ( kg/ m 3) CJC.~ Derivation of C,/C~. refer to Shen et al. i 15 I D Diameter {m ) Radial dispersion coefticient of solids (mZ/s) D,, Average particle diameter (m) Volumetric fraction of a phase (m~/m x) f g Gravitational acceleration constant ( m/:;2 } Expanded bed height { m) Wake exchange coefficient (m -~phase e ~changed/ Kw (m "~bubble s)) A~

177

Time ( s Temperature (K) Velocity {m/s ) Bubble velocity relative to the solids ahead of it (m/s) Superticial ~,,as.veloeitv. ( m/sl Coordinate. lateral distance measured from the injection point ( m ) Coordinate. heighl above distributor ( m )

Greek letters tS e p g

Volumetric fraction of bubbles in the bed ~m' bubble/m ~bed I Voidagc Drnsity ( k g / m ' l Viscosity (kg/m s) )

Sttbs('ripts

B d E F mr P W

Bubble Mixture of the emulsion phase and wake phase Emulsion Gas Under minimum Iluidizalion Particle Wake

References I I I W.G. Ms.,., Chem Eng. Prog. 55 t 1959) 4'4-56. 121 P.N. Rt~c. K.S. Sulhedand. Tran.~. Insl. Chem. Eng. 42 11964 ) T55T65. 131 K. Schugcrl, Prigdot Tcchnol. 3 I 1'476 ~ 267-278. 141 J,D. (;ahw, AIChi- J. IO 119(',4) ,Ll5-351). 151 R.R. Cranlicld, AIChE. S)mp. Ser. 1'46 i 1'4781 54-59. 161 Y F. Shi. L.T. Fan. Powder Tcchmd. 41 I i'485b 23-28. 171 J. Tomeczek, Z. Ja~,trtah, B, (;radon, Po~Idcr Tcchnol. 72 { 1~921 17181 S.R Tailhy, M.A.I'. Cocquerel, Trans, Inst. ('hrm. i:ng. 39 11961 ) 195-2l) 1. 1"41 O. Siinai, Ind. Eng. ('hem. Pn~ess L,N:s, Dex. 20 I 1'4811 533-538. I li)l G.K. Stephens. R. Sinclair, O.E. Potter, Powder Tcchnol. 1 { 1967) 157-166. I I ! I D. Kunii. O. l,e~cnspicl. Fluidi/alion Engineering. Wiley. New York. 1969, pp. 168-182. I 121 C. i:rcycr, O.t-. Pouer, Ind. En~. Chem. Fundam. i I 11978) 33~-344. [ 131 C.C. Lak~,hmanan, OE. Puuer. Chem. Eng. Sci. 45 I I ~ ) I 519-528. 1141 K.S. Lira, V.S, Gururajan, PK. Agar~sal. Chem. Eng. Sci. 48 t 1'493 I 2251-2265. I 151 L. Shen. M, Zhang, Y, Xu. Powder Technol. 8g ( 19951 2(}7-212 1161 J.A. Valenzuela. L.R. Glicksman, Polsder Technol. 38 11984) 6372. I 171 L.T. Fan, J.C. Song. N. Yulani. Chem. Eng. Sci. 41 11986) I i 7-122. 1181 K. Yonhida. D. Kunii. J, ('hem. Eng. Jpn. I { 1~'~8~ I I - l b . I 191 T. Chiba. H. Koba)a.,,hi, J. Chem. Eng. Jpn. I0 { 1977) 2{K~--21(). 1201 B. Kocatulum, E.A. Ba.~m¢, E.K. Levy, B. Kozanoghl. 1991 AIChE Annual Meeting. Los Angeles. CA. Nov. 17-__. Paper 103d, I~,~1. 1211 E.A. B:.semc. E.K. Levy. Powder Tcchnol. 72 (l~J2) 45-50. 1221 L.R. Glicksman. G. McAndre~.s. Powder Technol. 42 { 1985 ~ 15q167. ! 231 I. Bae)cns. D. Geldart, in" D. Geldart ( Ed. I, Gas Fluidized Technology, Wiley. England. 19,g6. pp. 97-122.