Werther - Fluidized Bed Reactors

(1)



₂₀₂₀_{12 W}_{12 W}_il_il_ey_ey_-V_-V_CH_CH_Ve_Ve_rl_rl_ag_ag_Gm_Gm_bH_bH_&_&_Co_Co_._._KG_KG_aA_aA_,_,_We_We_in_in_he_he_im_im

J

JOACHIMOACHIM W WERTHERERTHER,, Hamburg University of Technology, Hamburg, Germany Hamburg University of Technology, Hamburg, Germany

1 1. . IInnttrroodduuccttiioonn. . . 323200 1. 1.1. 1. ThThe e FlFluiuididizazatition on PrPrininciciplplee . . . . . . 323200 1. 1.2. 2. FoFormrms s of of FlFluiuididizezed d BeBedsds . . . . . . 323211 1.3

1.3. . AdvAdvantantagages es and and DisDisadadvanvantatages ges of of thethe

Fluidized-Be

Fluidized-Bed d ReactorReactor. . . 323222

2.

2. FlFluiuid-d-MeMechchananicical al PrPrininciciplpleses . . . 323222

2.1

2.1. . MinMinimuimum m FluFluidiidizazatiotion n VelVelociocityty. . . 323222

2.2

2.2. . ExpExpansansion ion of of LiqLiquiduid–So–Solid lid FluFluidiidized zed BedBedss. . 323244

2.3

2.3. . FluFluidiidizazatiotionnPrPropoperertitiesesofofTyTypipicacallBeBeddSolSolididss 324324

2. 2.4. 4. StStatate e DiDiagagraram m of of FlFluiuididizezed d BeBedd. . . 323255 2. 2.5. 5. GaGas s DiDiststriribubutitionon . . . 323266 2. 2.6. 6. GaGas s JeJets ts in in FlFluiuididizezed d BeBedsds. . . 323277 2. 2.7. 7. BuBubbbble le DeDevevelolopmpmenentt . . . . . . 323288 2. 2.8. 8. ElEluutrtriaiattioionn . . . . . . 323299 2. 2.9. 9. CiCircrcululatatining g FlFluiuididizezed d BeBedsds. . . 333300 2. 2.9.9.1. 1. HyHydrdrododynynamamic Pic Pririncncipipleless. . . 333300 2.9.

2.9.2. 2. LocaLocal l Flow Flow StrucStructure ture in in CircuCirculatinlating g FluidFluidizedized

Be

Beds ds . . . 333333

2.9

2.9.3.3. . DesDesign ign of Sof Soliolids Rds Recyecycle cle SysSystem tem . . . . . . . . . . . . . . . . . . 333344

2.10

2.10. . CocuCocurrenrrent t DownDownﬂow ﬂow CircCirculatiulating ng FluidFluidizeizedd

Beds (Downers) Beds (Downers) . . . . . . 333344 2. 2.1111. . AtAttrtrititioion n of of SoSolilidsds . . . 333355 3. 3. SoSolilids ds MiMixixing ng in in FlFluiuididizezed-d-BeBed d ReReacactotorsrs. . . . 333377 3. 3.1. 1. MeMechchananisisms ms of of SoSolilids ds MiMixixingng . . . 333388 3. 3.2. 2. VeVertrticical al MiMixixing ng of of SoSolilidsds . . . . . . 333388 3. 3.3. 3. HoHoririzozontntal al MiMixixing ng of of SoSolilidsds. . . 333399 3.4

3.4. . SolSolids ids ReResidsidencence-Te-Time ime ProPropepertirtieses . . . . . . 343400

3.5

3.5. . SolSolids ids MiMixinxing g in in CirCircuculatlating ing FluFluidiidized zed BedBedss 340340

4.

4. GaGas s MiMixixing ng in in FlFluiuididizezed-d-BeBed d ReReacactotorsrs . . . . . . 343400

4.1

4.1. . Gas Gas MiMixinxing g in in BuBubblbblining g FluFluidiidized zed BedBedss. . . . . . 343411

4.2

4.2. . Gas Gas MiMixinxing g in in CirCircuculatlatining g FluFluidiidized zed BedBedss. . 343411

5. 5. HeHeat at anand d MaMass ss TrTranansfsfer er in in FlFluiuididizezed-d-BeBedd Reactors Reactors. . . 343411 6. 6. GaGas-s-SoSolilid d SSepepaarratatiioonn . . . . . . 343433 7.

7. InjInjectection ion of of LiqLiquid uid ReaReactactantnts s intinto o FluFluidiidizezedd

Beds

Beds. . . 343433

8.

8. InInduduststririal al ApApplplicicatatioionsns . . . 343444

8.1

8.1. . HetHetererogeogeneoneous us CatCatalyalytic tic GaGas-Ps-Phahasese

Reactions

Reactions . . . . . . 343444

8.

8.2. 2. PoPolylymemeririzazatition on of of OlOleﬁeﬁnsns. . . 343477

8.3

8.3. . HomHomogeogeneoneous us GasGas-Ph-Phase ase ReaReactictiononss. . . 343477

8.

8.4. 4. GaGas–s–SoSolilid d ReReacactitiononss. . . 343488

8.5

8.5. . AppAppliclicatiationons s in in BioBiotectechnhnoloologygy . . . . . . 353522

9.

9. MoModedeliling ng of of FlFluiuididizezed-d-BeBed d ReReacactotorsrs . . . . . . 353544

9.1

9.1. . MoModeldeling ing of of LiqLiquiduid–S–Sololid id FluFluidiidizezed-Bd-Beded

Reactors

Reactors. . . 353544

9.2

9.2. . MoModeldeling ing of of GasGas–S–Soliolid d FluFluidiidizezed-Bd-Beded

Reactors

Reactors. . . 353544

9.2

9.2.1. .1. BubBubblibling ng FluFluidiidizezed-Bd-Bed ed ReaReactoctorsrs. . . . . . . . . . . . . . . . . . 353555

9.2

9.2.2. .2. CirCircuculatlating ing FluFluidiidizezed-Bd-Bed ed ReaReactoctors rs . . . . . . . . . . . . . . 353566

9.3

9.3. . New New DevDeveloelopmpmenents ts in in MoModedelinling g FluFluidiidizezed-

d-Bed Reactors

Bed Reactors . . . . . . 353577

9.3

9.3.1. .1. ComComputputatiationaonal Fll Fluid uid DynDynamiamics cs . . . . . . . . . . . . . . . . . . . . 353577

9.3

9.3.2. .2. ModModelieling ng of of FluFluidiidizezed-Bd-Bed ed SysSystemtemss. . . . . . . . . . . . . . 353588

1

100. . SSccaallee--uupp. . . 353599

References

References . . . . . . 363611

Symbols (see also

_!

Principles of Chemical Principles of Chemical

Reaction Engineering and

_!

Model Reactors Model Reactors

and Their Design Equations)

a

a: : vovolulumeme-s-spepeciciﬁc ﬁc mamassss-t-traransnsfefer r ararea ea bebe-

-twe

tween en bubbubble ble and and sussuspenpensiosion n phaphasesses,,

m

m11

A

A₀₀: : crcrososs-s-sesectctioionanal l ararea ea of of ororiﬁiﬁcece, , mm22

Ar Ar : : ArArchchimimededes es nunumbmberer, , dedefinfined ed byby Equation (5) Equation (5) A A_t_t: : crcrososs-s-sesectctioionanal l ararea ea of of rereacactotor, r, mm22 b b: : papararamemeteter r dedef. f. bby y EqEquauatitioon n (5(544)) c cvv: : sosolilids ds vovolulume me coconcncenentrtratatioionn c c_b_b: : bububbbble le atattrtritiition on rarate te coconsnstatant, nt, dedefinfined ed byby Equation (50), s Equation (50), s22 /m /m44 c c_c_c: : cycyccloloneneaattttrirititiononraratetecoconnststananttdedefifineneddbyby Equation (51), s Equation (51), s22 /m /m33 c c_j_j: : jejet t atattrtrititioion n rarate te coconsnstatantnt, , dedefinfined ed byby Equation (52), s Equation (52), s22 /m /m33 C

C _b_b: : coconcncenentratratiotion n in in bububbbble le phphasase, e, kmkmolol/m/m33

C

C _d_d: : coconcncenentratratiotion n in in sususpspenensision on phphasase,e,

kmol/m

kmol/m33

d

d _o_o: : oorriiﬁﬁcce e ddiiaammeeteterr, , mm

DOI:

(2)

(3)

1.

1. Introd

Introd

uctio

n

1.1.

1.1. The Fluidi

The Fluidi

zatio

n Principl

e

In ﬂuidization an initially stationary bed of solid

particles is brought to a ‘‘ﬂuidized’’ state by an

upwardstreamofgasorliquidassoonasthevolume

ﬂowrateoftheﬂuidexceedsacertainlimitingvalue

V

V __mf mf (where mf denotes minimum ﬂuidization). In (where mf denotes minimum ﬂuidization). In

the ﬂuidized bed, the particles are held suspended

by the ﬂuid stream; the pressure drop

D

p p_fb_fb of the of the

ﬂuidonpassingthroughtheﬂuidizedbedisequalto

theweig

theweighthtofofththeesosolilidsdsminminususthebuoythebuoyanancycy,,didivivid-

d-edbythecross-sectionalarea

edbythecross-sectionalarea A A_t_toftheﬂuidized-bedoftheﬂuidized-bed

vessel (Fig. 1): vessel (Fig. 1): D D p pfbfb

¼

A Att



H H



ð

11



ee

Þ



ð

rrss



rrf f

Þ



gg A Att

ð

1 1

_Þ

d d _p_p: : SaSaututer er didiamameteterer, , dedefinfined ed by by EqEquaua- -tion (6), m tion (6), m d d _p_p_i_i: : didiamameteter er of of papartrticicle le sisize ze clclasasss i i, , mm d d _t_t: : bbeed d ddiiaammeetteerr, , mm d d _v_v: : lolocacal l bububbbble le vovolulume me eqequiuivavalelent nt spspheherere diameter, m diameter, m d d vv00: : ininititiaial l bububbbble le didiamameteterer, , mm D D: : cocoefefficficieient nt of of momolelecuculalar r didiffffususioion, n, mm22 /s /s D D_sh_sh: : lalateterarallsosolilidsdsdidispsperersisiononcocoefefficficieientnt,,mm22 /s /s D

D_sv_sv: : ververtictical al solsolids ids disdisperpersiosion n coecoefﬁcfﬁcienient,t,

m m22 /s /s Fr Fr _p_p: : FrFrououde de nunumbmberer, , dedefinfined ed byby Equation (29) Equation (29) G G_s_s: : sosolilids ds mamass ss floflow w raratete, , babasesed d on on rereacactotorr cross-sectional area, kg m cross-sectional area, kg m22 _s_s11 h h: : heheigight ht ababovove e didiststriribubutotor r lelevevel, l, mm h

h_o_o: : heheigight ht ababovove e didistrstribibutoutor r whwhere ere bububbbblesles

are forming, m are forming, m h h_gs_gs: : gagas-s-toto-s-sololid id heheat at trtranansfesfer r cocoefefficficieientnt, , WW m m22_K_K11 h h_wb_wb: : wawall-ll-toto-b-bed ed heheat at trtranansfsfer er cocoefefficficieientnt, W, W m m22_K_K H H : : eexxppaannddeed d bbeed d hheeiighghtt, , mm H

H _mf_mf: : bebed hd heieighght at at mt mininimuimum ﬂm ﬂuiuididizazatiotion, n, mm

k k _G_G: : mamassss-t-traransnsfefer r cocoefefﬁcﬁcieientnt, , m/m/ss L L : : jjeet t lleennggtthh, , mm m m_a_a: : mamass ss of of elelututririatated ed sosolilidsds, , kgkg m

m__attatt: : mamass ss ﬂoﬂow w dudue e to to atattrtrititioion, n, kgkg/s/s

m m_b_b: : bbeed d mmaassss, , kkgg m m__ss: : ssoolliidds s mmaasss s ﬂﬂowow, , gg//ss n n_p_p: : nunumbmber er of of papassssagages es ththrorougugh h cycyclclononee p p: : pprreessssuurree, , PPaa Pe

Pe_r,_r,_c_c: : PPeclecletetnumnumberber,,deﬁdeﬁnednedbybyEquEquatioation (43)n (43)

Q Q₃₃: : cucumumulalatitive ve mamass ss didiststriribubutitionon r r _a_a: : atattrtrititioion n raratete, , dedefinfined ed by by EqEquauatition on (3(33)3),, s s11 r r _j_j: : rereacactition on raratete, , babasesed d on on cacatatalylyst st mamassss,, kmol kg kmol kg11 _s_s11 Re Re: : RReyeynnoolldds s nnuummbbeerr S S _v_v: : vovolulumeme-s-spepecicific fic susurfrfacace e ararea ea of of papartrti- i-cles, m cles, m11 t t : : ttiimmee, , ss TDH

TDH : : trantransposport rt disdisengengagiaging ng heiheightght, m, m

u u: : susupeperfirficicial al flufluididizizining g vevelolocicityty, , m/m/ss u u_b_b: : lolocacal l bububbbble le ririse se vevelolocicityty, , m/m/ss u u_c_c: : vevelolocicity ty at at cycyclclonone e ininlelet, t, m/m/ss u u_mf_mf: : susupeperfirficicialalmimininimumum m flufluididizizininggvevelolocicityty,, m/s m/s u u_o_o: : jejet t vvelelococitity y at at ororifiificece, , m/m/ss u u_sl_sl: : slslip ip vevelolocicityty, , dedefinfined ed by by EqEquauatition on (2(27)7),, m/s m/s u u_t_t: : sisingngle le papartrticicle le tetermrmininal al vevelolocicityty, , m/m/ss V V __bb: : vivisisiblble e bububbbble le floflow, w, babasesed d on on bebed d arareaea,, m m33mm22_s_s11 V

V __mf mf : : mimininimumum m flufluididizizining g floflow w raratete, , mm

3 3 /s /s V V __oo: : flfloowwrraatteeooffggaassiissssuuiinnggffrroommoorrifiificcee,,mm 3 3 /s /s x xii: : mmaassssffraraccttiioonnooffppaarrttiiclcleessiizzeeffrraaccttioionniiinin bedmaterial bedmaterial a a: : vevelolocicity ty raratitio, o, dedefinfined ed by by EqEquauatition on (1(14)4)

D

p p_d_d: : prpresessusure re drdrop op of of ththe ge gas as didiststriribubutotor, Pr, Paa

e

: : bbeed d ppoorroossiittyy

e

bb: : llooccaal l bbuubbbble le ggaas s hhoolldduupp

e

ii: : popororosisity ty of of cacatatalylyst st pparartiticlclee

e

mf mf : : bebed d popororositsity y at at mimininimumum m ﬂuﬂuididizizatiationon

k k**: : elelututririatatioion n rarate te coconsnstatantnt, , kg kg mm22 ss11

l

: : avavereragage e lilife fe titime me of of a a bbububbblele, , ss

m

: : sosolilid-d-toto-g-gas as mamass ss ﬂoﬂow w raratitioo

n

: : kkiinneemmaattic ic vviissccoossitityy, , mm22 /s /s

n

ijij: : ststoioichchioiomemetrtric ic nunumbmber er of of spspececieiess ii in in reaction reaction j j r r_f_f: : ﬂﬂuuiid d ddeennssiittyy, , kkgg//mm33 r r_s_s: : ssoolliidds s ddeennssiitty, y, kkgg//mm33

q

: : ststreress ss hihiststorory y papararamemeteter, r, dedeﬁnﬁned ed byby Equation (54) Equation (54)

q

bb: : papararamemeteter, r, dedeﬁnﬁned ed by by EqEquauatition on (2(23)3)

y

: : prpresessusure re raratitio, o, dedeﬁnﬁned ed by by EqEquauatition on (2(28)8)

(4)

In

InEqEquauatition on (1(1),),ththeepopororosisityty

e

ofofththeeﬂuﬂuididizizededbebedd

is the voi

is the voiddvolvolume ofume ofthetheﬂuiﬂuidizedized bed (vod bed (volumlume ine in

interstices between grains, not including any pore

volume in the interior of the particles) divided by

the total bed volume;

the total bed volume; rr_s_s is the solids apparent is the solids apparent density; and

density; and H H is the height of the ﬂuidized bed. is the height of the ﬂuidized bed.

In many respects, the ﬂuidized bed behaves

like a liquid. The bed can be stirred like a liquid;

objects of greater speciﬁc gravity sink, whereas

those of lower speciﬁc gravity ﬂoat; if the vessel

is tilted, the bed surface resumes a horizontal

po

positsitioion; n; if if twtwo o adadjajacecent nt ﬂuﬂuididizized ed bebeds ds wiwithth

di

diffffereerentntbebeddheheigighthtssarareecoconnnnececteteddtotoeaeachchototheher,r,

the heights become equal; and the ﬂuidized bed

ﬂows out like a liquid through a lateral opening.

Particularly advantageous features of the

ﬂuid-ized bed for use as a reactor are excellent gas–

ized bed for use as a reactor are excellent gas–

solid contact in the bed, good gas–particle heat

and mass transfer, and high bed–wall and bed–

internals heat-transfer coefﬁcients.

The ﬂuidization principle was ﬁrst used on an

ind

indusustritrialalscascaleleinin19219222forforthethegasgasifiificatcationionofoffinefine-

-grained coal [1]. Since then, ﬂuidized beds have

grained coal [1]. Since then, ﬂuidized beds have

been applied in many industrially important

pro-ces

cesseses. s. The The prepresesent nt spespectrctrum um of of appapplilicatcatioionsns

ext

extendendssfrofrommaanumnumberofberofphyphysicsicalalproprocescessesses,,sucsuchh

as

as cooling–hcooling–heating, eating, drying, sublimation–desudrying, sublimation–desubli-

bli-matio

mation,n,adsoadsorptirption–don–desoresorptioption,n,coatcoating,ing,andandgrangran-

-ulat

ulation, ion, to to many heterogemany heterogeneouneous s catacatalytilytic c gas-

gas-phase reactions as well as noncatalytic reactions.

phase reactions as well as noncatalytic reactions.

What follows is a survey of the ﬂuid

mechan-ica

icallpriprincincipleplessofofﬂuiﬂuidizdizatiationontectechnohnologlogy,y,gasgasandand

solid mixing, gas–solid contact in the ﬂuidized

be

bed, d, tytypipicacal l inindudustrstriaial l apappliplicacatiotionsns, , anand d apap-

-pro

proachaches es to to modmodelineling g ﬂuiﬂuidizdized-ed-bed bed reareactoctors.rs.

Further information is given in textbooks (e.g.,

[2]

[2]) ) and and monmonogrographaphs s (e.(e.g., g., [3–[3–8]). 8]). SumSummarymary

treatments can also be found in [9–19]. Other

use

usefulfulliteliteratratureureincincludludesesrepreportortssofofthetheEngEngineineer-

er-ing

ing FouFoundandatiotion n ConConfereferencences s on on FluFluidizidizatiationon

[20–22], the Circulating Fluidized Bed

Confer-en

encecess(e(e.g.g.,.,[2[23–3–2525],],anandd––foforrususeeofofththeeﬂuﬂuididizizeded

bed in energy technology – the Fluidized Bed

Combustion Conferences (e.g., [26–28]).

1.2.

1.2. Forms o

Forms o

f Fluidiz

ed Beds

As

As ththe e vovolulume me floflow w raratete V V __ o or r the the supsuperfierficiaciall

velocity

velocity uu

_¼

V V / / __ A Att of the ﬂuid increases beyond of the ﬂuid increases beyond

the value

the value V V __mf mf or or u umf mf (Fig. 2 A) corresponding to (Fig. 2 A) corresponding to

th

the e mimininimumum m ﬂuﬂuididizizatiation on popoinint, t, onone e of of twotwo

thing

things s happehappens: ns: inin ﬂuidization with a liquid ﬂuidization with a liquid , the, the

bed begins to expand uniformly; in

bed begins to expand uniformly; in ﬂuidization ﬂuidization

wi

with th a a gagass – – a a prprococesess s of of grgreaeateter r inindudustrstriaiall

impor

importance and tance and the one the one discusdiscussed almost sed almost excluexclu-

-si

sivevely ly in in ththe e fofollollowiwing ng mamateteririal al – – vivirturtualallyly

solid

solids-free gas bus-free gas bubbles begbbles begin to form (Fig. in to form (Fig. 2 2 B).B).

Th

The e loclocal al meamean n bubbubble ble sizsize e incincreareases ses raprapidlyidly

with increasing height above the grid because of

coalescence of the bubbles. If the bed vessel is

su

sufﬁfﬁcicienentltly y nanarrrrow ow anand d hihighgh, , ththe e bububbbbleless

ul

ultitimamatetely ly ﬁlﬁll l ththe e enentitire re crcrososs s sesectctioion n anandd

pass through the bed as a series of gas slugs

(Fig.

(Fig. 2 C). 2 C). As the gas As the gas velocvelocity increases furthity increases further,er,

more and more solids are carried out of the bed,

the original, sharply deﬁned surface of the bed

disappears, and the solids concentration comes

to decrease continuously with increasing height.

To

To acachiehieve ve ststeaeadydy-s-stattate e opopereratation ion of of susuch ch aa

‘

‘‘tu‘turburbulenlent’t’’ ’ ﬂuiﬂuidizdized ed bed bed (Fi(Fig. g. 2 2 D), D), solsolidsids

entrained in the ﬂuidizing gas must be collected

Figure 1.

(5)

and returned to the bed. The simplest way to do

this is with a cyclone integrated into the bed

vessel and a standpipe dipping into the bed. A

further increase in gas velocity ﬁnally leads to

the circulating ﬂuidized bed (Fig. 2 E), which is

characterized by a much lower average solids

con

concencentratratiotion n thathan n the the prepreviovious us syssystemtems. s. TheThe

hig

high h solsolids ids ententrainrainmenment t reqrequiruires es an an efﬁefﬁciecientnt

external solids recycle system with a specially

des

designigned ed prepressussure re seaseal l (sh(shown as own as a a sipsiphon inhon in

Fig. 2 E).

1.3.

1.3. Adva

Adva

ntag

es and

Disa

dvan

tages of

the Fluidized-Bed Reactor

The

Themajmajororadvadvantantageagessofofthethe(ga(gas–ss–solidolid))ﬂuiﬂuidizdizeded

bed as a reaction system include

1.

1. Easy hanEasy handling and trandling and transport of solidsport of solids due tos due to

liquid-like behavior of the ﬂuidized bed

2.

2. UniUniforform m temtemperperatuature re disdistritributibution on due to due to in-

in-tensive solids mixing (no hot spots even with

tensive solids mixing (no hot spots even with

strongly exothermic reactions)

3.

3. LarLarge solid–ge solid–gas exchgas exchangange e arearea a by virtue of by virtue of

small solids grain size

4. 4. HiHigh gh heheatat-t-traransnsfefer r cocoefefﬁcﬁcieientnts s bebetwtweeeenn b bed ed anand d imimmemersrsed ed heheatatining g oor r cocoololiningg surfaces surfaces 5.

5. UnifoUniform (solid) prodrm (solid) product in batchwiuct in batchwise processe processs

because of intensive solids mixing

Se

Settagagaiainsnsttththeseseeadadvavantntagagesesarareeththeefofollllowowiningg

disadvantages:

1.

1. ExpeExpensive solids separansive solids separation or tion or gas puriﬁcagas puriﬁca-

-tio

tion n equequipmipment ent reqrequiruired ed becbecausause e of of solsolidsids

entrainment by ﬂuidizing gas

2.

2. As a consequAs a consequence of high soence of high solids mixilids mixing rate,ng rate,

nonuniform residence time of solids,

back-mix

mixingingofofgasgas,,andandresresultulting loing lower cower convenversiorsionn

3.

3. In In catacatalytlytic ic reareactioctions, ns, undundesiresired ed bypbypass ass oror

broadening of residence-time distribution for

reaction gas due to bubble development

4.

4. EroErosiosion n of of intinternernals als and attritand attrition ion of of solsolidsids

(especially signiﬁcant with catalysts),

result-ing from high solids velocities

ing from high solids velocities

5.

5. PossibPossibility of deﬂuility of deﬂuidizatiidization due to agglomon due to agglomer-

er-ation of solids

ation of solids

6.

6. GasGas–so–solidlidcoucountentercurcurrerrentntmotmotionionpospossibsibleleon-

on-ly in multistage equipment

ly in multistage equipment

7.

7. DifﬁcDifﬁculty in scalulty in scaling-uping-up

Table 1 compares the ﬂuidized-bed reactor with

alt

alternernativative e gasgas–so–solid lid reareactiction on syssystemtems: s: ﬁxeﬁxed-

d-bed, moving-d-bed, and entrained-ﬂow reactors.

bed, moving-bed, and entrained-ﬂow reactors.

2.

2. Fluid

Fluid

-Mecha

nical Princ

iple

s

2.1.

2.1. Mini

Mini

mum Fluidiz

atio

n Velocity

The

Theminminimuimummﬂuiﬂuidizdizatioationnpoipoint,nt,whiwhichchmarmarksksthethe

boundarybetweentheﬁxed-andtheﬂuidized-bed

Figure 2.

(6)

conditions, can be determined by measuring the pressure drop

D

p across the bed as a function of volume ﬂow rateV _(Fig. 1). Measurement should

always be performed with decreasing gas veloci-ty, by starting in the ﬂuidized condition.

Only for very narrow particle-size distribu-tions, however, does a sharply defined minimum fluidization point occur. The broad size distribu-tions commonly encountered in practice exhibit a blurred range; conventionally, the minimum fluidization point is defined as the intersection of the extrapolated fixed-bed characteristic with the line of constant bed pressure drop typical of the fluidized bed (Fig. 1).

The measurement technique already contains the possibility of calculating the minimum ﬂu-idization velocity u_mf: The pressure drop in ﬂow

through the polydisperse ﬁxed bed at the point

u

_¼

u_mf, given, for example, by the Ergun rela-tion [29] (

_!

Fluid Mechanics), is set equal to the ﬂuidized-bed pressure drop given by Equa-tion (1). From the Ergun relaEqua-tion

D p h

¼

4:17



S 2 v

 ð

1

_

e

_Þ

2 e3 hu

þ

0:29S v



1

_

e e3 rf u 2 it follows umf

¼

7:14

ð

1



emf

Þ

n



S v



ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1

_þ

0:067 e 3 mf

ð

1

_

emf

Þ

2

 ð

r_s



r_f

Þ 

g r_f n2



1 S 3 v

v

u

t



1

2

6

4

3

7

5 ð

2

_Þ

Accordingly, to calculate u_mf, the characteristics of the gas (rf ,

n

), the density rs of the particles, Table 1. Comparison of gas–solid reaction systems [2, 18]

(7)

the porosity

e

mf of the bed at minimum

ﬂuidiza-tion, and the volume-speciﬁc surface area S v of

the solids must be known. The speciﬁc surface area deﬁned by

S v

¼

surface area of all particles in the bed volume of all particles in the bed

(this takes into account only the external area, which governs hydraulic resistance, not the pore surface area as in porous catalysts) cannot be determined very exactly in practice. Hence u_mf

should not be calculated on the basis of the measured particle-size distribution of a represen-tative sample of the bed solids; instead, it is better measured directly. Equation (2) can be em-ployed advantageously to calculate u_mf in an industrial-scale process on the basis of minimum ﬂuidization velocities measured in the laboratory under ambient conditions [30].

An equation from WEN and YU [31] can be

used for approximate calculations:

Remf

¼

33:7

ð

p

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1

þ

3:6



105



Ar



1

Þ

ð

3

Þ

where Remf

¼

umf d p n

ð

4

Þ

Ar

_¼

gd 3 p n2



r_s



r_f r_f

ð

5

Þ

Here the surface mean or Sauter diameter calcu-lated from the mass–density distributionq₃ (d ) of the particle diameters

d p

¼

1

R

d max d min d 1



q3

ð

d

Þ

d

ð

d

Þ

ð

6

_Þ

should be used for the characteristic particle diameter d _p.

Both the Ergun approach and the Wen and Yu simplification have been confirmed experimen-tally over a wide range of parameters. More recently, Vogt et al. [32] found that Equations (2) and (3) are also applicable to high-pressure fluidized beds in which the fluid is under super-critical conditions

2.2. Expansion of Liquid–Solid

Fluidized Beds

The uniform expansion of a bed on ﬂuidization with a liquid can be described by

u ut

¼

en

_ð

7

_Þ

according to RICHARDSONandZAKI[33]. Hereu_tis

the terminal velocity of isolated single particles; the exponent n is given as follows, provided the particle diameter is much smaller than that of the vessel: n

_¼

4:65 0 < Ret



0:2 4:4

_

Re_t0:03 0:2 < Ret



1 4:4

_

Re0:1 t 1 < Ret



500 2:4 500 < Ret

8 >

>

<

>

:

ð

8

_Þ

The Reynolds number used above is calculated via the single-particle terminal velocity u_t:

Ret

¼

ut



d p

n

ð

9

Þ

2.3. Fluidization Properties of Typical

Bed Solids

In ﬂuidization with gases, solids display charac-teristic differences in behavior that can also affect the operating characteristics of ﬂuidized-bed reactors. GELDART has proposed an

empiri-cally based classification of solids into four groups (A to D) by fluidization behavior [34]. The parameters employed are those crucial for fluidization properties: the mean particle diame-ter (d _p) and the density difference (rs



rf )

between solid and ﬂuid. Figure 3 shows the Geldart diagram with the interclass boundaries theoretically established by MOLERUS [35].

Figure 3. Geldart diagram (boundaries according to MOLERUS [35])

(8)

Solids of Group C are very fine-grained, cohesive powders (e.g., flour, fines from cyclones and electrostatic filters) that virtually cannot be fluidized without fluidization aids. The adhesion forces between particles are stronger than the forces that the fluid can exert on the particles. Gas flow through the bed forms channels extending from the grid to the top of the bed, and the pressure drop across the bed is lower than the value from Equation (1). Fluidization properties can be improved by the use of mechanical equip-ment (agitators, vibrators) or flowability addi-tives, e.g., Aerosil.

Solids of Group A have small particle dia-meters (ca. 0.1 mm) or low bulk densities; this class includes catalysts used e.g., in the ﬂuidized-bed catalytic cracker. As the gas velocity u

increases beyond the minimum ﬂuidization point, the bed of such a solid ﬁrst expands uniformly until bubble formation sets in at u

_¼

u_mb

>

u_mf. The bubbles grow by coalescence but break up again after passing a certain size. At a considerable height above the gas distributor grid, a dynamic equilibrium is formed between bubble growth and breakup. If the gas ﬂow is cut off abruptly, the gas storage capacity of the ﬂuidized suspension causes the bed to collapse rather slowly.

Group B Solids have moderate particle sizes and densities. Typical representatives of this group are sands with mean particle diameters between ca. 0.06 and 0.5 mm. Bubble formation begins immediately above the minimum ﬂuidi-zation point. The bubbles grow by coalescence, and growth is not limited by bubble splitting. When the gas ﬂow is cut off abruptly, the bed collapses quickly.

Group D includes solids with large particle diameters or high bulk densities; examples are sands with average particle diameters

>

0.5 mm. Bubbles begin to form just above the minimum fluidization point, but the character of bubble flow is markedly different from that in group B solids: group D solids are characterized by the formation of ‘‘slow’’ bubbles (Section 2.7). On sudden stoppage of the gas flow, the bed also collapses suddenly.

2.4. State Diagram of Fluidized Bed

Whereas the onset of the fluidized state can be described by the minimum fluidization velocity, the bed operating range and the gas velocity needed to create a given fluidized state can be estimated with the help of the fluidized-bed state diagram (Fig. 4) devised by REH [36]. This plot

shows the fluid mechanical resistance character-istics of the fixed bed, fluidized bed, and pneu-matic transport. The ordinate is the quantity

3 4 u2 g

_

d p



r_f

ð

rs



rf

Þ

and the abscissa is the Reynolds number Re_p

formed with the ﬂuidization velocity u and the particle diameter d _p. The state parameter in the ﬂuidized-bed region is the mean bed porosity

e

. The use of the diagram is facilitated by an auxiliary grid with lines of constant M and con-stant Archimedes number. While the dimension-less groups plotted as ordinate and abscissa each contain both the particle diameter and the ﬂuidi-zation velocity, this is not the case with the parameters Ar and M deﬁned by

Ar

_¼

g



d 3 p n2

 ð

r_s



r_f

Þ

r_f

ð

10

Þ

Figure 4. Reh status diagram with status points S and S1–S4

(9)

M

_¼

u

3

g

_

n



r_f

ð

r_s



r_f

Þ

ð

11

Þ

The Reh status diagram can answer a number of practical questions. If, for example, the proper-ties of the gas (

r

f ,v) and the solid (dp,

r

s) and the

ﬂuidization velocity u are given, the calculation of Ar and Re_p yields, via the status point S in the diagram (Fig. 4), the average voidage

e

in the ﬂuidized bed. Taking the line M

_¼

const. through S at the intersection with the line

e

_!

1 a t S1gives

information on the particle size which is just elutriatedwhen a particles with a size distribution are ﬂuidized, and the intersection of the same line with the ﬁxed-bed limit

e

_¼

0.4 (S2) indicates the

particle size at which ﬂuidization will break down if agglomeration occurs. The line Ar

_¼

const. through S can be used to find the minimum fluidization velocity at S₃or – as a measure of the upper limit of fluidization – the maximum fluid-izing velocity at S4.

An important practical point is that the state diagram implies a classiﬁcation scheme that

relates various fluidized-bed systems to one an-other [37, 38] (Fig. 5). When a new fluidized-bed process is being designed, the position of the state point in the diagram will identify related fluid-ized-bed systems with potentially similar oper-ating problems.

2.5. Gas Distribution

The gas distribution device must satisfy the following requirements:

1. Ensure uniform ﬂuidization over the entire cross section of the bed (especially important for shallow beds)

2. Provide complete ﬂuidization of the bed with-out dead spots where, for example, deposits can form

3. Maintain a constant pressure drop over long operation periods (outlet holes must not be-come clogged)

Figure 5. Reh’s ﬂuidized-bed state diagram with operating regions of different reaction systems

(10)

Often, the gas distributor design must also pre-vent solids from raining through the grid both during operation and after the bed has been shut off.

Porous plates of glass, ceramics, metal, or plastic are commonly used as gas distributors in

laboratory apparatus; a variety of designs are used in pilot-plant and full-scale ﬂuidized-bed

reactors (see Fig. 6). Many more designs can be found, for example, in [2] and [39].

The principal requirement – uniform distribu-tion of ﬂuidizing gas over the bed cross secdistribu-tion – can be met if the pressure drop

D

p_dacross the gas distribution grid is large enough. Suggested values for the ratio

D

p_d /

D

p_fb are 0.1–0.3 (with a minimum

D

p_d of 3.5 kPa) [40], 0.2–0.4 [41], and

>

0.3 [42].

For a given pressure drop

D

p_dthe gas velocity in the nozzle u_o can be calculated from

D pd

¼

r_o

2



C D



u

2 o

wherer_ois the gas density in the oriﬁce andC _Dis

the drag coefﬁcient. Applying the continuity equation

V:

_¼

N o



Ao



uo

either the number of nozzles N _o or the cross-sectional area of the individual nozzle A_o can be calculated for a given gas ﬂow rate V _.

Problems related to the design of gas distri-butors are attrition of solids (see Section 2.11),

erosion, and back-flow of solids. Erosion may occur at the distributor plate and at neighboring nozzles or walls due to gas jets as well as at the nozzle itself. Back-flow of solids into the wind-box is caused by pressure fluctuations. In order to prevent this either the design pressure drop has to be larger than the pressure fluctuations or – if this is not feasible for economic reasons – a design must be chosen which tolerates short periods of gas flow reversal without permitting the solids to penetrate into the windbox. For the latter case the bubble cap design has turned out to be advanta-geous [43].

In the operation of ﬂuidized-bed reactors, the quadratic response (

D

p_d

_

u2) of industrial gas-distributor designs must be kept in mind, because even if the ﬂuidization velocity is lowered only slightly, an unacceptably low pressure drop across the gas distributor may occur. Industrial experience with different distributor designs, practical design rules, and a discussion of dis-tributor-related problems, such as weepage into the windbox and erosion by grid jets and at grid nozzles, has been compiled in [44].

2.6. Gas Jets in Fluidized Beds

Gas jets can form at the outlet openings of industrial gas distributors and also where gaseous reactants are admitted directly into the ﬂuidized bed. A knowledge of the geometry of such jets, in

Figure 6. Industrial gas distributors

(11)

particular the depth of penetration, is important for the implementation of chemical operations in ﬂuidized-bed reactors, and not just from the standpoint of reaction engineering. It is also vital for reasons of design: the strongly erosive action of these jets means that internals, such as heat-exchanger tubes, must not be located within their range.

The literature contains many empirical corre-lations for estimating the mean depth of jet penetration L (e.g., [2–4]); these must, however, be used with care and, whenever possible, only within the range of parameter values for which they were derived. By way of example, MERRY

gives the following correlations for vertical gas

jets [45]: L d o

¼

5:2 rf d o r_sd p

 

0:3 ₁_:₃ u2 o gd o

 

0:2



1

"

#

ð

12

_Þ

and for horizontal jets [46]:

L d o

¼

5:25

"

rou 2 o

ð

1

_

e

_Þ

r_sg d p

#

0:4

ð

r_f r_s

Þ

0:2



ð

d _dp_o

Þ

0:2



4:5

ð

13

_Þ

Hered _ois the diameter of the outlet opening,u_ois the outﬂow velocity, and ro is the density of the

jet gas.

2.7. Bubble Development

For many applications, especially physical operations and noncatalytic reactions, the state of a ﬂuidized bed can adequately be described in terms of a single quantity averaged over the entire bed, such as the mean bed porosity

e

. In contrast, the design of fluidized-bed catalytic reactors requires that local fluid-flow conditions also be taken into account.

The local fluid mechanics of gas–solid fluid-ized beds are determined by the existence of bubbles, which influence the performance of fluidized-bed equipment in several ways: the stirring action and convective solids transport by the rising bubbles are helpful; the resulting intensive solids motion produces a uniform tem-perature throughout the fluidized bed and rapid heat transfer between the bed and the heating or cooling tubes submerged in it. The bubbles and

the motion of solids that they cause, however, also have some drawbacks: attrition of solid particles, erosion of internals, and increased solids entrainment by bubbles bursting at the bed surface. The existence of bubbles is particularly detrimental in the case of a heterogeneous cata-lytic gas-phase reaction, because the bypass of reactant gas in the bubble phase limits the con-version achieved in the ﬂuidized bed.

The ultimate cause of bubble formation is the universal tendency of gas–solid ﬂows to segre-gate. Many studies on the theory of stability (e.g., [3, 4]) have shown that disturbances induced in an initially homogeneous gas–solid suspension do not decay but always lead to the formation of voids. The bubbles formed in this way exhibit a characteristic ﬂow pattern whose basic properties can be calculated with the model of DAVIDSONand

HARRISON [47]. Figure 7 shows the streamlines of

the gas flow relative to a bubble rising in a fluidized bed at minimum fluidization conditions (

e

_¼

e

mf ). The characteristic parameter is the

ratio

a

of the bubble’s upward velocity u_b to the interstitial velocity of the gas in the suspension surrounding the bubble:

a

_¼

ub

umf =emf

ð

14

_Þ

The case

a >

1 is typical for solids of Geldart groups A and B. The gas rising in the bubble ﬂows downward again in a thin layer of suspen-sion (‘‘cloud’’) surrounding the bubble. An important point for heterogeneous catalytic gas-phase reactions is that the presence of a boundary between bubble gas and suspension gas leads to the existence of two distinct phases (bubble phase and suspension phase) with dras-tically different gas–solid contact.

Figure 7. Gas ﬂow for isolated rising bubbles in the Davidson model [47]

(12)

If

a <

1, some of the gas in the suspension phase undergoes short-circuit flow through the bubble, while only part of the bubble gas recir-culates through the suspension. This type of flow is typical for fluidized beds of coarse particles (Geldart group D).

Under the real operating conditions of a flu-idized-bed reactor, a number of interacting bub-bles occur in the interior of the fluidized bed. As a rule, the interaction leads to coalescence. As detailed studies have shown, this process is quite different from that between gas bubbles in liquids because of the absence of surface-tension effects in the fluidized bed [48, 49].

For predicting mean bubble sizes in freely bubbling ﬂuidized beds, a differential equation for bubble growth should be used in the case of Geldart group A and B solids [50]:

d dh d v

¼

2eb 9p

 

13



₃_ldv_u_b

ð

15

_Þ

with the following boundary condition ath

_¼

h_o:

d v0 m

¼

0:008e1_b=3 porous plate 1:3

ð

V: 2_o g

Þ

0:2

industrial gas distributor

ð

16

Þ

8 >

>

<

>

:

where h_o is the height above the grid where the bubbles form (for a porous plate, h_o

_

0; for a perforated plate, h_o

_¼

L ; for a nozzle plate, h_o is the height of the outlet opening above the plate; and for a bubble-cap plate, h_o is the height of the lower edge of the cap above the plate). V_0 is the

volume ﬂow rate of gas through the individual grid opening.

The local volume fraction of bubble gas

e

_b is given by

eb

¼

V

:

b=ub

ð

17

Þ

and the visible bubble ﬂow V _b is

V: b



0:8

ð

u



umf

Þ

ð

18

Þ

The upward velocity u_b of bubbles depends not only on the bubble size but also on the diameterd _t

of the ﬂuidized bed: where ub

¼

V : b

þ

0:71s_bs_

p

ffiffiffiffiffiffiffi

gd v

ð

19

Þ

b

¼

3:2 d 0:33 t 0:05



d t



1 m;Geldart group A 3:2 d _t0:50:1

_

d t



1 m;Geldart group B



ð

20

_Þ

Outside these limits,



b is taken as constant.

The differential equation (Eq. 15) describes not only bubble growth by coalescence but also the splitting of bubbles (second term on the right-hand side [51]). The crucial parameter here is the mean bubble lifetime

l

:

l

_

280

_

umf

g

ð

21

Þ

In practice, bubble growth is limited not only by the splitting mechanism based on the particle-size distribution of the bed solids, but also by internals (screens, tube bundles, and the like) that cause bubbles to break up. Computational tech-niques for estimating this process are given in [52, 53].

HILLIGARDT and WERTHER have derived a

cor-responding bubble-growth model for coarse-par-ticle ﬂuidized beds (Geldart group D) [50].

An example of a measured and calculated bubble-growth curve is presented in Figure 8.

2.8. Elutriation

When bubbles burst at the surface of the ﬂuidized bed, solid material carried along in their wake is ejected into the freeboard space above the bed. The solids are classiﬁed in the freeboard; parti-cles whose settling velocity u_t is greater than the gas velocity fall back into the bed, whereas particles with u_t

<

u are elutriated by the gas

Figure 8. Bubble growth in a ﬂuidized bed of ﬁne particles (Geldart group A; data points from [54], calculation from [50])

(13)

stream. As a result, both the volume concentra-tion of solids cv and the mass ﬂow rate of

entrained solids in the freeboard show a charac-teristic exponential decay (Fig. 9). With increas-ing height above the bed surface, the ‘‘transport disengaging height’’ (TDH ) is ﬁnally reached. Here the increased local gas velocities due to bubble eruptions have decayed, and the gas stream contains only particles withu_t

<

u. When the TDH can be reached in a fluidized-bed reac-tor, this is associated with minimum entrained mass flow rates and solids concentrations, and hence with minimum loading on downstream dust collection equipment. Design of the dust collection system requires knowledge of the en-trained mass flow rate G_s and the particle-size distribution of the entrained solids. For the design of the fluidized-bed reactor, the distributionc_v(h) of the solids volume concentration and, for gas– solid reactions, the local particle-size distribution as a function of height in the freeboard must be known.

For solids of Geldart group A, the TDH

can be estimated with the diagram shown in Figure 10 [55]. The following relation is given for the TDH of Geldart group B solids as a function of the size d _v of bubbles bursting at the bed surface [56]:

TDH

_¼

18:2

_

d v

ð

22

Þ

Equation (25) was, however, derived for a bench-scale unit and may not scale to plant-size equipment.

The mass ﬂow rate G_s of entrained solids per unit area leaving the ﬂuidized-bed reactor is the

sum of contributions from the entrainable parti-cle size fractions (u_t

<

u):

Gs

¼

X

i

xi



k*_i

ð

23

Þ

Here x_i is the mass fraction of particle-size fraction i in the bed material and k*_i is the

elutriation rate constant for this fraction. The literature contains a number of empirical corre-lations for estimating k*_i (e.g., [2–4]). More

physical-based are the elutriation models of WEN and CHEN [57] and of K UNII and LEVENSPIEL

[2, 58], which enable not only calculation of the exiting mass ﬂow rate but also estimation of the concentration versus height cv (h) in the

free-board. The model by SMOLDERS and BAEYENS

additionally takes the effect of variable freeboard geometry into account [59].

A literature survey on the factors affecting elutriation and the available modeling tools is given in [60].

2.9. Circulating Fluidized Beds

2.9.1. Hydrodynamic Principles

In REH’s state diagram of the ﬂuidized bed [36],

the circulating ﬂuidized bed (CFB) is located above the single-particle suspension curve for

Figure 10. Estimation of transport disengaging height (TDH ), according to [55]

umb

¼

Fluidization velocity at which bubble development

begins Figure 9. Schematic drawing of ﬂuidized bed and freeboard

(14)

Re

<

102and porosities

e

greater than about 0.8 (dashed line in Fig. 5). The shortcoming of this diagram is that it does not show an important parameter in the operation of a circulating ﬂuid-ized bed: the circulating solids mass ﬂow rate per unit area G_s. The diagram of Figure 11 [61] attempts to remedy this by plotting the mean slip velocity u_sl between gas and solids

usl

¼

u e

 ð

Gs=rs

Þ

1

_

e

ð

24

Þ

versus the mean solids concentrationcv

¼

1



e

,

with G_s as the parameter. The limiting condi-tions are high solids concentration (bed at mini-mum ﬂuidization) and c_v

_!

0 with u_sl

_¼

u_t

(isolated single particle). In the circulating flu-idized-bed region, slip velocity increases with increasingG_s and can become much higher than the single-particle settling velocity (the physical justification for this statement comes from the formation of strands or clusters of particles). In the entrained-flow region the slip velocities again decrease with decreasing solids concen-tration.

The ﬂuidized-bed state diagrams discussed thus far, as well as others (e.g., [62, 63]), are suitable mainly for the qualitative interpretation of ﬂow phenomena. A diagram proposed by WIRTH (e.g., [11, 64, 65]) also provides

quantita-tive assistance in the design of circulating ﬂuid-ized beds. The schematic in Figure 12 applies to a given gas–solid system described by a constant value of the Archimedes number Ar . The ordinate is the dimensionless pressure drop of the ﬂuid-ized bed

y

_¼

D p

ð

r_s



r_f

Þ ð

1



emf

Þ

gDh

ð

25

_Þ

the abscissa is the particle Froude number

Fr p

¼

u

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðrsrf Þ

rf gd p

q

ð

26

Þ

The dimensionless pressure drop

y

is the ratio of the pressure drop

D

palong the ﬂow path

D

hto the maximum possible value for ascending flow (the value that would be attained if the pipe cross section were filled with solids corresponding to the concentration at the minimum fluidization point). The parameter of the family of curves is a volume flow rate ratio

mrf

r_s

ð

1



emf

Þ

ð

27

_Þ

where

m

is the ratio of solid-to-gas mass ﬂow rates. The limiting curve bounds the region of stable, vertically upward gas–solid ﬂow on the low gas velocity side.

Figure 13 shows how the state diagram of Figure 12 is constructed for a circulating fluid-ized bed with siphon recycle. If solids holdup in the recycle line and siphon is ignored, this case represents operation with a constant bed mass independent of velocity. At high gas velocities and if acceleration effects are neglected, the bed material is distributed uniformly over the total height H _cfb of the fluidized bed (Fig. 13 C). The circulating fluidized bed then exhibits a single steady-state section with a constant pressure gradient (

D

p /

D

h). This pressure gradient can be calculated from the bed mass as

Figure 12. State diagram for the circulating ﬂuidized bed with siphon, according to WIRTH [64]

Ar

_¼

const.,parameter of family of curvesis the volume ﬂow rate ratio m rf /(rs (1



emf )); Fr p

¼

particle Froude number

for superﬁcial minimum ﬂuidization velocity (pumf ),

single-particle terminal velocity (pt), and transport velocity (pT), respectively

(15)

y _hom

_¼ ð

rs



rf

Þ

g H mf

ð

1



emf

Þ

ð

r_s



r_f

Þ

g H cfb

ð

1



emf

Þ ¼

H mf

H cfb

ð

28

_Þ

where H _mf is the bed height at minimum ﬂuidization.

The states identiﬁed by

y

homto the right of the

bounding curve in Figure 12 are accessible by increasing the gas velocity (corresponding to increasing Fr _p). With increasing Fr _p the volume ﬂow ratio increases; that is, relatively more solids are elutriated (and thus circulated).

If Fr _pis allowed to drop below the limit Fr p_max

(Fig. 13 B, Fig. 12) two steady-state sections appear in the riser tube: the one in the lower part is marked by a high pressure gradient, that in the upper part by a lower gradient. Figure 13 illus-trates the physical signiﬁcance of these two pressure gradients. In practice, the transition between the two linear regions takes place grad-ually. The height of the transition zone corre-sponds to the transport disengaging height (TDH).

The picture changes further if the gas velocity declines to values lower than the settling velocity

u_t of a single isolated particle. In this case (for

Fr _p

<

Fr _pt, Fig. 13 A, Fig. 12), no more solids can be elutriated, and the pressure gradient in the upper linear region vanishes. All the solid mate-rial is now in the form of a bubbling or turbulent ﬂuidized bed.

The solids concentrations averaged over the tube cross section (1

_

e

) can be calculated from the dimensionless pressure drop:

1

_

e

_{¼ ð}

1

_

emf

Þ 

y

ð

29

Þ

Besides the pressure and solids concentration pro-ﬁle, thecirculating mass ﬂowrate of solids G_s

_

A_t

is important for the design of the circulating fluid-ized bed. In particular, the design of the solids collection and recycle system depends very much on this quantity. The mass flow rate of solids depends on the flowregime. At gas velocities such that twosteady-state sections arepresent in the bed vessel (i.e.,Fr _pu_mf

<

Fr _p

<

Fr _pT), the mass ﬂow rate of entrained solids depends on the physics of the gas–solid ﬂow. Figure 14 plots the

Figure 13. Pressure proﬁle in the circulating ﬂuidized bed with siphon, according to W IRTH [64]

A) Fr pu_mf < Fr p < Fr pt; B) Fr pt < Fr p_max; C) Fr p > Fr p_max

Figure 14. Elutriation diagram when the circulating ﬂuidized bedcontains two steady-state sections, according to WIRTH[64]

(16)

dimensionless solids mass ﬂow rate versus Fr _p, with the Archimedes number as parameter. For a given Ar , the ﬂow rate tends to zero asFr _p

_!

Fr _pt

and reaches a maximum atFr _p

_¼

Fr _pT. The slope of the elutriation curve becomes greater with increasing Ar ; that is, the coarser the particles, the greater is the relative change in the circulating mass ﬂow rate of solids with a change in gas velocity.

At high gas velocities in the circulating ﬂuid-ized bed (i.e., when a single steady-state section exists), the entrained mass ﬂow rate depends on the particle Froude number and the solids holdup. More detailed information about the application ofWirth’stheoryinpracticemaybefoundin[11].

Whereas WIRTH’s analysis of the circulating

ﬂuidized bed starts from the pneumatic transport condition, the models of RHODES and GELDART

[66], as well as K UNII and LEVENSPIEL [2, 58], are

based on the bubbling ﬂuidized bed and describe the circulating ﬂuidized bed as a limiting case of a bubbling bed with a very high rate of solids entrainment.

2.9.2. Local Flow Structure in Circulating Fluidized Beds

The Wirth state diagram, as a first step toward the local characterization of flow regimes in a circu-lating fluidized bed, describes the vertical profile of the solids concentration. In the lower section of a circulating fluidized bed a dense region exits near the gas distributor. It has been observed that in this bottom zone bubble-like voids coexist with a surrounding dense suspension. The solids volume concentration is higher at the wall (c_v

_

0.4) then in the center (c_v

_

0.15) of the bottom zone [67]. The splash zone which links the bottom zone to the upper dilute zone is charac-terized by violent gas–solid mixing. Many recent experimental studies with various measurement techniques (e.g., X-ray tomography [68], capaci-tance tomography [69] and fiber-optical probes [70]) have shown that the upper section of the circulating fluidized bed exhibits characteristic horizontal profiles, with the concentration c_{v, wall}

near the vessel wall always signiﬁcantly higher than the value cv averaged over the vessel cross

section; for example, cv, wall

¼

2.3



cv [71].

Local measurements of the solids concentra-tion and solids velocity show that

upward-flowing regions of low solids concentration and downward-flowing aggregates of high solids concentration alternate in time at every point inside the fluidized bed, with downward-moving aggregates (strands, clusters) predominating near the wall and upward-moving regions of low suspension concentration predominating in the central zone. However, no significant downward flow of solids near the wall was observed in high-density circulating fluidized beds, e.g., [72]. The picture of the local flow structure in a circulating fluidized bed, as derived from these observations, is shown schematically in Figure 15.

A modeling approach which is based on the local flow structure of the CFB is the energy-minimization multiscale (EMMS) model [73]. It considers the tendency of a fluid in a gas–solid two-phase flow to pass through the particulate layer with least resistance and the tendency of the solids to maintain least gravitational potential. Least resistance means that the volume-specific energy consumption for suspending and trans-porting solids is minimized, and minimization of the gravitational potential is equivalent to the requirement that the local mean voidage

e

attains a minimum. The model has been applied as a description of fluid-mechanical phenomena in CFB risers of different sizes [74, 75] but also for the prediction of flow patterns of gas and solids in industrial-scale units, such as a CFB boiler [76] and a petrochemical processing unit [77].Another promising line of development is the introduction of the EMMS concept into computational fluid dynamical calculations of multiphase flows; first results obtained with a drag model based on the EMMS model are encouraging [78].

Figure 15. Schematic diagram of ﬂow structure in a circu-lating ﬂuidized bed

(17)

2.9.3. Design of Solids Recycle System

Solids carried over with the ﬂuidized gas are generally collected in cyclones. In the case of

bubbling beds, the solids can easily be returned to the bed through the standpipe of the cyclone, which dips directly into the bed.

Due to the large amounts of circulating solids,

circulating fluidized beds require very large cy-clones arranged beside and outside the bed, with special ‘‘valves’’ needed to connect the standpipe to the bed vessel. Figure 16 shows two design options, the siphon and the L-valve. With the siphon, the solids are fluidized (i.e., enabled to flow back into the reactor). In the L-valve design,

the mass ﬂow rate of the solids can be regulated by varying the gas supplied to the standpipe.

Because the solids path does not contain any sortof mechanical closure, the characteristic pres-sure distribution plotted in Figure 17 is obtained. The distribution of solids between the ﬂuidized bed and the recycle line is directly related to this pressure distribution. Operating properties differ from one recycle design to another [79].

2.10. Cocurrent Downﬂow Circulating

Fluidized Beds (Downers)

A certain drawback of circulating and bubbling fluidized beds when applied for gas-phase reac-tions is the backmixing which inevitably occurs in the gas phase. In bubbling fluidized beds it is the bubble-induced solids circulation, and in circulating fluidized beds the downflow of solids in the wall zone, which entrains gas in the upstream direction and thus lowers the yield of a catalytic reaction or gives rise to undesired consecutive or side reactions. These disadvan-tages caused by the hydrodynamic effects of both gas and solids flowing against gravity could be overcome in the so-called downer reactor, in which the flow directions of both gas and solids are downward, i.e., in the same direction as gravity [80]. Another incentive is the possibility

Figure 17. Pressure distribution in solids recycle system of a circulating ﬂuidized bed a) Fluidized bed; b) Return leg

Figure 16. Design options for solids recycle A) Siphon; B) L-valve

(18)

of realizing short contact times between gas and solids of around or even below one second.

Downer systems have been intensely studied [80]. Hydrodynamics [81, 82], gas mixing [83], and solids mixing [84, 85] have been investigated both experimentally and by numerical simulation [86]. It has been found that the hydrodynamics of the downer are also characterized by a wall zone of increased solids concentration. However, axial and radial gas-solids flow structures are much more uniform than in conventional fluidized beds. Another result is that the length of the flow development zone is much shorter for the downer than for the riser, which means that reactions with very short contact times can be carried out under near-plug-flow conditions. However, the solids feeding process and the geometry of the entrance region are critical points that deserve special attention [87].

The patent and open literature suggest various applications for downer reactors, e.g., residual oil cracking [88], coal pyrolysis [89], and biomass pyrolysis [90]. The catalytic pyrolysis of heavy feeds for the production of light oleﬁns has been investigated on the laboratory scale with prom-ising results [88]. However, no large-scale indus-trial process has emerged yet.

2.11. Attrition of Solids

The attrition of solid particles is an unavoidable consequence of the intensive solids motion in the ﬂuidized bed. The attrition problem is especially critical in processes where the bed material needs to remain unaltered for the longest possible time, as in ﬂuidized-bed reactors for heterogeneous catalytic gas-phase reactions. Catalyst attrition is important in the economics of such processes and may even become the critical factor.

Catalyst attrition in ﬂuidized-bed reactors occurs normally as surface abrasion (Fig. 18) which means that surface asperities are abraded and edges of the catalyst particles are rounded off. Fragmentation may also play a role, espe-cially for some fresh catalyst particles which on entering the reactor may simply be crushed into pieces. If in an industrial process extraordinarily high catalyst losses are observed it is advisable to examine catalyst samples under the scanning electron microscope. If the sample contains many fragments this could be an indication of

a wrong design (e.g., too high a velocity at the cyclone inlet or at the distributor).

When designing catalytic fluidized-bed pro-cesses, the attrition performance of candidate catalysts should be tested under standardized conditions in the process development stage. This test can be performed in a small laboratory apparatus; it consists essentially of an extended fluidization test in which the mass of solids carried out of the bed is recorded as a function of time. Figure 19 presents a typical test result: during the first hours of testing, both the attrited material and the fine fraction of the bed material are elutriated. Only after a relatively long oper-ating period is a quasi-steady state attained. The

Figure 19. Result of an attrition measurement

Figure 18. Attrition modes and their effects on the particle size distribution (q3

¼

mass density distribution of