Chapter -8-Mixing of Fluids

8/13/2019 Chapter -8-Mixing of Fluids

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lMirinq l Fluids 285

ChapterightMixing f luids

Levenspiel l consider.ed hen two fluids are nlixed rogelher, hemolecularbehaviorof the dispefsedluid falls between wo extremes.If moleculesare completely tiee 1o movc about, the dispelsed luidbehaves s a microfluid and exhibits o flr id segregation. t theopposileextreme, he dispersed luid remaiDsas clumps coitai ng alarge nu ber of lnoleculesand is termeda n1acrclluid.Fufihermore.as the macfofluid is transfbrmed o a nicrofluid by physical mixilgprocessese.9., urbulelceor noleculat diffusion), he degreeaDdscaleof segregalion i.e., thc averageof lie seglegaled lumps)decrease.An importantnlixiig opelatioll nvolvcsbringingdjflerent noleculai.species ogether o obtain a chemical eaction.Thc compoDentsmaybe miscibleiquids, mmiscibleiquids, ol idparticles nda l iquid.agasanda l iquid,a gnsandsolidpadicles. r two gases.n some ases,temperaturcditlerencesexisl betweenan equipmcntsurfaceand thcbulk fluicl,o[ between he suspendedartic]es nd the continuousphasc luid. Thc samemcchanismshil t enhancemass ransi-er yreducing he fi lm thickness re used o promotcheat translerbyjnc.easingthe tempcrat lre gradient r the tlim. Thcsemechanisms rebulk flow, eddy diffusion, ard moleculardilTusion.The pedbrnanceof equipment n which heat tLansfeloccurs s expressedn terms oftbrced convecliveheal tansfer coefficients.This chapler revie\ls the various ypes of impellers, he flow pat-terns gerleraledby theseagitatols, corelation of the dimensionlessparametersi.e.,Reynoldsnumber,Froudenurnber, nd powernumber).scale-up f lnixers,hea ransfercoef{icicl tts f. iacketedagilatedvessels,and tl'ie time required or heatingor cooling thesevessels.MIXING AND AGITATION OT FLUIDS

N4anyoperationsdepend o a great extent on eifective mixi[g offluids. Mixing ref-ers o any opelationuscd to charrgea norr-urlilbfmsystem nto a ul l i form onc (i.e., he ral ldomd;stribution f two ornTolerl i t ial lysepalated hascs): girarionmpljes orci lg a l luid byDechanicalmcensto llow in a circulatoly of other pattetn insidc avessel.Mi\ing is an integrai pallt of cheDical or physical processes


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286 ChemicalEnglnee g Processes

such as blending, dissolving, dispersion,suspension, nltlsification,heat transfer.and cheJnical eactions.Dispersion characteristics all be considerecl s the nixing of twoor more immiscible licluids, solids and liquids, or liquids and gases,into a pseudo-honogeneotsmass.Snall drops a.e created o provideoontactbctween mmiscible iquids. These iquids a.e lnixed forspecific purposes,namely solvont extraction. removal or additior ofheat,and o affect mass tansfer atesh reactors.The terlns dispeftionand emulsion are often used nterchangeably. ispersion s a generalterm that implies dislribution, whereasemulsion s a special case ofdispersio[. Dispersion is a two-phasemixnue in which drops maycoalcsce.The mate al present n a larger quaniity is referred to asthe continuousphaseand thc materialprcsellt n a smallerquantity iscajled he dispersed hase.An emulsion s a Lwo-phase ;xturc ol veryfine drops in which littlc or no coalescence ccll.s. The stability ofan emulsion clepends n surface on activity, which is a function ofparticle size. Colnmon dispersionsare water ard hydtocatbons,andacidicor alkal iDe olul ions ombiledwilh oryanic iquids.Table8-1summarizes he prircipal purposes or agitaling Iluids Coker[2].

AGITATION EQUIPMENTVarious ypes of vesselsand tanks of differing geometricalshapesand $izesare used for mixing fluids. The top of the vessel may beopen or sealed. he vesselbottom s nornally not l'lal

Table 8-t

Characteristicsor agitating luidsBlending f 1womisciblc , f n isclble iquids.Dissolvins ol ids n l iquidr .Dispersnrga gas in a lntrid ds fine bubbles(e.g.,oryscn f.on air in a suspen-sion ol micfoorgaDisB1br fenneotationor lor aclilrled sludge reatmen0.Agitation ol the lluid o increase ear tfaDsferbclwccn lhe llltid and a coilSuspension f finc solid pr jcles in a lrquid, such as in lhe caralyric hydro-gcnalionof a liquid wlreresolid catilysl and hydrogenbubbles arc dispcrscdjn the liqrrid.Dispcrsion f droplcls f one nmi$cible i . lu id n anorher e.g. . sonebcrerogeneouseaciion proccssof liquid huid exrfactio,r).

L2 .

i .

6.


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but roundedo eliminate hary o.ners t regionslrto which he luidcurents would not penetrate; ishedends ate most common.Theliquid depth s approximately qual o the dianeter of tle tank.Animpellers molLntedn anoverhung h,Lft,i.e.,a shaftsuppoted romabove). heshaft s motordriven; his s solEtimesdirectlvconnectedlo lhe :harl.brrr . rrr, 're flenconnecled.lh,' ,ughspeed-.eciucinggearbox. therattachmeDtsncludenletandortlet ines,coils. ackels.and wells or thermometers.iigure8-l showsa typical standardank

IIIFigure8-1. Siafdard ank contiguraiion.


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288 Chemical ngineeingPfocessesconfiguration. The geometric proporlions of the agitation system,which are considered typical standard esign are given in Table 8-2.Theserelative proporlions orm the basiso{ dle najor corelations ofagitation p(-Ifornlance rom various studres.There are cases where WDa = 1/8 and J/D r = l/10 fol someagitator correlatiols. Usually,4 baffles are used aod the clearancebetween he baffles and the wall is aboutq.l-0.15 J. This ensures hatthe liquid does not form siagnantpocketsbetween he balfle and thewali . The rumber of impellel bladesvaries rom 4 to 16, but isSenerallybetween6 and 8.Mixilg by agitation of iiquids normally involves the ffansfer ofmomenlum fton ao impelle. lo the liqllid. In some cases,mixing isachievedby gas injectioll or circulation via a pump loop. An jrnpeller,which is mounted or a shaft ddven by an elcctric ilotor, is dividedinto two operation categories:

Where monlentltln s t.ansferredby shearing tresscs,D which thetransfcr is perpendicular o the direction of flow. This caiegoryi nc l ude ' he fo ts { i ng iccandcone . rg i t r to r s .The momeltun is translerredby l1orma] stresses,n which thetransfer s parallel to thc direction of flow. This categoly ncludesrhepudd le . ro f ' e l l e r .nd l r r rho n i \e rag i l r t o r s .

Table8-2Geometric roportionsor a standaad gilalionsystemD o ID r 3

J 1DI 12L 1D e 4

Dr.w lD,r 5

B = numbef of blxdcs on lmpeilerR = number oi b:rftlesDA = agitator dianleterH - l iquid heichtDr = irnk diamclerE = heigh of lhe agiiator frcm thc botton ol fte tankJ = baffle widthL = agitalor blade lenglh

W = agirator blde width


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but roundedo eliminate h$p comersor tegionsDto whichthe luidcurrentswould not penetrate; ishedendsare most common,Theliquid depth s approximately qual o the clianetelof the fank. Arirnpellers rnounted n an ove rungshaft, i.e.,a shaftsupportediomabqve). heshai is motordriven; his s sometimesirectlvconnectedlo the hrft. bur s moreolreacunnected.l luough.peed educinggearbox.OtherattachmentsDcludeinletandoutlet ines,coils. ackets.andwe l l s o r he rmomerHr . .i gu re - t snou . l ) p rc i r lt r ndudrnk

-+lrfe"m"

Figurea-1. Standardank configuration_


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Agjtation plays an essential oLe n the success f many chenicalprccesses nd herc s a wide range f cornmerciallyvailablempellersthat canprovide he oplinun degree l agitalion br any process. heproblemarises n selecting he best l11peliefor the requitedpr.ocess.Equipment mentfacturersoften provide expert guidance.bul it isbenelicial or designersndengineerso acquireund4mentalilowledgeof various ypes of impeller's. he process bjectiveof an impeller sthe primary factor that detennines ts selection.These objectives,summalized n Table 8-1, togetherwith physicalpropertiessuch asviscosib'pla),an mportant ole n the selection f jftpellersin lamimr,transiiional. and turbulent operations. n genetal, mpellers can beclassilied nto two main groups.Impellers wilh a small blade area,which rotale at high speeds.These nclude u.bines and m4,ire propellers.Impellers with a large blade arca, which rolate at low speeds.These ncludeanchors,paddles, nd helical sdews-

The lelter nrpelle.sare very effeclive or high-viscosityiquids anddependon a large bladearca o pruduce iquid rnovemenl hrougholrtthe vessel.Since they are low-shear mpellers, Jreyare useful fornixing shear hickening iquids.Figure8 2 showsa typicalgateanchofagitator.ADchoragitatorsope.ate ely close o the vesselwall with aradial clearaace qlLalo 0.0275DA-The shearing ctionof the irnchofbladespast he vesselwall produces coltinual interchange f liquidlretweer he bulk liquid and lhe ljquid film between he bladesandthe wall. Fol heat traNfer appiications, nchorsare fitted with wallscrape.so prevent he blLildupof a slagnanl ilm between he anchorand the vesselwall. The anchor nrpeller s a good blendingand heattransl'er evicewhen he fluid \, iscosity s between5.000 and-50,000cP (5 and 50 Pas).Belo\,\'5,000 q there s rot enoughviscousdragat the ank wall to promoiepuolping. esulting n a swirling condition.At viscosities reater han 50.000 P (50 Pits),blendingand heatt.ansfei capabilitiesdecrease }spumpingcapacily declites and theimpeller "slips" in the fluid.Helical scrcwsoperaten the aminar ar,ge t nor]nallyhigh mpelle.to vesseldialneler ratio (DA/Dr) with a ladial clexranceequal to0.0375DA. The impeller usuallyoccupies ne-third1()one half of rtrevesseldiameter. hey functiorrby punping liquid frorn he bot|olnofa lank to the liquid sufnce. The liquid returns o the bottom ot the


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290Chemicl ngineeringrocesses

Figure 8-2. Gale anchoragitator.(SourcerHo and, F. A. and Bragg, R.FluidFlow or ChemicalEngineers, nd ed., Edwad Arnotd, gg'.)

tank to fill the spacecreated I/hen resh liquid is punped to thesurface.Figurc 8-3 shows he flow patternn a baffledheiicalscrewtatrk.Bafflesset away lom the anl(wall create urbulence nd, hus.enhancehe eltrainmentof liquid io contactwith the tankwall. Theseare not required if the helical screw s placed n an off-centeredpositionbecausehe system ecomeself-baffling. hese mpellers reusetul n heat translerapplicationwhen t is essentialhat rhe fluidclosest o the wall rnovesat high velocities.Turbulent npellcrs are classif'iecls axialor radial flow impellers.Axial flow impellers cause he tank fluid to flow parailei to thejmpeller's otation axis.Radial low impellerscause he tankfluid to


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\_/

Figure8-3. Flowpaftern n a bafited eiicalscrew yslem. Source:Holand,E A. and Bragg,R. Fluid Ftow or ChenricalEngjneers, rd ect.,eAwari

flow perpendicular o the irnpelier's totation axis. Small blade.hiehspeerJmpr l l e r . re \ed ln rn i \ l ow tu meLL i r rmi . . , , , i t r l i qu idsf i gu re . 4 n J 8 -5 . e . l ec t e l ) . sh . rud le i \ , t h r b l rde u rb in ( ,udmanl1epiope]ler type agitzttols.Figure 8 6 shows flat blade turbinesused o produceradial flow patternspetpendicula. o the vesselwall.In contasr, Figure 8-7 depicasma ne-type propellerswith axial flow


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292Chemical ngineeringrccesses

Figufe 8"4.Six tlat blade urbine. Source:Ho and,F A. anclBrcgg,R. FtuidFlow or ChemicalEngineers, nd ed., Edwad Arnotd,1995.)

Figure 8-5. Marine propeller (Source:Hoqand, F-A. and Bragg, R. Fluid Ftowfor ChemicalEngineers, rd ed., EdwardArnotd, 1gg'.)


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Mixing fFluids 293

( ) 't )

( - -\ \ )

r \\l// , ' \1^r -Figure 8-6. Radial flow patiern prodLrced y a flat blade iurbine. fsourcelHalland, E A. and Bngg, R. Fluid Flow for ChernicalEngineers,2rd ed.,Edwatu Anold. 1995.)

Figure 8-7, Axial llow pattern produced by a marineHoland, E A- and Bragg, R. Fluid Flow ior ChemicalEdward Amoki, 1995.)prcpetteL (Source:Engineerc,2nd ed..

r-=\

I?) l

I. \ l4'


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294Chemical ngi.eeringProcesses

patterns.Both of these ypes of impellersare suitable to mix liquidswith dynamic viscositiesbetween 0 alld 50 Pas.Severalmetl.]ods fselectingan impelier areavailable 3,4]. Figure 8 8 sl.rows ne methodbased on liqlrid viscosity and tank volume, and Table 8-3 illustratesanother basedon liquicl viscosity alone.Axial ilo$, devices such as l gh efiiciency (HE) impellers anclpitched blade tlrbines give better perfoinance than conventionalpitched blade turbines.They are best suited to provide the ess(]ntialflow patternsn a tank that keep he solids suspended. igh-efiiciencyimpellers cffectively convefi lnechanical energy to verticai flow

101 102oo 101

x

-J

10"

10"104103

102. l

1to"l 0z

1n ;

10u -

-710-rol loz io3 /


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lvliting f Fluids 295

taDte 6-JImpellerselectionguideType of impeller Range oI l iquid,CP Viscosity,kg/m - sec

r 0 r - 2l o 3 t 0 'l0-r 3 x 10'l o j - 3 x i o r ioo l0 l3 3 x l 0 'l o r 2 x 1 0 1S.urte: HalLa.l, F A., atu Chdprrr, t: 5: Liqlii lvlixingand Pro.ossingI StifiedT.Dks.Reinhold, .r' tut+, 1966

t02 2 x to ll0u 104l o u - 3 x l O a10'? 3 x lo jroj lo53 x i o r 3 x l di 0 " - 2 x i 0 "

required to overcome fhe elTects of gravity on solids iD sus-pension.They also plovide the same evels of solids suspensionatrcduced capital and opelating costs.FLOW PATTERJ\

In fluid .rgifation, the direction as well as the mngnitude of theveloc;ty is c tical. The dilections of the veiocity veciors rhroughoutan agitatedvesselare.eferred o as the flov patteln.Since he velocitydisi bulion is constant n the viscousand turbulenl ranges, he flowpattem in an agitatedvessel s fixed.During the mixing of fluids, it is essential to avoid solid bodyrotation aDda latge cerrral su*ace voltex. When solid body routionocclus, adequatemixing is not achievedbecause he fiuid rotates asif it were a single ass as shown in Figure fl-ge. Centrifugal brce ofthe fluid cnusesa cenfal surlace vortex fo be thrown outward by theimpeller. Entrainrrent of ai. rcsu1ls f the vortex reachesar irnpeller,reslrlting jn rcduced mixing of the fluids. This 'ituation can be aveftedby insralling balfles or the vesselwalls, which impede rotaliotal flowwithout interfering with radial or longitudinal flow. Effective bafflingis attainedby installjng vertical stdps peryendiculal o the wall of fhetank. Witi dre exceptionof large tanks, four baffles are adequate opreventswi.ling and vorLex ormation.For ptopellers, he width of thebaffle should be less ore eighteenth the diameter of the tanki fol


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Figure 8-9.Agitalor lowpatterns.a)Axialor radial mpeilers ithoutbafilesproduce ortex. b) Ofi-centerocation educeshe vortex. c)Axial mpellerwith baifles. d) Radial mpellerwith baffles. Source;Walas,S. M., ChemicalProcessEquiprnent-Selectionnd Design,Bulterworths eries n ChemicalEngineering, 1988.)

296ChemcalEngrneergProcesses

turbines, ess one-twelfth he tank diatneter.Figure 8-9 shows hevarious low pattertrs f radial and axial impellers.Reducingvortex lbrmation ll1ayalso be aohieved y placinganimpeller n an oif-centerposition.This createsan unbalancedlowpattern, educingor eliminatilg the swirl andthereby ncreasing rnaximizing the power consumption. he exactposition is critical,since oo far or too little off-centern olredirectionor the otherwillcausegreaterswirling,erratic vortexing,and dangerously igh shaftstesses.Changesn viscosityand anksizealsoaffect he flow paftemin suchvesseis.Off-cenlermountingol radial or axial flow impellersis readily employedas a substituteor baffled ank ostallations.t iscoilmon practicewith propelie.s, .lt lesswith turbiie agitators.Off-certer nlounting can also be useful for a turbine operated n thernedirnn iscosity angeand with non-Newtonianluids wherebafflescausestagnatioowith little swirl of the fluid. Off ceniern:lountir1gshavebeenquiteeffective n the suspetrsionf paperpulp-Figure8-10illu$trates n angularotT-centerosition br ptopellers,wl'i ich seflectivewithouiusing ballles.


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Fig re 8n0. Flowpalternot prcpe erc in an eccenlricaig e and off-ceniered


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296ChemicalEngineering rocesses

Once swirling stops, he spccil'jc flow pattcrn in the tank dependsor the type of impeller. Paddlc agitalors and tlat-blade tLrrbinespronote good radial los' in the plancof t he in1peller i ih the flowdividillg the wa11o fblm two separare irculiition parterns Figure 8 6).One portion tlows down along the wall and back ro thc center of theimpellcl' fron below, and the other flows up toward the surface andback to the inrpeller fiom above. Propclle. agitators drjve the liqlriddown to lhe bottom of tlte tank. whcrc the streamspreads adiall1, nall dircctions owatd tlie wall, flows upwa along l.tewall, andretumsto ihc suction of the propellet lion the rop. The earlier Figure 3-7shows he flow patte.nol a propelleragitator.Propellersa.e etnployedwhenbeavy sol id particles re suspcnded.Table 8 4 shows flow patternszlndapplicationsol sone corn-mercially available lnpellers-Generally, he axial 1'lowpatlern is moslsuitable lor llow sensjtiveoperation such as blending. heat transfer,alrd sol ids suspensionwhile the radial l low patrern s ideiLl ordispe$ion opcrations hat require highet shear evels thao areprovidedby axial f low impcllers.Myers el al. [5] hale described selectionof ilnpellcrswi h applications. llftlrerdettils on sclcctionareprovidedby Uhl and Gray f6l, cates et a1. 7l, Hicks et al. l8l and Dickey [9].POWER REQUIREMENT FOR AGITATION

The flow mechanisnr n a ni,\ing tank is very conplex. Va.ioustechniques,ncludirg computarioil4l luid dynamics CFD) and compu-tationirl luid miring (CFM) tools, are enployed togetherwith cxperi-menlal date to eslablish ntpfovelnei]ts n mixing \.vith ncreesed ield.Estimating tl'ie power consumptiotl for any agitator is essential otclesign.Cenerally, he desired equirements br-thesystem o be ixedwill categorize he type of i1npeller o be used. Laboratory tests onthe system can estabiish le ilppropriatespeeclbf the maintenanco t'isotropic urbulencen the nixing vessel. herefore. stimaring hepower consumplioll for a large-scaiemixing operation must inclLrdescale-upconside.ations.These requirementsmay bc detemlined ftomthe Narier-Stokes quation l analyzecly a dimensiolalanalysis fthe mixing opeiadon.The powerconsuned y an agitalor epends n i ls dinensions ndthe physicalproperties l lhe fluids being mixed (i.e., densityandviscosity). Since there is a possillility of a gasliquid sur-facebeing


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Table 8-4lmpellersand flow patterns

S. rce: Mrers, K., .t .1., Asrd,t,n Jdr ,' ..esi lhe Chemical rlsineer. Oct. 10, 1996.Rrpn.luced with pernisi.n' of tch.rtE

4qjnFfu'b95dipldi '

Dffi;Il ;da ' e6o

d 4 ;@'brtrbkhe fd=3 o

' { ' d N " q , h D 4 * & d

ffit " - l

ffirlijl44,


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300ChemicalEngineegProcessesdistorted,as in the fomation of a vorlex, g.avity forcesmust alsobe considered.Consider stired tank vessel avitrga Newtonianiquid of densityp and viscosityp is agitaaed y an impellerof diameterDA, rotatitrgat a rctational speedN. Irt the tank diarneterbe Dr, the impellerwidthW, and the liquid depthH. The powerP required or agitationof asingle-phaseiquidcanbe expr-esseds:

P = f(p', pb,N', go,Di, Df, wc, HfTherc are nine variablesand threeprimary dimensions,and hereforeby Buckinghan's heorem,Equation8,1 can be expressed y (8-3)dimensionlessroups.Employingdimensiotalanalysis;Equation8-lin termsof the thlee basicdimensionsmassM, length L, atrd imeT) yields:Power= ML2T 3.Substitution t the dimensionsnto Equation8-1 gives,ML2r-3= f{O4L 3)",(Ml--r1r;t, r, (LT*"f, L., Lr, Lc, Lhl (8-2)Equating he exponents f M, L, and T or both sidesof Equatioo8-2 gives

' (s )

M: 1=a+bL : 2= -3a -b+d+e+f+g+hT: -3 =-b c-2d

From Equation7-3

SubstitutingEquation8-6 irto Equarior8-4 gives2=-3 ( l -b ) b+d+e+f+g+h5=2b+d+e+f+g+h

From Equation8-5

b=3 c-2d , o r

(8-3)(8 4)(8-5)

(8-6)

(8-7)


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c=3 -b -2dFrom Equation 9-7

e=5 -2b -d f g -hSubstitutirg a, c, and e on the right side.of Equatipn 8-1f = f(Ot o, pb, N3-b 2d,gd, D5 2b-d-r-c-h,D+, Wc, H

Rearrangingand grouping the exponents ields,

p=xlorjol -u-l 't g-l '[ ,)'( * )-t'-"

(8-8)

(8-9)yields

n){r-ro)

Il (8-1r)I

-P =-ll u )"f r ffq,)'r*ff "t'l,ot="j tpNl6tri,^ tD^ %J o^ J c')The dimensionlessarametersre:The Power u.b.r. N" = .lg:. gL - drmen.ronalg rav i ta t ionx lons l rn t

:z.,ro.fT. t,tDr sec-I kg ' rn41 ' '""2

The Revnoldsno-b".- No" = PMitl. - N ,D ,The Froude number. Nr, = c


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302Chemical ngineeringro@sses

Substitutinghesedimensionlessumbersnto Equation8 12yields,oo,{^..:*+l(#)'(r+)'} (8 - 3 )SIMILARITYEquality i i l groupsn Equation -13assuresimilarity etweensystensof dilferentsizes.The typesof similarity are geometdc,kineinatic, nd dynamic. he ast hrce ermsof Equation ,13representthe conditions tor geometic simil(rrity, whrch require that all cor-respondingdimensionstr systemsof djfferent sizeshave the sameratio to eachother.For geometficsimilarity,Equation8 13 becomesNp = KNR: NFrd (8-14)The constant K and lhe exponellls Ll and d must be determined forthe llarticular type ol agitator, its size aDd locatiol in lhe tank. thedirrensionsof t l le tank. and the depft of thc l iquid.Kinc Ntit- l i //r i lddal,cxists bot$ccl1 wo srsteJlsul di l fereal sizcs*be]] the_\ fe gcontctfical ly inri lararid lhen the rl i t ios ]1 elocit iesbetween or]lsfondi[g ]toir1l n one systenr rc cquitl o those n theother.D|nLonic sinlilLlitj, exists betweel two systems when, in additionto being geometdcally and kinematically similar, the mtios of forcesbetween consponding points in one system are equal to fhose n the othel.The value of NR" determineswhether he flow is lrr;ti:ll| r:r lrtrbLrlrntand is a significant group alfecting the power.consumption.The

Frordc number N",, representing he ralio ol-iI1ertial to gravitalionallorccs, is only significant when the liquid in the tank swhls to suchan extent that a deep vortex is formed and the wave or surfaceeffectsbecome impoflant. In an unbaffled vessel, a balance between theinertial and gravitational forces detemtines the shape of any vortex.The Po$c| nurnbe|N,, may be consideledas a,i | : i rr, i l - l j r i1]l i 1r 'i l r ' .1- : : , i : , . : : r r - ,Experimeutal ata on powet consumption re generallyplottedasa l'u[ction of the PowernumberNp versusReynoldsnumberNR., hatis by rearangirgEquation -14.


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o=$4=r


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304Chemical ngineeringrocesses

l._vi,.ou.I rong. rurburni-.l'onq. I

to2

II+ 1Ortoo

6e"*Figure8-12.Power urve or the standardank conflgurationithout affles.(Source:Holland, F A. and Bragg, R. Fluid Flow for Chemical Engineers,2nd ed., Edward Amold, 1995.)numberor mixing increases eyondpointC in the unbaffled ystem,vortexing ncreases nd the Powernumber alls sharply.Fier|r 8,13hon' th. |.,,r. 'r) lur:tbei L li irrtio11 )i ti ic Re\jnolCs1LrrlbeI-orshexr'tiliiuli|r: llLriii,,.The ful1 ine gives the Newtonian Powernumberobtainedby Rushton et al. l10l for a flat-blade turbine system,whilethe dashed ine shows Metzner and Otto's L11lplot for shear hinningliquids. Figure 8 13 illustrates that at no point is the shear thinningpower curve higher than the Newtonian powgr curve. Therefote, theuse of the Newtonian power curye to determine he power will givea colseNative value when used or shear hinning liquids. Figule 8-]rtshows PowernLlmber orrelatiorls br various ],pesof agitators. n thefully turbulent low, the curve becomeshorizontai ancl he PowernumberN" js indepcldsntof the Reynolcls u]nber.Rushtonet al. uOl performedextensive neasLlrementsf the powerrequirementsfor geometrically similar systems and found that forbaffled tanks, the Froude number plays no part in deternining thepower reqliremelts, as vortices do not form in such systems. Forunbaffled systems, he Froudenumberplaysa part aboveNReof about

1o'l05o2o


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l ixing fFluids305

- Linr ot Rurhto, cortidr dd Ey.r.tt----- Linc of lldu|llr d|d Otlo

. = - - d14

tBeN-.....-

Figure8-13.Deviationrom Newlonian owercurve or shear hinning iquids.(Source:Holland,F A. and Brcgg,R. Fluid Flow or ChemicalEngineers,2nd ed., EdwardAhold, 1995.)300. They reportedNp = 6.3 in the lurbulent range01 10,000.Afterextensive uNe fitting of their experinentaldata,a single curve wasobtained or any particularunbaffledconliguration. f @ s plottedasa futrctionof NRewhereO is definedas

( D = N - lbr NRe< 300for N.. > 300P,rr[1" t.strn./uJ (8-16)

where a and b are constants or any configuration(Figure 8-14).Dickey alrd Fenic F2l observedhat the impellercharacteiistics avesignificatrt nfluenceon the Power numbercofielation.


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306Chemicl ngineeinq roesses

1 .P r o p e l l e F ,= D i R = 0a j 2 . 1 , b - 1 8 , B = 32,Propel lers,=Di R=4J = 0 , 1 t B = 33.Propelers, =20 R=0a = 1 . 7 i b = 1 8 ; B = 34 .P r o p e l l e B ,= 2 D ; R = 4J = 0 . 1 7 t B = 35. Flatblade sclurbine,

R ; 0 ; a : 1 1 0 i b : 4 0 . 0 06 Flatblade iscrurbine,R : 4 ' J = 0 1 7 i B = 6

7. CuNed lsde isc urblne,R= 4 ; = 0 . 1 1 " B - 68 AtrN-head isc urbine,R : 4 i J : o 1 T B = 69. Pllched ladelrbineR = 4 ; = 0 . 1 r ; B : 8

R = 4 J : 0 . 1 r ' B : 2R = 4 i J - 0 . 1 7 8 = 612.Diffuserng shroudedurbinosslEtor nShaving 0 blades,B = 6 .

Figure8-14.Powe.number ersusReynolds umber o elationor commonimpellers. Sour.ceiRuchtonet al.,Chem. Eng. Ptog.,46, No.8, 495, 1950.Repinted with permission of AlChE. Copyright @ 1950. A tights resetved.)

Two chafacteristics f Figure 8-14 are:1. At low NRe< 1.0,of baffles.2. At high Reynolds,formed, the Power= constant,

Np * l/Nr", independentof the presenceat which most mixing operations arc per-Dumber s constant, hat is, Np - P/pN3D5

Rushton et al. uol investigated the effect of varying the tanLgeometdcal ratios and the corrolatiol of the Power number withReynoldsnumber.At high Reynoldsnurnber, t was inferred that,

d=Np i t F .o .NFe33oO, N po'ii;#Giniah rrR=o Fa'roo

ReynordsN mb.r (NRe)


24/49

Mixing fFluids 307

. iD s relatively unchanged henDr/DA is varied rom 2 to 7 forturbine- al1dpropel]er-agitaLedaflled systems.. O is unchangedwhen tDa is varied lom 2 to 4.. O is unalteredwhenE/DA s charged iom 0.7 to 1.6.. O changes o O * (J/DA)0'3when J/Dr is changed rom 0.05to 0 .17 .. iD depends n the numbe. of blades n the turbine mpeller as:6 -18 /6 )08 t tU .6un ,1 O-(B i6 )0 i i f B > 6 (where = numbero f impe l l b la . l c . r .. If off centeredand inclined propellerswithout baffles or side-entedrg propellerswithoutbafflesare used,no vortex orms andthe O versusNo" curve for the coffespordingbaflled tank canbe used o estimatehe powerrequircmetrls.

These conclusionsare speculative rd experimental urves mustbe generated f more than one geometrical atio differs from thestandard alue.Thepower consurnedy an agitakrrat vadous otational peeds ndphysical roperliese.g., ' i$.orlr: dlld , jeit i l ) for a system's eo-metry can be determined iom the Power number correlation.Theprocedure nvolves:. CaicLr]ntin:lre rle:rolds unrher ,a. or rnixing-. Rcading hi Pore. nunbcf :\lp1io 1hc xpplrpilat.ccurli. and

ciLlculnl jng hc po\ c P : l i \ .n hp=Nr , .pN. iD ior p=opN3D5\.N[1."cNR")/b]

(8-r7)(8-18)

Equaliors 8-17 artl 8-18 al.e he power consunedby the agitator.Additionalpower is required o overcomeelectricalaDdmechanicallosses.A contingency f notor loadingas a percentagee.g.,85olc)saddedwhen selecting he motor Equation8 17 can alsobe rearrangedto detemrine mpeller diameterwhen t is desired o load an agitatorimpellei to a given power evel. The torquedeliveredo the fluid byan impeller fuom ts speedandpowerdrarl, s delermined y:

D \ r ^ N r 2 r r 52rN 2n (8 -19)


25/49

308Chemlcal nsineenns@cessesThe primary pumping capacityof an impeller is determinedby the

impeller diameter, he Pumpinguumber,and he rotatioral speed.ThePrmpingnLrrnber o is dcfired by [13]n, Q""Q NDi (8-20)The lumping number s used o determine he pumping rate Qp ofrn impe l le r .

where Qe = eflective purnpirg capacity, nr/secN = impeller rotational jpeed,sec IDe = impeller diamcter. nlHicks et al. [8] developed a correlat ion involving the Pumpingnumber and impeller Reynolds number for several atios of impellerdiemeter to tank diameter(Do/Dr) for pitched-blade urbines. Fromthis correlation,Q" can be detemined, and hus the bulk fluid velocityfrom the cross-sectional rea of the tank. The procedure or deter-mining the pammeters s iterative because he impeller diameter DAand rotational speedN appear n both dimensionless alameters i.e.,N^" and Nq).Figure8-15shows loTs l'Pumping urnbe|N, andPowetnuulberNp as lunctions of Reynol.l\ numbcr r{*" for a pitched-blade urbineand high-efficiency impeller. Hicks et al. [8] further introduced thescaleof agitation,So, as a measure or determiningagitation ntensityin pitahed-bladempellers. The scaleof agitation s basedon a char-acteristic velocity, n defined by

(8-21)wherc v = charactedsticvelocity, m/secAv = cross-sectional rea of the tank, m2

The charactedsticvelocity can be expressed s:

-r= Q"

"-''...,^i+] (8-22)


26/49

Figure8-15.Power umber ndPumpingurnber s tunctionsf Reynoldsnumber or a pitched-bladeurbine and high-efficiencympellet. Soutce:Bakker,A-, and GatesL. E., "ProperlyChooseMechanicalAgitatorc orViscous iquids,"Chem.Eng. Prog.,pp. 25 34, 1995.)

In geometricallyimilarsystems,he characteristicelocitybecomes

(8-23)Thus,during geometricscale-up, he characteristicelocity is heldconstart by holditrg NaNDA constant.Qp is determined rom thePumping number and Figure 8-15. SA s a linear function of thecharacteristic elocity and s determined y

v - N^ND^

S^=128 ' ' ' (8 24)Accordingly,a value of Sa equal o I represents low level andl0 showsa high level of agitation ntensity. he 1 10 rangeofagiaationntedsityaccounts or about9570or more of all turbine,agitationapplications, nabling t to be suited or a wide rangeofprocess perations.Gateset al. [l4] gaveguidelines n how to relateSo to specific roues\rpplicaLions


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310chemical ngineeringrocesses

NIIXING Tih{E CORRELATIONA distinctionwas madeearlierbetweenmixing ard agitation. hethird term in liquid mixing is blending.This lefers to the jnterminglingof miscible fluids lo produce somedegrce of uniformity A criteionfol good mixing may only be visual. For example, t could be aparticular olor l iom two different olor l iquids,or the color chargeof an acid-base ndicator tiat determines he Iiquid blerding times.Charactedzation f blendirg i. agitatedvesselss usually in terms ofmixing time. This is the timc requifed o achievesome specified

degreeof unilormity at'ter ntroduction of a tracer' Table 8-5 givesvarious techniques br determiningblending tinie.Each echnicluemeasLlres differelt degreeof unjformity, therelbre'the time required for blending may dilfer from one method to theother.The correlatioDof blending tlne as delived ftom dimensionalanalysis s applicable o all techniques.Uhl and Gray [6] summarizedmally of the experime.rtsand correlations on blending and mixingtimes.For a given ank and mpelleror geometricallyimilarsystems,the mixing time js predicted o vary ilvelsely with the stirrer speed,as confiuled n various tudies15,16,17,181.igurc8-16shows lotsof mixing time (tN) against th|r Reynolds number N"" for severalsystems. s an example, tu.binc with DA/Dr - l/3 and Dt/H = 1,the value of Nt is 36, for N*. > 103,comparedwith a predictedvalueof 38.

Table 8-5Methods or determining blending timeTechnique Tracer Blend time reached when

Grab sample

Dye inlroductionConductivitycell

An,vmalerinl that can

Dyed iuid.Concentradorof srlt

Samplesdo not vary more than1X9. from frnalconcenfiat ioD.Uniform color is atiained.Measurcd onductivity hdt reprcsents oncertrat ions within1XE of frral concentmlion.Neuiralization s complele asdeterminedby color changeAcid-bascndicator Acid G,rbase).

Sow?: Dickq, D.5., 'Dnncnsk\ol rnol,-sit.ftt lluid |gitoti.rt l\t" " Chem Eng,


28/49

E==

Prochazka ndLandau 19] developed mixing ime corelation ora single Ruslrton urbine mpeller n a baffled tank in the standardconfigurationor N^. > 104:

f iEYNoLDS Urv lBE, vF . ,D lp lFiguie 8-16, IVixing imes n agitaled essels.Dashed ifes representunbaffled anks; solid lines represents balfled auk. (Source:Mccabe,W. L., et al., Unit Operalions f ChemicalEngineering,th ed., Mccraw-HiBook Company,New Yotk, 19a5.)

For a propeller, he mixing t ime is given by:

x, ,'.,ri,:i .1'',,,,i:..l\D. j '1 . . 1

xr=-t,- ' i l | l r , , . iii i j i - l \ I

{8.-t j)

. . . t0 iNL=.r+slLl l"*[L' l\D" ,1 1X.JFor a pitched-bladeurbine, he nixing time is:

(8-26)

r q 1 7 \


29/49

312Chemical ngineeing rocesses

where4 = initial value of the degreeof inhomogeneity, hich vadesbetween1 and 3: a valLre f 2 is recommendedX" = final integral meanvalue of the local degreeof inhomo-geneityand is defined as:

(8-28)where C(t) = instantaneous oncentration

Ct = initial concenfationC^ = final concentationX" = 0.05 or most configurations.Moo Younget al. [20] corelatedtheir mixing results fromNt =KNi" (8-29)

where K = 36 and a = 0 for turbines n baffled tanks or 1,000< NRe< l0'. Sanoand Usui 2ll developed n expre\sionor mi\ing limesbv tracer niection for turbinesas:

(8-30)where np is the number of blades.Gray [22] found the mixing timesof helical ribbon impellers o be of the form

(8-31)

"-_fcttr c l L c"-c' l

Nt=30where N is tlle rotational speedof the helical dbbon impeller, and t isthe batch mixing time. Fasano et al. [23] expressed he blend time forturbulence conditions in a standardbaffled tank (i.e., NR" > 10,000) as:

. - t . \ 0 , . { . 5 1Nr=:.ell i fLl nJrT{Dr / \Dr i

4.065"..[3;)'(?l' (8-32)


30/49

Mxingof Fluids 313

where a and b are the t11ixillg ate constants.Table 8 6 showsvaluesof a and b for different il]rpetler types. The constantsare lor sufaceaddition, however,blend times for similar fluids arerelatively insensi-tive to addition location. Equation 8-32 is limited to the following:. Newtonian fluids of nearly the sameviscosity and density as thebulk fluid.. Additions of 5oloor less, of the fluid volume.. Additions made to a vessel already undergoingagitaaion blendtimes of sfatified fluids can be considerably onger).The estimatedblend time for 9570uliformity (tb.95ez)sing a standarddouble light helical ribbon impeller with (PilDA= l, W/DA = 0 1, andDA/Dr = 0.96) is given bY

15For N,." ( 100: tb,951i, i: (8 -33)For anchor mpelleru of standardgeometry (w/DA = 0.1, De/Dr =0.98, and Mr = 1.0), the estimated b fbr 100 < Nq" < 10,000 sgivenbytb,es% exp(12.9Nil;135)

\rhere DA = impeller diametel mDr = lank diameter,mH = impeller oI helix height, mN = impeller rolational speed,sec I

(8-34)

Table8-6Mixing ate constantsor full y turbulentflow regimes NF.> 10,000)

lmpeller ypeSix-biadeddlscFour-bladed45" pitchedThree-bladedhigh eff ciencl

1.06I.[J0.6414.2'12

2.1 '12.31)2 . 1 91.61

sautcc: FosolL et ol. []31, ,1Lfiane.l t peltet Geaheh uoastsLiquid )sitdtion, Chan.Eh&,142 6), Atgtst 199'1.


31/49

314Chemical ngneering rocesses

P' = pitch of a helical ibbon impeller, mW = blade width, mBakkel and Gates 23] compared oth Equations8-33 and 8-34 andinferl'ed that at a Reynolds number of 100, it will take an anchorimpeller more than 13 times as long to acbieve95o/o niformity as ahelical ribbon impeller operating at the samespeed.These mpellersrequire cooling to remove the excassheat due to their high powerinput. The mixing time that was considered elates o tanksoperatilgin closedsystems e.g.,batchreactors). n a continuous eed taDk, he

mixing time is generallyshorter han in a closed tank.

Example8-1Calculate he power for agitationof a liquid of density 950 kg/m3and viscosity 250 cP given the following configuration: number ofblades B = 6, agitator diameter0.61 m, and speedat 90 rym. Othefgeometricalatios tue shown n Figure 7-1.A disc-mountedlat turbineis used,

SolutionThe Reyno lds umber o r m ix ing s^, - pNDiN = the numbel of revolutionsper sec s (90/60) = 1.5 rev/sec.

tl ks 11-- ' - 't-*-, ).61oxr.5)(o

250x 10(e Im- lKg l

-."* |Nt" = 2,121Usingcurve6 in Figure8-14, hePowernumber stheoretical ower or urixing s Np=50.The


32/49

MixingfFluids315f r-^ -^,,1 Ip = NppNrDi 5.0 950 | 5 x 0.65 { "E.rF ' i .m5}Lm' sec' J

= 1,353.99= 1.35 W (1.82 p)

(NB: kW- 1.341 p)

Example8-2Calculate he theoreticalpower for a six-blade, lat-bladeturbine ,'without balfles, but with the standard ank conJiguration hown inTable8-2. Use the samedata as in Example8-1.

SolutionSince the tank is unbaffled, he Froudenumber s a factor and tseffect s calculatedrom

-- 0. 4Nn"=2,121The constants and b for an unbaffled ant R = 0, ar.e = 1.0 andb = 40. Using curve5 in Figure8,14, the Powernumber s Np = 2.0NP, wberem- a - log loNRe' - b

61))(09 .81

(1, N2Dogttl rev m Ilsec2 m It ;Pl


33/49

316Chemi@l ngineeirqProcesses

1.0- lo9to2,1zl= - 0.058240Nfl,= 0.14{05821.1212

Therefore,ower P= N" pN3D5oNfl,- 2 .0 950r .5J 0.u, ' , . ,212]e. t { . r ' )\ m" sec- )= 601 24 w= 0.6 t kw (0 .81 p)Studies on various turbine agitatols have shown that geometricrutios that vary from the standarddesigncan causedifferent effectson the Power numberN" in dle turbulert regions [24]

. Fof the flat, six-bladeopen turbire, Np - (wiDA)ru. For the flat, six-bladeopen tulbine,vnr-yingDA/Dr from 0.25 to0.5 has no eflect on Np.. Whentwo six bladeopen ulbinesare nstalledol1 he sameshaftand the spacing between the two inpellers (vedical distancebetween he bottom edgesof the two turbines) s at least equalto DA, the total power is 1.9 times a single 1lat-blade mpelleiFor two six-bladepitched-blade45') turbines,he power s about1.9 times that of a single pitched-bladempeller.. A bafIled,ve{ical square ank or a horizontalcylindrical ankhasthe samePower numberas a vefiical cylindrical tank

SCALE-IJP OF MXING SYSTEMSThe calculationof power requirementsor agitation s only a partof the mixer design. n anymixing prcblem, hereare severaldefinedobjectives such as the time required for blending two immiscibleliquids, ratesof heat lansfer rom a heatedacket per unit volume ofthe agitated iquid, and mass ansfer rute from gasbubblesdispersedby agitation n a liquid. For all theseobjectives, he process esultsare to achieve he optimum mixing and unilbrm blending


34/49

Mixing f Fluids 317The processresults aIe related to variables charactedzingmixing,namely geonetlic dimensions,stiller. speed rpn), agitator powel.,andphysical properties of the Jluid (e.g., density, viscosity, and surfacetension)or theit dimensionsless ombinations e_g., he Reynotdsnumber, Floude number, alld Weber number, pNrDi/o). Sometimes,empiricai relationships aro established o relate process results ardagrtationparameters.Often, however,such r.elationships re non-existent- Labolatory scalesof equifment using the same matedals ason a large scale are then experimcnted$ith, and the desired processresult is obtained. The laboratory system can then be scaled-up topredict the conditions o11 he ]argel systen.For some scalc-up ptoblems, generalizedconelalions as shown inFigures l l , 8-i2, 8 13,and 8-14areavailableor scale-up. owever,there is oluch diversity in d1epfocess o be scaled-up,and as such nosingle method cal1succcsslully handleall types ol scale,up problenrs.Va ous methodsol scale-uphavc been proposed:al l basedoigeomctric sinilality between thc laboratory equipment and the ful1scalepla0t. It is t1otalways possib]e o have the large and small vesselsgeometrically sinilar, although it is pefhaps the simplest to attain. Ifgeoineftic similarity is achievable,dynamic and kinematic similaritycannot often be predictedat the sanle ime. For these easons,experi-

ence andjudgmeit are rel icdon with aspects o scale-up.Thc main objectives n a fluid agitation processare [25]:. Equivalent iquid motion (e.g., iquid blendingwhere the l iquidmotion or coresponding velocities are :rpproximately he same nboth cases).. Equivalent suspensiotiof solids, where rhe levels of suspensionaie identical.. Eqllivalenl ratesof mass ransfcr, /here nass ffansfer s occur:rirgbetween a liquid and a solid phase,between iquid liquid phases,or between gas and liquid phascs,and the rates are identical.A scale ratio R is used or scale up fiom the st4nd.trdconfiguationa5sho \dnn lab le8 -1 . hc p rocedu re. :l. Determire thc scale-LrPatio R, assumiug hat rhe oiginirl lessclis a standard yl inderwith Dr, = H1. The volun-re r is

TU i r4- h2V,=" " r l . g , ='4 (8-35)


35/49

318Chemicalngineeringrocesses

The ratio of the volumes is thenv, ro1,+ D+'vt nD l4 Di,The scale-upmtio R is

(8-36)

(8-37)Using the value of R, calculate he new dimensiolts or allgeometric sizes.That is,Do, = RDa1, J, = RJ,, $y',= ft\i,r,Ez = REr, Lz = RLr, Hz = RHroro - Do : -Dr : -w : - H , J . z-E :" -Do , -D r r wr Hr Jr Er

2. The selectedscale-up ule is applied to determine he agitatorspeedN2 from the equation:

(8-3 ). where n = 1 lbr equal liquid motion. n = 3/4 for equal suspension f solids. n = 2/3 for equal rates of mass hansler (correspondingequivalentpower per unit volume, which results n equivalgnt ntefacialareaper unit volume)The value of n is basedon theoreticaland ernpiricalconsidera-tions ard depetrdson the type of agitationproblem.3. Knowing the value of N2, the requiredpower can be determinedusing Equation 8-17 and the generalizedPower number coraelation.

*= P"=flbllDrr \.Vtr ./

.',=.-,(+l=.-,(+)"


36/49

Mixing fFluids 319

Otherpossiblewaysof scalingup are constantip speed r(7rNDA),and a constart ratio of circulatingcapacity o headQ/h.S inceP* N 'D l andV - Di rhenp - ^ - N'D'^ (8-39)

(8-40)

For scale-up rom system I to system2 involving geometricallysimilar tanksand same iquid properlies,hp followirig equatiorscanbe applied:N1Da1 N2D42For a constaDtip speed,N" D^ ,Nr De.z

For a constant ratio of cjrculatitrg capacity to head, Q/h,Nr3n2 - Nr3 n2 (8-4r)

Example 8-3Scraperblades set to rotate at 35 rpm are used for a pilot platrtaddition of liquid ingredientsnto a body washploduct.What shouldthe speedof the bladesbe io a full-scale plant, if rhe pilot aud thefull-scaleplantsare geometrically imilar in design?Assumescale-up is basedon constant ip speed, iameterof the pilot plant scraperblades s 0.6 m, and diarneterof the full-scaleplant scmperbladesis8 f t .

SolutionThe diameterof the full scaleplant scraperblades= 8.0 x 0.3048= 2.4384m (2.4 m).Assumingconstant ip speed,N, D^ ,N, - D- (8-42)


37/49

320Chemical nsiieeinsPrccesses

where Nt = scraperspeedof pilot plantN2 = scraperspeedof full-scale plantDat = diameterof pilot plant scraperbladesDlz = diameterof full-scale pla[t scraperbladesN. = Nr Der- Do ,

_(3sxo.6)(2.4)=8.75ym

Example8-4During liquid makeupproduction,color pigmeflts i.e., solid havingidentical particle size) are added o the product via a mixer. In thepilot plant, this mixer runs at 6,700 rpm and has a diameterhead of0.035m. Full-scaleproductions geon.retricallyimilar and has a mixerheaddiameterof 0.12 rn. Determine hc speedof the full-scaleproduc-tion mixer head.What additional flfonnation s required or the motorto drive this mixer? Assume hat power curves are available or thismixer design, alld the scale-upbasis s constantpower/unit volume.

SolutionFol constanrpower per unit volume,Equation 8-39 is applied: P/V* N3D2a r NiDir = N;Dir. Therefore,

whereN, = 6,700 ymD.r r -0035mD,qz 0.12mr n o ls r2 / lN, =6.700 :r::: I \0 .12 l

N,=N, Do,l"' ' \Do, J


38/49

Mixing f Fluids 321

Nz = 2,946.7 pmNz = 2,950 pmThe powerrequired or mixing is P = NppNrDl, wherc he Powernumber Np) s a llnction of the Reynolds umber i.e.,Np = f(Nr")]:

^r.rn2P .

The plant must be providedwith the viscosityof the productand tsdens i t l f te r dd i l ion f rhep igments .

Example8-5A turbineagitatorwilh six llat bladesand a diskhasa diameter f0.203m. It is used n a tank with a diamete. f 0.61 m and heightof0.61 m. The width is W = 0.0405m. Four bafflesare used wirh awidth of 0.051 n. The turbineopentesar 2'75 ym in a liquid havinga densityof 909- g/m3and viscosityof 0.02 Pas.Calculate he kW powerof the turbine and kWrn3 of volume.Scaleup this system o a vesselwhosevolume s four timesas large, orthe caseof equalmass ransfermte.

SolulionThe Reynolds umber or mixing s NR..The numberof revolutionsper sec,N = 275160 4.58 rev/sec.,, pND':"' ' - p

(90q)(4.58t(0.20312kq rev , ..r.. I0.02 lmr sec te I= 8,s78.1

Nt" = 8,600


39/49

322ChemilEnsineeringro@sses

Using curve 6 in Figure 8-14, the Power numberN" = 6.0. Thepower of the turbine P = trtoPN3Dl:f , ? IP= (6.0,(e0qx4.581(0.2011+.trf. .m5llm- sec- I

= 0.1806 w (0.24hp)The originalank ,olume r - rtD+r/4. he ankdiameter rr = 0.61:

/.\rn 6r 134Vr = 0 178m3The power per unit volume is P/VP 0.1806v 0.178

=1.014kWm3For the scale-upof the system, he scale-up atio R is

nD3-"a D+,;17= ";IR=Llr

\vr /= Dt,

Drr(8-37)

where z = 4Vrvz=4 0.178)

=0.712 3IR=(4) l= 1.s87


40/49

Mixing fFluids 323

The dimensions f the argeragitatorand ank are:Da2= RDol = 1.58? 0.203 0.322mD..,= RDr, = 1.587 0.61= 0.968mFor equal mass ransfer rate n = 2/3

- 2n,=N,f] l ' (8-r8l \ R /2=4.5sr )j\ 1 .587 /

= 3.37 rev/secThe Reynolds number N*" is., - PN:Di:

(c09(3.37)(0.122- fkp rev , ..r""'l0.02 fm' sec t


41/49

324chemical nsineeringroessesThepowerperun i t o lumeP/V ( :P2 _ O-'.723v2 0;712

= 1.015 wm3MIXING TIME SCALE-UPPredicting}e rime br oblarniDgoncenrahonniformil) n r balchmixing operatiorcan be basedon model theory.Using the appropriate

dimensionless roupsof the pertinentvadables,a rclationshipcan bedeveloped etweenmixing times n the model and arge-scale ystemsfor geometricallysimilar equipment.Consider he mixing in both small and arge-scale ystems o occurin the turbulent egion, designated s S and L respectively.Using theNorwood and Metzner's cofielation [26], the mixing time for bothsystems s

Applying he scale-upule of equalmixing imes,andEquation -43,yields

rr(Nrolr.;'2/'rvopvzHg'.Dt3

Assuminggeometricsimiladty,Po"D,rsD^ .D,rs

t"(N"oL)'?/3*vooKHll'.D't (8,43)rearTanglns

(8-44)

(8-4s)

2/N, ) l\NsJ

Ht =HsD'"=Drs

3 4 1 1= s*)tfo*ltf "* )tfg")t\Drr/ [DorJ \Do"J HrJ

(8-46)


42/49

Mxingof Fluids 325

SubstitutingEquatiors 8-45 and 8-46 nto Equation8-44 gives2 3 4 1 1/ r r \ ; / n \ , / n \ ; / n \ , / n \ ,l l l '1"=1"+l' l+l"l+l ' l :* l ' B_411\Ns J \Do. _/ \Dor./ \ Do,./ [ Do,J

Ifo-16lDo"JI

[N,) - (oo,) ;l\ l - lD*OI

D Dpnt-i[ = p$1"where

r, _ 1u, 1r1o,)5r. lNrJ o*.JSubstitutingEquation8-48 nto Equatiotr8-50yieldse / o^.)o"r l^ . ) t= l ^ ' l l ' " 1P. \Dos. / \DosJ

of

. 2ful'=\Ns /(8-48)

The exponent r for the mixing time scale-up ule is 0.25.The powerP of the agitator or both large and small systemss

P, f Do,lt"P, l Do,

(8-49)

(8-50)

(8-51)

(8-52)


43/49

326Chemical ngineeringrocesses

The power per unit volume P/v for both large and small-scalesyslems s:

=L.f Ir)'Ps \ Drr-./

Substituting quations 46 and8 52 into Equction8-53gives

(8-s3)

(8s4)

(P/v)'-(P/v),, \ 5 . 7 5 . 3- lD* I ID^slD*J lr*l

/ \ 2 . 1 5-1D""\Dos. /

Table 8-7 summarizescorrelations or the effec1sof equipmentsize on the rotational speed needed or the same mixing time byva.ious nvestigators.The relationships n Table 8-7 show that the rotational speed oobtain the samebatch mixing time is changedby a small power ofthe increase n linear equiprnent imensionas equipnlent ize schanged.Equation 8 49 shows that greaterpower is required or alarge-scale ystem compared o a smaller system.Often, the powerrequired for a larger system may be prohibitive, thus modificationof the scale-up ule is needed e.g., . = 10ts or tL = 100ts) oobtain a lower power requirement. l should be noted that relaxa-tion of mixing time rcquirementsmay not poseother problems.Forexample, f the mixing is accompanied y a chemical reaction n aCSTR,assuminghat the NorwoodMetznef126lcorrelation or mixingtime (t) is sti1l applicable, t mustbe ensured hat the mixing time inthe arger scale tL = 10tsor tL = 100ts) s less han 57oof lhe averageresidence ime of the liquids in the reactor,otherwise he conversion


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t

;]

=

ianF

'".

sb_ 5l l ^ i o g i :1,

2 9 : n xE*-g:a 5< a

z

E

sz

oq)E

tlrl

E'=J

ozootID

_? :z< d@ . ; 2"i- Ji o3o> - ;6 ;> r l

E

EtEo{,

0,

oo(E

Go(ltN

Eo0

tt

gPEP6 N N N

: r'1

E I E 8


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328ChemilEngineeringro@sses

The power per unit volume P/V forsystemss: both large- and small-scale

Ps/Vs -p- InDt"_ ;r]"v;

=L.(P^l'Ps \ Drr- ,/

SubstitutingEquations 8-46 and(P/v), _ I oo, .)t t (oo. )'p/vt - tD*l lD* l

/ \2.75I Dor lI D"s /

Table 8-7 summaLizes orrelatiolssize on the rotational speed neededvarioLls nvestigators.The rclationships in Table 8-7 show that the rotational speed oobtain the same batch mixing time is changedby a small powel ofthe increase n lioeal equipn'ient imensionas equipmentsize ischanged.Equation 8-49 shows that grcater power is required for alarge-scalesystem cornpared o a smaller systen. Often, the powerrequired fol a larger system may be prohibitive, thus modifiaationof the scale-up ule is needed e.g., tt = 10ts or tL = l00ts) toobtain a lower power requiremert. It should be noted that relaxa-tion of mixing time requirementsmay not poseother problems.Forexarnple, f the mixing is accompanied y a chemical reaction irr aCSTR, assuming hat the Norwood-Metzner26] correlation or mixingtime (t) is still applicable, t must be ensurcd hat the mixing time inthe largerscale tL - 10ts or tL = 100ts) s less han 57o of the averageresidence ime of the liquids in the reactor,otherwise he conversion

(8-53)

8-52 nto Equation8-53 gives

(8-s4)

for the effects of equipmentfor the same mixirg time by


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MixlngfFluids329scale-up chart only applies to systems of sinilar geometry.Whenthe geonetry is diiTerent, pecialand specilic analysesof the system

Samant aDd Ng l28l coDparedvarious scaleup rules for agitatedreactors,They suggssted lat a scale-up ule of power per unit volumeand conslaDt verage esidence ime (where he power pcl unit volurnellnd average csidence ime cannot be incrcased) s the most suited nmany operatiorls. lowever, lhis still may not improve or prese e thepeformance of the systems.Therefbre,adequrte considerationmusbe given to a tradeolTbetweenperformance nd operating onsfaints.

REFERENCES1. Levenspiel,O., Chenical ReactionEngineering,3rd ed., John.Wiley & Sons,New York 1999.2. Keyode Coker, A., Modeling oJ Chenical kineticsa cl rcdctordesign Gulf Pnblishing ConpatryNey'Delhi 2001.3. Penny,W. R., "Guide o tiouble reemixers,"Chem.Eng.,77(12),r'7 , t9'70.4. Holland,F. A. andChapman, .5., Liquid MiJiilxgtnd Processiirg

in Stired Tunks,Reinhold,New York, 1966.5. Myers,K. J., Reeder,M., andBakker,A., "Agitating or success,"T'heChemicalEngifleer, p. 3942, 1996.6. Uhl, V W. and Gray,J. B., Eds. Miting Theory and Prdctice,Volume 1, AcademicPress nc., New York, 1966.7. Gates,L. E-, Henley,T. L., and Fenic,J. G., "How to select heoptimum urbine agttatot,"Chem.Eng.,p. 110,Dec. 8, 1975.8. Hicks, R. W., Morton, J. R., md Fenic, J. c., "How to designagitators br desired rocessesponse," hen1. ng.,p. lO2,Aptll 26. 19'76.9. Dickey, D. S., "Succeedat stirred tank reactordesign, Cfrem.Eng.,pp.22-31,Dec. 1991.10. Rushton, . H., Costich,E. W., and Everett,H. J., "Powerchar-acteristics f mixing npellers," CltemEng. Prog,46.395, 1950.ll. Metzner,A. B. and Otto, R. E., "Agitation of non-Newtonianfi 'rj.ds," IChEJ,3,pp. 3-10, 1957.


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330chemical ngineeringrocesses

12. Dickey,S. D. and Fenic,J. G, "Dimensional nalysisor f luidagitationsystens," Clrcm.Eng., Jan 5, 1976.13. Fasano, . B., Bakker, ., andPenny,W. R., "Advancedmpellergeometry oostsiquidagitation," hen.. n|,l0(8), pp. 110-116,August1994.14. Gates,L. E., Hicks, R. W., and Dickey, D. S., "Applicationguidelines for turbine agitators," Chem Eng., 83, pp. 165 170'Dec. 6, 1976.15. Cutter, . A., AlChEI, 12, 35, 1966.

16. Moo-Young,M., Tichar,K., and Dullion,F. A L.' AIChEJ' 18,1'18,19'12.17. van de Vusse, . G., "Mixing by agitation f miscible iquids,"Chem.Eng. Scl.,4, 178, 1955.18. Fox, E. A., and Gex, V E., "Singlephase lendingof liquids'' 'ArchEJ, 2, 539, 1956.19. Prochazka, . and Landau, ., Coll CzechChen]Cummun,26:2961 ,1961 .20. Moo-Young,M., Tichar,K., andTakahashi, . A L.' "The blend-irg efTiciencies f some npelleis ;n batch mixing'' ' A/Cftt"r,18(1),pp. 178 182, 1912.21. Sano,Y andUsui, H., "Interclations mongmixing ime,powernumbeL nddischargelow ratenumber n bafflcd mixing vessels,"l. Chem.Eng.,Japan, 8:47-52,1985.22. Gray, .8., "Batchmixingof viscous iquids," hen.Eng.Progr,59 ,No . 3 , p . 59 , 1963 .23. Bakker,A. andGatcs,L. E.. "Proper'ly hoosemechalrical gitatorsfor viscous iqri,tJs,"Chen. En1. Pro7., Dec. 1995.

24. Bates, . L., Fondy,P L., andCorpsteir. . R., E.C Proc.Des,2 ,310 , 1963 .25. Rautzen,R. R.. Corpstein.R. R, and Dickey, D.S., "How touse scale-upmethods or lurbincagitators,"Chen. Eng, Oct25, 19'.16.26. Norwood, K. W. and Metzner,A. B., "Flow patternsand nixingrates n agilatedvessels,"AlClE"/, 6,432, 1960.28. Samant,K. D. andNg, Ka, M., "Developmentof liquid-phaseagitated eactolsrsynthesis. imulationand scaie-up."AIChII'

Vo l .45 No . 11 , p .23712391 ,November999

1


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[ r l , ing i Ftuids 31

PROBLEMS8.1 A tank 1 .2m in d ianre le r .nd 2m h igh is n l lcd to a dep l l o f 1 .2n w i th a la tex

ha l ing a v jscos i i yo f 10 P and a densi ty o f 800 kg /nr r . The la ik is no t ba f f led .Alh ree b l .de 360 nn-d iamerer prope l le r s i is ta l led in inc tank 360 nn f ron thebot toD. The p i ich is l : l ( i l ch equa ls d iameter ) .T le no tor a i lab lc dcve lops8 kW. ls r l re no tor adequate o dr ive lh is ag i ta to ra t a speedof800 r /n in?

8,2 What is rhe nax inum sped l wh ich ag i la to ro f lhe tank doscr ibedn Prob . 8 .1 naybe dr iven f l le l iqu id s rep laced y oneha ing a v iscos i ty f I P and he sane densi ty?

8 .3 what power is .equ i red or the n ix ing opc.a t ion o fProb . 81 i fa prope l le r 360 nnin d iameter h r rn i rg a t 15 r /s is nscd and i f four ba les, eacn 120mm w ide , a re

8 . ,1 The pro lc l lc r in Prob . 8 .1 is rep laccdwi th a s ix b lade urb i f l e 400 mm in d iameter .and the f lu id to be ag i ta ted s a pseudop last ic oweFlaw l iqu id hav ing an aPpared lv i scos i l y f l 5 P shen t le ve loc i ty lad ien l s 10 s- . Atwhat speed hou ld he urbhero ta te to dc l i rc r I kW/nr o l l iqu id? For th is 1 lu id , = 0 .75 and p= 950 ke/mr.

8.5 A mixing rine of29 s was nre.sured for a 4.5_ft baflled lank with a 1.5_ll ix_bladeturb i ie and a l iqu id depth o14.8 f t . Tne iu rb ine speEdwas 75 r /m in , and the t ' lu idhas a v iscos i tyo f I cP and a densi ly o f 65 lb / f . . Es l i ' na tc the mix ing t ines i f .ninpe l le r one quar te r or one-ha l f the ank d ianeter sere used w i t l tne speeds hosenro g ive t le same power per un i t vo lume.

8 .6 A p i lo t -p lau t re .c lo r , a sca lemode l o f a product ion un i t . is o f ch s ize tha t t gcharged o lhe p i lo t -p lan t rcacto r s equ i va len i o 500 g of the samendter i . l chargedro the product ion un i i . l h c producl ion un i l i s 2 m in d ianeter and 2 n deep andc o n r a i n s a s i x - b l a d e t r r b i n e a g i l a t o . 0 . 6 m i n d i a m e t c r ' l h e o P t i n u n r . g i l a t o r s p e e din rhe p i lo t -p lanr reactor s lbund by exper inent o be 330 /n in . (a , )wh t a re lhes ign i l ican ld isens ions o f lhe p i lo t p lan l reacto ? ( r ) l f the .eact ion dass has theproper t icso fwater d t 70"C and the po{er inDut per un i t vo lune is to be consta l t ,a r w .1 s leed shou ld hc in rpe l le r u rn in t le h ree reactor? c ) At $hdt speed ho t ldi t ru rn i f rhe mix ing t ine is lo be lep t coDstamt?d l At wha l speed hon ld i t tun i flhe Rcyno lds n t rnber is he ld co ts tan t? f4 wl ich b .s is wou ld you recommcnd orsc l leup? why?

8.7 A s t i fed tank reactor 3 f t in d i lne te r w i l l a l2_ i . , f la t_b ladeurb ine h .s been usedIor a ba lch reac l ion n wh ic h theb lend ine ine o faddcd reagentss cons ide led i1 i ca l .S. t is facto ry c l t s were ob ta inedwi tn a s t i t rc rspedof400 r /n in . The same eacl ionis 1o be c ar r ied ou l in a tank 7 t in d iane le r . fo r wh ich a 3 I s landard urb i ne isara i lab le . d . /Wha l cord i l ions inou ld g ive the s .ne b lend ing ime in t he hrger t .nk?(b l wha l wou ld be lhc percent .gecha ige i i the powcr per un i t vo lune? Densi lyp= 60 b/ f t r r v iscos i ly11 5 c l .

8 .8 . A s ix-b laded isk tL , rb i re Da = 3 f f ) is used to d ispese hydroeen gas in to d s lu r .yreac lo r con ta in ing ne t ly l l ino lca te a i 90 'C a id 60 lb j t i i . ' : gange wi lh I percentsuspended a ta lystpar t ic les D, 50 l t r , p / = 4 g/cnn) . The reactor d ianeter i s 9 f ta n d i h e d e l h i s l 2 f i . T h e g a s l o w r a t e s 1 8 0 0 s i d f t l / n i n , h e o i l v i s c o s i t ys l 6 c ?.nd the densi ty s 0 .8 .1g /cn i l 90 'c . The reactor s fu l ly ba f f led . a) what lg i ta lo rspecd s needed o g ive 5 hp /1000ga l dur ing lhe re .c l ion? f4 What is the powerconsudption wilh gas flow on and rvitl gas flow off?


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332 Chemicl ngineeins @esses

E.9. Fo. the condi t ions fProb. 8.8,est inate he power equired or conpletesuspensionof rhe calalyst .8.10-A 15percent lur .y of20-to-28-meshimestoDer waie. is ro be kept i t r suspensionin a 20-fFdiameter ank using a six-blade s twbine, (d) If Da./Dt=U3, an,J WDa= 0.2,what s i iner speed s rcquired?@, Calculate he st i r rerspeed nd power requi .enenri f Da/Dt = 0.4.8.11.A foact ion n which the product forms r fystal l ine sol id has been studied n a1+t-diameteri loLplal t reactoreq ippedwiLh d 4 in. s ix-blade urbinewith curvedblades.Ai st i f ferspeedsess ha 600 /min. a sol id deposir omet i f tes orms on thiboi tom, and tbis condit ionnust be avoided the con merciol reactor .Densi ty ofthc l iquid is 70 b/ fp; viscosi ty s 3 cP. (a) What is ihe power consunpt ion n rhEsmal l reactor , and what is reconmended or an 8000-ga1 eactor i f geomerr ical

s imi lar i ty s preserved?@, How much night the required ower be oweredby ls inga differenl tyDe of agilator or different geomel.y?8.12.Gaseous LhyleneC:Ha) is to be dispemedn water n a turbine-agiraredessel tl l rc and a absolutepressure f 3 atnr . The vessel s 3 m in diameter wi th amaximum l iqtr id del th of 3 nr . For a f low rate of 1000 r/h of eurylene, easuiedat process ondit ions, peci ly d the diameterard speed f lhe turbine mpel ler , b,th power drawn by the agi tdto. , c) tho maximum vol t rne ofwater al lowable, nd(d) rhe nte nt which water s vapor ized y the elhylene eaving he l iquid sur face.Assume hat nonc of the ethyiene issolve sn the water and thai the ethylene eavingis saturatedwith warer .E. l3.For a f low rate ol250nr/h in the vesscl esf f ibed n Prob. 8.12,est imate he gasholdup, mean bubble diameter , nd in ier facial reaper unl t voiume.

Chapter -8-Mixing of Fluids

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Transcript of Chapter -8-Mixing of Fluids