Chapter -9-Heat Transfer in Agitated Vessels

8/13/2019 Chapter -9-Heat Transfer in Agitated Vessels

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Healiransfernagitationrocesses33

ChapternineHeatTransfern AeitatedVessels

9.1 ntoductionAgitatedvesselswith an extemal acket or an internalcoil areincreasinglymployedn biotechrology ndotherprocess pplications.The most commol type of jacketsconsjsts f an outercylinde. hatsunounds afi ofthe vessel. heheating r coolingmedium irculatesnthe annularpacebetween he jacket and vesselwalls. Altematively,condensationfvapor (e.g., team r a propdetary eat ansfer mediun)may serve bi heatingand vaporization f liquid (e.g.,are ragrant)may serve for cooling.Theheat s transferedhough the wall of the

vessel. irculation affles anbeused n theannular paceo increasehevelocityofthe liquid flowing hrough he acket, husenhancinghe heattlansf'er oefficient. n altematives to introducehe luid via a series fnozzles paced own he acket. n thiscase, he momentum f the etsissuing romthe nozzles evelops swirlingmotion n the acket iquid.The spacing etweenhe acketand vesselwall depends n the size ofthe vessel, owever,t ranges rom 50mm or smallvesselso 300 mmfor largervessels. igure9-1 shows ifferent onfigurationsfjacketedvessels. he pitch of the coils and he areacovered anbe selectedoprcvide the heat ransfer area equired.Standard ipe sizes rom 60 mmto 120 mm outside iameter reaareoften used.Half-DiDe onstructioncan produce jacler ccpable f wiLhstandinghighii pressure hanconventionalacket design.The rate of heat transfer o o. from anagitatediquidmass n a vessel epends n thephysical ropedies ftheliquid (e.g.,density, iscosity,andspecifrc eat)and of the heatingorcoolingmedium, he vessel eometry, nd the degree f agitation.Thetype andsize ofthe agitatorand ts location lso nfluencehe rate.Anagitator s selectedn thebasisof materiai roperties nd he processingrequired.The heat ransfer ormspart of a process peration uch assuspended.


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334Chemical nsineeins bcesses

S?ilally b filed jack t(a )

((n


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Heat ransfern agiiationmcesses35

Stiraed tank reactors in which an exothermic reaction isperformed may involve the removal of substantialanounts of heatfiom the reactingmixture.Refluxing of a boiling solvent s a commonmethod; the heat of vaporization of the solvent is removed by thereflux condenser, nd the condensed olvelt is returned o the teactorOthei methods nclude cooling thc walls of the reactorby meansof ajacket with a cooling medium, inserting a cooling coil, or using anexternal heat exchangerwith a pump around system: n many appli,cations using jacketed vessels,successivebatchesof matedal ateheated (or cooled) to a given iernperatute,and therefore the heattranstbr nvolves an unsleadystateprocess.Proper care s essential oterms of charging,agitatiol, and adequate ooling of the reactants oprevent the generatedL'ieatrom subsequently eading to a runawayreactl()n.Design Equation

Considera vesselcontainingan agitated iquid. Heat transferoccursmainly through forced convection n the liquid, conduction througtlthe vesselwaLI, and forced convection n the acket media. The heatflow may be based on the basic film theoty equation and can beexpressed y- Drivins forceKare = -Resistance

(e- l )vessel and its jacket each operateconditions.RearrangingEquation

ATorQ rluIn an idealized situation, thecontinuouslyundet isothermal

9 l becomes:Q = UAAr (9 2)11 a realistic continuoussituatio , where the vesselcontentsare atconstanl temperature,but with dift'erent acket inlet and oudet tem-peratures,Equation 9 2 is expressed s:


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336Chemicalngineeringrccesses

Q = UA-AT11ap (q l)whereATLMTDs the log nean tenpenture differencebetween he bulktemperaturef the vessel ontents,, and he emperaturen the acket,T. ATLMTDs exprcssed s

tn[(t, r,)/(t,

1__ l

t' -r,) t' -r,)T \ l. r / len te . i nglu i , l empera lJ ren the re . .e lleaving lrr id emperi lruren rhe \e.selen te r ingl r r i d empera tu ren rhe rcke lleaving fluid temperaturc n the jackel

(e-4)

(e-s)

wltete rlt2

T 1T2

The overall heat transfer coefliciellt U is deterrnined rom a seliesof resistances o the transfer of heat, namelyl+FF ,+" ' *FF ,*

h i k '

where li = coefticient on processside of heat transfer area, .e., insidesudace ofjacketed vesselor outsidesuface of internal coil,wn2'c= lbu l ingcc lo r . ' i de \e .se l .m"C/w= wall thickness f vesselor coil, mur= thernal conductivity,Wm"C= fouling factor, nside acket,m2"C/w= coelficienl n inside ufface l jaclei. w/m"CWhen the heat ransfer s through nternalcoils or tubularbat'fles,the difference etween he nnerand outerheat ransfer urfacesmay

be significant.Inside Film (hi) Coefficients

Wlren applying the following equations or calculating film coef-ficients in jacketed vessels, he physical property data should beaccurate.This is especially importatrt tbr thermal condllctivity k, asits value can have a major impact on the calculated ilm coefficientand vary widely.

FF.Xruk

FF._ lhj


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Heatransiern agilationrocesses37

The inside iilm heat transfercoefficient (hi) can be calculated romthe following Nusselt number corelatron:

#) (9-6)where Dr/H, WDA) representsadousgeometric orection actors.For a geonetricallysimilar system,Equation9-6 becomes:

(e7)

",'=..tu" .(*)',(+Nu=c.Nfr"Nh( L)"For agitated esseis,

(e-8)= heat ransfer oefhcient o vesselwall or coil, w/mz'C- agitatordiameter,m= tank diameter,m= agitatol speed rev/sec)= density, g/mj= thermalconductivity,Wm"C= specificheatcapacity, /kg"C= viscosiry t bulk fluid remperarure,(N.s)/m]l[kg/(m.sec)l= viscosityar the wall temperatlue,(N.s)/m'zlkg/(m.sec)]

The valuesof constantC aid the exponents , b, and c depend nthe type of agitator,whetherbafflesare used and their type, andwhether he transfer s via the vesselwall or to coi1s.Baffles arenormally used l mostapplications, nd the valuesof a, b and c inthe literature rc 213, l3, ard 0.14respectively.ables 14 and 9-15give typical cofielations or variousagitator ypes.Fouling Factors aDd Wall Resistances

Experience nd.iudgments to foulingseverity re requiredoestimateouling actors FFi,FFj) o dere.minehe overallheat ransfer

?"(YI(?i(r)"where hiDADTNp

kiCPp_


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338Chemical [email protected] vary with time and dependon the frequencyand efficiencyof vesselcleaning.Wall tesistances anbe significantand shouldbe calculated rom accuratehermalconductivitydata.Outside Coeffrcients h.) JacketedVesselsAnnular lacket with Spbal Bafflitg

In heat fansferapplications,his acket s consideted helicalcoilif certain actorsare Ltsedor calculating utside ilm coefficjents. heequivalentheat hansferdiameter,De, ot a rectangulat ross-sectionis equal o 4 w (w being the width of the annularspace).Velocitiesare calculated ron the actual cross-sectionf the flow area,pw (pbeing he pitch of the spiral balfle), and the effectivemass lowrateW' through hepassage.he effectivemass lowrate s approximately60Voof the total mass lowrateof the acket.

w'- 0.6At a gjven Reynolds number, heat transfer coeft'iciellts of coils,particularly with turbulent flow, are higher Lhan hose of long, sbaightpipes, due to flicfion. This also applies to flow through an amnlar

jacket with spiral baffling.At NR" > 10,000 the SiedeFTate equation for stiaight pipe, 1 +3.5(D"/D.) can be used to caiculate the outside film coefficient.

(,r_q)

$=oozz(N^")o',.'".f'"(f),.,,(+)} (9 -10)where D" = equivalentdiameier or heat ransfer, nm (fl)D. = Meanor centerline iameter f interl1al oil helix,mm (ft)

hi = heat ransfercoefficienton inside surfaceof jacket14 = viscosityat bulk fluid remperarure,(N.s)/m'?]Lkg/(m.sec)lA" = viscosityat the wall temperature,(N.s)/m'zllkg/(m.sec)lr . , _ p 'v 'D .-.' u


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Heat ansfer n agitationroesses 39

;*slilgiiiiigi;iiis374

Iz

n

E G - i G - D ' n ' n- - z z z z z z1 n 1 i . - - 9 v )

; i a ) )

.Dn?9:;x

z

z

|

o

F.9

llJ


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340ChemilEngineerirg rccesses

i,s iiiSl;*iii i3: c - : a ^J - a J r a\* _n \- -r - = J =. F : : i i K= t s i d -: : : ' - 4

Z =, n :j d o o x

: :

- i ' i G

z v.9 .9 .9

6 o B

E 6, i = = :

z


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Heattnslern agiialion rocesses41

;ri::E;;;:iaif;;;;i;;ii;: iEffE iirifiiiii:i:; :;;:;::i :;5; i i;EtltlAzz

tr

z

z

o

ut


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342Chemi@lEnsinees Processes

i i :ai; ;EtZ=,;i: +i?iia;,; , ;?t3i ';i:::?;;ft;i; : ; iii;* ilzriEiii

4 ?+

E E E . E: e rn; P ; 8 . 9

& a

:

z

=_B


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Heai ransfern agitationroesses343

. f . - , . . \ : i . f - 'ulu? :.:i5:*: ii i i+Es:::e: i:i l.s';;+Ei iiv:;iF" i: i-i'ii:;t::i;?i : i: ::i:; i:; . E;i ;i :,:;?:;; ;;;i: a;i ; 3i iE :

+ :

6 n

t 1

.6

v 6

zE

z

na9:97

c,'dFP


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3,14 hemical ngineeringro@sses

i

+ r 9

i E H7 q I -e

z t

*q SE : , :al^ E eE ri l^ * l 1 9 d t td t a a - t - a-o - l r j : b : :En E 3 : . . : .6 L r - e . E F iz :a : .E4YeEE f s Y5 r: EE n ' n r l5 ^ . a @ d ez -

3;i i v - :

E n n l: O

":-"1 1 1 32 l " 2: > 1 1 : ' " :E dr E ts i -E ,E '. ;+ i ;g"F': z , : ' c : . 1 r . iE ; ' -t z i iE, : :6 t 6+qieE E;iE-*: E:E:i=E d r r r r r r r z r l ' 1: : - r o o < z 1 ; , j r . ^o E E " a y ?,3 .9 .8 .E3 :> 7

- ,i -{

a : - : FEeU :P

i 3 - g b

z


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N*=:L I, kAr NR.< 2,100h n ^ , , , . . t ro . , [ o lo 'oi '=r.86(NR")"'(r")""tf,l ru_

Heat ransferin qitahonroesses345

(e-11)where L is the length of the coil or jacket passage,mm (ft).Annular lacket with No Baffles

In the case of steam condensation, film heat ffansfer coefficienth i s u .ed . n lhecase f l i qu id i rc u ia l ion .e loc i l i es i l l be ve ry owbecauseof the large cross-sectional rea.Ouloide ei l Lransferoefficienl"or unbaffledlecketsnder aminarflow conditions can be calculated rom,

hjD., . , . , . . , ro .a) iNro.r r lDelo ' fo 1o 'o r .ur t r \ReJ , r * t IuJ \u , . /

(No.)oo' (e-t2)

where Q1 = inside diameterof the jacketQ. = outside diameter of the jacketD.=1._D:,The Grashof umber o. s expressedy*- _ Djp':gpAro

where g = accelerationdue to gravityp = fluid density

/ \ 0 . 8,ll*lI D:,./


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346Chemical rgineering roesses

F = coelTicientof vdlumetdc expansiollAto = t1r"6i1"r"n"" between he tenperature at the wall and thatin the bulk fluidf$ = viscosity at bulk fluid temperaturc

Evidently, from the low value ol thethe contribution fron natural convectionnilicance is snall.The following equationlicients flom coils to tank

exponentn Equation -12,and,hence,ts practicalsig-can be used to predict heat tansfer coef-walls in agitated anks.

Dr ^l pNni "'/ copl'"1 o )"0&-'lr.JtkJlu.j (9 -13)where C is a constanl.Table 9-3 gives valuesof C for variousagitatortypes and sudace ul.Hcat Transfcr Area

Suface area or heatirg or cooling agilatedvessels an be providedby either exte.nal jacketing or intemal coils (or tubular baffles).Jacketing s usually preferred becauseof:

Table9-3Constant C) or various mpeller sAgitator SurfaceTurbineTurbinePaddlePaddlePropeller

Coi lCoi l

Coi l

0.621 . 5 00.360.870.460.540.83

Saurce:Chope ,N. P ahd Hi.ks,7: G., Handbook f ChemicalEngineerins alcul ions,McGtu|| HiU Book C0., 981.


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eatt.ansferin gila onprocesses47

Clieaperconstructio[ materialsbecausehe acket is not in contactwittr process luid.Less tendency o foul.Easier cleaning and maintenance.Fewer problems in circulating catalystsand viscous luids.Larger heat-fansfer surface, unless significant reactor volume jstaken up by the coils.. Helical jackets may allow thinner walls to be used for pressuevessels.. No rcstriction is plaoed on agitator type, whereas f a coil isi n \ l a l l ed l f es t r i c l sg i ta lo r imens ion , .

Coils should be considered nly ifjacketing alone does not providea suffic ient heat transferarea, fjacket pressureexceeds150 psig, orif highlemperature vacuum processilg is required.The coil ofl'ers headvantage f a higher overall film coefiicient because f thinner wallswith the latter condifons, but the wall resistancemay not be significantcompared o that on the processside (e.g., with a viscous iquid).Example 9-1

Determine the heat transfercoefficient from a coil immersed n anagitated vessel with a diameter of 3.048 nl. The agitator is a paddlemeasuring 1.01 m in diaaeter al1d evolving at 200 rev/nin.The fluid propefiies are:

p - densiry= '120kglmjg = viscosity 4.13cP = 4.13x l0 r (Pa s)Cp = specificheat= 2.9 krkg . Kk = thermaiconductivity= 0.17WmKAssumep/Ur)ora= 1.0.Solution

Frcm Table 9 3, for a paddle type agitator,C = 0.87. The heatftaosfer coefficient from Equation 9,8 becomeshg,=o.rzlro;.1'r1cnu1'rfuu|'ok, \Br\kJ(r '"J (e-r)


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348Chemicalngineeringrocesses

N = numberof revolutionper sec s 200/60= 3.3333 ev/sec.The Reynolds umber,NRe= pND2A/ rs:. , . . . . . , ( " )^, _ (720)(3.3313Y1l)" I kg . rev. m'- l"Re- 4. l3x l0- r | - , sec nt I. \ m. sec

= 592,794The Pmndtl number,Np. = Cpltk Ls*- . (z.qxloj)(+. t :vto' )1 r re . : : " . lL.K)0 .17 [ kg 'K m'sec I )

= '70.45The heat hansfercoefficients:

n,=o.r(ffi ) Oe ,'ts4)2t3't .4s)tFh" = 1,414W/m'?rTable9-4 shows he computeresults rom the MIXIR software.

Scale-Upvith IIeat TransferThe scale-upcriterion of constantheat tansfercoefficient s suitablewhen hepredominant roblemof the reactornvolves he removalofheat.The magnitude f the heat ransfercoefficients govemedbythe intensity of stiritrg within the rcactor, and is represented y:h?.r=c[ND;1"'[.*.1"'[l, l ' ' {e_r4)k \ p J \ k , \u* /

whereC is a constanthat depends n the agitatordesignandh isthe requirednside ilm heat ransfer oefficient.


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Heat ansfern agitationrocesses49Table9-4Heat transler coefticient to fluids in a vesselusing mechanicalagitated coils or lacket

DIAMETER OFTHERI.,A], CONDUCTIVITY, l{/M.K. IDIAYETER OF AGITATOR, M. IsrEED Or AGITATOR, rewlmin.:DNSITY oF FLUID, l


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350ChemielEngineenngroesses

l*, lout [oo, l ' 'ol\ l tD.Jo.xa=[que1"*Nr \ Do' -/

(9-r )

(9-20)

(e-2r)

(8-36)

(9 2J)

Assuming hat the ecluations in the turbulent angd, he Powernumberswill be equal.The ratio of thepowerperunit volume P/V)for largeandsmall scales an be expressedy(P/v), oNlD5^,/Dr,, Nl D?"(P/v), pN?D5A1/DL ui oi,Substituting f Equation9-20 nto Equation9-21gives(Plv) ,_( D^,) ' f oo, )- '"(P/vI lD*l l%./

- l'oo, )ou'-tD J (e-22)The powerper unit volume hus ncreases lightly.For equalheattransfer oefficients n smalland argescales,he arger ank will usean imDellerat a lower sDeed.

*n"* lL=|. -,|'v, \ DrrJ

N,,fur) '"N,_IV,JHavillg achieved the same heat transfer coefficient o[ the largerscale, he heat removal facilities must be increasedbecause he heat


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Heat ransfernagitaljonrocesses51

generation s propo.tioral to V2lVt, but the sudace areaof the vesselhas increasedby (V2lV1)2/3. his can be done by addjng coils in thereactor.Larger areas an be addedby using an externalheat exchangerand a pump aroundsystem. n somecases,t may be possible o lowerthe coolant temperatureand thereby ncrease he rate of heat flowtluough the existing surface.Howevet this is usually ixed by stabilityconsiderations,which require that the coolant temperaturebe withina few degreesof the reaction temperature.Liquid - Solid Agitation

In certain cases, he primary processobjective is to keep solidparticles n suspension. reasof applicationnvolve catalytic eactions,crystallization,precipitation, on exchange, nd adsorption.Axial llowand pitched-blade urbines are best suited n providing the essentialflow pattems n a tank to keep he solids n suspension. he suspendedsolid is chardcterized y two paraneters:. Particle density,pr.. Particle sizer the mean diameter, dp or the pa cle size distribution.Variouscorrelations reprovided or calculating he minimum speedof the agitator Nrii to keep a given solid in suspension. wietering

L2l developed he lollowing equation:..,'"="(+J"ont(p" p,-)uo'pl' d8' wro" (9 24)DR" fl"where Do = impeller diameter, nDr - tank diameter,mws = weight ratio of solid to liquid in percentage

PL = liquid densityPL = liquid viscosityY and o dependon the characteristics f the stifer'or agitator types of propellers, turbines with flat blades andpaddles,Y and (I are 1.5 and l .4,.espectively.The criterion orEquatior 9-24 is the absence f ary inmobile solid on the bottom ofthe tank.


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352ChemilEngineerin9rocesses

Weisman and Eff'erding [3] in constrast, related the degree ofagitation to the height Hs occupjed by the solid snspension,which isexpressedas:Hs-[E n,-r)pAl= 0.2]niprs)'*f%f ' l 0.r e s,Dr ln rgprvu5 D1 |

whereE = distance iom reactionbottom o agitatiotr ystemHs = height occupiedby the solid suspensionnr = ounber of stirring components1 to 3)V - volurne o be stirredes = volumetdc iaction of solidpM= detrsityof the suspensionu, = pan jc le ed imenra r io ra leEquation 25 was establishedor turbineagitatorswith flat bladesandZDA = 0.5. The criteria or Equation -25 elate o a specific ypeof suspension.he distributionof the solid as a functionof the heightin the liquid is not uniform in every case.Therefore, he unifolmity

can only be approximated y obtaininga circulation aaeQ as highas po$sible.Nienow [4] found that H,E = 7 rn tanks for whichH/Dr = 1.0.Recently,Corpstein t al. l5l found hat high efficiency mpellersprovidethe same evels of solids suspension t reducedcapital andoperatingcosts.They introduoed he term "jrrst suspended"or themostcomnonly encounteredevel of liquid solid agitation. his occu$when none of the sol id particles emains tationary r the bottom ofthe vessel or longer than l-2 sec.They developed corelation ofthe speed equired o achieveust suspendedonditionsas:'''=i[T)*]*r'(+)[+) (9-26)where k = applicable coefficient, k = 15.0 for a pitched-blade urbinelk = 23.0 for a high-efTiciency mpellera reference cale 0.29m)impeller diameter,mtank djanetet m


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Heal ransiern agiiationro@sses83f(X) = s611,1,oading factol., (X), is a non-linear functio, for upto 5olosolids loadingn = scale-upexponent

\ ,ulPiPsX

= just-suspendedpeed, l= terminal settling velocity for a particle, m/sec= dcnsity of liquid= density of solids= solids loading (solids nass/slurry mass)Therequiredpowercan be determined y:P = Npp,rN3Di

whereN = impeller otationspeed, rNp = impellerPowernumberP = Impellerpowerdraw,Wp.r= densityof slurry,kg/m3

(e-27)

Computatio[ fluid nixing and computational luid dynanic tech-niqueshave increasinglybeen used o elucidatesolids distribution inagitated vessels 6].

BATCII HEAITINGAND COOLING OF' FLUIDSHeating or cooling ol process luids i11a batch-operated essel scom]non in the chemical process ndustries.The process s unsteadystate n naturebecausehe heat flow and/or he temperatmevary withtime at a fixed point. The time required for the heat transfer cal1bemodified, by increasing the agitation of the batch fluid, the rate ofcirculation ol the heat rransfermedium in a jacket and/orcoil, or theheat transferarea.Bondy and Lippa [7] andDream 8l havecompileda colleclion ot' corelations of heat transler coefficients in agjtatedvessels.Batch proce$ses re sometimesdisadvantageous ecause:. Use of headng or cooljng medium is intermittent.. The liquid being p.ocessed s llot readily available.. The requiaementsor treating time require holdup.. Cleaning or .egeneration s an integtal pad of the total operat_ing period.


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354chemil Engineeing bcesses

The variables in batch heating or cooling prccessesare surfacerequirement, time, and temperature.Heating a batch may be by extemalmeans (e.g., a jacket or coil) or by withdrawing and recirculatingprocess liquid through an extemal heat exchanger. n either case,assumptionsare made to facilitate calcu]ation,namely,. The overall heat transt'er oefficient U is constant or the processand over the entirc sudace.. Liquid flowrates are at steady state.. Specific heats are constant or the process.. The heatingor cooling medium has a constant nlet temperature.. Agitation gives a uniform batch fluid temperature.. There is no phasechange.. Heat losses are negligible.The following discussesvarious heating or cooling prccess con-ditions in a batch vessel and the processing ime relationsl'lips.

BATCI{ HEATING: INTERNAL COIL,ISOTHERMAL HEATING MEDIUMWhen an ag?tated atch containing M of fluid with specific heat cand initial temperature is heated using an isothermal condensingheating medium Tt, the batch temperature 2 at any tim(- e can bederived by the differential heat balance. For an unsteady state operationas shown in Figure 9 2, the total number of heat transferred s q',and per unit tine 0 is:I I I

d,n' d ido_ :a_ Mc_ : : = uAAld0deAccumulation Transferin the batch rate

TV

whereAt=Tr - iEquating II and V gives

(e-28)

(9-29)


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Figure 9-2. Agitated atchvesssl.

Heal ransfern agitationrocesses55

(e-30)

(e-31)

(9 32)

Integrationof Equation9-32 tom tt to t2 while the batch pro-cessing ime passesrom 0 to 0 yields:

hf r, -r , l=uA 0\Tr-t, J Mc

Mc:=UAAId0RearralgingEquation9-30 givesdr UA ,^At MC

Integrationof Equation9-31between he limits givesi d t UA i -| = - l our T , - t Mc l

Ht exchangerwirbn t[e baich


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Heal ransfern aqitationrocesses57

^ 1r.386\(22.6'/e.5)(2.1x10,)" = (8soxq29r3ioo) -= 2.32ht

Computersoftwarc BATCH)was developedo determinehe timerequired or heatingor coolingprocessluids n a batchsystem. able9-5 givesthe conputer resultsof Example9-2.BATCII REACTOR HEATING AND COOLING

TEMPER{TURE PREDICTIONStart up of a jacketed batch reactor rcqulesand cool-down rates.This involves determiningheat transtbr luid tempelatules. n altemative sand incoryorate the results into a tinle depetdent^ . / r,-r, ) t 'u")u = l n l ' l . l - l\Tr - t r , \uAJ

controlof the heat-upand setting he acketto makea trial heat-upheat transfetequation:

(9-3.)Equatjon9-33 can also be used o calculatehe heat,up ime lornon-isorhermaleating e.9.,by hot-wateracketing), rovided hat hedifferencebetween he outlet and iqlet jacket temperaturess notgreater hatr lOEaof the differencebetween he batch and averasewater emperature9].

Table9-5Batch heating: nternalcoil isothermalheating

, oooIIEAT TRANSFXR SITRFACEAREA, m^2:sPEclFIc HBAT oF LIQUID. kJlkg.K:WEIGIA OF BATCH I-IQVID/ Kg.:INITIAI, BATCH TEI,IPERATORE, K:FINA]- BATCTI TEMPEBATURE, X:OVERALL IIEAT TRANSFER COEFFICIENT, i/d^2.K:TIl.tE, hr, :

9 . 2 9 02 . 1 0 02 2 6 7 9 . 5 0 0293.OOn3 9 8 . 0 0 0I 5 0 . 0 0 02 . 3 2 3


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35SChemr@l nqineeringrce$es

Assuming hat M, c, U,.. UAMc

Equation9-33 becomes/ - . \ ,0=hl l-L:lL l. '\Tr - t r l K

f t 1 - t 2 e ^ "

and A are constants,where

(e-34)

(e-3s)RearrangitrgEquation 9-35 gives the jacket temperatuleas afunctionof time as:

(9-36)Thos, by taking a seriesof readirlgs udrg a trial heat-up,K canbe detemi[ed. The heat-upandcool-down imes or varying ackettemperatures an then be predicted.

Example -3Assume that in Example 9-2, the ovela cycle time for a batchreaction s 8 hrs. The cycle tirne will include2 hrs for heat-upand3 hrs for cool-down.The batch will be heated rom 20'C to thercaction empemture f 60"C, hetrcooled o 35'C. Usilg a hot-waterjacket temperature f 80"C, it took 15 mir to heat he batch rom 20"Cand 30'C. Calculatehe ackettemperaturesequircd or heat-upandcool-down.

SolutionFrom Equation9-34,,. UAMc

(8soxe.2e)(22,1 .5)(2.r)(r,oo) I r , l ks.Kllsec.mrK kg J lK = 0.00017 ec


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Heat ransfern agitationrocesses59

The acket temperatureequired or a 2 hr heat-upcan be obtainedfrom Equation9 36 as:. , ^K0_r 1 ^Ko

f 0.000r7-Lx2x3.600secl20 * 60e\ sec /, _ "(o.ooorr

-.:.:.ooo,*)

Thejacket temperatureequled for a. . _Ke- r ' ^ K 0

(9-36)

3 lu cool-down is:

fo.ooorrlx:*.ooos*)60 - 35e\ soc /fo.ooorz-L':,:,ooo*"11 - e \ s e c /

= 30.3"C9SATCH COOLING: INTERNAL COILISOTHERMAL COOLING MEDIT]M

Consider he samearangenetrtas beforecontainingM of liquidwith specificheal c and nitial temperatu.e t cooledby an isothermal-vaporizingmediumof tenpemturel. If T is thebatch emperaturetanv time 8. dlen

d9'=-M" dr =uatde de (9'37)


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360Chemical ngineeringrocesses

wheieA t=T t r

Then-u"$=ga11 (e-3e)d0Subsr i tu l ingqua t ion l8 in to Equa l ion -Jq and rear rang-ing gives:? or ?u,q.i , T- t r 'oMc

(9-38)

(9-40)Integrationrom Tl to T2while he timepassesrom0 to e gives. I T, - t , I UA ^l l l l - - l = - . H\T, -t, / M"

o, 6=M"6[ r ' -q IuA \rr- t r , (9-4rwhercA = heat ransfersudaceareac = specificheat of batch iquidM = weight of batch iquidTt = initial batch emperatureTz = final batch empemturett = coolingmedium emperature

U = ovemll heating ratrsfer oefficient0 = timeBATCH HEATING: NON-ISOTHERMALHEATING \,IEDIUM

The non-isother-maleatingmediun has a constant lowrate Wh,spec.ific eat Ch,and inlet tempeEtureTt, but a variableoutlet tem-pelature.For an unsteady lateopefation:


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Heattransfer agitaiionroes*s 361 '.

I [ I I I Iv+ - M"+ - w\ch(T.-T.)= uAArrMrD ts-421de deThe log mean empemture ifferenceAt,_rro s:

Equating lI and Mn Equation -43 and rearranging ives:

^ . - T t -T tdrr MTn - ----:-----------tn l t - ' IlTz- t . /

(e-43)

w"c"(T, - Tr)_ T,_T,uA . fr,-t ' lr4 ' lI rz tJEquation9-44becomes:

, ,(r,-, _ ue\T , - rJ WhCh (9-45)

where K, =swhcr (9-48)Equating I and II in Equation9-42 and substitutingEqualion9-47into Equation9-42gives:

T , - e n - n ( 9 . 4 6 )

Rearranging quatjon9 46 gives

(4.117\^ W L C L


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362Chemi@l ngineeringroesses

Rearranging quatton -4g and inlegraltngrom l l to t2 r hi le theprocessing ime passes rom 0 to e gives:

*"$=*,",{r,-(,.?)}=*,",(ftj}',-o

' i a' ?w,c-lr,-r).^iT,- , i Mc I K, JIntegratingEquation9 50 gives. /r, -t , ) rwc, tt ' r , r)-m l ' l = l " l l ' l e\E- r r ' \ Mc i \ K, . /o,e-r K, )r M")r,[t,-,,)\K r - l , \whch , IT r - r2 ,

where A = heat transfer surfaceareac = specificheatof batch iquidCr,= heatingmediumspecificheatM = weight of barch iquidTl = heatingnedium tempemturetl = initial batch empemtuetz = final batch emperatureU - overall heat ransfer oefficienlWh = heatingmedium lowrate0 = time

(e 49)

(e-s0)

(9,51)

BATCE COOLING: NON-ISOTHERMAL COOLING MEDIUMWhen cooling a batch with internal coil and a non-isothelmalcoolingmedium, he following equation an be applied.


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Heattransturn agitationro@s*s363

*= - * " * -w c" ( r ) - r ' ) = UAAr l6p (e -s2 )de delwhereK2 = ew'c'

. . f r , -t , ) rw^c"r/r.-t)^a n o l n t ' t =\T , t rJ \ Mc / \ K , . /(e-53). =[ ", ]f t" ),"ft,- ' ,lK, -1. / \w"c.J \ r , - rp,

where A = heat transtbr surface areac = speciiic heat of batch IiquidC" = coolant specific heatM = weight of batch liquidTr = initial batch temperaturcTz = final batch temperaturetl = in;tial coolant temperatureU = overall heat fansfer coefficientW" = coolant flowrate0 = time

Example 9-4For the tank described n Example9 2, calculate he time reqLriredto cool the balch from 398 K to 313 K if cooling water is availa-ble at a temperatureof 303 K with a tlowrate of 4535.9 kg/hr.

SolutionSelectand apply the appropriate eat transfer ormula. When cool-ing a batch wjth internal coil and a non-isothermal ooling medium,the following equatioocan be applied.

ol - - * .11 - wcc.(12- t r )UAATLMTD ra52)d0 de


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364ChemilEngineeringrocesses

where K2= eulw c.. . ( r,-t,) rw^c-t(r.-r)-I = l " l l ' l H\T r - r r , \ Mc / \ K , . /

K" =eu^/-,(e-53)

l,rro;1"..1:.o001f I1rq...,s.";tq.a{'0,tl I I m' ks.K I= e i ( ^ - . _ . . _ > l sec .m 'K I& . f f lo rJ II hr 3,600"" I= 4.58

. /r , - t , ) / w^c, fK, l )-l n l l = l ' ' l l ' l H\T2- t rJ \ Mc / \ K, J, - l ie8 303 [1+.s. ls.o1r.ru;11+.ss1l3 r3- lOJ/ L(22.67e.s) (2 . t ) l t.s8 |

f , , , . , . . 1^ t K s K J I K e l \ - t -x u {_ . _ ._ . - >uLhr ks.K kg kJ I0 = 7.34hrTabie9-6 gives he computer csults rom the software BAICH)for batchcooling, ron sothermal ooling medium.

BATCH HEATING: EXTERNAL HEAT EXCHANGER,ISOTHERMAL HEATING MEDIUMFigure 9-3 illustratesthe arrangementn which the fluid in the tankis heatedby an external heat exchanget.The heating l]1edium sisothermali hereforeany type of exchangerwith steam n the shell


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Heat Ensfer in agitationproesses 365

Table 9-6Balch cooling: non-isothermal ool ing inediumHEAT TRANSFER SURFACE AREA, n^2:SPECIFIC ITEAT OF I,IQUID, KJlKg.K:cooLINC i4EDMt SPECIFIC ltEAT, kJ/kg.I


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366ChemielEnsineennsrcesses

I I I+ - rur.* = whch(r' t) - UAAILMTD (9-54,dr d0

Heat Heat entering Tmnsfer ateaccumulation thebatchby in the extemalin the batch recirculation exchangerThe log nean tempelaturedifference ATLMTDs: r

(r , -r)-(r , -11a I t ,tl-D ul t ' ' I\TL t 'J

=Jlrl (e-55)l r , -1,

Equat ingl and l l i n Equa( ion -54g ives :WhCh t' - t) = UA atlyp (9-56)That is:

l r ' - r lw"C"( t ' - r )=UA ) ' , re 57tml ' -tfl r ' - t , jRearrangingquation -57gives. lT , - r I UA'o l1' - ' ' j= wncn tq-58)Equation9-58 can be expressed s:

f, -t = ewt'cn f, -t ') (e-5e)


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Heat ransfer n agilaiionprocesses 67

where K3=ewhchT1-t- K3 Tr t ')

Therefore,

, ,= , - l . t - t )' lK,JEquxting anJ TT n Equatjonq-54 gives

Mc4=W.C.f t ' - r )deSubstitutingEquation9 6l into Equation 9-62 and rearang-ing yields

Mc.dt_ Ir_[t-,) l _,whch do L ' \Kr ,J_ (K. t)(r, -t)K3

(e-60)

(9-61)

(9-62)

(e 64)

RearrangingEquation 9-63 and integrating rom tl to t2 while thetime passes rom 0 to 0 gives:

'i q = sd)f %cnio,iT , - , \ K3 / \ Mc /Jowhichvieldsof , -r , )_ [ r , -r)1 wnc|-1." \ r , -rr . / \ Kj Jt v" I


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368Chemical nsineeng Prc@sses

^ / r , ) / uc )- 1r, - t , )" ' "=[r-r J[w6i '"tt '- ' ,J {q s)where A = heat transfersurfaceareac = specific heat of batch liquidCh = heating medium specific heatM = weight of batch liquidTr = heatingmedium emperaturetl = initial batch temperaturet2 = final batch temperatureU = overall heat ffansfer coefficientWh = heatingmedium flowmte0 = time

BATCH COOLING: EXTERNAL HEAT EXCHANGER,ISOTHERMAL COOLING MEDIUMWhen cooling a balch with an extemal heat exchanger and anisothermal ool ingmedium. he equerions:

I v \ l ^,^ \ r '- - ror e=l --:L lJ 5 l1nl r lL I" ' "-(xo-r.J[w.c"]"' l t .rl re-66)where Ko = suw.c. 'A = heat transfer surface aleac = specific heat of batch liquidC" = coolant specific heatM = weight of batch liquidTr = initial batch temperatureT? = final batch temperaturett = initial coolant temperatureU = overall heat transfercoefficientw. = coolant lowraree = time


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Heal ransfrn aqitationrocesses369

BATCH COOLING: EXTERNAL HEATEXCHANGER (COUNTER-CURRENTFLOW),NON.ISOTIIERMAL COOLING MEDIUMWhencoolinga batchwitLran external eatexchanger nd a non-jsothermal oolingmedium, he following equation an be usedl. /r, , ,) rx.-rt/ w,w-c )^I n l - l - l -\T) - r r r \M/ [Krw.Cw"cJ

^ /r


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370ChemilEngineeringrocesses

hf -' I I K' r )1. wow"c")e\T , - , , , / \ M /\K,w"C"-woc./

0l)I)(1,33e.8X4,53s.eX4.2)

(e-67)where

.,=*o{uo(uf;-)}[0. .l+ s.ssr.].ool 1 r )l=exD< t - - _ t )' I r .000 \ (r.3jq.8x2.r)4.sls.ex4.2),1

I L , hr 3 .6oosec e.K Ifsec.K kg hr lO 'J I

= 0.4509

. (:ss-:o:) /0.+sos-rr n l - l = l -\313-303/ \ 22,679.5)-(+1l t t - t '\Tt - tr wbw"c"w"c" wb5

^ ( (0.4s0ex4,535.ex4.2)01,33e.8)(2.1)0 :6 .55hrTable 9-7 shows the computer esults using an externalheatexchanger nvolving a non-isothermal ooling medium.

BATCH HEATING: EXTERNAL HEAT EXCHANGERAND NON-ISOTHERMAL IIEATING MEDIUMWhen heating a batch rcactor with an externalheat exchangerand

non-isothemal heating, he lbllowing equationapplies:

) '


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He.l kansfernagitaiior rocesses71

t a D t e 9 - lBatch heating/cooling of fluids exlernal heat exchanger:(counter-current tlow) non-isothermal cooling mediumT.EAT TRANSFERSURFACEAREA, n^2:SPECIFIC ltllAT OF LIoUID, k,t/kg.r


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372Chemical nsireeingPro@sses

Table9-8Rules-of-thumb:mixing and agitationL Mild agitdtion s obrained y circulaling he iquid wirh rn impelierarsuperficialvelocitiesof0.l 0.2 ft/sec.and nlenseagitatior a 0.7-1.0 ft/sec.2. IDtensities f agitarioDwilh ilnpeller n b:rffledunks afe measured y powertupnl.hp/1.000 al.and mpel lef ip speeds:

OperationBlendingHoffogencouscaclionReaction vith heat transferLiquidi iqui . lnr ix luresLiquid-gasn1ixrufesSluffies

Tip sped(ftlrnin)7.5 l0l 0 - 1 515 2t)1 5 2 0

hp/1,000 al0.2 0.50.5 r.5i.5-5.055 .0 010l

1.5 .6 .

Propoftions of a sliffed tank relative o the diameter D: liquid level = D:turbine inrpellef diameter = D/3i impelier level above bortoff = D/3; jmpellerblade with = D/15: tbur veftical bafflcs rvith widih = D/10.Propellers afe a maxinunr of l8 iD.: turblne impellers ro 9 ft.Gas bubbles sparged ri Lhcbotlom of the vessel will result in mild agiration aa s pcrficial gas velocity of 1 f/min aDd seveLagitation nl 4 ftllrlin.SuspensioDof soljds with a seltliDg velocity of 0.03 fthcc is accomplishedsith eilher turbiDe of pfopeller lnpellers, but when the sertling velociry isabove 0.15 frsec iitense rgitation with a propeller is needed.

7. Power o drive a mixtureof a gasnnd a ljquid caDbe 25qa 50t/. less han rhepower10dfive he iquid lone.8. In line blenders rc adequalcwhen a l-2 sec contact ine is suiiicicnt.withpower nputs f 0.1 0.2 bp/gal.

serious mpact on results-Poor inixing is a primary sourceofvadability in ploductsmade r batch reactors.The resultsfor areaction un in a pooriymixed CFSTRmay deviatestfol]gly romthose expected.There is lo single "correct" agitator type. Different agitatordesignsmay perlbm equally well, or equallypoor.ly,or a givenapplication.Although some detaileddesign calculationscan beperformed,workable designsare otien developedby trial and error.Many reactioDsnvolve shear-sensitive aterials,which severelylimit the maximum mixing rate and make impeller and reactordesign important.Mixing becomes he limiting factol..

Sauree: ttLrlat, S. M., CheDical Pfocess Equitdenr Selecrion and Design, aane\anh Scrjeshr Clertnlrl Lngitle?bi , l9il8.

3.


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Heat ransfernagiiationrocesses73

Table 9-9Mixing equipment specificationsMixer data sheet

ulor.q8cti _

jURRY llssn if?slll

DsignStlndrrds and nspction

Mltrials of consrlciion: - _ a M . . _ - l _ ;

n

R.ptn.tuc.d tlith ternissiul of PROCEDE.


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374ChemilEngineeringro@sses

TableReaclor vessel 9 -10specificationsVessel ata sheet

11@ruRNMyAEprLf rN. Bof Hrarc;E

Reprcduc..l rrith perrkistbh of PROCEDE.


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Heal ransiern aqjtationroesses3T5

DESIGN OF MIXING SYSTEMSThe lbllowing proceduremay be adopted n the designof a mixingvessel or a given process.1. Study heproperties f the iquid andphysical equircments, ndchoose he type of impeller.Select size ratios preferablythe same as the standardvalues(Table -2) o avoidexperimentationr based n smal1-scaletudies.Select mpellerdiameterDA for the largei system o accom-

modate he systembeing mixed. This leaves he impeller speedN as the only independent ariable.ChooseN based n scaleup studies r commonly sed ules.Calculate hepowerP, mixing time 0, gtc.Account br mechanicalIosses rd the ike whenselecting motor.ChangeN and P to slandard alues.Itemteand see f alternative esigns equiring owerpowerexists.Perform nlechalical designs e-g., o obtain shaft diameter,supports,bearingdesigns,etc.).Table9-10 showsa mixing equipment pecitication heet,which canbe helplul as a geneial checklist.Generally, he specificationsheetshould not be completely elied on for a mixirg problem,unless heproblem s known or data are knovrn th4t can be given to the manu-facturer e.9.,blendilg, dispe$ing,or dissolvingcrystals).For udqueproblems, aboratory data should be cal.riedout undel the guidaDceof technicaladvice rom the manufacturr r otherqualjfiedauthority,in order that adequate caleup dala are taken and evaluated. t isessential hat both a description and dimensiols are given tbr thevessel o be used.Otherwise,equest he matufacturer o recommend

the type best suited o the service. able9 11providesa rcactorvesselspecificationclatasheet.

2..3 .

4 .5 .6 .7 .8 .


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376Chemical ngineetingroesses

REFERENCESl. Chopey,N. P., Handbookof ChetuicalEngineeringCalcul.ations,pp. 7-28, Mccmw-Hjll Book Company,1984.2. Zwtetering, . N., "Suspendiigof solid particles n liquid byagitators,"Chem.Eng. Sci.,Vol. 8, pp. 244-253, 1958.3. Wei$man, . and Efferding,L. E., AICLEI, 6 (3), 419, 1960.4. Nienow,A. \'1., Chem.Eng. Sci., 23, pp. 1453-1459,1968.5. Corystein,R. R., Myers,K. J., ard Fasano, .,'The high efficiency

road to liquid-solidagitation,"Clrcm.Eng., Oct. 1994.6. Bakker,A., Fasano, ., andLeung,D. E., "Pinpointmixingprcblenswith lasers and simulation soflwale," Chetu.Eng., pp. 94-100,Januarygg4 .7. Bondy,R and Lippa, S., "Heat ranstern agitated essels,"Crem.Eng.,pp.62-:71,1983.8. Dream, R. F., "Heat fansfer in agitatedvessels,"Chem. Eng.,pp. 90-96,Jan. 1999.9. McEwan, J., "How to predictbatch eactorheatingand cooling,"Chem.Eng.,p. 179,May 1989.10. Walas,M.5., ChemicalProcessEquipmentSelection nd Design,ButterworthsSeries n ChemicalEngiDeering, 988-ll. Falconer, . L. and Huvard, G. S., "Inportant concepts n undergmduatekinetics andreactordesigncou$es," Chenicdl EngineeringEdLlcatiorx,p. 140-141, ol. 33, No. 2, Spring1999.

Documents

Chapter -9-Heat Transfer in Agitated Vessels