化工原理英文教材-分离设备部分chapter6

SeparationequipmentsTheseparationequipmentsinclude:

GravitysettlingCentrifugalsettlingfiltrationGravitysettlingprocessesDustparticlesmayberemovedfromgasesbyavarietyofmethods.Forcoarsesolidparticles,largerthanabout325-mesh（43μmdiameter),whichmayberemovedbyagravitysettling.agravitysettlingchamberlikethatshownschematicallyinFigurebelow.

Intheabsenceofaircurrents,particlessettletowardthefloorataspeedequaltotheirterminalvelocities.

Topreventtheairstreamfromliftingtheparticlesfromthefloorandre-entrainingthem.Theairvelocityshouldnotbegreaterthanabout3m/s.timerequiredbyparticlesorgastopassthesettlingdevice,t=L/u(uparallelvelocity)Timerequiredbyparticlestogettothebottomofdevice,t’=H/ut(utsettlingvelocity)Inordertoremovetheparticlesfromgas,theconditionshouldbesatisfied.t

t’L/u

H/utProductivityofgravitysettlingdeviceVVisgasvolumeflowratetobeprocessed.V=uA=ubH(Abottomareaofdevice)Sincet>or=t’andL/u

H/ut,u

utL/H.V=ubH

bHutL/H=utbL=utAConclusion:productivityofgravitysettlingdeviceisrelativetosettlingvelocityutandbottomareaofdeviceA,butindependentofheightofdeviceH.Inordertoincreasetheproductivityofdevice,thedevicecanbedividedintomanylayers.CentrifugalsettlingprocessesThegravitysettlingchamberisprobablythesimplestandearliesttypeofdust-collectionequipment.Practically,however,itsindustrialutilityislimitedtoremovingparticleslargerthan325mesh(43μmdiameter)Agivenparticleinagivenfluidsettlesundergravitationalforceatafixedmaximumrate.Toincreasethesettlingratetheforceofgravityactingontheparticlemaybereplacedbyamuchstrongercentrifugalforce.Separationofsolidsfromgases;cyclonesMostcentrifugalseparatorsforremovingparticlesfromgasstreamscontainsnomovingparts.TheyaretypifiedbythecycloneseparatorshowninFigure.Theincomingdust-ladenairreceivesarotatingmotiononentrancetothecylinder.

Thevortexsoformeddevelopscentrifugalforce,whichactstothrowtheparticlesradiallytowardthewall.Thecentrifugalforceinacycloneisfrom5timesgravityinlarge,low-velocityunitsto2500timesgravityinsmall,high-pressureunits.Inacyclone,dustparticlesquicklyreachtheterminalvelocities.Theradialaccelerationinacyclonedependsontheradiusofthepathbeingfollowedbytheair,andgivenbythefollowingequation.Whererisradiusofparticlemotion,uiiscirclevelocity

soterminalvelocityisCriticaldiameterCriticaldiametermeansthemindiameterofparticlescompletelyremovedbycyclone.ThecriticaldiameterofparticleremovedbythecyclonecanbederivedintermsofboththeterminalvelocityandtangentialvelocityuiForcyclone,thesettlingtimeiswrittenasfollowswhereBisthedistanceofparticletothewall,and

t

istheresidencetimeorsettlingtime.ResidencetimedependsonthetangentialvelocityuiandthenumbersofspiralsNCombiningtwoequations，thecriticaldiameterofparticleremovedbythecycloneisTheequationcontainseffectsofcyclonesize,velocity,viscosity,anddensityofsolid.Questions?Whenthediameterofcycloneincreases,ornumbersofspiralsNdecrease,whathappenstotheefficiencyofcyclone?Whentheviscosityoffluidsincreases,whatisgoingontheefficiencyofcyclone?FiltrationDefinition:Filtrationistheremovalofsolidparticlesfromafluidbypassingthefluidthroughafilteringmedium,orseptum,onwhichthesolidsaredeposited.Filtersmaybedividedintothreemaingroups,dependingontheservicetheyperform:1clarifiers2cakefilters3CrossflowfiltersSomeconcepts:Filtrate:liquidgotfromsolidliquidmixturebyfiltrationSeptum(filtrationmedia)likepaperorcloth.Cake:solidgotfromsolidliquidmixturebyfiltration.Slurry:solidliquidmixtureSlurryfiltration:Fluidflowsthroughafiltermediumbyvirtueofapressuredifferenceacrossthemedium.Mostindustrialfiltersareeitherpressurefiltersorvacuumfilters.Theyarealsoeithercontinuousordiscontinuous.ClarifyingfiltersClarifyingfiltersarealsoknownas“deep-bedfilters”becausetheparticlesofsolidaretrappedinsidethefiltermedium.Clarificationdiffersfromscreeninginthattheporesinthefiltermediumaremuchlargerindiameterthantheparticlestoberemoved.Theparticlesarecaughtbysurfaceforcesandimmobilizedwithintheflowchannels,asshowninFig.30-6aGascleaningFiltersforgascleaninginclude:padfiltersforatmosphericdust,granularbedsbagfiltersforprocessdusts.Inapadfilter:

airiscleanedbypassingitthroughpadsofcellulosepulp,cotton,felt,glassfiber,ormetalscreening;thepadmaterialmaybedryorcoatedwithaviscousoiltoactasadustholder.

Granularbedfilters:

containstationaryormovingbedsofgranulesrangingfrom30-meshinsizeinsomedesigns.

Abagfilter:

containsoneormorelargebagsoffeltorthinwovenfabric,mountedinsideametalhousing.Efficienciesaretypically99percent.LiquidclarificationClarifyingfiltersforliquidsinclude:ClarifyingfilterCartridgefilterUltrafilterCakefiltersThemechanismofcakefiltrationisshowninFig.30-6b.Herethefiltermediumisrelativelythin,comparedwiththatofaclarifyingfilter.theparticlesiscollectedontheseptumsurface.Afterbriefinitialperiodthecakeofsoliddoesthefiltration,nottheseptum;avisiblecakeofappreciablethicknessbuildsuponthesurfaceandmustbeperiodicallyremoved.DiscontinuouspressurefiltersPressurefilterscanapplyalargepressuredifferenceacrosstheseptumtogiveeconomicallyrapidfiltrationwithviscousliquidorfinesolids.Themostcommontypesofpressurefiltersarepressfilterandshell-and-leaffilter（叶滤机）.Filterpress（板框过滤机）Afilterpresscontainsasetofplate(frame)designedtoprovideaseriesofchambersorcompartmentsinwhichsolidsmaycollect（Fig.29.4).Theplates(frames)arecoveredwithafiltermediumsuchascanvas(cloth).Slurryisadmittedtoeachcompartmentunderpressure;liquorpassesthroughthecanvasandoutadischargepipe,leavingawetcakeofsolidsbehind.Theplate-and-framepressfiltershowninFig.Afterassemblyofthepress,slurryisadmittedtooneendoftheassemblyofplatesandframesfromapumporblowcaseunderapressureof3to10atm.Auxiliarychannelscarryslurryfromthemaininletchannelintoeachframe.Herethesolidsaredepositedonthecloth-coveredfacesoftheplates.Liquorpassesthroughthecloth,downgroovesorcorrugationsintheplatefaces,andoutofthepress.Filtrationiscontinueduntilliquornolongerflowsoutthedischargeorthefiltrationpressuresuddenlyrises.Theseoccurwhentheframesarefullofsolidandnomoreslurrycanenter.shell-and-leaffiltersForfilteringunderhigherpressuresthanarepossibleinaplate-and-framepress,toeconomizeonlabor,orwheremoreeffectivewashingofthecakeisnecessary,ashell-and-leaffiltermaybeused.ContinuouspressurefiltersBatchfiltersoftenrequireconsiderableoperatinglabor,whichinlarge-scaleprocessingmaybeprohibitivelyexpensive.Thecontinuousvacuumfiltersdescribedbelowweredevelopedtoreducethelaborrequiredforfiltration.rotary-drumThemostcommontypeofcontinuousvacuumfilteristherotary-drumfilterillustratedinFig.Ahorizontaldrumwithaslottedfaceturnsat0.1to2r/mininanagitatedslurrytrough.PrinciplesofcakefiltrationInfiltrationtheflowresistancesincreasewithtimeasthefiltermediumbecomescloggedorafiltercakebuildsup.Thechiefquantitiesofinterestaretheflowratethroughthefilterandpressuredropacrosstheunit.Astimepassesduringfiltration,ethertheflowratediminishesorpressuredroprises.Inwhatiscalledconstant-pressurefiltrationthepressuredropisheldconstantandtheflowrateallowedtofallwithtime.Lesscommonly,thepressuredropisprogressivelyincreasedtogivewhatiscalledconstant-ratefiltration.Incakefiltrationtheliquidpassesthroughtworesistancesinseries:

Thatofthecake

thecakeresistanceiszeroatthestartandincreaseswithtimeasfiltrationproceedsThatofthefiltermedium

whichistheonlyresistanceintheclarifyingfilter,isnormallyimportantonlyduringtheearlystagesofcakeIfthecakeiswashedafteritisfiltered,bothresistancesareconstantduringthewashingperiod.Theresistanceoffiltermediumisusuallynegligible.TheoverallpressuredropΔpatanytimeisthesumofthepressuredropsovermediumandcake.IfthepressuredropsofbothcakeandmediumareΔpcandΔpm,respectively,then

Δp=Δpc+Δpm

(7-49)PressuredropthroughfiltercakeTheactualchannelsinasolidbedareirregularinshape,haveavariablecrosssectionandorientation,andarehighlyinterconnectedTocalculateanequivalentchanneldiameter,itisassumedthatthebedhasasetofuniformcircularchannelswhosetotalsurfaceareaandvoidvolumemachthoseofthebed.Itisconvenienttobasethecalculationonthevolumefractionparticlesinthebedandthesurface-volumeratiofortheparticles.Thisratiois6/dpforasphere,since

andForothershapesorirregularparticles,theequationforsurface-volumeratioincludesasphericityφ

φ

isdefinedasthesurface-volumeratioforasphereofdiameterdpdividedbythesurface-volumeratiofortheparticlewhosenominalsizeisdp,Thus(7-50)Thevolumefractionparticlesinthebedis1-ε,whereεistheporosityorvoidfractionTodeterminatetheequivalentchanneldiameterDe,thesurfaceareafornparallelchannelsoflengthLissetequaltothesurface-volumeratiotimestheparticlevolumesL(1-ε),wheresisthecross-sectionalareaofthebed:

(7-51)Thevoidvolumeinthebedisthesameasthetotalvolumeofthenchannels:

(7-52)CombiningtwoequationabovegivesanequationforDe

(7-53)Theequivalentdiameteristoughlyone-halftheparticlesize.Theaveragevelocityinthechannelu´isproportionaltothesuperficialorempty-towervelocityuandinverselyproportionaltotheporosity:(7-54)ForflowattheverylowReynoldsnumbers,thepressuredropshouldvarywiththefirstpowerofthevelocityandinverselywithsquareofthechannelsize,inaccordancewiththeHagen-Poiseuilleequation(5-16)Theequationsforu´andDeareusedin(5-16),andacorrectionfactorkisaddedtoaccountforthefactthatthechannelsareactuallytortuousandnotstraightandparallel:(7-55)Severalstudieshaveshownthattheformoftheequationiscorrected,andexperimentsgiveanempiricalconstantof150(7-56)EquationiscalledtheKozeny-CarmanequationandisapplicableforflowthroughbedsatparticleReynoldsnumbersuptoabout1Thelinearvelocityuisgivenbytheequation(7-57)WhereVisthevolumeoffiltratecollectedfromthestartofthefiltrationtotimet.

Sincethefiltratemustpassthroughtheentirecake,V/AisthesameforalllayersanduisindependentofLSubstitutingufromEq.【7-57】inEq.【7-56】givesThefiltrationrateis(7-58)Aspecificcakeresistancerisdefinedbytheequation

(7-59)Therisconstant,whenthefiltercakeisincompressible.AcakeresistanceRcanbedefinedby

(7-60)Forequation【7-60】Risalsodefinedasfollow

R=rLFiltermediumresistanceAmediumresistanceRmcanbedefinedbyanalogywiththecakeresistance.Theequationis

(7-61)ResistanceRmisimportantonlyduringtheearlystagesoffiltration,itisnearlyalwayssatisfactorytoassumethatitisconstantduringanygivenfiltration.FromEq.【7-60】and【7-61】SinceR=rL,andanalogously,Rm=rLm,then(7-62)Constant-pressurefiltrationBasicEquationoffiltrationIftheratioofthecaketothefiltrateisdefinedbyv,then,therelationbetweenthethicknessofthecakeLandthefiltratevolumeVgivesasfollows

(7-63)BeforewededuceBasicEquationofconstantpressurefiltration,assumptionsare

made.Assumptions:1Cakeisincompressible2Flowinthecakeislaminar3ConstantpressureFiltrationrate:dV/Adt=drivingforce/resistanceFromexperiment,weknowRate=drivingforce/resistanceDrivingforce:

P(pressuredrop)Resistance(relatedtothicknessofcake,septumandviscosityoffiltrate):thethicknessofthecakeLis

V:thefiltratevolumev:theratioofthecaketothefiltrateA:filtrationareaSeptumresistancerelatestocakethicknessLeLm=vVm/AVm:equilibriumfiltratevolume---filtratevolumeproducedwhencakeresistanceisequaltoseptumresistanceResistancesRproducedbyviscosityoffiltrateandseptumResistanceR=(L+Lm)=v(V+Vm)/A

isproportionalityFiltrationrate:dV/Adt=

P/R=

P/v(V+Vm)/A

Where

P(total)=

Pc(cake)+

Pm(media)or

andBasicequationoffiltrationTheaboveequationisrewritten