FLUID-FLOW-THROUGH-PACKED-COLUMNS

1FLUIDFLOWTHROUGHPACKEDCOLUMNSSABRIERGUNCarnegieInstituteofTechnologyt,Pittsburgh,PennsylvaniaTheequationhasbeenexaminedfromthepointofviewofitsdepend-enceuponflowrate,propertiesofthefluids,andfractionalvoidvolume,orientation,size,shape,andsurfaceofthegranularsolids.Wheneverpossible,conditionswerechosensothattheeffectofonevariableatatimecouldbeconsidered.AtransformationofthegeneralequationindicatesthattheBlake-typefrictionfactorhasthefollowingform:1-6faa1.75+150artAnewconceptoffrictionfactor,/.representingtheratioofpressuredroptotheviscousenergytermisdiscussed.Experimentalresultsob-tainedforthepurposeoftestingthevalidityoftheequationarereported.Numerousotherdatatakenfromtheliteraturehavebeenincludedinthediscussions.TheexistinginformationantheflowoffluidsthroughbedsofgranularOsborneflryadds(23)uashesttoformu-solidshasbeencriticallyreviewed.IthasbeenfoundthatpressurelatetheresianteofferedbyIriceiattothelossesarecausedbysimultanstouskineticandviscousenergylosses,n'otiunoftheflu,Iasthesumoftwoternts,ofitioalrespectivelytoderfirstandthatthefollowingcomprehensiveequationisapplicabletoalltypespoweroft!srfluidvelocityandtotheofflow,productofthedensityofthefluidwithAPCl-e)tPU.1-sGU„secondpowerofitsvelocity:Lp,=150a+1.75.aDaAP/L=all+beV(1)hTHEpressurelossaccompanyingtheflowoffluidsthroughcolumnspackedwithgranularmaterialhasbeenthesubjectoftheoreticalanalysisandexperimentalinvestigation.Thepur-poseofthepresentpaperistosmnmar.icetheexistinginformation,toverifyfurtherexperimentallyatheoreticalde-retopmentpresentedearlier,andtodiscusspracticalapplicationsofthisnewapproach.Theexperimentalstudieshavebeenconfinedtogasflowthroughcrushedporoussolids.Thiscaseistheoneusuallyencounteredinpractice,butisnotidenticalwiththecasemostthor-oughlystudiedbypreviousinvestiga-tors,viz.,theflowoffluidthroughbellsofnonporo(ssolids,andmoreparticu-larly.througisolidshavinguniformgeometricshapes.Factorsdeterminingtheenergyloss(pressuredrop)inthepackedbedsarenumerousandsomeofthanarenotsusceptibletocompleteandexactmathe-maticalanalysis.Variousworkersinthefieldhavemadesimplifyingassump-tionsoranalogiessothattheycouldCoalResecrchLaboratory.Vol.48,No.2NY62592$11ifBRITISHLIBRARY,BOSTONSPALOAN/PHOTOCOPYREQUESTFORM'_°p`cooNo.1979Ossc,iption.,.h„baaa41piihinar,rn.M,ryCHEMENG.PROG.N.S.j`lowthroughpackedaaceofpybpUtion:''rVol.7'rcanowpp,sutilizesomeofthegeneralequationstenThese:factorsarereimportantandwillrepresentingtheforcesexertedbythebediscussedlater,buttheyareirreic:antfluidsinmotion(molecular,viscous,forthepurposeoftestingthelinearit.ofkinetic,static,etc.)toarriveatausefulEquation(2).Asatypicalplot.der.ob-expressioncorrelatingthesefactors.A,.rainedforgasSowthroughabeofffcrushedporoussolidsareshowninN.;taresurveyoftheliteraturerevealsvariousexpressionsderivedfrom-differentassumptions,correlatingtheparticularexperimentaldataobtainedwithorwith-outsonicofthedatapublishedearlier.Thesecorrelationsdifferinmanyre-spects;somearetobeusedonlyatlowfluidflowrates.whileothersareap-plicableonlyathigherrates.Aseparatesurveyofallthesevariouscorrelationsisnotincludedhere.Asmostauthoritiesagree,thefactorstobeconsideredare:(1)rateoffluidflow,(2)viscosityanddensityofthefluid.(3)closenessandorientationofpacking,and(4)site.shape,andsurfaceaitheparticles.Thefirsttwovariablesconcernthefluid,whilethelasttwothesolids,1.RateofFluidFlow,Itisknownthatpressuredropthroughagranularbedispropor)ionaltothefluidvelocityatlowflowrates,andapproximatelytothesquareofthevelocityathightests.ChemicalEngineeringProgressmarkcolumns,Publ,snar:iPam---ISNlSNSNQa.r''~IldYngwnlmereoutarotewhereAPisthepressureonalontlengthL,athedensityofthefluid,11itslinearvelocity,andaandbarefactorswhicharefunctionsofthe,system.AtransformationofEquation(1)whichyieldsalinearexpressionis:AP/LU=a+bG(2)where0,UhasbeenreplacedbyG,themassSowrate.Theabovetwo-termpreswre-dropequationhasbeenfoundtobeastirfactoryovertherangeofflowratesen-counteredinpeckedcolumns.Lindquist(19),Morcom(20).andErgunandOrning(7)haveplattedAP/LVaginstGandobtainedstraightlinesasexpectedfromEquation(2).Theformertwoau-thorshaveincludedintheirplotsfactorstiesofthsa-ithehikrttI.Theexperimentalresultsofthepresentinvestigationandthosementionedax,ve(:,19,20),aswellasthedataott:inmdfromtheliterature(3,22).militatethat.thetwo-termequationaccuratelycitetiaratherelationbetweenflowrateandptasuredrop.2.ViscosityandDensityofFluid.FromEquation(2)itisseenthatasthevelocitya'sproacheszeroasalient.theratioofpressuredroptovelocityad,be-comeconstant:iAPC/-eLms(3)U+0hihiifliwsacoalitonforvscousnv,.ActccordingtothePoiseuilleequationandDar'alaw,thefactoraispropcr:ionaltotheviscosityofthefluid.ThexherlimitingconditionisreachedathignflowrateswhentheconstantaisnegtigilItincomparisontobG.Thisisaconditionforcompletelyturbulentflowwherek-aeticenergylossesconstitutethewholevain-tance.TheeffectofdensityisalreadycontainedinG.Equation(2)asberewritten:API'-aa'pU+b9(P(4)raS_--IT-q-11-13a:nc,.a..,t,,.aaI