chapter -4-flow through porous media

8/13/2019 Chapter -4-Flow Through Porous Media

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Flowlhroughorousmedia 97

Chapter our

FlowThrough orousMedia

DESCRIPTIONF POROUSMEDIA

By a "porous medium" is meant a solid, or a collectionof solid particles,with sufficientopen spacen or around the particles o enablea fluid to pass

through or around them. There are va ous conceptualwaysof describingporous mgdium.

One concept s a continuoussolidbody with pores n it, suchas a brickor a block of saldstone. Such a medium s referred o as consolidated, ndthe poresmay be ulconnected "closedce11," r impermeable) r connected("open cell," or permeable).Anodrer concept s a collection(or "pile") ofsolid particles n a packedbed, where he fluid can pass hrough the voidsbetween he particles.This is relerrcd to as unconsolidated. schematicrepresentdtion s shown in Fig. 4-1. Either of these concepts may be

valid, dependingupon the specificmedium under consideration,and bothhave beenusedas the basis or developing he equations hat desc be fluidflow behaviorwithin the medium. n practice,porousmediamay mnge roma "tight" oil bea ng rock formation to a packed column containingrelatively argepackingelements nd large void spaces.

The pileof 50l id article, concept. u'eful or either onsolidatedrunconsolidatedmedia as a basis for analyzing he flow process,becausemany consolidatedmedia are actually made up of individual particles hat



98ChemielEnginee g Processes

a

F- L-I

\a)

T_

I

-- j#i(b)

FGUBE -l

medium.Porousmedia-(a) Consolidated edjum; b) unconsolidated

are ust stuck together e.g.sandstone). ne of the key propertiesof aporousmedium s theporositys or void ftaction,which s def,ned y

Totalvolume Volumeof solids

Totalvolume

, asolirl ^v.in\

AA

where soud s theareaof thesolidphasen a crosssection f area .We alsodistinguish etweenhe velocityof approach, r the ..super-

ficial" velocityof the luid,

vs= Q/A @_2

and the "interstitial"velocity,which s theactualvelocitywithin the poresor voids,

(4-3 )

(4-l )

Q _V"eAe

4.1.HydraulicDiameter

Becausehe fluid in a porousmedium ollowsa

cha[nelsof varying sizeand shape,one method

tortuouspath through

of describinghe flow



Flow hmugh orcusmedia 99

behaviorn theporess to considerhe lowpathasa "noncircularconduit."Thii rcqlirc;r rn .ri:':opriate definitionof the hydraulicdiameter:

Flowvolume

Internalwelted urface rea

a, , AiL

WE WOL

€ x Bedvolume

(No.of panicles)(Surfacerea/Panicle)

The medium,with overalldimensions4I, is assumedo be made up of acol lection l indi\ idualparticles nd may be ei lhercon.ol idated r un-consolidated. he numberofparticles n themediumcan be expresseds

(Bed olumeXFractionfsolidsnbed)No.particlesVolume/Particle

(BedvolumeXl e)

Volume/Particle

Substitutionof this nto Eq. (4-4) leads o

ol uniform sphericalparticles,^ 2de"n l ( t - e )

If theparticlesare not spherical,heparameter may be replaced y

d : t l ' d s -6 l as

, herc lt is lhe spher[ciryactor, defined by

Surfacearca of a spherewith same olume as hepafiicle

Surfaceareaof theparticle

and 4 is the diameterof a spherewith the samevolumeas theparticle.

4.2.PorousMediumFrictionFactor

The expressionsor the hydraulicdiameterand the superficial elocitycanbe ncorporatednto the delinitionof the rict ion factor o givean equivalentexDressionor the Dorousmedium riction factor:

"et etd€ e1tle3

' -t 4 L tD , t \ v i z2 t - ) l t l t l v l

-) L t l t v

, r : o , - r - ( * )

where a. : (particle surfacearea)/(particle olume). If the particlesaresphericalwith diameter,/, then as:6/d. Thus, for a medium composed

(4-4 )

(4s )

(4'6 )

(4-1 )

(4-8)

(4-e

(4-10)



100Chemi€lEngineerinstocesses

l"fcst referencesse Eq. (4-10) without the numerical actor 11 _? s th3

deflnitionof theporousmedium riction factor, .e.,

Here again, he usualporousmediumReynoldsnumber s definedby Eq.(4-12) without the numerical actor (2/3):

L l t - € ) v :(4 -11

4.3 Porous Medium Fleynolds Number

In like fashion, he hydraulicdiameterand the superficial elocitycan beintroducednto the definitionof the Reynolds urnber o give

^, DrVip 2dtV,p 2dv,pr vR e - : ; . - : : : : .

1t J\t - t)1t Jll - €Jl,

(4 - t ) \

4.4. RICTIONOSS N POFOUSMEDIA

A. Laminar low

By analogy ilh laminar low n a tube,he riction actor n lanrinarlowwouldbe

^, dv"pr rRe.PM :-_ .

l r - t ) l L

"16

/ :A/R"

or /PM:

for 1{q",pM< l0

(4-13)

(4-r4

However,his expression ssumeshat the total resistanceo flow is due othe sheardeformationof the fluid, as in a uniform pipe. In reality theresistances a resultof both shearandstretchingextersional) eformationas he luid moves hrough he nonuniformconverging iverging low crosssectionwithin the pores.The "stretchi[g resistance"s the productof the

extensionstretch) ate and the extensional iscosity. he extensionate nporousmedia s of the sameorder as the shear ate, and the extensionalviscosityor a Newtodan fluid is three imes he shearviscosity.Thus, npraclicea valueof 150-180nsteadof 72 s in closeragreement ith obser-vationsat low Reynoldsnumbers,.e.,

180(4-15)

This is known as the Blake Kozey equationand, as noted, applies orNR",PM 10.



Flowlhroughorousmedia 101

B. Turbulent Flow

At high Reynoldsnumbers high turbule[ce evels), he low is dominatedbyinertial forcesand "wail roughness,"as ill pipe flow. The porous medium

can be considered n "extremely ough" conduit, \'/ith e/d - 1. Thus, the

flow at a sufficieltly high Reynolds umber should be fully turbulent andthe friction factor should be constallt.This has beenconfirmedby observa-

tions, with the value of the constantequal o approximately1.75:

.fna: l . '75 for NR",pM 1000 (4-16)

This is known as the Bftke-Plumnel equation and, as noted, applies or

iy'a",p11 1000.

C. All Reynolds Numbers

An expressionhat adequatelyeprcsentshe porousmedium friction factor

over ail valuesof Reynoldsnumber s

This equatior with a valueof 150 nsteadof 180 ,scalled heErgun equationand is simply the sum of Eqs (4- 15) and (4-16). (The more recent

references avor the value of 180, which is also more conservative.)

Obviously, for 1{p..p14 10 the fi$t term is small relative to the second,

and the Ergun equation reduces o the Blake-Kozenyequation. Likewise,

for Np",p11 1000 he first term is much larger than the secold, and the

equation educes o the Burke-Plummereqration.

If the definitions of /pM and NRe.pM re itrserted rto the Ergun

equation, heresultingexpressionor the irictioral energy oss(dissipation)

per unit massof fluid in the medium s

6n,= r.75+;qrv Re.PM

. , = r.7sr ' ; t f- , " . |L+rso r(1.:u) ' / d \ E ' / d ' € ' p

(4-t7 )

(4-18



102Chemjcelngineerg Processes

4.5. PERMEABILITY

The "permeability" of a porousmedium(-Q is definedas the proportion-

ality constant hat relates he flow rate through he nedium to the pressure

drop, the cross-sectional rea, the fluid viscosity, and net Ilow lengththrough ho medium:

Thisoquationdefines hepermeability -&1Jnd s known as Dar.]] /dx,.The

most common unit for the penneability s the "darcy," which s dellnedasthe low rate n cm'/s that resultswhena plessure rop ol I atm s applied o

a porousmedium hat is 1 cm' in cross-sectionalrcaand 1 cm long, br a

fluid with viscosityof I cP. t shouldbe evident hat the dimensions f the

dar^cyare L2, and^ the conversion lactors are (approximately) 10-3cm'f darcy= 10 " ft'/darcy. The flow properties ftight, crudeoil bearing,rock fornations are often describedn penneabilityunits of millidarc ies.

lf the Blake Kozeny equation or lan'inar low is used o describe he

frilrtion oss,which s then equatedo AP/p from the Bernoulliequation, heresultineexoressionor the flow rate s

tlV,L

(4-1e

(4-20)

(4-21)

By cornparison fEqs. (4- 19)and(4- 20), tis evident hat thepemeability

is identical to thc tcnn in brackets n Eq. (4-20), which showshow thepemeability is relatcd to the equivalentparticle size and porosity of the

medium.SinceEq. (4-20) appliesonly for laminar flow, it is cvident hat

the permeabilityhas no meaningunder turbulent low conditions.

4.6. MULTIDIMENSIONALLOW

Flow ir1 a porous medium in two or three dimensions s important in

situationssuch as the production of crude oil f rom reservoir ormations.

Thus, t is ofintercst to considerhis situdtionbriefly and to point out somecharacteristics f the governingcquations.

Consider he flow of an incompressibleluid through a two-dimen-siolal porousmedium,as llustrated n Fig. 4-2. Assuming hat the kinetic

energy hange snegligibleand that the flow is laminar as characterized yDarcv's aw. the Bernoulli equationbecomes

^ -LPAI d |€ t \s: r- . r U8o{1=/

l LP \-

\ -+c^z )=e t=

or

^(e\ = -i d\.p Kp

Kp



104Chemical ngineeringroe$es

compressiblelow outside he boundary aye. neara solid boundary). t isinterestinghat the same quationgoverns oth of these xtreme ases.

The Laplac€equationalso applies o the distributionof electricalpotentialand curent flow in an electdcally onductingmediumas well asthe temperaturcdistribution and heat flow in a thermally conductingmedium.For example,f O =+E,y =+ , ar:dp/K =+re. where e is theelectricalesistivity /e RA/Ax), Eq. (4- 22)becomesOhm's a\,:

ff:-,",,, v2E:0, and *-#:,

cnd Y*Y:oox tr))

(4-21)

Also, with O =+ T, V =+q, and 1(/p + t, wherek is the thermalconduc-livity, the same quations ovem he low ofheat n a thermally onductingmedium e.g.,Fouier's lat'))l

By making use of theseanalogies, leclricalanalogmodelscan be con,structed hat can be used o deter.dne he pressure nd flow distributionin a porousmedium rom measurementsfvoltageand cu entdistributionin a conductingmedium, or example. heprocess ecomes orecomplex,however,whcn the local permeabilityvarieswith position within themedium,which s often the case.

4.7.HEATTBANSFERNPACKEDEDS

Forheatandmass ransferhrougha stationary r streaniine luid ro a singlesphericalparticle,t hasbeen holvn )Corlson1l.Vol L Ch.9. hatheheat ndmassranslercoefficienfscachimiting ow values ivenby:

*t:-Io, vzr:0,

N u' : 2.0+ O.6Prt/1r ' t la

where Gr' is the Grashofnumber -

(4-28)

whercNu'(: h.l/k) attd Sh'(=hDrllDJ are the Nusseltand Sherwood umberswirhrespect o the fluid, respectively.

kamers [2] has shown that, for conditions of forced convecrion. rhe heat transfercoefficient can be reDresenled v:

Nu ' :2 .o+13Pra$+ o.66ProrRe f

@.2e)

(4.30)

where t?i is the parlicleReynolds umber .dp/p based n the supedcialvelociry .of the luid, and Pr is &e PrandtlnumberCr"p/*.

This expressionhas been obfained on the basisof experim€ntal esulis obtainedwithfluids of Prandtl numbers anging ftom 0.7 to 380.

For natumlconvection, anz andMarshall 3] havegiven:

(4 .31)



Results or packedbedsarc much more diflicult to oblain becausehe ddving lorcecannot be measuredvery rcddily, Gupta and Thodus .ll suggest hat rhe j-faclor for heattransfer,r , forms thc most satisfactory asisof corrclalionorexperimentalesultsand havcproposedhat:

FJowthroughorousmedia 105

ei6 = 2.06Re",a t75 (4.12)

Nu a Relt oe (4.33)

where:e is the voidageof the bed,j', - S P;

'.atd

S/ ': Stanlon umber/Crpr..

The -faclors for heatandnass ransfer,/, and l. are ound o be equal, nd hereforeequaion4.28 can alsobe used or the calculation l mass ransfer ates.

Reproduciblc orrelarionsor the heat transfcrcoefficientberween fiuid fiowingthrough packed edand he cylindricalwall ofthe coniainer reverydiflicult ro obtain-The mafudifficulty s that a wide rangcof packing onditions an occur n the viciniryof the walls.However, he rcsults uoledby Ze|z ard Orhmer jl suggesthat:

It may be nored hat n this exprcssionheNusselt umberwith respect 0 he tubewalllr'r is rclatedo the Reynolds umberwith respccLo thepaticle Rel..

V4.8.PACKED OLUMNS

Since packedcolumnsconsistof shapedparricles ontainedwirhin a column, theirbehaviourwill in many ways be sinilar io that of packedbeds which have alreadybeen onsidered.hereare,however, cvenl nlpofiantdifferences hichmake ie directapplication f thc cquationsor pressure radient ifncult.Fircr. he sizeol rhepackingelementsn thecolumnwill generally e very much argerand heReynolds umberwilllherefore e such hal the low s turbulent. econdly,hepacking lemenrs ill normallybe hollow, and thereforehavea large amountof internalsurfacewhich will offer ahigher low reslstancehan heir extemal udace. he shapesoo arc specially esignedto producegood mass ransfcrcharacteristicsi$ relativelysmall pressure radienrs.

Althoughsomeofthc general rinciples lready iscussedanbe used opredicr ressurcgradient s a functionof flowrale. t is necessaryo rcly heavilyon the iteraturessuedby the manufacturercof the packings.

In general, ackedowers reused1brbnnging wo phasesn contactwilh oneanotherand bcrc will be strcng nieraction erweenhe luids.Nonnally ore of rhe fluids willpreferentially ct hepacking ndwill flow asa 6lm over ls surface:hesecondluid henpasseshrough he emaining olumeolthe colunn.Withgas orvapour)-liquid ystems,the iquid will normallybe the weuing luid and he gasor vapourwill rise hrough hccolumnmakingclose ontacr ith thedown lowing iquid andhaving irdedirectcontacwith thepacking lements. n example f thc iquid gassysiems an absorpfionrocesswhcrea soluble as s scrubbedroma mixturcof gases y means f a liquid, as shownin Figure4.3. In a packedcolumn used or distillation, he morc volatile componeni



106Chemi€lEngineengProc€sses

of, say, a binary mixture is progressivelyrransfered ro the vapour phaseand the lessvolatile condensesout in the liquid.

In order to obtain a good rate of transferper unit volume of the tower, a packins isselec(ed hich \rill promole high interfacial reabetweenhe tlvo phases nd a ighdegreeof turbulence n the fluids. Usually inqeased aroa and turhilence are achieved;the expenseof indeased capital cost and,/orpressurediop, and a balancemust be maalebelween hese actors when arriving at an economicdesign.

Liquidn

Fignre 4.3, Pacled absorptioncolunn

4.&1.General escriDtion

The constuction of packed owers is relatively straighdorward.The shell of the colunnmay beconstructed rom metal, ceramics,glass,or plasticsmaterial,or from metal with a

Uquid



Flowthrou9horousmedia 107

corosion-resislantining.The columnshould c mounlcd rulyverticallyo helpunifomliquid dislribulion.Detailednfomation on the nechanical esign ndmounting findus-trial scalecolumn she11ss giveDby BRoWNELLnd Youngt6l, MoLyNELxtitnd inBS 5500 8l

Thc bed of packing estson a support latewhich shouldbe designedo haveat least75 per cent ftee area or the passagef the gasso as to offer as low a resislance spossible. he simplest uppori s a grid wilh relaiivelywidciy spaccd arson which afew ayers f largeRaschig rpartition ingsarcstacked. nesuchanangements shownin Figure4.4. The gas njectionplatedescribed yl-ev sli6hn in Figure,l.5 sdesignedo provide eparaieassagewaysor gasand iquid so hat hey nccdnot vie for

passagehough thesame pening. his s achieved y providing hegas nlcts o thebedat a Dointabove he evel at which iouid eaves he bed-

Figure.1.,1. Grid bar suppofs or packedo$es

FiguF 4.5. Thegasnrjection latc(z')

At the top of the packedbed a liquid distributor f suitable esignprovidesor theuniform irrigationof the packingwhich is necessaryor satisfactory peration. our



108Ch€micalfgineergProcesses

examplesof different disrriburorsare shown n Figure a.6 tl0l , and may be describedas ollows:

(b)

(a) A simpleorifice ypewhich givesvery finedistribulionhough l mustbe correctlysized or a particular uty and shouldnot be usedwhere here s anv risk of rhehole'plugCing

The notched himneyype of disrjburor,whichhasa good angeof flexibitity orthe mediumand uppcr lowrates, nd s norprone o blockageThc notched roughdisftiburorwhich s spcciallysuitableor rhe targersizesoffower,and,becausef its large ie€ area, l is alsosujtableor rhehighergas alesTheperforateding type of distributoror usewith absomtionolunns wherehishga. rdres d rela rel) s 'nal l quiJ le\ arccn(oLnrerec.his lpe r c.pe.,ai i1

suitablewherepressureossmustbe minimiscd. or he argcrsizeof tower,whereinstallationbroughmanholcss necessary.t lnay be madeup in flanged ecrions:

FiguE 4.6 Types fliquid distriburo/ro)

Uniform iquid l'low s essentialf the bes use s io be madeof the packingand, fthe ower s high, e-disributing lares renecessary.hesc laiesarenceded t ntervais

(c)

(d)



Flowthmughorous edia109

of about2i 3 columndiametersor Raschig ings and about5-10 columndiametersfor Pall rings,but areusualiynot more han6 m apartllll.A "hold-down"plate s oftenplacedat the top of a packedcolumn to minimise movemenland breakageof thepacking

caused y surgesn ffowrates. he gas nlet shouldalso be designedor uniform flow

over the cross-sectionand the gasexit should be separate rom the liquid inlet. Further

detailson intemal ittingsaregivenby Lsva[g].

Columns for both absorptionand distillation vary in diameter from about 25 mm for

small laboratory purposes o over 4.5 m for large industrial operations; hese ndustrial

colunmsmay be 30 m or more n height.Columnsmayoperate tpressuresanging tom

high vacuum o highpressure,he optimumpressurccpending n both hechemical nd

the physical propertiesof the system.

4.8.2.Packings

Packings an be divided nlo four mainclasses-brokensolids,shaped ackings, rids,

and structuredpackings.Broken solids are the cheapest orm and are used h sizes rom

about10 mm to 100mm accordingo the sizeof the column.Although hey requendy

form a good corosion-resistant material they arenot as satisfactory as shapedpackings

either in regard to liquid flow or 10 effective surfaceollered for transfer. The packing

shouldbe of as unifom size aspossibleso as to producea bed of uniform characteristics

with a desired voidage.The mostcommonly sedpackingsreRaschigings,Pall ings.Lessing ngs,andBerl

saddles.Newerpackings nclude Nutter rings, lntalox and ntalox metal saddles,Hy-Pak.

and Mini rings and, becauseof their high perfonnancecharacterislicsand low pressuedrop, hese ackings ow accountor a arge hare f themarket.Commonly sed acking

elementsare illustrated in Figue 4.7. Most of thesepackingsare available in a vr'ide

range f materials uchasceramics, etals, 1ass,lastics,arbon, ndsometimesubber,

Ceramicpackingsare resistant o conosion and comparalively cheap,but are heavyandmay require a strongerpackingsupport and foundalions.The smaller mefal rings are also

availabie made rom wire mcsh, ard tbesegrvemuch-improved ransfer characterisiics n

smallcolumns.A non-poroussolid should be used f there s any risk oi crystal fo.mation in the pores

when hepackingdries,as hiscangivedse to serious amageo the packingelements.

However, omeplastics renot verygoodbecausehey arenot wettedby many iquids.

Channelling. hat is non uniform distribution of liquid across he colunm cross-section,s

much essmarkedwith shaped ackings,nd hei resislanceo flow s much1ess. hapedpackingsalso give a more effective surfaceper unit volume becausesurfacecontactsare

reduced o a minimum and the film llow is much improved comparedwith broken solids.

On the olher hand, he shapedpackingsare more expensive,particularly when small sizes

are used.The voidageobtainable jth thesepackings aries ton about0.45 to 0.95.

Ring packingsare either dumped nto a tower, dropped n small quanriries,or may be

individually stackedf 75 mm or larger n size. To obtain high and uniform voidagc and opreventbeatage, i is often found better o dump the packings nto a tower ful] of iiquid.

Stacked ackings, s shown n Figure4.10,have he advanlagehat he flow channels

are vertical and there s much less tendency or the liquid 1() low to the walls than with



110Chemi@l ngineednsrccesses

(e) (f)

Fieure4.7. (a)Cenmic Raschisdngs; (r) cflmic kssing nn$ (.) Cermic Berl sa.tdle; d) p,ti riieQrstic): (d)P'u rins (n€lat)i (.f) M.ral Nurbr nns$ (t) nddc Nrtrer ring



Flow hrough orcusmedia111

Figtte4,1. continLed

nndom packings.The propertiesof some conmonly used ndustrial packngs are shownin Table4.1.

The size of packing used nfluences he height and diameter of a column, the pressure

drop and cost of packing. Generally, as the packing size is increased, he costper

unitvolume of packing aDd he Fessure &op per unit height of packing fie reduced,and themass ransfer efficiercy is reduced.Reduced llass tansfer efficiency resilts in a taller

column being needed, o that the overall column cost s not always reducedby increasing

the packing size. Nolmalty, in a column in which the packing is nndomly arranged,

the packing size should not exceedoDe-eighthof the column diameter. Above this size,

liquid distribution, and hence he mass ransfer efliciency, deteriorates apidly. Since costper unit volune of packingdoesnot fall much for sizes above 50 mm whereasefficioncycontinues o fall, ftere is seldomany advantagen usingpackingsmuch Iarger han 50 mmin a rardomlypacked olurnn.

For laboralorypuryosesa number of specialpackingshavebeendevelopedwhich are, ngeneral, oo expensive o.large diarneter owers.Dixon packings,which are Lessing ings

made from wire mesh, and KnitMesh, a fine wire meshpacking, are typical examples.

Thesepackings give very high interfacial areasand, f they are flooded with liquid beforeoperation, all of the surface s aclive so thal the tmnsfor characteristicsare very good

even at low liquid rates. The volume of liquid held up in such a packing is low and thepresswedrop is also lo\r. Some of thesehigh efficiency woven wire packingshavebe€nused n coltmns up to 500 mm diameter.

Crid pnckings,wiich xrc relxtivelJ, asy |(r fabricalc.arc rsurLlly Lscdn col mnsof sqoxlescdion. rnd freqrertlJ in coolirg rolverswhich are describerln Volume ,

Chapler l:1. They may be made from wood, plastics, carbon, or ceramic maferials, and,because f tbe rclatively large spaces etwe€n he ndividual grids, ihey give low pressure

drops. Furlher advantagesie in their easeof assembly, heir ability to accept luids with



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114Chemicalngineering.o@sses

suspendedolids, nd hejrease f weltingevenat very ow liquid ares. he mainproblemis thatof obtaining ood iquid disrribution ince, r high tiquid aies, he iquid ends o

cascade tom one grid to the nex withour being broker up into tine dropleis which aredesirableoi a high nlerf f f iatuf ldce. 1 c\dmpte t c cootinpouer aiking. Cootf lo

3'02r s shown n Figure4.8.This is simitar o rhe stmctured ackingJdescribedater,ancl onsists f vacuum ormedPVC sheers tampedogctherwithin a meralandplasricsframe to folm a module which canbe 0.6 m or 1.2 n i; deprh.Srrucruredpackinis maybe broadly classified nto either the knined or rhe non-lnitied type, ana bott typis rnaybe assembledn a segmentedway or in a spiral form. In the lafter, corugut.d ;[ip, oidbbons oil abouta centre \is to form a flal cakeof the equisitcowerdiameterwhichis usually ess han I m_Theseelements re henstacked neupon he other o Drovidelhenece+ar) eddeplh. n rhe igidLlpeot sLrucrureoacUng.hcse.orrugnr" j .F.. , .of melalor plasticareassemblcdo form interseding penchannels.he she€tsmav. naddi l ion.eperforalednd he)provide niformiquid lowo\er bolh iderwhi le apourf lou. upwardsndprovidesnrmare onracr i lh r t -e rquid. ne,urh rlpe of pacUng.Mellapak(33)s shown n Figure4.9, andothers uchas cempakil4l -" ut.o uuoiUtf .Low pressure ropsof lypically50 N/m2per heorericajtage repossiblewirh HETp.s,rangingrom 0.2 to 0.6 m, voidagesn excess f95 per

cent, and high specific surface areas.The resulting higher capaciryand efficiency wiihstructured ackingss, howeverachieved t higher nirialcapital osr hanwith the olherpackings iscussedn rhissectionl15].

FiguE 4.8, Msco Coolno3 extendedurface, ootine operpactring



Flowlhrcughorousmedia 115

Figu€ 4.9. structured packinss (4) meralgauze (r) carbon(.) corcsion esisDn ptdslic

4.8.3.Fluid low in Dacked ohmns

It is important to be able to predicr rhe drop in pressure or rhe flow of the two fluidstreamshrough a packedcolumn. Earljer in this chapter he drop in pressurearising from

the flow of a singlephase hroughgranularbeds s considercdand the samegeneral ormof approach s usefully adopted or the flow of two fiuids &rough packedcolumns. Itwas noted that the expressions or flow through ring,type packingsarc less reliable thanthose for flow through beds of solid particles.For the typical absorptjoncolunn there sno very accurateexpression,but thereare severalcorrelations hat are useful for designpurposes. n the majority of cases lre gas flow is turbulenr and the generalform of rherelaiion belween the drop in pressure AP and the volumetric gasffowrateper unit areaof colurnn c is shownon curveA of Figure4.10. ,AP is rhenproportionalo r 3appro\ imarely.n rgreemenrirh he urreA of Figure . lOal hiehRelnolds umbars.If, in addition to the gas flow, liquid flows down the tower, (he passage f the gas s not



J16Chemic. l ngineer ingrocesses

eE

v

ligur 4.10. Prcssurc rops n wetpackineslogdilhnricaxet

significandy ffected t low liquid ratesand he pressure rop ine is similar o line A,although or a givenvalueof 116 he valueof AP is somewhatncreased.When dlegas rale reachesa cetain value. the pressuredrop then dses very much more quickly

and s proportiondlo i/U5,as shownby the secdonXY on curvc C. Over this sectionthe iquid flow is interferingwith the gas low and hehold-upof liquid s progessively

inffeasing. The fre€ space n the packirgs is thercfore being continuously taken up bythe iquid, and hus he resistanceo flow risesquickly.At gas lows beyondY, APrises very steeply and the liquid is held up in the column. The point X is known as theloadingpoint,andpointY as he floodingpoint or thegiven iquid ffow. f the lowrate

of liquid s increased, similarplot D is obtainedn which he oadingpoint s achievedat a lovr'er as ate houghat a similarvalueof -AP. Whilst t is advantageouso haveareasonableold-up n the columnas hispromotesnterphaseontact, is nol praclicable

to operate nder foodingconditions, ndcolumns rebestoperated ver hesectionXY.Since his is a sectionwith a relativelyshof range n gasflow, the safepractices 1()design for operation at the loading point X. Ii is of interest to noie that, if a column isfloodedand hen allowed o drain. he valueof AP for a given gas low is increasedover hat or an cntirclydry packing sshownby curveB. RosEandYoung[ 6]correlated

rheir experimenialpressuredrop data for Raschig rings by the following equation:

-o", : -o"r( t*f )

where: 4P,,, is thepressure op affoss he wet drained olumn.AP,r is theFessuredrop acrosshe dry column.and

d,, is ihe nominalsizeof ihe Raschig ings n mnl.

This effect will thus be most significant for smaupackings.

(4.34)



Flowthroughorousedia 117

Therc ie severalwaysof calculatirg hepressurerop across packcd olumnwhengasand iquid are lowing simultaneouslynd he colunrn s operating elow he oadingpoint.

Oneapproachs to calculatehepressurerop or gas low only and henmuitiply hispressurerop by a factorwhich accountsor theeffcctof the iquid ffow. Equarion .19may be used br prcdicting the pressuredrop lor the gasonly. and rhen rhepressurcdropwith gasand iquid Rowing s obtained y using he correctionaclors or the iquid flowralegivenby SHERwooDnd PigfordllTl

AnotherapFoach s thalof MoRRrsndJacksonllslwho arrangedxperimentalara ora wide angeof ring andgrid packingsn a graphicalorm convenienlor thecalcularionof the number f velocilyheadsr' lostperunit height.of acking. { is subsriruredn rheequation:

-LP : :NpcuL l(4.3s)

wherer- AP = pressurerop,

pc = gasoensrry,

rc : gasvelocity,based n thecmply columncrcss-sectionalrea, ndI : heightof packing.

Equation .35 s in consistent nits-Forcxample,with pc in kg/m3, G in mA, I in m.and y' in m-r. -AP is rhen n N/m'?.

Elnpirjcal orelationsof experimentalata or pressurcrop havealsobeenpresentedby Leva[]9l.rndby ECKERTt al.[20]orPall rings.Wherc hedata .reavailable,he nosraccurate ethod f obtaining hepressurerop or fiow through bedof packings fromlhe manufacturer'swn literature. his is usuallypresenteds a logarithmic lot of gas

rate against ressurc rop,with a parameterf liquid nowrateoD he graphs, s shownin Figure4.16, although t shouldbe stressedhat all of thesemcthodsapply only roconditions l or below he oadingpointX on Figure4.i0. ff applied o conditions bovethe oadingpoinl the culculated ressurerop wouldbc too ow. It is therefore ecessaryfirst o checkwhctherhecolumn s operating t or belou, hc oadingpoint,andmethodsol predictingoadingpointsarenow consjdercd.

Loading and floocling points

Although he loadingand loodingpointshavebeenshownon Figure4.10, here s nocompleiely eneralisedxpressionor cdlculatinghe onsetof loading,allhoughone ofthe ollowingsemi-empiricalo elationswill oftenbe adequate. oRRrs ndJAcKsoN,''gave heir esults n rhe orm of plotsof rt(,J(r/,Jr)al the odding ate or va.iouswelling

ratesLw (m3/sn). ,,6 and,r. areaverage asand iquid velocities ased n the emptycolumnand t: (/kclpi) is a gasdensity ofiection actor,wherepi is the densiryof air at 293 K.

A uselul graphicalcorelation for fiooding rareswas first presented y SHERwooDet dl.[21]and ater developed y Lobo€rdl.l22l or random-dunped ackings, s shownin Figure .1I n which:

W) f:n e)" ',r*oa"s^i",JE)



118Chemical nqneering rocesses

;6t g

0.01

0.0010,01

Figlre 4.11. oeneralhed orreiaiionoriooding rares n pacled owc4 l

where:16 is the vclocityof rhegas,calculated ver rhewholecrcss-secrionf rhebcd,.S, is ihe surface reaof the packing er unit volumcof bcd,

I is theaccelerationue o gravity,

I,' is lhe mass ateof flow perunit areaof the iqujd,

G' is the mass ateof fiow peruni areaof thegas,andp. is the viscosity f waterat 293 K approximalely mN s/m'?, nd

sulfix G refers to the gasand suflix a o the liquid.

The area nside he curve epresenlsossible onditions f operation.n these xpres-sions. he ratiospc/pr andpr/pu havebcen ntroduced o that he relationshipan beapplied or a wide rangeof liquidsandgases.t may be noted hat, [ the effecrive alueof a is increasedy usinga rotaiingbed, hen higher lowrures an be achieved eforethe onsetof flooding.

dH2A-N2DH2O CO'

b Butydc cid-A4cH3oH Akv Turbin€ il Air

> B 1 0 0 O Ai r< 10 Coi l Alro O i l N o . A rr OilNo. 1 CO,E oi lNo r H2a oi lNo 2 At? Ol lNo.2 CO,+ oi t No.3 Air

L' 14d 1F;



There are several waysof calculating the prcssuredrop acrossa packedcolunn whengasand iquid are iowingsimultaneouslynd hecolumn s operating elow he oadingpoint.

Oneapproachs to calculateheprcssurerop br gas low only and henmultiply rhisprcssure rop by a factorwhicbaccountsor rheeffec of the iquid flow.Equalion .19may be used or predictingheprcssure rop or thegasonly, and rhen he prcssureropwith gasard iiquid flowing s obtained y using heconection actors or thc iquid flowrarc i renb) SHLRiooDndPiglorJl lTl

Anotherapproachs thatofMoRRrs ndJacksonll8]who arrangedxperimentalata ora wide angeof ring andgrid packingsn a graphicalorm convenicntor lhe calculalion

of thenumbcrof velocityheadsN lostpcr unii heightofpacking. r' is substituredn rhe

Flowhrolqh orous edra119

^P - +Npcu? (,r.35)

where:- AP : pressure rop,pc : gasclenslty,

uc : gasvelocity,based n the emptycolumncross-sectionalea,andI : heishtof packing.

Equation .35 s in consisteni nirs.For example,with pc in kg/nr, ,6 in m/s, in m,and r' in m r, -AP is rhen n N/m'?.

Empiricalcorelations fcxperimental aia or pressurerop havealsobeenpresentcdby Levalg] andby ECKERT/ al.[20]or Pallrings.Where he daia

arc available,hemoslaccuralemelhodof obtaining hepressurerop or fiow through bedofpacking s fromthe manufhclurer'swn literature. his s usuallyprcscnled s a logarirhmic lo of gasrate againsl ressurc rop, with a parameter i liquid flowrateon the graphs, s shownin Figure4.16, although r shouldbe stressedhat a1lof thesemelhodsapply only tocondltlons t or below he oadingpointX on Figure4.10. f applied o conditions bovethe oadingpoint he calculated ressureropwouldbe 1oo ow. It is thereforc ecessaryfirst o checkwhcther hecolumn s operating t or below he oadingpojnl,andmethodsof predictingoadingpointsarenow corsidered.

Loaclingan.l flooding points

Although he loadingand loodingpoinishavebeenshownon Figure4.10, here s no

completely eneraliscdxpressioDor calculatinghc onsetof loading,although ne ofthe ollowirg semi-empiricalonclalionswill oftenbe adequalc. oRRrs ndJ.rcrsori' 'gave heir esultsn lhe olm of plorsof ry'(uc/rr) al the odding ate or variouswettingrates ,$, (m3/sm). ,G and ur areaveragc asdnd iquid velocities ased n rheemprtcolumnand1/ = (.//kclp/) is a gasdensity onection acror,wherepr is rhedensiryof air at 293 K.

A usefulgraphicalcorrelation or floodlng atcswas first presenredy SHERwooDe, dl.[21]and ater devclopcd y Lobo€rdl.t22l or random-dumpedackings, s shownin Figure4.ll in whichi

(4r)o',o'*oo*'"#Je)s)€l



120Chemical nsineeirqProcesses

Liquid distribution

Provision f a packingwith a high sufacearcaperunit volumemay not result n goodconlacling f gasand iquid unless he iquid is disrributed niionnly over rhe surfaceof lhe packng. The need or liquid distribution nd redisrriburionnd correcr ackingsizehasbeennotedprcviousiy.The effectivewettedarcadecreasess rhe iquid rare sdecreased nd, for a given packing, dere is a minimum liquid rate for effective use ofthe surface area of the packing. A useful measureof lhe eflectivenessof wetting of theavailable rea s rhewetting atc /-,, defined s:

Volumetrici{tuid ateocr unit cross-sectionalreaof column

Packing u aceareaperunit volumeof column

L

Apr.sB S,

Q,: t exp( a2 x'z) (4.31)

(4.36)

Thus the welling rate s analogouso the volumctric iquid rate per unir lengthofcncumferencen a weltcdwall colunn in which he iquid flowsdown he surface f acyljnder. f the liquid rale were oo low, a continuousiquid film would not be formedaround he circumferenccf the cyiiDder ndsomeof the rea wolLldbe neffective.

Similareffecls ccur n a packedcolumn,lthoughhe low parternsndarrangementf

thesurfaces re her obviouslymuchn1ore omplex.MoRRrsndJackson[l8] ave ecom-mendedminimumwetting ates f 2 x l0-5 mr/s m for rjngs25-75 mm n diameler ndgi idi ofpirch e* rhar50nm. cnd1.3 l0-s n'/ \ m tor dgerpacungs.

The distributionof liquid over packingshas beenstudiedexperimenlally y manyworkersand, for instance,Toun and Lmuex(45.46) howed hat lor a single point feed rhedistribulion s siven bvl

where0, is the fraciionof thc liquid collected t a disrance liom rhe centreand cand a are constanls epending n the packlngarrangemcnl.onnant2TlMANNNG ndCannon[28]andthers aveshown hat his maldisiributions onecausc ffalling rransfer

coefficients ith tall towers.A nomographwhich relates iquid rate, tower diameter and packing size is given inFigure4.13[10]The wefiing areLw maybe obtained sdn absolute alue rom the nnerright handaxis or as wetinq nction from the outerscale.A valueof wetting ractionexceedingniiy on lhat scdle ndicateshat hepackings satisfaclorily er.h should enoted hat many organic iquldshavc avourable ettingpropenies nd vr'cuingmay beeffective t much owcrrates,houghmatelials uchasplaslics ndpolished rainlessleclaredifficult to wet. Figure4-13does,however, epresenihe best available ataon thesubject f welling. n the example hown n Figure4.13, he arrowedinc conespondsothe case f a liquid flow of 0.018m3/s n a colunn of 1.6m diamerer nda packing izeof 25 mm, whichgivesan approximate etting ateof 5 x 10-5 mr/m s, correspondingto a total wettingof more han I on rheourside ighGhandcalei his s saiisfacrory.



Fiowihroughoro smedia 121

-eE

o', E

B

o 0 4

Iv{m3hzs)

Fieuo 4,13. Nomographbr rheestinaiion t thedegEeof wefting n I pmkc.tcojutul29l

In many ndustrial pplicationsf packed otumrs, t is deslrablco know thc volumerrichold-up fihe liquid phasen thecolumn.This nfonnationmightbc reeded, or exanple,if the iquid were nvolved n a cbcmical eaclion r if a conrrolsysrem or rhecolumnwercbeing designed. or gas,liquid systemshe hold-upof liqujd Hi,j for conditions

below he oadingpointhesbecn oundlgl to vary approximatelys he0.6powerof lheliquidrate.and o. rings and saddleshis s givenapproximateiyy:

/ . / \ 0 6

H", :0 .1$ l ; ) (4.38)

wherci ,' is rhe iquid flowmte kg/n,s)t

d is theequivalent iamelcr f rhepacking nxr), an{l,?,, s the hold-up mr of liquid/m3of column).

Thuswith 2-5mm Raschig ings,L' of 1.0kg/m2s and d :20 mm, 4, hasa valueof0.021mj/mr.

,{;13z,it:-q



122Chemicalnginee.ingfocesses

4.9 FLOWNPACKEDEDS

The chemical and energ/ industriesdealpredominantlywith nultiphase and multicomDo-oent lstemsn which onsidemblet lenl ionsdevotedo bcreacinghe nlerfacidton;crbetweenhe phaseso enhance roperry ransfen andchemical eactionsat theseextendedsurfacenterfaces.s a.esult,packed edsareext€nsiveb/sed n th6chemical rocessn-dustries.Someexamples regasabsorption, ataMc reactors,and deepbed ltration.

4.9.1 FriclionFaclorCo elations

Tfie friction factor for packedbeds, pb, is de ned by

"a3 DplLPl

J p b i . . . - -' ' ou l r

where € is the po.orr4, (or yoid yolunefraction), Dp is tbe particl€ diamerer,and r, is thesuperfcial wlocitJ. The s,rpercial velociry s obrainedby dividing rhe volumetric ow rateby the total ooss-sectionalareaofthe b€d.Notethat the actual ow area s a fraction ofth€totalcross-sectionalrea.

(4.3e)

(4..41)

Forpacked

beds, he Reynoldsnurnber s de ned by

^ Dpu"o IRepr -l iJ+ 14.401

For laminar oq the relationshipb€tween he liiction factor and th€ Reynoldsnumber sgivenby

r *=P Re,a1o

which s Lno\ n as heKozcn\-Carnanqua on.In thecase fturbulent ow, .e-,Rej,,> 1000,h€ elationshipetween erband , js

glvenby theBurke-Plumnerequation n the for.m

f tu= 1.'75 Rep, 1000 (4.42)

T\e so-calledEryun equarion 1952) s simply the summationofthe Kozeny-Camanandthe Burke-Plummer quations

1 5 0(4.43)



Ftowthroughorousmedia 123

Exsmple4.l A column f0.8 m2cross-sectionnd30m heightspacked ith spherjcal

particlesfdiametermm.A uid withp:1.2kg/m3 andp= 1.8 l0-5 kg/m.s owsthrcugbhebedatamass ow ateof0.65kg/s.Ifthe pressurerop s measureds3200 a,calculateheporosity fthe bed:

a) Analytically, b) Numerically.

Solution

Assumption

1 Thesystem s isodtemal.

Analysis

The supe.cial velocity through hepackedbed s

0.65u ,=

,1 .2^ ,= 0 .67 rmr "

Substitutionf the valuesnto Eqs. 4.35)and(4.36)gives he friction actorand heReynolds umber sa function lporosity n he orm

, . ' Dp l ^P . . ' I r o"

to 11 . )200 ' l. . . . / i trpb=r , puI

=T-.1{Lr"oatt ,3o) l='164\r-e/ r l l

R "^=D,ut_L _ 1,6_:_.10,0q1l{L.2' . l . _,_.r | \' u r-. 1 r.r-;ro-Jl .-"uolr-,J(2)

SubstitutionfEqs. 1)and 2) ntoEq. 4.6-5) ives

e3 0 .4 i6€22 .455€ i .979 :0 (3 )

a) Equation 3) can be solvedanalytically y using he prccedure escribedn Sec-tion 4.7.1.2 n AppendixA. In order o calculatehe discriminant,he ems M andly'mustbecalculatedromEqs. A.7-5) nd A.7-6),espectively:

{3)(2.455 {0.476)2M =_ : +_0 .793

9

i r ' _

_ rq i (0 .47612.455ri 27 r { t .g7q )+ (2 r {0 .416 , .

_O. rno

Therefore,hediscriminants

n=m3 i-t ' t2:q0.79y3+ e.7gg\2 1.137

SinceA > 0, Eq. 3)hasonlyone eal ootasgivenby Eq. A.7-7). he erms SandZin this equationarecalcLllateds

s= tru " [ t '' -

{o.zoo+,,137r" '' 1 1

I =1ru- .61 ' ' . -1o. tsou\ tn l t3 _ 0.o44



124Chemical nqineenngroesses

Henceheaverageorosity fthe bed sn 416

. _ t .2 j t 0 .644=- :_0 .740I

b) Equation3) is rearangedas

F(4 :e3 - 0 .416? 2.455 1 .979o

From Eq.(A.7-25) he temtionschemes

0.02 i-r f (q-r.t' r = ' t | -

F ( i i . , , r ) -F (099 . / ,

Assuming starting alue f€, :0.7, the terationsrcgivenn the able elow:

(4)

(5)

0----dr| 0.'7462 0.'7453 0.'t45

4.9"2 HeatTransfer orrelation

Wf taker3l) (1972) roposedhe ollowing orrelationor heatransf€rnpacked eds:

Nup,: (0.4R";f + o.2R#) P.o4 (4-44)

TheNusselt umbern Eq. 4.6-6)s definedby

th \Dp (Nup r : - - r l

€(4 .45)

Equation4.40)s validwhen

3.7<Repr<8000 0 .34<€<0.74 Pr ,z0 .7

A11 opertiesn Eq.(4.40) areevaluated t the averageluid tempemturen the bed.

Calculationof the heat ranskr rute Once he averageeat ransfercoefcient rsdetermined,he rateof heat ransfer s calculatedtom

Q= axv h\^TLM (4-46)

whercy is the total volume of thepackedbed and a, is the packingsurfaceareaper rmitvolume ened by

6a l . )

" '=-- (4'4',7)



4-9.3 MassTranslerCorrelation

Dwivedi ndUpadhyay12X1977) roposedsingle onelationor bothgases nd iquids npackednd fluidized edsn terms fthe -factoras

0.765|

0.165ta_ae\. €J t ft: n-+ \O' ' " ' b 8 ) { R e ; ' r o t 3 6

which svalid or 0.01< Re;, < 15,000. he erms i,, andRe;D nEq. 4-48) re onedDy

-,,=(f)s*'rand

Re|6=

Calculation of the mass ranskr rate

Flowhroughorous edia l2s

(4-4e)

(4-50)

Onceheaverage assransferoefficientis determined,he ate of mass ransfer fspecies4, n, is givenby

(4-st)

Example .2A packed edof porosity 45 ;n apipe,2.5cm n ;nternal iameter y using aph-

thalene pheresmm ndiameter ure ir at 40'C flowsat a super ial velociry f9 m/sthroughhebed.Determinehe ength fthepackeded equiredor heavemgeoncentra-tion of naohthaleneaDorn theair to reach25% ofthe saturation lue.

rhe: a,V k"l(^ce\mMt

Solution

Physicalproperties

Diffusion oefficientfnaphthalene,4 )inair(

/ r r r \ l / 2{DAB) l t J : r rA6 r j oo l - | - r 0 .b2 ,

\ J U U l

Forair t40'C (313 ): r : 16.95 10-6m2ls

TheSchmidt umbers

16 .05 : t0o ^ -_" - Des - 661 l0 o - - - "

Assumptions

1. Steady-stateonditions revail.2. Thesystems sothermal.3. The diameter lthe naphthalenephercs oesnot change ppreciably.

6) at40"C 313 ) is

ro ' ) {= ) :6 .61 ,10 6m2 /s



126Chemicalngineeringrocesses

AnalysisSystem: ir in thepacked ed

Understeady onditions,he conservationtatementornaphthalene,pecies4,becomes

_ Rateofmoles of,4 in: Rateofmolesof,4 out

The terms n Eq. (1) are expressed y

Rate f moles f,4 in= d V \k,JQ:c ruRate f moles f"4 out= QGA)out: (irD2 4) po@A)ab

( l )

(2)

(3)

Since he concentrationat the surlace ofthe naphthalene pheres s constant, he expressionfor (Ac,a).rr',becomes

(4)

SubstitutionfEqs. 2H4) intoEq. 1)andnoringhatv = (1rD2 4)L gjve

r-- '" r"fr "^' '" ' l rs)\*c)a, L cA )

Note hat or a circularpipe, .e.,atr= 4/ D, the above quationeduceso Eq.(5)

The interfacial areaper unit volume, du, is calculated as

6( l , ) 6r l 0 .4s) , ^" - * -oa*=oo"

Todeterminehe avengemass ransfer oefrcient rorn Eq.(4.6-0), rst t is necessaryocalculateheReynoldsumber

Dpuo f0.005)19)( cp r= -_G l3 \ l I=_zo ) )

Substitutionfthis valuentoEq. 4.6-10) ives

',",,ffi *ffi =d##+#ffir :o rso

inwhich<jMp,sgiven y Eq. 4.6-l ). Therefore,heaverageassransferoeficients

( l . r o o l86 - -& . , -(oo l86 ) rq )

^s"-, rd.EiIJG'-" ' / 'The length ofthe bed s calculated rom Eq. (5) as

r: -t-u666,ln(l

- o 2s) o 02 n

Colnln€nt The useofa packedbed ncreaseshe mass ransferareabetweenair and solidnaphthalene.This in tum causesa dmstic decreasen the lengthofthe equipment.



Flowlhrough orousmedla 127

Further rcadingBranan CR. Rules ofThurnb for Chenical EngineeB. Honslon, TX: Cxlf Pxb Co.,

I994 .

Leva M. R€considerpacked lower pressuredrop correlations. Chem EnB Prog 88:

65.-72, t992.

couhon JM. JF Rlchardson.JR Blackhusr, JH Harkef. chemical Eneineerins. vol.6.

.1Lh d. New York: Perganon Pres, 1991.

REFERENCES

r. Conlson JM, JF Richa.dson, R Bl.ckhus , JH Harkei. Chemical Engineerlng. Vol. L

4th ed. Nea York: Pe.samon Press. 1991.

2. KRAMERS,.: Pbri.d 12 (1946)61, Helt transiir iom sphcrcso flownrg nedia.3. R{Nz,w E. and MARSHALL,N. .: Cherr.Eie. Ptue.48 (1952) 4l, 1t3. Evaporationrom drcps.4. CunA, A. S. and THoms,G.: A.t.Ch8.J1,91.t963) 51. Directanalogy etweenmassandhear iansfer

to bedsof spheres.5. zENe F. A. and OrH\jER, .F.: Fl,idiltioa a..t FLui.l aridle s)sr?,r (Reinhold, 960).

6. BRoVNELL,. E. md YouNc,E. H.1Pn e$ E4tip,ent DeJrg\ v,rs,l D,stgn (Chapmrn& HaI, 1959).

7. MoLYMG, F : Cncni.a/ PlanrDerts,, Vol, I (Buftesor1hs, 963).

8. BS 5500: 1978: r;,n lvcldedPmrlE v?rreli (BnrishStandadsnstitL on, London).9. LEVA.M.: ?blecr Pa.trnss an.1Pa.kel rover Deliqi lJ.S Stonewtu€Co., 1953).10. NofionChemical occssProducts iv., Box 350,Akrcn,Ohio:HydrontlLtd,,King St.,Fc.ton.Stokcon

11, EcGRr, J. S.: Cncn.E,is.Pr,s. 57 No. 9 (1961)54.Design echniquesor desiening acked owe6.12. CooLRo is a proddct ivhco LId,,CrotdonSnircy.13. Mellapak s regisreredradena* of Snlzer UK) Ltd., lnborcugh, Hants,14.cenpak is a Eeisiered radenrt ol Clitsch U() Ltd. Knkby Srophcn, nnbria.15. CENG. C. K., C/€,,. E s, Alrat), 91 No 5 (March5 198.1) 0. Plcted colunn ntemals.16. RosE,H. E. and YouNc.P.E: Pttc.lnsl. Mech C,is.1B (1952) l4. Hydraulic haractcristicsf packcd

toweNopemting nder ount€rcurcntlow condnions.17. SsERwooD,. K. lnd PlcFoRD. . L : abriptioh atu| *ta.ria, (Mccrae'Eill, 1952).18. MoRRrs, . A. and J^c$o"_,J:,4rJa?r,", tu,c6 (Butiesodhs,1953).19. LEv , M.: Cr,n trg. Pms. Symp.Ser.No. 10,50 (195,1)1 59.Flow hrongh rigatcd unpedpacting

Pressu€ rop. oading.Roodnrg20. EcKERr. S.. FoorE,E. H.. and HUNlNcror. ', . L.: Cr?n t a, P.,s. 54, No. I (Jan. 95E)?0 5. Pall

rings new ype of lowerpacking.

2l. sHERworD,. K., SlnpLEy, , H., andHoLLowa. F. A. L.: htd. Erg. Chen.30 (193a)165 9. Flooding'c o , r ie . r pdc\edo ' | t r .

22. LoBo.W. E.. RrEND, , HASHMALL,., nd zENz.F.: I/"hs. A,t. 1n . Ch.h. Lne. 1711945) 93-710.Liniting capacny idunped lowerpackings.

23. EckEkr, . S.: Ch.ft. Eng.P/,s.59 No 5 (i963) ?6. Towerp.ckings comparativecrtbrnancc.

24. LE\a, M: Chen.EnB.Pas. 88 No, | (1992)65. RccotrsidcrackedrowerpressuF-droporelations.25. TouR,R. S. lnd LERNTAN..: Truht.Ah. tat. Chett.ErE. 35 (1939)709 |8. An nnprovcd evice o

demo.stratche awsof iequencydistribution.With snecialeferencco liquid now in packedowers.

26 .TouR.R.S.andLERMAN,F. :Trans.A, t .h6 lChem.En:1 ,35(1939)719-42 .Theunconnnedd is l r ibn l ion

oi liquid nr towerpacking.2?. NoNAN, w, S. zarr, /r st. ChenLEng. 29 11951)226 39. Tbe perfom .ce of grid p&kcd iowes,28. MANNT._C,, E. and ANNoN,M. R,: r1t'& cr?,,. 49( 95l) 347 9. Distillalionnprcvene. by control

oi lhasecha.nellingn p&ked cohmns.

29. LE\A,M.t TowerPatkingtandPd.ked brer D.sigr (.U.5. lonewlE Co., | 953).

30. NorrorChenicrl Prccesslroducrs iv.. Boi 350,Akron,Ohio:HydronylLid., Kins St., enton,Stoteon'

31. Whitaker.S.. l9T2.Forcedconlectionheattransiirrcorclationsfor o w in pipes,past at plates.

ingle cylinders, snrelespheres. nd or o w in packedbedsand ube bundlcs,AIChE Journal 8, 361-

32. Dllivedi, PN. and S.N. Upadhyay.1977,Particlc-uid nass transfef n xedand uidized beds.

Ind. Eng. Chcm. ProcessDes Dcil i 6. 157



128Chemi€lEngineedngrocesses

PROBLEMS

Porous Media

I . A packedbed is composedor crushed ock with a d€$ity of I 75 b-/fi3 of sucha size and shape tha the ave.age ralio of surface area to volune for rle

Frlicles is 50 n.']/in.3- hebed s 6 ft deep, asaporosiryof0.3,and s coveredby a 2 ft deep ayerof water hat drainsby graviry hrough he bed.Calculalethe ffow rate of water hiough lhe bed n gpn/frt, assuminSt exitsat I ahnprcsure.

2. An impnrily in a walerslreamat a v€rysmallconcentmiions to be emovedtra charcoal ricklebednlter.The filter is in a cylindrical olunn tlra is 2 f indiameter. and lhe bed s 4 fl deep. The water h tept at a level thal is 2 ft abovethe rop ot the bed, and it trickles through by Sraviry flow. If lhe charcoalparticleshavea geometric urface rea 1o volume aiio of48 in. ' and they

packwith aporosityof0.45.whal h the low raie ofwaler throlgh thecolumn,in gpm?

3. A lrickle bed nlter is conposedora packedbed of broken rock. The shape fthe ock s such hal theaverageatio ofthe surface rea10volume or ihe rockparlicless 30 n.-' The bed s 2 ft deep, asa porosityof0.3, and s covered ya layer of water hat s 2 ft deepand dminsby gravity hmugh lhe bed.(a) Deternrinehe volune flow rate of the water hrongh he bedper unit bed

aiea (in spm/ft').(b) If lhe water ls pumped upw-ard brough th€ bed (e.s. io flush jt ouri. calcl-

lale th€ low rate in spm/# of bedarea) ha will be cquired o fllidiz the

(c) Calculale he correspotrdinglow ra|e rhar would sweep he rock particlesawaywith the water.The rock density s l20lbn/ftr.

PackedColumns

4. A packed ohmn ihat is 3 fi in diamelerwith a packinghe;Bht f 25 is used oabso$ an impu ly Fon a methane asstream slngan aminesolnlionabsor-ben1. he sas low rare s 2000scfnr,and the jquid hasa densiry f 1.2g/cm3andd vi co. r ) o l 2 cP l 'hecolurnn pe,ale. t I arr dno80 - .deermineheliquid ltow rate ai which loodingwould occur n the colnmnand the pressur€drop al 50% ofthe flooding iquid rate or the oilowingpackings:(a) 2 in. ceranricRasch'g inss(b) 2 in. plasticPall rings

5. A packedcolumn s used o scrubSO, from air by using raler. The sas low

rale s 500scfm/ft'. and the columnoperates t 90"Fand I alm. Illhe columncontainsNo. I plastic ntaloxpacking,what s the maximum iquid flow rale(peruni crosssecrio of colunn) thal could be usedwithou floodins?



l0_

7.

8-

Flowthfoughofousmedia 129

A st.ippingcolumn ackedwlrh 2ln. meralPall ingsuses ir a 5 psigand 80'Cto sirip an impurity lion an absorberoil (SG:0.9, viscosity 5 cP,?: 20'C). If the flow rate of lhe oil is 500 b,i/nin and that of the air is 20

(a) Whal is the minimnn colnmndiameter hat can be usedwithout flooding?(b) If the colnnn diancter s 50'%greaterhan he minintrn size.whar s ihe

pre$ue drop per ft ofcohtmn height?

A f a c \ e d o l u a n L a \ 0 t s T l a ' a r ee r J n d n h r r rJ n dL o n . a i n c . 2 5mRaschigringsisrsedra gasabsorplion rocessoremole an npurily fron rhe

gasstream y absorbjngt iD a liqnjd sohcnt.The iqnid,whjch hasa vlscosityof 5 cP ard SG: Ll, enters he op of tbe colnmnat a rate of 2.i kg/G mr),

and he gas,whichcanbeassrmedo have hesaneproperiies sair, eniershebotromoflhe colnnn ai a rate of0.6 kg(s mr). Thc columnopcmtes t atmo

spheric resstreand 25'C. Deiermine:(a) The pressnre rop throush he colnmn, n inches fwarer.(b) Howhish the iq id rateco ld be noeased elbre hecollmn wolld flood.A packedcolnmn s used o absorbSOr fronr nne gasnsingan ethanolaninesolution.The collmn is 4 ft i diameter, as a packedheightof 20 ft, and is

packed\rith2 in. lasticPall rings.Theflnegas sata lenperatnreof I80"F ardhasan aaerage olccnlarwcighrof 31.The amincsohtion hasa specinc ravjty

of 1.02and a vjscosity t thc opcraiiDgcmperatlreof 1.5cP. frhe gasDrlstleave he cohtnn al25 psigand a florv ale of 10.000 cfn, detemino:(a) Thc naxinum alloivablclow rateof the iqnid ir

spm)rhatwould es r in

a prcsnre drop that is 50% ofrhat at which loodingwotrldoccur.(b) The hoBcpowcr hat would bc rcquircd or thc blower ro move the sas

rhrr .sh rhe oLunrnf rheblo*er . 800o l t . i ( f l .A packedabsorption ower is nsed o removeSOr from an air streambyabsorplion n a solvent. hetoweris5 fl in diameterand 0 t highand contains1.5 n. plasticPallrings. The lemperalue ard .essxre n rhe tower are 90"Fatrd 0 psig.The gasstrean low rate s 6500sclm.The liquidsSG s 1.25. ndi

"c o . ) ( 2 ' c P .

(a) Whdi is the liqnid flow rale (in 8pn) at which he colnmnwill flood?(b) lf the cohmn op€rates t a liquid flow ralc tliat is 75% of lhe flooding

al e. wha s lhe rotal pressure .op llroLrgh he lower n psi?Apacked absorytioncolnnn emoves n mtnrity from a eassirean byconlaclwith a liqnid solvent. hecolumn s 3 f1 n djameler nd contains 5 t ofNo. 2

plasllcSuper nlalox packing.Tl1e ashasaDMW of28, enlers he colxmtrat120'F,and eaves l l0 psisat a rateof 5000 cfn.The iquidhasan SG of 1.15and a liscosily of0.8 cP. Delermnre:(x) The flow rate of rhe iquid in spm that would be 50% of thc flow ratc at

which the colunn would flood.(b) The pressure rop th rcugh the columD.n psr.(c) The horsepower fthe blower eqnired o nove rhegas hroBgh he colunrn

if il is 60% eincierr.



130Chemi@l nsineerinsrccesses

NOTATION

A arca,IL'?l

4 particle surfac€area/per unit volme, [1/L]

, diameter, [L]d parficle diueter, |LlDh hy&aulic dianeler, [L]q €n€rsy .lissipated pe; ;nit mass of flnid, tF LIM : I,: fitlG sasmass u{, IM/r'zrlr permeability,L'1]

Jiu porousmediariclioDactor,Eq. 131li. t lz lensth. L], liquid nals flrx tM/L1lar,ar, mass fsolids Mltr' ioradon ate, pm. /t ln nunber of ffanes. t lxRe,pM porousmed;a eynolds-nunber,q. 13-13),-]P pressure.F/r = M/Lt'l

O volumetric low rate, L3ur conpressibilityarameter,q. 13-44),-], time, i]We wettedperimeter,L],.t, z coordina €nections,L]^ ( ) ( ) , O ,

o porosily or void rraction. [lo polenlial (: P+ psz). F /t: : M/Lt'l

I viscosity, [M/Lt]p densily, tM/Lrl1// sphericily actor,I l

Subscripts

1,2.3 referencepoinlsf filrer frame sidei iftenntials superficial



Flowthroughofousmedia 131

NOMENCLATURE

B

c

DDL

DR

di

G

Ti]l,] cross{€ctionEl ma of bed d colnm

c@fficien in equarion4,49

Pmeabiliry coefficiert (eguation,l.2)Constant n eguarion4,28 (15 for sphericalparricle9

Specific hea a co.stant pre$ureCefficien in equarion4,49

Axial dispe4ion oemcient

Radial dGpe6ion oefficieni

Dimerer of rube or column

Equivalent dianeter of po€ slee = e/ss a usedby

Noninal p@ting size (e.g. dianeter for a Raschig ring)

Fncrional voidage of bed of parriclesor packing

Wall coftcrion faclor (equdion 4.23)

Cas nds flowra€ undd nooding onditions

Accelerdtion due to g vityLiqnid nold-up n b€d,volune ofliquid pe.uni

Heat mnsfer coefficient

M6s tnnstlr coefficientj f4tor for nas tEnsf€rj-factor for heat trmsrer

Constmt in ffop equations4.1 and 4,2Dimensionle$ @nsunt id equation 4,6Koredy consimi in equatiod 4-9Shape actor in equation 4.22

Consistencycoefiiciont for poweFhw nuid

- .

J4<gK

i. . .

kgs

i'.

in M, L , T ,0

L2L t

L2

L2T- 0-1

^

L 2 T I

LzT-\LL

L

LL

"t-T INf- 2T I

a 2

t4r 30 t

T-M-rr;T

MLT J'-'

t/f--jT' 2

r

KO



132 ChemicalEngjneeringPro@sses

I Liquid nass nownte

t/ Liquid mass elocityt vohneric liquid ratea; Volun€tnc iqnid rat€per unit area,,, weftins rare ,2/s )I Lengtbof bedor heightol collnn packingl' Le.gth of now pdsaAe$rcush bedl, Length of cncuhr tubcN Nunb€r of velocily heads ost thrcuet unit heigbr of bed

(equation .47)z Floq behaviour index for nower'law-nnida/ Expone.r n equation .17

LP Pressuredrop acrcss bed or colunn-LP, t PF. .u c drop c . , . b@oi L l ) p lcunS

LP,,, Pressuredrop ucro$ bed of wel packinggr Fractio. of l iquid collect€d at dnb.ce r fton centE line of

peking in equation .49R Drag force per unit ma of tubeFallRr Drag force per unit surface aea of panicles

S Surface rea per u.it volume of panicle or packingS, Surface arcaper unii volune of bed Gpecific surlace)S" Surface ea of coniaine. per unit volune of b€d

. Avenge fluid velocity basedo. .ross sectional Ea A of

Meanvelocityof duid in tubeVolumetic Rowrateot gas p€r unit dea of cr$s s4tionVolumedc noqrlte of liquid per unit trm of crcss secrionMetu veloci.y in pore channelVoltrne of duid flowins in tine rSideof cube

Coef6cient in equation r. 7

Coefficiem i. equation 4 17Coenicient f D i n equarions1.37, :19

Densiqr onmtion etor J(p6lp/)C6hof nunbe. (parlicle) (Volume l, Chapter 9)Nusclt nDnber or tubewall (44lr)Nuselt nnnber(panicle) illt)P*teI ntnber (ucrtleDL)at @ctkDRJPfmdtl .nmber (crrlt)Reynordsnunber for flow ths\*, tnbe (u,r/ tL)

Modifed Reynolds unber based n poresizeas used yCman (equadon.13)

A"', Modifed Reynolds unbe . based n panicle ize .zlplr.)R4MR Metzner nd ReedReynolds unber equton 4,27)(Rcr),, Reynolds umhor or powe.law fluid n a granular €d

(equation .28)s. Schnidt nunber (p/pD)s/ shesoo.l nunber (parlicle) nDzrlD)S, Sruron number pznitlet ttt/Crput,Suf6x A refeA LoJir JL2Sl K

G @rars o gdst rcfe4 ro iquidu refes to water a 293 K0 refeB to stmdard condilions

"^ t

v'

ff1

M T I

M L 2 T rL3T t

LT-'tlT t

LLLL - i

t "_, t .M L r T - 2ML-IT'2ML rT 2

Mr--rT 2

Lo-rT-2LL rL-'L rTl r I

ltT I

L r r

T]T I

L:)

LLML-rT-r

T rML- 'T- I

ML-I

ML rT 2

i

chapter -4-flow through porous media

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