P. 1 

# OAR Box 1110 Prepped byRyan Dugan



### Document

Number: 

# 1 ) IV-A-1 Docket Number: 

# A-82-3 9

Printed 4/14/20081:23:54

PM Sheet 1 of 156P. 2 

### EPA-600/2-77-17 2 August197 7 Environmenta l Protectio n Technolog ySeries 

# HI-*'/



# VENTUR I SCRUBBE R PERFORMANC E ^ODE L

o ' *«* > *** ,

Industria l Environmenta l Researc h Laboratory

Offic eofResearc h an d Developmen t U.S . Environmenta l Protectio n Agency Researc h Triangl ePark , Nort h Carolin a 2771 1_E^ _



## RESEARC HREPORTIN

GSERIES Researc h reports o fth e Offic e o fResearc h an d Development , U.S
. Environmenta l Protec tio n Agency , have bee n groupe d int o nin e series . Thes e nin e broa d cc^ccisr . vore established t o facilitat e furthe rdevelopmen tan d applicatio n o fenviro^ r??;'••.'. ] v 

### : ; 

### - nology . Eliminatio n o ftraditiona l groupin g was consciousl yplanne d t o fc'
. ';•:-, •• > : 

### •: : transfe ran d a maximu m interfac e i n relate d fields
. Th e nin e sen'?* ars :

1 . Environmenta l Healt h Effect s Researc h 2 . Environmenta l Protectio n Technolog y 3 . Ecologica l Researc h 4 . Environmenta l Monitorin g 5 . Socioeconomi cEnvironmenta l Studie s 6 . Scientifi can d Technica l Assessmen tReport s (STAR ) 7 . InteragencyEnergy-Environmen tResearc h an d Developmen t 8 . "Special " Report s 9 . Miscellaneou s Report s Thi s reporthas bee n assigne d t o th e ENVIRONMENTA L PROTECTIO N TECHNOLOG Y series . Thi s serie s describe s researc h performe d t o develo p an d demonstrat e instrumen tation , equipment , an d methodologyt o repai ro rpreventenvironmenta l degradatio n fro m poin tan d non-poin tsource s o fpollution . Thi s wor k

provide s th e nev

/ o rimprove d tech nolog yrequire d fo rth e contro l an d treatmen to fpollutio n source s t o mee tenvironmenta l qualit ystandards .

REVIE WNOTIC E Tni s reporthas bee n reviewe d b yth e participatin g Federa l Agencies , an d approve d fo r publication . Approva l doe s no tsignif ytha tth e content s necessaril yreflectth e views an d policie s o fth e Government , no rdoe s mentio n oftrad e name s o rcommercia l product s constitut e endorsemen to rrecommendatio n fo ruse . Thi s documen ti s availabl e t o th e publi cthroug h th e Nationa l Technica l Informatio n Service , Springfield , Virgini a 22161 .P. 4 

### EPA-600/2-77-17 2

. Augus t197 7 

# VENTUR I SCRUBBE R PERFORMANC E MODE L

by Shui-ChowYung , Seymou rCalvert, an d HarryF . Barbarik a A.P.T. , Inc . 490 1 Moren aBoulevard , Suit e 40 2 Sa n Diego , Californi a9211 7
ContractNo . 68-02-132 8 Tas k No . 1 3 ROAP No . 21ADL-00 2 Progra m Elemen tNo . 1AB01 2
EP ATas k Officer : Lesli e E . Sparks Industria l Environmenta l Researc h Laboratory Offic e ofEnergy , Minerals , an d Industry Researc h Triangl e Park , N.C
. 2771 1

Prepare d fo r U.S
. ENVIRONMENTA LPROTECTIO N AGENC Y Offic e ofResearc h an d Developmen t Washington , D.C
. 2046 0P. 5



### ABSTRAC T Areviewan

d evaluatio n o f th e availabl e ventur i scrubbe r design equation s ar e presented . Calvert' s differentia l equatio n fo r particl e collectio n an d Boll' s differentia l equatio nfo r pressur e dro

p ar e selecte d fo r numerica l solutio nan d th e result s presente d graphically . The particl e collectio nan d pressur e dro

p o f ventur i scrub
ber s ca n be approximate d b ythe collectio noccurring inthe ven tur i throa t an

d b ythe drop acceleratio n los s respectively . Sim
plifie d equation s wer e derive d b yapplying Calvert' s an d Boll' s equation s t o th

e ventur i throa t section . The newdesignequa tion s ar e muc hsimple r t o us e an d compar e wel l wit havailabl e performanc e data . Thi s repor t wa s submitte d in partia l fulfillmen t o f Contrac t Numbe r 68-02-1328 , Tas k Numbe r 1 3 b yAi r Pollutio nTechnology , Inc . unde r th

e sponsorshi p o f the U.S . Environmenta l Protectio n Agency . Thi s repor t cover s the perio d Marc h1 , 197 6 t o Ma y30 , 1976 , an

d work wa s complete d a s o f Jun e 30 , 1976 .

ENVIRONMENTA L PROTECTIO N

AGENC Y 

### AP R 

### 2 5 198 8 CENTRA LDOCKE T SECTIO N nP. 6



### CONTENT S
Abstrac t Page i i Figure s i v Table s i x Abbreviation s an

d Symbol s x Acknowledgemen t x v Introductio n Summar yan d Conclusion s Literatur e Search Compariso n o f Mode l wit hExperimenta l Data . Performanc e Mode l Comparing Mode l Prediction s wit hPerformanc e Dat a 1 4 1 6 4 1 6 1 11 4 7 . Desig

n Analysi s 12 8 8 . Entrainmen t Separato r 16 1 Reference s ... . 19 1 Appendi x. 19 5

i nP. 7

FIGURE S Numbe r Pag e 1- 1 Ventur i Scrubbe r Sy.ste m3 3- 1 Targe t Efficienc yResult s o f Variou s

Investigator s 2 0 3- 2 Dra g Coefficien t o f a Spher e 2 7 4- 1 Dimension s o f OA P Ventur i Scrubbe r . . 4 3 4- 2 Compariso n o f Predicte d Pressur e Dro p

wit hExperimenta l Dat a fromWe n and Uchid a 4 4 4- 3 Compariso n o f Predicte d Pressur e Dro p

wit hExperimenta l Dat a fro mWe n and Uchid a 4 5 4- 4 Compariso n betwee n Behi e and Beeckmans '

Predictio n and Experimenta l Dat a from We n and Uchid a 4 6 4- 5 Compariso n o f Predicte d Pressur e Dro p b y Modifie d Calvert' s Equatio n wit hDat a fro m We n and Uchid a 5 1 4- 6 Prototyp e Ventur i Scrubbe r Use d byBol l 5 2 4 7 Compariso n o f Boll' s Pressur e Dro p Dat a

wit hTheor y5 3 4- 8 Dimensio n o f Pease-AnthonyVentur i

Scrubbe r Use d b

yBrin k and Contant . . . 5 5 4- 9 Compariso n o f Brin k and Contan t Experi
menta l Dat a wit hTheorie s 5 7 4-1 0 Dimension s o f th e Ekma n and Johnston e

Ventur i 5 8 4-1 1 Compariso n o f Elema n and Johnstone' s

Pressur e Dro p Dat a wit hTheorie s .. . 5 9 5- 1 Char t fo r Obtainin g u l fo r a Circula r

Duc t 7 2
i vP. 8



### FIGURE S (continued ) ' • Numbe r Pag e 5- 2 Char t for Obtaining u ^ for a Rectangula r Duc t 7 3 5- 3 Char t for Obtaining p* , for a Circula r Duc t 7 4 5- 4 Char t fo r Obtaining p ^ for a Rectangula r Duc t 7 5 T- 5 Char t for Obtaining Penetratio n fo r Circu
lar Duc t 7 6 5- 6 Char t fo r Obtaining Penetratio nfo r Circu
lar Duc t 7 7 5- 7 '.':•.art

for Obtaining Penetratio nfor Circu
- "a r Duc t 7 8 5- 8 Char t fo r Obtaining Penetratio nfo r Circu
- " : r Duc t 7 9 5- 9 Char t fo r Obtaining Penetratio n fo r Circu
lar Duc t 8 0 5-1 0 Char t for Obtaining Penetratio nfor Rectan gula r Duc t 8 1 5-1 1 Char t f« . r Obtaining Penetratio n fo r Rectan gula r Du- t 8 2 5-1 2 Char t t o Obtai n Penetratio nfo r Rectangula r Duc t 8 3 5-1 3 Char t t o Ob t i n Penetratio n for Rectangula r Duc t 8 4 5-1 4 Char t t o Obtai i Penetratio n for Rectangula r Duc t 8 5 5-1 5 Char t t o Obtai nPenetratio nfo r a Rectan gula r Duc t 8 6 5-1 6 Char t t o Obtai nPenetratio nfor a Rectan gula r Duc t 8 7 5-1 7 Concep t o f a Hypothetica l Sectio n ... . 8 8

vP. 9



### FIGURE S (continued ) Numbe r Pag e 5-1 8 Char t fo r Obtaining L H

### for a Circula r Duc t 9 0 5-1 9 Char t fo r Obtaining L H

### for a Rectangula r Duc t 9 1 5-2 0 Ventru i Scrubbe r fo r Sampl e Calculation . . 9 3 5-2 1 Predicte d Grad e EfficiencyCurve 9 8 5-2 2 Predicte d Grad e EfficiencyCurve H O 6- 1 Experimenta l an d Predicte d Performanc e o f AAF Kinpacto r 3 2 Ventur i Scrubbe r 11 6 6- 2 Experimenta l an d Predicte d Performanc e for AAF Kinpacto r 3 2 Ventur i Scrubbe r 11 7 6- 3 Predicte d an

d Experimenta l Penetratio n for Ventur i Scrubbe r Used b yBrin k an d Contan t 11 8 6- 4 Predicte d an

d Measure d Penetratio n for Chemic o Ventur i Scrubbe r 12 1 6- 5 Predicte d an

d Experimenta l Grad e Efficiency Curve fo r Chemic o Ventur i Scrubbe r ... . 12 2 6- 6 AP S Electrostati c Scrubbe r 12 3 6- 7 Experimenta l an d Predicte d AP S Ventur i Scrubbe r Performanc e 12 4 6- 8 Predicte d an

d Experimenta l Performanc e fo r Ventur i Rod Scrubbe r 12 6 7- 1 Ventur i Scrubbe r Integrate d Penetration , "Pt " versu s "d n 

### r n 

### / d " , wit h" K " as para P Di l p g p g meter , " a =2.5 " 13 4 7- 2 _Ventur i Scrubbe r Integrate d Penetration , P t versu s d rn/ d , wit hk a s parameter , a= 5 . . . P ^ ° . ? g . .. . ? g . .... . . . 15 5 7- 3 Ventur i Scrubbe r Integrate d Penetration , P t versu s d cn

/d„ n, wit hK a s parameter , a=7. 5 . . .P?° . ? g . .. . ? g . ... . . . . 13 6

v iP.1 0



### FIGURES , .(-continued ) Numbe r E.^8^ . 7- 4 "Pt " versu s "B " wit h" K" a s parameter , " a =2.5 " ? g

### 13 8 7- 5 "Pt " versu s "B " wit h" K" a s parameter ,

g , a 

### =5 " ? g

### 13 9 7- 6 "Pt " versu s "B " wit h" K" a s parameter , " a =7.5 " P g

### 14 0 / 

### d C 

### n/ dversu s "B " wit h" K" a s para paSO ' p g p g ' mete r 14 1 7- 8 Effec t o f Throa t Lengt ho nPenetratio n. . . 14 2 7- 9 Iffec t o f Throa t Lengt ho nPerformanc e . . . 14 4 7-1 0 "redicte dVentur i Scrubbe r Performance , Kr n 

### versu s B ? . 1 4 5 7-1 1 Effec t o f Ga s Velocit yandLiqui dt o Ga s Flo wRat e Rati o o nPerformanc e Cu t Diamete r 14 7 7-1 2 "B " v s " K c 

### " fo r ventur i throa t o f infinit e lengt h. pb 

### V

14 8 7-1 3 Predicte dVentur i Performance , "d p a 

### 5 o " ver su s Q T 

### / Q f 

### wit h"u G 

### " an d" P " a s Parameter . . 14 9 '<J„ wit h"u^ " an d" F " a s r 7-1 4 Aerodynaai c Cu t Diamete r Versu s Pressur e Dro p wit ] Liqui dt o Ga s Rati o a s Paramete r . 15 0 7-1 5 Impactio nparamete r v s aerodynami c cu t diamete r fo ~ a ventur i desig n15 4 7-1 6 Pressur e dro p v s aerodynami c cu t diamete r fo r ventur i desig nexampl e 15 7 7-1 7 Impactio nparamete r v s Q T 

### / Q r 

### fo r ventur i desig nexampl e 16 0 8- 1 Cyclon e wit htangentia l ga s inle t 1^ 5 8- 2 Generalize dfloodin g an dpressur e dro p correlatio nfo r packe dbed s (Perry , 1963) . . 17 4

v nP.1 1

. FIGURE S (continued ) Numbe r EfLE ? 8- 3 Theoretica l an d experimenta l collectio n efficiencie s o f rectangula r aeroso l jets . . \i(. 8- 4 Theoretica l impactio n efficienc ya s a func
-

. tio n o f inertia l paramete r fo r differen t target s 17 7 8- 5 Frictio n factor , f , versu s Reynold s num ber , N nnfo r wir e mes hentrainmen t se - ' R e , G parato r wit hentrainmen t loa d 18 2 8- 6 Pressur e dro p du e t o presenc e o f liqui d i n th e knitte d mes hwit hth e crimp s i n th e sam e directio n 18 3 8- 7 Pressur e dro p du e t o presenc e o f liqui d i n th e knitte d mes hwit hth e crimp s i n th e alternat e directio n 18 3 8- 8 Dra g coefficien t versu s Reynold s numbe r afte r Fous t e t a l (1959 ) , wit hsphericit y tya s th e paramete r 18 7 8- 9 Dra g coefficient s fo r flo wpas t incline d fla t plate s (dat a fro mA . Fag e § F.C . Jo hansen , (1927 ) 18 7

v mP.1 2

TABLE S
Numbe r Pa § e 2- 1 Correlatio n fo r Particl e Collectio n i n Ventur i Scrubbe r 5 2- 2 Correlation s fo r Pressur e Dro p i n Ventur i Scrubbe r 8 2- 3 Entrainmen t Separato r Desig n Equation s . . 1 2
"- I Empirica l Equation s fo r Averag e Liqui d Dro p Siz e and Thei r Applicabl e Range s . . 2 5 3- 2 Correlation s fo r Pressur e Dro p i n Ventur i Scrubbe r 3 7 -i-l We n and Uchida' s Experimenta l Pressur e Dro p Dat a o n O.A.P . Ventur i Scrubbe r .. . 4 2 4- 2 We n and Uchida' s Experimenta l Dat a and Prediction s b

yBol l and byBehi e and Beeckmaw s 4 8 8- 1 Be d Porosity , e , fo r Variou s Packin g Material s 17 1 8- 2 Experimenta l Value s o f j , Channe l Widt h a s Fri

1 1 . tio n o f Packin g Diamete r 17 1 8- 3 Packin-
- Factor s "F" , fo r Dumpe d Piece s (m 2 /m 3 , 17 2 8- 4 Packin g Fictor s "F " fo r Grid s and Stacke d Piece s (m 2 /m 3 ) 17 3



### i xP.1 3

2 

### ABBREVIATION S AN

D SYMBOL S Lati n A= cross-sectiona l area , cm 2 

### A= cross-sectiona l are a a t th e duc t inlet , c

m A= tota l projecte d are a o f baffle s pe r rowin

th e directio n o f inle t ai r flow , cm 2 

### A ^ = rati o o f exi t t o inle t duc t cross-sectiona l

area , dimensionles s A= throa t cross-sectiona l area , cm 2 

### a 2 

### = specifi c are a o f mesh , cm 2 

### /cm 3 

### B = dimensionles s liquid-to-ga s flow-rat e rati o

parameter , dimensionles s

- i ^ T M i ' ur^ 

### xL L ( bo C 

### D o Q 

### G P 

### G\ u

### G o "do> B

_ = dimensionles s paramete r

4 B D 

### p ^G^ d b= duc t breadth , c m b= spacing betwee ntw o consecutive baffle s in sam e row , c

m C = Cunningha msli p factor , dimensionles s C B 

### = drag coefficient , dimensionles s C p 

### = initia l drag coefficient , dimensionles s c = concentratio n o f particles , g/cm3 

### c = capillarynumbe r c , = numbe r concentratio n o f drops , #/cm3 

### c . - concentratio no f particle s inth e mai n 1 r



### strea mo f gas , g/cm 3 

### D = diffusivit yo f particle , cm 2 

### / s d = cyclon e diameter , c m d = collecto r o r packing diameter , c m d, = liqui d dro p diameter , c

m d = equivalen t diameter , c m e qnP. M 

### Abbreviation s an dSymbol s (continued ) d= meandro p diameter , c m mr d = nozzl e diameter , m m n d = initia l inle t o r outle t duc t diameter , c m o d = particl e diameter , c mo r ym P d = aerodynami c particl e diameter , ym A d = cu t diameter , ym A p s o ' d D r = require d cu t diameter , ym A d = ventur i throa t diameter , c m E = collectio n efficiency , fractio n H , = edd ydiffusivit yo f liqui d drops , cm 2 / s E = edd ydiffusivit yo f particles , cm 2 / s F = dro p flux , g/cm 2

- s F = packin g factor , m 2 /m 3 F, , = foa mdensit y f = empirica l constant , dimensionles s f = frictio n factor , dimensionles s f = averag e frictio n facto r o f th e ventur i

throat , dimensionles s f = averag e frictio n facto r o f th e convergen t

section , dimensionles s f- , = av^rag e frictio n facto r o f th e divergen t

section , dimensionles s g = coniersio n facto r H , = fractiona l liqui d hold-up , fractio n j = rati o i f channe l widt ht o packin g

diametei , dimensionles s K = inertia l parameter , dimensionles s K . = inertia l paramete r a t ventur i throat , p t r '

dimensionles s K = initia l inertia l parameter , dimensionles s p o ^ ' K = inertia l paramete r fo r mas s media n particl e

diameter , dimensionles s k = Boltzman' s constan t

x iP.1 5 

### Abbreviation s andSymbol s (continued ) dimensionless'lengt hparamete r 3 £ C 

### D o p 

### G/ u 

### Go- U 

### do X 

### °' 5 2 d 

### d P 

### L ^ u 

### G o I = length , cm & = ventur i throa t length , cm £ 2 = thicknes s o f mes hpad , c m M= liquid-to-ga s mas s flow-rat e ratio , dimensionles s m r 

### = ga s mas s flo wrate , g/ s m T

### = liqui dmas s flo wrate , g/ s N= numbe r o f je t stage s i nth e tub e bank , i.e. ,

(numbe r o f rows ) - 1 N= numbe r o f collectio ntransfe r unit s n= cyclon e vorte xcomponent , dimensionles s n= numbe r o f zigza g baffl e row s P = dro p fligh t pat hlength , cm Pt( d) = particl e penetratio nfo r particle s wit h

diamete r d, fractio n

P P t = overal l penetration , fractio n p = loca l pressure , dyne/cm 2 

### p r 

### = componen t o f "p " associate dwit hwal l

friction , dyne/cm 2 

### Q , = sourc e strength , #/cm 3 

### Q r 

### = ga s volumetri c flo wrate , cm 3 

### / s Q T

### = liqui dvolumetri c flo wrate , cm 3 

### / s R= radiu s (fo r circula r duct ) o r half-widt h

(fo r rectangula r duct ) a t th e star t o f a give nduct , cm R , = washin g facto r fo r divergen t section , dimensionles s a R ^ = washin g facto r fo r A^entur i throat , dimensionles s S = dimensionles s paramete r characterizin g slop e

o f th e give nduc t 2 ta n3 d d

### P L 

### ' " " °' 5 

### I ta n g 

### ^ ^ L / U 

### G o \ 3 RC 

### D o P G

### \ u 

### Go- u 

### do /

x uP.1 6



### FIGURE S (continued ) Numbe r Pag e 8- 3 Theoretica l an d experimenta l collectio n efficiencie s o f rectangula r aeroso l jets . . 17 5 8- 4 Theoretica l impactio nefficiencya s a func
tion o f inertia l paramete r for differen t target s 17 7 8- 5 Frictio n factor , f , versu s Reynold s num ber , N nr



### fo r wir e mes hentrainmen t se Re , G parato r wit hentrainmen t loa d 18 2 8- 6 Pressur e dro

p due t o presenc e o f liqui d in the knitte d mes hwit hth e crimp s in the sam e directio n 18 3 8- 7 Pressur e dro

p du e t o presenc e o f liqui d in the knitte d mes hwit hthe crimp s i nthe alternat e directio n 18 3 8- 8 Drag coefficien t versu s Reynold s numbe r afte r Fous t e t a l (1959 ) , wit hsphericit y tya s th e paramete r 1 8 7 8- 9 Drag coefficient s fo r flo wpas t inclined fla t plate s (dat a fro mA . Fag e $ F.C . Jo hansen , (1927 ) 18 7

v mP.1 7 

### Abbreviation s an dSymbol s (continued ) p = ga s density,"g/cm 3 

### ' - G p = manomete r flui ddensity , g/cm 3 

### p . = liqui ddensity , g/cm 3 

### p = particl e density , g/cm 3 

### 6 = divergenc e angl e o r baffl e angle , degree s 6 1 = convergenc e angle , degree s 6 2 

### = divergenc e angle , degree s n= singl e dro p collectio nefficiency , fractio n y G

### = ga s viscosity , pois e y r = liqui dviscosity , pois e v - - kinemati c viscosit yo f gas,cm 2 

### / s ty= rat e o f deposition , g/ s a= surfac e tension , dyne/c m A P = pressur e drop , c mW.C . A P , = dr ypressur e drop , c mW.C . A T = temperatur e change , ° K Superscrip t * = dimensionles s paramete r Dimensionles s number s N R

### , = dro p Reynold s numbe r base do ndiamete r N R

### = initia l dro p Reynold s numbe r N o = particl e Schmid t numbe r N'S h= 

### particl e Sherwoo dnumbe r

xi vP.1 8



### ACKNOWLEDGEMEN

T A.P.T. , Inc . wishe s t o expres s it s appreciatio nfo r excellen t technica l coordinatio n an d fo r ver

yhelpfu l assistanc e i n suppor t o f our technica l effor t t o Dr . Lesli e E . Sparks , EP AProjec t Officer .

x vP.1 9



### CHAPTE R1 INTRODUCTIO

N Ventur i scrubbe r i s one typ e o f ga s atomize d spra yscrubber . I t employ s graduall yconverging , then diverging sections . The ventur i throa t i s th e sectio n betwee n th e converging an

d diver
gin g sections . Usuall yliqui d enter s th e ventur i upstrea

mo f th e throa t throug

hnozzles . Alternately , the liqui d ma yflow along th

e converging sectio n wall s unti l reaching th e throat . At th e throat , the liqui d i s shattere d int o drop s b yth e high velocit ygas . Sometime s the liqui d i s introduce d a s pre-atomize d drop s a t o r befor e th e throa t throug

ha pressur e nozzle . The ventur i ma

yhave a round , square , o r rectangula r cros s section . Fo r th e rectangula r duct , th e breadt ho f th

e duc t i s usuall yin
varian t an

d onl yduc t widt hdiverge s o r converges . Ventur i scrubber s have bee n widel yrecognize d a s having a highcollectio n efficiencyfo r fine particle s an d have bee n successfull yused fo r year s t o remove particle s an d mist s fro

m ga s streams . Particl e collectio nefficiencyi na ventur i scrubbe r generall yincrease s wit hpressur e drop . Highpressur e dro p (10 0 c

mW.C . o r 4 0 in . W.C. ) ventur i scrubber s can effi
cientl ycollec t submicro n particles . The ventur i scrubbe r ha s severa l distinc t advantage s whe n compare d wit hothe r scrubbe r types . The scrubbe r constructio n i s simple , thu s the initia l capita l investmen t i s low . Through adjusting pressur e dro p b yvarying liqui d flo wor ga s velocity , i t ca n be mad e t o collec t eve n submicronfum e wit hgood effi
ciency . Du e t o th

e absenc e o f moving parts , i t ca nbe used fo r th e collectio n o f stick yparticles . The ventur i scrubbe r als o ha s disadvantages : I t require s hig hpressur e dro

p for .th

e collectio n o f submicron particle s whic hresult s i n a hig hoperating cost , an d it s applicabilit y

### fo r mas s transfe r problem s i s limite d due t o th e co-curren t natur e o f th

e gas-liqui d flow . To preven t possibl e wate r pollu
tion problems , i t als o require s wate r treatmen t facilities . Figur e 1- 1 describe s a commonl yencountere d ventur i scrubbe r system . I t consist s o f a ventur i scrubber , a n en trainmen t separator , liqui d treatmen t facilities , an d ga s an

d liqui d movers . The atomize d liqui d drop s o r liqui d entrainmen t mus t b e separate d fro

mthe ga s strea

mbefor e th

e ga s i s emitte d int o th e atmosphere . Ther e ar e a numbe r o f device s whic har e commonl y use d a s entrainmen t separator s whic har e adde d eithe r withi n th e ventur i cutle t duc t o r i n anothe r vessel . Zig-zag baffles , cy clone separators , an d guid e vane s causing rotatio no f the ga s strea mar e frequentl yuse d fo r thi s purpose . In th e presen t study , onl yth e designo f ventur i scrubbe r itsel f an

d it s entrainmen t separato r wil l be reviewe d an d evalua
ted .Emissio n Fro m Sourc e
Oi 

# Hntrainmen t f \ Separator V

) 

# "0 - Pum p Liqui d

Treatmen t Fa n Stac k

Figur e 1-1 . Ventur i scrubbe r syste m

h oP.2 2



### CHAPTE R2 SUMMAR YAN D CONCLUSION S Ventur i scrubber s are used extensivel yfo r the collec
tion o f smal l particles . The majo r impedimen t t o thei r practi
ca l us e i s tha t the yhave hig

hpressur e drop s whic hresul t i n highoperating cost . Wit ha bette r understanding o f the fundamental s o f the operatio no f thi s typ e o f scrubber , the pressur e dro

p coul d be lowere d withou t affecting particl e collection . The objective s o f the stud yreporte d her e wer e t o (1 ) reviewan

d evaluat e al l availabl e ventur i scrubbe r perfor
manc e model s an

d designmodel s (2 ) recommen d the bes t mode l an

d (3 ) prepar e a designmanua l base d on thi s model . LITERATUR E SEARC H Particl e Collectio n Efficiency . The particl e collectio nefficiencyo f a ventur i scrub
be r i s influence d b yman yparameters , suchas particl e siz e an d siz e distribution , ga s velocity , liquid-to-ga s ratio , etc . Ther e are severa l mathematica l model s availabl e fo r the predictio n o f particl e collectio nefficiencyi na ven tur i scrubber . Al l model s ar e base d on particl e impactio n on liqui d drops . Tabl e 2- 1 summarie s al l models . Pressur e Drop Pressur e dro

p i n a ventur i consist s o f two parts , namel yacceleratio n los s an d wall-frictio n loss . Mos t o f th e losse s are due t o acceleratio nan d thes e ma

y be calculate d fro

mhydrodynamics . Wall-frictio n los s depend s o

n scrubbe r geometr

yan d usuall yi s determine d experimentally . Tabl e 2= 2 list s severa l availabl e corre lation s fo r th

e predictio n o f pressur e dro p in a ventur i

### TABL E 2-1- . CORRELATIO NFO RPARTICL E COLLECTIO N I NVENTUR I SCRUBBE R Investigato r Correlatio n Ekman § Johnston e (1 9 51 ) Pt(d p 

### ) = ex p 3 nP s 490,00 0 Calver t (1968 ) d c _u

### r \ / 3 c u G

### (u G 

### -u r 

### ) A\4r d 

### n d z

Calver t (1970 ) Pt( d) = ex p 2 

### Q L U 

### G P 

### L d 

### d 5 5 

### Q GP 

### G F (K pt 

### , f ) F(K pt 

### , f ) = ^ Pt / K . f + 0. 7 

### 1



# -« 

# H-^ry 0.4 9 0. 7 + 

### K p t 

### f 

## (K p 

## t £ + 

## °' 7 

## ) Morishim

a e t a l (1971 ) Pt(dp 

### ) = ex p - (R t + 

### R d 

### ) L

R . 3 £ 

## 2 l 

# i/-*(•-*) « x 3£ Q /--ma

x^n \ 

## 2d , J 

## " u d

## X 2 

## " U 

## d d X 1 Drop p ^ Akbru t (1972 ) Pt( d ) = ex p 

# 2 J Wld

# c U 

# d d z

Bol l (1973 ) Pt(dp 

### ) = ex p 0

c



### continue d

### TABL E 2-1 . (Continued )

Investigato r Correlatio n Behi e § Beeckman s Pt( d ) = ex p (1973 ) 

## LJ p 

## L d 

## dU 

## GU 

## c d z
Taher i $ Shei h (1975 ) 

## i £ = - ui£ - + E a t G

## a z p 3 2 

### c + 

### 9 2 

### c



## — d 

## d( 

## V u 

## d } c c 

## d

3c 

### d 3c 

### d 3T ~ = 

### " U 

### d 3Y ~ + E 

### d 3 2 

### c , a 2 

### c , 

## -A 

## + d 3y 2 

### 3 ^ + Q 

### d

wher e A

c

E = P F = f = P t



### m . m L P Pt( d ) cross-sectiona l area , cm 2



### concentratio no f particulates , g/cm3 

### numbe r concentratio n o f drops , #/cm3 

### dro p diameter , c

m edd ydiffusivit yo f drops , cm 2 

### / s edd ydiffusivit yo f particle , cm 2 

### / s dro p flux , g/cm 2



### - s empirica l constan t inertia l paramete r a t ventur i throat , dimensionles s length , c

m ga s mas s flowrate , g/ s liqui d mas s flow , g/ s dro p fligh t pat hlength , c m penetratio nfo r particle s wit hdiameter , d , fractio n P sourc e strength , #/c m continue dP.2 5



### wher e Q r 

### = volumetric'ga s flowrate , cm 3 

### / s ' .

Q , = volumetri c liqui d flowrate , cm 3 

### / s s = specifi c surfac e o f drops , cm 2 

### /cm 3 

### o f ga s t = time , s u , = drop velocity , cm/ s u r 

### = ga s velocity , cm/ s u = dro

p particl e relative velocit ycm/ s x= rectangula r coordinate , perpendicula r t o th e direction'o f flo

w X= dimensionles s distanc e y= rectangula r coordinate , perpendicula r t o th e directio no f flow z = rectangula r coordinate , inth e directio n o f flow P T 

### = liqui d density , g/c m n = singl e dro

p collectio nefficiency , fractio nP.2 6

TABL E 2-2 . CORRELATION S FO R PRESSUR E DRO P I NVENTUR I SCRUBBE R Investigato r Correlatio n .tro^o v(1955 ) 3 ,,1- 08 l G t 0. 6 AP= A

P, - 1.3 8 x1 0 3 ixC'l*I Q r \ 

# ^1

' o s hi c aet

a1 . ;1960 j (1965 ) A P= p r u a+ D 

# k\
a r , 0

^ G'
m. „ C n+ 4 f

. - 2ta nO itc +C 1- 2 o 

### b = ( r 

### - 1 ) 4 £

_

l_ ~P d mt c .- i iC /- i 

## ^d' l j 

## F " u 

## '

K m d o / Geisek e(1968 ) A P g S c

& c ra GAu G+m LAu L A m L, .

IIX.-m 1 _+11 . "J I Lj L 2 

# ) ]

;1964 ) AP= 0. 3 (AT ) 

# _!?£ {_• 

# %) 2 

## « c"

## V
ohat ae t

al . •'.'1954 ) AP=

- g , D ' J



# r — ^
o ta n 0 1 5 ta n0 2 J t ci ^ l,l T U
(continued )P.2 7



### TABL E 2-2 . (Continued ) Investigato r Correlatio n •Volgin e t a l (1968 ) n°' 2 6



### A P = 3.3 2 xIO" 6 

### u, 2 

### U ) ( 

### , t ) 0 I.i* 3



### Calver t (1968 ) A P = 1.0 3 xIO" 3 

### u 2 

### I ~

Gt\Q G 

### Gleaso n e t a l (1971 ) AP = 2.0 8 xIO" 5 

### u G 2 

### (0.26 4 Q + 73.8 )
Bol l (1973 ) Un- - u2 w _+. id

u, \ 

### P G

### 2 g c 

### g c

### J Q

### G \ d t /

+ 

# (M^ Df

f U 

# GU 

# c d t + 'C £ e

q 

# : 

# g. y

x : f u 2 

### d

x eq Behi e d- Beeck
ma n (1 9 73 ) d

p 

### -J^- d



### )[2 C 

### D P 

### G C 

### V U 

### d } 

### -4
- d t

Hesket h (1974 ) A

P = 1.3 6 xIO" " u G 

### ^ P G

### A t 0



### - 13 3



### Q [0.5 6 + 

### 935 ^ + 1.2 9 x1 0 " ^

M. . , . „ „ ln 

### ~ 5 iV '

wher e A= throa t cross-sectiona l area , cm 2



### duc t cross-sectiona l area , cm 2 

### liqui d dro

p diameter , c

m equivalen t duc t diameter , c m A

eq (continued )P.2 8



### d= throa t diameter , c m d= inle t o r outle t duc t diameter , c m o * f = frictio nfactor , dimensionles s f = averag e frictio nfacto r o f th e throa t T - averag e frictio nfacto r o f convergen t section , dimensionles s f j = averag e frictio nfacto r o f th e divergen t section , dimensionles s g = conversio nfacto r 6 

### c 1 = throa t length , cm M= liquid-to-ga s mas s rati o m „ = ga s mas s flo wrate , g/ s m= liqui dmas s flo wrate , g/ s Q „ = ga s volumetri c flo wrate , cm 3 

### / s Q = liqui dvolumetri c flo wrate , cm 3 

### / s u „ = ga s velocity , cm/ s u „ = ga s velocit ya t th e throat , cm/ s u , = liqui ddro p velocity , cm/ s u = liqui dvelocity , cm/ s t = time , s z = rectangula r coordinat e i nth e directio n o f flow , c m A P = pressur e drop , c m W.C . AP , = dr ypressur e drop , c m IV.C . A T = temperatur e change , ° K p = ga s density , g/cm 3 

### p = manomete r flui ddnesity , g/cm 3 

### mJ 

### ' & 

### 0 ! - convergenc e angle , degre e 0 2 

### = divergenc e angle , degre e C = coefficien t o ndivergen t los s o f ga s flow , dimensionles s £ = head-los s rati o fo r throat , dimensionles s C j = head-los s rati o fo r divergen t section , dimensionles s
1 0P.2 9



### scrubber . Correlation s b yMatrozo v(1953) , Volgi n e t al . (1968) , Gleaso n e t al (1971 ) an d Hesket h(1974 ) ar e experi
menta l correlations . Al l other s are theoretica l equations . Entrainmen t Separato r The entrainmen t separato r i s a nintegra l par t o f th e scrubbe r system . Generally , an ydevic e tha t can be used t o collec t particle s canals o be employe d t o knoc k ou t entrain
ment . However , du e t o economica l reasons , onl ya fe wfind practica l usage . Calvert , e t al . (1975 ) have evaluate d severa l suitabl e entrainmen t separator s experimentally . Tabl e 2- 3 list s severa l comir.o n entrainmen t separator s an d thei r design equations . CONCLUSION S Th e principa l objective s o f thi s stud ywer e achieved . The following conclusion s ca n b e drawn . (1 ) Collectio n b

yatomize d liqui d drop s i s th e prin
cipa l collectio n phenomena ina ventur i scrubber . Eve n thoug heachinvestigato r presente d a differen t equatio n fo r th e predictio n o f particl e collectio ni na ventur i scrubber , mos t o f thes e equation s canbe reduce d t o th e sam e basi c model , i.e. , r z 

### 3 u Q , n



### -i n Pt . ( V



### =_ / 2 U g ( ; G . V



### ^d z (2-! )
wher e Pt( d ) = penetratio n fo r particle s wit hdiamete r d ,

fractio n u = relativ e velocit ybetwee n dus t an d drop , cm/ s u r 

### = ga s velocity , cm/ s d j = dro

p diameter , c

m n = singl e drop collectio n efficiency , fractio n Q = liqui d volumetri c flowrate , cm 3 

### / s z = length , c

m
1 1

### TABL E 2-3 . ENTRAINMENT SEPARATORDESIG NEQUATION S Separato r Typ e Investigato r Design Equatio n GravitySettle r E = u t 

### b £
Sieve Plat e Taher i { j Calver t (1968) ' E = 1 - ex p (-4 0 F 2 

### K )
Mes h Bradi e $ Dickso n ' (1969 ) E = 1 e x 

## P C- f I a 

## 2 £ 

## 2 1 ) Packe d Bed Jackso n§ Calver t (1966 ) P t = 1 ex p 

## ^TT +

## j' ) ( e- H

### ) a ~ Kp 

### Tube Ban

k Calver t § Lundgre n

(1970 ) E = 1 ( 1 - n. ) N Cyclon e Leit h6 Lich t (1971 ) l nP t = - 2 p , /2d , u ^ 2 

### 5TT G 

### \ d c (n+l) t 2n+ 2

0. 3 

### n= 1 

### rT

### i

_2M j ( 

### 0.39 3 d c )



## ~T7 5 o. i i »


### Zig-za g Baffle s Calver t e t a l (1974 ) n = 1 - ex p u t c 

### nw e 57. 3 u n

### bta

n 0 b 

### con t i nuedP.3 1



### TABL E 2-5 . (continued ) Wher e a 2 

### = specifi c are a o f mesh , cm 2 

### /cm 3



### b= settle r widt hor baffl e spacing withi nrow , c m d = cyclon e diameter , c m d = packing diameter , c m F , = foa

mdensity H , = fractiona l liqui d hold-u p inth e be d j = rati o o f channe l widt ht o packing diamete r K = inertia l parameter , dimensionles s

- p F 

### I = settle r length , c m l z

### = thicknes s o f mes hpad , c m N= numbe r o f je t stage s in the tube bank
= (numbe r o f rows ) - 1 n = cyclon e vorte xo r numbe r o f zig-zag rows Q p = volumetri c ga s flowrate , cm 3 

### / s Pt(d, ) = penetratio nfo r drop s wit hdiamete r d, ,

fractio n T = ga s temperature , °K t = residenc e time , s u = ga s velocity , cm/ s u = dro

p termina l settling velocity , cm/ s u = centrifuga l ga s velocity , cm/ s u = tangentia l velocit yo f gas , cm/ s w= widt ho f baffle , c m 6 = be d length , cm p , = dro

p density , g/cm 3 

### u r 

### = ga s viscosity , pois e 0 = angl e o f inclinatio n o f the baffl e t o th e flo wpath , degre e n = targe t efficiencyo f cylindrica l wire , fractio n n- = collectio nefficiencyfo r a give ndro p dia
3 

### mete r i none stag e o f rectangula r je t impinge
ment , fractio n z= packe d bed porosit y

1 3P.3 2



### (2 ) Ageneralize dmetho dfo r applyin g equatio n2- 1 t o predic t particl e collectio ni na ventur i wa s developed . (3 ) Particl e collectio npredicte db yequatio n2- 1 agree s satisfactoril ywit hperformanc e data . (4 ) Mos t o f th e particl e collectio noccur s i n th e ventur i throat . Th e solutio nt o equatio n2- 1 fo r th e ventur i throat , usin g th e inertia l collectio nefficienc y correlatio npropose db yCalver t (1970 ) an d assumin g a zer o initia l dro p velocit yis , I nP t ( d) 

### L_P 

### = B po ( de ) 4 

## V^de) 1 

## ' 5 

## •^(l-uJ J 0. 5



### 5.0 2 K 0 

### ' 5 

### /l- u 

### * + °
- p o \ u 

### d e K . 

# a-w i V' ^ 4 K p o + 

### 4. 2 - 5.0 2 K-( l + 

### ^tan-(^ f (2-2 ) wher e Uj

_= - —= dimensionles s dro p velocit y

d eu Gt (2-3 )

u , = 2 d e 

### /L+jV
. (h + S\ f L+ 8) 

### \-T-) 

## \ 8

## ) \ 

## s ; 0- 5 (2-4 )

^G/\ p G /

C D o (2-5 ) C d

_ p u G 

### K= — n

### P N= inertia l paramete r base do n p o 9 U r 

### d , throa t velocity , dimensionles s (2-6 ) 1 4P.3 3

5 & 

### t C 

### D o P 

### G 2 d 

### d p 

### L = dimensionles s throa t lengt h(2-7 )
and , C = Cunningha msli p factor , dimensionles s C, - = initia l dra g coefficient , dimensionles s d= particl e diameter , cm I - ventur i throa t length , c m u , = liqui ddro p velocity , cm/ s u r 

### ,, . = ga s velocit ya t th e ventur i throat , cm/ s bL 

### p p = ga s density , g/cm 3 

### p . = liqui ddensity , g/cm 3 

### p = particl e density , g/cm 3 

### \i r 

### = ga s viscosity , pois e b 

### Equatio n2- 2 slightl yunderestimate s th e particl e collec
tio noccurrin g i na ventur i scrubber . Fo r mos t industria l ven tur i scrubbers , particl e collectio nca nb e predicte dclosel y byneglectin g th e firs t termi nth e righ t han dsid e o f equatio n (2-2) . (5 ) Pressur e dro p prediction s b yth e modifie dCalvert' s equatio nan db

yBoll' s equatio nagre e wit hexperiment l data . Th e modifie dCalvert' s equatio nha s th e followin g form ,

AP = 1.0 3 x1 0 u * u 2 

### \~) (2-8 )
wher e A P = pressur e drop , c mW.C .

Q r 

### = ga s flo wrate , cm 3 

### / s (6 ) Th e us e o f a dra g coefficien t fro mth e "Standar dCurve " give s a bette r fi t betwee nmode l andexperimenta l dat a tha ndoe s Ingebo' s correlation .

1 5P.3 4

CHAPTE R3 LITERATUR E SEARC H Th e literatur e surve yan d backgroun d informatio n dis ^ cusse d i n thi s chapte r summariz e wha t coul d b e distille d fro m a surve yo f th e backgroun d informatio n an d represen t wha t wa s know n a t th e onse t o f thi s study . COLLECTIO NMECHANIS M Th e basi c approac ht o th e stud yo f collectio n o f smal l particle s i s throug hth e evaluatio n o f uni t mechanism s tha t ca n occu r i n th e contro l device . Th e "Scrubbe r Hand
book" , Calvert , e t al . (1972) , discusse s fiv e basi c uni t m e c ha n i s m s , n arn e l y: (1 ) Collectio n bydrop s (2 ) Collectio n b

ycylinder s (3 ) Collectio n o f particle s bybubble s (4 ) Depositio n fro ma movin g aeroso l i n pipe s and duct s (5 ) Collectio n o f particle s b yliqui d jets . O f th e five , collectio n bydrop s i s th e predominan t mechanis m occurrin g i n th e ventur i scrubber . Particl e collectio n b yliqui d drop s ma yaris e throug h severa l mechanism s o r phenomena , suc ha s inertia l collection , interception , diffusion , electrostati c collection , and gravitationa l collection . Al l investigator s hav e conclude d tha t inertia l impactio n i s th e principa l mechanis mo f par ticl e collectio n i n a ventur i scrubbe r fo r particle s large r tha n 0. 5 y

mi n diameter . Fo r particle s smalle r tha n 0. 1 y m i n diameter , diffusiona l collectio n prevails . Inertia l Impactio n Adro p movin g throug ha ga s wil l swee p ou t a cylindri
ca l volum e equa l t o th e produc t o f dro p cros s sectiona l area , relativ e velocit ybetwee n ga s and dro p and time . However , no t al l o f th e particle s i n thi s ga s volum e wil l necessaril y imping e upo n and b e collecte d b yth e drop . 

### 1 6P.3 5



### - A s th e ga s strea

m approache s th

e drop , th

e flui d .stream

line s spread aroun

d it , whil e a particl e suspende d inth e ga s strea mtend s t o move in a straigh t line due to it s inertia . Therefore , a s th

e ga s flow s aroun

d the drop , th

e particl e keep s moving toward th

e drop . Due t o th

e flui d drag som

e particles , especiall yth

e smalle r ones , wil l be deflecte d fro m thei r pat h toward th

e dro p an d carrie d b

yth e ga s aroun

d the drop . Th e trajector

yo f th

e particl e determine s th e targe t effi
ciencyo f th

e drop . Targe t efficiencyi s defined a s th e rati o o f th e numbe r o f particle s striking th e dro p t o th e numbe r whic h woul d strik e i t i f th e streamline s wer e no t diverte d b yth e drop , I f th e particle s bounc e rathe r tha nstic k on impaction , thi s definitio n o f efficiencyi s incorrect . Thu s a n assumptio ni s alway s mad e tha t al l th e particle s adher e on striking . Thre e factor s determin e th e inertia l impactionefficiency . The firs t i s the velocit ydistributio n o f th e ga s flowing b

y th e drop , whic hdepend s on th e dro p Reynold s number . The se con d facto r i s the trajector yo f th

e particle . Thi s depend s on th e mas s o f the particle , it s ai r resistance , th e siz e o f th e drop , an

d the flowrat e o f th e ga s stream . The third fac
to r i s th

e adhesio n o f th

e particle s t o th

e drop . Eac ho f thes e factor s i s discusse d below . The drop Reynold s "N R

### , " numbe r i s defined as ,
u 

### o _^ G d 

### d v, N

### Re d - -^ ^»- «

' G wher e " u " i s th

e undisturbe d upstrea mai r velocity , wit h respec t t o th

e drop ; "p r 

### " am

d "y r 

### " ar e respectivel ythe ai r densityan

d viscosity , an

d "d, " i s the dro

p diameter . A t hig h value s o f "Np,"(potentia l flow) , th e parting o f the ga s stream line s occur s clos e t o th e drop . Excep t nea r th e dro p surface , the flowpatter n correspond s t o tha t o f a nidea l gas . Whe n th e Reynold s numbe r i s low , flowi s governed.b yviscosit y(viscou s flow ) an

d th e effec t o f th

e disturbanc e create d b ythe dro

p i s

1 7P.3 6



### notice d a t relativel ylarg e distance s upstream . The sud"de n spreading o f th

e streamline s a t hig hReynold s number s enhance s th e influenc e o f particl e inerti a an d therefor e cause s a highe r collectio n efficiencythana t lo w"N R

### ,. " I f al l fiel d force s ar e ignored an d i f i t i s assume d tha t th e particle s obeyStokes ' law , thenth e equation s o f particle s motio n can be derive d b yequating the particl e inerti a forc e t o the ai r drag o

n the particle . The equation s indimensionles s for mare : 

### K

p

# J- ( 

# a G

# - y

# (3-2 ) d v K —E . = (v r 

### - v J (3-3 ) P d t GP 

### where : C p d 2 

### u K

### = P P o (3


### _ 4 

### ) P 9 V G

### d c 

### u = J - ; v= -E - (3-5) ; (3-6 ) P „ ' P U 

### o U 

### o U 

### G, _V 

### G U 

### G = 

### ~ ; V 

### G (3-7) ; (3-8 ) u u o o 2 u t t = 2

_(3-9 )

d 

### d wher e K = inertia l impactio nparameter , dimensionles s

p = particl e density , g/cm 3 

### d = particl e diameter , c m P u = undistrube d upstrea mga s velocitywit h o respec t t o the drop , cm/ s y „ = ga s viscosity , pois e d , = dro

p diameter , c

m

1 8P.3 7



### C = Cunningha

mcorrectio n facto r t = time , se c u = particl e velocit ycomponen t i n th e Xdirectio n v= particl e velocit ycomponen t in th e Ydirectio n U p = ga s velocit ycomponen t i n the Xdirectio n v f 

### = ga s velocit ycomponen t i n th e Ydirectio n The dimensionles s inertia l parameter , K , whic hcharacter
ized th e motio n o f th

e particle , ha s a physica l meaning . I t i s th e rati o o f th

e particl e "stopping distance " t o th e radiu s o f th e collector . The particl e stopping distanc e i s tha t distanc e i t woul d trave l befor e coming t o res t i f injected int o a stil l ga s wit hvelocit y" u " , whe nal l force s on th e particl e excep t th e drag forc e ar e zero . The solution s t o the equation s o f motio ndepend upo nthe velocit yfiel d assumed . Figur e 3- 1 show s theoretica l an d ex perimenta l targe t efficiencie s fo r a singl e drop . A s reveale d b ythi s figure , targe t efficiencydepend s on drop Reynold s num be r an d inertia l impactio nparameter . Walto n an

d Woolcock' s (1960 ) experimenta l dat a agre e quit e wel l wit hLangmui r an d Blodgett' s (1946 ) an d Hem e an

d Fonda' s (i960 ) theoretica l calculation s fo r potentia l flow 0 

### Tha t Walto n an d Woolcock' s dro

p Reynold s number s oftenfel l substantiall y belowth

e criterio n fo r potentia l flo wwa s apparentl yunimpor
tant . Fo r potentia l flowan d for value s o f " K " greate r than 0.2 , th e experimenta l value s o f inertia l collectio nefficiency for sphere s ca

n be approximate d b yth e correlatio n (Calvert , 1970) :
n P = 

### ( Kp + P O . 7 ) 

### t 3 

### " 10 

### ) Diffusiona l Collectio n Smal l particles , in th e sub-micro n siz e range , are
1 91. 0

o o

u rt 4- 1 > - U W I— I 

### u f- H u . U J E 

### w D i < E l.Ran z ^ Won g (1952 ) experimenta l dat a

700<N Re <565 0 2.Walto n f

, Woolcoc k (1960 ) experimenta l data , 65<N R<89 0 3.Hem e § Fond a (1960 ) theor yfo r poten tia l flo w 4.Langmui r $ Blodge t (1946 ) theor y 5.Hem e § Fonde , theor yfo r viscou s flo w 6.Calvert' s approximatio n :

0. 5

0.0 1 0. 1 1. 0 INERTIA L PARAMETER , K 1 0 10 0 Figur e 3-1 . Targe t efficienc yresult s o f variou s investigators .P.3 9



### rarel ycollecte d b

yinertia l impactio no r interceptio n becaus e the

yfollowthe ga s streamline s surrounding th e collecting body , an d thei r rati o o f d / d i s small . Ina stil l gas , smal l particle s move freel yacros s ga s stream line s due t o random bombardmen t fro

mga s molecules . Som e o f the particle s hi t th e collecto r an

d are remove d fro

m th e gas . I f one estimate s tha t the.aeroso l concentratio nnea r th e collecto r surfac e take s th e form , Hid

yan d Broc k (1970 ) r • c^i-jS ) (3-n ) wher e " r " i s th

e collecto r radius , "6 " i s th e distanc e fro

m c ' th e collecto r cente r an d "c " i s the concentratio n o f par 1 r 

### tide s i n th

e mai n bod

yo f the ga s stream , the nthe concen tration gradien t at th e collecto r surfac e is : 9 6 c .

__i_ 5 = 

### r ^ r c c (3-12 ) The rat e o f deposition , 4>(g/ s i f c 

### j i s 

### g/ cm3 

### ) , o n a 

### spherica l collecto r fo r a ga s at res t i s equa l to : cf ) = 4 T T D ^ r c . (3-13 ) Y

### p c 1 Particl e diffusivitie s ar e severa l order s o f magnitud e smalle r than diffusivitie s o f gases , an d are close r t o th

e value s obtaine d fo r diffusivitie s o f solute s in liquids . The particl e diffusivit yma yb e calculate d fro ma nequatio n b yFuch s (1964 ) D = -— k T C 

### j (3-14 ) P 3 

### * ^ G d 

### p wher e D = diffusivit yo f particle , cm 2 

### / s

k = Boltzmann constan t = 1.3 8 x10" 1 6 

### erg/° K
2 1P.4 0



### T = temperature , ° K C = Cunningha

mcorrectio n factor , dimensionles s U p = ga s viscosity , pois e d = particl e diameter , c m P Fo r a n aeroso l flowing pas t a spherica l collector , the rat e o f diffusio n increase s an d become s a functio no f th e Reynold s an

d th e Schmid t numbers . The Schmid t numbe r "N - " S c i s a dimensionles s grou p indicating the rati o o f convectiv e an d diffusiv e trans f numbe r i s define d as an d diffusiv e transfe r rate s (at constan t N D

### ) . The Schmid t Ke

N S c = p^ " C 3 " 15 ) 

### Fo r lo wdiffusivities , leading t o highSchmid t number s (N „ = IO 6 

### ) , an

d lo wReynold s number s (N R

### , < 3 ) Levic h (1962 ) showe d that :

ty= 2 K D p 

### r d

### c . N Red 

### " N Sc 

### >' 3 

### (3-16 ) Fo r larg e Reynold s number s (60 0 - 2,600 ) an d (N gc 

### = IO 6 

### , Akselrud (1953 ) showe d that ,

ty= 1. 6 T

T D p 

### r d C i 

### N Red 

### - N S c 

### ^ 3 

### (3-17 ) Fo r Reynold s numbe r = 10 0 - 70 0 an d Schmid t numbe r - IO 3 

### , Garne r e t al . (1958 a an d 1958b ) showed that , ty- 1. 9 T

T D p 

### r d

### c . N Red 

### - N S c 

### ^ (3-18 ) Johnston e an

d Robert s (1949 ) presente d a nexpressio nfo r estimatio n o f singl e drop collectio n efficiencydue t o Brownian diffusion . Thei r expressio n i s

4 D N » P \ | u 

### G" U 

### d | d 

### d n = ,—_ p 

### j S h

### (3-19 )

2 2P.4 1



### wher e n = singl e dro p collectio nefficiency , dimensionles s D = particl e diffusivity , cm z 

### / s ' - d , = drop diameter , c m U p = ga s velocity , cm/ s u , = dro

p velocity , cm/ s N 

### 'cv , = 

### particl e transfe r numbe r analogou s t o th e Nussel t numbe r fo r hea t transfe r o r the Sherwoo d numbe r t o mas s transfer , dimensionles s B yusing th

e semi-theoretica l equatio no f Frossling fo r "N ' " i e S h' ' ' '

N' s h

### « 2 + 

### 0,55 2 N R 

### - N S c 

### - (3-20 ) equatio n 5-1 9 become s

4 D n= u 

### G _u 

### d d 

### d ( 2 + 0.55 2 N R 

### - N Sc 

### 3 

### ) (3-21 ) wher e N „ = Schmid t numbe r define d b yequatio n3-1 5 N R

### j = drop Reynold s numbe r LIQUI D DRO P SIZ E As mentione d earlier , the principa l collectio nmechanis m occurring in a A^enturi scrubbe r i s th e collectio n o f particle s b yliqui d drops . The collectio nefficiencyo f a dro p depend s o n it s size . Thus , i norde r t o mode l th e particl e col
lection b

ya ventur i scrubber , we mus t have som e knowledg e abou t the atomize d liqui d dro p size . Hesket he t al . (1970) , base d ona stud yperforme d o

na smal l ventur i scrubber , claime d two type s o f atomizatio n ca n occur . Cloud-Typ e Atomizatio n Thi s typ e o f atomizatio nca nbe achieve d whe nnozzle s large r than 1 m

m i.D . ar e used an

d whe nga s velocit yi s above th

e critica l ga s velocity . The critica l ga s velocit yi s

2 3

### define d b yth e following equatio n
u n

### , .. . , (cm/s ) G ' critica l 0. 5 

## 2 (mm 2 

## ^D.)] + 466 

## ' 3 

## t 3 

## " 22 

## > Thi s typ e o f atomizatio n yield s smal l drop s an d give s lowe r dro

p acceleratio nwhic hresult s in bette r particl e collectio n than dro p typ e atomization . Drop-Typ e Atomizatio n Severa l correlation s ar e availabl e fo r estimating th e averag e liqui d dro

p siz e indro

p typ e atomization . Thes e cor relation s ar e base d on differen t mechanism s o f atomizatio nunde r variou s operating conditions . Eachi s applicabl e t o a certai n rang e o f operatio n condition s an d physica l propertie s o f fluids , sucha s viscosity , density , an d surfac e tension . The yare summarise d i n Tabl e 3-1 . Mos t o f the dat a take n i npneumati c atomizatio nar e fo r liqui d injection , eithe r paralle l or opposit e t o the ga s flo wan d wit ha smal l apparatus . Ventur i scrubber s ar e quit e larg e i n compariso n an d normall yhave th

e liqui d injectio n acros s th e ga s flow . Whil e i t i s questionabl e tha t thes e correlation s woul d appl yt o a ventur i scrubber , the yhave bee n s o applied . The mos t widel yquote d correlatio n i s tha t o f Nukiyama an d Tanasawa , whic hgive s the Saute r meandiameter , eve n thoughalmos t al l investigator s doubte d it s applicabilit y t o a full-siz e ventur i scrubber . Bol l (1973) , afte r com paring th

e result s o f Nukiyama an d Tanasawa wit hthos e o f severa l subsequen t investigators , state d tha t Nukiyama an d Tanasawa correlatio ni s subjec t t o a n uncertaint y facto r o f two . In a late r study , Bol l e t al . (1974 ) measure d th e atomize d drop siz e i n a full-scal e ventur i scrubbe r b ymean s o f a transmissometer . Theyshowe d tha t th e N- T equatio n give s value s o f mean dro p siz e tha t ar e accurat e withi n abou t 50 % fo r L/G' s an d throa t velocitie s o f commercia l
2 4TABL E 3- 1 EMPIRICA L EQUATION S FO RAVERAG E LIQUI D DRO P SIZ E AN D THEI RAPPLICABL E RANGE S Investigator s Equation s Applicabl e range s u G ,(cm/s ) m G 7ir L y L (poise . Nukiyam a§ Tanasaw a (1938,1939,1940 ) d d= 5.8 5 U G \ P L / ,888 1 (o p L ) « 

# r&r 10 1 * -soni c velocit y 1. 8 -1 5 0.1-0.4 6 Mugel e(1960 ) d , B



## a r= A 

## ( N 

## R e ) d_.,. . ,"/u L

### u r n 

### Gretzinge r § Marshal l (1961 ) d = 0.2 6 m 

### m

T 

### m . N Re G (A,B, C ar e constants )
O.l f 1 0 -soni c velocit y 1. 8 -1 5

Ki m$ Marshal l (1971 ) d = 0.51 2 m a 0 -* 1 y L 0. 3 2



### (u 2 G P G • ) 0. 5 7 A

0. 3 6 0. 1 6

+ 1.8 9 0. 1 7 

### m ,

m n 1 0 - s o n i c velocit y 1 -1 5 0.01-0. 3

0. 5 " f 7. 5 x10 ' soni c velocit y 0.06-4 0

n = - 1 fo r 

# "fe m L < 3 n = -0. 5 fo r m G /m T> 3 0.01-0. 5



### w h er e d , = Saute r mea n dro p diameter , c m d = mea n dro p diameter , cm mr ' p . = liqui d density , g/cnr



### n u nozzl e d i arn

e ter , cm reiative.velocit y, cm/ s a = surfac e tension , dyne/c m Q = volumetri c flo wrate , cm/ s 

### G y . = liqui d viscosity , pois e m= mas s flo wrat e o f liquid , g/ s L i m= mas s flo wrat e o f gas , g/ s u A= flo ware a o f atomizin g ai r u = relativ e velocit ybetwee n ga s an d liquid , cm/ s

C OP.4 4



### interest . Fo r th

e particula r ventur i geometr ythe yused , the N- T equatio n consistentl yove r estimate s mean dro p dia
mete r a t high-ga s velocitie s an d unde r estimate s i t at low-ga s velocities . The ypresente d th

e following empirica l equatio n t o correlat e thei r dro p data . d = 6.7 5 xIO 6 

### + 5.2 8 xIO 1 2 ( Q L / Q G ) 

### ^ 12 

### (3-23 ) d u1. 6 0 2



### i wher e d , = Saute r mean dro p diameter , y

m Q L 

### /Q G

### = liquid-to-ga s ratio , m 3 

### /m 3 

### u . = ga s velocit ya t liqui d injectio npoint , cm/se c DRA GCOEFFICIEN

T The inertia l impactio nparameter , " K " i s als o a func
tion o f th

e relative velocit ybetwee n particl e an d drop . The atomize d liqui d drop s wil l b e accelerate d b yth e gas . The effec t o f acceleratio n on the drag coefficien t ha s bee nstudied b yHughe s e t al . (1952) , Ingebo (1955) , Torobi n e t al . (1960) , Crowe (1961) , an

d others . Hughe s e t al . stat e tha t a s a genera l rule , acceleratio n drag exist s an d tha t i t i s highe r than th e drag fo r stead

ymotion . Ingebo' s result s disagre e wit hthi s statement . H e obtaine d acceleratio ndrag coefficient s lowe r than thos e predicte d b yth e standard curve , (se e Figur e 3-2) . According t o Ingebo , th e drag coefficient s "C D 

### " fo r drop s can be correlate d fairl ywel l wit hthe Reynold s numbe r according t o the following empirica l expression : C n

### = U—

(3-24 ) f XT

0. 8 i f JN 

### Red wher e C ^ = drag coefficien t N, = dro

p Reynold s numbe r Thi s expressio n i s applicabl e fo r a Reynold s numbe r rang e o f 6 t o 80 0 an

d sphere s wit ha diamete r rang e o f 2 0 t o 12 0

2 6P.4 5

Nj^ e -Reynold s Numbe r Figur e3-2 . DRA GCOEFFICIENTO

FASPHER

E.

2 7P.4 6



### microns . Calver t (1968 ) use d the Ingebo dat a an d simplifie d th e above equatio n t o

C = IA - fo

r J 0 0 < N D

### , < 50 0 T3-25 ) ^ n wRed ^ ° i0 J 

### Red However , thi s expressio n i s applicabl e fo r a Reynold s num be r rang e betwee n 10 0 an d 500 . Whil e thi s rang e i s mor e narro wthan the rang e o f the origina l correlation , i t i s the rang e tha t i s o f interes t fo r ventur i scrubbers . Calver t stated tha t thi s correlatio n i s als o a fairl ygood approxima
tion fo r th

e Reynold s numbe r u p t o 1,000 . The Ingebo correlatio nan d th e Standard curve have been use d i n the modeling o f ventur i scrubbe r b ydifferen t investigators . However j Bol l (1973 ) conclude d tha t i nth e cas e o f a venturi , the Standard curve o f the drag coeffi
cien t i s the bette r choiee . H e argued tha t Ingebo injecte d the particle s o r drop s a s a smal l concentrate d streamint o th e cente r o f a muc hlarge r duct . Thus , th e highcentra l concentratio n o f slowl ymoving drop s o r particle s woul d have muc hth

e sam e effec t as a stationaryporou s bod yin th e duct . Consequently , some o f the ga s mus t hav e flowe d aroun d th e mas s o f drop s rathe r than betwee n them , reducing th e actua l ga s velocit yin the vicinit yo f the individua l drops . Thi s woul d have lowere d the actua l drop accelera
tio n an d reduce d the apparen t drag coefficient , accounting fo r th e lowC „ values . Dickinso n an

d Marshal l (1968 ) approximate d th e Standard curve b yth e followin- g correlatio n C 

## D = 

## °- 2 2 + 

## HT7' 1 + 

## °- 1 5 N 

## Red ) C 3 

## " 26 

## )

Red

2 8P.4 7



### SCRUBBE RCOLLECTIO

NEFFICIENCY Calver t (196 8 , 1970 ) , b yperforming a materia l balanc e fo r dus t ove r a differentia l scrubbe r volume wit hth e assum p tion o f constan t liqui d holdup , obtaine d a differentia l equatio n fo r th

e predictio no f ventur i scrubbe r performance . Thi s equatio n i s 

## d

c . 3 K l " a " d zf3 

## . 27 1 

### wher e c = dus t concentration , g/cm 3 

### u = u -u , relative velocit ybetwee n particl e an d r p d ' r 

### liqui d drop , cm/ s n = singl e dro

p collectio n efficiency , fractio n d , = dro

p diameter , c

m u f 

### = ga s velocity , cm/ s z = distance , c

m H , = drop holdu

p o r volume fractio no f drop s a t an ypoin t

_ \ 

### u d 

### A QT

### = liqui d flowrate , cm 3 

### /se c u , = dro

p velocity , cm/se c A= cross-sectio narea , cm 2 

### B ysubstituting the defining equatio n o f "H, " an d " u " int o equatio n 3-27 , one obtain s

d c1 ' 5 l u p - u d|/ Q L \, f . 9R ,

- —= 5 TC- hd z(d>-28 )

u 

### d d 

### d\ V Anothe r assumptio n i n the derivatio n o f thi s equatio ni s tha t particl e velocit yi s the sam e a s ga s velocity . Calver t -(1970 ) an

d Calver t e t al . (1970 ) applie d equatio n 3-2 8 t o th e ventur i throa t an d obtaine d the

2 9P.4 8



### following simplifie d equatio nfo r predicting particl e penetratio n

Pt(d p 

### ) = ex p 2 Q 

### L u 

### Gt p 

### L d 

### d 5 5 Q G

### y G F(K p t ' f 

### (3-29 ) wher ePt(d„) = penetratio no f particle s wit hdiamete r d K V *p ' 

### fractio n QT

### = liqui d flowrate, ' cm 3 

### / s Q G

### = ga s flowrate , cm 3 

### / s d , = averag e liqui d drop diamete r give nb y th e empirica l correlatio no f Nukiyama an d Tanasawa , c

m u = velocit yo f the ga s i n th e throat , cm/ s b t 

### \. c

### ga s viscosity , pois e p , = liqui d density , g/cm 3 

### K . = inertia l paramete r evaluate d at th e velocity 

### p t ^' o f th ega s i nth ethroat . "F( K f) " i s aparamete r define db yth efollowin g equatio n p t , F(K p t 

### , f) K



### p tL 1. 4 I n 0.4 9 0 . 7 + K K

« . f + 0. 7 P t 0. 7 (3-30 )

r - ( K « . f
, t f P 1 + 0.7 ) 

### "f " i s a

n empirica l parameter . Fo r hydrophobi c aerosol s a valu e o f 0.2 5 i s suggeste d b yCalver t fo r thi s parameter . Fo r hydrophili e particl e raaterial s i t i s usuall yequa l t o 0.5 . Bol l (1973 ) took int o accoun t the particl e collection , occurring in tli

e ventur i throa t a s wel l a s in th e divergen t an d convergen t sectio n o f tli e venturi , an

d presente d th

e following integra l equatio n fo r the calculatio n o f particl e penetratio n
3 0P.4 9



## - f,\P- p 

## G \l U 

## G' U 

## d l. t 

# "i'-M-pr/-^— n d t N 

# c= 

# ^ i 

# - s

# \-pf/~5r~ nd tC3 

# " 31 ) wher e N= numbe r o f collectio n unit s

= - ln Pt( d )

P M= rati o o f liquid-mas s flowrat e t o gas-mass flowrat e P G

### = ga s density , g/cm 3 

### p . = liqui d density , g/cm3 

### n = targe t efficiency , fractio n t = time , s d , = liqui d dro

p diamete r give n b

yNukiyam

a an d Tanasawa correlation , c m u G

### = ga s velocity , cm/ s u , = liqui d dro

p velocity , cm/ s
" |Up-u,[ " i s the relative velocit ybetwee nga s an d drops . Thi s velocit ydepend s o nthe geometr

yo f the ventur i scrub
ber . Bol l assume d tha t the ga s i s incompressible . Thus , th e ga s velocit yat an ylocatio ni nth

e scrubbe r i s givenb y m p U 

### G = 

### 3Tp ^ ( 3



### - 32 

### ^ wher e m p = ga s mas s flowrate , g/ s A= cross-sectiona l are a o f th e scrubber , cm 2 

### The dro p velocit yi s equa l t o th e tim e integra l o f dro

p acceleratio n
u 

## d = u 

## d i +

## f(^r) dt 0 

# • "d i*fi~ ^37 ^ c 

# ° d tC3

# "33 ) O L u 

### wher e u, . = initia l velocit yo f th e drop , cm/ s C D

### = drag coefficien t
3 1P.5 0



### Bol l use d th

e Standard curve fo r C D

### fo r soli d sphere s due t o Lappl e an

d Shepherd (1940) . Boll' s equation , i.e. , equatio n3-3 1 ca nbe reduced t o Calvert' s differentia l equation . Thus , thes e two equation s are essentiall yth e same . Behi e an

d Beeckman s (1973 ) als o gave a differentia l equatio n fo r aeroso l captur e inthe ventur i scrubber . Thei r equatio n i s



# - a(. »o- \ \«$X

iz(3 

# " 34 )
wher e c = dus t concentratio n, g/cm 3



### F = dro

p mas s flu

x, g/cm2



### - s P L = 

### liqui d density , g/cm 3 

### n = targe t efficiency, fractio n u r 

### = ga s velocit y, cm/ s b 

### u , = dro

p velocit y, cm/ s d , = dro

p diamete r , c

m z = th e distanc e fro

mthe origi nin th e directio n o f ga s flow, cm Thi s equatio n i s equivalen t t o Calvert' s differentia l equatio n fo r particl e collectio n i na ventur i scrubber . Calvert , Bol l an

d Behi e an

d Beeckman s al l assume d tha t th e particl e velocit yi s the sam e as ga s velocity . How ever , Drop

p an d Akbru t (1972 ) , afte r evaluatio no f ventur i performanc e dat a take nfro msevera l powe r plants , conclude d tha t th e mode l wil l over-predic t the efficiencyo f a ventur i scrubbe r fo r bi g particle s i f ga s velocit yi s substitute d fo r particl e velocity . Thi s i s becaus e whil e th e fine par ticle s move at practicall yth e sam e velocit yas th

e gas , th

e velocityo f larg e particle s differ s markedl yfro mth e ga s velocity . Bi g particle s move a t a lowe r velocit ythanth e ga s whic hresult s in a lowe r impactio n param-eter an d lowe r ef
ficiency . Drop

p an d Akbru t propose d th e following equatio n t o predic t ventur i scrubbe r performance . 3 2P.5 1



### Pt(d p 

### ) = exp|-; f



# [ 3 A n^ c I 2 

# J 

# ^* du

# d d z (3-35 ) wher e Pt( d ) = penetratio nfo r particle s wit h

diamete r d , fractio n

P Q T

### = liquid-flowrate , cm 3 

### / s Q r 

### = gas-flowrate , cm 3 

### / s u = particl e velocity , cm/ s u , = dro

p velocity , cm/ s Thi s equatio n ha s th e sam e for mas Calvert' s differ
entia l equatio n excep t particl e velocityi s use d i n Drop p an d Akbrut' s equation . Calver t derive d hi s equatio nb yconsidering particl e collectio n b

yal l liqui d drop s existing ina uni t volume . Ekman an

d Johnston e (1951 ) employe d anothe r approac ht o arrive a t a

n equatio n fo r the calculatio no f particl e collectio n i n a ventur i scrubber . Theylooked upo na singl e liqui d dro

p a s a uni t an

d followe d the dro

p t o determin e it s particl e collectio nfo r it s entir e flying pat hlength . Tota l particl e collectio no f the ventur i scrubbe r i s then the su mo f th

e collectio no f al l liqui d drops . Ekman an

d Johnstone' s equatio n is , Pt( d ) = ex

p 3 nP s 490,00 0 (3-36 ) wher e Pt( d ) = penetratio nfo r particle s wit hdiamete r

d , fractio n P n = singl e drop impactio nefficiency , fractio n P = lengt ho f effective patho f liqui d drop , c m s = specifi c surfac e o f drop s formed i n scrubber , cm 2 

### /cm 3 

### Morishima e t al . (1 9 72 ) use d the sam e approac ha s Ekman an d Johnston e an

d considere d th

e particl e collectio n in the

3 3P.5 2



### ventur i throa t an

d i n th e divergen t section . Theyarrived at the following equatio n

Pt(d ) = ex

p ["
- (R t 

### + R d 

### ) Q^ l (3-37 )

" R" an d "RJ " are , respectively , the washing facto r o f ga s i n th e ventur i throa t an d i nth e divergen t section . Wash
in g facto r i s define d as th e volume o f ga s swep t clean b y a liqui d drop pe r uni t volume o f liqui d drop . Fo r ventur i throa t an

d divergen t section , the defining equation s fo r thes e two washing factor s are ,

wher e £ = ventur i throa t length , c m X= dimensionles s distanc e x

~ £ 

### t d , = drop diamete r fro mNukiyama an

d Tanasaw a correlation , c

m n = targe t efficiency d^

_t , c

m £ Q

### " 2 tan 9



### -

2 

### d = ventur i throa t diamete r O = divergenc e angl e Al l investigator s cited earlie r had assume d tha t the liqui d dro

p distributio n i s unifor macros s the duc t an d ther e i s n o turbulen t mixing betwee ndrop s an d particles . In reality , the drop concentratio n acros s the ventur i
3 4P.5 3

throa t i s fa r fro munifor m(Taher i an d Haine s (1969 ) , Bol l (1973)) . Taher i and Shei h(1975 ) too k turbulen t mix
ing and liqui d dro p distributio n acros s th e duc t int o accoun t an

d obtaine d th e followin g equation s fo r predict
ing th e transpor t and diffusio n o f th e particle s and wate r drops . 

## i £ = 3 t 

### 3 c u , —+ E

3 z j 

### 3 c 3 2 c + 3 2 c



### 3T 2 

### " 3y '

o t U d 3 z + E 

### 3y 2 T

T n

—d d ( UG- Ud ^ C C d 3 2 c 

### 3x < (3-40 ) (3-41 )
wher e c = particl e concentration , g/cm 3

c , = numbe r concentratio n o f liqui d drop , #/cm 3 Up = ga s velocity , cm/ s u. , = dro p velocity , cm/ s E = eddydiffusivit yo f particle , cm 2 / s E , = eddydiffusivit yo f drop , cm 2 / s x= rectangula r coordinate , perpendicula r t o directio n o f th e flow , c m y= rectangula r coordiante , perpendicula r t o th e flow , cm z = rectangula r coordiante , i n th e directio n o f flow , c m Q , = sourc e strengt ho f drops , #/cm 3 I n al l th e abov e mentione d performanc e models , th e liqui d drop s wer e assume d t o hav e on e size , namel yth e Saute r mea n diamete r calculate d fro mNukiyam a and Tanasawa' s empirica l correlation . I n reality , th e liqui d dro p siz e varie s widel y Morishim a e t al . (1967 ) performe d a mathematica l analysi s t o determin e th e influenc e o f liqui d dro p siz e distributio n o n th e particl e impactio n and diffusio n collectio n effi
ciency . The yfound tha t a s th e rang e o f siz e distributio n 

### 3 5P.5 4



### widens , the impaction efficiencydecreases . PRESSURE DRO P Pressur e drop s fo r ga s flowin g throug

ha ventur i scrub
be r consist s o f the frictionlos s along the wal l o f th e scrubbe r an

d th e acceleratio no f liqui d drops . Frictio n los s depend s largel yuponth e geometr

yo f the scrubber . Acceleratio n losses , whic har e frequentl ypredominan t i n th e ventur i scrubbe r pressur e drop , are fairl yinsensitive t o scrubbe r geometr yan d inmos t case s ca

nbe predicte d theoretically . Ther e ar e severa l correlation s available , bot htheo
retica l an

d experimenta l correlations , fo r th e predictio n o f pressur e dro

p in a ventur i scrubber . The yare summa rized in Tabl e 3-2 . Correlation s b

yMatrozov , Yamauch i e t al. , Volgi n e t a l Gleason e t al. , an

d Hesket har e experimenta l correlations . Matrozov' s correlatio n an d Volgin' s correlatio nwer e obtaine d mainl yo

n small-siz e ventur i scrubbers . Yama uch i ' s correlatio n wa s base d o nexperimenta l dat a taken fro ma ventur i scrubbe r wit hhightemperatur e ga s flow (100° C - 900°C) . Hesketh' s correlatio n i s a nexperimenta l correlatio n he obtaine d afte r h e had evaluate d dat a obtaine d fro

mman yfixed throa t ventur i scrubbers . Equation s propose d b yYoshida e t al. , Calvert , Tohat a e t al. , Bol l an

d Behi e an

d Beeckman s are theoretica l correlations . Calver t derive d hi s equatio nb yus e o f Newton' s la

wt o obtai nth

e forc e require d t o chang e th e momentu mo f liqui d at a given rate . Wal l frictionan d momentu mrecoveryb

ythe ga s in th

e divergen t sectio n wer e neglecte d in th e derivation . Al l othe r theoretica l equation s wer e derive d fro m th e equation s o f motio nan d momentu mbalance . Geiseke' s equatio nals o account s fo r th e mas s transfe r betwee n liqui d an d gas . Boll' s equa tion i s simila r t o tha t o f Geiseke' s excep t Bol l had
3 6P.5 5

TABL E 3- 2 Investigato r CORRELATION S FO RPRESSUR E DRO P I NVENTUR I SCRUBBE R

Correlatio n Matrozo v(1953 ) A P = AP d+ 1.3 8 xIO" 3 u£{ 8 / Q L 0- 6 3

Yoshid a e t al . (1960 ) (1965 ) A P =

a = P G U G t 

## TT, a + b/^ L
2 ta n 0 i + 4 f ' t / d t



# t T: + 

# n 1 

# " 2

# a

r t o 

## b= 

## u t 

## - D 4 f t l t

m 

# 3 7 ^tSd-^rf 1



# - a* ) t K m

\ o / Geisek e (1968 ) A P = 7 6 2 S e 5 c 

## [mG

## Au G

## + m L Au L

A m L 1



## — ( U G l + U 

## G 2 

## " uL l 

## - U 

## L 2 

## ) J Yamauch i e t al (1964 ) 

### A P = 0. 3 (AT)" 0 

### - 2 8 

### - J P G U G t / x+ - L S , QG "
Tohat a e t al . (1964 ) A P = P G U G t

' C f A\2



### T V J 2 g [ 5 ta n O i ' 5 ta n 0 2 

# •] ' f



# * 4 S r
(continued )

3 7P.5 6



### TABL E 3-2 . (continued ) Investigato r Correlatio n Volgi n e t a l (1968 ) A P = 3.3 2 xIO" 5 

### u G 2 

### ^ ) C* t 

### ) 0. 2 6 0 1. 4 3



### Calver t (1968 ) AP = 1.0 3 xIO" ' ^( ^
Gleason e t a l (1971 ) AP = 2.0 8 x10" 5 

### u G 2 

### (0.26 4 Q L 

### + 73.8 )
Bol l (1973 ) 2 2 u

### rt ~ u

### r •A p_b l b P 7 " 2 §r 

# •uN^) *

M + l ) f 2 g I 

### f u 2 

### u d 2 QI d "-• 6 e q 2 g 

### c / $ i f u 2 

### d x e q Behi e § Beeck
man s (1 9 73 ) d p 6 F * d dp d ) ! I T d d 2^ C 

### D P

### G (u 

### cr u 

### d ) 2

### —r ~ d t

Hesket h (1974 ) 

### A

P = 1.3 6 x10~ " u G 2 

### p G

### A t 0



### - 13 3 

### 0.5 6 + 9 3 5!o^ / + 1 

### ' 29X1 0 

### \0 ^
wher e A . = throa t cross-sectiona l area , cm 2



### duc t cross-sectiona l area , cm 2 

### liqui d dro

p diameter , c

m equivalen t duc t diameter , c m A= o d j = 

### e q (continued ) 3 8P.5 7

wher e d = throa t diameter , cm

d = inle t o r outle t duc t diameter , cm o ' f = frictio n factor , dimensionles s f = averag e frictio n facto r o f th e throat , di me n sionles s c = averag e frictio n facto r o f convergen t sectio n f , = averag e frictio n facto r o f th e divergen t section , dimensionles s g = conversio n facto r " c I = throa t length , cm M= liquid-to-ga s mas s rati o ni p = ga s mas s flo wrate , g/ s m- liqui d mas s flo wrate , g/ s Q r = ca s volumetri c flo wrate , cm 3 / s 0 . = liqui d volumetri c flo wrate , cm 3 / s Up = ga s velocity , cm/ s u „ = ga s velocit ya t th e throat , cm/ s u , = liqui d dro p velocity , cm/ s u . = liqui d velocity , cm/ s t = time , s 5 = rectangula r coordinat e i n th e directio n o f flow , c m AP - pressur e drop , cmW.C . AP , = drypressur e drop , c mW.C . AT = temperatur e change , ° K p = ga s density , g/cm 3 p = manomete r flui d dnesity , g/cm 3 G r - - convergenc e angle , degre e S' 2 = divergenc e angle , degre e x, = coefficien t on divergen t los s o f ga s flow , dimensionles s £ . = head-los s rati o fo r throat , dimensionles s £ , = head-los s rati o fo r divergen t section , dimensionles s
3 9P.5 8

neglecte d th e mas s transfe r betwee n phases . Equation s b y Tohat a e t al. , Yoshid a e t al. , and Bol l contai n term s attribute d t o wal l friction . Whil e Tohat a e t al . an d Yoshid a e t al . ha d use d differen t value s fo r th e frictio n factor s i n th e covergen t throa t and divergen t section , Bol l suggeste d a singl e valu e fo r al l sections . Avalu e o f 0.0 2 7 wa s suggeste d b yBol l fo r th e frictio n facto r "f " becaus e i t give s a slightl ybette r fi t i n th e shap e o f th e pressur e dro p curve s h e obtained , experimentally .



### 4 0P.5 9

CHAPTE R4 COMPARISO NO F MODE L WIT H EXPERIMENTA L DAT A Ther e ar e numerou s ventur i scrubbe r performanc e dat a reporte d i n literature . However , mos t o f thes e dat a wer e foun d t o b e o f a limite d valu e fo r th e testin g o f perfor
manc e models . Thi s i s because , som e importan t information , suc ha s scrubbe r geometry , wate r injectio n method , particl e siz e distribution , etc . wa s generall yno t given . I n th e followin g sections , onl ythos e dat a whic hhav e bee n ob
taine d unde r contolle d condition s an d fo r a well-define d scrubbe r syste mwil l b e utilize d t o tes t th e performanc e models . COMPARISO NO F PIlEDICTE D PRESSUR E DRO P WIT H EXPERIMENTA L DATA Dat a b yWe n and Uchid a We n an d Ucnid a (1972 ) obtaine d pressur e dro p dat a 0: 1 a pilo t scal e O.A.P . ventur i scrubber . Thei r pressur e dro p dat a ar e shown i n Tabl e 4-1 . Figur e 4- 1 show s th e dimension s o f che scrubber . Figure s 4- 2 throug h4- 4 compar e pressur e dro p predic
tion s b

yvariou s model s wit hWe n an d Uchida' s data . Fo r the O.A.P . scrubber , th e wate r injectio n nozzl e i s a t th e star t o f th e convergen t section . Accordin g t o We n an d Uchida , th e ga s cool s down quickl yt o scrubbe r outle t t.?i:;peratur

e onc e i t i s i n contac t wit hwate r (withi n 5 cm frcv d th e wate r injectio n point) . Thus , i n calculatin g th e xaxxC

.ctc- d pressur e drop , th e volumetri c ga s flo wrat e was-did i L..- . te d fo r thi s temperatur e dro p plu s th e volum e increas e du e t o vaporize d water . A s can be see n fro mFigure s 4- 2 t o 4-4 , Calvert' s equatio n consistentl yove r estimate s the.pressur e drop . Prediction s b vVolgi n e t al . and Hesket har e alway s lowe r tha n data .



### 4 1P.6 0

TABLE4-1 . WE

NAN D UCHIDA' S EXPERIMENTA LPRESSUR EDROP DAT AO NO.A.P . VENTURISCRUBBER
Run No . 

### 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 • Ga s Temp . ° c

Inle t 154. 4 

### 16 0 16 0 157. 2 148. 9 154. 4 

### 13 5 154. 4 

### 16 0 148. 9 148. 9 148. 9 148. 9 121. 1 148. 9 148. 9 148. 9 121. 1 148. 9

„, , Outle t

46. 1 43. 3 46. 1 43. 3 37. 8 43. 3 4 3. 3 43. 3 46. 1 46. 1 46. 1 37. 8 43. 3 43. 3 46. 1 46. 1 37. 8 

### 3 5 40. 6 ' Inle t ga s

Flo wrat e Am 3 /mi n 29. 4 30. 8 

### 2 9 34. 8 34. 2 28. 5 28. 6 30. 3 29. 8 25. 5 25. 5 31. 2 25. 5 25. 5 25. 5 25. 5 31. 2 25. 5 25. 5

• Liqui d

Flo wrat e £/mi n 37. 9 37. 9 37. 9 37. 9 37. 9 56. 8 37. 9 37. 9 56. 8 37. 9 37. 9 37. 9 56. 8 37. 9 37. 9 56. 8 37. 9 37. 9 37. 9 Pressur e

Dro p c mW.C . 22. 2 21. 8 19. 8 30. 5 

### 2 9 22. 9 21. 6 21. 3 24. 1 21. 8 19. 8 

### 2 9 22. 9 21. 6 21. 3 23. 4 31. 5 25. 9 21. 8

4 228. 9 cm

O J



### Figur e4-1 . Dimension s o f OA Pventur iscrubber .P.6 2



### QCalvert' s Prediction i 

### ^Hesketh' s Prediction

1 0 2 0 3 0 4 0 EXPERIMENTA

L PRESSURE DROP , c mW.C , 5 0 6 0 Figur e 4-2 . Compariso no f predicte d pressur e drop wit h

experimenta l dat a fro m\^en an

d Uchida .

4 4P.6 3



### 3 6
c_ >



### o

~ 2 8

: — i

0 0 "nr.
'_ > ABoll' s equatio n

Q Volgin' s equatio n

1 6 2 0 2 4 2 8 3 2 3 6 EXPERIMENTA L PRESSUR E DROP , c mW.C . Figur e 4-3 . Compariso n o f predicte d pressur e dro p wit h

experimenta l dat a fromWe n an d Uchida .



### 4 5P.6 4

3 6

2 3 2 u 

## I 2 8

LOO O ^ 2 4
<

cc 2 0
1 6

i ? 1 2 1 62 02 42 8 3 2

EXPERIMENTA L PRESSUR E DROP , c mW. C 

### 3 6 Figur e 4-4 . Compariso n betwee n Behi e and Beeckmans ' predictio n

an d experimenta l dat a fromWe n an d Uchida .



### 4 6P.6 5



### Prediction s b

yBol l an

d b yBehi e an

d Beeckman s are slightl y better , bu t stil l have . a tendencyt o unde r estimat e pressur e drop . The onlydifferenc e betwee nmodel s b yBol l an

d b y Behi e an

d Beeckman s i s tha t Behi e an d Beeckman s neglecte d wall-frictio n loss . In a ventur i scrubber , mos t o f the pressur e drop i s due t o acceleratio n o f liqui d drops . Tabl e 4- 2 prove s thi s statement' . Tabl e 4- 2 lists'We n an d Uchida' a dat a alon

g wit hprediction s b yBoll' s equatio n an d b yBehi e an

d Beeckman' s equation . Behi e an d Beeckmans ' equatio n always predict s a lowe r pressur e dro p thanBoll' s equation . The differenc e betwee n th e prediction s b

ythes e tw o equation s i s equa l t o the wal l friction . The las t colum n i n Tabl e 4- 2 show s the value s o f wal l frictio nfo r al l runs . Fo r thi s particula r scrubbe r geometry , the con tributio n o f wal l frictio ni s les s than ten pe r cen t o f the tota l loss . Calvert' s equatio n i s base d o n th e assumption s tha t al l liqui d drop s accelerat e t o the ga s velocityinth e throa t an

d tha t non e o f th

e dro p momentu

mi s converte d t o pressur e i n the diffuser . I t i s possibl e tha t insom e scrubbers , liqui d drop s d o no t have sufficien t residenc e tim e t o accelerat e t o th e ga s velocit yinth e throat . I n orde r t o take thi s fac t int o account , a correctio nfacto r wa s develope d an

d added t o Calvert' s equation . The new equatio n nowread s 2 / Q *de U 

### Gt'- L 

### l C 4 

### " 1 

### ) wher e A

P = pressure , c

m W.C . U p = ga s velocit yinthe throat , cm/ s Q . = liqui d flo

wrate , cm 3 

### / s Q p = ga s flowrate , cm 3 

### / s

4 7P.6 6



### TABL E 4-2 . WE NAN D UCHIDA* S EXPERIMENTA L DAT A AN D PREDICTION S B

YBOL L AN

D B Y BEHI E AN

D BEECKMAN S Ru n No . 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 Experimenta l AP , cm W.C . 22. 2 21. 8 19. 8 30. 5 2 9 22. 9 21. 6 21. 3 24. 1 21. 8 19. 8 2 9 2 2. 9 21. 6 21. 3 23. 4 3 1 ^ 25. 9 21. 8 Pr e

Bol l 19. 2 19. 9 18. 9 22. 7 20. 4 27. 5 19. 1 19. 8 28. 7 16. 8 16. 8 20. 4 24. 9 17. 4 16. 8 21. 9 20. 3 17. 2 16. 7 diction , cmW.C . Behi e (., Beeckman s 17. 4 1 8 17. 1 20. 4 18. 1 25. 3 17. 4 17. 9 26. 4 15. 3 15. 3 18. 4 2 3 15. 9 15. 3 20. 4 18. 3 15. 7 15. 2 Wal l Frictio n cmW.C . 1. 8 " 1. 9 1. 8 2. 3 2. 3 2. 2 1. 7 1. 9 2. 3 1. 5 1. 5 2 1. 9 1. 5 1. 5 1. 5 2 1. 5 1. 5



### 4 8P.6 7

wT i 

### wner e U 

### j f e

### = correction , factor , dimensionles s an a u

J J 

### de d e u Gt 1 - X ? 

### + (X14



### - X 2 

### ) 0



### - (4-2 )

3 £ C,, . p_ X= D ° G + 

### !

1 6 d 

### d P 

### L U p = ga s velocityi n th e throat , cm/ s u , = dro p velocit ya t th e exi t o f th e throat , cm/ s I = throa t lengt ho r distanc e betwee nliqui d injectio npoin t and th e exi t o f throat , c m d ^ = dro p diamete r fro mNukiyam a and Tanasaw a correlation , c m P G

### = ga s density , g/cm 3 

### p , - liqui ddensity , g/cm ; 

### C n

### = dra g coefficien t a t th e liqui dinjectio n poin t "C ^ " iv . th e dra g coefficien t obtaine dfro m Standar d D o to curv efo r

si: ; ;;res , Dro p Reynold s numbe ri s define da s

N _d d( U G t' U do ) R e. d (4-3 )


### wher e N. , , = dro p Reynold s numbe r

k e , d. 

### u , = initi. 1 dro p velocity , cm/ s v= kinemati c viscosit yo f gas , cm'/ s Th e physica l meanin g o f " l ] 

### 5 e 

### " i s th e fractio no f ga s velocit yt o whic hth e liqui ddrop s hav e accelerated . I f liqui ddrop s ar e accelerate dt o ga s throa t velocity , "u ^ i s equa l t o 1 and equatio n4- 1 reduce s t o Calvert' s equation . Pressur e dro p predictio nbyequatio n4- 1 i s

4 9

### lowe r tha n Wen an

d Uchida' s dat a a s show ninFigur e 4-5 . Wal l frictio r an

d pressur e recoveryinth e diffuse r wer e neglecte d in th e correctio n facto r t o Calvert' s equa tion , however , Boll' s prediction s ar e no bette r thanth e modifie d Calvert' s equation . Prediction s base d o n th e "standard " drag coefficien t ar e bette r tha

n thos e base d onIngebo' s correlation , a s show n in Figur e 4-5 . Becaus e Ingebo' s drag coefficient s ar e low , dro

p velocit yan

d pressur e dro

p prediction s ar e low . Boll' s Dat a Bol l (1973 ) derive d a n equatio n t o predic t the pres sur e dro

p i n a ventur i scrubber . H e obtaine d som e pressur e dro p dat a on a prot o typ e ventur i scrubbe r t o confirmhi s equation . Th e cross-sectiona l dimension s o f the ventur i scrubbe r throa t wa s 35. 6 c mx30. 5 c

m(1 4 x1 2 inches) . The throa t lengt hwa s 30. 5 c m(1 2 in.) . The convergenc e an d divergenc e angle s wer e 25 ° an d 7° , respectively . Figur e 4- 6 i s a sketc ho f th e ventur i scrubbe r use d b yBol l Figur e 4- 7 show s the compariso nbetwee n Boll' s dat a an d theorie s b

yvariou s investigators . The pressur e dro p wa s expresse d i n terms o f the numbe r o f throa t velocit y heads , i.e. , -A P Numbe r o f velocit yhead s los t = i Pr

2 2 

### § c P 

### L wher e A

P = pressur e drop predicte d b ytheory , c

mW. C 2 

### g = 9 8 0 cm/ s p p = ga s density , g/cm 3

, 3 

### p . = wate r density , g/cm ' U p = ga s velocit yi n th e throat , cm/ s A s can be seen , Calvert' s equatio n predict s to o hig ha pressur e drop for liquid-to-ga s rati o above 0. 7 £/m 3 

### . Hes Keth' s equatio n give s to o lo wa pressur e drop . Volgin' s equatio n give s a differen t slope . 5 0P.6 9



### 3 4
3 0 _

u
u o a. Q 

### w2 0 cc ; = > u. LC PC Q 

### w t-m 

### u r—1 Q 

### w CC 

### 1 0 — i 1 1 1 1 1 1 1 r

/ \ C n

### fro

mstandard curve _£ Y^ n fro

mIngebo' s correlatio n

c J ••:••!:-:•- ! :-! - ---A " 

# ... . A '

1 0 Figur e 4- 5 J 4 1 I I I ' ' ' i 2 0 3 0 EXPERIMENTA

L PRESSURE DROP , c

mW.C. 3 4 Compariso no f predicte d pressur e drop b ymodifie d Calvert' s equatio nwit hdat a fro mWenan

d Uchida .

5 1Liqui d Inle t

O n tN j

Figur e 4-6 . Prototyp e ventur i scrubbe r use d b yBol lP.7 1



### 2. 0 

### 1. 8 

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## o <

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### 1. 6

1- 1 

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### o o

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### 1. 0
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### :x,\ccj /"• V- i7 7 ,~ .: ! 

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### equat i £J\1.9 1 c

mnozzle s "Tn~:rj:::": " "

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# /¥ /'•'•'•' / -• - 

### squatio n u Gt 

### =915 0cm/ s > .idf.jl.di^LdL : :~-jy

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• • •' ! xJ^'

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## Cftf-

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' :'/{'•'•''•

. . • :•!.. « d/V y

---:|':- H
: :_di:_: . j_. r i.:: : 

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r c.c.yCC-x YrfX''- : : y:. : f/\v\- :..!.•• : V |... : 

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## IA \

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## diii>^pr n h—:-:-::-• ] r—'?-•
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### equatio nC^xl

- . . * :.:..-...;:-.. . .:.f

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* * 5 « « - i

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# I I

• - ! ••:: - 

### 0. 2 0. 4 0. 6 0. 8 1. 0 1. 2 1. 4

LIQUI D T

O GAS RATIO , 1/m 3 

### o f ga s 1. 6 Figur e 4-7 . Compariso n o f Boll' s pressur e drop dat a wit htheor y

5 3P.7 2



### The rang e o f ga s velocit yi nthroa t covere d b yBol l wa s *5. 8 m/ s - 91. 5 m/ s (15 0 - 30 0 ft/s) . The lin e representing th e prediction s b

yBoll' s equatio n wa s ^ n averag e curve fo r the predicte d pressur e drops . Ever , thoug

hBoll' s equatio nslightl yunde r estimate s pres sur e dro

p at lo wvalue s o f liquid-to-ga s rati o an d slightl y ove r estimate s a t hig hliquid-to-ga s ratio , th e agreemen t betwee n hi s dat a an d equatio n i s considere d t o be satis
factory . Predicte d pressur e drop s b ymodifie d Calvert' s equa tion for throa t velocitie s o f 40. 5 m/ s an d 91. 5 m/ s ar e als o show

n in Figur e 4-7 . Sinc e Bol l operate d hi s ventur i scrubbe r in thi s throa t velocit yrange , the are a bounde d b

ythes e tw

o theoretica l line s represent s the rang e o f expecte d pressur e drops . Th e fac t tha t Boll' s theoretica l curve , whic hi s the averag e o f predicte d pres sur e drops , lie s withi n thi s are a signifie s tha t the modi
fied Calvert' s equatio n an d th e mor e complicate d Boll' s equatio n predic t pressur e drop i n equa l accuracy . Brin k an d Contant' s Dat a Brin k an d Contan t (1958 ) performa thoroug hstud yon a n industrial-scal e Pease-Anthon yventur i scrubber . The scrubbe r ha

d a rectangula r cros s section . It s throa t r.easure d 15. 2 x86. 4 c

m( 6 x3 4 inches ) wit ha straigh t sectio n 30. 5 c

m (1 2 inches ) long . The angl e o f th e con vergen t sectio n wa s 25° ; the divergen t sectio n had a nangl e o f 2.2 ° for 15 2 c

m( 5 ft ) following th e vnetur i throa t an d then a n angl e o f 15° . Figur e 4- 8 i s a sketcho f th e Pease Anthon yventur i scrubber . Brin k an d Contant' s pressur e drop dat a ar e compare d wit htheorie s b

yvariou s investigator s i nFigur e 4-9 . Again , Calvert' s equatio n consistentl yove r predict s the pressur e dro

p an d Hesketh' s equatio nconsistentl yunde r estimate s th

e pressur e drop . Bot hBoll' s equatio nan d

5 4Liqui dInle t

on o n



### Figur e 4-8 . Dimensio n o f Pease-Anthon yventur i scrubbe r use d b y Brin k an d Contant .P.7 4



### th e modifie d Calvert' s equatio n compar e favorabl ywit h experimenta l observations . A s can be seen fro mFigur e 4-9 , Boll' s equatio n i s inbette r agreemen t wit hBrin k an d Con tant' s dat a fo r 9 0 spra yjet s an

d the modifie d Calvert' s equatio n i s in bette r agreemen t wit h4 5 spra yje t data . Overall , th

e modifie d Calvert' s equatio n predict s slightl y bette r than Boll' s equatio nfo r thi s particula r scrubbe r geometry . Ekman an

d Johnston e Dat a Ekman an

d Johnsto n(1951 ) have measure d pressur e drop acros s a laboratory-scal e ventur i scrubber . Figur e 4-1 0 show s th

e ventur i scrubbe r used b yEkmanan

d Johnstone . The ventur i throa t wa s 3 c m(1-3/16" ) indiamete r an d 3. 8 c mlong . The convergen t an d divergen t angle s wer e 25 ° an d 7° , respectively . Wate r wa s introduce d inthre e ways : fro ma singl e 3 2 m

mje t injecte d downstrea malong the axi s o f the throa t radiall youtward fro ma bras s pip e 3 2 m min inside diamete r wit hfour 18. 5 m mholes , an

d radiall y inward fro

ma singl e 3 2 m

mje t at th

e entranc e o f th

e throa t Ekman an

d Johnston e recorde d a highe r pressur e drop fo r radia l inward injection . Figur e 4-1 1 compare s Ekmanan d Johnstone' s experimenta l dat a wit htheoretica l prediction s . A s ca n be seen , onl y Boll' s equatio n an

d th e modifie d Calvert' s equatio nar e in agreemen t wit hdata . Conclusion s Base d o n thi s evaluation , we ca nconclude tha t bot h Boll' s equatio n an

d th e modifie d Calvert' s equatio nare ade
quat e for th

e predictio no f pressur e dro p in a ventur i scrub
ber . Sinc e th

e modifie d Calvert' s equatio n i s simpler , we wil l choos e i t a s th e ventur i scrubbe r designequation . However , the metho d fo r applying Boll' s equatio n t o predic t pressur e dro

p wil l als o be given .

5 6P.7 5

2. 5

io o o Q < U J X >- > i — i U o o u > < O CC X H O

X < a , < 2. 0

1. 5

1. 0 1. 0 1. 2 1. 4 1. 6 1. 8 2. 0

LIQUI D TO GA S RATIO , l/m 3o f ga s Figur e 4-9 . Compariso n o f Brin k and Contan t exper i

menta l dat a wit htheories .

5 7Liqui d

Ga s

o n Oo

Figur e 4-10 . Dimension s o f th e Ekma n and Johnston e venturi .P.7 7

] . 4

0. 4 0. 6 0. 8 1. 0 LIQUI D T O GA S RATIO , £/m 3 

### 1. 2 1. 4 1. 6
Figur e 4-11 . Compariso n o f Elema n an d Johnstone' s pressur e dro p dat a wit htheories .



### 5 9P.7 8



### PARTICL E COLLECTIO

N Mos t author s (excep t Taher i an d Sheih ) cited i

n th e las t chapte r us e the sam e basi c mode l for th e predictio no f particl e collectio n in a ventur i scrubber , i.e. ,

dc u 

### r 

# " '^ K ^ K n d z(4 

# " 4)
wher e c = dus t concentratio n u = relative velocit ybetwee ndus t an d drop , cm/ s U p = ga s o r dus t velocity , cm/ s A= duc t cross-sectiona l area , cm 2 

### r , = drop radius , c m
= singl e drop collectio nefficiency , fractio n Q , = liqui d volumetri c flowrate , cm 3 

### / s z - axia l distance , c m Bol l (1973 ) an

d Behi e an

d Beeckman s (1973 ) had demonstrate d th e succes s o f thi s equatio ni npredicting ventur i scrubbe r perfor
manc e b ycomparing theoretica l prediction s wit hexperimenta l data . Thus , we wil l choos e thi s equatio n a s the particl e col
lectio n design equatio n fo r ventur i scrubber . N o genera l solutio n for thi s equatio nwa s foun d inthe literature . In orde r t o calculat e th e particl e collectio nef
ficiency , one mus t integrat e thi s equatio nnumerically , takin g int o accoun t the scrubbe r geometry . I t i s inconvenien t t o us e thi s equatio n t o predic t ventur i scrubbe r performance . Ageneralize d method for predicting ventur i scrubbe r performanc e b

yequatio n (4-4 ) wa s develope d i n thi s study . Thi s metho d i s simila r t o tha t used b yHolland s an

d Goe l (1975 ) t o obtai n pressur e drop in ventur i scrubber . Detaile d deriva
tion o f th

e generalize d metho d wil l be presente d in the nex t chapter .

6 0P.7 9



### CHAPTE R5 PERFORMANC E MODE L I nthi s chapter , w e wil l presen t th e generalize dmetho dfo r predictin g ventur i scrubbe r performanc e b yusin g bot hBoll's pressur e dro p equatio nan dCalvert' s modifie dpressur e dro p equatio ncombine dwit hCalvert' s differentia l equatio nfo r particl e collection . Th e metho dwa s develope db yHolland s an d Goe l (1975) . However , the yonl ycovere dBoll's pressur e dro p equation . Thei r metho dwa s extende dt o Calvert' s differentia l equatio nfo r particl e collection . MATHEMATICA L MODELIN G Th e basi c equation s governin g th e particl e collectio n andpressur e dro p i na ventur i scrubbe r iver e develope db

y Calver t (1968 , 1970 ) andBol l (1974) ; rewritte nher e afte r som e rearrangemen t the yare :

A 

### u Q , d c r X 

### L c u G

### (u G 

### -u r 

### ) A\4r d 

### nd z ( 5 

### _! ) du d3 

### p G 

## ^ 2 

## c D 

### d z 4 p L

### d d

### u d 

### d p du 

### G3 P 

### G C 

### D ( U 

### G" U 

### d) 2 m 

### L (V m G 

### ) fp 

### G U 

### G rc

### „
—= p r

### u r



### - ———

—- (5-3 ) d z " <-

> d z 4 p . d , u , Am r 

### 2d , P 

### L ddGh B.C . a t z = 0 , c-=c^; u , = u , • u r 

### =u r 

### : p=p „

' o dd o GGo o wher e A= duc t cross-sectiona l area , cm 2



### c = dus t concentration , g/cm 3 

### C p = dra g coefficient , dimensionles s d d

### = dro p diameter , cm d , = hydrauli c diamete r o f th e duct , cm f = frictio nfactor , dimensionles s 6 1P.8 0

ni p = ga s mas s flo wrate , g/ s m . = liqui d mas s flo wrate , g/ s p = pressur e Q = liqui d volumetri c flo wrate , cm 3 / s r , = dro p radius , c m u , = dro p velocity , cm/ s u „ = ga s velocity , cm/ s u = relativ e velocit ybetwee n ga s an d liqui d drop , cm/ s z = rectangula r coordinat e i n th e directio n o f flo w p , = liqui d density , g/cm 3 p p = ga s density , g/cm 3 n = singl e dro p collectio n efficiency , dimensionles s Severa l assumption s wer e mad e i n th e derivatio n o f thes e equations . The yare : (1 ) Th e flo wi s one-dimensional , incompressibl e an d isothermal . (2 ) Liqui d drop s ar e uniforml ysprea d acros s th e duc t and th e dro p diamete r i s invarian t wit haxia l distance . (5 ) Drop s ar e o f unifor mdiameter . W e wil l introduc e severa l additiona l assumptions : (4 ) Ther e i s n o wal l los s o f liqui d drops . (5 ) A t an

ycros s sectio n o f th e scrubber , liqui d fractio n i s small . Therefore , a t an ylocation , th e ga s velocit yca n b e calculate d b yth e followin g equation : m

u Gp G A wher e m

p = ga s mas s flo wrate , g/ s A= duc t cross-sectiona l area , cm 2 p r = ga s density , g/cm 3

6 2 £
- (5-4 )P.8 1

Duc t cross-sectiona l are a depend s on locatio n an d ca n b e b e determine d from th e followin g genera l formula :
j = 1 fo r rectangula r duc t j = 2 fo r circula r duc t wher e A= cros s - sectiona l are a o f th e duc t a t th e star t o f

o a section , cm 2 R= radiu s (fo r circula r duct ) o r hal f widt h(fo r rectangula r duct ) a t th e star t o f a give n section , c

m 8 = hal f angl e o f divergenc e o r convergence , degre e "3 " i s positiv e whe n duc t i s divergin g an d i s negativ e whe n duc t i s converging . Equatio n (5-5 ) assume s tha t fo r rectangula r duct , duc t breadt hremain s unchanged ; onl yduc t widt hi s convergin g o r diverging . (6 ) Th e dra g coefficien t i s governe d b yth e followin g relationshi p a s suggeste d b yHolland s and Goe l (1975 ) . C D= (constant ) N~°- 5

wher e C ~ = dra g coefficien t applyin g a t z=0 , dimensionles s

u „ = ga s velocit ya t z=0 , cm/ s Go & J u , = dro p velocit ya t z=0 , cm/ s do K' ' "C n" i s determine d fromth e "standar d curve " usin g a Reynold s numbe r calculate d o n th e basi s o f th e relativ e velocit y applyin g a t th e beginnin g o f th e duct , i.e. ,

6 3P.8 2



### u „ - u , j d , v= ' G o do l d Re, o v

### ( b 

### " 7 

### J wher e N R

### = dro p Reynold s numbe r a t th e beginnin g o f

th e duct , dimensionles s d , = dro p diameter , c m VQ= kinemati c viscosit yo f gas , cm 2 

### / s Th e equatio nfo r th e standar dcurve , du e t o Dickinso n andMarshal l (1968 ) , i s :

C n

### = 0.2 2 + 2 4 

### (l +0.1 5 N°" 6 

### \ (5-8 ) D o N\ Re,o ) vJ



### Re. o v

### ' (7 ) Liqui ddro p diamete r i s tha t predicte db yNukiyam a andTanasaw a correlation . (8 ) Particle s ar e flowin g a t th e sam e velocit ya s gas , the nEquatio n(5-1 ) ca n b e reduce dto : 

### d c 1 

### ' 5 

### l U 

### G- U 

### dl/V \ .

- —= —h i d z (5-9 )

u 

### d d

### d \%l (9 ) Particl e collectio ni s primaril ydu e t o inertia l impaction . W e wil l us e th e simplifie dequatio n b yCalver t (1970 ) t o estimat e th e singl e dro p targe t efficiency .

/ K\ 2
' P' (5-10 ) K +0.7 / P C ' p d2Iu r

- u, I wher eK

- PP' Gd ' (5-11 ) P9 U

Gd d I f on edefine s tota lpressur eas :

P T= p + , -iP Gu 2 G(5-12 )
6 4Equatio n (5-3 ) ca n b e writte n a s P.8 3



### d p T 3 P G / C D \U G " U dl U G " U dl/ m L \(M+1 ) f P G V d z 4 p L \ d d A 2d , (5-13 ) wher eM = m T

/m „ LL >


### = liqui dt o ga s mas s flo w rat erati o Th ehydrauli c diamete r "d , " i s give nfo r

acircula r duc t by : d, = 2( R+ zta n8 ) (5-14 )
an d fo r a rectangula r duc t by :

d = 2 b( R + zta n g ) hb+ R+ z ta n £ wher e R= radiu s (fo r circula r duct ) and half-widt h

(fo r rectangula r duct ) a t th e star t o f a give n section , cm b= duc t breadt hfo r a rectangula r duct , c m (5-15 )

Equation s (f-2) , (5-9 ) and (5-13 ) ar e th e governin g equation s fo r ventur i scrubbe r performance . Thes e equation s ar e no wnon-dimensionalized , usin g "u n" a s th e characteristi c ' & Go velocit yscale , "%p r u 2 " a s th e characteristi c pressur e scale , 

### an a d d p d 

### uG

o r.S a s th e characteristi c lengt hscal e ^^D o P G\Go~ U dc / f° r th e equation s belo w (i n th e cas e o f d , , R Q , an d b , duc t lengt h"£ " i s use d a s characteristi c lengt hscale) , i.-e. , 

### u u uG

o (5-16 )



### 6 5P.8 4

* = 

# i 1 

# ^

3 C D o P G *G

o G o d o 0. 5 (5-17 )

D * P T 1 2 -2 P r U p GG o ( 5 - 1 S )

B yusin g thes e definitions , w e obtai n

u„- u , = 'G

o U p u ,

G o d ' G" d (1 + z tan 3 \j " u r 

## I R

## / G o

*G o u G o 

## 1 * ta n

## B I

t±\ R3 C n „ Pp lu r -u .

D o G\ Go d o o.s * J d (5-19 )

Le t S = 2 tan 3 d d P L u G o 0- 5

3 R C n ^ Pr

- \tl p -U , D o " u \ G o d o (5-19b )
"S " i s th e dimensionles s paramete r characterizin g th e slop e o f a give n duc t and i t ha s th e followin g characteristic s

S < o fo r convergen t sectio n S = o fo r ventur i throa t S > o fo r divergen t section . B ysubstitutin g equatio n (5-19b ) int o equatio n (5-19) , w e have :

u r -u , = U

p L i d G o ( 1 + Sz*)" 3 ' - u *

6 6Fro mequatio n(5-10 ) w ehave : P.8 5

K + 0. 7 P , Pd'

^1 PP 9 " Gd d
( 1 + Sz*) ^ " C ^d~2 "

P, P 9 *Gd d


### • U 

### d i 

## V U 

## d

Up-u.1+0. 7 -.2 ( 1 + Sz* ) - 1 u 0 . 7 K p o (5-20 )

wher eK p o C ' p p d p 2U G o 9 ^ Gd d B ysubstitutin g equation s (5-17) , (5-19) , an d(5-20 ) int o equatio n(5-9) , w ehave : I. 3 d c _1.5 R/ Q L \S |( 1 + Sz*)" J -Ud l ^L \S c d r 1 ta nB IQ G / u^ f | ( - iI071^ * (5 " 2 1 )

1 + Sz* ) - 1 -u*| + p l

'd ' i c p o
J d1 * r-- G o Q L Le t B = —

^ GP Gr D o \ U Go- u d o 0. 5 (5-22 )
the nw eobtai n

I nP t 1 + Sz*)~ 3 -u* | d l Sz*) ~ ]- u d z :

+ 0. 7 K 

### P° . (5-25 )

6 7P.8 6

wher e L = dimensionles s duc t lengt h
5 C D o l

p G 2 d d p d U pu ,

Go - d o u G o 0, 5 I = duc t length , cm Equatio n (5-25 ) i s th e genera l equatio n t o predict , particl e collectio n b

yinertia l impactio n i n a ventur i scrubber . B yfollowin g th e same procedure s a s th e derivatio n o f equatio n (5-23) , th e followin g equation s ar e obtaine d fo r dro p velocit yand pressur e drop : 0. 5

du * d dz * ( 1 + Sz*)" J U d 1( 1 + Sz*) " " I ? ii * (5-24 ) dp * = M dz * ( 1 + Sz*) ' 'J - u > ( 1 + Sz* )



## n- u 

## ; 0. 5

+ ( M+ 1 ) f ( 1 + Sz*)" 2 j

d * L h (5-25 )
.C . a t z * = 0 , .u*=u * , p * = 0

' ddo ' • * i d * = 2R * ( 1 + Sz* ) Circula r duc t [ A= 2 b * R*( l + Sz* ) hb * + R*( l + Sz* ) Rectangula r duc t (5-26 )
f = frictio n factor , dimensionles s i * = b/l - dimensionles s duc t breadth , !.* = \\r>\ = • dimens i onles s radiu s

6 8P.8 7

Th e firs t termo n th e righ t han d sid e o f equatio n (5-25 ) represent s th e pressur e chang e associate d wit hth e accelera
tio n o f liqui d drops ; th e second termi s th e wal l frictio n loss . Fro m

thi s equation , i t seem s tha t th e contribution s o f th e liqui d acceleratio n los s an d th e wal l frictio n los s t o th e tota l pressur e los s ar e additive . Therefore , on e may wr ite : P T = P d + P (5-27 ) wher e P T

P d * =

W tota l pressure , dyne/cm 2 componen t o f p* , associate d wit hliqui d flow , dyne/cm 2 wal l frictio n componen t o f p£ , dyne/cm 2 B ythi s definition , w e have :
dz * M( l + Sz* ) J ( 1 + Sz* ) u - ( 1 + Sz* ) -3

an d d p w= ( M+ 1 ) f ( 1 + Sz* ) dz * d * L

h 2 j U 

## S 0. 5 (5-28 )
(5-29 )
wit hboundar ycondition s

a t z * = 0 , p * = 0 , p * = 0 w (5-30 ) Equation s (5-23) , (5-24) , (5-28) , an d (5-29 ) ar e th e fina l form s o f th e governin g equations . Fo r eac hsectio n o f th e ventur i scrubber , it s pressur e dro p an

d particl e penetratio n ca n b e calculate d fromequation s (5-23) , (5-24) , (5-28) , and (5-29) . Sinc e pressur e drop s ar e additive , th e overal l pressur e dro p fo r th e ventur i

6 9

### scrubbe r is , P.8 8



### AP , £ (AP ; 

### (5-31 ) wher e A

P = overal l pressur e drop , dyne/cm (AP) . = pressur e dro p o f a section o f th e ventur i scrubber , dyne/cm 2 

### The ventur i scrubbe r i s a scrubbe r wit ha convergen t section , a throa t section , an d a divergen t sectionconnecte d in series . Particle s tha t ar e collecte d inone sectio n canno t b e collecte d i

n anothe r section . Therefore , i f th e particl e penetratio n for eachsectio n i s known , th e overal l penetra tion fo r the ventur i scrubbe r wil l be ,

Pt( d ) = n P i Pt(d p 

### ) (5-32 ) wher e Pt( d )

P Pt( d ) 1 

### P overal l penetratio n fo r particle s wit h

diamete r " d " , fractio n penetratio n o f a section , fraction
SOLUTIO N The analytica l solutio nt o equatio n(5-29 ) is ,
> * = (M+l) f

F w h o w (5-33 )

wli er eF A - 2

4 ( A0>5 -1 ) v

### r J 

### fo r

circula r

duc t (5-34 )

1 + 

### R*(Ar 

### -l)(l+b*+R* )

2(b * + R* ) fo r rectangula r

duc t

7 0P.8 9

an d A= th e rati o o f exi t t o inle t cross-sectiona l are a r = (1+SL) J d, * = dimensionles s hydrauli c diamete r a t duc t h o ; inlet , c

m f = frictio n factor , dimensionles s Avalu e o f f=0.02 7 wa s suggeste d b yBol l becaus e i t seeme d t o giv e a slightl ybette r fi t i n th e shap e o f th e pressur e dro p curve s tha n othe r value s o f "f" . Equation s (5-23) , (5-24) , and (5-28 ) ar e solve d b y numerica l integratio n on a digita l computer . Figure s 5- 1 throug h5-1 6 sho wth e result s o f a numerica l integratio n fo r * th e rang e o f L , S , and K „ o f interes t and fo r u , =0 . Thes e

° p o d o figure s alon g wit hequatio n (5-32 ) ma yals o b e use d t o deter
min e penetratio n fo r u , 5^0 . Th e metho d i s discusse d i n th e followin g paragraphs . Th e dro p velocit ya t th e beginnin g o f th e divergen t sectio n differ s fromzero . W e wil l us e th e divergen t sectio n t o illustrat e th e metho d o f applyin g Figure s 5- 1 throug h5-1 6 t o determin e th e particl e collectio n efficienc yo f a sectio n wher e a t it s inle t th e liqui d dro p velocit yi s no t zero . Refe r t o Figur e 5-1 7 i n orde r t o find th e penetratio n o f th e divergen t sectio n ABCD , w e projec t i t i n th e upstrea m directio n wit hth e sam e divergenc e angl e "6" , i.e. , ad d an imaginer ysectio n FEBAt o th e upstrea mo f ABC D a s depicte d i n Figur e 5-1 7 b

yth e dashe d lines . Th e resul t i s tw o ven tur i divergen t section s connecte d i n series . Th e outle t o f th e imaginar yadde d on sectio n i s th e inle t o f th e rea l sec tion . B

yequatio n (5-32 ) th e particl e penetratio n fo r th e rea l divergen t sectio n ABC D i s equa l to , P t ^ABC D p l b• ii) J

FEB A

7 1P.9 0

z 

### d? n 723.0 0

<^> PL , 2.0 0

1.0 0

0.7 5

0.5 0

0.2 5 

### s i- u 1 0 - 5 

# if r 

# T r_T 

# 7 r n 

# 7 T -1' ! -0.5 " -0. 2 i -0. 1 -0.0 5 -0.0 2 . -0.0 1

0.0 1 ( L + L H ) F Figur e 5-2 . Char t fo r obtainin g u ^ fo r a rectangula r duct .'•••Wi. 6. 0

3 - PL , *xi P . 4. 0

2. 0

1. 5

1. 0

0. 5 

# T—rp-rrjifrr ii— | M f . rrq 1 | i<|ii iy.1—71—i f 1 in n S=-2 0' 1 -1 0Ii-5. 0-2. 0-1.0 ! -0. 5 -0. 2-0.1.-0.0 5 -0.0 2-0.0 1 chang e o f scal e

0 0.0 1 

### * S

0. 1 1. 0 1 0 10 0

(L+L H ) F Figur e 5-3 . Char t fo r obtainin g p * fo r a circula r duct .6. 0 SF-°' 5 = -2 0'•• ' ; - 1 0 . . 

## TH ! r 

## ___ T 

## p T 

## _—j— j j j wjj r 0 . 5 I ! ? 

# I ' I" !

•0. 1 ! -0.0 5 -0.0 2-0.0 1 ; 4 . 0 - chang e o f scal e 2. 0 F-1-SL H ;
1. 5

-^ 1 O n C M

U H * T 3 C X 1. 0-

0. 5

0 1 

## J I IIIIII I I i n i lit i i i i i u ii i i i i i i m o. i 1. 0 1 0 10 0

( L + L H ) F Figur e 5-4 . Char t fo r obtainin g p* . fo r a rectangula r duct .

### 0. 0

- Jam

4- > C-r C
PL , 

### 0.0' —

0. 0

—0.0 2

0.0 1

0.0 1 10 0
L + L

- ) 

### Figur e 5-5 . Char t fo r obtaining penetratio nfo r circula r duct .C Q

PL , 1 6

1 2 —

0 8

0 4 pfwuiaw i g*mixr<r.

i .;..J::lil:..t....;...J....i. . C i rcuJa r duc t

. . . .......... t „ .

0.0 1 0. 1 1 0 ( L + L H ) F Figur e 5-6 . Char t fo r obtainin g penetratio n fo r circula r duct . 10 0. 3

o o eq

a , 

### c P-, I . 2 . . . I. I, . .1 . 

### Circula r duc t u

# nTr~rnrTT~TrT
- J.

.0 1 ( L + L H ) F Figur e 5-7 . Char t fo r obtainin g penetratio n fo r circula r duc tU 3 p a 4- > a , PL , . 2 

# :.cc\c\

Circula i •duc t

. . . ,. - d i r\

:.;... . : •p ° : ir :

~ F=1-SL,,. : \J

. . . j. . . .

1
••• •i ••

. . . . i . . . i

-•••>- -
:::'!:: :

••• •j :•• •

... . I... .
... . i... .

... . |...
. 1

•' • ' \

• • ' • : '/j::: ' 

# Lr ; | i ._.!... . ....!.. .

• • •' •i

.... i . -

...,i.. . ....j... .
—(.
_ _J _

... L . i ...p. .

. . L.. .

1

...... . j... . .... • ' •1

—

.... ... .

—

- •

... ...j . . .

-+- • J . . .

r

:

. . . i... . "... .

L.. .

riffd "

. . i .
....j... . 

## T

. i

• • 

## ^ c
,..).. .:... . 1 ::|::r
. z

,... i i?.*
—

... . 

# 3

.. . }....

" ~ J|F* : . .

- •

L.U L i

! • ••

• i&Pfs'^ :.•:: : L i

. . :.. .

. . i . . ^^•"'^"T

.... . . . . ;

•-- •:^_ — - i

—j... . '.'.'J,** ^rc. j — i 1 —

- • •j--- -
y... „ i . . 1

)-•• ' ....;.. .

.. . r .

...J.. . .-J — i ........ . ._..!... . .i... . .. . X I

. ..J . .. . .. . I —o-v -'•-

—0.0. U " !" ' ' ' ' " 4 0.0 2 III , r

..... . 1.0 5 J 

### hap . I . 

## ; ^h ...|.^e» ^ 0 . 2 " i i 

### ~±.: r:: : 

### iso . 

## 5

. . .i... . ..„j. „

...... . i , i 

## T — i — ...L.. . 

# y : \- l- h -..? o 2. 0

r 0 . i . 1 0 2 0 5 0 

# 4 i- r '

:::::. :

. . J 

## i . . ; .

•• i ^

-* ••- •j- •• •
:::;:,':,, :

i... .

• 

# " H " I

.. . j...:. .

•;•;;; " CTC.

. . .i... .

. .j.. .
•- - . - i •- - • — 4 —

- - •;•;; ;

:•••• !

1 

# , 1 N • ...... .

.. . L .

....L.. . ....j... . T '

— H ...,|...
. ]

i *t —i— -i- j ...!... .

1 ...j... . ...!... .

....... . ...i.. . i i ...i.. . "V "

••+ - ...:... . ... .

—

—

— - 

## :±fc

• -

_ 

## u —-* - m

-.::.'.

m

i . . i'i;,i r 0 . 1 1 0 1 0 0 . ( L + L n ) F Figur e 5-8 . Cliar t fo r obtainin g penetratio n fo r circula r duc t1. 0

o o o m 4- > ft
PP

( L + L I( ) F Figur e 5-9 . Char t fo r obtainin g penetratio n fo r circula r duct .0. 0

c n
4- > ft ft 

# r^rnrrnT i T^TTTTIT O

0.0 4

0.0 3

0.0 2

0.0 1 _

0.0 1 Figur e 5-10 . Char t fo r obtainin g penetratio n fo r rectangula r duct . 10 00 0

t o C

Q ft ft i 0.1 6

0.1 2

0.0 8

0.0 4

0 

# j-^rmT n pn ' Rectangula r

duc t

0.0 1 

# jTf n TT 

# T " i—rrrrrr T • ii] 

## i-i i

( L+ L H ) F F'igure 5-11.Char t fo r obtainin g penetratio n fo r rectangula r duc t 

## I lit !

10 00 . 3

0 0 PQ

OL ,
f--1 0 . 2

0 . 1 

# r^T^rTTTTrr~~nr—rnrrTrr n T"~'prnTTT w

# • { . i r' l j I n

i i i •i M 

## i j J III I 

## iii i i i IIIII I 0.0 1 0. 1 1. 0 1 0 10 0 ( L + L H ) F Figur e 5-]2 . Char t t o obtai n penetratio n fo r rectangula r duc to

o O

Q 4-> D H

I 0. 4

0 . 3

0. 2

0. 1

0 •HMBH^U . w'.iujuun.am^mm^.
! _iii i Rectangula r

duc t j K = J. 0 p o 

## I i n

i IIIIIII I i iiiiiii i 

## j i i m m J 

## I MM M 0.0 1 0 . 1 1. 0 1 0 10 0 (1 . • lj,) F Figur e 5-13 . Char t t o obtai n penetratio n fo r rectangula r duc t1. 0

o o C Q

+ J % 0. 8

0. 6

0. 4 -

0 . 2

0 0.0 1 0. 1 1. 0 1 0
Figur e 5-14 . Char t t o obtai n penetratio n fo r rectangula r duc t 

# I I l. l Mi '

10 0o

o 2. 0

1. 8 1. 6 - 1. 4

« 1. 2
D w 1. 0

^0. 8 0 . 6 0 . 4 

### 0. 2 0 i

—rnrrTTTT RcctanguJa r

duc t --3-"""TTM7'*"s"T"*"l"T ' 1 ! I ili l

0.0 1 

### L . > ' i

i i I i Ji.~^--JL^i~.JjJLJjJjLj L o. i i. o (L+L H ) F 1 0 10 0 Figur e 5-15 . Char t t o obtai n penetratio n fo r rectangula r duc tPQ 2. 4

2. 2 2. 0 - 1. 8 - 1. 6 - 1. 4 1. 2 OO D H

c r H U H 1. 0 0 . 8 0 . 6 0. 4 - 0 . 2
0.0 1 0. 1 1 . 0 (L+Ij, j F 1 0 10 0 Figur e 5-16 . Char t t o obtai n penetratio n fo r rectangula r bed ,P. 6

U 

### F

# rl

, : ^ u d

G u, = 0

£, , • * . u G= U G o

. U, = u , d d o

Figur e 5-1.7 . Concep t o f a hypothetica l sectio nP. 7

I f w e adjus t th e lengt ho f th e imaginar ysectio n i n suc ha wa ys o tha t th e liqui d dro p velocit ya t th e inle t o f th e imaginar ydivergen t sectio n i s zero , the n "Ptp prn " an d "Ptpp BA " ca n b e obtaine d fromFigur e 5- 3 throug h5-1 6 an d penetratio n fo r th e rea l sectio n ca n b e calculate d from equatio n 5 - 35 . . Th e lengt ho f th e imaginar ysectio n "£,," , ca n b e deter
mine d b

yintegratin g equatio n 5- 2 wit hth e followin g boundar y conditions : a t z = 0 , u j = u 

### do z = -£ H , u d= 0 Figure s 5-1 8 and 5-1 9 ar e th e result s o f th e integra
tio n fo r a circula r duc t and a rectangula r duc t respectively . "L H " i s th e dimensionles s counterpar t o f '*£„ " and i s define d by , £ 

### H



### L

I n calculatin g "Ptpp~ n " and " P1: PFBA" ' ^• t * s necessar y t o us e th e ga s and liqui d parameter s a t th e inle t o f th e imaginar yadde d o n section , i.e. , a t z = -P,„ . Fromth e geometr y o f th e duct , parameter s a t z= -ly, ar e relate d t o th e know n parameter s a t z=0 , i.e. , a t th e inle t o f th e rea l duct , b y th e followin g equations ,

L ' = ( L + L H ) (1-SL H ) - l/ 2 (5-57 ) S ' = S (l.-SL H ) ~J / 2 _ 1 (5-38 )
u * ' = u * (l-SL H ) j • (5-39 )



### 8 910 0

o C M O

1. 0

0 . 1 0 . 7 5 1. 0 1 . 2 5
.1 . 5 'd o Figur e5-18 . Cliar t fo r obtainin g I, fo r acircula r

due lP. 9

U -a rc r H 3 o o C o i u o

o

oa c •r- i c • H ro +- > O i- H o

r ro U

L O o * 1 1 t- M t•I I

O P/ H 

### W" j 3 *

9 1P.1 0

and B'" = B(1-SL H )"J / 2 '""(5-40 ) wher e prim e ('• ) refer s t o z = -£,, . Detaile d derivatio n o f thes e equation s i s give n i n Appendi xA . SAMPL E CALCULATIO N T o illustrat e th e applicatio n o f thes e figure s t o predic t th e performanc e o f a ventur i scrubber , w e wil l calculat e th e pressur e dro p an

d particulat e collectio n fo r th e ventur i scrubbe r shown i n Figur e 5-20 . IV e wil l predic t it s perfor
manc e fo r th e followin g operatin g conditions : Q G= 80 0 Am 3 /mi n Q L /Q G= 1.3 3 £/m 3 Ga s temperatur e = 20° C Particl e Collectio n Convergen t Sectio n - Wate r i s injecte d a t th e star t o f th e throat . Therefore , ther e i s n o particl e collectio n i n th e convergen t section . Throa t Sectio n - Th e wate r i s assume d t o b e injecte d wit h n o axia l momentu ms o tha t "u , " i s equa l t o zero . Th e ga s velocit ya t th e inle t o f th e throa t i s calculate d t o b e 8,06 0 cm/sec . Thus , th e dro p diamete r accordin g t o Nukivam a and Tanasaw a is : 5 0 / Q L d , = — + 91. 8 — 

### dU 

# GK

= 0-01 0 7 c

m Dro p Reynold s numbe r



## _d 

## d]V u 

## do | 1. 5

N Re, o 0.010 7 (8060-0 ) = 57 5

0.1 5 9 2

### LIQUI D INLE T

Breadt h= 81. 3 c

m Figur e 5-20 . Ventur i scrubbe r fo r sampl e calculation ,P.1 2

Fro mStandar d curve , o r fromequatio n (5-8) :

JD o = 0.2 2 +

0.2 2 + 2 4

N Re, o 24 ( 1 + 0.1 5 N°- 6)

vRe,o ^
57 5 1 + (0.15)(575 ) 0. 6

= 0.54 5 1 IC - /p„\/U „ "U j 3 t D o / r Gw G o d o 0. 5 

# 2d d

# w< 'C o

= 2.7 9 

### '\\( p 

### l u Go V X G / \0 / D o \G o do >

= 2.0 3 Fo r ventur i throat , S=0 . Sinc e u , =0 , w e hav e L, j = 0 J H an dF= l K u G o d p a=(8060 ) (IQ- 8 ) (d p a }

p o 9 u Gd d(9 ) (1. 8 xIO"" 4 ) (0.0107 )

= 4.6 5 d 2

p a o r d= (0.21 5 K

\°' 5 ym

A p a \p o

Rea d "- F I n Pt/B " fromFigure s 5-1 0 t o 5-1 6 fo r L=2.7 9 and S= 0 fo r variou s " K " , w e obtai n th e following : p o ' 6



### 9 4P.1 3



# V 0. 2 0. 5 0. 7 1 2 5 1 0 d „ , ymA

p a ' 0.2 1 0.3 3 0.3 9 0.4 6 0.6 6 1.0 4 1. 5 

### - F ln 

### Pt/ B

0.04 4 0.17 6 0.27 2 0.4 1 0.7 7 1. 3 1. 7 Pt( d ) vpa ' 0.9 1 0. 7 0.5 8 0.4 4 0.2 1 0.07 1 0.03 2 Divergen t Sectio n - A t th e exi t o f th e ventur i throat , th e dro p velocit yis :

u * F 2 = 0.7 8 (Figur e 5-2 ) i.e.,u d= (0.78 ) (8060 ) = 628 7 cm/ s u * = 0. 7 8 A t th e star t o f th e divergen t section , ga s an d dro p velocitie s ar e th e sam e a s a t th e throa t exit . Therefore , a t th e begin
nin g o f th e divergen t section :

u n= 806 0 cm/ s G o an d u , = 628 7 cm/ s d o Dro p Reynold s numbe r i s d d ( U Go" U d)

_

(0.0107 ) (806 0 - 6287 ) 'R e , o 0.1 5

= 12 6

Fro mStandar d curv e o r b yequatio n (5-8 )

9 5P. M

C n= 0.9 3 Do S 2

_ta n 3 R d dP L 0. 5 u Go C nP „ \u r

-u . Do GxG

o d o

= 0.17 7 3 zS o ^ G/ U Go' U d o 2d dP L' U G o 0. 5

12. 5 l\' e nee d "L,_/ ' whic hca n b e foun d byusin g Figur e 5-19 ,

u * •- = 2. 0
Therefore , L H= 2. 0(0.78) 2= 1. 2

L+ L H= 13. 7 F= 1 - SL H= 1 - 0.17 7 (1.2 ) =0.7 1 Thus , ( L+ L ? ] ) F

L H F
an dSF" 0

- 5

p o 10. 8 0.9 5 0 . 2 u r d2 Go p a 9 U Gd d 4.6 5 d2 p a

o r p a (0.21 5 K ) °' 5 um

A vp o 

# *.i%i°^ > Q-/\p r /

C, , \u „ -u , S G ' G ' D o \Go d o

u 0. 5 Go

= 2.5 4
9 6P.1 5

Rea d"- F I nPt/B " fro m Figure s 5-1 0 t o 5-1 4 a t SF-°- 5 =0. 2 an d ( L + L tI ) F=1 0 . 8 an d 0.95-fo r variou s K , w e obtain : I I po '

K P O 0. 2 0. 5 0. 7 1. 0 2. 0 5. 0 1 0 d,ym A p a ' 0.2 1 0 . 3 5 0.3 9 0.4 6 0.6 6 1.0 4 1. 5 (-

F l n Pt/B ) . 0.03 7 0.14 8 0.23 3 0.3 5 0.6 8 1.2 5 1.7 5 Pt( d )

P a L+L H 0.8 9 0.6 2 0.4 7 0.3 2 0.1 1 0.01 8 0.003 5 (-

F l n Pt/B )

L H 0.03 5 0.14 2 0.21 3 0.31 5 0.5 7 0.9 3 1.1 5 Pt( d ) 1

p a Lj . 0.8 9 0.6 3 0.5 0 0.3 6 0.1 6 0.0 5 0.02 5
Th e penetratio n fo r th e whol e ventur i scrubbe r i s calcu
late d wit hth e hel p o f equatio n (5-32) , i.e. , * Pt( d ) . « . Pt( d ) T T vpa ; throa t ^ pa' L + L 

### Pt( d 

### J = ^ pa ' Pt( d) T vpa ' L H H

d pa ,ym A1 0.2 1 ! P t 1 0.9 1 0.3 3 0.6 9 0.3 9

0.5 5 0.4 6

0.3 9 0.6 6

0.1 4 1.0 4

0.02 5 1. 5

0.004 5 Figur e 5-2 1 show s th e resul t o f thi s calculation . Fo r thi s particula r scrubbe r geometr yand operatin g conditions , the particl e collectio n i n th e divergen t sectio n contribute s littl e t o th e overal l scrubbe r collectio n efficienc ya s shown i n th e figure . Pressur e Dro p W e wil l us e bot hth e modifie d Calvert' s equatio n an d Boll' s equatio n t o predic t th e pressur e dro p o f th e sampl e ventur i scrubber . 9 7P.1 6



### 1. 0

%

<



### ~ 0. 1

Wr 

### u < a.



### 0.0 1 0. 1 

### I J I J l l 

### JIJ J

VENTUR I THROA

T ONLY

* - IIIIII I 

### J I I llll l

1. 0 PARTICL E DIAMETER , ym A 1 0

Figur e 5-21 . Predicte d grade efficiencycurve .

9 8P.1 7



### Modifie dCalvert' s Equatio n- Modifie dCalvert' s equatio nis :

A P = 1.0 3 xIO - 3 

### u * u 2 

### [ —) dG t\Q G / 

### Fo r th e presen t example , u r 

### =806 0 cm/ s b t 

### and{ —1 = 1.3 3 x10' 3 

### K- \ Q G 

### / Therefore , dro p diamete r byNukiyam a an dTanasawa :



### dU 

# G

# V

= 0.01 0 7 c m Dro p Reynold s numbe r
N

### _d 

### d( U 

### Go" u 

### do ) Re, o v 

### 0.010 7 (8060-0 ) _rnr 

### 0 .1. 5 Fro mStandar dcurve , o r fro mequatio n(5-8) :

C D o 

### - 0.54 5

3 £ 

### t S o P GA

### - an dx= + 1

1 6 d d

### p L



### = 1.3 5

* - ? u 

### d" 2 

### 1 - x 2 

### - (x 1 

### * + x 2 

### ) 0



### - 5



### = 0.8 0 9 9P.1 8

Therefore , pressur e dro p is :

A P = (1.03xl0" 3 )(0.80)(8060) 2 (1.33xl0" 3 )

= 71. 5 c i W.C . Boll' s Equatio n - Th e procedur e t o calculat e th e pressur e dro p usin g Boll' s equatio n i s t o calculat e wal l frictio n los s an d acceleratio n los s separately . Th e su mo f th e tw o losse s i s th e tota l pressur e drop . (1 ) Convergen t sectio n A . Wal l frictio n

= ( M+ 1) F F 1 wd * w

h o f = 0.02 7

wA2 r 1 +

an d A r = R*(A r -l)(l+b*+R* )

2(b * + R* ) exi t cross-sectiona l are a inle t cross-sectiona l are a A t th e convergen t sectio n inle t Go 

### M I 

### b R = = =

- = 2 50 0 cm / 0 6 2 c m 81. 3 c m (0.5 ) (6 5 2b( R+ I • 4 ) =

tan -- 3 2 

### 6 ) . 7 c

m
h ° b+ R+ £ ta n6 (2)(81.3 ) 32. 7 + (62 ) ta n 20 ' 81. 3 + 32. 7 + (62 ) ta n 20 °

= 6 5. 8 c m (5-15 )

10 0P.1 9

B yth e definitio n o f dimensionles s parameters , w e hav e

R * = h o A= 81. 3 6 2 32. 7 6 2 65. 8 6 2 1.3 1 0.52 7 1.0 6 (81.3)(20.3 ) (81.3 ) (65.4 ) = 0.3 1 Therefor e ,

F w 1 1 + 0.527(0.31-1)(1+1.31+0.527 ) (0.31) 2 2(1.31+0.527 )

= 7.4 8

> * = w AP 

## w c PG 

## " G 

## ° - (0.027H7.48 ) = Q i g 1.0 6
A p w (0.19)(1.2xl0~ 3 )(2500) 2

(2)(980 )

= 0. 7 3 cm

W.C . B . Acceleratio n los s Ther e i s n o wate r i n thi s section , therefor e acceleratio n los s i s zero , i.e. ,

Ap , = 0 Tota l pressur e dro p i n convergen t sectio n

A p = A p + A p , = 0.7 3 cmW.C ,

10 1P.2 0

2 ) Throa t sectio n A . Wal l los s A t th e throa t inle t

and G

o b R 6 h o M =
= = = =

_ 806 0cm/ . 8 1 ( 0 0 1 8 

### ^L 3 c m 5 ) (2 0 1 c m !i d= se c

• 3 ) =

1 .33 : 1 0

vcl. 0• 2

- 3 c m

= Q P P , 1.2x1 0 - 3

I * = 18 ' 1 h o 30. 5 0.59 3
A r = 1 F w= 1 Therefore ,

and > * =

w AP = (1. 1 + 1 ) (0.027 )

0.59 3 0.095 6 (0.0956)(1.2xlQ- 3 )(8060) 2

(2)(980 ) 3. 8 c mW.C . B . Acceleratio n los s FromNukiyam a and Tanasaw a correlation , u e hav e d , = 0.010 7 c

m d u , = 0 d o Dro p Reynold s numbe r d d( U Go~ u do ) _(0.0107 ) (8060-0 ) N R e , o 0.1 5 57 5 10 2P.2 1

Fromequatio n (5-8) : 2 4 C D Q= 0.2 2 + ^£ 1 ( 1 + (0.15)(575) 0

- 6 ) 0.54 5 2 d . 3 £ ^D o /^G\/ U Go" U d o 0. 5 U Go

= 2.7 9 Fo r ventur i throat , 6=0 , S=0 , F=l . FromFigur e 5-4 , w e obtain :

M = 1. 6 Sinc e p AP ,

* - fo r (L+L H ) F = 2.7 9

, Av e hav e

AP , 2 g P G U G o

5 c 1.6 M P G U G o 2 g F 2 s c

= (1.6)(1.1)(1.2xlQ- 3 )(8060) 2

(2)(980 )

= 7 0 cm

W.C . Therefore , tota l pressur e dro p i n ventur i throa t

A p = /d p + Ap , = 2.7 9 + 7 0 w

= 7 2.7 9 cm

W.C ,

10 3P.2 2

(5 ) Divergen t Sectio n A . Wal l los s A t divergen t sectio ninle t 'Go b R M I 805 0 cm/ s 81. 3 cm/ s (0.5)(20.3 ) 7.5 ° 1. 1 17 1 c m = 10. 2 c m

. = 2 b( R+ I

ta n B ) h o b+ R+ I

ta n 6 (2)(81.3 ) [10. 2 + (171 ) ta n 7.5 ° 81. 3 + 10. 2 + (171 ) ta n 7.5 °


### d f h o 46. 7 c m d h o 46. 7 17 1 = 0.27 3 (81.5)(65.4 ) (81.3)(20.3 ) 3.2 2
R10. 2 

### b 17 1 81. : 17 1 0.0 6

= 0.47 5

and

. 22 2 1 + 0.06(5.22-1 ) (1+0.0 6 + 0.475 ) 2(0.475+0.06 ) 0.11 5

w = (1. 1 + D (0.027 ) ( 0 .115 ) = Q
_ 0 2 5

0.27 3

10 4P.23 ^

A P w Sinc e pf . = —, w e hav e



## Ii ~ P 

## Gu 

## G o to c A= (0.025)(1.2xl0' 3 ) (8060) 2 ? w(2)(980 )

= 0.9 9 c

m W.C . . B . Acceleratio n los s I n th e divergen t section , liqui d dro p diamete r i s th e sam e a s i n th e throat , i.e. , dj=0.010 7 cm . A t th e divergen t sec tio n inlet , dro p velocit yi s equa l t o th e velocit ya t th e throa t exit . Fro m Figur e 5-2 , w e obtain : u^F 2 = 0.7 8 fo r (L+L H ) F = 2.7 9 and SF-° S = 0 .* . u , = (0.78 ) (8060 ) d o ^ ' v

= 6 28 7 cm/ s u = 806 0 cm/ s G o Dro p Reynold s numbe r

d 

### d( U 

### Go" u 

### do ) N Re, o (0.0107 ) (8060-6287 ) = U6

0.1 5 Usin g equatio n 5-8 , w e obtai n C n=0.9 3

s = 2 ta n 6 d d P L. / U G o D o 0. 5 3 RCp . P r \u

_-u .

D o G\ Go d o

= 0.17 7


### 10 5P.2 4

L = C. . p„ / u„ -u , £ „ D o K G/ G o d o 0. 5

d d P L u, .

Go

= 12. 5 Fro mFigur e 5-19 , w e obtain : 

### L H 2. 0 u : Therefore , L H= 2. 0(0.78) 2= 1. 2

L+ L H= 13. 7 F= 1 - SL H= 1 - 0.17 7 (1.2 ) = 0.7 ! Thus , ( L+ L { I ) F=10. .

L H F=0.9 5
a n dSF" 0

- 5 = ( 0.177 ) (0-788 ) " °' 5 = 0.19 9 Fro mFigur e 5-4 , w e obtai n 'p * F 2 ^ 

## y M = 1. 0 L + L T 

## 'pa F 

## " v M 

### I = i. i J 

### H 

# (n) L + L 

### H = ri.o)(i.i )

C O . 788) 2 = 1.7 7



### 10 6P.2 5

(p* \ = (1,1 ) (1,1 ) = 1.9 5 ^ d > L (0.788) 2 

### H 

## (PS) L

## - (P3) LtL u

## - (P3 ) = -0.17 9

H L H 

### Ap * Sinc e p* ; = , w e hav e

d1 .. . 2 2 g GG o 6 c Ap * = (0.179)(1.2xl0- 3 )(8060) 2 d(2 ) (980 )

= - 7. 1 cm

W.C . Negativ e pressur e dro p i s equivalen t t o pressur e recover yby th e gas . Tota l pressur e dro p i n th e divergen t sectio n i s the n equa l to :

A p = 0.9 9 - 7. 1 = -6.1 1 cmW.C . Th e pressur e dro p fo r th e whol e ventur i scrubbe r i s equa l t o th e su

mo f convergent , throa t and divergen t sectio n loss . A p (overall ) = 0.7 3 + 72.7 9 - 6.1 1

= 6 7. 4 cmW.C . Th e differenc e i n prediction s b yth e modifie d Calvert' s equatio n and b

yBoll' s equatio n i s 4. 1 cmW.C . However , th e modifie d Calvert' s equatio n i s simple r t o us e a s prove n b y thi s calculatio n example . PARTICL E COLLECTIO NINTH E VENTUR I THROAT Fo r a ventur i scrubber , mos t o f th e particl e collectio n actio n occur s i n th e throa t sectio n wher e th e relativ e velo
cit ybetwee n particle s and drop s i s highest . Thus , i t woul d b e desirabl e t o obtai n an expressio n fo r particl e collectio n i n a ventur i throat . 10 7P.2 6



### Fo r particl e collectio n ina ventur i throat , equatio n (5-23 ) reduce s to :

^ Pt(d p 

### ) B 1 - u '

u ' 0. 7 K p o dz * (5-41 )
Equatio n (5-24 ) fo r liqui d dro p velocitybecomes : 

### d u 

# 5 dz * 

# (^a) 1 

# -

2 U 

### * a (5-42 )
We wil l solve thes e tw o equation s for th

e specia l cas e u 5 =0 , i.e. , initia l liqui d dro p velocit yi s zero . B y rearranging equatio n (5-42) , we have :

d z * = 

### 2u *

^ u 

### d du * 

## (i.»3) " d B ysubstituting equatio n(5-45 ) int o (5-41) , we obtain : 

## 1 

# j^i$_\. l

# ['i

# c-»tr 1 - u * + 0.7 \ d 

### d

# F~ p o (5-43 )

(5-44 )
The close d for

msolution s t o equation s (5-44 ) an d (5-42 ) are : 1*Pt ( d p ) l B K. . . /1-u * + 0. 7

p o d K

p o 

### 4

# Soi 1 

# ^) 1 

# '5+ 4 

# - 2 

# ( 1 

# - u 

# J)°' 5

5.0 2K

0 ' P
K p o vp o / 

## I-TTTTJ 4K

P

## o + 4 

## ' p o 2- 5.0 2Ku ' b1 + rr p o \K r0. 5 / - . . 0 

### po /

J (5- 4 5 ) 10 8P.2 7



### an d 

### u * =

= 2 Cx * - x 2 ) (5-46 )
wher e x= 5 l



## t 

## S o P 

## G 1 6 d dp L + 1 = £ ( L + 8 ) (5-47 )



### p o d p a U G t

9 ^ G d d (5-48 )
(5-49 ) I = ventur i throa t length , c m C n= dra g coefficien t fo r drop s a t th e ventur i throa t inlet , dimensionles s "C ^ " i s a functio n o f dro p Reynold s numbe r and i s obtaine d fro m"Standar d Curve. " Dro p Reynold s numbe r i s define d as : 

### N d d U G t Re, d (5-50 )



### v Fo r an infinit e lengt hventur i throat , u | approache s unit y an d equatio n (5-45 ) reduce s to :
P t ( d ) = ex

p 4 K +4.2-5.02K 0

- 5 

### BP ° E2 . \ po / V 0. 7 c 5
_ 5 1 K n+ 0. 7 p o (5-51 ) Equation s (5-45 ) and (5-51 ) wer e use d t o predic t th e particl e collectio n fo r th e ventur i scrubbe r mentione d i n th e las t section . Figur e (5-22 ) show s th e calculatio n result s alon g wit hth e grad e efficienc ycurv e obtaine d i n th e las t section . A s ca n b e seen , ther e i s littl e differenc e betwee n th e thre e curves . Fo r thi s particula r scrubbe r geometry , w e can assum e tha t th e ventur i throa t i s o f infinit e lengt han d it s particl e .collectio n i s tha t predicte d b yequatio n (5-51) . 

### 10 9P.2 8

1. 0

< 0 . 1

- J

0.0 1 0. 1 

## .U^fe4aM : 

## .-f ;! 

## *: y ! I »J, l Iij ,

- - *t- t-

- > ' 

### i i I I iii i i. o PARTICLEDIAMETER , ym A 

### 1 0

Figur e 5-22 . Predicte d grad e efficiencycurve .

11 0P.2 9

PARTICL E COLLECTIO NB Y.DIFFUSION I n al l previou s developments , particl e collectio n by impactio n i s assume d t o b e th e onl ycollectio n phenomeno n occurrin g i n a ventur i scrubber . Thi s assumptio n i s tru e fo r particle s wit hdiameter s large r tha n 0. 5 micron . Particle s smalle r tha n 0. 1 y mi n diamete r ar e rarely
collecte d b

yinertia l impaction , becaus e the yfollo wth e ga s streamline s surroundin g th e liqui d drops . Fo r particle s i n thi s siz e range , diffusiona l collectio n i s usuall yth e pre dominan t collectio n phenomenon . I n th e followin g sections , we wil l deriv e a n expressio n fo r th e predictio n o f particl e collectio n b

ydiffusio n i n a ventur i scrubber . Again , w e wil l us e Calvert' s differentia l equatio n a s ou r startin g equation . Hi s equatio n is :



### d £ 

### d 

## l.slV^d i

U d d d N



### w n d z (5-52 )
wher e c

U G 

### u , Q r particl e concentration , g/cm 3 ga s velocity , cm/ s dro p velocity , cm/ s liqui d flo wrate , cm 3 / s ga s flo wrate , cm 3 / s singl e dro p collectio n efficiency , dimensionles s Accordin g t o Johnston e and Robert s (19 4 9) , singl e dro p diffusiona l collectio n efficienc yi s give n b yth e followin g equation : 4 D " /v r .- , = 2

_2 + 0.55 2 (N D 0

- 5 ) - ^ 

## hr u 

## di d 

## d[ ( Re

## > P (5- 5 wher e D 

### N P R e 'X rm particl e diffusivity , cm 2 / s dro p Reynold s number , dimensionles s kinemati c viscosit yo f gas , cm 2 / s



### 11 1B yusin g th e sam e dimensionles s parameter s define d earlie r (equation s (5-16) , (5-17) , (5-20 ) and (5-22 ) w e hav e 4 D n = 2 + 0.55 2 u 

### G o 'G o ' u d o 0. 5 i^rM



### NRe, o \^CC ( 1 + Sz*) ^ - u * d G o ( l + Sz*)~ J- u * (5-54 )

and - ^

c wher e B 4 B D

P 1 u G o d d u d (Q,,\P^ (l+Sz*)~ J - u * 0. 5
0. 5 U 

### G o C ^ \Q r /p

_\u, ~ - u , Do \ X G / G xG o d o



### u 0.55 2 4 B D 

### G

o 0. 5

u Go" u do , le t B 

### D Go d 

### N 0. 5 / C \ Re, o I D 

### dz ; (5-5 5
(5-56 ) (5-57 ) (5-58 )

w e hav e d c D / + E (1+Sz*)" 3 - u j 0. 5 

### dz : (5-59 ) Upo n integration , w e obtain :



# L A InPt, , - I 2dz * 

### P

### c* o u 5 Cl+Sz*J J - u* 10 * 5 

### dz ; (5-60 )
Equatio n (5-60 ) i s th e fina l equatio n describin g th e par ticl e collectio n b ydiffusio n i n a ventur i scrubber . Plot s simila r t o Figure s 5- 1 throug h5-1 0 ca n b e constructed .



### 11 2P.3 1

Fo r ventur i throa t (S=0 ) and fo r th e specia l cas e tha t initia l dro p velocit yi s zer o (u* j =0 ) , th e analytica l solu
tio n t o equatio n (5-60 ) is : InP t B D (d p )=8+2 E ln(l-uj ) 

### 8



# V ^ (5-6 1 )



### 11 3P.3 2

CHAPTE R6 COMPARIN GMODE L PREDICTION S WIT H PERFORMANC E DATA Ther e ar e numerou s ventur i scrubbe r performanc e dat a scattere d i n literature . However, ' mos t o f thes e dat a ar e o f littl e us e i n mode l compariso n becaus e eithe r scrubbe r geometr yinformatio n o r particl e informa
tion , e.g . siz e distributio n an d loadin g ar e no t availabl e I n th e followin g sections , onl ythos e dat a wit hwel l de
fine d scrubbe r geometr yand particl e parameter s wil l b e compare d wit hth e mathematica l model . Dat a b yCalvert , e t a l Calvert , e t a l (1975 ) measure d th e performanc e o f a n America n Ai r Filte r Kinpacto r 3 2 ventur i scrubber . Th e scrubbe r i s use d t o contro l th e emissio n froman asphal t aggregate s dryer . Th e scrubbe r operatin g condition s durin g th e tes t wer e a s follows : 1 . Ga s flo wrate s wer e a s shown i n th e tabulatio n below .

Ga s Parameter s Temperatur e Pressur e durin g p i to t run s Actua l m 3 /mi n ACF M D S m 3 /mi n DSCF M Vo l %H 2 0 vapo r Inle t Duc t 149° C +73. 5 c

mW.C . 79 9 28,20 0 42 9 16,30 0 2 1 Ou t

Scrubbe r Outle t Duc t 57° C + 0. 5 c m\iX.

_

- 1 3 e t Chimney

49° C +0.0 2 c

mW.C . 67 0 2 5,70 0 50 0 19,00 0 11. 8 !



### 11 4P.3 3

2 . Wate r flo wrat e t o th e ventur i scrubbe r wa s re porte d b

yth e plan t a s approximatel y1.0 6 m 3 /mi n (28 0 GPM) . Wate r temperature s wer e 32° C (90°F ) an d 63° C (145°F ) fo r th e inle t and outle t streams , respectively . Th e performanc e predicte d b yequatio n 5-2 5 i s compare d wit hexperimenta l measurement s i n Figur e 6-1 . Th e predictio n agree s wit hth e averag e o f th e measurements . Prediction s b

yCalvert' s equatio n fo r ventur i scrubbe r ar e shown i n Figur e 6-2 . A s ca n b e seen , th e experimenta l result s li e betwee n prediction s fo r f = 0.2 5 and 0.5 . A"f " valu e o f f = 0. 4 wil l giv e bette r fi t betwee n Calvert' s mode l an

d dat a tha n othe r value s o f "f" . Brin k and Contant' s Dat a Brin k and Contan t (1958 ) obtaine d performanc e dat a o n a Pease-Anthonyventur i scrubbe r installe d i n a phos
phori c aci d plant . Th e dimension s o f th e scrubbe r ar e shown i n Figur e 4
- 8 . Brin k an d Contan t gav e a grad e effi
cienc ycurv e fo r th e followin g scrubbe r operatin g conditions : 1 ) Throa t velocit yo f gas : 66. 4 m/se c (21 8 ft/sec) . 2 ) Liqui d flo wrate : 75 7 £/mi n (20 0 GPM) . Figur e 6- 3 show s th e mode l prediction s fo r (1 ) par ticl e collectio n occurrin g i n th e ventur i throat , (2 ) combine d particl e collectio n i n ventur i throa t and di
vergen t section , (3 ) particl e collectio n occurrin g i n th e ventur i throa t an d th e throa t i s o f infinit e length . Th e particl e diameter s give n b yBrin k and Contan t ar e actua l size . However , aerodynami c particl e diamete r i s use d in th e mathematica l model . Aerodynami c particl e diamete r i s relate d t o actua l diamete r b yth e followin g expres s ion :



### 11 5P.3 4

1 . Q 

# r T1— t 1 M i i I

<

< 

### 0. 1

d J



### 0.0 1 Experimenta l dat a

Predicte d b

y Equatio n5-2 3 an d b yinfinit e throa t mode l l l » » I I

» I I 

### . \ i

## M P o . 1 1. 0

PARTICL E DIAMETER , ym A 1 0 i^ur e 6-1 . Experimenta l an d predicte d performanc e o f AAF Kinpacto r 3 2 Ventur i scru bber .

116P.3 5



### 1, 0



### o l— l r O. l

H W

C J <


### 0.0 1 0. 1 1, 0 1 0 PARTICL E DIAMETER , ym A Figur e 6-2 . Experimenta l an d predicte d performanc e fo r AAF Kinpacto r 3 2 ventur i scrubber .

11 7P.3 6



### 1. 0

c 2
2 C < H W Z U J C t u J C J l— l C K < 

### 0. 1 Predicte d fo r

ventur i throa t wit hinfinit e throa t lengt h

0.0 1 

## T — I » I ! \X

Brin k § Contan t dat a

Predicte d fo r

ventur i throa t onl y Predicte d overal l 

### JIllll l 0. 1 1. 0 PARTICL EDIAMETER , ym A 

### 1 0

F i gur e 6- 5 Predicte d and experimenta l penetratio n

fo r ventur i scrubbe r use d b yBrin k an d Contant .



### 11 8P.3 7

d = d / p C'\0 ' 5 (6-1 ) p a p \ M p / vJ where : d = aerodynami c particl e diameter , ym A p a J

r ' d = actua l particl e diameter , y m p = particl e density , g/cm 3 C ' = Cunningha msli p factor , dimensionles s Aerodynami c diamete r wa s transforme d t o actua l dia
mete r base d o n equatio n 6-1 . Aparticl e densit yo f 2. 6 (fo r MgP 2 0 5 ) wa s assume d i n th e calculation . A s ca n b e seen , th e experimenta l dat a hav e a highe r penetratio n tha n predicted . Thi s discrepanc yprobabl yi s cause d b

ynon-unifor mlicjuid^drop distributio n a s mentioned . b yBol l (1973) . Fo r thi s particula r ventur i scrubber , th e predictio n base d o n infinit e throa t lengt hassumptio n i s clos e t o th e predictio n fo r th e actua l scrubber . Dat a b yCalver t e t a l Calver t e t a l (1974 ) measure d th e performanc e o f a Chemic o ventur i scrubbe r operatin g o n th e flu e ga s fro m a coa l fire d utilit yboiler . Th e scrubbe r migh t mor e accuratel yb e describe d a s a variabl e annula r orific e typ e becaus e .it s throa t i s forme d b ya movabl e "plum b bob " concentricall ymounte d i n a conica l "denta l bowl. " Th e scrubbe r operatin g condition s durin g th e tes t perio d wer e a s follows : 1 . Ga' 3 flo wrate s wer e a s shown i n th e tabulatio n belo wan

d o n th e followin g page : Duc t Inle t Outle t Temperatur e 16 3 . 0°C(325°F ) 5 4 . 0°C(130°F ) Pressur e durin g pito t run 60. 0 cmH g 60. 0 cmH g Am 3 /mi n 13,40 0 12,70 0 ACF M4.75x10 s 4.5xl0 5 D Nm 3 /mi n 6,30 0 7,15 0

11 9P.3 8

Duc t Inle t Outle t DSCF M2.4x10 5 2.7x10 5 %H 2 0 vapo r (vol. ) 6.0 % 15.0 % Th e flo wmeasure d b yth e outle t velocit ytravers e i s judge d t o b e mor e reliabl e becaus e th e velocit ydis
tributio n wa s muc hmor e regula r tha n a t th e inlet . Base d o n 7,12 0 DNm 3 /mi n (2.7x10 5 DSCFM) , th e inle t flo wrat e woul d b e 15,30 0 Am 3 /mi n (5.4x10 5 ACFM) , whic hi s %%highe r tha n th e desig n flo wrat e o f 14,20 0 Am 3 /mi n (5xl0 5 ACFM) . 2 . Slurr yflo wrat e t o th e scrubbe r wa s reporte d b y th e plan t a s approximatel y24. 6 m 3 /mi n (6,50 0 GPM) . Sinc e th e throa t lengt hand divergen t angl e fo r thi s scrubbe r wer e unknown , w e wil l assum e tha t i t i s equiva
len t t o th e ventur i throa t o f infinit e length . Th e throa t velocit yo f th e ga s wa s calculate d t o b e 4 2 m/se c and th e liqui d t o ga s rati o wa s 1.7 5 £/m 3 . Figur e 6- 4 show s th e mode l predictio n alon g wit hexperimenta l data . Th e agree men t betwee n th e two i s reasonabl ywell . Figur e 6- 5 com pare s dat a wit hprediction s b yCalvert' s equatio n fo r ventur i scrubber . Avalu e o f 0. 5 fo r th e empirica l constan t wil l mak e th e mode l agre e wit hdata . Dat a b yCalver t e t a l Calver t e t a l (1976 ) reporte d th e performanc e tes t conducte d o n an AP S electrostati c scrubber . Whe n th e charg e insid e th e scrubbe r i s turne d off , th e electro
stati c scrubbe r become s a ventur i scrubber . Th e dimension s o f th e scrubbe r ar e shown i n Figur e 6-6 . Th e measure d per formanc e o f th e scrubbe r i s shown in Figur e 6- 7 alon g wit h prediction s b

yequatio n 5-2 3 and b yCalvert' s equatio n fo r f = 0.2 5 and f = 0.5 . Th e scrubbe r operatin g conditio n was : 1 . Q L /Q G= 1- 4 l/m* 2 . Q r = 2 1 Am 3 /mi n

12 0P.3 9

1 . 0



### 5 

### 0. 1

C U
c

0.0 1 T 1 1 IIM»

Predicte d Experimenta l' dat ai 

### I Ilillll l JI» iiiir 

### o. i 1. 0

PARTICL EDIAMETER , ymA 1 0 Figur e 6-4 . Predicte d and measure d penetratio nfo r

Chemic o ventur i scrubber .

12. 1P.4 0



### 1 . 0 

### ! ij-.r_.rgs L

<


### o Calvert' s

equation , f

-0. 1 2 U J 

### u t- H H P S <



### 0.0 1 0. 1 I Ll . I 1. 0 PARTICL E DIAMETER , ym A 1 0 Figur e 6- 5 Predicte d an d experimenta l grade efficiency curve fo r Chemic o ventur i scrubber .

12 2t- o CA I -eL O 

### LIQUI D INLE T

T-J. — -I- + 

# k 30.5 " c m \ 

### A \

. \ ) 

## t -eh O •e o u r 1 _J L 

### 15.2f p 36. 8 cm— ^ c m

Figur e 6- 6 - AP S Electrostati c Scrubbe rP.4 2

1. 0

o C J

<

« 0. 1

0.0 1 

## TTT

Experimenta l Dat a



### I I I I llll l fo r in
finit ethroa t lengt h 

## I I I IM I o. i 1. 0

PARTICL E DIAMETER , ym A 1 0 Figur e 6-7 . Experimenta l an d predicte d AP S ventur i scrubbe r performance .

12 4P.4 3



### A s ca nb e seen , i nsmal l particl e regions , neithe r mode l agree s wit hexperimenta l data . Th e model s predic t to o hig ha penetration . Betwee nth e tw o models , equatio n 5-2 3 give s a bette r predictio ntha nCalvert' s equation . Dat a b yCalver t e t a l Calver t e t a l (1974 ) obtaine dperformanc e dat a o n a nEnvironeerin g Venturi-ro dscrubbe r (Mode l A3 3 Hydro
Filter ) . Thi s devic e consist s primaril yo f severa l par alle l rod s whic har e positione di na duc t wit hsom e spac e betwee nth e rod s s o tha t ga s ca nflo wbetwee nthem . Wate r i s introduce dupstrea mfromth e ro dbe dandi s atomize db y th e ga s strea m

a s i t flow s betwee nth e rods . Strictl y speaking , thi s scrubbe r i s no t a ventur i scrubbe r bu t i s on e typ e o f ga s atomize dspra yscrubber . Th e scrubbe r wa s installe dt o contro l th e emissio n fro m a niro nmeltin g cupola . Th e scrubbe r operatin g con dition s durin g th e performanc e tes t run s were : 1 . Q L 

### /Q G

### = 2. 4 l/m 3 

### 2 . Ga s velocit yi nth e spac e betwee drod s wa s cal
culate dt o b e 19 6 m/ s Thi s scrubbe r operate s lik e a rectangula r fre e jet . Sinc e w e d o no t kno wth e expansio nangl e o f th e je t and th e tota l je t length , w e wil l assum e tha t th e scrubbe r operate s lik e a ventur i throa t wit hthroa t lengt hequa l t o fiv e time s andte ntime s th e je t width . Figur e 6- 8 show s th e calculatio nresult s alon g wit hexperimenta l data . Th e experimenta l dat a li e i nth e are a bounde db y th e curve s fo r throa t lengt hequa l t o fiv e time s andte n time s je t width . CONCLUSION S Base do nthes e comparisons , th e followin g conclusion s ca nb e drawn : 1 . I f th e ventur i scrubbe r geometr yi s wel l defined , the nth e mode l predictio nagree s wit hexperimenta l data . 12 5P.4 4

1. 0

O. l CJ < D S P- ,
< QX. t-m U J U J a , U J u ax. < C u 0.0 1 . .

0.00 1 

### I I I | | l 

### M 1— T

Predi c .infin i .lengt h



### Pred i lengt h time s J » IIIM I 

### i . J L o . i 0. 5 1. 0

PARTICL E DIAMETER , ym A 

### 5. 0 Figur e 6- 8 Predicte d and experimenta l performanc e

fo r ventur i ro d scrubber . 

### 12 6P.4 5

2 . liquatio

n 5-2 5 give s bette r prediction s tha n Cal
vert' s model . Anothe r advantag e o f equatio n 5-2 3 i s tha t i t contain s n o empirica l constants . However , Calvert' s mode l i s simple r t o us e tha n equatio n 5-23 . 3 . I f th e ventur i scrubbe r throa t lengt hi s long enoug h(dimensionles s throa t length , "L" , large r tha n 2) , the n th e scrubbe r performanc e ca n b e approximate d b yth e particl e collectio n occurrin g i n a straigh t tub e o f in
finit e length .



### 12 7P.4 6



### CHAPTE R7 DESIG NANALYSI S In thi s chapter , we wil l discus s the factor s tha t affec t the performanc e o f a ventur i scrubber , design techniques , an

d th e optimizatio no f th e ventur i scrubbe r design . Severa l factor s have a ninfluenc e on the per formanc e an

d th e designo f a ventur i scrubber . Som e o f thes e factor s are : 1 . Throa t lengt ho f the scrubbe r 2 . Throa t velocit yan d liquid-to-ga s rati o 3 . The siz e distributio no f th e particle s t o be collected . Effec t o f Inle t Particl e Siz e Distributio no nPerformanc e The overal l (integrated ) penetration , Pt" , o f an ydevic e o n a dus t o f an

ysiz e distributio nwil l b e W 

### w =

# w- f

vt 

# ( d

# p) dw 

# t 7 

# " 1 

# ) o wher e P t = overal l penetration , fractio n P t Id \ = penetratio no f particle s wit hdiamete r d W= tota l weigh t o f particle , g d w= particl e weigh t corresponding t o the interva l

d '(d ) o f particl e "size , g The numbe r an

d weigh t siz e distributio n dat a fo r mos t industria l particulat e emission s followth e log norma l law . Hence , the two wel l establishe d parameter s o f the log norma l la w la wadequatel ydescribe th e siz e distribution s o f particulat e matter . Thes e parameter s ar e th e geometri c mean weigh t dia
meter , " d " , an

d the geometri c standard deviation , "° g 

### " • The log-norma l particl e distributio n densityis :

12 8P.4 7



### d w 

## wc 

## d ( 

## mdp ) = f id 

### ? ) = 

### (2Trf-l na ex p l nd - l nd \ 2



## P E £ (2)°- 5 

### m g (7-2 ) Bycombinin g equation s 7- 1 and 7-2 , w e hav e 

## F t -ftt ( d ) f ( d ) d (lnd p 

## )

• / P t 

### ( d 

### p)/~ F 6X P

1 P/ (2TT ) ln a 

### lnd - lnd \ 2 

### P ' P M
, ,0. 5 

### (2 ) i n g 

## d(l

n d j (7-3 )
Fo r convenienc e w e wil l us e th e followin g transforma
tions . Let :

x= l nd - l n d 

## ER £ (2)°' 5 l n a 

### g dx= (2) 0 

### ' 5 

### d/l

n d\ ln a X 

### P / (7-4 ) (7-5 ) Equatio n7- 7 i n term s o f xwil l b e com e P t 

# =

# xhC P t

ex p (-x 2 ) d x (7-6 )


### Bysubstitutin g th e expressio nfo r P t (equatio n5-23 ) int o th e abov e equatio nan d performin g th e require dintegra
tion , w e canobtai nth e overal l penetratio nfo r th e whol e particl e population . Thi s integratio ni s tedious . Thus , th e followin g simplificatio ni s made :

12 9P.4 8



### Base d on th

e conclusio no f th

e las t chapter , the per formanc e o f a ventur i scrubbe r can be approximate d b ythe particl e collectio n occurring ina straigh t tube o f infi
nit e lengt hi f the dimensionles s throa t lengt hi s large r than 2 . Sinc e mos t industria l ventur i scrubber s have dimensionles s throa t lengt hbetwee n 2 an d 3 , w e wil l us e th e infinit e throa t lengt hmode l t o represen t the perfor
manc e o f th

e ventur i scrubber. . The penetratio nfo r th e ventur i scrubbe r i s thengive n b yequatio n 5-46 , i.e. , Pt(d p 

### ) ex

p 4 K + 4. 2 p o 5.0 2 K 0 

### ^

p o 1 + 

### 0. 7 ta

n 

# 5 - 0. 7 

### K 

# TM + 

# °- 7 p o (7-7 )
wher e Pt( d )

P = penetratio nfo r particle s wit hdiamete r d , fractio n B = dimensionles s liquid-to-ga s rati o paramete r

K 

### p o c G /\P G /

C D Q 

### = inertia lparamete r

= d2 

### u

G t

u u 

### d C Gt

Vr = 

### P _

P 9»Gd d 

### particl e diameter , c m liqui d dro

p diameter , c

m Cunningha

msli p factor , dimensionles s ga s throa t velocity , cm/ s particl e density , g/cm 3 

### liqui d density , g/cm 3 

### ga s density , g/cm 3 

### ga s viscosity , pois e

13 0P.4 9

Th e diamete r fo r whic hcollectio n efficienc yi s 50? . i s designate d cut . diamete r " d , i.e. , pa 5 o P t = 0. 5 whe n d = d

p pa s o I n term s o f cu t diameter , equatio n 7- 7 become s ln(0.5)=- B 4 Kr,< n+"4- 2- 5.0 2K°" 5 ( 1 + p^—\tan" 1
. PP5 ° ' K P 5 o / S K + 0. 7 p 5 0 p 5 0 

### 0. 7 (7-8 ) wher e " K " i s th e inertia l paramete r fo r d

Ps o r pa 5 0 and i s define d a s u r . d 2



## K = G



### } 

### P^ ° Ps o 9 y Gd d (7-9 ) B yrearrangin g equatio n7-8 , w eobtai n

B = l n(0.5 ) ( K + 0.7 ) vJ ps o _ 4 K + 4. 2- 5.0 2K c n( 1 + %^—\ tan" 1 p s o p s o IK / I K



### Jj£LL_ 10. 7 (7-10 )
Bysubstitutin g equatio n 7-1 0 int o equatio n 7-8 , w e hav e l n(0.5 ) (

K + 0.7 ) Pt( d) = ex p P 5 0 ( K + 0.7 ) ^p o J
4 K + 4. 2- 5.0 2K 0 ' 5 ( 1 + v p o p s o \ K 

## ° - 7 

## W > < £ £ 22.

0. 7 4K p5f l+4.2-5.0 2K- Q( 1 + ^ 0. 7 i 5 0 T T t a n 5 0 10. 7 (7-11 )

13 1P.5 0



### Fro mequatio n7-4 ,

d= dexp p a p g 0 . 5



### (2 1 xl na , Byusin g thi s expression , w e ge t fo r th e inertia l parameter , 2(2) 0



### - 5 

### xl na

v- i 

### u

_d 2 

### u

_d

_2 

### K= „ G t 

### P a 

### = G t p g ext p o " 9 u G

### d d

### \ 

### \~*d (7-12 )

= bKP g w h 0 . 5 

### er e b= ex

p (2(2 ) ' xl no K= P g G t p g 9^" ^ (7-12a ) Sinc e K / d\ 2 

### P s o _f pa 5 

### p \ p g vp g / le t Y= u 

### p a 5 0



### P g the nK= Y 2 

### K Ps o p g (7-13 ) Bysubstitutin g equation s 7-1 2 an d7-1 3 int o equatio n7-1 1 and afte r rearranging , w e get ,
Pt(d p 

### ) = exp 0.69 3 (Y 2 

### K+ 0.7 ) P g ( bK p g

### + 0.7 )
4 bK p g + 

### 4. 2 - 5.0 2 C 

### bK p g 

### )
- ( 1 + 

### ft^-jtan* 1
" " 

### 0. 7 b

K 

### _E& 0. 7
4 YK 

### p g + 4 

### " 2 

### " Pg

5.0 2 YK°' i [ l + J;, 7 

### Itan" 1



### -

Y^ K Pg Y 2 

### K

C£A 0. 7 (7-14 ) 13 2P.5 1



### B ysubstituting equatio n7-1 4 int o equatio n 7-6 , we have
P t a TrO.sJ 

### 0.69 3 (Y 2 

### K + 0.7 )

ex 

### P < " x 2 + 

### ( bK +0.7 ) P g 4 bK + 4. 2 - 5.0 2 ( bK ) 0 5 

### 1 P g Pg ' 

## n \ 

## i bK K 

## pg / ^ °' 7 

### 4 Y 2 

### K + 4. 2 P g 5 

### . 0 2 Y

### K - ( 1 + 

### ^ 7 

### P g ta n 7



### (7-15 ) 

### d x
Equatio n 7-1 5 i s th e fina l equatio n relating th e overal l penetratio n "Pt " t o inle t particl e siz e distribu
tion ( d , a ) an

d t o the inertia l paramete r fo r the mean v

### pg ' g J

v 

### particl e diamete r " K " . P g Figure s 7- 1 throug

h7- 3 ar e plot s o f "Pt " versu s ( d / d ) wit h" K " a s paramete r fo r variou s " a " values . * • paso ' pg ' pg *g Thes e plot s ar e exac t solution s o f equatio n7-15 , accounting fo r log-norma l particl e siz e distributio na s give nb y equatio n 7-2 . The overal l penetratio n ca nals o be determine d b yknow
in g th e siz e distributio nan d liquid-to-ga s mas s flo wrat e ratio . B

ysubstituting equation(7-12 ) int o equation(7-7) , w e obtain , Pt( d ) = ex

p - B 4 bK +4. 2

Pg bK p g 

### + 0. 7 5.0 2 ( bK pg 

### )-( 1 + „

(l+^tan" ^ \ Pg / W 

### p g + 

### 0. 7 (7-16 )

13 3P.5 2

1. 0

2 O

W UJ & , < Cr i UJ > o 0.0 5 r 4

0.0 2


### Figur e7- 1 Ventur i scrubbe r integrate d penetration ,

"Ft " versu s "d p50 /d p g " , wit h"K p g' a s parameter , " o =2.5 " F g



### 13 4P.5 3

< U J •z. U J 1. 0

0 .
0. 2 0 . 1 0.0 5
0.0 2
0 . 0 1 0.00 5
0.00 2 0 . 00 1 

# 1 iIIIM i 

# 1 IMUI , i)!l ' l)A'"l'. U2. 0 0.0 1 0.0 20.0 5 0. 1

d/d Pso / p g Figur e7-2 . Ventur iscrubbe r integrate dpenetration , P t versu s d,d

, wit hK

a s parameter , ^=5 .



### 135P.5 4

2 O t- H H < U J U J P M

> o 1. 0

0 . 5^JU:lis f
Q. 2 Q. 1 Q.Q 5
0.0 2 0-0 1 0.00 5 0.00 5 0.0 1 0.0 2 Q.Q 5 Q. l 0. 2 0. 5 1. 02. 0

P 5 0 / • P g Figur e7-3 . 

### Ventur i scrubbe r integrate d penetration ,

P t versu s d_

_/d„„ , wit hK a s parameter , sr o o =7.5 . g 

### Pso/ d 

### p g '

13 6P.5 5

Equatio n 7- 6 no wbecome s 4 bK P t - 1

T T 0 5 

### ex

p -x 2 

### B 

### P

g + 4. 2 bK 

### Pg + 0 

### 5. 0 

## K 

# p S + 

# °' 7 

# V

b

# w J



# °- 7J d

x (7-17 ) 

### P g 

### ^ Pg ' Figure s 7- 4 throug h7- 7 ar e th e solution s fo r equa tio n 7-17 . Throa t Lengt ho f th e Scrubbe r Fo r a ventur i scrubber , mos t o f th e particl e collec
tio n occur s i n th e ventur i throat . Fro mth e result s o f th e las t chapter , fo r a well-designe d scrubbe r ther e i s onl y a sligh t differenc e betwee n th e grad e efficienc ycurve s o f th e ventur i throa t and th e whol e venturi . Thus , i n th e follow
ing desig n analysis , w e wil l assum e tha t particl e collec
tio n onl yoccur s i n th e ventur i throat . Thi s approac hwil l giv e u s a conservativ e design . Fo r particl e collectio n i n a ventur i scrubber , th e collectio n efficienc yi s predicte d b yequation s (7-4 5 t o 7-47 ) Figur e 7- 8 show s th e graphica l formo f thi s equation . Thi s figur e applie s bot ht o th e circula r duc t and th e rec tangula r duct . Unde r a specifi c operatin g condition , th e performanc e o f th e ventur i scrubbe r depend s o n th e throa t lengt ha s reveale d byFigur e 7-8 . Th e longe r th e throat , th e mor e efficien t th e scrubber . Thi s dependenc e i s mor e profoun d fo r large r particles , i.e. , large r K . Thus , i n design
in g a ventur i scrubber , w e shoul d us e a lon g throat . How ever , w e shoul d no t us e a longe r throa t tha n necessar y becaus e th e pressur e dro p wil l increas e wit hincreasin g throa t length . Th e fina l choic e o f throa t lengt hshoul d b e a compromis e o f th e two . Aclos e inspectio n o f Fig
ur e 7- 8 reveal s tha t a dimensionles s throa t lengt ho f 2 t o 3 woul d b e sufficient . Furthe r increas e i n th e



### 13 7P.5 6



## o I — I E - < OX. E-<
C M

< U J > o 

### 0. 5

0. 1 -
0.0 5 "

0.0 1 -
0.0 5 -

0.00 1 

### 0. 5 Figur e 7- 4 'Pt " versu s

' a =2.5" . g •B " wit h" K 

### Pg a s parameter ,



### 13 8P.5 7



### 1. 0

0.0 1 

### 0. 5

: i"ur e 7-5 . "Pt " versu s "B " wit h" K " a s parameter ,

" a = 5 " ' g * "



### 13 9P.5 8

2 O <

< Q i U J > O 

### a , 

### 1. 0

0. 1
0.0 5

0.0 1 500 0 

### 0. 5 Figur e 7-6 . "Pt " versu s "B " wit h" X

"a „ = 7.5" . ] a s parameter ,



### 14 0P.5 9

0. 5

o L O rt Cnh 3 X3 o o 0. 1

0.0 5

0.0 1 0. 5 100 0 150 0 200 0

Figur e7- 7 pa5 0

P g versu s "B " wit h" K " a s paramete r
14 12. 0

C Q a. 1. 0

0. 8

0. 6

0. 4

0 . 2

0 0.0 1 

## 1 ) 1 1 

## IT

i i i !



### M ! •

- ' i i i i !

• ! !--i -- l 

### M l ! ; i ' ' I | ! •i 

### 4-h-l I I M IliJL

J ' i i i i ii ^ 10 0 

### Figur e7-8 . F.ffec t

o f throa t lengt ho

npenetration .

### dimensionles s throa t lengt hwil l increas e pressur e dro p wit hlittl e gai n in scrubbe r performanc e (Figur e 7-9) . I t i s possibl e t o predic t th e performanc e cu t diam
eter , " d " fro

mFigur e 7- 8 i f th e scrubbe r operating conditio n i s known . Figur e 7-1 0 i s a simplifie d plo t o f Figur e 7-8 . Fo r an industrial-siz e ventur i scrubber , "B " i s usuall ylarge r than1 . A s ca nbe seenfro

mFigur e 7-10 , the performanc e " K " i s almos t constan t fo r dimensionles s

Ps o throa t length , "L" , large r than2 , an d " K " become s a functio n o f "B " o r liquid-to-ga s mas s flow-rat e ratio . Fo r a ventur i scrubbe r wit hdimensionles s throa t lengt hbetwee n 2 an d 3 , th e correctio n facto r "u , " i n th e modifie d Calvert' s pressur e dro p equatio n i s approxi
matel yequa l t o 0.8 . therefore , th e expecte d pressur e dro p i s A P (c mW.C. ) = 8.2 4 x10"4u G

### (|^ ) l^ \ (7-18 ) Throa t Velocit yan

d Liquid-to-Ga s Rati o The principa l collectio n mechanis moccurring in a ven tur i scrubbe r i s th e collection , b

ydrops . I t i s a know n fac t tha t the targe t efficiencyo f a dro p increase s b

y decreasing the diamete r an d increasing th

e relative velo
citybetwee n the ga s an d the drop . However , smalle r drop s accelerat e faste r tha ndo bigge r drop s wit hth e result s tha t th e relative velocit ygoe s t o zer o earlie r in th e cas e o f smalle r drops . Consequently , ther e exist s a n optimu

mdro p diamete r for particl e collection . Sinc e atomize d liqui d dro p diamete r i s a function o f ga s velocityan d liquid-to
ga s flo wratio , therefore , ther e exist s a noptimu

mcombina
tion o f throa t ga s velocit yan d liquid-to-ga s ratio . Figur e 7-1 1 show s th e theoretica l effec t o f throa t ga s velocit yan

d liquid-to-ga s flo wrat e rati o onth

e perfor
manc e cu t diamete r o f th e ventur i scrubber . Propertie s 1 4 3-1 ^

0.0 1 50 0 100 0 Figur e 7-9 . Effec t o f throa t lengt ho n performance ..0 0 5 0

1 0 5 —

0. 5

0 . I 0.0 5 50 0100 0

Ps o 

# (ki b

9 "G^ d Figur e7-10 . Predicte dVentur i scrubbe r performanc eK 5 0vs . B .P.6 4

o f ai r and wate r a t roo mtemperatur e wer e use d t o con struc t thi s figure . Fo r othe r liquid/ga s combination s . an d conditions , on e shoul d construc t differen t plots . Optimum

liqui d dro p diamete r ca n easil yb e obtaine d fromFigur e 7-11 . Fo r instance , i f th e ga s throa t velocit y i s known , the n th e optimumdro p diamete r wil l be tha t whic hgive s th e smalles t aerodynami c cu t diameter . I f th e scrubbe r require d .performanc e cu t diamete r i s known , optimum

throa t velocit yan d ga s -to-1iqui d rati o ca n b e determine d fromFigur e 7-11 . Figur e 7-1 2 show s th e relationshi p betwee n "B " and " K " . Thi s curv e wa s calculate d fromequatio n (7-8 ) and i s applicabl e t o al l scrubbe r operatin g conditions . Fro mthi s graph , w e can calculat e th e anticipate d cu t diamete r and pressur e dro p fo r variou s throa t velocit yand liquid-to-ga s rati o co m binations . Figur e 7-1 3 show s suc ha calculatio n fo r air
wate r syste m

a t 25°C . Figur e 7-1 4 i s th e cu t diamete r pressur e dro p relationshi p wit hwate r flo wrat e a s paramete r fo r thi s system . Desig n Procedur e Th e informatio n presente d i n thi s chapte r allow s on e t o desig n a ventur i scrubbe r t o mee t a require d "PT" . Th e genera l metho d doe s no t us e Figure s 7-1 3 and 7-1 4 .sinc e the y represen t th e specifi c cas e o f a n air-wate r syste ma t 25°C .

. I f th e condition s ar e clos e t o thos e fo r thes e tw o figure s the n th e procedur e i s simplified . Th e genera l procedur e i s a s follows : 1 ) Determin e require d cu t diameters : Firs t find th e aerodynami c geometri c mas s mea n diamete r o f th e incomin g dus t a t th c temperatur e expecte d in th e venturi . Then , construc t a plo t o f K v s d or r (required ) by , p gp a J

o a ) Obtainin g severa l K - B pair s usin g Figure s 7- 4 t o 7- 6 (dependin g o n o p ) . b ) Knowin g d , obtai n d 5 0 fo r eac ho f th e K - B pair s usin g Figur e 7-7 . 14 6P.6 5

5,00 0

1,00 0

a , 

## o ax. r~m 

### 5 io o c y

— i

1 0 

### T1 I I llll l T1 1 1 IM I

! 

### I f M fl l 

## tI M M o. i 1 . 0

AERODYNAMI C CU T DIAMETER , um A 

### 1 0 Figur e 7-1 1 Effec t o f ga s velocit yan d liqui d t o ga s flo w rat e rati o on performanc e cu t diameter .



### 14 7P.6 6

1 0

I o

—I IC3 

### °- ' 

### °: 

### 1. 0 JIID o I c
" 0. 5 0 5

0 . 1 

### T—n— I I IM M

0. 1 

### J I MM M I I J ! J M J

I I I llll l p5 0 0. 5 21. 0

= d p5 0 C ' p p u G t 1 0
9 y Gd d Figur e7-12 . "B" ' v s " K ' ' fo r

ventur ithroa t

o f infinit e length . p M

14 8P.6 7

< £ P . Di U J

i — i Q E - r> u u

o o Oi U J < 

### 1. 0

0. 5

0. 1 0. 2 Figur e 7-13 , 

### 3. 0 0. 6 1. 0 Q L /Q G , £/m 3 Predicte d ventur i performance , "d . Q L /Q Gwit h"u G " and "AP " a s parameter . pa 5 o 

### 6. 0

vs



### 14 95 . 0 T! 1 »||l l 

# ! ! « \ 

# ! U H ! » U M U

t n O <
Q i H U J < l- H Q C J U
>- Q O CX. 1. 0
0 . 5

0 . 1 

### J I lllll l J _ 

### J I I I I I M J I IM M 1 . 0 1 010 0 PRESSUR EDROP , c mW.C . 1 ,00 0 Figur e 7-1 4 Aerodynami c cu t diamete r versu s pressur e dro p wit hliqui d t o ga s

rati o a s parameter .P.6 9

2 ) Determin e performanc e cu t diameters : Firs t determin e vis
cosities , densities , an d Nukiyama-Tanasaw a coefficient s fo r th e ventur i conditions . The nconstruc t a numbe r o f performanc e curve s correspondin g t o differen t Q T / Q r ratio s a s follows : L L i a ) Selec t a "u ~ " 1 G o b ) Dro p diameter , d, , fro m Nukiyama-Tanasaw a relatio n (Tabl e 3-2 ) c ) N Rfrom

equatio n (5-7)(assumin g u , =0 ) d ) Cr , fro m

equatio n(5-8 ) J D o e ) Paramete r B fro mequatio n(5-22 ) (assumin g u , =0 ) f ) K from

Figur e 7-1 2
' P5 0 b g ) d fro mequatio n(7-9 ) bJ pas o MK J • h ) K fro mequatio n(7-13 ) ' p g MK i ) A P fro m

equatio n(7-18 ) Repea t step s (a ) throug h(i ) fo r severa l velocities . Plo t per formanc e K v s d curve s o n th e sam e plo t a s th e requiremen t

p g pas o y^ curv e fro mSte p (1) . Plo t A P v s d o n a separat e graph . 3 ) Determin e require dpressur e drops : Th e intersection s o f th e requiremen t an d performanc e curve s determin e th e prope r desig npoints . Th e correspondin g pressur e drop s require dca n the n b e foun dfro mth e plo t o f A P v s d n r . Th e require dpressur e r pa s o l r drop s wil l correspon dt o a certai nQ T / Q ~ ratio s so.tha t th e fa n cost s versu s th e wate r an d pumpin g cost s ca n b e compare dt o allo w selectio no f th e optimu mdesign . 4 ) Determin e throa t cross-sectiona l area : Usin g th e selec
te doptimu mcombinatio no f A P an d Qi/Q p procee da s follows ,

a ) Fro mth e desig nK solv e equatio n7-12 a fo r u „ a s a functio no f d , .

b ) Substitut e thi s equatio nfo r d , int o th e Nukiyama
Tanasaw a relatio nan d solv e fo r u ~ .

c ) Divid e th e volum e flo wrat e b yu ~ t o ge t th e throa t cross-sectiona l area . 15 1P.7 0



### 5 ) Determin e throa t length : Usin g th e desig nvelocity , perfor mstep s (2a-d ) an dthen , solv e equatio n(5-47 ) fo r I base do nth e desire dL ( 2 t o 3) . 6) Determin e convergence , divergenc e angles : Thes e hav e littl e effec t o nparticl e collectio nbu t the yd o hav e som e ef
fect s o npressur e drop . O f th e two , divergenc e angl e i s mor e important . Divergenc e angl e shoul db e designe dsuc hthat ,

a ) Boundar ylaye r separatio ndoe s no t occu r b ) Momentu mrecover yoccur s i nth e divergen t sectio n Th e genera l procedur e woul db e facilitate dbyus e o f a pro grammabl e calculato r o r a digita l computer . A s a check , o r i f th e condition s ar e clos e t o thos e o f a nair-wate r syste ma t 25°C . Figure s (7-11 ) an d(7-14 ) ca nb e use di na nalmos t purel y graphica l procedure . Th e graphica l procedur e i s a s follow s (air-wate r a t 25°C) , 1 ) Determin e require dcu t diameter : Sam e a s genera l pro cedur e . an dequatio n(7-12a ) t o calculat e th e performanc e d„ c 

### „ v s

n vjr 

### p a s o 2 ) Determin e performanc e cu t diameter : Us e Figur e 7-1 1 quatio n(7-12a ) t o calculat e t h Kcurve s fo r variou s Q T 

### /Q ~ ratios . p g X 

### L ' X 

### G 3 ) Determin e require dpressur e drops : Sam e a s genera l procedur e excep t us e Figur e 7-1 4 t o fin drequire dpressur e dro p Step s (4-8 ) sam e a s genera l procedure .

15 2P.7 1

Ventur i Desig n Exampl e Th e proble mo f designin g a ventur i scrubbe r t o contro l dus t fro m

a typica l asphal t plan t drye r i s illustrated . Th e dus t ha s a log-norma l distributio n o f diameter s describe d b

ya geometri c standar d deviation , o =5. 0 and a geometri c mas s mea n particl e diameter , d = 1 8 u m (physical) . Th e particl e densit yi s 2. 6 g/cm 3 . Th e flu e ga s flo wrate i s 56 7 Am 3 /mi n wit ha ga s temperatur e o f 116°C . Th e uncontrolle d emissio n rat e i s 2,31 0 kg/hr . Base d o n a loca l Ai r Pollutio n Contro l Distric t rul e fo r th e amoun t o f weigh t processed , th e emissio n shoul d no t excee d 2 5 kg/hr . Th e require d efficienc yi s then : (2,310-25)/2,31 0 x10 0 = 98.9% . Thus , th e desig n shoul d mee t a n efficienc yrequiremen t o f 99% . Ste p 1 . Specifyin g th e require d cu t diameters : First , th e aerodynami c geometri c mea n diamete r mus t b e found . Fo r ai r a t 116° C th e Cunningha msli p correctio n facto r fo r 1 8 y

mparticle s i s C * = 1.013 . Thus , d =1 8 (1.01. 3 x2.6) 0

- 5 = 29. 2 ym A pg a Next , a plo t o f th e require d cu t diameter s ( d 50 ) fo r a n overal l penetratio n o f 0.0 1 i s mad e byusin g Figure s 7- 5 and 7-7 . Th e point s whic har e shown i n Figur e 7-1 5 a s cir
cle s ar e liste d below :

B 4. 3 

### 2. 8 2. 2 1. 6 1. 4 K

1,00 0 1,50 0 2,00 0 5,00 0 10,00 0 

### d

pa s o ym A 

### 0 0 0 0 0 6 4 5 8 5 5 4 1 3 0 Ste p 2 . Specifyin g th e performanc e cu t diameters : Firs t th e flo wparameter s mus t b e found . Fo r ai r a t 116° C and wate r a t 25°C , 

### 15 3P.7 2



### 10,00 0

5,00 0

a

1,00 0

50 0 0. 2 0. 4 0. 6 d 

### paS0 , ^ m A 

### 0. 8 1. 0 1. 2 Figur e 7-1 5 Impaction paramete r vs aerodynami c cu t

diamete r for a ventur i design .

15 4P.7 3



### Ga s Viscosity , y G

### =

_ 2.2 3 x1 0 ^ g/cm-se c Ga s density , p G

### = 0.90 7 kg/m 3 

### Ga s kinemati c viscosity , v „ = 0.24 6 cm 2 

### /se c Liqui ddensity , p T

### = 99 7 kg/m 3 so , P L

—= 1,09 9 P „ 

### d^(cm ) = J1L

. - + 8 7 (J*-) du G o (cm/sec ) 0/ \ Q r / 1. 5 

### an dth e Nukiyam a an d Tanasaw a equatio nfo r dro p siz e reduce s t o , 

## Si *Go L, 

### "" l

/ J 

### '~ y 

### -J \ Q r Othe r desig nequation s t o b e use dare ,

an d u 

### G o d 

### d

N 

### R e o = 

### —^ " (5-7 ) 

# C 

# ° 0 = 

# °* 2 2 + 

# ^ U+ 

# °' 1 5 N



# ^o ) (5 

# "8 ) 1 Q 

### L P 

### L L 

### D o W 

### GP 

### G K= 0.208 7 + 

### ^ 6 + 

### M 8 p s 0 B B 2



### 0. 5 * B < 5 (Base do n Figur e 7-12 ) 

# v»-( 9 

# >C dd 

# ) " xl0

< (PmA ) (7 

# " 9 ) K 

# p g= K 

# P-

# fc,)

. .. . A A P » 8.2 4 x1 0 ' u ^ Solutio no f thes e equation s fo r variou s ^ L an d u 

### G o ca n b e greatl yfacilitate db yus e o f a programmabl e calculator . 15 5P.7 4

Th e solutio n t o th e desig n equation s ar e plotte d o n Figur e 7-1 5 and 7-1 6 fo r Q,/Q r ratio s o f 0.001 , 0.0015 , and 0.002 . L L i Ste p 3 . Determin e th e require d pressur e drops : Th e intersection s o f th e performanc e line s wit hth e require
men t lin e i n Figur e 7-1 5 determin e th e cu t diameter s (bot h require d an

d performance) . Thes e cu t diameter s ar e repre sente d o n Fig . 7-1 6 a s triangles . Th e require d pressur e drop s correspondin g t o thes e cu t diameter s ar e then ,

^ L d pas o A P Q r ym

AcmI.C . 0.00 1 0.4 2 6 7 0.001 5 0.5 7 4 0 0.00 2 0.67 5 3 2 Base d o n th e flue-ga s rat e o f 56 7 Am 3 /mi n thes e Q T /Q r ratio s represen t wate r requirement s o f 0.5 7 m 3 /mi n (15 0 gal/min ) 0.8 7 m 3 /mi n (22 5 gal/min ) and 1.1 3 m 3 /mi n (30 0 gal/min) , respectively . Base d o n pum p and wate r cost s versu s fa n cost s th e designe r ca n selec t th e optimum design . Ste p 4 . Determin e throa t cross-sectiona l area . I n orde r t o carr you t th e calculatio n illustratio n w e wil l assum e tha t Q,/Q r = 0.00 2 and d^ 0 . n= 0.67 5 ym Ai s th e optimum . Fro m

Figur e 7-1 5 th e require d K = 980 . KP g

u 

### G t d 2 u,- . = P § G t = 98 0 9 ^ G d d 9(980 ) (y G ) (d d ) 9(980 ) (2.2 5 x10" 1 *)d d d 2 (29. 2 x10' 1 *) 2 p a vJ
= 2. 3 xIO 5 d d 

### 15 6

### 10 0

u
u CL , 

### < 5 0

1 0 1. 2 Figur e 7-16 . Pressur e drop vs aerodynami c cu t diamete r

for ventur i design example .P.7 6

Fro m th e "Nukiyama-Tanasaw a correlatio n for'th e pre sen t example , 

# ( QV' 5

—1 = —+ ' 7.7 S xI P " 3 

# J U 

# G t Su b stitutin g int o th e expressio n fo r ,: u r . " w e hav e



### u r

### . = 2. 3 x1 0 L i t 

### 5 0

L uG t + 7.7 8 xIO' 3



### u r

### . = 5,30 0 cm/se c b t Throa t cros s - sectiona l are a 56 7 xIO 6 (60)(5300 ) Ste p 5 . Determin e throa t length : 1,78 3 cn r

d , = -^
- + 7.7 8 x10" 3 = 0.017 2c m a530 0 M= U G t d d P G = (5300)(0.0172)(9.0 7 x10~" ) = __n '^R e ' " .i T •* / u y G2.23x1 0
C D Q= 0.6 2 Therefore , throa t le n 

### gt h

# - (i)(^mi)( 1 \ CL

: \3/ \0.6 2/\9.0 7 xIO" 1 4/

= 20.3 Lc

m I f desig n L = 2 , the n throa t lengt h= 40. 6 c m Suppos e th e ga s temperatur e wa s 25°C , the n th e previousl yconstructe d performanc e curve s (Figure s 7-1 1 and 7-13 ) coul d b e used .



### 15 8P.7 7



### Step (1 ) : A t 25° C C = 1.00 9 fo r d = 1 8 y mso , d =1 8 P pg a (1.00 9 x2.6 ) 1 2 

### = 29. 2 ymA . Sinc e thi s i s th e sam e d

. Pg a a s before , th

e K - d requiremen t pair s ar e th e ' pg pas o n r 

### same . Ste

p (2) : Using Figur e 7-1 1 an d th e equatio n fo r K , Figur e IT O 

### 7-1 7 i s generated . The shade d triangle s represen t the design point s wher e th e performanc e an

d require d K ' s match . Thu s th

e results , usin

g Figur e 7-1 4 ar e l/m 3 

### 1.0 3 1. 1 1.5 5 1.8 5 2. 8 d

pa s o ym A 0.3 0 0.4 1 0.5 5 0.5 8 0.6 4 A

P c mW.C . 14 0 7 4 4 4 4 0 4 4 Thes e result s ar e clos e t o wha t we obtaine d using th e gen era l procedur e an

d a highe r temperatur e gas .

15 9P.7 8

20,00 0

10,00 0 -

5,00 0 -

P . 2,00 0

1,00 0

50 0 X 1 I ADesig n Point s Ga s Temperatur e = 25° C d„_

_= 29. 2 ym

A

1 2 Q L /Q G , £/m ; 0.5 5 0.5 8 0.6 4

Figur e 7-1 7 Impactio n paramete r v s Q,/Q r fo r

ventur i desig n example .

16 0P.7 9

CHAPTE R8 ENTRAINMEN T SEPARATO R Al l scrubbe r system s includ e a n entrainmen t separator , eithe r a s a n integra l par t o f th e scrubbe r configuratio n o r a s a separate , clearl yidentifiabl e device . Ther e ar e a numbe r o f device s whic har e commonl yuse d a s entrain
men t separators . Zigza g baffles , knitte d mesh , packe d beds , cyclon e separators , an d guid e vane s causin g rotatio n o f th e ga s streamar e frequentl yuse d fo r thi s purpose . Calver t e t a l (1975 ) ha d performe d a detaile d studyo f entrainmen t separators . Th e followin g i s a n abstrac t o f thei r study . ENTRAINE D LIQUI D INFORMATIO N I n orde r t o desig n a prope r entrainmen t separator , o r t o predic t th e collectio n efficienc yo f a n entrainmen t se parator , certai n entrainmen t liqui d informatio n i s needed . Thi s includes : 1 . Entrainmen t dro p and siz e distribution . 2 . Quantit yo r inle t loading . A n extremel yimportan t facto r i n choosin g an d design
in g an entrainmen t separato r i s dro p siz e distribution . Differen t entrainmen t separator s ar e limite d t o certai n dro p diameters , belo wwhic hthei r efficienc yfall s of f sharply . Th e siz e o f th e drop s depend s upo n th e wa ythe y wer e formed . Entrainmen t rat e and siz e distributio n dat a fo r ga s atomize d sprayscrubber s suc ha s Venturi s hav e no t bee n reported . Estimate s ca n b e made , a s discusse d below , bu t theyar e veryroug hbecaus e o f uncertaintie s i n predictin g th e characteristic s o f th e initia l atomizatio n an d th e dro p separatio n occurrin g withi n th e ventur i diffuse r and simila r flo welements .

16 1P.8 0

Dro p diamete r ca n b e predicte d b ymean s o f th e cor relatio n b

yNukiyam a and Tanasaw a (1938-40) . Fo r ai r an d wate r a t standar d condition s th c N+ T correlatio n fo r Saute r mea n diamete r is : d s (cm ) = 5fl

- ° + 92. 0 | —| (8-1 )

u (cm/sec ) where : d = Saute r (volume-surface ) mea n diamete r o f

s drops , cm u r - ai r velocit yrelativ e t o drops , cm/ s L i ' 3 Q, , = wate r flo wrate , m/ s Q r = ai r flo wrate , m 3 / s L i Accordin g t o Steinmeye r i n Perr y(1973) , th e Saute r mea n diamete r i s typicall y70 1 t o 90 % o f th e mas s media n diameter . I f th e dro p siz e distributio n i s lo g normal , thi s implie s tha t th e geometri c standar d deviation , " a " i s abou t 1. 6 fo r 90 % and 2. 3 fo r 701 . T o illustrat e th e applicatio n o f th e abov e t o th e predictio n o f entrainmen t characteristic s fo r a ventur i scrubber , w e ca n conside r th e cas e o f a throa t ai r velocit y o f 10 0 m/se c and wate r t o ai r rati o o f 1 £/m 3 (1 0 " 3 m 3 / m 3 ) . Th e ga s pressur e dro p woul d b e abou t 8 0 c mW.C . and th e Saute r mea n diamete r compute d fromequatio n (8-1 ) i s 7 9 ym . Fromth e typica l ratio s o f mas s media n t o Saute r diameter , w e woul d expec t th e mas s media n dro p diamete r t o rang e from 8 8 t o 11 3 ym , wit h" o " from1. 6 t o 2.3 , respectively . On e woul d therefor e predic t tha t th e cumulativ e entrain
men t concentratio n woul d b e relate d t o dro p diamete r withi n th e rang e o l highan d lowvalue s tabulate d on th e followin g page .

16 2P.8 1

Dro p diameter , y m4 5 1 0 1 5 2 0 Hig hconcentration , cm 3 /m 3 0.03 5 0.1 1 2 8 2 0 Lo wconcentration , cm 3 /m 3 - - 0.002 5 0.0 6 0. 6
I f th e entrainmen t containe d 10 % solid s byweight , th e residua l particl e concentration s afte r evaporatio n woul d b e suc htha t i f on e wante d t o limi t th e particl e loadin g du e t o entrainmen t t o 0.0 1 g/m 3 (0.004 4 gr/ft 3 ) th e separatio n o f al l entrainmen t large r tha n 5 y mdiamete r fo r th e hig hestimat e an d 1 6 y mdiamete r fo r th e lo wwoul d b e required . Sinc e particl e loading s o f thi s magnitud e ca n b e significan t fo r plum e opacity , th e exampl e show s th e efficienc ywit hwhic hentrainmen t mus t be . controlle d an d th e necessit yfo r goo d dat a o n entrainmen t siz e distribu
tio n an d concentration . DESIG NEQUATION S FO RENTRAINMEN T SEPARATOR S Th e desig n an d operatio n o f mos t entrainmen t sepa rator s ar e governe d b ythre e factors :

1 . Pressur e dro p 2 . Collectio n efficienc y 3 . Reentrainmen t velocit yan d reentrainmen t rat e Knowledg e o f th e pressur e dro p throug ha separatio n syste mi s importan t i n calculatin g th e energ ylos s incurre d an d i n selectin g th e prope r pump s an d othe r auxiliar y equipmen t t o overcom e tha t energ yloss . Collectio n efficienc yo r overal l collectio n efficienc y i s define d a s th e fractiona l collectio n o f th e droplet s by th e separator , i.e .

, effluen t concentratio n n = 1 - influen t concentratio n

1 6 5P.8 2

Whe n th e ga s velocit yi n th e entrainmen t separato r i s high , som e separate d droplet s i n th e separato r wil l b e reentraine d i n th e ga s stream . Becaus e o f thi s reentrain
ment , th e observe d collectio n efficienc yo f th e separato r i s les s tha n th e primar ycollectio n efficienc ywhic hi s define d a s th e efficienc ya n entrainmen t separato r woul d hav e i f reentrainmen t wer e no t present . Reentrainmen t velocit yi s th e ga s velocit ya t whic h drop s ar e firs t observe d t o becom e reentraine d i n th e gas . Th e onse t o f reentrainmen t wil l var yfo r differen t kind s o f entrainmen t separator s and differen t operatin g condi
tions . Reentrainmen t velocit ydetermine s th e maximumallow
abl e ga s velocit yi n th e separator . Reentrainmen t rat e and dro p siz e distributio n ar e neede d fo r th e predictio n o f emission s fro mth e system . Onc e desig n equation s predictin g th e primar yeffi
ciency , pressur e drop , and reentrainmen t ar e available ; th e operatin g characteristic s o f th e entrainmen t separato r ca n b e established . Si xdifferen t kind s o f entrainmen t separator s wil l b e discusse d i n thi s section : cyclone , packe d bed , zigza g baffles , tub e bank , mesh , an d siev e plate . Cyclon e Th e cyclon e i s th e mos t commonl yuse d entrainmen t separ a to r fo r ventur i scrubbers . Commerciall yavailabl e cyclone s i n standar d design s fo r entrainmen t separator s hav e a maxi
mu mcapacit yo f up to ' 14 1 m 3 /se c (300,00 0 CFM ) o f gas . Effi
ciencie s o f abou t 95 % ar e claime d fo r 5 y mdiamete r drop s i n a wel1-designe d cyclone . Som e manufacturer s us e a bun
dl e o f smal l cyclone s (multicyc 1 ones) , whic hca n efficientl y collec t drop s a s smal l a s 2 y mi n diameter . However , thi s arrangemen t reduce s th e capacit yo f th c device .



### 16 4P.8 3

Primar yEfficienc y- Leit hand Lich t (1971 ) derive d a n equatio n t o predic t primar ycollectio n efficienc yi n coni
ca l botto mcyclone s a s picture d i n Figur e 8-1 . Wit hsligh t modificatio n i t can b e applie d t o cylindrica l cyclones . Th e equatio n fo r predictin g primar ycollectio n effi
cienc yi s :

• 2 i 1 PA I n P t = 2 2 d , u t d t g 9 p G (n+l) t 2 n+ 2 (8-2 )
where : n = 1 - r T 28 3 * - -> • 3 0. 1 H

,-0.39 3 d c ) 2. 5 (8-3 )
P t


### " d

u t g t penetration , fractio n dro p density , g/cm 3 ga s viscosity , pois e dro p diameter , cm tangentia l velocity , cm/se c mea n residenc e tim e o f th e ga s i n th e cyclone , se c cyclon e diameter , c m Th e mea n residenc e tim e o f th e ga s streami n th e cyclon e is :

V Q r (8-4 )

wnere : V effectiv e volum e o f th e cyclone , cm 3

volumetri c ga s flo wrate , cm 3 /se c
= u G A
16 5P.8 4

Figur e 8-1 . Cyclon e wit htangentia l ga s inle t 

### 6 6P.8 5

inle t area , cm 2 u G= inle t ga s velocity , cm/se c Th e effectiv e volum e o f th e cyclone , " V " i s define d a s th e volum e o f th e cyclon e minu s th e volum e occupie d b yth e exi t duc t an dexi t ga s core . Th e diamete r o f th e exi t ga s cor e ca nb e assume dequa l t o th e diamete r o f th e exi t duct . Leit han dLich t (1971 ) gav e th e followin g equation s fo r th e determinatio no f effectiv e volum e o f a conica l botto mcyclone . V = V + 1/ 2 V , e i 2 (8-5 ) wher e V

= annula r shape dcolum e abov e exi t duc t inle t t o mid-leve l o f entranc e duc t 

### \ ( S 

### - | ) 

### (d

2 

### - d' ) 4 v2 J

K c e J (8-6 )
V = volum e o f cyclon e belo wexi t duc t inle t 2 t o th e natura l lengt ho f th e cyclon e
* d c *(L+S-h s ) d ^ / + d 2

— S . ( h-S ) + ^—L_|i+5

_+ £ _ 4 s 1 2 \ d, . d * \ c c ^ d 2 L e (8-7 )

w here : d= d-( d- b)

c c e ' S + L- h s

h- h (8-8 )

an dL = natura l lengt ho f th e cyclon e

16 72 1/ 3 >/ 3 2.3d . ab . (8-9 )

a , b , d , d , S , h , har e cyclon e dimension s define d i n Figur e 8-1 .
Pressur e Dro p -Shcphar d an d Lappl c (1940 ) derive d a n equatio n fo r a cyclon e wit hinle t vane s fo r pressur e dro p a s a functio n o f inle t ga s velocit yand th e cyclon e inle t and outle t dimensions : 2 AP = 0.00051 3 p r

— G\ab > 7. 5 ab

d 2 t e (8-10 ) wher e : AP = pressur e drop , cmW.C . P G= ga s density , g/cm 3 Q r = ga s volumetri c flo wrate , cm 3 /se c a = cyclon e inle t height , cm b= cyclon e inle t width , cm d = cyclon e exi t pip e diameter , cm Equatio n (8-1!) ) ca n b e modifie d b ywritin g i t a s a functio n o f th e geometri c averag e o f th e ga s velocit ya t th e cyclon e inle t an

d outlet : A P - 0.000513p G v^ y e (8-11 ) Shepar d and Lappl e als o develope d a n equatio n fo r a cyclon e withou t inle t vanes : 2 

### ' fyA[16ab \ A P = 0.00 0 5 1 3 p . ah . d 2 e (8-12 )

16 8P.8 7

Packe d Be d Packe d bed s o f standar d desig n wit ha capacit yo f u p t o 6 5 m 3 /se c (140,00 0 CFM ) ar e available . The yca n remov e drop s a s smal l a s 3 y mi n diamete r a t 80-90 % efficiency . Superficia l ga s velocitie s rang e from7 5 t o 24 0 cm/sec , and pressur e dro p i s generall ylow , 0.05
- 0. 1 cmW.C . pe r cmo f be d length . Cros s flo wbed s ar e claime d t o hav e hig hdrainag e efficienc yand therefor e ar e les s pron e t o plugging . Up streamwashin g i s recommende d t o avoi d pluggin g i f solid s ar e presen t i n th e drop s t o b e removed . Packin g i n differen t materials , shape s and size s i s available . Variou s ring s ar e claime d t o hav e hig hcol
lectio n efficienc yand lo wpressur e drop . Packe d bed s ar e ofte n use d fo r mas s transfe r becaus e o f thei xhig hinterfacia l area . Thu s the yar e sometime s employe d whe n simultaneou s mas s transfe r and entrainmen t separatio n ar e desired . Primar yEfficienc y- Jackso n and Calver t (1966 ) and Calver t (1968 ) hav e develope d a theoretica l relationshi p betwee n particl e collectio n efficienc yand packe d be d operatin g parameters : P t = 1 ex

p

. 2 

### 2(j + 

### r ) (e-H, ) i- K (8-13 )
d d d U G 9 ^ G d c
wnerc :

'd

r A rati o o f channe l widt ht o packin g diamete r fractiona l liqui d hold-u p in th e be d be d porosit y, fractio n (Tabl e 8-1 ) be d length , cm

16 9d , = packin g diameter , cm u r = superficia l ga s velocity , cm/se c d , = dro p diameter , cm Th e experimenta l dat a o f Jackso n (1964 ) wer e analyze d t o determin e appropriat e value s o f "j " t o us e i n equatio n (8-13 ) wit hal l quantitie s i n th e equatio n known excep t "j" , whic hwa s calculated . Th e result s ar e give n i n Tabl e 8- 2 whic hlist s "j " value s fo r variou s type s and size s o f pack
ing material . Fo r th e manufacture d packin g materials , "j " i. s fairl yconstan t a t abou t 0.16-0.19 . Th e ver ylo wvalu e o f 0.0 3 fo r cok e ma yb e du e t o th e smal l passage s withi n th e cok e itself , whic hmak e eac hlarg e piec e o f cok e func
tio n effectivel ya s a numbe r o f smalle r pieces . Pressur e Dro p - Perr y(1963 ) give s a generalize d pressur e dro p an

d floodin g correlatio n plo t whic happear s a s Figur e p2p m0. 2 8-2 , wher e a dimensiona l group o f functio n [_ L , P G P L g 0 2 (centipoise ) , i s plotte d agains t a dimensionles s group

L / P G\^ 2 o f functio n —j
—

1 , wher e "G " and "L " refe r t o th e ga s G\ P L / and liqui d mas s fluxe s respectively . "V" i s th e rati o o f wate r densit yt o entrained
- liqui d density . Value s fo r th e packin g factor , "F" , fo r dumpe d pieces , stacke d piece s and grid s ar e give n i n Table s 8- 3 and 8-4 . I f "F " i s no t known , — 3 ma yb e use d instead . Tub e Bank Tub e bank s mad e o f streamline d strut s hav e bee n use d a s entrainmen t separator s bu t n o experienc e wit hround tube s ha s bee n reported . Particl e collectio n efficienc y and pressur e dro p fo r roun d tub e bank s hav e bee n studie d and th e characteristic s appeare d promisin g fo r entrainmen t separatio n application . i

17 0P.8 9



### TABL E 8- 1 BE D POROSITY , e , FO RVARIOU S PACKIN

GMATERIAL S Nam e

Siz e (cm ) 1.2 7 1. 9 2.5 4 5. 8 5. 1 Stonewar e

Raschi g Ring s

0.57 * 0.6 7 0.6 8 0.6 8 0.7 5 Carbo n

Raschi g Ring s

0.71 *

0.7 5 0.6 7

__ Stee l

Raschi g Ring s (1/16 " thick )

0.9 2 0.9 2 Stonewar e

Ber l Saddle s

0.6 5 0.6 9 0.7 0

- - Stonewar e

Intalo x Saddle s

0.7 0 0.8 1 Stee l

Pal l Ring s

0.9 3 0.9 4 

### *Treybal l (1955 ) Al l othe r dat a fro mPerr y(1963 )

TABL E 8- 2 EXPERIMENTA

L VALUE S OF j , CHANNE L WIDTH A S FRACTIO NOF PACKIN

GDIAMETE R
Siz e (cm ) 1 2 7
2 . 5 4 5. 8
7. 6 - 12. 7 Typ e o f Packin g '

Ber l Saddles , marbles , Raschi g Rings , Intalo xSaddle s Ber l Saddles , Raschi g Rings , Pal l Ring s Ber l Saddles , Raschi g Ring s Pal l Ring s Cok e 3 0.19 2
0.19 0
0.16 5
0.0 3 

### Adapte d fro

mJackso n (1964 ) an d Calver t (1968 ) 171 .P.9 0

Tabi c f-5 . PACKIN GFACTORS , "F " , FO RDUMPE D PIECE S (m 2 /m 3 ' l

Rasc hi g r inj; s , cerami c

. l d c m wal l

. 5 2 c mwa l 1

. 6 5 c m

wa l 1 .9 5 c mwal l Rasc hi g r i ng s , carbo n .1 6 c mwal l .5 2 c mwal l .6 5 c mwal l

. 7 9 c mwal l Raschi g rings , meta l .O S c mwal 1 .1 6 c mwal. 1 Les s in g ring s , porcelai n .5 2 c m wal l .6 5 c m wal l Lessin g rings , meta l .0 8 c mwal l .1 6 c mwal l [0.6 4 J

5,25 0

5,25 0

2,30 0 Nomina l siz e o f

[0.95 J [1.27 ] [1.59 J
3, 2 8 0

1,54 0

1,28 0 98 0 56 0

1,3 4 0 9 5 0

(1,060 ) packing , c m [1.9 ] (2.5 )

5 I 0

92 0 52 5

51 0 58 0 72 0 45 0
(800 )

(630 ) (472 ) I-.2 ]

36 0

(587 ) [3.8 )

-15 0

4 3 0

27 2

(295 ) [5 ]

21 0

21 0

1S 7
(360 1
(200 ) [8 ]

12 1

U S

10 5 [10 ]

9 8

Tabl e 6-3 . PACKIN GFACTORS , "F" , FO RDUMPE D PIECE S (m 2 /m 3 ) (continued ) Nomina l siz e o f packing , cm [0.64 ] [0.95 ] [1.27 ] [1.59 ] [1.9 ] [2.5 ] [3.2 ] [3.8 ] [5 ] [S ] [10 ] Par t i t ion r i ng s Pal l rings , plasti c Pal l rings , meta l Ber l saddle s 2,95 0 51 ( 23 0 79 0 17 1 15 8
56 0 36 0 47 5 52 2 10 S 20 0 intalo xsaddles , 2,38 0 1,08 0 66 0 cera m i c intalo xsaddles , plas t i . Super- i ntalox , cerami c Tellerette s

?nthese s denot e a valu e o f a / c 3 , rathe r tha nempirica l )'•. 1 0 5 8 2 9 2 6 6
21 3 14 8 17 1 13 1

6 9 10 0 13 0 26 2 19 0



### 17 2P.9 1

abl e 8-4 . PACKINGFACTORS,"F " FO RGRID S AND STACKE D PIECE S

(m 2 /m 3 ) . Nomina l siz e o f packing , cm 2. 5 3 1 0 1 3 1 4 1 5 Woo d gri d Meta l gri d Gri d tile s Checke r brick , £=0.5 5 Raschi g rings , cerami c .6 3 cm wal l .9 5 c mwal l Raschi g rings , meta l Partitio n rings , diamete r 7. 6 cmlengt h 10. 2 cmlengt h 15. 2 c m lengt h Partitio n rings , squar e se t 7. 6 cmlengt h 10. 2 cm

lengt h 15. 2 c m lengt h 2 0

8. 2 1 1 8. 2

9 5 5. 9

1 6 3 6 2 1
(1,200 )

(690 ) 4. 9

12. 8

(725 ) (705 )

(460 ) (450 ) 11 8 13 5

(410 ) (375 )

(275 ) (260 ) Parenthese s denot e a valu e o f a/c: 3 , rathe r tha n empirica l r .

17 3P.9 2

O H <D

o
t u o b o

- 3
Q . 0. 5
0. 2 0 . 1
0.0 5

0.0 2

1 0.0 1 0.00 5

0 .00 2 0.00 1 0.0 1 0.0 2 L 

### x= — G IPrA 

### V 2 \ p L / 

### (dimensionless ) Figur e 8- 2 Generalize d flooding an d pressur e dro

p correlatio nfor packe d bed s (Perry , J965 )

17 4P.9 3

Primar yEfficienc y- Calver t and Lundgre n (1970 ) found tha t th e collectio n efficienc yfo r closel ypacke d rod s i s give n b yth e equatio n fo r rectangula r je t impaction . Th e collec
tio n efficienc yo f eac hstag e o f impactio n ca n b e found in Figur e 8-3 . Eac hrav : o f tube s excep t th e firs t represent s on e stag e o f impaction . "6 " i s use d a s a paramete r i n Figur e 8- 3 an

d i s define d by : 2 £/ b (8-14 ) wher e : b= je t orific e widt h I = distanc e betwee n orific e an d impingemen t plan e " K " , th e inerti a parameter , i s define d wit hdro p radius , " r " , rathe r tha n diameter . P Efficienc yfo r th e ban k o f tube s i s give n by : E = 1 (1-Oj )

N (8-15 ) wher e r . ' ]
N collectio n efficienc yfo r a give n particl e diamete r i n on e stag e o f rectangula r je t im
pingemen t numbe r o f stage s i n th e tub e bank (numbe r o f rows ) - 1 I f th e tube s ar e widel yspaced , the targe t efficiency , "'"" , can b e calculate d fromFigur e 8-4 . In thi s cas e th e efficienc yfo r th e entir e tub e ban k is :



### l - d-n^) n (8-16 )

17 5P.9 4

1. 0

< IS

>r U z ^0. 5 t u
O I—I H U (J J

- J o u

( K )

P 

## 0 0. 5

2 p C u *p o 1. 0

V * 9 y 1 . 5

G2 Figur e 8- 3 - Theoretica l and experimenta l

collectio n efficiencie s o f rectangula r aeroso l jets .

17 6P.9 5

U U J

t U 

# — c Rectangular half body

__(ribbon

with wake)

Probable

curve for recessed

trap



### o. i 1 0 10 0 C p , d\ u INERTIA L PARAMETER , K = S—3—G _

P 9p G

### d c 

### Figur e 8- 4 _Theoretica l impactionefficiencyas

a functio n o f inertia l paramete r for differen t targets .

1 7where : a ' = cross-sectiona l are a o f al l th e tube s i n on e ro w A= tota l flo ware a n = numbe r o f row s Pressur e Dro p - Pressur e dro p fo r ga s flo wnorma l t o bank s o f round tube s can b e predicte d b ymean s o f Grimison' s cor relation s (Perry , 1973) . A s a n approximation , Lappl e (Perry , 1973 ) suggest s tha t 0.7 2 velocit yhead s ar e los t pe r ro wo f tube s i n arrangement s o f th e kin d commonl yuse d i n hea t ex changers . Calver t and Lundgre n (1970 ) found tha t fo r closel y space d tub e bank s Lapple' s approximatio n agree d satisfactoril y wit hexperimentall ydetermine d pressur e drops . Houghto n and Radfor d (1939 ) studie d streamlin e stru t bank s and foun d tha t fo r a center-to-cente r spacin g o f 2 stru t width s (i.e . ope n spac e = stru t width ) th e pressur e dro p wa s abou t 0.1 6 velocit yhead s pe r row . Thi s ca n b e expresse d as : A P = 0.1 6 Np G(5. 3 xIO--* ) (u£) 2 c mW.C . (8-1 6 a ) where : u i i s th e actua l ga s velocit y Mes h Knitte d mes ho f varyin g densit yand voidag e i s widel y use d fo r entrainmen t separators . Ther e ar e basicall ythre e differen t kind s o f mesh : (1 ) Layer s wit hcrim p i n th e sam e directio n - eac hlaye r i s actuall ya neste d doubl e layer . (2 ) Layer s wit hcrim p i n alternat e direction s - thi s result s i n a n increas e i n voidage , reduce d sheltering , a decreas e i n pressur e dro p pe r uni t lengt han d an increas e i n targe t efficienc ype r layer . (3 ) Spirall ywoun d layer s - th e pres 

### 17 8P.9 7

sur e dro p i s lowe r b yabou t 2/ 3 tha n in layer s wit hcrim p i n th e sam e direction , bu t th e creepin g o f fluids , whic h contribute s t o reentrainment , i s expecte d t o b e higher . Standar d mes h10-1 5 c mthic k havin g a densit yo f abou t 0.1 5 g/cm 3 i s use d t o remov e drop s large r tha n 5 y m i n diameter . Ga s velocitie s rang e from0. 3 t o 5 m/se c an d liqui d flo wrat e i s limite d b yth e drainag e capacit yo f th e mes ht o 2. 5 x1 0 " 3 g/se c cm 2 o f mesh . Alowe r densit ymes h mad e o f standar d wire s i s use d whe n 10-20 % highe r fio wrate s ar e desired . Ofte n two mes htyp e separator s in serie s ar e use d t o remov e drop s i n th e 1- 5 y m diamete r range . Th e firs t inesh , normall ymad e o f fin e wires , coalesce s th e smal l drops , and th e secon d mesh , mad e o f standar d wires , remove s them . Th e firs t mes hi s operate d beyon d th e floodin g velocit yand th e secon d unde r floodin g velocity . Amajo r disadvantag e wit h thi s arrangemen t i s a pressur e dro p whic hma yreac h2 5 cm W.C . Som e manufacturer s us e tw o o r thre e stage s o f mesh , th e firs t bein g coarse r and th e fina l bein g finer , t o remov e larg e and smal l drop s successively . Ames htyp e separato r ha s th e advantag e tha t i t ca n b e mad e t o fi t vessel s o f an yshape . Anymaterial s whic h ca n b e drawn int o th e shap e o f a wir e ca n b e use d fo r fab
rication . However , mes hseparator s ar e limite d i n appli
catio n becaus e the yplu g easily . Thi s can b e avoide d b y upstrea m

washing , whic hwil l decreas e remova l efficienc yand increas e pressur e drop . Primar yEfficiency-Bradi c an d Dickso n (1969 ) presen t th e fol
lowin g expressio n fo r primar yefficienc yi n mes hseparators :

17 9

### C = 3-ex p ( - | ^ a 2 

### £ 2 n 

### ) (8-17 ) where : a 2 

### = specifi c are a o f mesh , surfac e are a o f wire s pe r uni t volume o f mes hpad , cm 2 

### /cm 3 

### l y= 

### thicknes s o f mes hpa d in th e directio no f ga s flow , c m n = collectio n efficiencyo f cylindrica l wir e The collectio n efficiencyo f cylindrica l wir e " n 

### " can be obtaine d fro mFigur e 8-4 . The facto r o f 2/ 3 i nth e exponentia l wa s introduce d b yCarpente r an

d Othme r (1955 ) t o correc t for the fac t tha t al l th e wire s inthe knitte d mes har e no t perpendicula r t o th e flow . Tha t facto r i s th e rati o o f the projecte d are a o f wire s perpendicula r t o th e flowt o the cross-sectiona l are a o f wire s along th e wir e length .

4(l-e ) a 2 

### = - r 

### —

(8-18 ) c Pressur e Drop - York an d Poppel e (1963 ) have suggeste d tha t th e tota l pressur e drop inth e knitted mes hi s the su mo f th e pressur e dro

p inth e dr yknitte d mes han

d th e pressur e drop due t o the presenc e o f liquid : A P = AP d r y

### + AP L 

### (8-19 ) wher e : AP , - pressur e drop inabsenc e o f liquid , c mW.C . AP , = pressur e dro

p due t o presenc e o f liquid , c mW.C . York an d Poppel e considere d th e mes ht o be equivalen t t o numerou s smal l circula r channel s an d use d th e D'Arc y formul a for pressur e drop in a pip e t o correlat e th e dr y 

# I

18 0P.9 9



### pressur e dro p throug hth e mesh . Yor k andPoppele' s dat a fo r knitte dmes hwit hcrimp s i nalternate dandi nsam e directio nar e plotte di nFigur e 8-5 . Thei r dat a ar e clos e t o thos e obtaine db yStasange e (1948 ) an dShurin g (1946) . Simila r curve s obtaine db yBradi e andDickso n(1969 ) fo r spiral-woun dandlayere dmes har e als o plotte di nFigur e 8-5 . Figur e 8- 5 shoul db e use di ndeterminin g dr ypressur e drop , whic hi s calculate dfro m th e expression : A P f £ 2 

### a 2 

### p G

### u ^ dr y (8-20 ) Th e uni t o f "AP , " i s i ndynes/cm 2 

### . I t ca nb e converte d t o cmW.C . b

ydividin g i t b

y981 . Pressur e dro p dat a du e t o presenc e o f liqui dar e no t availabl e fo r al l operatin g condition s o r fo r mes ho f dif
feren t styles . Value s o f "AP T 

### " obtaine dbyYor k an dPoppel e ar e presente di nFigure s 8- 6 an d8-7 , wit hliqui dvelocit y wher e a s th e parameter . Liqui dvelocit yi s define da s 

## " X "L " i s th e volumetri c flo wrat e o f liqui dan d"A " i s th e cross-sectiona l o f th e mes hi nliqui dflo wdirection . Th e specification s o f th e knitte dmes huse dar e show ni nth e tw o figures . Maximu mAllowabl e Ga s Velocit y- Severa l factor s gover n •th e allowabl e ga s velocit ythroug hwir e mes hfo r a give n se t o f conditions : 1 . p T

### an dp r Lin 

### 2 . Liqui dviscosit y 5 . Specifi c surfac e 4 . Liqui dentrainmen t loadin g 5 . Suspende dsoli dconten t Applicatio no f th e Souders
- Brow nequatio nfo r th e calculatio no f allowabl e vapo r velocit yfo r wir e mes hmis t eliminato r base do nga s andliqui ddensitie s ha s bee n suggeste db

yYor k (1954) . 18. 1P.10 0

1 . 0 0. 5

0 . 1 0.0 5

0.0 1 fI I I I'M I

Satsange edat a(1948 )

Spiral-woun dmes h

1 IIIIIII I 1 0 10 0 1 i i i i i" f 1,00 0 10,00 0 N Re, G P Gu G /a 2 y G Figur e 8-5 . Frictio n Factor , f , versu s Reynold s

number , N Rr

fo r wir e mes hentrainmen t separato r ' wit hentrainmen t load .

18 2P. 1



## rm— r 11 1 i

HIIII I I lll l I I •I •l m lll l
•3* MUI D <q d V (• 0

K*) O o S H 0) c x : +- > O -r- l +- » t- l

- a s Q J - H Q

J 3 3 X. JC

- 3 O * tn +- < •r H Q J O ~ - H a> o o

v O ^ C 3

Q
. i J Q
. *—- * \ O a n 3 < D S H 3 i/ i IT ; Q J S H D O Q

J U. •*- > C H 0 > - P E U -i- l - H C C S

H O J M 'J Ifl Q J O i Q J U JZ mC a,+- > + J ( j

< D S H •H T 3 D • P (T t c o 3 0 0

Q O •r- l U H 

# r M I I 1111 1 M i i (IIIM I

-

' • h O

O l C O

\0 L O t o

E • J < ^

a c ; c H C E O - H - M « + J - H 1 0 TJ S Q J - H Q

J 3 3 - C X t j a - i/i4J • H Q J •cur- t EG O - H h*+IT I T ) O I D If l

a Q J Q J +- > E o 3 t/ > Q J J 4 ' J tr , t/ ) Q J Q J Q ) O 4- > - a

J -f . 3-. Mm n4l j v o o

18 3P. 2

u r =30. 5 a- l Gma x:

> 0- 5 (8-21 )
wher e " a " varie s wit hoperatin g condition s and mes hde
sign . Fo r mos t cases , a - = 0.35 . Zigza g Baffle s Baffle s ca n efficientl yseparat e drop s greate r tha n 1 0 y mi n diameter , whil e som e o f th e bette r designe d de
vice s ca n separat e dro p diameter s o f 5- 8 ym . Commo n ga s velocitie s ar e 2.0-3. 5 m/sec , and th e pressur e dro p fo r a 6-pas s separato r i s abou t 2-2. 5 cmW.C . Th e mos t commo n baffl e shap e i s zigza g wit h3 t o 6 passes . Thes e ca n b e fabricate d froma continuou s wavy plat e o r eac hpas s i s separated , i n whic hcas e th e sepa ratio n distanc e i s normall ysmalle r tha n th e widt ho f th e baffles . Cross-flo wbaffle s ar e claime d t o hav e highe r drainag e capacit ytha n countercurren t flo wbaffles . Primar yCollectio n Efficienc y- Amode l t o predic t primar y efficienc ywa s developed , base d o n turbulen t mixing . Th e primar ycollectio n efficienc yo f a continuou s zigza g baf
fl e sectio n is :

n= l ex

p u . nw 8

t c 57. 3 u r btan ( (8-22 )
wher e
t c

4 G n primar ycollectio n efficiency , fractio n dro p termina l centrifuga l velocity , i n th e norma l direction , cm/se c superficia l ga s velocity , cm/se c numbe r o f bend s o r row s angl e o f inclinatio n o f th e baffl e t o th e flo w path , degree s
18 4P. 3

w= widt ho f baffle , cm b= spacin g betwee n tw o consecutiv e baffle s i n sam e row , cm Th e dro p termina l centrifuga l velocit yca n b e deter
mine d b

yperformin g a forc e balanc e o n th e drop . Th e resul t i s : 0. 5 t c 4 d d P d a

3 C D P G (8-23 )
wher e d d =

p d = a = C D = dro p diameter , cm dro p density , g/cm 3 acceleratio n du e t o centrifuga l force , cm/sec 2 dra g coefficien t ga s density , g/cm 3 I f th e dro p Reynold s numbe r i s lo w(N „ n < 0.1) , Ke , u Stokes ' lawapplies . Fo r thi s condition , th e dra g co efficien t i s give n by : C 2 4 D N (8-24 ) Re, D ;her e N R~ = dro p Reynold s numbe r d d u t c P G

B ycombinin g equation s 8-2 3 an d 8-24 , w e obtain :
u t c ' d p d a

1 8 y r (8-25 )

18 5P. 4



### Th e acceleratio ndu e t o centrifuga l forc e i s define db y th e followin g equation :

t 2 2 

### 2 (u r 

### ) 2 u r 

### si n6 a 

### = G

_= 

### G (g


### _ 2 6 ) 

### wco t 0 wcos 3 

### 9 where : ul = actua l velocit ybetwee nbaffles , cm/se c U p = superficia l ga s velocity , cm/se c I f N R

### y. >0.1 , anothe r appropriat e dra g coefficien t shoul db e use di nequatio n8-23 . Foust , e t al . (1959 ) gav e a plo t o f dra g coefficien t a s a functio no f Reynold s numbe r i nFigur e 8-8 , whic hca nb e use dt o determin e " u " . Th e effec t o f surroundin g drop s o nth e motio no f anyindi
vidua l dro p i s neglected . Pressur e Drop-Determinatio no f th e pressur e dro p i s base do n th e dra g coefficient , ; 

### 'fn" , fo r a singl e plat e hel da t an angl e "8 " t o th e flo wa s presente di nFigur e 8- 9 (Fag e an dJohanson , 1927) . Neglectin g th e effec t o f neighbor
ing plates , pressur e dro p ma yb e expresse das :

nu p 

### A A P = E 1.0 2 x10" 3 

### f n

### p r 

### —-AS- (8-27 ) 1 U \3 J

A. 

### 1 = 1 L 

### t where : Z\ P = pressur e drop , c mW.C . A= tota l projecte dare a o f baffle s per - ro wi nth e directio no f inle t ai r flow , cm ? 

### A= duc t cros s - sectiona l area , cm 2 

### Th e summatio ni s mad e ove r th e numbe r o f row s o f baffle s . 18 6P. 5

I d ,0.'.)')

1 ,'•")') Q CJ
fci O i — fc, fci O
a ; io n
1 0 - -

_

-

-

-

-

- VM > 1 1 IIII I1 1 1

^V^S V N/^Siv X ^\^$N^ v \^>^> ^ 

### N^$>^ r""

" X . ^ S Ns^^' ,N,,,,N,,,,,,,,, »-^ _ ^ \ . ^ „^ ^ _ 

# \ s 

# J N 

# \^- ~ ^ v^^"^--^ ^ - _ : = 0. 1 J.- »

. - o. 7. ' o = n . mi n

• =0. SOc ,

_= \ . oo o -

-

_

-

-

- "

. 0 . 1 O.O'l lo.O l 1 M 1 0 0100 0| 0(iiii i1 0 Revn o Id s 'iii:**Sc

r R e , M < ! .1 1

dt c ( , figur e B'8- Dra g coefficien t versu s Revnold s nirr.lter afte r

Fcns t e t a l (1959) , uit hsphericit yC * a s t h e parameter .



## i r T

### r

0 . 8

Plat e I n c 1 ine dt o ]- " 1 o u

J I J I Angl e o f 1 1 1 c . i dc i i c c
4 0 SO A N( 7 Li . 0 1 INCIDLNC!: , degree s ;u.r e 8 ' *"' . !) ra g •coefficient s fo r flo upas t incline d

fla t plate s (dat a fro mA . Pag e j P . 7 . . Johanseii , (1927 ) .



### 18 7P. 6

Th e actua l ga s velocity , "Up" , i n th e baffl e sectio n shoul d b e use d in Equatio n (8-27) . Th e actua l ga s velocit y i s relate d t o superficia l velocit yby :
u ^ = u G /co s 6 (8-28 ) Not e tha t th e angl e o f incidenc e fo r th e second and sub
sequen t row s o f baffle s wil l b e twic e th e angl e o f inci
denc e fo r th e baffle s i n th e firs t row . TrayTower s Tra ytower s ar e vertica l channel s i n whic hth e liqui d and ga s ar e contacte d i n stepwis e fashio n o n tray s o r plates . Th e liqui d enter s a t th e top and flow s downwar d b

ygravity . O n th e way , i t flow s acros s eac h trayand throug ha downspou t t o th e traybelow . Th e ga s passe s throug hopening s i n th e tray , the n bubble s throug h th e liqui d t o for m a froth , disengage s fromth e froth , and passe s ont o th e nex t trayabove . Ther e ar e variou s traygeometries . Th e siev e trayand bubbl e cap ar e th e two mos t commo n types . Siev e Plate s - Primar yefficienc y- Taher i and Calver t (1968 ) derive d an equatio n fo r siev e plat e primar ycol
lectio n efficiency : E = 1-ex

p (-4 0 F 2 K p ) (8-29 ) wher e 0.3 0 < F £ < 0.65 , 

## k " = -AA± (8-30 ) 9 ^G d h where : ¥ r = foa mdensity , rati o o f clea r liqui d heigh t t o tota l foa

mheigh t v , = velocit yo f ga s throug hhole , cm/se c 

### 18 8P. 7

d , = hol e diameter , cm Pressur e Dro p - Perr y(1963 ) ha s suggeste d tha t th e pressur e dro p i n siev e plate s ca n b e calculate d accor din g t o : A P = h+ h+ h , + h wowd

p r (8-31 ) wher e : h w wei r height . = 4- 9 cm , assum e 5 cm , i f unknow n Q T o w = hea dove r

th ewei r

= 0.14 3 F ww . 1 P G V h l d P dryplat e hea d los s = —— - ~ c 2 p L 2

= residua l pressur e dro p = 0.01 3 wate r

—= 1.1 4 0. 4 (1.2 5 - f h ) + ( 1 - f h ) 2 (8-32 ) where : F w 

### Q L wcolumn wal l curvatur e correctio n facto r = 1. 1 liqui d flo wrate , her e i n m 3 /h r wei r length , m fractio n o f th e perforate d ope n are a i n th e plat e Rubble-ca p Tray s - Equation s use d t o predic t primar ycol
lectio n efficienc yan d pressur e dro p o f siev e plate s can als o b e applie d t o bubble-ca p trays . DESIGNPROCEDURE S Th e genera l step s i n designin g an entrainmen t separa to r ar e a s follows :

18 9P. 8

1 . Base d o n proces s conditio n an d separato r con figuration , construc t th e grad e efficienc y curv e fo r th e separation . Equation s fo r pri
mar yefficienc yca n b e use d fo r thi s purpose . I n cas e th e ga s velocit yi s highe r tha n th e reentrainmen t onse t velocity , reentrainmen t shoul d b e subtracte d fromth e primar yeffi
cienc y. 2 . Comput e th e collectio n efficienc yfo r tli e whol e populatio n o f th e drops . Thi s ca n b e don e eith.er graphicall yo r mathematically . Fo r graphica l solution , plo t Pt . versu s fractio n smalle r tha n d , • (wher e Pt • i s penetratio n fo r dro p siz e d , •) . d i 1 * Jdi- ' Th e are a unde r th e curv e i s th e overal l pene tration . Outle t loadin g i s equa l t o inle t loadin g time s overal l penetration . 3 . Comput e expecte d pressur e drop . I n th e proces s o f designin g a n entrainmen t separator , th e step s shoul d b e repeate d fo r differen t propose d sep arato r configurations . Th e fina l configuratio n ca n the n b e selecte d afte r optimizatio n analysis .



### 19 0P. 9



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### Carpenter , CL . an

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19 2P.1 1



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d W . Licht . The Collectio n Efficiencyo f Cyclon e Typ e Particl e Collector s - ANewTheoretica l Approach . Pape r presente d a t San Francisc o meeting o f AIChE . Decembe r 1971 . Levich , V. , "Physiochemica l Hydrodynamics" , Prentice
Hall , Englewoo d Cliffs , NewJersey , 1962 . Matrozov , V.I. , 0 . Soobscheniya , Nauchno-Tekhnicheskik h Rabotak hNIVIF , Nos . 6/7 , 152 , 1953 . Morishima , N. , T . Yoshida "Dus t Collection onAtomize d Droplet s Calculatio n o f Collectio n Efficiencywit hCon sideratio n give n t o Drople t Siz e Distribution " Kagak u Kogaku , p

p 1114-1119 , 1967 . Morishima , N. , T . Yoshida , Y . Kosoka , an d Y . Nonaka "A n Examinatio n o f Ventur i Scrubbe r Design " Funta i Kogaku Kenky

u Kaish i (J . Res . Assoc . Powde r Technol. ) Vol . 9 , No . 6 , p

p 357-362 , 1972 . Mugele , R.A. , AIChE Journal , 6_ , 3 , 1960 . Nukiyama , S . an

d Y . Tanasawa , Trans . Soc . Mech . Engrs . (Japan) , 4 (14) , 86 , 1938 ; 4 (15) , 138 , 1938 ; 5 . (18) , 68 , 1939 ; 6 (22) , II-7 , 1940 . 19 3P.1 2



### Perry , J.H . Chemica l Engineering Handbook . 4thEdition . McGraw-Hill . Ne wYork . 196 3 Perry , J.H . Chemica l Engineering Handbook . 5thEdition . McGraw-Hill . NewYork . 1963 . Satsangee , P.D . Master' s Thesis . Polytechni c Institut e o f Brooklyn , 1948 . Schurig , W.F . D.Ch.E . Dissertation . Polytechni c Institut e o f Brooklyn . 1946 . Shepherd , CB . an

d C.E . Lapple . IE C Chem . 31 , 1246 , 1940 . Taheri , M . an

d CM . Sheih , AIChE Journal , 12 , 153-157 , 1975 . Tohata , H. , T . Nakoda , an d I . Sekiguchi , "Pressur e Losse s on Venturi-Mixers" , Kagaku Kogaku , ^_8 , 64 , 1964 . Torobin , L.B. , W.H . Gauvin , Canad . J . o f Chem . Eng . 38 , 142 , 1960 . Volgiii , B.P. , T.F . Efimova , an d M.S.Gofman , Int'l . Chem . Eng. , £ , 113 , 1968 . Walton , W.H . an

d A . Woolcock , i n"Aerodynami c Captur e o f Particles" , ed . E.G . Richardson , Pergamo n Press , Oxford , 129-153 , 1960 . Wen , CY . an

d S . Uchida , "Simulatio no f S0 2 

### Absorptio n in a Ventur i Scrubbe r b yAlkalin e Solution" , Proceeding s o f Secon

d Internationa l Lime/Limeston e Wet-Scrubbing Symposium , NewOrleans , Louisiana , 1972 . Yamauchi , J. , T . Wada , an d H . Kamei , "Pressur e Drop Acros s the Ventur i Scrubbers , "Kagaku Kogaku , 2_7 , 974 , 1963 . York , O.H . Performanc e o f Wir e Mes hDemisters . Chem . Engr . Prog . Vol . 50 , No . 8 , 421 , 1954 . York , O.H . an

d E.W . Poppelle . CEP . 59^ , 45 , 196 3 Yoshida , T. , N . Morishima , an d M . Hayashi , "Pressur e Los s in Ga s FlowThroughVentur i Tubes" , Kagaku Kogaku , 2_4 , 20-2 7 20-27 , 1960 . Yoshida , T. , N . Morishima , M . Suzuki , an d N . Hukutome , " "Pressur e Los s fo r the Acceleratio n o f Atomize d Droplets" , Kagaku Kogaku , 29_, 308-315 , 196 5
19 4P.1 3

APPENDI XA . DERIVATIO NO FSCALIN GFACTO R I nsolvin g equatio n5-2 3 weassume du* $ = 0 . I norde r 

### do t o fin d Pt( d ) fo r othe r value s o f u l , we mak e us e o f th e p do following artifice . Imagine the givenduc t t o be projecte d in th e upstrea

m directio n unti l a distanc e 1 „ i s reached suchtha t a t z = -1 H 

### , the liqui d velocit yi s zero . Tha t is , th e distanc e 1 „ i s tha t lengt ho f a hypothetica l duc t having zer o initia l liqui d velocit ywit hestablishe d liqui d velocity u , at it s exit . In thi s Appendix , we wil l distinguis h quantitie s referring t o th e hypothetica l duc t fro mthos e referring t o the given duc t b yusin g a prime (' ) withth e former . The n fro

m the geometr

yo f th e duct , we ge t r ' = r - L tan B o o H an d ' A 1 

### = A1 o o \ 1 H

### ta

n B \ j (A-l ) (A-2 ) Fro mcontinuit yo f ga s flow , w e have

= u 

### G o l 1 

### ' 1 „ ta

n 6 \ " J 

### (A-3 )
Fro mth e definitio no f C ~ , w e have Do ' C = C ' L D o u D o b O

| u Go- u d o | 0. 5

Do u Do

— I T0. 5 G o G o d o

= C Do G

o d o u G o 0. 5 1 „ ta n8 J / 2 (A-4 )

19 5P. M



### Using equation s A- l throughA- 4 an d th e definition s o f th e variou s dimensionles s parameters , th e following relation s are obtained :

L ' = ( L + L R 

### ) ( l - S L H 

### ) (A-5 )
S ' = S ( l - S LJJ)'^ 2 ' 1 

### (A-6 )

u 

### d ' = u 

### d ( x

### " s L H ) 

### ( A



### - y 

### ) 

# Wl p 

# GC 

# D i \^ W

= 

# W Wi VQjta / / „ - „ 7<>. 5 G / r

## / u 

## G 0 

## - u 

## d 0 

## r/ . h tan 

## A i /2



### = B ( l- S L H 

### ) " j / 2

### (A-8 ) whic hgiv eth edesire dscalin g factors .

19 6P.1 5

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### Ventur iScrubbe r

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f arevie w an devaluatio no f availabl eventur i scrubbe r desig nequations . Calvert' s differentia lequatio nfo r particl ecollectio nan d Boll' s differentia lequatio nfo r pressur edro p wer eselecte dfo r numerica lsolution , an dth eresult s ar epresente dgraphically . Particl ecollectio nan dpressur edro p o f ventur iscrubber s ca nb eapproximate db yth ecollectio noccurrin g i nth eventur i throa t an db yth edro p acceleratio nloss , respectively . Simplifie dequation s wer e derive db yapplyin g Calvert' s an dBoll' s equation s t o th eventur ithroa t section . Th e ne w desig nequation s ar emuc hsimple r t o us ean dcompar efavorabl ywit havailabl e performanc edata .

-.7 . KE YWORD S AN D DOCUMEN T ANALYSI S 3 DESCRIPTOR S 

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