ELSEVIER Powder Technology 86 (1996) 137-14.4

Prediction of Venturi scrubber grade efficiency curves using the contacting power law

R.W.K. Allen Department of Mechanical and Process Engineering, University of Sheffield. Sheffield SI 4Dl], UK

Received t June 1995; revi~ed 12 July 1995

Abstract

The link between the collection efficiency of a Venturi scrubber and its operating pressure drop was first established by $emrau in 1958. Friedrich L6ffler used it as a starting point for the predictive rnedet for which he won lhe File ration Society Gold Medal in 1980, The apl~oach taken in that study was not widely followed by subsequent modellers but, in conjunction with previous work, it does lay the foundati~ for a useful desi g n approximation which allows grade effieie hey curves to be predicted from empirical data determined at other operating conditions, In this paper, a range of detailed grdde efficiency measurements conducted on a fun.scale plant are reported. The curves are shown to depend only upon pressure drop across the scrubber, there being no independent effect of gas velocity, liquid to gas ratio, or dust size distrihetion, The implications of this for design are discussed and the grade efficiency prediction technique is demonstrated.

Keywords: Ventufi scrubber; Cont•tiag [~wer law; Particle size; Efficiency collection

1. Introduction

The collection of panicles in Venturi scrubbers is domi- nated by inertial impaction, with diffusion only being impor- tant for particles smaller than about 0.3 tan. Inertial impaction results from the relative velocity between the dust particles and droplets and, in the continuum regime, may be eharac- terised in terms of a Stokes number, K:

g = ppa%,

9/ado

where d and dD are the particle and drop sizes, respectively, and v, the relative velocity between them. Other symbols take their usual meaning. In the commonest designs of scrubber, which are gas atomised, the necessary high levels of relative velocity are achieved at the expense of gas phase pressure drop.

The link between performance and pressure drop was first established by Semrau etah [ 1 ]. They demonstrated a rela- tionship of the form:

rj= 1 -exp[ - n A p v]

The constants a and 7 are usually thought of as characteristics of the dust with -y, in particular, said to account for the effects

Elsevier Science g.A. ~DI0032.5910(95)03046-C

of dust size distribution (see, for example, Cooper [2] ). The validity of this relationship has been questioned by some workers: for example, EL, nan and Johnstone 13], Gieseke [4] and Muir et al. [5] all suggested that efficiency can be less than that predicted from the contacting power concept at low gas velocities. This finding has been confirmed by Mien and van S~mten [61 who have shown that. for a 'badly' designed Venturi scrubber, there exists a minimum ratio of liquid flow to gas flow which ensures good distribution of liquid across the throat and performarg:e up to the level pre- dicted by the contacting power concept.

The equation is normally considered to he entirely empir- ical but can, in fact. be shown to have an approximate theo- retical basis.

L6ffler and Schuch [71 started their analysis with acon- sidaration oftha contacting power law and correctly identified its inabilities to model the detailed phenomena which occur in Venturi scrubbers. Most attempts to descrihe thishahaviour have generally adopted either a differential material balance approach or, like LOftier, have considered the efficiency of a single drop over its entire flight length and integrated this over all the drops. In each case, the ~sulting differential equations have eitber been solved numerically or further sim- plified to yield an analytical solution.

138 R. V~ K, AIletz/Powder Technol¢~gy 86 (1996) 137-144

Analytical models have generally ~tarled from a simple one-dimensional material balance over a differential element of the scrubber, ca.::

+ ~ A ' [Q,G(dr,)]{'n'do'-14], , • J =t I)

This equation is essentially the same as that derived by L6fllcr and Schuch from the consideration of drop flight. Here Qi and Q~ are liquid and gas flows, respectively, c is the dust concentration, UD the drop velocity, r h the target cfliciency of an individual drop, G(dlj) the drop size distribution and

f QiG(do) ddtj AuD

is the volume fraction of droplets in the differential volume, commonly termed the 'holdup', Ha. Making the simplifying assumptions that the droplets are monodisperscd and that the fraction of liquid entrained is constant (i.e., there is no evap- oration or interchange with the film atthe walls), this reduces t o

de 3v~H~I, dz

c 2dov~

where

Q, /-/d ~ - - uoA

which was suggested by Calvert 181. Most of the published models can be manipulated into a variant of this form. The different solutions arise principally from the different as sumptions m ado in describing the droplets and lheir motion. Calvert etal. [9,10] developed their solution by considering that collection efficiency varied linearly with the relative droplet velocity, which they related to the superficial gas velocity through a factor, 'f' and by further assuming that collection occurred only in the throat and that the droplets accelerated from an initial relative velocity ratio,]', to the full throat velocity, vt; ~ f f = 1). The final equation was

c~ t 55QsF ! "'

where

1 [-_0,7_Kzf+l.4L IK~+0.7~ 0.49 "1

and

] ' 9~/o The limitations of this medel, particularly in the use off,

arc well known and will not he discussed. Yung etal. l 11 ]

have, however, shown that the model predicts reasonably well the form of the experimental data if the right value o f f is used. Lbffler and Schuch I71 make the interesting observa- tion that, for most operating conditions of practical interest, f(K2,l) car, be approximaled by

F(K2,f) =0.312 Kd 2

The simplest model for pressure drop considers only the acceleration of the droplets and, by a differential momentum balance, one obtains:

Q, -dP=~h ~ v~qdUo

Making the usual approximations of zero initial axial liquid velocity and the droplets accelerating to the gas stream veloc- ity, this can be integrated for the throat section to yield:

A p = ~1 E l'gl"

Substitution of this and LGfller's simplification into Cal- vert's approximate model gives

r / = l - ¢ . , ~ - k ~ d 2 A P ~ )

where k is a constant. This is a form similar to the contacting power law. It suggests that for a monodisperse particle, y ~ i. The use of this result to manipulate grade efficiency data will be discussed below.

2. Grade efficiency measurements

The experimental programme was undertaken on the 2 mUs pilot plant test facility described in Allen and van Samen [6]. The efficiency of the scrubber, as a function of particle size, was measured against the following operating parameters: • overall pressure drop • gas flow rate and throat velocity • Venturi geometry • dust type

The pt,ot plant facility is shown in Fig. 1. Two geometries of Venturi scrubber were tested: an industrial prismatic unit with an adjustable aspect ratio (5:1 to less than 2:1 ), and a classical long throat design with a length ratio of 13:1. These are shown in Fig. 2. Both units used wetted wall irrigation.

The grade efficiency measurements were made by dispers- ing pro-sized dust at a c~ntrolled rate into the inlet duct and measuring the fraction which penetrated the scrubber by extractive sampling in the outlet duel using an Andersen Mklll in-stack cascade impactot. Two grades of silicon oxide test powder were used. These are designated type A and B and had nominal size distributions of 95% by weight smaller than 5 and 15 tzm, respectively. Their full size distributions, measured by liquid-borne sedimentation, are given in Fig. 3.

1

R W. K Allen/Powder Teclm~logy 86 [1996) r3~144

Recycle pump

Scale (al0prox,) () 1' rn

Fig. I. Schematic of experimental plant.

Their dispersion was achieved using an industrial sand blast- ing nozzle operated with compressed air at 5,5 bar. The air was pre-ionised using .,~Op,, radioactive sources to reduce any static charge induced oa the particles by this dispersion tech- nique. The degree of dispersion was tested in two ways. Firstly, samples extracted using the SPS mini-scrubber ( Allen and van Santen 16] ) were re-analysed by liquid-borne sedimentation. The results (closed circles in Fig. 3) indicate that the particles were not measurably comminuted by the dispersion process. Secondly, measurements were made of the air-borne size distribution by sampling in the inlet duct with the cascade impactor. The agreement in the resulls (crosses in Fig. 3) confirms the success of the dispersion technique in reducing the powder to primary particles, The agreement also indicates that either technique may be used to pro-size the dust. Liquid-borne measurements were there- fore chosen, principally because of their greater simplicity and larger measurement range. The cascade impactnr was subsequently only used to measure the outlet size distribution, where liquid-borne techniques were inappropriate.

The principle of the cascade impaetor is well established. The sampling train used in these tests is shown in Fig. 4. The impaetor was fitted with a standard goose-neck sampling nozzle and inserted bodily into the duet through a standard 100 mm sampling port. This was fitted with an extension piece so that the bulk of the impactor could be held out of the gas flow, thereby reducing the risk of flow disturbance. Iso- kinetic sampling was used throughout the experiments with different nozzle sizes being used where necessary to maintain a required impactor sampling rate of 15 to 20 l/rain. The dust

139

Sr, ower bet D,¢ mel(,f wa!l ~njecllCm ~ "

~nN~lmn

k~36 J lf~ d~.meter

8 r e ~ l ~

l h ~ a , ~ w,~h

@ 373 136

10 Is~ sG lal I (b)

Fig. 2. Sc~matic of Vcntuil lest sections. ( a ) Adjllslab~ ptismaU¢ Ventari; (b) fixed cil~ular throat V¢l'~uii.

feed rate was adjusted for each measurement to give a col- lected weight of approximately 10 mg in a sampling period of 2 min. A single layer of Whatman glass fibre fiher material was used as ,~ ~na! s,'age collector and glass fibre substrales were used on each of the collection stages. Weighing was carried ou't on a precision balance to 0.05 me. A Stalrmand half-area mixing baffle was located four duct diameters upstream of the sampling port to ensure a uniform dust dis-. tfibution, Because of the care taken to condition the gas flow, i mpaetor samples indicated no systematic variation in particle size across the duct and hence single point measurements were considered sufficient to determine the outlet size distri- bution. A typical analysis is given in Fig. 5.

Grade efficiency measurements were made for both Ven- turk with two grades of dust. The experiments are summar- ised in Table I_ The conditions investigated were: throat velocity (67 to 103 m/s), liquid togas ratio (0.36 to 1,15 If rn 3) and overall pressure drop (270 to 840 mm of water (w.g.)).

Z 1. Grade efficiency at constantpressure drop

Previous studies [ 1,6] indicate that the overall efficiency of a Ventun scrubber for a given type of dust over a wide range of operating conditions is solely a function of pressure drop. This suggests that the grade efficiency should also be independent of operating conditions.

influence of liquid to gas ratio, The effect of Liquid to gas ratio was investigated at three levels at two pressure drops, 400 and 600 mm w.g. The results are presented in Fig. 6. 'l'hese indicate no systematic trend,

Influence of Venmrigeometry. Comparative tests were per- formed on the circular and prismatic Ventaris at two pressure drops, 270 and 800 mm w.g. The results (Fig. 7) again show no systematic trend despite the very different contributions made by the wet and dry pressure drop components.

140 R. W.K Allen/Pawder Technology ~6 (1996) 137-144

9s

)

~ j

d ~

v~ ce n i m ~ t e r

. . . . . . . n:alerp ....... H )

B~r~chon o~ olrllow

Du¢l ~vol(

Fig. 4. S c h e m a t i c of A n d e r s e n i m p o r t e r sampl ing t ra in .

~9 B

Colcatale~ gro~e o ~B 99 et htlency ~ l c ~ ~ +"

~O Inlet ~lZe

* ~e=h¢Ole c~¢o~e ,mpoclor 0

0 2 Overclll prv~re drop 29S m~ wg g'v,~rolt ¢olketl,on etf,¢,ency S~ 2"9 %

, , , I 1 i t , , , , 0 1 OIz 013 OI i ,110 2 3 5 ~0

Pothole ~tze ( ml,¢rol~S )

Fig. 5. Typical grade efficiency determi.ation ( R u n N S ) ,

o /

/ / / ' o Dusi A m

----~u)

V ./" °: ................ o f " ~ . ~ m Andrea~en pipette r~ea~a=emer, t • o - ~ o f d'~spe~ed dus t

@ Re~l~cate p i p { t t e e~ntr l fo*je i=L~ ' ' I . . . . =,L'Ubure~e~ta of e ~ p e r s e d ~as~ 05 10 I~IQ ÷ kr orne cascs, e i ra ,actor

PcarllCt~ ~lZ@ {~ust A ) m,cron~

I 05 I0 50 100 e I000 1500

PC~rllCle s~ze Cdusl ~} nllcron[,

Fig, 3, Size distribuli0ns of types of t~ [ dust,

These results arc highly significant. They indicate that, at least over the typical operating ranges considered, Ventari performance is independent of liquid to gas ratio, throat velocity and throat design. T h i s supports the contacting power concept. It also suggests that there is no ' o p t i m u m '

Vcnturi design or 'optimum' drop size at which enhanced collection can be achieved and that, given good liquid distri- bution, the efficiency is simply a function of the pressure drop.

Influence of dust type. Dust size distribution is the primary factor determining the relationship between pressure drop and overall collection efficiency. The grade efficiency, however, being the efficiency as a function of size, should itself he independent of size distribution. This was tested using the two test dusts A and B. The results, determined at three levels

OI C~ 05 ll0 ~ 3 l 5 7

99 S 8

9a t / l ~, )s,Js

99 8

50 %

3C ~

,o 2~',' % ° , . . . . . . . . . . . . . . . . . . , .

• Lkl5 )t) ~ lOB o )~, • ~13 60~ llO W~ 6~

02 05 lo 2 3 5 lO

P~rtlcte s,),P ( m,gron~ )

Fig. 6. C o m p a r i s o n of grade efli¢ieocies at the same overall pressure drop,

R. W.K. Allen/Powder Technology 85 (19~6) 137-144 141

9 9 9 . ~

99,~ 99

Ruin Venturl Pressure No T~pe D~op • •

- (rnm w9~ e ~ ' ' :~ - *6s C,r~ e~3 _ , 4 / o o~..m~

0 G/* Prtsrr. 7fl7 - /

(Obst type a ) /

, , 4 g00mm wcj 270ram wg

®

Z c m Run Ventorl Pressure ~) No T~,pe Oroo

(ram wt~) O GI"[ Circ 275 • G2 I~,~ rn 270

(DIJSI type B)

I r , 1 1 , , 4 I . - -- , -J Ol 0.2 0S 10 Z L

02 05 lO 2 5 I0

P~rllcle Sl2e (rnlcmns)

Pig. 7. Cmnparison of circular and prismatic Vex, luffs.

9999 ,.

q5 elO~ ~q '-.I~ mm ~ 290 ~,~ ~g

70 El Run Oust ~'~Pr ~ [- . . . . . . . -¢- / ~o • . 4 a e~ o

I (B) ....... f i p , ~

113 :-).t . , _ l ~ z , . , l J &~ • ~z" A 2~B o~ o~ io z 3 ~,

03 05 l0 cA ) 2 ~ z.

Oi~ 05 ]0 2 3 ~ 5

Pl~rll¢l@ $lZ~ ( microns ]

F ig . & Varialian of grade efficiency with pressure drop and dugt type.

of pressure drop, are given in Fig. 8. The expected agreement is seen at the lowest pressure drop (290 mm w.g.) but, even allowing for the slightly different conditions at the highest value, a divergence is found at higher pressure drops. Such differences, might be ascribed m "dry serubfiing' by which, at high concentrations, large particles sweep smaller ones out of the gas stream. However, in these experiments the dust concentrations were necessarily low, of the order of a few g/ a~ ~, ~o sac:, effects should have been minimal. A more plau- sible explanation is that the reported deviation is the result o[ experimental errors in measuring the fine tails of the feed size distributions for the coarse dust.

Dust composition, especially differences in hydrophobic- ity, would be expected to have some effect on the shape of the grade efficiency curve. This was not investigated here.

3. Venluri sc~bber design

A common me~hocl of presenting grade efficiency data is to express the particle size corresponding to agiven efficiency as a function of pressure drop. Typically, this is the size corresponding to 509'0 efficiency; the 'cut size', d ~ Such data are presented in Fig. 9. This considers all the dala sets measured here. For most of these, extrapolation to 50% effi- ciency was required because of the limiting lower size meas- urable with the Andersen impactor (about 0.3 txm). Two methods of extrapolation were used; simple graphical extrap- olation from the lowest measured point to the origin, and log- normal extrapolation based on a least-squares fit to the tails of the distributions, Clearly, the difference between these two methods increases with increasing pressure drop (increased range of extrapolation). The line in Fig. 9 represents a least- squares fit to all points. Considerable scatter is seen in these data. Thi s reflects the very real difficulty of obtainingaccurate performance measurements, especially in the sub-0.5 Fm region. The use of design methods, based on simple also cor- relations, is therefore likely to give inaccurate results.

Instead an alternative approach is recommended which assumes the existence of grade efficiency data measured under known conditions. This can be scaled in order topredict the grade efficiency curve under the new conditions by the simple application of the contacting power law, using "~=: l,

(a)

o~

oe I

T

Pressure tire D (ram ~.'] I

% , "'.%y" ~o .........

DI u~

Fig. g. Relationship between panicle cut diameter ~m4 p,'esstwe drop. N,ote: D[ determined by lip, eat extrapolation of grade efficiency ce.Jrves m (0, 0 ) . / )2 detmnined by leasl-~uares lining of log-normal distribution through taft of grade e~eiency curves.

142 R. t£ K. Allot / Powder Terkualogy g6 (1996) 137-144

95

85

~° ?5

$5

GO

-o--i~l~m.;

0 5 1 t ,5 2 2.S 3 3.S

Table I

Suromary of grade efficiency measurements

.%1 call Sizt, lit nit )

Fig. 10. Grade efficiency as a function of pressure drop.

Run Dusl Throat Throat Liquid la no, type selling a velodly gas ralio

(In/s) l l/m ~)

Pressure drop ( Into wg.) Overall efficiency

Totul Dry (%)

G2 B 8 66.5 1.06 270 154 96,1t3 G3 B 9 IH L ,06 434 243 98,07 G4 B 10 114 1.06 787 470 99.06

G5 A 9 84 1,06 434 243 96.86 G6 A l O 114 I 06 737 470 99.22 G7 A 9 84 0.5 394 292 96.83

G9 B CIRC I 0"~ 0.93 813 126 99.1 GI0 B CIRC 103 0.57 602 126 98.68 GI I B CI RC 87.9 I. I I 685 [,9 98.69 GI2 B CiRC 87.9 057 393 fi9 97.85 GI3 g CIRC 96.6 0 74 604 R6 98.69 GI4 I]. CIRC 96.6 0,31 390 g6 97,g3 GI5 II CIgC 93 3 0.39 387 80 97.81 GI6 I~ CIRC 87,9 0.67 430 70 98.05 GI7 U CIRC 79 0.57 275 53 96.89

N2 A CIRC 8 L7 0.36 298 94,29 N3 A CIRC 80.8 0.83 475 97.55 N4 A CIRC 93.3 1.01 840 99,38 N5 A CIRC 93,3 0.17 298 94.29 N6 A CIRC 933 0.53 555 98!4 N7 A CIRC 8.1.7 1.15 650 9879

' Numbers refer lu prismatic Ventun; C[RC refers IO circular Volturi

Thus if, for a given particle size, -q~ and rt2 are the efliciencics

at API and AP~:

:,°l,_-I. Fig. 10 shows four sets o f data taken at varying levels of

pressure drop. The same data, with some others, are replotted

in Fig. I I but, in each case, with the ordinate being scaled

using the contacting power law, The agreement can be seen

to be very good. This indicates that pilot plato data, obtained

under one set of operating conditions, can be accurately

scaled to predict grade efficiencies at other operating condi-

tions by the simple use of the contacting power law. Thus,

data obtained at low pressure drops can be used to obtain

inlbrmation about higher pressure drop behaviour, yielding

more information at the tail of the grade efficiency curve. It

R, tEK, Alte,q/ Powder Technology 86 (1996) 137-144 143

100

95

7S

70

. .. r... ~ . ~ T t . . . . - - :

tJ

I | . . . . . . . . . . . . . . . . . . . . . . .

O.S 1 1 ] 2 2.S 3

Mean Size I pm)

Fig. 1 l , Grade efficiency ctlrves at 600 mm predicled from oilier cxperitllenls.

3,5

further suggests that the mini-scrubber design procedure, pro- posed by Allen and van Santcn, [6] can be adapted to produce comprehensive grade efficiency data fur design purposes.

4. Conclusions

( I ) The grade efficiencies ofgas-atomised Ventari scrub- bers have been investigated on a 2 m3/s scale.

(2) Over the range of conditions investigated here. liquid to gas ratio and throat velocity had nu independent effect un the scrubber grade efficie hey curve, which was simply a func- tion of the overall pressure drop,

(3) Particle cut size data as a function of pressure drop have heen extrapolated from this work. Whilst they give the expected dependence, they show gross variations. Methods using the cut size approach for predicting pressure drop are therefore unreliable for Venturi design.

(4) Scrubber grade efficiency may be adequately described by suitable scaling of existing empirical data by the simple application of the contacting power law.

5. List of symbob

A duct area (m) c dust mass concentration (kg/m ~) d particle diameter (m) f,f~ droplet velocity ratio at atomizat[un G(do) droplet size distribution Hd liquid holdup fraction k constant

g inertial parameter (Stokes number) K~ inertial parameter defined on %t AP pressure drop (N/m 2) Q flow rate (m3/s) u, o velocity (m/s) z axial length along serobher (m)

Greek letter~

constant in contacting power law exponent in contacting power law fractional efficiency, at given particle size gas viscosity (kg/'ms) density (kg/rn 3)

Sll&~cripts

D droplet g o°~s i at inlet I liquid o at outlet p particle r relative (to gas) t throat

Acknowledgements

The work of A. van Santen in producing the experimental data, which have been previously reported to SPS members, is gratefully acknowledged.

144 R.W,K. A11en l Pnwder Technol~gy g6 (1996) 137- 144

Referenres

[ l ] K,T, Semrau, C,W, Maryoowski. K.E. Lunde and CE, Lapple, ing, Eng, Ckem.. 50 (195g) 1615-1620

[2] D.W. Cooper, Armo.~. Env., 10 (1976) 1001-1004 [3] F.O. Ekman and H.K Johnslone, Ind. Erll,,. Chem., 43 ~ 1951 } 1358. [4] J. Gieseke, Pressure loss in Venturi .scrubbers, PItD. Thesi,~, University

of Washington, 1964. [5] D.M. Muir, C.D. Grant and Y. Mibeysi, Filtration .~m'iety Syrup ~

Fihratiop~ Productivily and Profit,*, 20-22 Sept, 1977, Olympia, London.

[6] R,W,K, Allen and A. van Sanlen, l.~v Warld Cfmgr. Particle T¢chnolvgy. Niirnberg. G~rmany, f9R6

[71 F Lbffler and G. Schueh, Proc. Filtration Sf~ciety, Filtrati~Jn or Separation. Jan,/Feb. I~ l . pp. 70-74.

[8] $. Calvert. in A,C. Stem (ed.I. Air P~pltutimn. Academic Press. New York, 1968, pp. 457~196.

[9] $. Calvert, YIIChEJ.. 16 (1~70) 392 396. [ 10] S. Calvert. D. Lundren and D.S. Mehta, JAPCA, 22 ( 197o ) 529-532, [I l lS.C, Yung. S, Calvert and HF. Barbarika, Veutm'i Scrubber

Performance M¢Mel, EPA Rep. No. 600/2-77-172. 197"/.