Predicting the Liquid Flux Distribution and Collection Efficiency in

Ind. Eng. Chem. Res. 1999, 38, 223-232

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Predicting the Liquid Flux Distribution and Collection Efficiency in Cylindrical Venturi Scrubbers Nochur V. Ananthanarayanan and Shekar Viswanathan* Department of Chemical and Environmental Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore

A simplified two-dimensional model to predict liquid flux distribution and collection efficiency in cylindrical Venturi scrubbers with Pease-Anthony mode operation is evaluated with experimental data from a pilot-scale unit. Prediction of the liquid flux distribution near the point of injection appears to be far from agreement with experimental values while the accuracy of prediction has been found to improve with distance from the injection point. The initial location of the liquid source immediately after atomization has been found to affect the liquid flux distribution significantly. Although the overall liquid distribution pattern is found to be in good agreement with the experimental data, the prediction of liquid distribution appears to be a strong function of jet penetration length and turbulence caused by operating conditions. Concentric injection at high liquid rates could result in collision between jets from nozzles as they converge at the center of the scrubber. Turbulence caused by interaction between the jets is accounted for by using varying Peclet numbers. A dimensionless group, Venturi number, developed from jet penetration correlation has been found to predict conditions that give rise to uniform flux distribution and maximum collection efficiency. Venturi numbers between 1 × 10-3 and 1.5 × 10-3 appear to predict conditions for cylindrical Venturi scrubbers (with radial injection into the throat using nozzles) for optimal liquid utilization and maximum collection efficiency. Introduction The Venturi scrubber is a simple, yet highly efficient, device for fine particulate removal from industrial exhaust gases. It is a high-energy-impaction, atomizing system, which has a converging section, a throat, and a diverging section (Figure 1). Cleaning in Venturi scrubbers is accomplished mainly by inertial impaction and interception while various flux forces, such as diffusiophoresis and thermophoresis, assist in the removal of submicron dust. Its advantages include lower initial costs for comparable collection, low floor requirements, absence of internal moving parts, and capabilities to handle wet and corrosive gases. The large power requirements for operation represent its main drawback. A gas stream (normally air) containing particles is accelerated through the scrubber (direction parallel to the scrubber axis, x). On the basis of liquid (normally water) injection, there are two alternative modes of operation, namely, the wetted-wall approach and the Pease-Anthony approach. In the first case, the liquid is introduced along the walls of the scrubber as a film. In the latter approach, liquid is injected through nozzles in the form of a jet perpendicular to the gas stream (radial direction, r). In either case the high velocity gas stream atomizes this liquid into fine droplets and accelerates them. This results in heterogeneous twophase flow inside the unit. The drops move both axially (predominantly because of momentum) and radially (initially because of liquid momentum and later because of diffusion). When the injected drops reach the wall, they form a film on the wall and hence flow at less than drop velocity. This film does not participate in the cleaning process and causes two-phase frictional pres-

Figure 1. Venturi scrubber used in the experimental investigation.

* To whom correspondence should be addressed. Tel: 658744309. Fax: 65-8725483. E-mail: [email protected].

sure losses. The symmetry makes it possible to model half of the scrubber in the radial direction. At the same

10.1021/ie9803321 CCC: $18.00 © 1999 American Chemical Society Published on Web 12/12/1998

224 Ind. Eng. Chem. Res., Vol. 38, No. 1, 1999

time, it is important to keep track of drops that cross the scrubber axis (r ) 0). Several attempts have been made in the past to theoretically calculate scrubber efficiency, but with moderate success. The efficiency models of Calvert,1,2 Boll,3 Placek and Peters,4,5 and Cooper and Leith6 are one-dimensional and assume complete utilization and uniform distribution of the mother liquor with varying or average drop size distribution. These models are generally found to overpredict the particle collection efficiency. The reasons are as follows: (a) In practice, there cannot be complete utilization of the liquid since film on the walls does not participate in the collection process.7,8 (b) The distribution of liquid is far from uniform.9,10,11 The first drawback was ameliorated in the model of Azzopardi and Govan8 by accounting for entrainment and deposition of drops at the wall along the Venturi scrubber with reasonable accuracy. Pulley12 has used the above model with corrections to the single droplet collection efficiency to predict particulate collection over a wide range of operating conditions. His predictions were superior in comparison to those of the Boll3 and Yung et al.13 models based on mean-square error values. This model, however, does not account for nonuniform distribution of liquid drops. In general, there is limited data on liquid flux measurements in Venturi units. Viswanathan et al.7 measured the liquid flux distribution in a rectangular Pease-Anthony type unit. Koehler et al.14 measured the same using a cylindrical Venturi unit operating with the wetted-wall approach and axially downward injection method. These methods are different from that of the Pease-Anthony units where the liquid is injected inward into the scrubber, perpendicular to the flow of gas. Koehler et al. proposed a model that predicts the total amount of gas-borne liquid flow as a function of axial distance by using three empirical constants obtained by a statistical fit on their data. However, their method is scrubber-specific and does not predict radial flux distribution profiles as a function of operating conditions. Subsequent work by many researchers15-18 has established that nonuniformity of the flux distribution is of utmost importance in estimating collection efficiencies realistically. Liquid jet penetration and liquid injection velocity were found to be critical in defining the flux distribution. The recent work of Ananthanarayanan and Viswanathan18 takes into account incomplete utilization of the liquid by eliminating film flow predictions using empirical correlations. These models have been validated with both pilot- and industrial-scale rectangular units and have been found to predict collection efficiencies accurately. The objective of this work is to develop a realistic twodimensional mathematical model for cylindrical Venturi scrubbers with Pease-Anthony mode of operation to predict the liquid flux distribution and collection efficiency. The model developed in this work is verified with the experimental data collected on a pilot size unit by Haller et al.19

main collection process for particulate matter occurs in the Venturi throat, a region where large relative velocities exist between the drops and the dust, with the drop concentration distribution being mostly nonuniform. The present work is to develop a simplified model for cylindrical units that takes into account (a) jet penetration length (assumed to be the same as that for a rectangular unit), (b) maldistribution of liquid drops, (c) initial liquid momenta, (d) drop movement in the axial direction by convection and in the radial direction solely because of convective diffusion, (e) nonuniform inlet dust size distribution, (f) dust motion in the axial direction through a convective mechanism and in the radial direction through a convective diffusion mechanism, and (g) particulate matter collection by droplets through inertial impaction. The model assumes uniform drop size, constant film flow, no drop-to-drop interactions, uniform inlet distribution of particles, and no interaction between particles. Since, in all practical applications, the separation distance between the liquid injection orifices is very small, negligible variation in the drop concentration can be assumed in the θ direction, making the model twodimensional.9,15 Only a slice of the scrubber is considered for simulation, because of system symmetry in the radial and θ directions. This makes the entire system axisymmetric and thereby reduces the physical area to be considered for simulation. Droplet Motion. The droplet motion in this model is predicted as a steady-state process. The two-dimensional steady-state continuity equation for liquid drops can be written as

Theoretical Model

The mean droplet diameter is calculated using Boll’s equation10

The performance of a Venturi scrubber greatly depends on the liquid injection arrangement, drop size, liquid flux distribution, and initial liquid momenta. The importance of a realistic concentration distribution of liquid drops can be appreciated by recalling that the

(

)

∂Cd ∂ 1 ∂ (VdxCd) ) Edr + Qd - Qf ∂x r ∂r ∂r

(1)

In eq 1, the change in concentration due to bulk motion is equated to the change due to diffusion plus the drop source strength minus the amount of liquid flowing as film on the walls. The fraction of liquid flowing on the walls for known operating and design conditions was obtained from the correlation derived for rectangular units by Viswanathan et al.:20

F)

89.379

( ) L R0 G d0

1.007

(VGth)0.888

Liquid Droplet Velocity. The drop velocity in the axial (x) direction can be determined from a force balance on the drops as shown by Viswanathan:15

dVdx 3 (VG - Vdx) ) CDNµG dx 4 D 2F V d

d

(2)

dx

The value for CD is calculated using the equation16

CD ) 25.8/NRe0.81

(GL)

42200 + 5776 Dd )

(3)

VGth1.602

1.932

(4)

Ind. Eng. Chem. Res., Vol. 38, No. 1, 1999 225

to cell by the sum of bulk and turbulent velocities. To evaluate the movements of each mass particle, the bulk velocity, eddy diffusivity, gas stream drag, and initial liquid momenta are calculated. The initial position of the liquid drops (jet penetration) is very important because it affects the flux distribution significantly. In this work, the initial position of the liquid drops is assumed to correspond to the point of jet atomization as measured in a rectangular Venturi scrubber:7 Figure 2. (a) Twelve 2.5-mm nozzles arranged concentrically. (b) Typical Eulerian grid chosen for modeling.

Eddy Diffusivity. The eddy diffusivity of the drop and particle can be calculated using the concept that the velocity fluctuations in turbulent flow are sinusoidal and Stoke’s law applies to the drag on drops:15

Ed b2 ) 2 EG ω + b2

Ep b2 ) 2 EG ω + b2

(5)

The value of ω was taken as 300 and EG/VGDeq ) 0.01 ) 1/NPe. Particle Motion. The two-dimensional, steady-state, continuity equation describing the transport of particulate matter, neglecting longitudinal diffusion, is

∂(CpVG) ∂x

)

1 ∂

[

r ∂r

Epr

]

∂Cp ∂r

-

m* πη F i i

∑ i)1

Dd2(VG - Vdx)CpCd

4

(6)

This steady-state equation is similar to eq 1 obtained for droplet motion, except that the source term in eq 1 has been replaced by a dust removal term. The single drop collection efficiency, η, can be calculated from the following by taking into account inertial impaction:1

ηi )

(Ψ +Ψ0.7)

2

(7)

where Ψ is the impaction parameter, defined as the ratio of particle stopping distance to the droplet diameter

Ψ)

FpDp2|VG - Vd| 9µGDd

Determination of the Overall Collection Efficiency. The overall collection efficiency at any axial location can be calculated by determining the concentration of particulate matter at that location by an integration process. The overall collection efficiency is given by

ηov ) 1 -

∫Np(x,r) dr ∫Np(0,r) dr

(8)

where Np(x,r) is the number of particles in the cell located at (x, r). Numerical Procedure. Because the system is axisymmetric, the total volume chosen for simulation accounts for one nozzle (θ direction), the entire length of the scrubber (x direction), and half of the diameter of the scrubber (r direction). The physical space is divided into cells of a fixed Eulerian grid (Figure 2), and the Lagrangian mass particles carry the fluid from cell

FjVj l* ) 0.1145 d0 FGVG,th

(9)

The flux distribution at any axial position is obtained by applying a finite difference formula on eq 1 and representing it in tridiagonal matrix form. Values of the drop concentration for each cell are then calculated by the Gauss elimination procedure and backsubstitution.21 Particulate matter is introduced as uniformly distributed dust particles moving with the same velocity as the gas stream. The particle distribution at any axial position is then determined by solving eq 6 in a way similar to that of the flux distribution. From the concentrations, the overall cleaning efficiency at any axial location is calculated using eq 8. Results and Discussion Liquid Flux Distribution. The model results are validated by first comparing the theoretical flux distribution with experimental values measured in a pilotscale Venturi scrubber19 and then the particulate collection efficiency. Parts a and b of Figure 3 provide a comparison of experimental and predicted flux distributions at six different positions along the throat, for two operating conditions. Figure 3a shows the model predictions at a mass liquid-to-gas ratio of 1. It is found that although the predicted flux values do not match the experimental values at positions closer to the liquid injection point, a more reasonable prediction of liquid flux is obtained at the end of the throat. However, the measured flux distribution is found to be more uniform than predicted values. At a mass liquid-to-gas ratio of 2.5, the model prediction (NPe ) 100) is less uniform in comparison to the experimental values at all locations, as shown in Figure 3b. A comparison of the results in parts a and b of Figure 3 (NPe ) 100) indicates that the model prediction of the liquid flux distribution is better for lower liquid loading. The reason for this discrepancy is a combination of two factors: (a) the concentric liquid injection system used to spray the liquid; (b) the jet penetration correlation used to locate the initial position of drops. For a mass liquid-to-gas ratio of 1, the penetration length is 50% of the throat radius, whereas for 2.5 it is found to be 130% of the throat radius. Increasing jet penetration is likely to increase the interaction between the jets as they converge to the center of the throat. This would cause additional turbulence inside the system in the region of jet atomization. This excess turbulence would aid in the spread of the liquid drops and can be accounted for in the model by using lower Peclet numbers. Because of the lack of experimental data, there is no criterion to determine exactly the region of additional turbulence caused by jet interaction in concentric injections. Hence, a trial and error approach was adopted for selecting the Peclet number that would adequately represent this phenom-

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Figure 3. Comparison of liquid flux distributions at six locations (from the point of injection) in the throat. (a) VGth ) 70 m/s; ML/MG ) 1.00; NPe ) 100 (predicted, s; experimental, 0). (b) VGth ) 70 m/s; ML/MG ) 2.5 (predicted (NPe ) 100), - - -; predicted (NPe ) 10), s; experimental, 0).

Ind. Eng. Chem. Res., Vol. 38, No. 1, 1999 227

Figure 4. Comparison of liquid flux contours in the throat section: (left) predicted; (right) measured. (a) VGth ) 70 m/s; ML/MG ) 1; NPe ) 100. (b) VGth ) 70 m/s; ML/MG ) 2.5; NPe ) 10.

enon. In this work, a lower value for the Peclet number was used in the region of jet penetration greater than 50% of the throat radius. Figure 3b also shows the liquid flux distribution predictions, using a Peclet number of 10, for a liquid-to-gas ratio of 2.5. The predicted flux

distribution is found to be in better agreement in comparison to the results for a Peclet number of 100. Parts a and b of Figure 4 show the predicted and experimental flux contours in a section along the throat for the two operating conditions. The contours represent

228 Ind. Eng. Chem. Res., Vol. 38, No. 1, 1999

Figure 5. Overall collection efficiency along the throat (VGth ) 70 m/s; ML/MG ) 1).

lines of constant liquid flux normalized with the average liquid flux. These figures depict the entire spread of liquid in the throat and hence the degree of liquid utilization, which is of utmost importance in determining collection efficiency and scrubber performance. These predicted values are in reasonable agreement with the measured values. The published models for predicting flux distribution16,18 have demonstrated a reasonable match only at the end of the throat. This is because the dispersion process is so complicated that there may be limitations in representing the various phenomena occurring closer to the point of injection and subsequently solving them using advanced computational methods. Because jet penetration length and film flow data are not available in the literature for cylindrical venturis with concentric liquid injection, the corresponding correlations from rectangular venturis were used in this work. Moreover, the laboratory-scale unit modeled is very small and could behave differently from larger scale units in the range of operating conditions used in this study. Even with these limitations, the proposed approach predicts reasonable values and consistent trends of flux distribution along the throat. Collection Efficiency. Haller et al.19 used quartz dust comprising different size particles, with a median particle size of 1 µm, in the determination of particulate collection efficiency. Figure 5 compares the collection efficiency along the throat for a gas velocity of 70 m/s and a mass liquidto-gas ratio of 1. The model overpredicts the collection efficiency in the first half of the throat and then underpredicts it in the second half. An accurate prediction of the collection efficiency as a function of axial distance from the point of liquid injection has never been shown previously. Since there are no other collection efficiency data available along the length of the throat, further independent verification of the model could not be done. The difference between model predictions and measured values can be explained by a comparison of measured and predicted flux distributions (Figure 3a). Because the measured flux distribution appears uniform in comparison to predicted values near the liquid injection, the experimentally measured lower efficiencies in this region can be explained only as a result of incomplete atomization of the injected liquid. This may result in part of the injected liquid moving as a column

Figure 6. Comparison of the overall collection efficiency as a function of liquid loading.

and hence with a less than expected number of collector drops by the model. If complete atomization is assumed, the rate of particulate collection with respect to distance (slope of the curve in Figure 5) would gradually decrease

Ind. Eng. Chem. Res., Vol. 38, No. 1, 1999 229

Figure 7. Comparison of predicted grade efficiency curves with experimental data.

as the drops are accelerated to the gas velocity in the throat, as shown by the model predictions. From the experimental data, it can be seen that the collection efficiency increases linearly up to a point and then increases at a slower rate up to the end of the throat. Atomization of the liquid column along the throat produces more droplets (more surface area for collection). These droplets produce intermediate multiple relative velocities, thereby enhancing the collection efficiency. This compensates for the tail-off in the collection efficiency and explains the higher efficiency values measured closer to the end of the throat. The process of partial liquid atomization along the throat may not be easy to incorporate in the model equations. Even after complete atomization, there could be interaction between the droplets and the drops may coalesce or breakup as they traverse the unit.15 Because the

present simplified model assumes complete atomization at the point of liquid injection and neglects drop interaction, the deviation in efficiency prediction along the throat can be expected. It is also important to note that the trend shown by the experimental data indicates a strong dependence of the particulate collection efficiency on the liquid distribution and utilization. Thus, a realistic prediction of the liquid distribution would give rise to more accurate predictions in the collection efficiency. Figure 6 shows the overall collection efficiency as a function of liquid loading. At a constant gas velocity, when the mass liquid-to-gas ratio is high (>1), the liquid jets converge at the center of the scrubber because of high penetration length. At very high liquid loading (>2), it is expected that the jets may interact, thus causing more turbulence. It is important to include this

230 Ind. Eng. Chem. Res., Vol. 38, No. 1, 1999

Figure 8. Comparison of the overall collection efficiency as a function of Venturi number and throat gas velocity (numbers within brackets indicate the mass liquid-to-gas ratio).

turbulence effect for realistic predictions of the liquid flux distribution and hence the collection efficiency. In Figure 6a-c the model predictions (NPe ) 100) for lower liquid rates (e1) are in good agreement with the experimental data. In this region the jet interaction may be minimal as a result of lower penetration. However, at higher liquid rates (g1), the model predictions of the collection efficiency (and the liquid flux distribution) with a Peclet number of 100 do not agree with the experimental data. Hence, the use of a lower Peclet number (NPe ) 10), for the region of high liquid loading, shows predictions of the collection efficiency (and the liquid flux distribution) that are in good agreement with the measured values. The comparison of grade efficiencies is shown in Figure 7. The model consistently predicts lower grade efficiencies for all particles, with the deviation increasing with decreasing particle size. The experimental

values are comparable with predictions only for particle sizes higher than 0.7 µm. The measured grade efficiencies for smaller particle sizes appear to be very high in comparison to data measured on an industrial-scale rectangular scrubber at comparable operating conditions.22 Because most of the industrial scrubbers are rectangular, there is no reason to believe that cylindrical units perform significantly better (as the experimental data suggests) at similar operating conditions. Moreover, a statistical analysis on the measured values could be a useful indicator in accessing the percentage error in the experimental data and the validity of predictions. The size of the unit could also have implications on the liquid flux distribution and collection efficiency especially at the very high turbulent conditions under which the scrubber operates. Hence, a cautious interpretation of the grade efficiency data is warranted. Application of Venturi Number Concept. It has

Ind. Eng. Chem. Res., Vol. 38, No. 1, 1999 231

been shown recently18 that the liquid flux distribution is a function of operating variables such as the throat gas velocity and liquid-to-gas ratio and design variables such as the nozzle diameter, number of nozzles used, and aspect ratio (ratio of depth to width of the throat). Starting from the jet penetration correlation (eq 9), one can derive the following relationship:

[

l* 0.1145 Fj L R0 Z ) 16 R0 π FG G* d0 nj

]

The combined effect of all of the above-mentioned parameters in terms of a dimensionless group called the Venturi number has been shown as a key tool in assessing Venturi scrubber performance. The Venturi number is defined as

Venturi number, VN )

(

)

L R0 Z G* d0 nj

where G* ) 1000G and Z ) aspect ratio () 1 for cylindrical units). Figure 8 shows the overall collection efficiency at three different gas velocities as a function of the Venturi number. It can be seen that the collection efficiency does not increase appreciably beyond a particular liquid loading. On the other hand, an increase in the liquid rate results in a higher pressure drop. It is not desirable to compromise on pressure drop for a marginal increase in the collection efficiency. Therefore, there exists a cutoff mass liquid-to-gas ratio at which the collection efficiency reaches an asymptotic maximum, beyond which any addition of liquid would not further improve the collection efficiency. This cutoff point provides optimal liquid utilization to achieve this asymptotic maximum. From Figure 8, it can be seen that this condition corresponds to a Venturi number of 1.5 × 10-3. It has been shown by Ananthanarayanan and Viswanathan18 that the optimal design and operating conditions for rectangular units lie in the Venturi number range of 1.00-1.5 × 10-3. From these observations it can be concluded that the Venturi number concept applies to cylindrical units alike, and it can be used to estimate optimal operating and design conditions. Moreover, its ease of use could be of great advantage in designing new scrubbers and/or analyzing existing scrubber performance. It can also be seen from this figure that the collection efficiency increases with the throat gas velocity for the same Venturi number. However, the increase in the collection efficiency becomes insignificant beyond a particular gas velocity. Because the Venturi number is independent of gas velocity, it is desirable to operate the scrubber in the range of 70-100 m/s to achieve maximum liquid utilization and collection efficiency. Conclusions and Recommendations From this work, the following conclusions can be drawn: (1) A two-dimensional model incorporating jet penetration correlation derived from studies made on a rectangular unit can reasonably predict both flux distribution and collection efficiency in cylindrical units. (2) In the region of high mass liquid-to-gas ratio, the turbulence caused by interaction between the jets can be accounted for by using a lower Peclet number.

(3) The model consistently underpredicts grade efficiencies for all particle sizes. However, the predicted grade efficiencies are comparable to the efficiencies obtained from an industrial-scale scrubber operating under similar conditions. (4) A dimensionless group, Venturi number, predicts conditions that result in optimal liquid utilization and highest collection efficiency. These conditions for this cylindrical unit occur at a Venturi number of 1.5 × 10-3 and fall within the same range as that of the rectangular units. It is recommended that (a) jet penetration and atomization for concentric liquid injection in cylindrical venturis be experimentally studied, (b) the fraction of liquid flowing on the walls should be measured and correlated for various operating parameters as this amount does not participate in the collection process, and (c) the units used for experimental investigations should not be very small in size as sufficient residence time and area would give the drops time to move and behave in a more predictable and consistent manner. Notation b a ) instantaneous drop acceleration, m/s2 b ) 18µG/(FD2) C ) concentration, number/m3 CD ) standard drag coefficient CDN ) modified drag coefficient, CDN ) CDNRe D ) diameter, m d0 ) orifice diameter, mm E ) eddy diffusivity, m2/s F ) fraction of total injected liquid flowing as a film on the scrubber walls Fi ) mass fraction of particulate matter belonging to the ith class G ) gas flow rate, 1000 m3/s b g ) acceleration due to gravity, m/s2 L ) liquid flow rate, m3/s l* ) jet penetration length at which the droplets form, mm m* ) number of selected mean diameters describing the particulate matter size range ML ) mass flow rate of liquid, kg/s MG ) mass flow rate of gas, kg/s NPe ) Peclet number NRe ) Reynolds number Qd ) liquid drop source strength, number/m3‚s Qf ) amount of liquid flowing as a film on the wall, number/ m3‚s R0 ) radius of the throat, mm V ) velocity, m/s X ) length along the axis, m x, r, θ ) cylindrical coordinates Greek Symbols F ) density, kg/m3 ηi ) collection efficiency of particulate matter belonging to the ith class by droplets µ ) fluid viscosity, kg/m‚s ω ) frequency of air fluctuations, rad/s Subscripts d ) drop eq ) equivalent f ) film G ) gas j ) jet or liquid ov ) overall p ) particle/dust

232 Ind. Eng. Chem. Res., Vol. 38, No. 1, 1999 th ) throat x, r, θ ) cylindrical coordinates

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(13) Yung, S. C.; Calvert, S.; Barbarika, H. F.; Sparks, L. E. Venturi Scrubber Performance Model. Environ. Sci. Technol. 1978, 12, 456. (14) Koehler, J. L. M.; Feldman, H. A.; Leith, D. Gas-Borne Liquid Flow Rate in a Venturi Scrubber with Two Different Liquid Injection Arrangements. Aerosol Sci. Technol. 1987, 7, 15. (15) Viswanathan, S. Modeling of Venturi Scrubber Performance. Ind. Eng. Chem. Res. 1997, 36 (10), 4308. (16) Fathikalajahi, J.; Talaie, M. R.; Taheri, M. Theoretical Study of Liquid Droplet Dispersion in a Venturi Scrubber. J. Air Waste Manage. Assoc. 1995, 45, 181. (17) Fathikalajahi, J.; Taheri, M.; Talaie, M. R. Theoretical Study of Nonuniform Droplets Concentration Distribution on Venturi Scrubber Performance. Part. Sci. Technol. 1996, 14, 153. (18) Ananthanarayanan, N. V.; Viswanathan, S. Estimating Maximum Removal Efficiency in Venturi Scrubbers. AIChE J. 1998, 44 (11), 2549. (19) Haller, H.; Muschelknautz, E.; Schultz, T. Venturi Scrubber Calculation and Optimization. Chem. Eng. Technol. 1989, 12, 188. (20) Viswanathan, S.; Gnyp, A. W.; St. Pierre, C. C. Estimating Film Flow in a Venturi Scrubber. Part. Sci. Technol. 1997, 15, 65. (21) Ayyub, B. M.; McCuen, R. H. Numerical Methods For Engineers; Prentice-Hall: New York, 1996. (22) Brink, J. A.; Contant, C. E. Experiments on an Industrial Venturi Scrubber. Ind. Eng. Chem. 1958, 50 (8), 1157.

Received for review May 29, 1998 Revised manuscript received October 1, 1998 Accepted October 16, 1998 IE9803321