Bubble Swarm Characteristics in Bubble Columns

AKHILESH KUMAR,I T. E. DEGALEESANY2 G . S . LADDHA2 and H . E . HOELSCHER

School of Engineering, University of Pittsburgh, Pittsburgh, Pa. 15261, USA

New correlations have been proposed for estimation of gas phase holdup, characteristic velocity, interfacial area for mass transfer and mean bubble size of bubble swarms under dispersed and fluidized operation of bubble columns employing single - and multi-orifice distributors. The analysis of results include available literature data of other investigators.

ubble column operation in both dispersed and B fluidized regimes has become of major commer- cia1 interest and a considerable relevant literature has now developed. However, there remain uncertainties about the design and performance of such columns and in particular for the behaviour of bubble swarms produced from single - and multi-orifice gas sources. Table 1 presents list of definitions of regimes and a summary of reported correlations for the different operative regimes are placed 'on deposit'.++

This paper reports new data on the gas phase holdup, bubble swarm velocity, interfacial area of contact for mass transfer and mean bubble size in bubble columns operated in the dispersed and fluid- ized regimes employing single - and multi-orifice plate gas distributors.

Existing correlations for gas holdup (Rennie and Evans"', Hughmark"'), in such systems do not satis- factorily predict holdup in the dispersed and fluid- ized operational regimes of bubble columns. Equations for bubble swarm velocity (Marucci's', Yoshida and Aita'4', Viswanathan"' are either restricted to very low ranges of gas velocity or require a knowledge of gas holdup. Further, correlations based on single bubble data (Van Krevelen and Hoftijzer"') and those reported based on single-orifice bubble swarm data for air-water system alone (Leibson et a]"') are dimensionally inconsistent. Finally, there is no re- liable equation for predicting mean bubble size, es- pecially for the range above critical Reynolds number.

In this report, useful and dimensionally consistent correlations are presented for prediction of mean bubble size on the basis of data generated from holdup and the direct area measurements (by chemical reac- tion method) of this work as well as those of Sharma and M a ~ h e l k a r ' ~ ~ ~ ' ) .

This paper also examines interfacial area data for their dependency on gas rate and other pertinent variables such as orifice Reynolds number. Correla- tions reported earlier (Sharma and Ma~helkar'~**', Calderbank"", Calderbank and Moo-Young('", Chhabra and Mahajan"") were found to have restricted ap- plication.

lHiroshima University. Hiroshima, Japan. 2A.C. College of Technology, University of Madras, Madras 600 026.

++Appendix for Table 1 is available, at a nominal charge from the Depository of Unpublished Data, CISTI. National Research Council of Canada, OTTAWA, Ontario. K1A 052.

On a propose des nouvelles correlations pour l'evaluation de la rktention en phase gazeuse, de la vitesse caradhristique de la zone interfaciale pour le transfert de masse et d a dimensions moyennes des bulles en groupes; on a employe ?I cette fin un systhme disperse et fluidis6 de colonnes d bulles avec des distri- buteurs d orifices simples et multiples. L'analyse des r b l t a t s comprend ceux qu'ont publib d'autres chercheurs.

Conclusions and significance

The gas velocity u, has a marked effect on holdup (see Figure 2) . Liquid rate, column diameter, orifice size and the number of orifices in the distributor have negligible effect on gas holdup in the range studied. All attempts to correlate these results via semi-log plots or log-log plots produced markeo curva- ture. The following equation was found best to cer- relate 382 holdup data points (z < 0.35 and u, < 15 cm/s) covering various systems considered in this work with an average deviation of 2 8.34% and a maximum deviation of 30.4%. x = 0.728 U: - 0.485 (u:)' + 0.0975 ( ~ : ) 3 . . . . ..(l)

where u: is defined as a dimensionless gas velocity given by UIl r l ( r A p g l p 3 I".

The gas rate was observed to influence the bubble swarm 'characteristic velocity', Go. A minimum in the u, - U, relationship was observed a t u, = 0.7 cmlsec. The physical properties of the liquid systems have a small effect on U,. The following equation correlated the U. data for all the gas-liquid systems irrespective

TABLE 1

REGIMES OF BUBBLE COLUMN OPERATION - DEFINITION

Dispersed regime

Fluidized regime

Froth regime

Foam regime

- The dispersed gas moves freely as dis- crete bubbles in the liquid continuous phase, x < 0.1. This occurs at very low gas rates.

- The gas is dispersed into swarms of bubbles moving up the column with a maximum holdup of x = 0.25 at higher gas rates, common in industrial ap- plications.

- The gas rates are kept so high that the gas phase holdup is more than about 50% resulting in froth condition for the dispersion.

- At very high gas rates, the gas phase holdup reaching about the froth turns into foam due to high rates of coalescence of gas bubbles supported by liquid films.

The Canodian Iournal of Chemical Engineering, Vol. 5 4 , December, 1976 503

1. wmpresswl ail suppiy 2. pressure regulator 3. vent L. rolameter 5 . saturators 6. manometer 7. three-woy stop cock 8. witice gas d;slrtbu!or 9. bubble cdumn 10. liquid inlel(at:onstant

rate 1 11. interface contrdlerand

liquid overtbw}

. . . . . . . . . . . . . . . . . . . . Water Kerosene Aq. glycerol (40%) Aq. sodium hydroxide (2M)

Figure 1 - Schematic diagram of experimental bubble column Setup.

1.00 0.88 72 0.7872 1.12 31.19 1.108 11.50 63.95 1.077 1.18 74.5

of the orifice and column geometries in the range studied here (see Figure 4 ) .

- U: = 1.4 + 0.116 u,, + 0.0045 U: + O.oooO8 u:. . . . . . . . (2)

where 2 is defined as uo/(-yAp glp:)" ' . The average de- viation of 382 data points is f 6.7% from the correlation line with a maximum deviation of 21.2%. The above data could also be correlated by a dimensionless form of equation in terms of u: as follows with an average deviation of f 7.56% and a maximum deviation of 22.4 %.

U: = 1.37 + 1.90 U: + 1.42 (u:)~ - 0.16 (u:)~. . . . . . . . (3)

(Note: Further discussion is based on Equation (2) in a later section of the paper)

The mean bubble size obtained from interfacial area data by the chemical method plus similar results reported by Sharma and Mashelkar'8"' for the reaction systems and the photographic bubble size data of Leibson et al"' and Van Krevelen and Hoftijzer") are shown in Figure 5.

The following equations f i t the d,, data above and below the critical Reynolds number, ( R e ) = 2100, for orifice diameters between 0.0419 and 0.6 cm. For 1 < ( R e ) N < 10

with an average deviation of * 10.54%. For 10 < (Re)N < 2100

(5)

with an average deviation of * 12.63%. For 4000 < ( R e ) N < 70,000

with an average deviation of * 9.4%. The effective interfacial area 'a' for gas-liquid

contact can be expressed as a function of gas ug, orifice Reynolds number and system properties and correlated by the following equations : For 100 < ( R e ) N < 2100

- 9.094 (u:)z + 1.828 ( ~ : ) 3 . . . . . . . . . . . . . . . . . . . . . . (7)

TABLE 2

DETAILS OF SYSTEMS AND COLUMN GEOMETRIES INVESTIGATED.

System

1. Air - Water 2. Air - Water 3. Air - Water 4. Air - Water 5. Air - Water 6. Air - Water 7. Air - Water 8. Air - Water 9. Air - Glycerol (40%)

10. Air - Glycerol (40%) 11. Air - Glycerol (40%) 12. Air - Kerosene 13. Air - Kerosene

Reacting system

14. Air/COz - aq. NaOH (2M)

15. Air/COz - aq. NaOH (2M)

5.0 5.0 5.0 5.0 5.0 5.0 7.5

10.0 5.0 5.0 5.0 5.0 5.0

10.0

10.0 - -

~ -

k cm

0.087 0.153 0.196 0.196 0.265 0.309 0.153 0.153 0.153 0.196 0.265 0.087 0.196

__

0.153

0.153 ~

~

- -

N

26 49 33 45 21 29 49 49 49 33 21 26 33

-

65

1 ~ -

Range of u, cm/s

0.29- 6.89 0.57 - 12.49 0.61 - 13.83 0.38 - 11.05 0.26 - 14.01 0.21 - 13.83 0.4 - 6.95 1.54- 9.42 0.22 - 5.82 0.22 - 4.42 0.14 - 5.59

0.27 - 4.6 0.24 - 3.68

0.23 - 7.07

0.1 - 7.0

TABLE 3

PHYSICAL PROPERTIES OF SYSTEMS AT 28°C

Liquid

Surface

dyne/cm

a ( & ) 1 ' 4 / (Re):' = 0.0437 u:

- 0.0291 (u:)~ + 0.0059 ($I3. . . . . . . . . . . . . . . . . . . . (8)

with an average deviation of * 16.79% and -+ 13.87; respectively.

Ex fierirnent

Column: Thick Walled Corning Glass

Gas Distributor: Conical head with replaceable oritice dT = 5,7.5, 10 cm

plates; dN = 0.087, 0.153, 0.196, 0.265, 0.309 cm For bubble swarm studies: Air-Water, Air-40 percent glycerol and Air-Kero- sene For area studies: air/COz - 2M NuOH (reaction system)

Figure 1 gives details of the apparatus and ex- perimental setup. Table 2 presents the list of experi- ments conducted in this work. Table 3 gives the physical properties of systems at 28°C. The column operation in this work followed standard procedures (Rennie and Evans'", Mashelkar and Sharma")) de- scribed elsewhere (Akhilesh"") . The calculations made for obtaining the various quantities were based on the equations presented in Table 4.

Systems Used:

504 The Canadian Journal of Chemical Engineering, Vol. 54 , December, 1976

O 5 7 i

._ 5 0.3

e - 0.2

.A

U

n-

X

0.1

0 0 0.2 0% 0.6 0.8 1.0 * u , dimensionless

9 LEGEND symbolsystem - cm 9 a&

dT d N

5.0 0.087 21 Present work to to 1 o air -water

0.309 49 g~ air -water 1.5 0,153 49 -do - e - d o - 10.0 0.153 49 - d o -

~~

5.0 0.153 t o . q - d o -

Q air- aq. glycerot

0.265 L9 5.0 0.007 26

0.196 331 - d o - Q air- kerosene

air/c%-2M NoOH 10.0 0.153 65;l - d o - ( 5 )

air - toluene } 5.0 0.1 26 Viswanathan air - L O % glycerol

n air-water 61.0 0,074 900 Freedman&

Figure 2 - Correlation of holdup data.

Davidson'" '

Results and discussion

The gas velocity u, in bubble columns showed a remarkable effect on the holdup and characteristic velocity of bubble swarms. These holdup data ( x <0.35) were in good agreement with those observed for columns of diameters 2" or larger when orifice sparger type distri- butors were used. The effect of physical properties on hold- up could be taken into account by the group (yApg/p:)1'4 in Equation (1). The apparent discrepancy in the fit of this correlation to some important literature data is dis- cussed below.

Effect of column diameter on holdup

Even though Baird and Rice(14) report column diameter effect on axial dispersion coefficients using the reported

LEGEND symbol source & ref & sparger symbol source & r e f AT sparger

A - A Fai r et a?) 1"&2" fritted- Falr et al 18" orifice glass ~

B - B Shulrnan & 2,1LL" prcus- Molstad" plate --- Towell eta1 L 1 . 5 orifice

(IS)

- d o - 4 2 * - d o - (ZU

c-C Hughmark@) 1" orifice A - d o - 16" -do-

x Freedman& D-D - d o - 2 -do- €-E -do- Davidson(21) 24" orifice {;z! -do-

(Ohki & Inwe'"'' 6" -do-

Figure 3 - Comparison with Hughmarks correlation of holdup.

data of Argo and Cova(16), Reith et al('@ and Okhi and Inoue(17), there is uncertainty about the effect of column diameter on gas phase holdup in bubble columns. Fair et a P S ) have reported that column diameter effect was seen in their holdup data obtained in 1" and 2" dia columns fit- ted with fritted glass gas distributors and those obtained in 18" and 42" dia columns with orifice sparger distribu- tors. Here they compared two sets of data, each set ob- tained by using a specific type of gas distributor. However, their data for the same type of gas distributor, either fritted glass (in 1" and 2" dia columns) or orifice sparger type (in 18'' and 42" dia columns), showed no appreciable effect of column diameter as long as the type of gas dis- trubutor used was the same in the smaller and larger columns. Similarly, Shulman and Mol~tad( '~) have re- ported no appreciable effect of column diameter in their work on 2" and 4" dia. columns with porous plate distri-

TABLE 4

EQUATIONS AND DATA USED

Quantity - I - - - -- Equation or Data I Reference x

U O

-

C*

k2

DA 4.

~ (K; = 0.149 I/g ion; Ki' = 0.102 l / g ) 8389 l/(mol. s)

i = f (NaOH]

d,. = 6 X / U

Yoshida and Akita(')

Thornton@B)

Nijsing et aI(W

Danckwerts and Sharma(28.2g)

Nijsing et al(27) Danckwerts and Sharma(28) Nijsing et aI(27) l -

- ________~.___~ -

The Canadian Iournal of Chemical Engineering, Vol. 54 , December, 1976 505

V'"" ' " " ' . ' ' ' " " " ' ' ' " " " ' ' '"".I

Sl. No.

1. 2. 3. 4. 5. 6. 7. 8. 9. . 10. 11. 12.

- --__

e om air-woler [present work] 5,7.5,10 @ air- kerosene I- do -1 5

, Experimental Predicted - --

Ua d a s D x 4. 4 x cm cm-1 ( R e h Eq. (1) Eq. (6) Eq. (8) -

cmls

1.524 0.042 0.51 0.50 19,832 0.060 0.798 0.451 3.353 0.078 0.56 0.84 43,632 0.130 0.576 1.353 6.706 0.130 0.53 1.46 87,185 0.220 0.439 3.006

6.706 0.150 0.53 1.69 87,185 0.130 0.439 1.776

- -___

13.410 0.190 0.56 2.04 174.498 0.325 0.330 5.904

0.61 1.77 1.97

0.180 0.200 0.150 0.58 1.54 0.150 0.51 1.77

0.048 0.51 0.57 0.048 0.64 0.45

1.524 0.048 0.53 0.54 19,832 0.060 0.798 0.451

t 0 mr-water [Freedma?'] 61 A * atr/O,-CuCI I Shormd"" I 6.6 10

0 air-water [Relth et of? 5 1' o air-aq glycerol [present work1 5 4 +&

,,,, aYStPm cm symtd

.. I d o - - d o - 74 1

ug , c rn lsec

Figure 4 - Correlation of characteristic velocity data.

butors' used in both the columns. A comparison of these data for the three types of distributors viz., fritted glass, porous plate and orifice sparger (shown in Figure 3 of Fair el u P S ) ) clearly indicate that fritted glass and porous plate distributors gave higher holdup than orifice type distri- butors. Similar observations have been made by Sideman el a P O ) . Also the present data on holdup obtained in 2", 3" and 4" dia columns did not show any appreciable effect of column diameter and agreed closely with those reported by Freedman and Davidson(") ( d ~ = 61 cm), Fair el U Z ( ' ~ ) ( d ~ = 18" and 42"), Towell el al(22) ( d ~ = 41.5" from Figure 7 of Ref.(22)) using orifice type distributors. I t is also of interest to note that the holdup data of Reith el uZ('") ( d ~ = 29 cm) for 2.4 M NuCZ solution as the liquid phase, followed closely the present set of holdup data after accounting for the interfacial tension and density (physical properties from Lange's Handbook of Chemistry were used) through the use of the property group ( - y a p g /p ; ) " ' , though Reith el ul attribute the high holdup for this system to ionic effect. I t is also equally interesting to find the data of Argo and Cova(I6), obtained at high pres- sure conditions (at 750 and 1500 p.s.i.g.) in a 17.63" dia column and normal pressure data from a 4" dia column, agree closely with the present data on holdup. The data of Towell et aZ(*') for 16" and 41.5" column (Figure 7 of Towell el U Z ( ~ ' ) ) showed an opposite trend with regard to the effect of column diameter and height on holdup contrary to the expectation(2.'8~22) that increase in the column diameter and its height would decrease the average holdup for any given gas velocity. Whereas their data(22) on 41.5" dia column and part of 16" dia column followed closely the

dN N cm

0.153 65 0153 1

O.oL2 1 0161 1 0-321 1 0012 1 0161 1

0.198 1 0.1 8 1 0.5% 1

0.63 20

Figure 5 - Correlation of mean bubble size data.

present correlation line showing a higher holdup, the other part of their data on 16" dia column agreed with the cor- relation line of Hughmarkcl) proposed for columns of 4" and above.

The correlation line of the present holdup data is compared on Figure 3 on logarithmic coordinates for air-water system (line F-F) with the three correla- tion lines proposed by Hughmark"' for l", 2" and large column diameters (4" and above) respectively shown by curves C-C, D-D and E-E. It may be ob- served, from this plot suggested by Hughmark, that the data points of Fair et a1 for 18" and 42" columns as well as the data of Towell et a1 for 41.5" column agree more closely with the correlation line of the present data. Also the data of Yoshida and Akita"' for 7.5 cum dia column agreed with the correlation line for 2" columns suggested by Hughmark (line 0-0) which agrees closely with the line F-F of the present data. However, their data on 15, 30 and 60 cm dia columns agree closely with the correlation line F-F of the present data only up to a Vsc value of 0.1 ft/sec ( U , C cmls) and show deviation above this value as shown by the dotted line G-G. Similarly the data of Reith et al"') and Ohki and Inoue"" for large diameter columns (ranging 8-29 cm) also show the same trend as that of Yoshida and Akita at Vsc above 0.1 f t / s while their data below 0.1 f t / s for all column sizes agree closely with those of the present

506 The Canadian Iownal of Chemical Engineering, Vol. 54 , December, 1974

Figure 6 - Comparison of predicted and experimental interfacial areas.

data. The reasons for this discrepancy in some of the large column data of different authors are not clear. One may attribute this discrepancy to the pos- sible differences in the design of orifice sparger gas distributors used by different investigators. In the present work special care was taken in the design of gas distributor which comprised orifice plates (without burrs a t the orifices) of approximately the same diameter as that of the column and held by the conical distributor head located within the bottom ex- panded end-section (of Elgin design) such that the liquid velocity in the annular area between the conical distributor head and the glass column was not very different from that prevailing in the column.

Effect of gas velocity on characteristic velocity

The characteristic velocity, c, of the bubble swarm was found to correlate well with u, when the physical property group (yA~g/p: )~" was taken into account. This is shown in Figure 4 for the various systems considered, viz., air-water, air-glycerol, air-kerosene, air /COz - NUOH, and O2 - CuCI. The observed minimum (at /(y A! g/&)'/' = 1.4 and u. 2: 0.7 cm/s) and the increase in u, beyond up of 0.7 cm /s may be due to the crowding and in- creased bubble population at which bunching of bubbles into groups of bubble-ensembles occurs, each ensemble with a few bubbles acting as a loosely held unit, moving as a single assemblage at terminal velocities much above those of the small, individual bubbles in the ensemble. I t may be noted that orifice size of the distributor as_well as continuous phase velocity showed little effect on u.. Lite- rature data of Viswanathan'l), Freedman and David- son(*'). Reith el Van Krevelen and Hoftijzer(") and Mashelkar and S h a ~ m a ( ~ r ~ ) on bubble holdup analysed in terms of io, showed good agreement wtjh the present data as shown in Figure 4. In this Figure data on 'Lo for larger diameter columns (including those for which reported holdups were lower than predicted in this work) have also been plotted for comparison with the z, correlation of the present data given by Equation (2). Only at very high gas flow rates these data show deviation from the correlation h e . I t is of interest to record that the bubble columns of this work, operated under dispersed and fluidized regimes, correspond to the laminar and churn-turbulent regimes indicated by Wallis'2s). Equation (9.36) of Wallis when written assuming a uniform void profile (with C, = 1) gives the following simplified relationships for and 7.

- U: = 1.53 + u:. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .(9)

whlch when written in terms of holdup, x, yields x = u:/ (u: + 1.53). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ( lo )

and gives a fair representation of the data in Figure 2. The minimum value of 1.4 for U. given in Equation

(2) agree closely with the value of d2 reported by WalliscM1.

Analysis of bubble size data

The effective interfacial area and mean bubble size control the mass transfer rates in bubble columns. In this investigation the bubble size data were ob- tained from the measured interfacial area and es- timated holdup by use of Equation (1). The effective interfacial area data were obtained employing the chemical reaction method (Mashelkar and SharmaC8*@', Mohunta et alCW') involving air/COT2M NaOH ays- tern using a 0.153 m orifice for the single - and multi-orifice distributors. The holdup and U. data obtained for the reaction systems showed good agree- ment with the correlation lines for other non-reacting systems shown in Figure 2 and Figure 4 respectively for both the single - and multi-orifice distributors.

The derived data on mean bubble size, dv,, as com- puted from interfacial area and holdup by the use of the equation

d., = 6x/0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (11)

have been analysed along with computed data on d.. from the effective interfacial area data of Sharma and Mashel- kar(8s") and photographic data of Leibson et and single bubble data of Van Krevelen and Hoftijzer(Q. A plot of these data in terms of &,/(yd:/Apg)' ' ' versus orifice Reynolds number is shown in Figure 5. I t is seen that for 100 < ( R e ) N < 2100 the mean bubble diameter increased with ( R e ) N . Leibson el 01'') correlated their bubble size data in the range 100 < ( R e ) N < 2100 by an equation based on their air-water system which did no? include phy- sical properties, i. e.,

0.33 d , = 0.18 ( d ~ ) ' J . 6 (Re), . . . . . . . . . . . . . . . . . . . . . . . . . . (12)

However, the data on d,. of various other systems considered here indicated the effect of system prop- erties and the Equation ( 6 ) was found to correlate best the experimental and reported data (Van Krevelen and Hoftijzer'O', Leibaon et al"') in the Reynolds number range of 100 to 2100.

The dtj8 for (Re)N > 2100, showed a steady decrease with the orifice Reynolds number. The data of Leibson et a1 for 10,000 < (Re)N < 60,000 showed wide scat- ter in d"" values spread from 0.2 m to 0.6 m in this region. This scatter may be attributed to the dif- ficulty of obtaining truly representative photographs of bubble swarms in a turbulent mass of fluid a t these high Reynolds number ranges even a t high camera shutter speeds. However, some data from their plot were comparable with the d., data from Themr ical areas' considered in this study. The analysis of d,. data from the 'Chemical area method' as ob- tained in this investigation along with the data of Sharma and MashelkarC8*0) gave the correlation rep- resented by Equation (5) for d,, in the range of Reynolds numbers from 4,000 to 70,000 for various orifice sizes ranging from 0.153 to 0.6 em. The re- ported photographic mean bubble diameter data of Towel1 et a1(**) are also shown plotted on Figure 6 for comparison with Equation 5. These show good agreement while slightly increasing the range of applicability of Equation 5 to an orifice Reynolds number of about 90,000.

Analysis of effective interfacial area

The effective interfacial area data obtained in this investigation as well as those reported by Sharma

The Canadian Iournal of Chemical Engineering, Vol. 5 4 , December, 1976 507

and Mashelkar‘8*s) were analysed taking into account the generalized relationships for gas phase holdup and average bubble size. Equations (7) and (8) were found to correlate all experimental data, satisfactorily. The observation made by Sharma and Mashelkar indicating that interfacial area is proportional to G’’.~ is an over simplification which does not recognize the many other factors influencing interfacial area. It is valid only for the limited range of the data analysed by them. Equations (7) and (8) indicate tha t the in- terfacial area of contact is not only affected by gas velocity but also by Reynolds number (based on noz- zle diameter), nozzle size and system properties. Equations (7) and (8) were also used for comparing predicted values with the experimental area data of P a n Krevelen and Hoftijzer‘E). This comparison is shown on Figure 6 .

Applicability of the proposed correlations to large size columns

There is general lack of data on mean bubble size and interfacial area for large sized columns. However, a few data are available in the work of Towell e t a F . In view of the maximum observed discrepancy in their reported holdup from the present proposed correlation for holdup, (involving a large size column of 16” diameter which also formed the basis for Hughmark’s correlation line for columns of 4“ or larger shown by line E-E of Figure 3) an attempt was made to predict interfacial area by using Equa- tion ( l l ) , using the present proposed correlations for estimation of holdup and d,, respectively by Equations (1 ) and ( 6 ) . These predicted values are compared in Table 5 with the reported experimental data of Towell et a1 (from Table 1 of their work). It may be seen that the present proposed correlations pre- dict bubble size and interfacial area with reasonable agreement thereby indicating their applicability to larger columns.

Nomenclature

interfacial area of contact per unit volume of dispersion, cm2/cm3 solubility of carbon dioxide in mixed electrolyte, viz., NaOH +- Na2CO3. mollcm3 solubility of carbon dioxide in pure water, mol/cm3 diffusivity of carbon dioxide in water, cmz/s Average bubble diameter in the dispersion, cm diameter of orifice of distributor, cm Sauter-mean diameter or volume-surface ratio of bubble, cm diameter of column, cm acceleration due to gravity, cm/s2 height of liquid level above the distributor in the column before the dispersion of gas, cm height of liquid level above the distributor in the column at steady bubble column operation, cm temperature insensitive constants but deuendent on the ionic species for HaOH and NaaCOa res- pectively.

= second order reaction rate constant, crnalmol s = initial concentration of sodium hydroxide, moll1 = initial concentration of sodium carbonate, mol/l = Reynolds number for gas flow through the orifice,

(dN UN p, / I.(,,), dimensionless = superficial gas velocity based on column cross-

section, cm/s = dimensionless gas velocity defined as u , / ( Y A p g /

= superficial gas velocity based on orifice area, cm/s = dimensionless velocity defined as u o / ( y A p g / p : ) 1 / 4 = characteristic velocity of bubble swarm, cm/s = bubble terminal velocity, cm/s = superficial gas velocity based on column cross-

section, ft/s = fractional gas holdup = surface tension of liquid, dyne/cm = density, g/cm3 = viscosity, poise

Pi)“‘

Subscrifits

I = gas phase 1 = liquid phase

Ref m m e s (1) Rennie. J. and Evans, F., Brit. Chem. Ens. 7, 498 (1962). (2) Hughmark, G. A., Ind. Eng. Chem. Proc. Des. Dev. 6, 218 (1967). (3) Marucci, G., Ind. Eng. Chem. Fundam. 4, 226 (1966). (4 ) Yoshida, F. and Akita, K.. AIChE Journal 11. 9 (1966). (6) Viswanathan, K. S., “Hydrodynamic Studies in Bubble Columns”.

M.Tech. Thesis, University of Madras (1972). ( 6 ) Van Krevelen. D. W. and Hoftijzer. P. J.. Chem. Ena. Proa. 46. . .

29 (1960). Leibson. I., Holcomhe, E. G., Cacaso. A. G. and Jaemie, J. J., AIChE Journal 2, 296 (1966). Sharma. M. M. and Mashelkar, R. A Paper presented at Tripar- t i te Chemical Engineering Conferznee. Symposium on “Mass Transfer with Chemical Reaction”, Montreal, Sept. 1968. Mashelkar, R. A. and Sharma. M. M., Trans. Inst. Chem. Eng. 40, TI62 (1970). Calderbank, P. M.. Trans. Inst. Chem. Eng. 36. 443 (1968). Calderbank, P. M. and Moo-Young, M. S.. Proc. Symp. on “Dis- tillation”. Inst. Chem. Eng.. 69-72 (1960). Chhahra, P. S. and Mahajan, S. P., Indian Chem. Eng. 16, CHE 5fi (1974) ~-. .,.

(13) Akhilesh Kumar. “Studies in Bubble Columns”, M.Tech. Thesis, University of Madras (1974).

(14) Baird, M. H. I. and Rice, R. G., Cham. Eng. J. 9. 171 (1976). (16) Argo, W. B. and Cova. D. R., Ind. Ens. Chem. Proc. Des. Dev. 4.

352 (1915) --- \ - - - - I .

(16) Reith. T.. Renken. S. and Israel. B. A., Chem. Eng. Sei. 23, 619

(17) Ohki. Y. and Inoue. H., Chem. Eng. Sci. 25, 1 (1970). (18) Fair J. R Lambright A. J. and Andersen, J. W., Ind. Eng.

(19) Shulman, H. L. and Molstad, M. C., Jnd. Eng. Chem. 42, 1058

(1968).

Chem. Pro:. Des. Dev. 1: 33 (1962).

i i c x n i ._”””,. (20) Sideman, S., Hortaseu, 0. and Faulton, J. W., Ind. Eng. Chem.

(21) Freedman. W. and Davidson, J. F., Trans. Inst. Chem. Eng. 47. 58 (I), 33 (1966). 251 I l R f i R I . - - - \ - - - - , -

Towell G. D., Strand B. S. and Ackerman, G. H., AIChE - I. Cherh. E. Symp. Ser.’No. 10. 91 (1966). Wallis, G. B., “One dimensional two-phase flow”, McGraw-Hill. New York, 1969. Wallis G B., Int. J. Multiphase Flow 1 491 (1974) Mohudta, D. M Vaidyanathan A. S. ’and Laddha, G. S.. Indian Chem. Eng. 11,’”rans. 73 (1969j. Thornton, J. D.. Chem. Eng. Sci. 5. 201 (1966). Nijsing, R.A.T.O., Hendricks, R.H. and Kramers, H., Chem. Eng. Sci. 10, 88 (1969). Danckwerts, P.V. and Sharma, M.M., Trans. Inst. Chem. Ens. 44, CE 244 (1966). Danckwerts, P. V. and Sharma, M. M.. Brit. Chem. Eng. 15, 622 (1970).

Manuscript received December 18, 1976 ; accepted for publication August 6. 1916.

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508 The Canadian Iournal of Chemical Engineering, Vol . 5 4 , December, 1976