size of bubbles and gas holdup in bubble columns

Memoirs of the School of Engineering, Okayama University Vol. 20, No.2, February 1986

Size of Bubbles and Gas Holdup in Bubble Columns

* *Toshiro M~YAHARA and Teruo TAKAHASHI

(Received January 16, 1986)

SYNOPSIS

Bubble columns are extensively used in the

chemical industry. This paper evaluates the present

state of the art on the size of bubbles from a sieve

plate and gas holdup, mainly on the basis of the results

of the authors, including previous ones.

The size of bubbles formed from a sieve plate has

an insignificant effect of chamber volume, and gas

holdup shows some different behavior, depending on the

hole diameter to liquid depth.

INTRODUCTION

Bubble columns are widely used in chemical process industries as

contactors for carrying out gas-liquid or gas-liquid-solid reactions

such as oxidations, hydrogenations, chlorination, coal liquefaction,

aerobic fermentations, etc., because of their simplicity of

construction and their high volumetric coefficient, leading to a

large number of publications. Therefore, we have come across a

considerable number of relevant papers on the size of bubbles and gas

holdup available to the design and the operation of bubble columns.

However, there remains uncertainties in the correlating equations

because of different results of each investigator. The authors have

also investigated these properties.

* Department of Industrial Chemistry

2 Tashiro MIYAHARA and Teruo TAKAHASHI

This paper reveals the present state of the art on the size of

bubbles and gas holdup from point of view of the results of the

h (12-14) h . h .aut ors toget er Wlt prevlous ones.

1. EXPERIMENTAL APPARATUS AND PROCEDURE

The experimental apparatus is shown diagramatica11y in Figure 1.

CD Column<l> Viewing box3 Pressure tap4 Air chamber5 Perforated plate6 Compressor7 Air filter8 Buffer tank9 Orifice flow rate meter

[]:J®5

@

<D

@

@

@

14

Fig. 1 Schematic diagram of experimental apparatus

Three different transparent acrylic-resin columns 1 were used, with

internal diameters of 5, 10 and 15 em. Most of the sieve plates 5,

shown in Table 1, which show plate P-1 - P-22, were made of brass, with

holes arranged in the form of equilateral triangles, except for plate

P-4, for which the arrangement was square. To examine the effect of

plate materials, polyethylene, po1yviny1ch1oride, acrylic resin and

teflon sieve plates, which are plate P-23 - P-31, were used;the column

diameter was 5 em, all the sieve plates employed for the purpose had

the number of holes of 15 and the pitch of 1 em, and distilled water

was used as liquid. Details of the geometry are given in Table 1.

Only teflon plate has a characteristic of non-wettabi1ity, showing

a contact angle of liquid on a plate of more than 90 degrees.

The liquids used for most of the tests were distilled water and

Table 1 Details of plates employed

Plate d [m] m[-] P[m] l[m] P/d [-] DT[m] Material Contact_________~ ~ ~~g1~lE~Ql_

P-l 0.0005 19 0.01 0.001 20 0.05 Brass 0.52P-2 0.001 19 0.01 0.001 10 0.05 Brass 0.52P-3 0.0005 37 0.007 0.001 14 0.05 Brass 0.52P-4 0.0005 37 0.002 0.001 4 0.05 Brass 0.52P-5 0.0005 19 0.001 0.001 2 0.05 Brass 0.52P-6 0.0005 19 0.002 0.001 4 0.05 Brass 0.52P-7 0.0005 19 0.003 0.001 6 0.05 Brass 0.52P-8 0.0005 19 0.004 0.001 8 0.05 Brass 0.52P-9 0.0008 19 0.003 0.001 3.75 0.05 Brass 0.52P-I0 0.0005 85 0.01 0.001 20 0.1 Brass 0.52P-ll 0.0013 84 0.01 0.0008 7.69 0.1 Brass 0.52P-12 0.0018 84 0.01 0.0008 5.56 0.1 Brass 0.52P-13 0.001 1 - 0.001 - 0.15 Brass 0.52P-14 0.001 2 0.01 0.001 10 0.15 Brass 0.52P-15 0.001 3 0.01 0.001 10 0.15 Brass 0.52P-16 0.001 5 0.01 0.001 10 0.15 Brass 0.52P-17 0.001 10 0.01 0.001 10 0.15 Brass 0.52P-18 0.001 15 0.01 0.001 10 0.15 Brass 0.52P-19 0.001 17 0.01 0.001 10 0.15 Brass 0.52P-20 0.0005 10 0.01 0.001 20 0.15 Brass 0.52P-21 0.0005 13 0.01 0.001 20 0.15 Brass 0.52P-22 0.0005 17 0.01 0.001 20 0.15 Brass 0.52P-23 0.0005 19 0.01 0.002 20 0.05 Polyethylene 1.22P-24 0.0005 19 0.01 0.002 20 0.05Polyvinylchloride 1.08P-25 0.001 19 0.01 0.002 10 0.05Polyvinylchloride 1.08P-26 0.0015 19 0.01 0.002 6.67 0.05Polyvinylchloride 1.08P-27 0.0005 19 0.01 0.002 20 0.05 Acryl resin 0.87P-28 0.0005 19 0.01 0.001 20 0.05 Teflon 1.66P-29 0.0008 19 0.01 0.001 12.5 0.05 Teflon 1.66P-30 O.OOIDI 19 0.01 0.001 10 0.05 Teflon 1.66P-31 0.0015 19 0.01 0.001 6.67 0.05 Teflon 1.66

~~!;ll;:;..~IJi

'"'""-~:::::

!:;l"

~~

~g,.~'"

w


ethanol. The liquid depth was 25-100 em.

Photographs were taken of bubbles at intervals of approximately

5 em along the column. The negatives were enlarged, and the major

and minor axes of each bubble, assumed to be ellipsoidal, were

measured. The volumetric mean bubble diameter was calculated from

the expression

E6Vb /n: )1/3( n (1)

The number of bubbles was 40-100, a level of which is reliable for

statistical purpose under the above experimental conditions (6) .

Since under these experimental conditions, there was no appreciable

variation in the size of bubbles in the longitudinal direction along

the column, bubbles were photographed at a position 40-45 cm above

sieve plate, except when we were examining the effect of the number

of holes. Then, the photographs were taken at a depth of 25 cm.

Gas holdup was calculated by the usual static pressure method.

2. RESULTS AND DISCUSSION

2.1 Size of Bubbles Generated from a Sieve Plate

1) Effect of hole number

According to the previous work(15), the size of bubbles formed

at single orifice is influenced by the volume of gas chamber; the

same is true of bubbles generated from a sieve plate. On the other

hand, the report by Koide et al. (6) suggested that the size of bubbles

from sieve plate is independent of gas chamber volume. In an attempt

to find out the effect of the number of holes on the relationship

between bubble size and chamber volume, we examine the bubble size

for three cases of the chamber number N <1, l<N <9, 9<N (15), thec c c

results being shown in Figure 2. As can be seen, the effect of

gas-chamber volume is much weaker with increase of the number of

holes, the critical point being aroud 15 in the region of column

diameters of 5-15 cm as shown in Figure 3. This is probably due to

the liquid flow around the bubble induced by bubble formation.

Accordingly, our subsequent experiments were carried out using 15 or

more holes.

2

'"7lLJ 101

£:??:::-

0 6

~ 4--a:O't--0M 21"0

100

'"7l10

1U£:?~-0 6"00

4-.......--a.Q1

0 2roM

100

n~

101

c:?...-.-0"0 6S-a:: 4O't

---0M1"0 2

Size of Bubbles ulld GIiS Holdu!J ill Bubble Columns

KeyI I

Tadaki et a1.15) I (a )NcC- J

0 0·75 Ke, NcC-]~ e 2·98 .6. 0·543 EthanolI- CD 12·7 ... 3.17 do=0.000393 -l- I:,. 13-6 m-f- Air-water -

~CD.4ID CD CD ~ CD CDCDCD CD CD CD~~ ~ ~oI- ~eee e 0 -~e e e e~ ee"eee .6.c9

'0 o 0 cA::>O d' 0 00 -~~

P-13. do=0.00/m.H=0.25m. m=l II I I

I I I(b )Key NcC- ]

I- 0 0·86 -f- e 3·41 -- CD 14·3-- Air-water

-- -- CD CDCD CD~5ac5=O -- e &e e e -

e00 00

- 0 -.P-15. do=O.OOj m, H=0·25m, m=3. P/do=10

I I 'I

KeyI Koide et al.6) I ( c )

NcC- J_ 0 O· 71 Key doCmJ mC-]

e 3.16 ... 0·0005 31CD 10·0 .6. 0·001 31

- Air-water I:,. 0.001 85- ~i.A ,

e eg~~

P-19. d =O·OOlm, H=0.25m.m=17. P/do=lOI I I I II I I I I I I I II I

5

6 10 0

Nw2 4

[-J6 10 1 2

Fig. 2 Effect of chamber volume

2) Bubble size distribution

Figure 4 shows the volumetric mean diameter of bubbles for a

low and a high value of pitch to hole diameter ratio p/d. Wheno

P/do

is high, the volumetric mean diameter d30

shows a minimum value,

whereas it does not show for low vales of p/d. At gas velocityo

corresponding to the minimum bubble diameter, bubbles are generated

from all the holes. The above result for low value of p/d is dueo

to the coalescence at the moment of bubble formation.


JKey doCm] P/do C-

° Ne <'1e 1<Nc<9 0·001 10<D 9<NcI:J. Nc<l.tI. 1<Nc<9 0·0005 20.... 9<Nc

6

4n

I

U 2

.II

4 ~:=-===~-t-¢=!-

M-~ 10

1

:g-a: 6-2}oM

1"0

2(15 )

10°0 2 4 6 8 10 12 14 16 18 20

m [-J

Fig. 3 Effect of number of holes

102

Air-water

n 6 '0' .-.-."-~CY<¥O°-oCb-O-°OO-E 4 ,o~O_(5ODU Key Plate P/doC-J

00 P-1 20M

1"0 2 P-6• 4

163

Vc=130xlO- 6 m 3

2 4 6 10-2 2 4 6 10-1 2·

Uge Cm/s]

Fig. 4 Volumetric mean diameter of bubbles

generated from sieve plate


Key Ugc Cm/s] Key Ugc Cm/s] 10([)

a 0·00365 a 0·0042 lL. e 0·0081 0·00754<II e- ([) 0·0178 0·0184III10

([)

!<II • 0·0856L.

01 nc ~20 Air-water Air-water

~U P-l P-6 I

~ a: 40 H=0·7 m H=0·7m iL.

<II 60 Vc =130x 106 m3Vc=130Xlo-Gm3g<II

.!) NE 1II d:JC "080

I<II <II> - P/de =20 P/de = 4290~ 1II:J C q>E III

~~:J .cu

995 2 5 2 5 10-2 2

d em] d em]

Fig. 5 Bubble size distribution

Figure 5 shows the bubble size distribution correspondinq to

Figure 4. The data are fitted well by a logarithmic normal probability

distribution, the results agreeing with those of Tadaki et ale (15)~Towell et ale (17) and Akita et ale (1). The distribution function can

be expressed by

7

f(d, d )g

Here,

r-= - 2 21/(t2nlns)exp[~{ln(d/d )} /{2(lns) }j

g(2)

(3 )

s =- 2 1/2exp[E{ln(d/d )} In]

g( 4 )

The size of bubbles for bubble columns is usually calculated as

Sauter mean diameter d32 . The Sauter mean diameter can be expressed

on the basis of logarithmic normal probability distribution as


2exp{-(lns) } ( 5)

Since s is close to unity as shown in Figure 6, we expect that

d30 is nearly equal to d32 according to Eq. (5) .

2

.4 52

e P-7(9 P- 8ill P - 9<t P-10

Key Plate

2 4 6

Nw [- ]4 6

__~_~~-e~-;-Tadaki et at ~5)

65

2

10'Key Plate

6 e P-1~ P-2

4 () P-30 P-6

nI

U

(/)

Fig. 6 Geometric standard deviation

3) Mean bubble diameter

Figure 7 shows the correlation for the dimensionless bubble

diameter against the dimensionless parameter N (15) for P/d >8,w 0

the experimental results and the correlation of Koide et al. (6) also

being shown. The solid line is

( 6)

where

f (Nw

)

f (Nw

)

f (Nw

)

f (N )w

2.92.9N -0.188

w1. 8N 0.5

w3.6

N <1w=

l<N <2w

2<N <4w=

4<Nw

The dashed lines in the same graph are the correlation of Tadaki et

al. (15), the experimental results of this study being close to the

result of Tadaki et ale for Nc

=4. The value of Nw=2 corresponds to

Size of Bubbles and Gas Holdup in Bubble Columns 9

~ 5

4 Key Plate Liquid Vc [m 3 J H [mJ

0 P-1 Water 130x 10-6 0·7

2e P-1 Water 666x10-~ 0.7

n CD P-1 Water 130x10· 6 0.5I e P-2 Water 130 x10- 0·7 _.- 6)

U Q P-2 Water 666x10-6 0.7P-3 Water 130 xlO-6 0.7 Koideetal.

101 ()M () P-3 Water 666x10-6 0·7- 0 P-10 Water 1025x10-6 0.7~.......0 6 • P-1 Ethanol 130xlO-6 0·7"0

_~::_~_:i~_c!_~_~~~.:g4-a:' _ -" L:,. l::l: .,-- " ....

$ Eq. (6 )--r--=::::'~ ...."0 2M

Koide et at. 6 ) 15 <P Ido<601"0

100+ 53 vol~/o Glycerine aq.X 80vol~/o Glycerine aq.L:,. Water

6 ... 1vol."Io Isoamyl alcohol aq.5

2 4 6 100 2 4 6 101 2 4 5

Nw C-J

Fig. 7 Correlation of volumetric mean diameter

of bubbles

the transitional points at which bubbles are generated from all the

holes.

The following correlation has been found to be valid at low

values of P/d as shown in Figure 8.o

3.6 P/d <8o(7 )

4) Effect of inorganic electrolyte~

The addition of inorganic electrolytes to water has an

insignificant effect on the size of bubbles generated from plates

for P/d >8, whereas the bubble size for plates of P/d <8 showso 0

complicated characteristics as dependent on concentrations and sorts

of electrolyte, the bubble size being always smaller than that

obtained by Eq.(7). The most likely reason is the inhibition of

coalescence between adjacent bubbles at the plate due to the existence

of inorganic electrolytes though P/d is small.oMarrucci(9) has recently proposed an idea for the thinning

process of liquid film. This theory indicates that the bubble

coalescence is hindered by the value of crbk 2/0.


20 ,....,..'T""T"""n----y--r-r-r..,...,IT-r--...,

nI

UlOM~,..........-..-8 5~

~oSo 2n5)

Air-wateor system3 -6 3H=O.7 m Vc= 1 OxlO m

20

Fig. 8 Effect of P/do

Then, crbk2/0 represents the difficulty of bubble coalescence.

The correlation of the bubble size for the addition of inorganic2electrolyte is illustrated in Figure 9 by a vs. crbk /0; where a is

LiquidPlateKey

1·0 @ aaO.g \ ~~ t"$-;0.8 '- $ 7) -~'------t

" Koide et al. V"'- --- -- - - - - -_.\. -- --- - ----0·7......

IL..I 0·6

H=0.7 mVc =130x lO-p

m3

100 mol/m3NaCI

1000mol/rrfNaCIlOOmol/m3BaCI2100mol/m3 NaCIlOOOmollm3NaCI1000mol/m3NaCI

P-6P-6P- 6P-7P- 7p-g

oeeCD()

~

~ 0·5

0·4

0·3

0·20.1 '--..L---'----''--...J..--'----'_...J..---'----''--........--'----'

a 4 8 12 16 20 24

Crk~6 [-]

Fig. 9 Effect of inorganic electrolytes


the ratio of dimensionless bubble diameter in aqueous inorganic

electrolytes to that in pure water.

The dashed line in this graph shows the result of bubble diameter

for porous plate at the critical gas velocity below which bubble

diameter does not depend on gas velocity, which was found by Koide

et al. (7). It is clearly seen that the addition of inorganic

electrolyte strongly affects the size of bubbles from porous plate.

5) Effect of plate materials

The size of bubbles from plates of non wettable materials, whose

characteristics depend on a contact angle of liquid on a plate of

more than 90 dgrees is independent of Nw

for both P/do >8 and P/do <8

as shown in Figure 10.

11

54 Key Plate

d30=0.007 m

-e~-~-c:e-<S~~cj)~-j)]'ite

Air- water system

nE

102U

0M 6I"U

4

22

•~

oe

4

P - 28P - 29P - 30P - 31

6 2[-]

4 6 2

Fig. 10 Volumetric mean diameter of bubbles from

various plates of non-wettable materials

The size of bubbles is about 7 rom, while the size distribution

follows a normal probability distribution approximately when the

standard deviation is given by

s'id 1/2 = 0.08 (8)o

as shown in Figure 11 above N =2 at which bubbles are generated atw

all the holes.

12 Tashiro MIYAHARA and Terua TAKAHASHI

Key Plate

5.--...,.--r--'r"""T'".......,..~--.,..-r--r-T-r-r-T"'T~-...,

4n

N--E 2u

N

;:'°10-1"'0:---l/} 6

42'---I--I-...l....l....L.J.~::-----L~..l.-..L....I.........J.-I..~---'

246 246 2

[-J

Fig. 11 Standard deviation

Table 2 Bubble size correlations in bubble column

Investigator Correlation

Koide et al. 6) d { /(ad )}1/3=2 94N 0.07130 gpR, 0 • W

Kumar et al. 8) d32{~pg/(ad02)}1/4=1.56Rego.058

l<Re <10

d32{~pg/(ado2)}1/4=0.32RegO.425 .g

10<Re <2100

d32{~pg/(ado2)}1/4=100Reg-0.4 g

Akita et al. 1)

4000<Re <70000g

(u /~)-0.12( 0 3/ 2)-0.12x gc g T g T vR,

6) Previous bubble size correlations

A number of correlations for bubble size have been proposed,

however, the scatter in reported data does not allow a single

correlation. Some of the important correlations have been listed in

Table 2.

Figure 12 shows the comparison among Eq.(6), the correlations

sho~m in Table 2 and the present measurements.

Size of Bubbles and Gas Holdup in Bubble Columns 13

N

00·5-xo

1-8 0.2

nEu

2

1

-----Koide et al.6)-'- Kumar et al.8)-"- Akita et al.l)

_ ..__ Air-water system

. "--"-- ~Eq. (6) ..~- ---:::-:-~ _ ~..;a:-=_~~=--=@i"i-

.:==~"~,~~ ~~. Ke Vc x 10 6Cm 3 ]

~. 0 130~ p- 1 • 666

H=0.7m, Dr=0.05m

2 5Ugh

10 20[m/s]

50 100

Fig. 12 Comparison between previous correlations

and bubble size measurements

2.2 Gas Holdup in Bubble Column

1) Maximum gas holdup

Gas holdup in bubble columns increases with increasing gas

velocity in the uniform bubbling regime, where bubbles rise

independently with fairly uniform spacing between them, represents

the maximum value and decreases in liquid circulation regime where

the dynamic interaction of gross circulation and large bubbles becomes

frequent and violent.

The maximum gas holdup is given for air-water system by the

following equation(18)

(1 - w) = ° 0083{mP/(d D 2)}0.29max' 0 T ( 9)

The critical superficial gas velocity which is defined as the

velocity at the point of incipient regular circulation, where a

transition from bubble to turbulent circulation flow occurs, depends

on clear liquid height under a uniform stable gas distribution and isgiven by (10)

14

ugc

Tashiro MIYAHARA and Teruo TAKAHASHI

0.042H- 0 • S (10)

Bubble columns are usually operated below the critical gas velocity.

2) Gas holdup in bubble column

Generally, as is well known, the liquid in bubble column flows

up in the center of the column and down near the wall, though it is

considered that bubbles rise uniformly over the cross-section of the

column. For the gross circulation of liquid, the radial

non-uniformity of gas holdup could be observed. The radial variation

of gas holdup is given as lS )

(11)

where n, ~c and I~ - ~ )/~ are empirical constants.c w cFigure 13 shows the vertical profile of mean liquid fraction

Air-water systemzxl00 [m]

o 5 10 15 20 25

..!. 0·5~

I

5 10 15 20 25Zxl00 [m]

(a) ( b)

Kev Hl mJ0 0.03

• 0·05Q 0·07.()- 0.1() 0·15lD 0·2

Fig. 13 Vertical profile of mean liquid fraction

on a sieve plate, measured by means of y-ray techniqu~~6)The mean

liquid fraction decreases suddenly near the surface of a sieve plate,

then shows a constant and decreases near the top of the froth as can

be seen from Figure 13. The region, in which gas holdup is roughly

constant, increases with liquid depth, bubble column corresponding

Size of Bubbles and Gas HolduP in Bubble Columns

to this case, i.e., the long constant gas holdup region.

Now, the gas holdup in shallow liquid is correlated well with

the Froude number based on liquid depth(16). The gas-to-liquid

holdup ratio in a deep liquid of D.3 m to 1 m depth is presented in

Figure 14 in terms with (l-W)/W against Fr. The dashed lines are

given by the following equations(16)

15

(l - W) /W

(1 - W) /W

-4Fr<8.5xlD-48.5xlD <Fr<l

(12)

(13)

2 5 10-4 22Fr =Ugc/(gH) [-]

5 5

Fig. 14 Gas liquid holdup ratio versus Froude number

From this chart, gas holdup is satisfactory agreement with Eq. (12)

for large d /H, whereas for small d /H it is larger than that ofo 0

Eq. (12) and d /H does not affect gas holdup for large Froude numbers.oWhen d /H is less than about 3xlO-3 , gas holdup is independent of

oliquid depth. For this reason, it is presumed that liquid depth

usually does not affect the gas holdup in bubble column.

Figure 15 shows the correlation of gas holdup in terms of

(l-W)/W against Fr' (=u 2/(gd)) for d /H<3xlD- 3 • From this figure,gc 0 0

the following empirical equation is obtained

16 Toshiro MIYAHARA and Teruo TAKAHASHI

10° Air-waterKe Plate H[m] Ke Plat HEm]

5 0 P-1 O· 7 • P-l1 O· 3 -;::.::;:;e P-l 0·5 6 P-12 1·0 Eq (1~. ~(I) P-1 0·3 A P-12 0·6 . ~. 0 ~ ~

e P-2 0·7 A P-1 0·3 '2 ~ P- 3 O· 7 ~ P-30 0.3 .

() P-lO 1·0 v P-31 0·5 NJ/ Air-watern () P-l0 0·6 .~ H)' • P-lO 0.3 . Ke Plate H[m]

o P-11 1.0 .20°/0 ':20°1. ~ P -31 0·3

~ !3 P -11 O· 6 ..-(~ " P-28 0·7~ P-23 0·7- 5 v P-30 0·7........ ~ir-ethanOI~ ~ P - 31 0·7

~I!#i KeYIPlatel HEm]'V P-27 0·7...

2 &~~. ~~ '1 P- 1 0·7'V P - 28 O.~- v P -28 O·!---- Y"

ty/.v P -30 0·5

10-2 /10-3 2 5 2 5 10-' 2 5 10° 2 3

Fr' =Ug~ I(g do ) [-J

Fig. 15 Correlation of gas holdup

(1 - Il-') /Il-' 0.4/Pr' Fr' = U 2/(gd), d /H<3xlO- 3gc 0 0

(1 - Il-')«l - Il-')max

(14)

It seems that (l-Il-')/Il-' in d /H>3xlO- 3 or turbulent circulation flowo

regime could be estimated by Egs. (12) and (13).

4) Previous gas holdup correlations

Some previously important correlations for gas holdup in bubble

columns having a sieve plate are shown in Table 3.

Figure 16 shows the comparison among Eg. (14), the correlations

in Table 3 and the present measurements.

CONCLUDING REMARKS

The size distribution of bubbles formed from a sieve plate

may follow a logarithmic normal probability distribution when the

geometric standard deviation is close to unity, whereas the size

distribution of bubbles from a sieve plate of non-wettable material,

being independent of the plate geometry, follows a normal probability


Table 3 Holdup correlations in bubble column

Investigator Correlation

17

Hughmark 3) (1-1jI)=[2+(0.35/U ) {(Po/p ) (a/a ) }1/3]-1gc N W W

Gestrich et a1. 2) (1_W)=0.89(H/DT

)0.036(-15.7+109 K) (db/DT

) 0.3

x{(U 2/(gd )}0.025(2.6+1ogK)KO.047 - 0.05gc b

3 4K=P10 /(g~l ), d b=0.003 m

Kumar et a1. 8)

9)Mersmann

* *2 _*3(1-1jI)=0.728U -0.485U +O~D915U

{ 2 3/( 4~ )}1/24( / )5/72xPR, a ~R, pg PR, Pg

llP=P -P1 9

Kato et a1. 4,5) (l-IjI)=U /vgc b

vb

=O.31+0.4 U O.8(1_eY)gc 1.3

8=4.5-3.5e- 25 • 5DT

y=-716U 1. 8/8gc

distribution.

The gas holdup on a sieve plate is different above and below

a value of d /H of 3xlO-3 • The gas holdup in bubble column is wellocorrelated with the Froude number based on hole diameter, as

independent of liquid depth.

NOMENCLATURE

A = Hamaker constant [ J ]

18 Toshiro MIYAHARA and Teruo TAKAHASHI

Air-water. system

0.5 ----- Hughmark 3> /_.- Gestrich et al.2) /',/'_ .. - Kumar et al.8) .'_ ...- Mersmann11) / dt.'.{j.:o,.............. Kata et al.4 ) /' h··r;v~;.~./

/ /A>...../' /'.• Q.. . / ,/, , ~ / ,,"

p- 2 / /4;/'VC~1;~·:1~~6m:;..~'Eq.{14J

Dr :0·0 5 m /0;~....//o ..../.

;j<"0.01L..-_L....-..L.......L-'-L..J-I...L..I...._....L--'-....I.....l.....I....I....&....I...I.._......

0·001 0·002 0·005 0·01 0·02 0·05 0·1 0·2

Ugc [m/sJ

0·2

n 0·1I

u 0·05~

- 0·02

Fig. 16 Comparison between previous correlations

and hqldup measurements

C

DTd

d30d32d

gd oFr

Frh

Fr'

2c l do 2 1 1nRT (dC

l) 1+(dlnf1/dlnc

l) 1+(x

1v

1!x

2v

2)

concentration of component 1

= parameter of bubble coalescence proposed by

Marrucci

column diameter

bubble diameter

volumetric mean diameter of bubbles

Sauter mean diameter

geometric mean diameter

hole diameter

Froude number U 2/(gH)gC2Froude number U h /(gd )

Ug

2/ ( 'do)Froude number gc g 0

activity coefficient of component 1

gravitational acceleration

N ]

mol /m3 ]

[ - ]

[ m 1[ m ]

[ m 1[ m ]

[ m ]

[ m ]

[ - ]

[ - ]

[ - ]

[ - ]

[ m/s 2

24V (Pl-p )g/(nd P)c g 0 c

H

1

m

k

NcNwPcP

R

n

Reg

RT

r

sg

UghUgcv

l,v

2Wexl ,x

2


liquid depth

thickness

hole number

{(2nO/(Arb

)}1/3

chamber number

we/Frh

0 .5

pressure in chamber

pitch

gas constant

total number of moles of ions per mole of

Reynolds number = d U hP /Uo g g gcolumn radius

radial distance

bubble radius

standard deviation

geometric standard deviation

hole velocity

superficial gas velocity

molar volume of component 1 and 22

Weber number = P1Ugh /0

mole fraction of component 1 and 2

[ m ]

[ m ]

[ ]

[ lim[ ]

[ ]

[ Pa ]

[ m ]-1 -1{J.K .mol ]

electrolyte [ - ]

m

m

m

m

m/s

m/s ]

m3/mol

19

Greek letters

a ratio of dimensionless bubble diameter in aqueous

gas holdup

gas holdup at center and wall

mean liquid holdup

liquid holdup

inorganic electrolytes to that in water

~g'~l = viscosity of gas and liquid

v l kinematic viscosity = ~l/Pl

P ,Pl,P = density of gas, liquid and waterg w

0,0 surface tension of liquid and waterw

ljl

REFERENCES

[

[ Pa.s.]2[ m /s ]

[ kg/m3 ]

[ N/m ]

[ - ]

[ - ]

[ - ]

[ - ]

(1) K. Akita and F. Yoshida: Ind. Eng. Chern., Process Design

Develop., 13 (1974), 84.


(2) W. Gestrich and W. Rahse: Chemie-Ing-Tech., !l (1975), 8.

(3) G.A. Hughmark: Ind. Eng. Chem., Process Design Develop., 6

(1967), 218.

(4) Y. Kato and A. Nishiwaki: Intern. Chem. Eng., 12 (1972), 182.

(5) Y. Kato, M. Nishinaka and S. Morooka: Kagaku Kogaku Ronbunshu,

1:. (1975), 530.

(6) K. Koide, T. Hirahara and H. Kubota: Kagaku Kogaku, iQ (1966),

712.

(7) K. Koide, T. Hayashi, M. Nora, Y. Takemura, N. Kawamata and

H. Kubota: J. Chem. Eng. Japan, ~ (1972), 236.

(8) A. Kumar, T.E. Dega1eesan, G.S. Laddha and H.E. Hoelscher:

Can. J. Chem. Eng., 54 (1976), 503.

(9) G. Marrucci: Chem. Eng. Sci., ~ (1965), 975.

(10) T. Maruyama, S. Yoshida and T. Mizushina: J. Chem. Eng. Japan,

14, (1981), 352.

(11) A. Mersmann: Ger. Chem. Eng., 1:. (1978), 1.

(12) T. Miyahara, Y. Matsuba and T. Takahashi: Kagaku Kogaku

Ronbunshu, ~ (1982), 13.

(13) T. Miyahara, S. Kaseno and T.Takakhashi: Kagaku Kogaku

Ronbunshu, ~ (1982), 643.

(14) T. Miyahara, Y. Matsuba, S. Kaseno and T. Takahashi: J. Chem.

Eng. Japan, 15 (1982), 391.

(15) T. Tadaki and S. Maeda: Kagaku Kogaku, ~ (1963), 402.

(16) T. Takahashi, T. Miyahara and K. Shimizu: J. Chem. Eng. Japan,

7.- (1974), 75.

(17) G.D. Towell, C.P. Strand and G.H. Ackerman: AIChE-I. Chem.

Eng. Symp. Series (London), No.10 (1965), 97.

(18) F. Yamashita and H. Inoue: J. Chem. Eng. Japan, 8 (1975), 334.

size of bubbles and gas holdup in bubble columns

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