liquid distribution in a packed column

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Chemical Engineering Science. 1973 Vol. 28 pp. 1677-1683. Pergamon Press.

Printed in Great Britain

Liquid distribution in a packed column

KAKUSABURO ONDA, HIROSHI TAKEUCHI, YOSHIRO MAEDA

and NOBORU TAKEUCHI

Department of Chemical Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Japan

.

(F ir st received 26September 1912; accepted 24 November 1972)

Abstract-The effects of liquid flow rate, packing size, surface tension and viscosity of irrigation

liquid on the liquid spread factor are studied, and the values of the liquid spread factor are correlated

for a wide rangeof packing size.

The distribution of the liquid in a packed column is predicted by using a diffusional model with a

new boundary condition. The boundary condition at the wall is based on the assumption that the pene-

tration of the liquid into the wall takes place by the similar mechanism to the transport phenomena

considering the dependence of the equilibrium wall flow rate on the liquid flow rate. The experimental

results agree well with the theoretical ones for pure water and the surfactant solution.

INTRODUCTION

THE PACKED

column is one of the most common

units employed in diffusional process of absorp-

tion, distillation, humidification etc. For the

performance of a packed column, the distribution

of the liquid over the packing is of importance. It

is, however, very difficult to predict the liquid

distribution of a practical column.

f(G z) = Kw(z),

f(a, z) = @(w(z))

(3~21, (3x31

In general, the theoretical model for the liquid

distribution in a packed bed is based on a dif-

fusional-type equation given by Eq. (1).

(1)

where D is a constant and is designated as the

liquid spread factor. Solutions of this equation

can be obtained with a wide variety of boundary

conditions which are determined from the

behaviour of liquid flowing through the packed

bed. It is necessary that the liquid flow in the

vicinity of the wall of the column is accurately

represented, to predict the local liquid flow rate

in the packed bed.

The several investigators have solved Eq. (1)

with the following boundary conditions at the

wall.

af

>

r

r=(I =

0

G9[

_ x

>

r a

= -(G z) --Yw(z)) (4)[41

dw z)

=f(a, z) - kw(z) = -jy-

(5)

[51

in which

K k k p

and y are the constant show-

ing the wall effect. Equation (2) is the case that

regards the wall as a perfect reflector. This is

clearly unsatisfactory from a physical stand-

point, because the liquid actually flows on the

wall. Equation (3) or (3) is the case that allows a

finite amount of liquid on the wall. However this

condition does not allow arbitrary change in the

liquid flow on the wall at any value of the packed

depth z. Equation (4) corresponds to the con-

dition that the convective heat transfer taken

account of a film resistance occurs on the bed.

Equation (5) which is similar to Eq. (4) is the

condition by an analogy with the process of

accumulation i.e. absorption-desorption mech-

anism. This implies the assumption that the ad-

sorption rate is proportional to Aa, z) and the

desorption rate to w(z), and that the difference

between these quantities is equal to the amount

of liquid transfered from the packing to the wall.

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K. ONDA, H. TAKEUCHI, Y. MAEDA and N. TAKEUCHI

In addition to these boundary conditions, the

condition suggested by Jameson[6] is based on

the assumption that the liquid flowing on the

wall is returned to the packing by the factor F

that is, the boundary condition is established by

considering the wall flow as an extension of

packed bed.

for the solution of Eq. (1) are proposed as follows:

={w*(z) -w(z)} = y.

(6)

According to the recent papers by Onda[7]

and Porter[3] on the wall flow in packed column,

it was shown that the proportion of the wall flow

rate to the total flow rate increases as the liquid

flow rate decreases, and conversely. Therefore

in the boundary condition, it is necessary that the

variation of the liquid flow rate is taken into

account. Then a new boundary condition is

established.

Equation (6) implies the assumption that the wall

flow rate w*(z) which is in equilibrium with the

liquid flow rate in the vicinity of the wall,f(a, z),

exists and that the penetration of the liquid into

the wall takes place by a similar mechanism to

the transport phenomena, that is, the difference

between the equilibrium wall flow rate w* (z) and

the practical wall flow rate w(z) is considered as

a driving force.

The experimental works in literature have

been concerned only with water. It is important

to study with surfactant solutions, because it

seems that surface tensions have a great effect on

liquid spread.

For z = 0, the liquid is supplied in point source

or uniformly distributed over the packing, it is

obtained that

f=f,, = const., r = 0 for point source feed

or

The purpose of the present paper is to study

the effects of liquid flow rate, packing size, sur-

face tension and viscosity of irrigation liquid on

the liquid spread factor D, and to discuss the

validity of the new boundary condition from the

comparison between the liquid distributions.

f=fo = const.,O 5 r

02

or

ln =-ln47rD--&

(f-3)

(8)

in which Q is the total liquid flow rate of the

point source. Therefore D is determined by

plotting In (fz/Q) vs.

r2/z

which give a straight

line. From the slope and intercept of this line, one

may obtain the values of D respectively.

The experimental results obtained in this way

are given in Figs. 4 and 5 which show the relation-

ship between

D

and packing size

dp

for ceramic

Raschig rings and Berl saddles (4 mm-4 in.), re-

spectively. These figures also include the values

reported by several investigators for large pack-

ings, which almost agree with the values in this

work. The dependence of

D

on

d,

is 0.5 for

Raschig rings and Berl saddles, and a straight line

4 68, 2 4 6

d

p cm

Fig. 4. Effect of d on D for Raschig rings.

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6

4 _ Berl saddles

-

l-2.5 cP) and the liquid flow rate (L = 3000-

x

30000 kg/m2 hr) was almost negligible.

From the facts described above, rearranging

the experimental results, the correlation is ob-

E

tained as follows.

0

2

Q- D =

0.00231 x

dP .5 cr. (10)

In Fig. 7, Eq. (10) is shown with the experimental

data.

8

t

\

0=0 169

x

do

P

37-

Fig. 5. Effect of

d,

for Berl saddles. The symbols are the

same as those in Fig. 4.

in Fig. 4 or 5 represents

D = 0.169 x

dpo.5.

(9)

Though the hold-up is larger in smaller packings,

these figures indicate that this is not significant.

Therefore 4 mm Raschig rings were used also

for surfactant solutions.

When the surface tension of the liquid was

I I

I

I ,111

2 4 6

8 102

varied by addition of surfactant, the dependence

of D on surface tension u was l KI for 4 mm

d q

dynes/cm05

Raschig rings as shown in Fig. 6.

Fig. 7. Correlation of liquid spread factor.

The dependence of D on the viscosity (p =

Evaluations ofC and w* (z)

C. dynes/cm

Fig. 6. Effect of cron D.

The column being sufficiently short, it is pos-

sible to neglect in Eq. (6) Cw*(z) as compared

to Cw(z), then

dw(z)

-=-Cw(z).

dz

(11)

By integration Eq. (11) leads to

In w(z) = In wo-Cz.

(11)

Therefore C is determined by plotting In w(z)

vs. z.

The value of C obtained for pure water by

using Eq. (11) almost agree with k reported by

Dutkai[5], so that C for 6 in. column was deter-

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K. ONDA, H. TAKEUCHI, Y.

MAEDA and N. TAKEUCHI

mined as 4.2 m-l. When the surface tension of

liquid was adjusted to 47 dynes/cm, C was ob-

tained as 3-O m-l, thus C depends on u for which

Dutkai had payed no attention. This dependence

means that the wall flow builds up more slowly at

low surface tensions.

On the other hand, the relationship between

W and fm was presented as Eq. (12) correlated

with Porters data[3] and as Eq. (13) obtained in

this work. These equations do not give a straight

line for the column (6 in.) and packing (l/2 in.

Raschig rings) used in this work.

the total liquid flow rate as a parameter of the

packing depth. This is interpreted as follows, that

is, the liquid of u = 47 dynes/cm is more liable

to wet the ceramic packing than pure water.

Therefore the proportion of the wall flow is small

for lower liquid flow rate, and increases with

liquid flow rate. On the other hand, for u = 73

dynes/cm the proportion of the wall flow is large

because the liquid is not liable to wet the pack-

ings. With increase of the liquid flow rate, how-

ever, the proportion of the wall flow decreases as

the liquid is liable to flow through the packed bed.

w, = 0.202 XfmO for cr = 73 dynes/cm

wr3

W = O+IOOO54l

m1 73

or u = 47 dynes/cm.

(13)

For the estimation of w*(z), these equations

were used.

In this paper, C and W were investigated for

u = 73 and 47 dynes/cm and their dependencies

on o were remarkable as mentioned above. Their

dependencies will be clear in the later papers.

In order to verify the equations obtained for

the liquid distribution, the liquid flow rate in each

segment were measured for various depths of

packing, and the experimental results represented

as the proportion to the total liquid flow rate were

compared with the theoretical values. For the

liquids of u = 73 and 47 dynes/cm, the experi-

mental results for l/2 in. Raschig rings are plotted

together with the theoretical curves in Fig. 9

respectively. The experimental values agree well

with the theoretical one.

When the liquid was irrigated uniformly over

the packing, with increase of packed depth the

liquid will spread through the packed bed and on

to the wall until equilibrium configuration is set

up, which undergoes no further change with in-

crease of the packed depth. Figure 8 shows how

the liquid builds up on the wall with increase of

lcor

90-

- ater Co=73 dynes/cm)

80-

----Surfactant rolution ~=47)

o Porters data 073)

7or

L. kg/m. hr

Fig. 8. Relation between proportion of wall flow and liquid

flow rate as a parameter of packed depth. Uniformly dis-

tributed feed. 1/2 in. Raschig rings. 6 in. column.)

Fig. 9. Comparison of the experimental results with theoret-

ical curve for liquid distribution. Point source feed.

L =

2441

kg/m2 hr. 6 in. column.) ---Theoretical curve for w = 73,

0 Experimental points for T= 73,

- Theoretical curve

for cr = 47,O Experimental points for c = 47.

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CONCLUSION

The effects of liquid flow rate, packing size,

surface tension and viscosity of irrigation liquid

on the liquid spread factor were studied, and the

liquid spread factors for the packings of Raschig

ring and Berl saddle were correlated with Eq.

(IO).

For the liquid distribution through the packed

bed, a new boundary condition was proposed,

and the experimental results for pure water and

surfactant solution agreed well with the theo-

retical values. Consequently, when the relation

between the equilibrium wall flow rate and the

liquid flow rate at infinite depth of packing is

determined for more various systems, the liquid

distribution in a packed column can be deter-

mined more generally.

NOTATION

a

radius of the column

C wall effect coefficient

packing size

liquid spread factor

liquid flow rate per unit area in packed bed

value off for z = 0

value off for z = 00

constant in Eq. (5)

constant in Eq. (5)

constant in Eq. (3)

liquid flow rate per unit area

total liquid flow rate of the point source

radial variable in cylindrical coordinates

wall flow rate

equilibrium wall flow rate

value of w for z = 0

wall flow rate per unit periphery for z = w

packed depth

constant in Eq. (4)

constant in Eq. (4)

surface tension of irrigation liquid

viscosity of irrigation liquid

REFERENCES

I1

1

CHILA Z. and SCHMIDT O., Co t. Czech. Chem. Comm. 1958 23 569.

i2i PORTER K. E. and JONES M. C., Trans. Insfn Chem. Engrs 1963 41240.

131 PORTER K. E.. Truns. Insrn Chem. Enars 1968 46 T69.

i4i KOLAR V. andSTANEK V., Colln. Czech. Chem. Comm. 1965 30 1054.

[5] DUTKAI E. and RUCKENSTEIN E., Chem. Engng Sci. 1968 23 1365.

[6] JAMESON G. J., Trans. ZnsrnChem. Engrs 196644T198.

171 ONDA K.. TAKEUCHI H. and TAKAHASHI M., Kaguku Kogaku 1969 33 478.

i8j TOUR R. s. and LERMAN T., Trans. Am. l nsrn Chem. bgrs 1944 40 79.

191 CHILA Z. and SCHMIDT 0.. Colln. Czech. Chem. Comm.

1957 22 896.

[iOj HOFTYZER P. J., Trans. Insin Chem. Engrs 196442 109.

[ 1 ] ONDA K. and KATO T., Master Thesis in Nagoya Univ. 1969.

[12] DUTKAI E. and RUCKENSTEIN E., Chem. Engng Sci. 1970 25 483.

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liquid distribution in a packed column

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