Cocurrent gas—liquid flow in packed columns

Cocurrent gas—liquid flow in packed columns

Chemical Engineering Science, 1974, Vol. 29, pp. 1661-1685. Pergamon Press. Printed in Great Britain COCURRENT GAS-LIQUID FLOW IN PACKED COLUMNS B. ...

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Chemical Engineering Science, 1974, Vol. 29, pp. 1661-1685. Pergamon Press.

Printed in Great Britain

COCURRENT GAS-LIQUID FLOW IN PACKED COLUMNS B. E. T. HUTTON and L. S. LEUNG Department of Chemical Engineering, University of Queensland, St. Lucia, 4067 Brisbane, Queensland, Australia (Received 23 October 1973; accepted 18 December 1973) Abstract-A model is proposed for cocurrent gas liquid flow through a packed bed. For a given packing, gas and liquid flow rates, we proposed that (i) liquid holdup is a function only of pressure gradient and liquid flow rate and (ii) pressure gradient is only a function of liquid holdup and gas flow rate. Equations are presented which permit the prediction of pressure gradient and liquid holdup for cocurrent upflow and cocurrent downflow in a packed bed. Predictions from the model are shown to be in reasonable agreement with the experimental observations of Turpin and Huntington.

INTRODUCTION

Commerical packed towers for gas-liquid contacting are generally operated countercurrently with liquid flowing downwards under gravity and gas flowing upwards. In recent years there has been a growing interest in cocurrent operation [l-l 11. Very high gas and liquid flowrates are possible in cocurrent operation as the flowrates are not limited by flooding. The main applications for cocurrent operations in packed towers are in gas absorption accompanied by a fast chemical reaction, physical absorption and stripping in which one equilibrium stage only will be required for the separation[l, 5,9]. For the design of a cocurrent gas-liquid contactor, it is necessary to know, for a given set of gas flowrates and liquid flowrates, the pressure drop, liquid holdup, interfacial area and mass transfer coefficients. Some empirical correlations are available in the literature for predicting these quantities. Turpin and Huntington [8], for instance, correlated their pressure gradient results for cocurrent flow through packed columns by the following equations:

= 8.37-

1*372(ln z’)-0*0315(ln

+ 0.0078 (In z ‘)’

(lb)

for 0.2 < z’ d 500 for cocurrent

downflow

where tD.nG~//.d”~’

” =(DpG~/~~)o'767 DP = diameter of packing particle 0, = (2/3X4) * (e/l -E) GG= superficial gas mass velocity

GL = superficial liquid mass velocity Reiss compared his experimental results with a modified form of an empirical equation proposed earlier by Larkins[4], viz.

0.146 loglox + 066

2’)’ x

=

(2)

($ >“* B

+ O-0123 (In z’)’ for 0~3~z’~SOO for cocurrent

upflow

(la) where 6, indicates the value of pressure gradient calculated from single phase correlations for the liquid flowing alone in the b&d at the same temperature and pressure as the two phase case; and 8, 1681

1682

B.

E. T. HUTTON and L. S. LEUNG

indicates the value of pressure gradient calculated from single phase correlations for the gas flowing alone in the bed at the same temperature and pressure as the two phase case. Similar empirical equations are also available for correlating liquid holdup. While these correlations may be useful in correlating experimental results, they are empirical in nature. It is doubtful if they are applicable outside the range of the experimental variables used in, arriving at the correlations. In this paper we extend our model[l2] for countercurrent two phase flow to the case of cocurrent flow in packed towers. From the model, equations for predicting pressure drop and holdup for known flowrates and a given packing are developed. The derivation of these equations does not depend on actual experimental results. The predicted pressure drop and holdup are shown to be in reasonable agreement with published experimental measurements. THE MODEL

For countercurrent gas-liquid flow in packed columns in which both phases are continuous we have previously proposed [ 121 that for a given gas liquid system and a given packing, the liquid holdup, h, in the column is dependent only on the liquid rate L, and the pressure gradient in the column, (dpldz) i.e. h = h(L, dp/dz).

(4)

Here the effect of liquid flowrate on (dp/dz) is taken into consideration by its effect on holdup. The form of Eq. (4) is taken as the same as the Ergun Eqs. [13,16] for flow through packed beds using an effective voidage available for gas flow defined as (1-c-h-K)

c = volume fraction

Two forms of Eq. (3) have been proposed previously. For low values of the Reynolds number of liquid flow, liquid holdup in packed columns can be predicted by consideration of laminar liquid flow down inclined surfaces against a pressure gradient, giving L

=

h’m ~0s’P 3pLa:(c + h)* (1-c-h)h*cos’P 2pra:(c

+ h)’

11 (6)

At. high liquid Reynolds numbers in the so called gravity inertia regime, Buchanan [ 151 proposed a model of liquid running down inclined surfaces of length equal to a piece of packing with the liquid losing a fraction of its kinetic energy at the end of every such surface. We have previously extended Buchanan’s[l2] equation to include the effect of pressure gradient. For cocurrent uptlow through a packed column the equation is given by

(3)

The effects of gas flowrate on h are taken care of by its effects on the pressure gradient. We further assume that the pressure gradient is a function only of the gas flowrate and holdup, i.e.(g)=&)(h,G).

very high gas and liquid flow rates, there would be little deadspace in the column. K can be assumed to be 0 and Eq. (4) can be written as

occupied by solid

h = liquid holdup per unit volume of column

K = effective deadspace volume per unit volume of column. For cocurrent flow Eqs. (3) and (4), are also applicable. As cocurrent flow is generally operated at

Similarly L for cocurrent

=$“‘[g +$($)3’”

(8)

downtlow.

The derivation of Eqs. (7) and (8) are given in the Appendix. Cocurrent gas-liquid flow in packed columns is generally carried out at very high gas and liquid flowrates, operating mainly in the gravity inertia regime. Thus Eq. (7) or (8) is more applicable here than Eq. (6). We can now combine Eq. (5) with either Eq. (7) or (8) to predict liquid holdup and pressure gradient at a given set of gas and liquid flowrates. Figures la and lb compare the predicted holdup from the model with the measured holdup reported by Turpin and Huntington[8]. The agreement is good both for cocurrent upflow and cocurrent downllow for a gas velocity up to 3.06 m/set. At the higher gas velocity of 5.05 m/set the measured holdup is significantly higher than predicted values. The discrepancy at the high gas flowrate is

Cocurrent gas-liquid flow in packed columns

1683 DISCUSSION

(a)

Superficiql liquid velocity.

m/s

Fig. l(a).

likely to be caused by the carryover of liquid droplets in the gas stream, a factor not considered in the model. Our model assumes both the liquid phase and the gaseous phase are continuous, analagous to annular two phase flow in a vertical tube. Figure 2 compares the pressure gradient predicted from the model with the measured gradient reported by Turpin and Huntington [8]. Agreement is reasonable and is no worse than predictions from other empirical correlations.

Cacumnt gas liquid upflow

Supsrficial liquid velocity.

m/s

Fig. l(b). Results of Turpin and Huntington. Superficial gas velocities for cocurrent upflow. (0) 5.05 m/set (0) 3.06 m/set (0) l-53 mlsec. Cocurrent downflow: (0) 5.05 m/set (0) 3.06 m/set (Cl) 1.53 mlsec.

The overall agreement between model predictions and the experimental results of Turpin and Huntington [8] is encouraging considering that our equations are not ‘derived’ from experimental results. Comparision with the experimental measurements of other workers is not possible as full details of their results were not published. Further experimental work will be useful in testing the validity of the model.

Flow

pattern

For cocurrent gas-liquid flow through packed beds different flow patterns have been observed depending of flowrates. Similar flow patterns are also observed in two phase flow in a vertical tube. A semi-quantitative flow regime diagram for two phase flow in packed beds has been presented by Weekman and Myers[7]. This may be used as an approximate guide for predicting flow patterns in a packed bed. An equation describing two phase flow is generally restricted to one particular type of flow pattern. Our model has been developed for the flow pattern in which both the gaseous phase and the liquid phase are continuous in the packed bed. This is equivalent to annular flow in two phase flow in a tube. Application of the model equations outside this flow pattern will not be valid. Further work will be useful in developing quantitative flow regime diagrams describing the range of flowrates within which a particular flow pattern would occur. (b) Mass transfer coefficient This paper is not directly concerned with predicting mass transfer coefficients in cocurrent flow in packed columns. It is likely that a relationship exists between pressure gradient, and the mass transfer coefficient as suggested by Calderbank and Moo Young [ 141for single phase flow in packed beds and by Reiss [9] for cocurrent two phase flow in packed beds. Further, Reiss presented empirical correlations relating k,a and k,a with pressure gradient. If these correlations are valid, they can be combined with the equations presented here for the prediction of k,a and k,a at a given set of gas and liquid flowrates. Further work in this area may be very useful in providing design equations for cocurrent gas liquid contacting in packed towers. CONCLUSIONS

A model based on the interactions between liquid holdup, pressure gradient gas flowrate and liquid flowrate is presented for cocurrent gas-liquid flow in packed beds. Calculated pressure gradients and liquid hold-ups are found to be in reasonable agreement with the limited published results of Turpin and Huntington[8]. Further work will be required to establish the general validity of the model and to relate pressure gradient with the mass transfer coefficient. Acknowledgements-Financial

support from the Aus-

tralian Research Grant Committee for this work is gratefully acknowledged.

B. E. T. HUTTONand L. S. LEUNG

1684 NOTATION a

a, ; G g gc h b K kg 1 L’ ; dp

Q ST L V VG

Z ZT

specific interfacial area, m-’ specific packing surface area, m2/mJ solids fraction dimensionless equivalent diameter, m gas mass velocity, kg/m%ec gravitational acceleration, m/se2 gravitational conversion factor liquid holdup liquid film mass transfer coefficient, m/set effective voidage correction factor, dimensionless gas film mass transfer coefficient, m/set characteristic packing length, m liquid mass velocity, kg/set m width of surface dimensionless constant gas pressure, N/m2 two phase pressure gradient, N/m’ liquid velocity, kg/m*sec distance measured down slope, m shape factor dimensionless superficial liquid velocity, m/set liquid film velocity down plate, m/set superficial gas velocity, m/set distance measured vertically, m total height, m

[7] Weekman V. M., and Myers J. B., A.I.Ch.E.J., 1964 10 951. [8] Turpin J. L. and Huntington R. L., A.E.Ch.E. J. 1%7 13 11%. [9] Reiss L. P., I and E. C. Process Design and Development 1967 6 486. [lo] Kaminskii V. A. and Aloev A. S., Translated from Zhurnal Prikladnoi Khimii 1969 42 5, 1182-1183. [ill Gianetto G., Snecchia V. and Baldi G.. A.LCh.E. Sixty Fifth Annual Meeting. New York,‘November 26-30, 1972. WI Hutton B.E.T., Leung L. S. Brooks P. C. and Nicklin D. J., On Flooding in Packed Columns, Chem. Engng Sci. [131 Ergun S., Chem. Engng Progr. 1952 48 89. [141 Calderbank P. H. and Moo Young M. B., Chem. Eng. Sci. l%l 16 39. [151 Buchanan J. E., Ind. Eng. Chem. Fundamentals 1%7 6 400. cl61 Morton F., King P. J. and Atkinson B., Trans. Inst. Chem. Engr. 1964 42 149. APPENDIX Derivation of Eqs. (7) and (8) The assumption made here is that energy losses in laminar flow over the surface are negligible, compared with the kinetic energy dissipated in turbulence at the end of the flow element. The model shown in Fig. 3 is similar to that of

Greek symbols

angle to vertical film thickness, m frictional pressure gradient (liquid), N/m3 void fraction effective void fraction angle to horizontal liquid viscosity, kg/m set gas viscosity, kg/m set liquid density, kg/m3 gas density, kg/m’ 112

REFERENCES [l] McIlvroid H. G. Mass Transfer in Cocurrent Gas-Liquid Flow Through a Packed Column, Ph. D. Thesis Carnegie Institute of Technology 1956. [2] Larkins R. P., Two Phase Cocurrent Flow in Packed Beds, Ph. D. Thesis University of Michigan 1959. [3] Dodds N. S., Stutzman L. F., Sollami B. J. and McCarter R. J., A.1.Ch.E. J. 1960 6 390. [4] Larkins R. P., White R. R., Jeffrey D. W., A. I. Ch. E. J., 7 1961 231. [S] Wen C. Y., O’Brien W. S. and Fan L. T., J. Chem. Engng Data 1%3 8 42. [6] Wen C. Y., O’Brien W. S. and Fan L. T., J. Chem. Ennna Data 1963 8 47. II

Fig. 3.

Cocurrent gas-liquid flow in packed columns Buchanan[lSl except that we include the effect of the gas pressure gradient. Between (1) and (2) potential energy is converted to Kinetic energy. F = fraction of kinetic energy lost between (2) and (3) i.e.

v,‘v,‘=F

1685

Now, the film thickness at position r down the plate is given by: 6(r) = I-‘/&V,). The mean film thickness over the plate is given by

v,

8 mean = l/1

I’0

G(r)dr

V,’ - V,’ = F V,’

and V,’ = V1*, i.e. the liquid velocity is the same at each element. So, (l-F)V,2=

V,

(A.1) 1 and 2 for the

Applying Bernoulli’s equation between liquid: PL VI2 -+PLgz~+P,,-~

6 mean =

6 mean =

dp (2, - 21)

2

=

9 +

p&z,

P@-f$

+

- z*)

But L’ =-..!Z.a. sin 0

and, v,’ = v,2 + 2g(z, - 22)+ $(z,

h = a, . (6 mean)

- *z)$

F

z,-2,=1sin8

“=1-F.

V22=V,Z+2glsinO+dp21sinf3. dz pl.

(A.2)

Substituting these,

Substitute into (A.l) from (A.2) (l-F)(V,‘+2g1sinf3+$~lsinB)=V, L = v,z 2gIsinB+~(~)fsinO).

x 1- (1 - .)I’*

2 =L

Apply Bernoulli’s equation between a point ‘r’ down the slope and the initial position ‘1’.

x [ (A.4)

1-(1-F)“* F”2

I

and S’= [$J

Substitute for V, from (A.3) and (A.4) and

1

(mlsec)

z,-z,=rsinO V,2=V,Z+2grsinB+dpLrsin0 dz pr

F’12

[

(A.3)

[1-($F)“‘].

(A.5)

let n = & (

> V2_2glsinB+~*lsin0 -+2grsinO+--_-sin0 r n pL dz n

dp 2

(-4.6)

dz pr.

By a similar analysis for cocurrent upwards flow we obtain the following relation V, = 2 g +:z

[

l_

I

“*(sin ey*(lh

+ r)“*.

(A.7)