Chemical
Engineering
Science,
1974, Vol. 29, pp. 493-500.
Pergamon Press.
ON FLOODING B. E. T. HUTTON,
Printed in Great Britain
IN PACKED
L. S. LEUNG,
P. C. BROOKS
COLUMNS and D. J. NICKLIN
Department of Chemical Engineering, University of Queensland, St. Lucia 4067, Brisbane, Queensland, Australia (Received 11December 1972; accepted 18 July 1973) AbstractA mechanism flooding in pressure is proposed is shown differences in flooding mechanism also.
columns, based be consistent wetted wall
INTRODUCTION
work flooding in columns was out by et al. in 1938, their correlation slightly modified Lobo et [2] whose or a form of [3], is widely used for predicting ing Bow in packed The Lobo though extremely is empirical nature and not purport present a
accepted Lobo flow rates. our proposed agreement with
pioneer
ism of
terms of
Justifications
of
Lobo
Plot
analysis are in the [4,5]. The of flooding packed columns uncertain. The of flooding wetted wall however, has extensively studied, and theoretically 191. The theoretical analysis Cetinbudaklar and is perhaps most successful. a linearized, amplitude, stability sis for gas and flows with laminar or laminar velocity they show a disturbance the gas-liquid will cause when the velocity is a critical The critical were shown be in agreement with data for flooding gas over a range of velocities in used sizes wetted wall It is to postulate the mechanism flooding proposed Cetinbudaklar and for wetted columns may applicable also packed columns. this paper show that an extension not valid. mechanism of in packed based on interaction between pressure gradient, and liquid rates is here. The of this is to the mechanism flooding in columns, not replace the
interactions between and experimental observations. and packed are con-
for predicting velocities calculated are shown be in experimental
data. LIQUID FLOW AND PRESSURE
For low of the number of flow, Davidson[20] that the holdup in columns can satisfactorily predicted consideration of liquid flow inclined surfaces. was later by Buchanan 11. For Reynolds numbers, effects become and viscous at the interface may neglected. In regime Buchanan a model liquid running inclined surfaces length equal the length a piece packing, with liquid losing fraction of kinetic energy the end every such He showed predictions from model were agreement with liquid holdup packed columns. and Buchanan’s do not the effect pressure gradient holdup, an which is for normal of packed as the gradient is generally small. operation near at the point, however, effects of gradient are We shall Buchanan’s analysis include the of pressure on liquid For low Reynolds numbers, to as gravity-viscosity regime Buchanan, the equation relating rate (Q, pressure gradient can readily derived (Appendix 493
494
B. E. T. HUTTON
+h2(1-c-h) cos2~ 2pLao2(c+ h)3
et ul.
For a given packing, K can be estimated from experimental results and Eq. (3) using l1 in place of E. For the results of Morton et al. [24] for 8 in. Raschig rings, for instance, a value of K = 0.2 gives reasonable agreement (Fig. 1) between the experimental results and modified Eq. (3) over a range of gas flow rates.
(1)
1
At high liquid Reynolds numbers, in the so-called gravity-inertia regime, the corresponding equation is (Appendix 1b)
-Modified
where S’, the shape factor, is defined by Eq. (B.5) in the appendix. Equations (1) and (2) give the liquid flow rate (L) as a function of liquid holdup (h) for a given gas pressure gradient (A&Z). For zero pressure gradient the equations reduced to Eqs. (1) and (2) given by Buchanan. PRESSURE
GRADIENT
--Data
Carman-Kozeny equatia of Mortan
et cV.@l
EQUATION
Many empirical equations are available in the literature for predicting pressure gradient in countercurrent flow of gas and liquid[22-241. Morton et al.[24] showed that pressure gradient in a packed column for countercurrent flow can be represented by an equation of the CarmanKozeny type for flow through packed beds. In the ranges of normal operation (i.e. below the “loading” point), the following equation was suggested and shown to agree well with experimental data; AP
G
11
E3
34 inch
Raschlg
rings
I.0
(3)
Above what is often considered as the loading point, Eq. (3) gives an underestimate of the value of pressure gradient. Morton et al.[241 suggested the use of an effective gas density in Eq. (3) to take into account the presence of entrained droplets. However the pressure gradient so calculated for columns packed with random Raschig rings is still lower than that measured by up to 50 per cent. We suggest an alternative method for modifying Eq. (3) for high liquid holdup by using an effective free voidage E’, in place of the true voidage l. It seems likely with the geometry of Raschig rings that part of the free void, E, [defined as (1 - c - h)] may be ineffective for gas flow (i.e. there is dead space in the void). It seems reasonable to define an effective voidage l1by l1 = ( 1 - c - h - K ) where c = volume fraction of rings (mYm3) h = holdup of liquid (m3/m3) K = effective voidage correction factor, representing the effective volume of dead space per unit bed volume. (mYm3)
Liquid
rate, - 8.7 kg/m’sec
Fig. 1.
Note that we are only interested in obtaining a realistic functional relationship between gas flow rate and holdup for use later to test our model and that we are not concerned with developing correlations for predicting pressure drop in packed columns. In using Eq. (3), we imply that pressure gradient in packed columns in countercurrent flow is similar to pressure gradient in packed columns in single phase flow, and that the contribution of the liquid flow rate to the pressure gradient is taken account of by its effect on holdup; thus decreasing the effective free void in the pressure gradient equation. A CRITERION FOR FLOODING
Our criterion for flooding is similar to that used by Wallis [5] and Broz [27] where they state that flooding occurs when the derivative of liquid flow rate through the packing with respect to holdup,
495
On flooding in packed columns at constant gas rate, becomes zero. i.e. (WC?& = 0. In our Eqs. (1) and (2), the liquid flow rate is given as a function of the holdup (h) and gas pressure gradient (Ap/Z). Equation (3) gives the gas pressure gradient (Ap/Z) as a function of the liquid holdup (h) and gas flow rate (G). Substituting the gas pressure gradient (Ap/Z) from Eq. (3) into either Eq. (1) or (2) we obtain a relationship between the liquid flow rate (Q, liquid holdup (h) and gas rate (G). So for the gravity-viscosity regime, substituting Eq. (3) into Eq. (1):
and in the gravity inertia regime:
a,G2
+
--
Ps
II
pQa, O’l [ G
+T[yl”‘]
1 (l-c-h-K)3
1 l/2
(l_c~h_K)31_“Z
h3p,g co9 p L=3p,Aa,2(c+h+K)3h3 co.9 p 3pLa,2(c+h+K)3(1-c-h-K)3
a,G2 +-
-p*a, pgg [ G
h3 co9 /3 +2p,,a,2(c+h+K)3(1-c-h-K)2
and for the gravity-inertia Eq. (3) into (2):
regime,
[ G
1
Thus at flooding in the gravity-viscosity h2pd cos2 p
(5)
’
(l-c-h-K)3
pLav2(c+h+K)3
substituting
l/2 11
xCLgaD 11 0.1
(4)
I
regime,
h3p,g cos2 p -pLavZ(c+h+fQ4
x
11 O’l
’
(l-c-1h--K)4
4
h2(cosZP)(c+h+K)-3 [ pLa,2(1-c-h-K)3 h-t K)+
pLaC2(1-c-h-K)3 h3 co9 p +pLa,2(c+h+K)3(1-c-h-K)4
Curve I Flooding 2 Flooding
h cos2 p +pLa,2(c+h+K)3(1-c-h-K)2
4 Flooding. 5 Flooding, 6 Flooding.
Inertia model Viscous model grid pocking dumped pocking stacked
cos2 p -- h3’ 2 pLa,2(c+h+K)4(1-c-h-K)2 h2 cos2 p +pLa,2(c+h+K)3(1-c-h-K)3
I =
0 (6)
=‘i7)
Equations (6) and (7) have multiple roots of h and the required value of h is that in the practical range ofOt0 (l-c--K). From h we can calculate the liquid flow rate at flooding, at a given gas flow rate from Eqs. (4) and (5). In the calculations, a value of S, = 1.8, and 8 = 60” are used as suggested by Buchanan [2 11. Figure 2 compares the calculated flooding flow rates for the gravity viscosity regime and the gravity inertia regime with the experimental data of Morton er a[.[241 on the Lobo plot. It can be seen that at low liquid Reynolds numbers, the gravity viscosity model gives reasonable agreement with the Lobo correlation while at high liquid Reynolds numbers, the inertia model gives reasonable agreement. lot
_ (cosz/3)h3(c+
1
Fig. 2.
rings
B. E. T. HWTON et al.
496 DISCUSSION
Quantitative prediction offloodingflow rates The present analysis strongly suggests that flooding in packed columns is caused by the interactions between pressure gradient and holdup at given gas and liquid flow rates. Any reliable equation, for describing pressure gradient in terms of gas flow rate and holdup for a given packing and liquid gas system, may be used for quantitatively predicting flooding flow rates from this present analysis, Such an equation is often not available 61 =
to initiate type (i) holds if the effecin a wetted-wall and the effective
volume occupied by the gas e’ = volume occupied by the gas and liquid and is generally greater than 0.80 up to the onset of flooding. For packed columns,
volume occupied by gas-volume of dead space volume of packings + volume of liquid, gas, including dead space
for most types of packings in practice. Thus the quantitative prediction of flooding flow rates from the present analysis for columns of different packings is not possible. The initial aim of this work, however, is to elucidate the mechanism of flooding in packed columns and not to replace the Lobo correlation. Comparisons wall columns
the gas velocity reaches a value instability. The reverse situation tive voidage is low. Note that column there is no dead space, voidage is given by
between packed columns and wetted
For wetted-wall columns, Cetinbudaklar and Jameson showed that flooding is caused by wave type instability without consideration of pressure gradient. We believe that for countercurrent gas liquid flow at least two types of instability can occur to initiate flooding: Type (i): instability due to interaction between holdup and pressure gradient as proposed here for packed columns. Type (ii): wave type instability at the interface without reference to pressure gradient as proposed by Cetinbudaklar and Jameson for wetted wall columns. If the liquid rate is progressively increased from zero at a given gas rate in countercurrent flow, the type of instability that will occur depends on the configuration of the system, and in particular on the effective voidage, l1. If c1 is high, (as in wettedwall columns) type (ii) instability will set in before
Just before the onset of flooding, l1 in packed columns is generally less than about 0.4. Most investigations on wetted-wall columns have used tubes of about 1 in. (or more) in diameter. If the size of these columns were reduced, the effective voidage would be smaller. It is interesting to compare the critical velocities calculated for the two instabilities for different size wetted-wall columns, shown in Table 1 for a fixed superficial velocity of gas. The equation used for pressure gradient is that for incompressible isothermal flow between two parallel plates, using a roughness factor for the gas liquid interface selected from the correlation by Wallis[5] of roughness factor with film thickness. Detailed description of the calculation procedure is given in Appendix l(c). It can be seen that for narrow bore wetted-wall columns, type (i) instability will set in first (i.e. as we suggest for behaviour of packed columns), while for large bore wettedwall columns, type (ii) instability will occur first (i.e. as Cetinbudaklar and Jameson show for conventional wetted-wall columns). The intention of Table 1 is to show the transition in behaviour only. It is not intended for quantitative prediction of critical velocities, as there is uncertainty about the roughness factor used. New types of packings In recent years several new types of packings
Table 1
G Plate spacing (b) (ml 7,416 7.416 7.416
0,024 0.0146 0.0076
Flooding liquid Reynolds No. calculated from present method 6.3 x IO4 4.8 x IO* 34
Flooding liquid Reynolds No. calculated from equations of Cetinbudaklar and Jameson [ 121 50
120 1100
497
On flooding in p acked columns
have been marketed[251. Many of these are claimed to permit substantially higher throughput than conventional packings such as Raschig rings. Many modern packings give much higher effective voidage during operation (by minimizing the volume fraction of solids packing and dead space). We postulate that columns packed with these “high capacity” packings operate more like conventionally sized wetted-wall columns with type (ii) instability at the onset of flooding. An understanding of the nature of flooding in packed columns will be useful in the design of packings.
L W ;
Z’ L: G’ Greek
Acknowledgements-The
authors wish to acknowledge valuable discussions with Messrs. R. G. Rice, E. T. White and R. H. Weiland, Department of Chemical Engineering, University of Queensland. Financial support from the Australian Research Grants Committee is gratefully acknowledged. NOTATION A
cross sectional area available for flow, m2
specific (packing) surface area per unit volume of packed bed, mz/m3 b spacing between (vertical) plates, m solids fraction (dimensionless), m3/m3 f; width of vertical plates, m equivalent diameter of cross section available & for gas flow, subscripts: s for superficial, a for actual, m D volumetric liquid flow rate, m3/s f friction factor G mass velocity of gas kg/m%ec g gravitational acceleration, m/se? g: gravitation conversion constant h liquid holdup, m3/m3 effective voidage correction parameter, mYm3 K 1 characteristic packing length, m L’ liquid rate kg/hr.m width of surface dimensionless constant gas pressure, N/m* F! AP change in gas pressure, N/m* Q liquid mass velocity, kg/m%ec distance down slope, m s: shape factor, dimensionless au
CES Vol. 29 No. 2-L
symbols
void fraction, dimensionless effective void fraction, dimensionless angle to horizontal angle to vertical liquid viscosity, kg/m set gas viscosity, kg/m set liquid density, kg/m3
CONCLUSION
A mechanism for flooding in packed columns based on interactions between holdup and pressure gradient is proposed and is shown to be consistent with experimental observation. Differences in the mechanism of flooding between wetted-wall columns and packed columns are considered. The design of new packings for packed columns is discussed in the light of this work.
superficial liquid velocity, mlsec velocity of liquid film down the plate, m/set width of surface, m variable film thickness, m distance measured vertically, m distance measured along the axis of flow, m superficial gas velocity, m/set liquid flow rate, kglsec gas flow rate, kglsec
V
gas density, kg/m3 film thickness, m i- shear stress, N/m* interfacial shear stress, Ti
N/m2
REFERENCES
T. K., SHIPLEY G. H. and 111 SHERWOOD HOLLOWAY F. A., fnd. Engng Chem. 1938 30 765. VI LOB0 W. E., FRIEND L., HASHMALL F. and ZENZF.A.,Trans.A.I.Ch.E. 194541693. [31 CHEN N. H.. Chem. Enang 1962 109. Petrol. Ref. 1963 [41 TAO L. C., Hydrocarbon-Proc. 42 205. PI WALLIS G. B., One Dimensional Two Phase Flow,
pp. 336-339. McGraw-Hill, New York, 1969. J. F. and SHEARER C. J., J. Fluid 161 DAVIDSON Mech. 1965 22 321. 1957 2417. [71 MILES J. W., .I. FluidMech. 1957 2 554. P31 BROOKE B. T.,J. FluidMech. 1959 6 161. 191 BROOKE B. T.,J. FluidMech. [IO1 YIH C-S., Proc. 2nd U.S. Congr. Appl. Mech.,
[Ill [121 [I31 iI41
[ISI [IhI [I71
[181 [I91
Am. Sot. Mech. Engrs 1954 623. YIH C-S., Physics ofFluids 1963 6 321. CETINBUDAKLAR A. G. and JAMESON G. J., Chem. Engng Sci. 1969 24 1669. NICKLIN D. J., Ph.D. Thesis University of Cambridge 1962. HEWITT G. F. and WALLIS G. B., United Kingdom Atomic Energy Authority, A.E.R.E.RH022,1963. WALLIS G. B., United Kingdom Atomic Energy Authority,A.E.E.W.-Rl23,1961. NICKLlN D. J. and DAVIDSON J. F., Proc. Symposium on Two Phase Flow, Institution of Mech. Engineers, February, 1962 (Paper 4). HEWITT G. F., LACEY P. M. C. andNICHOLLS B., Symposium on Two Phase Flow, Exeter, June 1965 2B401. TAILBY S. R. and PORTALSKI S., Trans. Instn Chem. Engrs. (London) 196139 328. CLIFT R., PRITCHARD C. L. and NEDDERMAN R. N., Chem. Engng Sci. 1966 2187.
B. E. T. HUTTON et al.
498
J. F., Trans. Instn Chem. Engrs. 1959 37 131. J. E., Ind. Engng Chem. Fundls PII BUCHANAN 1967 6 400. WI LEVA M., Tower Packings and Packed Tower Design, W.S. Stoneware Co., Delaware, pp. 37-50, 1953. 1231 ECKERT J. S., Chem. Engng Prog. 196157 54. B., ~241 MORTON F., KING P. J. and ATKINSON Tram lnstn. Chem. Engrs. 1964 42 149. Koch Sulzer Rectification Columns Bulletin KS 1 WI J. F., B.E. Thesis, University of 1261 STUBINGTON Queensland 1969. [201 DAVIDSON
Integrating,
and using the boundary condition x = 0,
7=-7i T=pLgxCOSp----_i.APX Z’
A force balance on the gas side yields: $4,’
= rix Wetted surface area AP
%?E=T’ ge
APPENDIX l(A)
Wetted surface area total volume
=7&(1--E) Ape T1 = Z’(1 --E)a,’
The gravity-viscosity model
The model is similar to that proposed by Davidson [20] and Buchanan [2 l] with the exception that the effect of pressure gradient is also considered. The basis of the model is countercurrent flow of uniform stream of gas and liquid in an inclined channel of length 2’ of rectangular section, as shown in Fig. A. 1.
(Al)
(A2)
For a Newtonian fluid, and laminar liquid flow, dv
T=-,LL-
Substituting
T
from (Al) and Tifrom (A2):
,XCOSp--X-
/dv=-&p
v=--
dx
:
zl(f!e+Jdx
1 pLw2cos/3 ---Apx2 2 2’2 CL/.(
Apex
Zl( 1 - +I j
The constant of integration, C, is evaluated by using the boundary condition v=O,x=8 PL,~~COSP ---A@’
C =I
The volumetric surface
2’2
2
CLL(
Ape8
Z’(l-4)U”
)
flow rate of liquid per unit width of
Fig. A. 1. -= D We assume: (a) steady state is maintained (b) pressure gradient exists only in the axial direction (c) film thickness of the liquid stream is constant over the length of the element (d) cross-sectional area of the element is constant (e) physical properties of the liquid are independent of static pressure (f) no slip at the liquid-solid interface. Momentum balance on liquid film in axial direction over a system of thickness Ax, of length Z’ and extending a distance W in the Y direction.
W
I
‘vdx lfi2 ZL [ 3cLL Z/+“(l -e)
= P:,~~COS p -- Ap z+
3@L
1
Substituting holdup (h) = &z,( 1 -E) D
p&h” cos p
w
3PLU”3(1- l)3
Ap
--
[ Z’
I[
h3
3p,,a,3(
1-
E)3
1
lh2 + 2/LLLU,3(1--E)3.
The superficial liquid velocity can be written as L=~a,cosp
Divide by Z’WAx and take the limit as Ar approaches zero.
Also, AP AP y=-$osp SO, h3cosZ/3 + lh2 co2 p L = p,g ~0s’ B h3 -- AP 1 - e)3 2/.LLfX,2( 1 - l)3 3/&&,2(l - & ( z I[ 3/.&,,a,2(
On flooding in packed columns APPENDIX
The gravity-inertia
499
l(B)
Zglsin @-:(%)/sin
model
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 lower end of the flow element. The model shown in Fig. B. 1. is similar to that of Buchanan [2 l] except that we include the effect of the gas pressure drop.
(B.3.)
0)
Apply Bernoulli’s equation between a point r down the slope and the initial position 1.
= r sin e
Z, -Z,
Vr2= V,:2+2grsini+dpJrsine
dZ
Substitute
(B.4.)
PL
for VI from (B.3.) and (B.4.) and let n =
F/l-F
V2=2g1sin0 r n
2 dp /sin0 PL dZ
+2grsin0--dpZrsin0
n
dZ PI.
Fig. B. 1 Between (1) and (2) potential energy is converted kinetic energy. F = fraction of kinetic energy lost between (2) and (3): i.e.
Now, the film thickness at position r down the plate is given by: 6(r) =
L’I(pLVr).
Themean film thickness over the plate is given by Vz2 - VSz = FVz2
6mean=
And Vzz = VIZ, i.e. the liquid velocity is the same at each element. So. (I-F)V*‘,2=
Applying liquid:
v3
Bernoulli’s equation between
q+prgz,+
[ p .C$,]
6mean=
I/I
‘8(r) dr
s0
L’
pJ(2g-22/pL(dp/dZ))riz(sin
(B.1.)
I
1 and 2 for the
’ J o (I/nd:r)l12 6 mean =
=
L’
-+PP,gz* 2
. p/2
pJ(2g-22/pL(dp/dZ))1’2(sin0)1/2 x (n+ I)“*-
PrV.z2
0)Li2
n112
1
+ [P@-gz*] But,
And, L’=-L
a,, sin e
h = a;(6
Z,-ZZ,=Isin8
mean).
Substituting these,
Vzz= V12+2glsinB-j!jIsin8~
(B.2)
h=
(n+ 1)*/z- 1
Qfi
p,(sin 8)3/*(g- 1/pL[dp/dZ])L~2/1~z
Substitute into (B. 1.) from (B.2.) E = L mlsec
(1
+I( V,2+-2g1sin13--1dplsin0 PL dZ
>
= VS2
= v,*
h=
@
B. E. T. HUTTON et al.
500
and S’= [_L]“‘c’“+;Q,~-l]
(B.5) I
03.6)
APPENDIX
Applying the flooding criterion to (C.4.): dD pLgd@ Pf(d + b - 2fQ5b*G 2 -=--,uL(b-26)5(d+b)4;r d6 FL
l(C)
Calculations for the wetted-wall column For counter-curreet flow of gas and liquid between vertical, parallel flat plates, the following equation described the liquid flow [26]. D = z+_($)]$~($)@$L)
(C.4.)
+ 10S3f(d+b-26)5b4G,2_10iYf(d+ b-26)5b4G, 3pL(b-26)5(d+b)4p, 3pL(b-2q6(d+ b)4p, 6 (d+b-26)5b4G 2 58*f(d+ b -2S)*b4G,z -2pL(b-2S)4(d+b)ip11+2pAb-26)4(d+b)4p0
(C.1,) (C.5.)
where (C.2.) G = G L),sz= G d2bZ(d+b-2S)2 (I ’ Da2 ’ (d+b)*d’(b-2s)z Substituting into (C.2.) for G a; D,: (d+b-26)5b4G, d(b-26)5(d+ b)$g So (C.l.) becomes
(C.3.)
By fixing, G,, we solve this equation (CL) for the flooding film thickness and hence the flooding liquid flow rate from (C.4.). We repeat this for varying values of b the plate spacing. At the flooding film thickness, the actual gas velocity between the plates can be calculated from (C.3.) and so the corresponding flooding liquid flow rate can be calculated from the model of Cetinbudaklar and Jameson [12]. The friction factor, .L used in our calculations is derived from Wallis’s correlation [S] for the friction factor.