I n d . Eng. Chem. Res. 1987,26, 1546-1550
1546
Liquid Weeping Accompanied by Bubble Formation at Submerged Orifices Yasuharu Akagi,* Kenji Okada, and Kunio Kosaka Department of Applied Chemistry, Okayama University of Science, Okayama 700, Japan
Teruo Takahashi Department of Industrial Chemistry, Okayama University, Okayama 700, Japan
As a fundamental study of sieve tray, the weeping phenomena a t submerged orifices were examined in detail based on the pictures taken by a high-speed camera and on the data of pressure fluctuation in the gas chamber. T h e chamber pressure decreases excessively because of the formation of the larger bubble. Therefore, the liquid weeps immediately after the detachment of a bubble from the orifice. The effects of the orifice diameter, the orifice number, the pitch of orifices, the chamber volume, the gas flow rates, and the physical properties of liquid on the liquid weeping rates were investigated experimentally. The ranges of gas flow rate with the weeping and the weeping rates were correlated by these variables. Sieve trays have been used as a gas distributor in plate and bubble columns. It has been said that liquids are likely to weep and therefore stable operational ranges are narrow. On the other hand, the sieve tray has been used in the plate column of countercurrent type because of the easy weeping of liquid. Thus, the liquid weeping at sieve trays is an important hydraulic parameter by which the column geometries and the operational conditions are influenced. We have reported the new correlation for the critical gas velocity of weeping and then have reported the first correlation for the liquid weeping rates (Akagi et al., 1981). As a fundamental study of weeping at sieve trays, McCann and Prince (1969) analyzed the weeping phenomena accompanied by bubbling at the submerged single orifice and correlated the liquid weeping rates. However, they did not measure the weeping rates in the lower region of gas flow rates. Tsuge and Hibino (1978) examined the relation of pressure fluctuation in the chamber and bubbling for the weeping free single orifice. Miyahara et al. (1984) and Miyahqra and Takahashi (1984) measured the bubble volume in single bubbling regime with liquid weeping, varying widely the orifice diameter and the chamber volume, and reported a fact that the bubble volumes with weeping were fairly larger than those without weeping. In this study, the weeping phenomena at submerged orifices were examined in detail based on the pictures taken by a high-speed camera and the data of pressure fluctuation in the gas chamber. The weeping ranges and weeping rates were correlated by orifice diameter, orifice number, pitch, chamber volume, and physical properties of liquid. Experimental Section The apparatus is shown schematically in Figure 1. The orifice plates were made of brass, and 1-13 orifices were drilled. The diameter ( d ) of orifices was 2-6 and 8 mm. The pitch (p), (ratio of distance between orifices to diameter) was varied by the range 1.5-6.0 at orifice number (n) = 2 and d = 5 mm. The thickness (T) of plates was mainly 1mm, but plates having thicknesses of 5 and 10 mm were used to examine the effect of T. The liquid depth (DL) on the plate varied from 5 to 40 cm, and the chamber volume (VJ varied from 40 to 28000 cm3. To keep the liquid level on the plate constant, the liquid that was supplied from the tank was always kept overflowing. The air was supplied to the apparatus through the buffer tank. The flow rates were measured in two ways, that is, 0888-5885/ 87/ 2626-1546$01.50/0
by the soap film meter in the case of low flow rates and by the rotameter in the case of high flow rates. In all runs, the pressure in the upper stream of the needle valve was always kept about 3 X lo4 Pa higher than that in the chamber. Therefore, the air volume from the needle valve to the orifice can be regarded as the chamber volume. The weeped liquid was collected by the liquid funnel and was measured by the graduated cylinder at the outside of the column. As the liquid surface in the funnel rose and fell with the weeping, the chamber volume varied slightly during each run. The chamber pressure was measured by using the pressure transducer and recorded by the oscillograph. The weeping phenomena was examined by the photographs taken by the high-speed camera. Water, aqueous glycerin solutions, and aqueous methanol solutions were used in this study. The ranges of physical properties of liquids are as follows: density (pL) = 840-1194 kg/m3, viscosity (pL) = 9 X 104-1.7 X Pa s (0.9-17 cP),and surface tension (a) = 3.1 X 10-2-7.2 X N/m (31-72 dyn/cm). Experimental Results Figure 2 shows the pictures taken by a high-speed camera of the bubble formation, the detachment, and the liquid weeping, varying V,. These pictures were photographed under conditions in which the upper and lower sides of the plate could be seen at the same time. The seven pictures were selected from many pictures that were photographed at the rate 200 flames/s to demonstrate a cycle of the phenomena (bubble formation, detachment, and liquid weeping). The chamber volume (V,) was varied at constant d and the volumetric gas flow rate (Q ) in this figure. The liquid weeping rate (QJand the cycle have also been shown in the figure. Except for the middle row, although the liquid drops have adhered to the surroundings of the orifice at the lower side of the plate, these drops do not influence the liquid weeping rates. It is clear that the liquid weeping occurs immediately after the detachment of a bubble and Q1at V, = 5 X m3 is smaller than that of the others. The values of V, and OT increase with VC. Figure 3 shows examples of the experimental results of 81, the frequency (f) of bubble formation, VB and Ql/f. In the lower region of gas flow rates, Q1and f increase linearly with Qg,and VB and Q1/f are nearly constant. It is supposed that as Q1gives the same behavior as f , the same phenomena occurs at the orifice in this region, and therefore the cycle of bubbling and weeping decreases with
toT)
0 1987 American Chemical Society
Ind. Eng. Chem. Res., Vol. 26, No. 8, 1987 1547 radius of curvature of the interface means the reduction of pressure behind the interface (inside the bubble), more gas will flow into it from the chamber, forcing a further increase of the radius of the curvature and consequently reducing the pressure in the chamher as well (d). The decrease of pressure inside the bubble during this depressurization step is more rapid than the decrease of chamber pressure due to the loss of gas dicharging through the orifice. As a result, a pressure difference develops across the orifice. The rate of this gas flow is determined by the magnitude of the pressure difference (UG) so developed. The pressure decrease of the chamber is 140 Pa (14.3mmHnO). The measured bubble volume is larger than the volume ohtained when the surface tension and buoyant forces are equated; that is, VB = 2 r d o / A p g (1) The chamber pressure decreases excessively because of the formation of the larger bubble, and therefore the liquid weeps through the orifice into the chamber. Ql/f depends on the pressure difference, UL. It is found that when the phenomena is observed in the case where n > 2, a huhhle forms a t any orifice and, on the other hand, the liquid weeps at all orifices in the lower region of Q,. The number of bubbles forming simultaneously increases with Q, in the upper region of Q,. Figure 5 shows examples of the experimental results of liquid weeping rates (QJ. Though the chamber volume (V,) influences little to QIin V, 5 2 X m3, QI decreases with increasing V, in V, > 2 X m3. The experimental results of Q, reported by McCann and Prince (1969) are also shown in Figure 5. The measuring method is the same as that of this study. Though Q, in only the upper region of Q, (QI decreases with increasing Q,) is reported, their tendency agrees in both data. But if both data are compared a t the same V,, McCann and Prince's data are fairly small. The sieve plate is set a t the liquid surface for the prevention of turbulence of liquid surface by the huhble collapse in McCann and Prince's measurement. It seems that as our apparatus does not have the sieve plate, our data are larger than McCann and Prince's data. Figure 6 shows the effects of the number of orifices (n) and pitch @) on QI. In the case of n > 2, the effect of n on QI is small in Q, < 5 X 10" m3/s, in which a bubble
Figure 1. Experimental apparatus.
increasing Qc When Q, further increases beyond this region, VBstarts to increase with increasing Q, because the increase o f f becomes small. Also Q,/f decreases with increasing Q, in this region. It is clear that QI decreases through the maximum value with increasing Q, and reaches zero. Figure 4 shows the chamber pressure fluctuation and the high-speed pictures a t point I in Figure 3. A cycle was divided into periods of weeping, bridging, and bubbling by examining the high-speed pictures. As soon as a bubble releases at the minimum pressure point (a), the liquid flows down into the chamber (h). The liquid weeps for about 0.6 s SO that the chamber volume decreases slightly. Also the air continues to flow into the chamher. Therefore, the chamber pressure rises rapidly in the period of weeping. The weeping ceases at point e when the chamber pressure rises about 80 Pa (8.2 mmH,O) and the period of bridging (c) begins. As the liquid-gas interface is kept steady at the orifice and the air flows into the chamber at a constant flow rate in this period, the chamber pressure increases proportionally with time. Accordingly, as the chamber pressure increases, the interface curves upward in a dome shape and the radius of curvature becomes small. However, there is a limit to the pmible values of the curvature; that is, when the curvature becomes equal to the radius of the orifice, the hubble can no longer reduce its radius of curvature. A t this stage, the interface has become a hemisphere with its radius equal to the radius of the orifice. Forcing more gas into the chamber beyond this stage will force the interface to expand into the liquid, greatly increasing its radius of curvature. Since the increase in the dz0.005 m 0, = 1.14X1OS d / s Vc = 5~10%~ Ql = 1.55x10-6 d l S e, 0.13 s
= z ~ r o m3 -~ QI= 1.75xlO-' m3k V,
eT=0.32 s
---
V, = 5 ~ 1 0 - m3 ~ QI
= 1.16X10-6 m3/s
e,= 0.46 s Figure 2. Photographs of bubble formation and liquid weeping
a*-
i
1548 Ind. Eng. Chem. Res., Vol. 26, No. 8,1987 5
I
I
I1
I
I X d
2-----
3
10
x"
100
1x16~1 "C Figure 6. Effect of number of orifices (n) on liquid weeping rates 0,
Figure 3. Experimental results of liquid weeping rates (QI), frequency of bubble formation @,bubble volume (VB), and Ql/f.
(BO. a %**I
owrwnp
x*r*inp
ID
-
rr
5
D
O
D
O
0
O
0
0
.m--
..
o--+.--c I
o---a-.-s-rs ____________.___ 0
0
0
0
0 0
l i l
0
vr
1x0
, d I W
r",
Figure 7. Liquid weeping region.
lower region-of Q,. But in the upper region of Q,, QIand Q, that the weeping ceases increase with p ~ On . the other hand, QI increases with a decrease in the lower region of
Q,. Figure 4. Chamber pressure profile and photographs of bubble formation and liquid weeping at volumetric flow rates of gas flowing into chamber (Q ) = 1.25 X 10" m3/s and liquid weeping rates (QJ = 0.63 X 10" mf/s.
09
["/SI
Figure 5. Effeds of volumetric flow rates of gas flowing into chamber (QJ and chamber volume (VJon liquid weeping rates (QJ.
forms at any oritice and the liquid weeps at all orifices. But Ql increases with n in the upper region of Q That is, the maximum value of QI, Q, at the maximum and Q, that the weeping ceases increase with n. The effect of p on QI is small in the lower region of Q, at n = 2, but QIdecreases with increasing p in the upper region of Q,. If the effects of physical properties, mainly viscosity ( p d of liquid on Ql, are examined, the effects are small in the
&
Ranges of Gas Flow Rates with Liquid Weeping As mentioned above, Qlincreases linearly with Q, in the lower region of Q,. In the upper region of Q,, QIdecreases rapidly with increasing Q,, but sometimes a little liquid will weep even at very large Q,. It was assumed that the weeping did not occur when Ql was smaller than 0.1 X lo4 m3/s. In the single orifices, the ranges of gas flow rates in which the liquid weeps through the orifices are not influenced by V, in V, 5 2 X m3, but these ranges m3 (see become narrow with increasing V, in V, > 2 X Figure 5). Also these ranges become wide with increasing d. As shown in Figure 6, though the lower limits of these ranges arenot influenced by n,the upper limits increase with n. Figure 7 shows the ranges of orifice diameter (d) and chamber volume (VJ taken with weeping. The liquid does not weep in all V, at d = 0.002 m, in V, > 2.5 X m3 at d = 0.003 m, and in V, > 1 X m3 a t d = 0.004 m. It was considered that the liquid will not weep, as the resistance due to the surface tension is large at small d and as the decrease of chamber pressure accompanying the bubbling is small a t large V. Reynolds number of the gas phase (RecL) a t the lower limit of the ranges is correlated in the single orifice as shown in Figure 8 and is expressed for ( N C / d 95 1.5 X lo7 as ReoL = 7.0 X 104d-2.5 (2) and for (N,/d2.5)> 1.5 X lo7 as ReoL = 1.14 X 10-z1N~2d4.0
(3)
On the other hand, Reynolds number of the gas phase
Ind. Eng. Chem. Res., Vol. 26, No. 8, 1987 1549 5 (x 103 ~ m 3C ~ I 0 Aqueous
0.004 u
glycerin
( d =0.005m
T=O.Wl m I
0.005 0.001-0.010
e 0.008 0.001 D
0.5
Water
~&qutousglyccr~n mclhan
0.2
a5
0.1
1
4
( d l T ? ' ? b / U w ~io' * [-I
Figure 10. Correlation of total pressure difference in chamber (APT). 1
Figure 8. Correlation of Reynolds number of gas at lower weeping point (ReGL).
I
I
Po
1
1
1
1
1
d = 0.005 m
41rwater system
T =0.001 m
1
DL = 0.05 m
I
Po
7 Y
a)
3
b)
Figure 9. Sketchs of bubble formation and liquid weeping phenom ena.
3 2 1 1
(ReGu)at the upper limit of the ranges is also divided in two regions by N , and d and can be correlated for (Nc/d2.6) 5 1.2 x 10' as ReGU = 6.5 x 107(pL,d/~L2)-0.17d1.5 and for
1
>
1WOO 4 8 8 15000 7 1 6 28WO 137.2
3
Moo
Figure 11. Effects of Reynolds number of gas based on orifice (Rec) and chamber number (N,) on resistance coefficient due to liquid through orifice (&).
(6)
100
1
(*lo])
The bubble forms only one at the same time for n L 2 in the region of Qg from the lower limit to 5.0 X lo4 m3/s. If it is assumed that an orifice is used for the gas flow, ReG can be calculated by eq 2 or 3 even for the plate of n 1 2. As all orifices are used for the gas flow in the region of Qg from 2 X lO"-lO X m3/s to the upper limit, the upper limit of Q, increases with n. Therefore, if the gas velocity based on the all orifices is used, ReG can be calculated by eq 4 or 5.
Weeping Rates As shown in Figure 4,the chamber pressure rises by the accumulation of gas and then the bubble forms at the orifices. The enlargement and detachment of bubble occur in a moment and besides the buoyancy act to form the bubble. By these facts, the chamber pressure decreases excessively and the liquid weeps immediately after the detachment of a bubble through the orifice into the chamber. Equations 7 and 8 were obtained for the periods of bubbling and weeping in the single orifices, respectively (Figure 91,
+ kd-Ugh2PG 2g
(7)
where (Pc)B and (Pc)w are the chamber pressures during
10033
C I-
(Re&
ReGL 5 ReG 5 ReGU
g
1w
10
Therefore, the ranges of ReGwith weeping are
= DLpL
490
2000 9.80 5000 244
>
(4)
~1 ReGu = 1.4 x l o 1 4 ( p ~ a d / ~ ~ 2 ) - 1 ' 2 d 1 ' 5 N(5)
- PO
low
D
> 1.2 X lo7 as
(Pc)B
50 O 2 L 5 200 0.980 500 2.44
7 A
1
1
1
0 Water
I
0.1
9 Aqueous glycerin
4
AquQOuS methanol
100
10
1
NC
I
500
c-I
Figure 12. Correlation of coefficient a in eq 11.
the bubbling and weeping, respectively, Po is the pressure above the liquid layer, and Ugh and Ulh are the superficial gas and liquid velocities through the orifices. If Po is eliminated from eq 7 and 8,
If the maximum pressure difference ( A P T ) in the chamber was used as (Pc)B - (Pc)w, it could be correlated by d , T , and u as shown in Figure 10. (PJB - (P,)w = 2.2 X 10-3(al/T)-0.45(~/~,)1'4n-o'1Po (10) For correlation of the liquid weeping rates by eq 9 and 10, the resistance coefficients of liquid (k,) were calculated
1550 Ind. Eng. Chem. Res., Vol. 26, No. 8, 1987
by using the measuring data, and the examples have been shown in Figure 11. The resistance coefficients of gas (kd) were calculated by the correlated equation of Hunt et al. (1955). The values of k, decrease linearly and increase through a maximum value with increasing ReG. The effect of N , on k, is little in the lower region of N , and k, can be correlated by division into three regions of ReG. On the other hand, in the upper region of N,, k, increases with N , and can be correlated by division into two regions of ReG. Then kw is expressed as
flow rates of gas flowing into the chamber (Q,)that the weeping ceases decrease with V , in the upper region of 4,. (4) The effect of the number of orifices (n)on Q1is small in the lower region of Qg,but Q1and Q, that the weeping ceases increase with n in the upper region of Q . (5) The ranges of Q, with the weeping vary by and V,, etc., and these ranges were correlated by these factors. (6) The weeping rate was expressed by eq 9, and the pressure fluctuation (APT) in the chamber and k, were correlated by eq 10 and 11,respectively.
k, = aReGb
Nomenclature DL = liquid depth on orifice, m d = orifice diameter, m f = frequency of bubble formation, s g = gravitational acceleration, m/sz k d = resistance coefficient due to gas through orifice k, = resistance coefficient due to liquid through orifice n = number of orifices N , = chamber number (=4Vcp~/(ad2(Po + Phs))) p = pitch, ratio of center-to-center distance between orifices to orifice diameter (PJB= chamber pressure during bubble formation, Pa (PJw = chamber pressure during liquid weeping, Pa Phs= pressure due to liquid on orifice, Pa Po = pressure of atmosphere, Pa APG = pressure difference in chamber for bubble formation, Pa SL = pressure difference in chamber for liquid weeping, Pa APT = total pressure difference in chamber, Pa Q, = volumetric flow rate of gas flowing into chamber, m3/s QI = liquid weeping rate, m3/s ReG = Reynolds number of gas based on orifice ReGL= Reynolds number of gas at lower weeping point ReGu = Reynolds number of gas at upper weeping point T = plate thickness, m Ugh = superficial gas velocity based on orifice, m/s Ulh = superficial liquid velocity based on orifice, m/s V, = bubble volume, m3 V, = chamber volume, m3
(11)
Coefficient a and exponent b can be correlated by (a) N , C 10 for region I a = 330(d/d,)'(DL/ T)0.5( u/ uw)3,5
b = -0.15(d/T) - 1.0
(12)
for region I1 a = 1000(d/ d,) - 2 . y
/
n1.2
b=O
(13)
for region I11 a = 3.8
X
b = 3.5
(b) N ,
(14)
> 10
for region I' a = 3.8(d/d,)2(o,/T)o'5(a/aw )3.5N c
b = -0.15(d/T) - 1.0
(15)
for region 11' a = 1.3 X 10-11N,2
b = 3.5
(16)
where the standard diaqeter (d,) is 0.001 m. Figure 1 2 shows the correlation of a for regions I and 1'. Though k, is independent on N , for N , < 10, k, increases with N , for N , > 10. Conclusions The liquid weeping phenomena and the weeping rates accompanied by bubbling a t the submerged orifices were investigated and the following knowledge was obtained. (1)The liquid weeps immediately after the detachment of a bubble from the orifices. (2) The liquid does not weep a t small orifice diameter ( d ) and large chamber volume (V,). (3) The effect of V , on the liquid weeping rates (Q1) is negligible in V , 5 2 X m3, but Q1and the volumetric
d
Greek Symbols viscosity of gas and liquid, respectively, Pa s density of gas and liquid, respectively, kg/m3 OT = cycle time of bubble formation and liquid weeping, s u, u, = surface tension of liquid and water, N / m
bG, yL = pG, pL =
Literature Cited Akagi, Y.; Nishikaze, M.; Yamamoto, S.; Takahashi, T. Kagaku Kogaku Ronbunshu 1981, 7(5), 442. Hunt, C. A.; Hanson, D. N.; Wilke, C. R. AZChE J . 1955, 1(4),441. McCann, D. J.; Prince, R. G. H. Chem. Eng. Sci. 1969, 24, 801. Miyahara, T.; Iwata, M.; Takahashi, T . J . Chem. Eng. Jpn. 1984, 17(6), 592. Miyahara, T.; Takahashi, T. J . Chem. Eng. J p n . 1984, 17(6), 597. Tsuge, H.; Hibino, S. J . Chem. Eng. Jpn. 1978, 11(2),173.
Received for review June 16, 1986 Revised manuscript received April 17, 1987 Accepted May 1, 1987
