Ind. Eng. Chem. Res. 1988,27, 2331-2341 Luyben, W. L. Process Modeling, Simulation, and Control for Chemical Engineers; McGraw-Hill: New York, 1973; 429-451. Morari, M.; Economov, C. G.; Zafiriov, E. Robust Process Control; Prentice Hall: Englewood Cliffs, NJ, 1988, in press. Soule, L. M. “Feedforward Control Improves System Response”. Chem. Eng. 1970, 77(24), 113-116.
2331
Stephanopoulos, G. Chemical Process Control; Prentice Hall: Englewood Cliffs, NJ, 1984; pp 411-427.
Received for review August 6 , 1987 Revised manuscript received June 17, 1988 Accepted July 5, 1988
SEPARATIONS Entrainment from Sieve Trays in the Froth Regime Henry Z. Kister* and Joe R. Haas+ C F Braun, Znc., 1000 South Fremont Avenue, Alhambra, California 91802
The effects of tray geometry and operating parameters on sieve tray entrainment in the froth regime were investigated. The study was based on published entrainment data for the air-water system a t tray spacings exceeding 300 mm. Several distinct modes in which the above variables affect entrainment are described. A new correlation is presented for predicting entrainment as a function of tray geometry and flow rates for the air-water system. The correlation was shown to give reliable predictions of the effects of various design and operating parameters on entrainment and a good fit to experimental data. The sieve tray is one of the most extensively used vapor-liquid contactors in distillation and absorption operations because of its simplicity and low cost. One of the most common phenomena to adversely affect the capacity and efficiency of sieve trays is excessive entrainment. When entrainment appears to exceed about 5% of the liquid flow rate, remedial steps were recommended at the design stage (Lockett, 1986). These steps include increasing column diameter, tray spacing, or judicious variation of tray geometry. Entrainment recycles liquid in the wrong way through a column, thus reducing the driving force for mass transfer. This lowers tray efficiency. Quantitatively, the effect of entrainment on tray efficiency is complex; a detailed analysis is described by Lockett (1986). Entrainment from sieve trays has been extensively studied in the past 2 or 3 decades, yet factors affecting it are poorly understood. Several conflicting trends have been reported for the effect of operating and design variables on entrainment (e.g., Friend et al. (1960), Bain and Van Winkle (1961), and Kister et al. (1981b)). Recent investigations (e.g., Lockett et al. (1976) and Porter and Jenkins (1979))have shown that some of these trends can be explained if the nature of the dispersions formed on the sieve tray is taken into account. Using this approach, it has been demonstrated (Kister et al., 1981a; Kister and Haas, 1987) that the various data sources describing entrainment in the spray regime are in good agreement with each other and can be successfully correlated. However, the behavior of entrainment in the froth regime is not well understood. This paper is concerned with entrainment in the froth regime. The spray and froth regimes are the most common regimes on commercial-scale sieve trays handling nonfoaming *Author t o whom correspondence should be directed. Present address: UOP, Inc., 25 E. Algonquin Rd, Des Plaines, IL 60017-5017.
systems. In the spray regime, gas is the continuous phase, while liquid is present in the form of drops dispersed in the gas. In the froth regime, liquid is the continuous phase, while gas is distributed as bubbles in the liquid. Between these two regimes of dispersion there exists a transition during which an inversion of the continuous phase occurs. The transition from the fully developed froth regime to the fully developed spray regime occurs gradually over a mixed frothlspray region. At a constant gas velocity, tray dispersion changes from froth to spray as the clear liquid height decreases. The froth regime commonly occurs at moderate and high liquid flow rates, moderate and high pressures, and low and moderate gas velocities. Kister et al. (1981b) carried out extensive entrainment measurements in the froth regime and the partially developed spray region. While they investigated and correlated the behavior of entrainment in the partially developed spray region, no attempt was made to investigate or correlate the trends shown by the froth regime data. In this paper, we extend the previous investigation and study the behavior of entrainment and its dependence on tray geometry and operating parameters in the froth regime.
Background
A change in entrainment behavior near the transition from the froth regime to the spray regime has been observed by several investigators (e.g., Shakhov et al. (1964), Lockett et al. (1976), Stichlmair (1978), and Kister et al. (1981b)). This change can usually be recognized by a minimum in a plot of entrainment versus liquid flow rate at constant gas flow rate. Work by Kister et al. (1981b) suggests that the minimum specifically marks the transition from the froth regime to the partially developed spray region. In the partially developed spray region, entrainment dependence on tray geometry and operating parameters was shown to be similar to that observed in the fully developed spray regime and can be correlated by 0 1988 American Chemical Society
2332 Ind. Eng. Chem. Res., Vol. 27, No. 12, 1988 Table I. Key to __ Figures 11-13 ____._____ ref Bain and Van Winkle, 1961 Frient et al., 1960 __I_
Lemieux and Scotti, 1969 Kister et a]., 1981b
d,, mm 1.6-3 2 4.8-9.4 12.7 12.7-25.4 6.4-12.7
12.7 19.0 12.7
Brook et al., 1955 Benke, 1974 Calcaterra et al., 1968 Nutter, 1973 Table 11. Key to Figure 14 .__l__l ref Thomas and Ogboja, 1978 Hunt et al., 1965
4.8 6.4-19.0 9'5 12 7
dH, mm
25.4 25.4 25.4 6.4 6.4 6.4 6.4 6.4
S, mm 305-610 305 305 457 457 457 4-57 457 482 914 324-654 610
S, mm 305 381 457 305 406 508 610 711
Af, fractional
0.073 0.096 0.078 0.069-0.094 0.10-0.16 0.11
0.10 0.06 0.04 0.05-0.16 0.08 n 079
A f , fractional 0.124 0.124 0.124 0.054 0.054 0.054-0.19 0.054 0.054
h,, mm
0-25 0-25 0
25 25-76 0 25 25 64 25 . 1i
51
h, or h,, mm 76" 76" 76" 46' 46, 9gb 46, 99' 46, 99' 46, 99'
L, m3/(h m) 4-18 7-43 7, 14 49-134 2-28 7-26 2-28 5-30 24, 47 19 6-18 13, 26
L , m3/(m h) 4-18 4.5-36 4.5-36
F. 0.9-2.1 1.2-3.3 1.O-2.3 1.7-2.2 0.5-2.2 0.5-1.5 0.5-1.5 0.5-1.0 0.4-1.1 1.4-2.2 0.7-1.5 1.4-3.3
F8
0.8-1.1 0.9-1.6 0.9-1.6 0.9-1.6 1.0-2.9 1.0-4.0 1.0-3.4 1.0-3.6
symbol 0 A
V 0 63 B X
+ *
IB
0
symbol X
*
+ A 0 0
0 V
"h,. 'h,.
spray regime correlations (Kister et al., 1981b; Pinczewski and Fell, 1982). The above change in entrainment behavior was explained by Pinczewski and Fell (1982). They state that, in the froth regime, most holes are bubbling; entrainment is produced by breakup of liquid sheets defining emergent bubbles. This mechanism forms small drops (typically 200 pm) at low projection velocities, resulting in low entrainment. In the fully developed spray regime, most holes are continuously jetting; entrainment is produced by atomization of liquid by gas jets passing through the tray holes. This mechanism forms large drops (typically 1000 pm) at high projection velocities, resulting in high entrainment. In the partially developed spray region, both bubbling and jetting occur simultaneously at adjacent tray holes. Entrainment produced by the holes undergoing intermittent jetting far outweighs that from holes which are bubbling, which explains the similarity in behavior to the fully developed spray regime. The minimum in the curves of entrainment versus liquid flow rate (above) can be explained in terms of the same mechanism. In the spray regime and the partially developed spray region, increasing the liquid rate promotes bubbling and suppresses jetting a t the holes. Therefore, entrainment decreases as liquid flow rate is raised. In the froth regime, increasing the liquid flow rate elevates the froth envelope; the breakup of the emergent bubbles then takes place closer to the tray above. Therefore, entrainment increases as liquid flow rate is raised. The minimum in the curve of entrainment versus liquid flow rate therefore occurs a t the transition between the partially developed spray region and the froth regime. The transition from froth to partially developed spray regime explains only some of the conflicting trends that have been reported on the effects of tray geometry and operating variables on entrainment. These trends which occur in the forth regime are discussed below.
-
Factors Affecting Entrainment in the Froth Regime By choice of specific froth regime entrainment data, this section presents empirical observations on the trends of entrainment variation with flow rates and tray geometry.
Rather than attempting to explain these trends, measured data are used to demonstrate the trends. This set of data illustrates why there is so much confusion in the literature. Some explanatory comments in terms of our new correlation are provided later in this paper. Published data were surveyed to illustrate these trends. Since the bulk of the published data is for the air-water system, all the experimental data used in this work are for the air-water system. It has been demonstrated (Hunt et al., 1955; Porter and Jenkins, 1979; Kister and Haas, 1987) that entrainment correlations derived for the air-water system can be extended to systems of commercial importance. Data Bank. The data bank for this investigation includes published data for froth regime entrainment contained in the references described in Tables I and 11. The complete data bank contains over 400 experimental data points. The data bank consists of all points that were found to be outside the spray regime and the semideveloped spray region by criteria discussed in our previous articles (Kister et al., 1981a,b; Kister and Haas, 1987). Factors affecting entrainment in the froth regime are discussed below with the aid of several illustrations (Figures 1-10). Experimental data points on these illustrations are connected by heavy lines. The dashed lines in Figures 1-10 are the corresponding values of predictions from the new correlation developed by the authors which is discussed later in this article. Effect of Hole Diameter. Figures 1 and 2 illustrate the effect of hole diameter on entrainment at a low and a high liquid flow rate, respectively. Three types of behavior are apparent: 1. Entrainment rising significantly and steadily with hole diameter. This behavior is similar to that in the spray regime (Kister et al., 1981a). The diagrams indicate that high gas rates, low liquid rates, and large hole diameters favor this behavior. 2. A small, almost marginal rise of entrainment with hole diameter. This behavior appears to be favored by small holes and higher liquid rates. This is consistent with the observations of Hunt et al. (1955). When their hole diameter was varied between 3.2 and 9.5 mm, it did not affect entrainment; an increase from 9.5 mm to 12.7 mm
Ind. Eng. Chem. Res., Vol. 27, No. 12, 1988 2333
". o5
L
=
A,
=
HW
=
s
=
3 CU,M/H 0.10
L DH A,
M
25.4 M M 460 MM
H
= = = =
19 C U , M / H 1 2 , 7 MM
M
0.10 25.4 MM
460 M M
08
10
1.5
Superficial F factor Superficial F factor
20
25
m / s (kg/m3?
Figure 3. Effect of tray spacing on entrainment, large tray spacings; (A)data by Kister et al. (1981b); (A)data by Benke (1974).
m l s (kg/m3
Figure 1. Effect of hole diameter on entrainment, low liquid rate; data by Kister et al. (1981b). =
.,,
lH =
--
L
A, H
S
-
=
= =
25 C U , H / H M 0.10 25.4 M M 460 M M
,\
=
iw =
11 C U . M / H M 9 . 5 MM 0,08 50,8M M
I 325 M M
m
1
m
-1:
:I I
c
Ee
01 .- 01 e
W
8
1.0
Superficial F factor
1
,001 ,001
,
05
7', ,
I
0.8
1.0
,
I
125 15
Superficial F factor
, ,
,
,
, 1
2.0 25 m/s (kg/m3,4!
Figure 2. Effect of hole diameter on entrainment, high liquid rate; data by Kister et al. (1981b).
significantly raised entrainment. 3. A large jump in entrainment with hole diameter appearing to take place with large hole diameters (>13 mm). Such a jump appears to be favored also by low liquid rates and low gas velocities. A t the low gas velocity end of Figure 1, an increase of 50% in hole diameter generates a 5-fold increase in entrainment. This effect has not been previously reported. Effect of Tray Spacing. Figures 3 and 4 illustrate the effect of tray spacing on entrainment at high and low tray spacings, respectively. Entrainment appears to diminish as tray spacing is increased and to be roughly inversely
1.5
2.0
2.5
m /s (kg/m3P
Figure 4. Effect of tray spacing on entrainment, low and moderate tray spacings; data by Calcaterra et al. (1968).
proportional to the tray spacing to a power of 2-3. This behavior is similar to that observed in the spray regime (Kister et al., 1981a) and is consistent with the data of Hunt et al. (1955). Effect of Fractional Hole Area. Figures 5 and 6 illustrate the effect of fractional hole area on entrainment at a low and a high liquid flow rate, respectively. Two types of behavior are apparent: 1. Entrainment rising rapidly with diminishing fractional hole area. This behavior is similar to that observed in the spray regime (Kister et al., 1981a) and appears to be promoted by high gas velocities, low liquid flow rates, and low fractional hole areas. 2. Entrainment being only slightly affected by fractional hole area. This behavior appears to be promoted at low gas velocities, high liquid flow rates, and high fractional
2334 Ind. Eng. Chem. Res., Vol. 27, No. 12, 1988
L = DH =
4 CU.M/H 12,7 MM
H~
25,4
=
M
MM
/AF
=
0,059
I
001 Superficial F factor
125 1.5
Superficial F factor
m/s (kg/m3?
Figure 5. Effect of fractional hole area on entrainment, low liquid rate; data by Kister et al. (1981b).
in
oa
05
2
2s
m / s (kg/m3(2
Figure 7. Effect of weir height on entrainment, low liquid rate; data by Kister et al. (1981b). Ir
1
L
=
25
D~
=
1 2 , 7 MM
H~
=
25,4 MM
S
=
460 MM
CU.M/H M
I
-
L
i
L
nH
=
.
A,
=
' S
=
25 :u
MIH
M
12.7 M M 0.10 460
Superficial F -factor m / s (kg/m3b Superficial F factor
m / s (kg/m3p
Figure 6. Effect of fractional hole area on entrainment, high liquid rate; data by Kister et al. (1981b).
hole areas. This behavior is also consistent with the data of Hunt et al. (19551, who noticed no effect of fractional hole area on entrainment. Effect of Outlet Weir Height. Figures 7 and 8 illustrate the effect of weir height on entrainment at a low and a high liquid flow rate, respectively. Three types of behavior are observed: 1. Entrainment diminishes with increasing weir height. This behavior is similar to that observed in the spray regime (Kister et al., 1981b; Kister and Haas, 1987) and is favored by low weirs and low liquid flow rates.
Figure 8. Effect of weir height on entrainment, high liquid rate; data by Kister et al. (1981b).
2. Entrainment is unaffected by weir height. This behavior is favored by high weirs and high gas and liquid flow rates. 3. Entrainment increases with weir height. This behavior is favored when liquid rate is high and gas rate is low. Effect of Liquid Flow Rate. Figures 9 and 10 illustrate the effect of liquid flow rate on entrainment at a fixed tray geometry and for trays with different fractional hole areas, respectively. Three types of behavior are observed: 1. As liquid rate increases, entrainment decreases, then reaches a minimum, and then increases. This is the
Ind. Eng. Chem. Res., Vol. 27, No. 12, 1988 2335
D,,
=
12.7
AF
=
0.107
H~
=
50.8 MM
s
=
460 HM
HM
\ \
\
FsZ15
125
10 Liquid rate (m3/hm)
Figure 9. Effect of liquid rate on entrainment; data by Kister et al. (1981b). 03I
_ _ _ _PREDICTED _-----
-e
.
F .01$
e : a
,001I 1
K~STER
\
2
5 Liquid
10
flowrate,
20
*
. c n .
50
I
m3/h m
Figure 10. Effect of liquid rate on entrainment a t Fs = 1.0.
Uclassicalnentrainment minimum behavior described by Porter and Jenkins (1979) and illustrated in Figure 9 and in the curve for the data of Kister et al. (1981b) for the 10.7% and 16.1% fractional hole area trays in Figure 10. Kister et al. (1981b) showed that this behavior is observed with most sieve tray designs. The minimum in the entrainment curves can be predicted from the Porter and Jenkins (1979) correlation; Figure 9 indicates good agreement between these predictions and actual data. With other sieve tray geometries, the agreement was often less satisfactory (Kister et al., 1981b). 2. A rapid drop of entrainment with an increase of liquid flow rate takes place over a narrow region of liquid flow rates. Lockett et al. (1976) observed a sharp drop in entrainment as liquid flow rate was raised (Figure 10). Data by Kister et al. (1981b) for a similar tray design confirm this observation but suggest a much milder drop (Figure 10). So far, this behavior has only been reported in low fractional hole area trays (Lockett et al., 1976; Kister et
al., 1981b) or with large (19-mm) hole diameters (Kister et al., 1981b). 3. Regions are observed in which liquid flow rate has little effect on entrainment (Figure 10). Such regions have been reported with trays having large (>19-mm) hole diameters (Thomas and Ogboja, 1978; Kister et al., 1981b), low (K0.06) fractional hole areas (Thomas and Ogboja, 1978; Kister et al., 1981b), and 0-mm weirs (Kister et al., 1981b). Effect of Gas Velocity. Figures 1-9 illustrate the effect of gas velocity on entrainment for various tray geometries and liquid flow rates. Entrainment appears to always increase with gas velocity, but the rate at which it increases with gas velocity (i.e., the slopes of the curves in Figures 1-8) varies. In the spray regime, entrainment is proportional to gas velocity to the power of 4-5 (Kister et al., 1981a,b), which would give a slope of 4-5 for a log-log entrainment versus gas velocity curve. The slopes of curves in Figures 1-8 range from close to zero to 4-5. The following observations are made: 1. The slopes of the curves in Figures 1-8 appear to increase with gas velocity. At higher gas velocities and low liquid flow rates (i.e., as the spray regime is approached), the slopes appear to approach the spray regime value of 4-5. 2. In most cases, the slopes of the curves in Figures 1-8 appear to approach a value of about 2-3 when gas velocity is sufficiently reduced. This behavior is consistent with observations by Hunt et al. (1955). 3. Slopes approaching zero appear to be favored by low gas velocities (Fs < 0.8), by large hole diameters (>19 mm), and by low weirs (h, = 0).
Froth Regime Entrainment Correlation Existing Correlations. Most published correlations suitable for froth regime entrainment predictions (Hunt et al., 1955; Bain and Van Winkle, 1961; Fair, 1961) were developed in the late 1950s and early 1960s. At that time, the available data bank was much smaller than it presently is, and the impact of flow regimes on entrainment was yet to be appreciated. Two of the four correlations (Bain and Van Winkle, 1961; Fair, 1961) use a single equation (or plot) for describing both froth and spray regime data; another (Hunt et al., 1955) is based entirely on data obtained in a 150-mm laboratory column with no liquid cross flow. Stichlmair (1978) was the first to apply a flow regime approach to correlating entrainment, but still with a narrow data bank. Almost all data used for deriving the above correlations were for hole diameters 6.4 mm and smaller. Although it was known that larger holes tend to increase entrainment, insufficient data were available to quantify this effect (Hunt et al., 1955; Fair, 1961). As stated by one correlation developer (Fair, 1961), his correlation intended to provide a simple design tool; a more elaborate correlation based on the limited data available then could not be justified. We compared predictions from the two more popular entrainment correlations (Hunt et al., 1955; Fair, 1961) to the present data bank. We found predictions from both correlations to give good agreement with some data points, especially those data for hole diameters of 6.4 mm and smaller. Agreement with other data points was less satisfactory, and considerable scatter was observed (e.g., Figure 11;data sources are identified in Table I). Neither correlation was capable of predicting most of the distinctive trends discussed earlier. Large differences between correlation predictions and data were observed at low liquid rates (12.7 mm), small fractional hole areas (46 mm) by means of a constant head tank. The Hunt et al. (1955) correlation is given by
Because of the considerations above, we felt that Hunt et al.’s correlation can provide a suitable basis for developing an improved froth regime correlation. Major modifications, however, were required to the correlation in order to improve the data fit and to predict the observed trends. Correlation Strategy. In light of the above, the following strategy was adapted for developing an improved froth regime correlation: 1. Modify the Hunt et al. (1955) correlation to improve its fit to data measured under hydraulic conditions that promote uniform froth formation, and extend it to fit the data measured under nonuniform froth conditions. The modified correlation predicts the froth regime entrainment,
Ef.
2. Combine the froth regime entrainment prediction, E,, with a previous expression (Kister et al., 1981a; Kister and Haas, 1987) for predicting the spray regime entrainment, E,. This step ensures no conflict between Ef and E, predictions. Either E, or Ef was assumed to be controlling and is used to predict entrainment. This requires testing against the current data bank, as well as a previous data bank (Kister et al., 1981a,b) consisting of spray regime data. Further, this approach requires verifying that E, was the controlling term for the bulk of the spray regime data
and Ef was the controlling term for the bulk of the froth regime data. 3. Some departures from the predictions were observed under conditions that appeared to coincide with the excessive tray weeping. The data in this region were correlated by a term E,. By use of the same approach as for Efand E,, entrainment now becomes the largest of Ef,E,, or E,. 4. The final expression developed above predicts entrainment without prior determination of the operating regime. Further, the correlation itself predicts which hydraulic condition (spray, froth, nonuniformity under weeping conditions) is primarily responsible for entrainment generation. Correlation Development. In order to apply eq 1, or a similar correlation, clear liquid height data are required. Such data are rarely available, but clear liquid heights can be successfully predicted from published correlations. Colwell’s correlation (1981) was shown to correlate published froth regime clear liquid height data with an average absolute error of 8% and to perform better than previous correlations. Since then, Bennett et al. (1983) proposed an alternative clear liquid height correlation which claims to reduce the above error further. We preferred Colwell’s (1981) correlation for this work, because of its demonstrated capability to predict experimentalfroth height data to within *8%. The correlation by Bennett et al. (1983) also contains a froth height calculation, but its reliability was not reported. Colwell’s correlation was also successfully applied by Lockett and Banik (1986) and Hsieh and McNulty (1986) to predict clear liquid heights for their weeping correlations, and recommended by Lockett (1986) for general use in the froth regime. The denominator in eq 1 (S - 2.5hJ is the effective tray spacing, i.e., the distance between the top of the froth envelope and the tray above. In the absence of an adequate froth height prediction method, Hunt et al. (1955) assumed a froth density of 0.4, hence the 2.5 coefficient of the h, term. Data surveyed and correlated by Colwell (1981) show that this assumption is oversimplified and that froth density is a function of the gas velocity, clear liquid height, fractional hole area, and gas and liquid densities. With such a reliable froth height correlation available, the assumption of constant froth density can no longer be justified, The effective tray spacing was therefore expressed as S - hf, with hf calculated from Colwell’s correlation (1981). Figure 11 indicates that, at low entrainment values, Hunt et al.’s (1955) correlation tends to underestimate entrainment, while the reverse occurs at a high entrainment value. This suggests that a lower exponent may be more appropriate in eq 1. A further improvement to the data fit was achieved by empirically adding a hole diameter dependence and a correction term, 1 + 5; to the equation. The modified equation thus obtained is 2
Ef = lll( L, S - hf dH0,5(l+ () The term 1 + {was added to correct entrainment predictions for nonuniformity of the froth. During entrainment experiments (Kister et al., 1981b), one of the authors visually observed the froth to be nonuniform at low gas velocities, low liquid flow rates, when the hole diameter was large, when the weir heights were zero or low, and when the fractional hole area was low. Gas appeared to be forming channels through a shallow liquid layer, and the height of the liquid appeared to be strongly dependent on the outlet weir height.
Ind. Eng. Chem. Res., Vol. 27, No. 12, 1988 2337 Work by Lockett et al. (1976),Muller and Prince (1972), Payne and Prince (1975),and Priestman and Brown (1981, 1985, 1987) is relevant for deriving an expression for f. Lockett et al. (1976) suggested that the above nonuniformity is caused by orifice jetting. Muller and Prince (1972) and Payne and Prince (1975) distinguished an “imperfect bubble” region at low gas velocities and shallow liquid depths. In the uniform froth regime, bubbles grow at the tray orifices and then detach themselves and travel to the froth surface. In the imperfect bubble region, the shallowness of the liquid level prohibits bubbles from growing to full size, and they break the liquid surface before detaching from the tray orifices. As hole gas velocity increases beyond about 15-20 m/s, the mechanism of vapor passage through liquid changes from imperfect bubbles to jetting. Priestman and Brown (1981, 1985, 1987) closely investigated the transition between imperfect bubbling and jetting and noted the formation of “pulsating jets” when hole gas velocity ranged between 10 and 15 m/s. In the transition region, liquid moves into the orifice and forms a sheet that protrudes across the orifice and tapers the gas passage area. This causes the gas to speed up through the shrinking opening. As it speeds up, it gains momentum that enables it to eventually entrain the protruding liquid sheet. The gas velocity then falls, the liquid begins to rebuild the sheet, and the cycle repeats. Comparison of predictions from our spray regime entrainment correlation (Kister et al., 1981a) to experimental data at low liquid rates generally indicated good agreement at hole velocities greater than about 15-20 m/s. A t lower gas hole velocities and low liquid rates, our spray regime correlation largely underestimates entrainment (Kister et al., 1981b). This supports the argument that a nonuniform froth, rather than a partially developed spray region, exists on the tray at these lower velocities. Imperfect bubbling and pulsating jets are likely to be the dominant entrainment-generation mechanisms in this nonuniform froth. Visual observations by one of the authors are also consistent with these suggestions. This supports allowing for the froth nonuniformity by introducing a correction term to the froth regime equation, rather than to the spray regime equation. Clear liquid height measurements by Lockett et al. (1976) have been particularly valuable in correlating 5: They observed uniform froth behavior when clear liquid height (h,) exceeded the clear liquid height which occurs at the froth-to-spray transition (h,,) even when the hole velocity was as low as 20% of the froth-to-spray transition velocity (Pinczewskiand Fell, 1972). At lower clear liquid heights, nonuniformity was observed. We utilized this observation for empirically deriving the following expression for -C
f = &0.00225 -l) hct
for hct’hc
for h,, Ih, (3) The clear liquid height at the froth-to-spray transition (hd) can be calculated from Jeronimo and Sawistowski’s (1973) correlation. This correlation predicts the transition clear liquid height data of Pinczewski and Fell (1972) with an average error of *8% and has been successfully used in our spray regime entrainment prediction correlation (Kister et al., 1981a; Kister and Haas, 1987). For the air-water system, this correlation is given by 0.4974Af4’791d~0.833 (4) hct = 1 + 0.013L4.59Af1.79 {=0
At very low gas velocities, high weirs, larger hole diameters, and larger fractional hole areas, some departures from the predictions of eq 2 take place. This appears to coincide with the onset of significant tray weeping. In this region, the following expression was found to give a good fit to entrainment data: 0.3d~p~ E, = (5) hc(S- W2 The pitch, p , can be calculated from the fractional hole area and the hole diameter. For an equilateral triangular hole pitch, p = 0.951d~/Ap~
(6) Lockett and Banik (1986) observed nonuniform froth behavior with high weirs and very low gas velocities under weeping conditions. It is likely that E, empirically accounts for this nonuniformity.
Discussion The present authors have previously (Kister et al., 1981a; Kister and Haas, 1987) presented a correlation for predicting entrainment in the spray regime. This correlation is E, = 4.742(10/~1/2)1.u (7) X( I O / U ~ ~ where
and hL = 1
996 + O.O0262h.(T) hct
0.5U-n)
(7b)
n = 0.00091dH/Af (74 The following equation is proposed here for predicting sieve tray entrainment for the air-water system at atmospheric pressure, under either froth or spray regime conditions: E = E, or Ef or E, (whichever is largest) (8) where Ef, E,, and E, are given by eq 2, 5, and 7, respectively. Equation 8 is based on the premise that the dominant entrainment generation mechanism accounts for all the entrainment from the tray. This is a simplification of the actual physical process, as a number of mechanisms may significantly contribute to entrainment under some hydraulic conditions. However, as the data fit testifies, this simplification provides an adequate approximation for estimating entrainment. Equation 8 can provide a criterion for identifying the dominant flow regime on the tray on the basis of entrainment. Accordingly, when E, is the largest term, spray regime orifice jetting is the dominant entrainment generation mechanism. When Ef or E, is dominant and f (eq 3) is small or zero, froth is the dominant entrainment generation mechanism. Where Ef is dominant and f is large, imperfect bubbling and pulsating jets are the dominant entrainment generation mechanisms. When E, is dominant, froth nonuniformity due to weeping is the dominant entrainment generation mechanism. Generally, E, is only important at very low vapor rates, when entrainment is of little practical concern, and can often be neglected. The criterion proposed above is in good agreement with our initial criterion, which was based on the location of the
2338 Ind. Eng. Chem. Res., Vol. 27, No. 12, 1988 PAR I TY :LINE
0 601 ~ L L UA T E D
EYT?AlNMEN'
kc
L
Cl
L QU'J
01 E N T R A I N E D / K G GAS
Figure 12. Comparison of froth regime entrainment data to predictions from eq 8 (E,or E, dominant); see Table I for legend
w a C 0 Y \
2
-
0,:
C
n c z Y
P
. + z 3 0
J
0 Y
0.01
n Y
.Y 3
Y
0,001
E
o.oai
0.01 0.: K G L I Q U I D ENTRAINED/KG
CALCULATED ENTRAlhMENT,
GAS
Figure 13. Comparison of data to eq 8 predictions, with E, dominant [diagram contains all data points with E. dominant which were not previously (Kister et al., 1981a,b) compared to predictions]; see Table I for legend.
minima in the entrainment versus liquid flow rate curves as per Porter and Jenkins (1979). Following correlation development, we reclassified our data bank according to the largest term in eq 8. This reclassification interchanged the venue of less than 10% of our data points, most of which were regarded as "borderline". Figure 12 compares entrainment data to predictions from eq 8 with Ef or E , dominant. Table I identifies the symbols and data sources. Compared to existing correlations (e.g., Figure 1l), the new correlation substantially improves the data fit. The plot includes several points that were measured in the semideveloped spray region by one of the authors and previously gave a poor fit to the spray regime correlation (Kister et al., l'981b). The agreement between the data and predictions is much better. Figure 13 shows data points that were either previously overlooked by the authors or considered previously to belong to the froth regime, and for which the E, term was dominant in eq 8. Symbols and data sources are defined in Table I. Again, the predictions fit the data well.
0.001 CALCULATED E N T R A I N M E N T ,
0.01 KG
LIQUID
0.: ENTRAINED/KG G A S
Figure 14. Comparison of data by Thomas and Ogboja (1978) and Hunt et a]. (1955) to predictions from eq 8; see Table I1 for legend.
Figure 14 compares predictions from eq 8 with the data of Thomas and Ogboja (1978). Table I1 identifies the symbols used in this diagram. These data were obtained using a high (76-mm) weir at close tray spacing (305-457 mm). The tray geometry was unique, with large hole diameters (25.4 mm) and with inlet and outlet calming zones occupying greater area than the bubbling zone. For a tray geometry so different from those used in deriving Colwell's (1981) froth height correlation, it is unlikely that Colwell's correlation will give accurate predictions. For this reason, froth heights were calculated by using a correlation specifically derived by Thomas and Ogboja (1978) for their tray. Points for which the froth height reached to within 80 mm of the entrainment collector were excluded from Figure 14; at smaller effective tray spacings (S - hf),our correlation is extremely sensitive to errors in froth height. Considering the unique features of that tray, the agreement between these data and our predictions in Figure 14 is remarkable. Figure 14 also compares correlation predictions with data by Hunt et al. (1955). These data were obtained in a laboratory-size(150-mm-diameter) column *withno liquid cross flow. Our equations for E, and f cannot be used for zero liquid cross flow, but for most of the data by Hunt et al., it is reasonable to assume that Ef dominated and {was zero. This is because Hunt et al. maintained a high clear liquid height on their trays by a constant head tank and because hole diameters on their trays were small; these conditions are conducive to "uniform froth" operation. Figure 14 shows that our correlation fits these data well. Figure 15 compares our correlation prediction with data by Lockett et al. (1976). The trends are similar, but there are significant deviations between predicted and measured values. Two reasons can explain the deviations. First, Lockett et al. (1976) inferred entrainment rates from a material balance on a tracer, based on the assumption that the tray is perfectly mixed. Kister et al. (1981b) pointed out that this assumption is not valid and that passage across the tray in many of Lockett et al.'s runs was more likely to be plug flow. Data obtained by Kister et al. (198lb) on a tray of similar geometry as that of Lockett et al. (1976) also showed similar trends but a much less sudden drop in entrainment. The second reason is that, for the tray geometry and operating conditions used by Lockett et al. (1976),entrainment is very sensitive to weir height. The sensitivity can be predicted from eq 3 and only
Ind. Eng. Chem. Res., Vol. 27, No. 12, 1988 2339 D,,
0,15
=
A,
=
HW
=
S
=
Table 111. Recommended Range of Application system air-water only, atmospheric pressure gas velocity 0.3-3.5 m/s liquid flow rate 2-130 m3/(h m) tray spacing 300-1000 mm 1.5-25 mm hole diameter fractional hole area 0.04-0.20 weir height 0-80 mm
6.4 M M \ 0.051 \ 0 MM \ 360 M M \
‘
\ \
. 4 VI
\ \
0 Y
a
\
-
Y
z
\
c
z
Y
e
.
3
correlation at tray spacings less than 300 mm. Note, however, that the data in Figure 16 fall on a line which parallels the parity line. A crude approximation of entrainment at tray spacing down to 225 mm can therefore be obtained by applying our correlation and multiplying the calculated value by [l + 0.008(300 - S ) ] .
\
4
\
0,lO
Y W
t r Y E
\
%
t
w z
0.05
\
\
z \
\ \ \
\ \
L I Q U I D FLOW R A T E , CU.M/H M
Figure 15. Comparison of data by Lockett et al. (1976) to predictions from eq 8. 1,(
. 4 VI
0 Y
a
z Y
4 c t Y z
e
-
3 J
w Y
0.1
F
z yl
z 4
A,
SYMBOL
t Ly z
HW
MM
n
0,096
0
c 3
0,096
25,4
0.096 0.122
25.4
c1 4
z w
O
