Ind. Eng. Chem. Process Des. Dev. 1981, 20, 298-307
298
methanol by eq 27 and then decompose by eq 31. 4.36C + 4.44H2O + 1.0302 = 2.14c02+ 2.22(CH2)+ 2.22H20 -79.5 kcal/mol (37)
Figure 9. Overall reaction stoichiometry in the production of 1octene by five processes. Points a, b, c, d, e refer to the five processes.
(c) Indirect liquefaction with CO-rich synthesis gas by blending the synthesis gases of eq 16 and 17 to obtain an H 2 / C 0 ratio of 0.5/1, and then react by eq 25 to form 2.29C + 0.6202 + 1.11HzO = 1.11(CH2)+ 1.18c02-49.77 kcal/mol (35) (d) Indirect liquefaction with the H2-rich synthesis gas of eq 17, and react as in eq 29 1.245C + 2H20 + 0.24502 = O.578CO2 + 0.667(CH2)+ 1.333H20 -17.8 kcal/mol (36) (e) Methanol route by blending the synthesis gases of eq 16 and 17 to obtain an H2/C0 ratio of 2; produce
The consumptions of raw material per mole of CH2 produced is given in Table 11. These reactions are also diagrammed in Figure 9. The idealized direct conversion consumes the least resources. In principle, direct liquefaction would be superior to gasification, provided that the kinetics is fast enough to complete the conversion. Among the gasification routes, the H2-rich gas from the Lurgi dry ash gasifier would consume less C and O2than the CO-rich gas from the slagger gasifier. However, the former consumes much more steam, generated at the rate of 10.0 kcal/mol, which has to be rejected at low temperature as liquid water. If the high-temperature heat needed for a mole of steam would have to come from combustion of 0.11 mol of C, then the overall efficiencies of process ( c ) and (d) become more nearly comparable. The methanol route lies between these two in efficiency. Literature Cited Anderson, R. 6. "Catalysis", Emmett, P. H., Ed.; Reinhold: New York, 1952; Vol. 6, p 99. Fumlch, G. "Fossil Energy Program Summary Document", Chapter 3, DOE/ ET-0087, U S . Department of Energy, 1979. Hottel, H. C.; Howard, J. 6. "New Energy Technology", Chapter 3, MIT Press: Cambridge, Mass., 1971. Kolbel, H. Chem. Ing. Tech. 1957, 29, 505. Stull, D. R.; Westrum, E. F.; Slnke, G. C. "Chemical Thermodynamics of Organic Compounds", Wiley: New York, 1969. Wei, J. Ind. Eng. Chem. Process Des. Dev. 1979, 18. 554.
Received for review February 22, 1980 Accepted October 31, 1980
Clear Liquid Height and Froth Density on Sieve Trays Charles J. Colwell Engineering Technology Department, Exxon Research and Engineering Company, Fbrham Park, New Jersey 07932
New correlations are presented that predict clear liquid height and froth density on sieve trays far more accurately than other literature methods. Such correlations are especially useful in calculating tray residence times, pressure drop, and efficiency. These new correlations are broadly applicable since they have a more fundamental basis and were derived from tray hydraulic data from diverse experimental units. The predicted clear liquid heights agree with the data within f7% of the average whereas the froth density agrees within f8%.
Scope The clear liquid height correlation consists of a semiempirical adaptation of the Francis weir formula, which is used here to relate froth height to the rate of froth flow across a tray. Since this equation requires uniform flow over the length of the outlet weir, experimental data were taken from rectangular trays in preference to circular trays to avoid weir constriction effects and irregular liquid flow patterns. In addition, runs expected to exist in the spray regime were screened out of the data sources prior to the development of the correlation. In spite of these restrictions, however, the new clear liquid height correlation is more fundamental and more widely applicable than other available literature correlations. Since application of the 0196-4305/81/1120-0298$01.25/0
Francis formula concept should fundamentally apply to the flow of froth and not clear liquid, the accompanying froth density correlation is needed to convert froth height to clear liquid height. The analysis shows significant froth density correlating parameters to be the Froude number and the hole to bubble area ratio. To apply the results, a rapidly converging trial-and-error calculation is proposed. Conclusions and Significance Clear liquid height prediction methods available in the literature for sieve trays consist of variations of the classical Francis weir equation or of strictly empirical correlations. None are highly accurate, and some authors even doubt the validity of the Francis weir equation as applied to trays. The cause for concern is quite apparent since the con@ 1981 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 2, 1981 299
tacting of vapor and liquid is often a violent, nonuniform two-phase mixture with nonuniform flow patterns. This work shows that a simple form of the Francis weir equation can be applied and does provide accurate predictions for rectangular trays operating in the froth regime. The following model assumes the Francis weir equation applied to the flow of froth on a tray and that the froth density is uniform. (1)
To predict clear liquid height, the above equation must be used in conjunction with a compatible froth density correlation, provided in the following two expressions. i
where
(
q = 12.6F,O4 i B ) 4 ' 2 5
(3)
The use of eq 1 for round towers requires a correction to account for weir constriction effects, which are most important in smaller towers. A limited amount of data from a 1.22 m diameter tower suggests, however, that this equation provides reasonable approximations for larger, commercial size sieve trays. The clear liquid height results are also extended to two special tray design situations. These include trays containing a calming zone or blanking before the weir and trays with splash baffles. Background Many distillation tray design parameters are directly or indirectly dependent on clear liquid height and froth density. Their proper use requires accurate prediction methods to relate these two quantities to tray geometric details and operating conditions. Several examples where clear liquid height and froth density are commonly used in tray design include predicting pressure drop, downcomer filling, gas and liquid residence times, and mass transfer efficiency, both in fundamental expressions for gas and liquid phase transfer units as well as the crossflow mixing effect. Clear Liquid Height. The Francis weir formula has for many years formed the basis of clear liquid height determinations. The following expression given by Bolles (1963) applied to the flow of unaerated liquid and is used for bubble cap trays. h, = h,,
+ 6.65(
5)
213
(4)
On sieve trays, however, it is more correct to consider liquid flowing over the weir as a froth rather than a clear liquid, and thus the above equation does not apply directly. Furthermore, the equation lacks a vapor rate dependency which is prevalent on sieve trays. The earliest attempt to include a vapor rate dependency was made by Hutchinson et al. (1949) via the aeration factor model. This approach applied a corrector to eq 4, known as the aeration factor, p. This factor decreases as vapor rate increases. Values for the aeration factor can be found in the work of Fair (1963). Other, more empirical, clear liquid height correlations unrelated to the Francis weir formula can be found in the literature [Gerster as referenced in Fair (1963), Sterbacek (1967), Rane and Pavlov (1968), Brambilla et al. (1969),
Thomas and Campbell (19671, and Hofhuis and Zuiderweg (1979)]. The accuracy of several of these correlations was investigated and is reported in a later section. Froth Density. Early significant work on correlating froth density includes the work of Crozier (1956) on bubble cap trays for which the F factor, FB, was the primary correlating parameter. The aeration factor mentioned previously is also an indirect measure of froth density. Studies of a more fundamental nature over the past 20 years have developed froth density characteristics on the basis of minimizing the dissipation of energy over the volume of froth [Azbel(1963), Kawagoe et al. (1976),Kim (1966), Takahashi et al. (1973), and Unno and Inoue (1976)l. These studies show various forms of the Froude number as the significant correlating parameter. Recently, Hofhuis and Zuiderweg (1979) experimentally show froth density measurements as separated into the free bubbling, froth, and spray regimes. Results in the froth regime from the air/water system agree reasonably well with the present work.
Assumptions and Limitations Assumptions inherent in the direct use of the Francis weir formula include uniform flow per unit of weir length, no obstruction to the free flow of froth over the weir, a uniform froth existing as a continuous layer adjacent to the tray deck, and the retention of these froth characteristics as the fluid flows over the weir. Thus, as this work shows, the Francis weir formula can be applied very accurately to clear liquid height data from rectangular trays operating in the froth regime. Data from round towers and from trays with abnormal features, such as splash baffles and calming zones, were avoided in the clear liquid height correlation development. These are treated as special cases in a later section. Data from round towers and trays with splash baffles were used, however, to correlate froth density. The use of round tower data presents two problems regarding clear liquid height. First, the flow over the weir is nonuniform, as documented by Bell (1972). Second, some degree of weir constriction or downcomer entrance limitation will always exist. Recently, Lockett and Gharani (1979) showed that, even on rectangular trays, very small downcomer widths restrict flow and thereby increase clear liquid height. By analogy, a significant restriction is likely to exist on small, round towers. As tower diameter increases, some restriction will always remain in the vicinity of the two ends of the chordal downcomer segment. The impact of this effect, however, would be expected to diminish in larger, commercial size towers. A round tower correction factor developed by Bolles (1946) for bubble cap trays is available in the literature. Its applicability to sieve trays has not been verified, however. Differences in round vs. rectangular sieve trays have also been noted by Thomas and Ogboja (1978) and Rane and Pavlov (1968). A comparison is made with a limited amount of round tower data as part of the results of this study. As vapor velocity on a sieve tray increases from a very low value, the vapor/liquid mixture passes from a liquid continuous free bubbling regime into the froth regime and then into the liquid discontinuous spray regime. The free bubbling regime is seldom encountered in normal sieve tray operation. The transition between the froth and spray regimes, however, has an important practical impact on several areas of tray performance and design. Identifying the nature of these regimes as well as defining where the transition occurs is currently an active area of research. At the present time, available transition criteria in the
300
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 2, 1981
literature are highly inconsistent. In this study, the spray regime was avoided for correlating purposes because of the presence of nonuniform froth densities. Additional concerns centered on the spray regime are first, the validity of measured clear liquid heights and second, the fundamental applicability of the Francis weir concept when the bulk of the liquid phase is discontinuous. In spite of these concerns, existing clear liquid height correlations are nevertheless often applied in commercial tower design in the spray regime. Thus, the new clear liquid height correlation is still recommended for use in the spray regime. Experience shows, for example, that satisfactory results are obtained when using these clear liquid heights in estimating tray pressure drops and downcomer fillings in the spray regime. A designer should nevertheless be aware of potential risks when applying these results or any other available correlations in the spray regime. Data Used in Correlation Development and Testing The data sources used are summarized in Tables I and 11. Runs operating in the spray regime were screened out from the data employed to develop correlations according to the froth/spray transition criteria of Porter and Wong (1969). To correlate clear liquid height, only rectangular tray data without splash baffles, calming zones, or screens over the weir were used. These additional types of data were used, however, to test the clear liquid height correlation, including new simulator data presented in this paper. In the references used for experimental froth densities, both clear liquid heights and froth heights were measured experimentally. Froth heights were measured visually except in one reference which employed a gamma ray technique [Bernard and Sargent (1966)l. Only directly measured clear liquid heights were accepted in both the froth density and clear liquid height data. This includes measurements by manometer, bubbler, or blocking and draining. Clear liquid heights obtained indirectly by subtracting dry tray pressure drop from total tray pressure drop are considered to be approximate, but not definitive, and were thus not used. This is due to the fact that hole irregularities (punch direction, smoothness of holes, tolerances, etc.) may significantly affect the dry tray pressure drop. One exception was made in the work of Rush and Stirba (1957). However, these data were used only for testing purposes. For this reference, the dry tray pressure drop recommended by McAllister et al. (1958)was used to obtain experimental clear liquid heights. Momentum heads calculated by the following equation as given by Thomas and Campbell (1967) were added to manometer and bubbler measurements unless the reference stated this had already been done. h M = 1000:
q&
- 1)
0
13
5
s
E
i
.-
E,
B E
B E
N
N
@?
@?
ri
ri
2 2
*N
K : *
M. t-
0
42
x
I
d/
m
E
5
(5)
In references that reported froth density directly (rather than clear liquid height and/or froth height), clear liquid heights were corrected for the momentum head and froth densities then re-evaluated. Correlation Development Clear Liquid Height. Under the assumptions stated previously, the fundamental form of the Francis weir equation may be written as
i
m
0
$3
0 X
E a 0
0
m
2
t-
m
0
42
?
0
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 2, 1981 301 94-
70
E L
Line
J 40
* rl rl
o
3ot
N
2 g z
o
Fosr and Gerrter 1 1 9 5 6 )
6
Gilbert (19591
50
60
10
Biambilla el.a1.(19691
00-
9
‘ 0
0
w-
10
20
40
30
70
80
90
hc, MEASURED, mm
03
w a
ari
rl
In 0
riww
orl
orlo
0
00
0
000
0 0
Figure 1. Parity plot. Data used to develop clear liquid height correlation;rectangular trays.
E E E
E
Inherent in this expression is the following relationship between clear liquid height, froth height, and froth density.
0
c-0
m
*o*
w
J,=-
hC
(7) hF The factor Cd is the “weir coefficient”, which is discussed in hydrodynamics texts, for example Daily and Harleman (1966). This reference provides the following approximation for c d . how
Cd = 0.61 + 0.08 -;
how
- I8.135
hwo
hwo
2)
1.5
Cd
= 1.06( 1 +
;
how
- > 8.135 hwo
(8a) (8b)
where (9) = hF - hWQ f is a dimensional constant which can be fundamentally derived. In the correlation work presented here, however, the basic form of eq 6 was preserved, and the value o f f was forced empirically to give the best fit to the data. An average value off was determined to be 7.3, and thus the new proposed clear liquid height correlation becomes hQW
s se
9
d +n i .> :
e f
2 c
a
Y
The value of J, used to determine experimental values of f were calculated from the froth density correlation as discussed in a subsequent section. For reference purposes, Table 111compares the accuracy of several clear liquid height correlations cited in the literature. Figure 1compares predicted vs. actual clear liquid heighb from the data used to develop eq 1. The agreement is demonstrated to be quite good, with an average accuracy of i 7 9%. Predicted clear liquid heights are also compared to several seta of data which were not used in the correlation development. The purpose of these comparisons is to demonstrate applicability in nonideal situations and to determine the magnitude of errors which may be en-
Ind. Eng. Chem. Process Des. Dev., Vol. 20,No. 2, 1981
302
6U
1
1
1
,
1
1
,
1
1
1
1
,
1
1
50 E
40-
Zu
I-'
-
-0
w
30-
E P
-
a
20-
Y
u
_1
-
oataAt3.6dm3/r.m
0
10-
-Calculated
,h,
-
OataAt7.3dm3/s.m
0
-
BY Equatlon 1
MEASURED, mm
Figure 2. Parity plot. Clear liquid height; rectangular tower with screen over weir; data of Harada (1964).
t 70
v
z
401
30
1
,
1-
I
20
lo -
0
10-
0
14
-
-
D
22
-
7.2
-
Calculated BY Eq. 1
I
20
1-
/
i 0
10
20
30 h,
40
50
60
70
80
MEASURED, m l l
i
Figure 3. Parity plot. Clear liquid height; round tower, 0.305 m diameter; data of Harris and Roper (1962).
countered. These results are summarized in the following discussion. Figure 2 compares predicted values with the data of Harada (1964), for which the test rig incorporated a rectangular test tray with a screen placed over the weir. The effect of the screen was to add some additional resistance to liquid flow and thereby increase the clear liquid height. Thus, the experimental values are underpredicted on the average. Nevertheless, the average accuracy of these predictions is f15%, and the use of eq 1 would have provided an acceptable first approximation to these data. The next comparison (Figure 3) shows that clear liquid heights are highly underpredicted for a small, round tower of 0.305 m diameter. This result is expected since weir constriction effects are a dominant factor in small towers. Thus, large errors can be anticipated in predicted clear liquid heights for such cases. Figures 4,5, and 6 show clear liquid heights in two larger, 1.22 m diameter round tower simulators, which approximate commercial size. Figure 4 presents the results of Nutter (1971) a t liquid loadings of 3.6 and 7.3 dm3/s.m. The data at 3.6 dm3/s.m are uniformly underpredicted while clear liquid heights at the higher rate are well pre-
60
+. 5 0 1 t? zc
40
0
Data At 3 . 5 dn?/s.m
b
Oata A t 24 dm3/r.m
- Calculated BY EQ. 1 u
1 VAPOR V E L O C I T Y , VB,
2
3
nVr
Figure 6. Clear liquid height. Round tower, 1.22 mm diameter; air/Isopar-M system; this work.
dided. A greater difference between measured clear liquid heights at these two liquid rates would be expected. The measurements at 3.6 dm3/s.m are therefore believed to be abnormally high. The reason for this discrepancy is not understood; nevertheless, the average accuracy of f12.6%
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 2, 1981 303 Table 111. Comparison of Various Correlations with Data Used to Develop Clear Liquid Height and Froth Density Correlations reference unaerated Francis weir model aeration factor model Hutchinson as referenced in Fair (1963) Gerster as referenced in Fair (1963) Hofhuis and Zuiderweg (1979) this work
equation A. eq 4 (used for bubble cap trays) h, = h,, + 6.65(Q~/Z,)”’ h,= p[h,, t 6.65(QL/Zo)z’3] h,= 6.1 t 0.725hW,- 0.24h,,FB
av abs error, %a,b 97 32
+
1.23(QL/I,)
h , = 600fp1’4(h,,/1000)1’z~/1000)1~4 eq 1 h, = $hwo t 7.3($1‘2Q~/Cd~o)z‘3
37 16 7
B.
Crozier (1956) Azbel (1963) Takahashi (1973) Kawagoe (197 6 )
In $ = - 0 . 5 8 6 F ~+ 0.45 (used for bubble cap trays) q = (Fr‘)ll2 q = [(86/5)(Fr’)]1/2 q = 1.6(Fr’)”’ + 0.22Fr’
17 42 47 15
Kim (1966)
R = 1 + (Fr‘/6) +
23
Hofhuis and Zuiderweg (1979) this work
2
2
q = (R(Fr’/2))lf3 q = 10.6Fr0.z’ q = 1 2 . 6 ~ r 0 . 4 ( A , / A ~ ) - 0 .(eq z5
11
3)
8
*
( l / N ) z ~Ih,, ( pr& - h , measl/hc, m w ) , where N = no. of data points. ( l / N ) z ~I$prd ( data points. This equation fltted to the results in the work of Hofhuis and Zuiderweg (1979).
on Figure 4 is considered good. Additional round tower data from Exxon Research and Engineering Company show reasonably good agreement for four liquid loadings on the air/water system (Figure 5 ) and for two liquid rates for the air/Isopar-M system (Figure 6). Geometric details of the trays used in these teats and operating conditions are given in Table IV. The prediction accuracy of the combined data (Figures 5 and 6) is &8% on average. These data together with Figure 4 suggest that reasonable first approximations can be obtained from eq 1on commercial sized towers. Additional study is needed, however, to confiim this result over wider ranges of operating conditions and tray design parameters than the data presented here. Froth Density. The froth density correlation presented below follows the theoretical format presented by several references, notably Azbel (19631, Kawagoe et al. (1976), Kim (1966), and Takahashi et al. (1973). These authors showed, first, that the Froude number is a theoretically significant independent variable. In these references, Froude number is defined as follows.
Fr’ =
VB2
Second, the theoretically derived froth density expressions take the following general format. $=- 1 ?+1 where 9 = f(Fr? (11) The functionality of f(Fr? varies among the various authors mentioned above (Table IIIB).
where N = no. of
Table IV. Tray Geometric Details and Average Operating Conditions. Exxon Research and Engineering Company Clear Liquid Height Data tower diameter 1.22 m tray spacing 610 mm hole diameter 1 3 mm bubble area 0.868 mz ratio hole to bubble area 0.094 downcomer segmental chord height 229 mm weir height 5 1 mm weir length 0.95 m tray thickness 3.2 mm pressure 104 kPa liquid temperature 22 “ C (water runs) 34 “C (ISOPX-M runs) vapor density 1.15 kg/m3 liquid density 1000 kg/m3 (water runs) 763 kg/m3 (Isopar-M runs)
The importance of eq 2 is primarily a matter of mathematical convenience in that ? can be more easily set up for linear regression analysis than if $ were regressed directly. Thus, for a given system and tray design, a plot of In 9 vs. In Fr’ will generally form a straight line. The present analysis was therefore reduced to an empirical regression of q. The present work adopts a more useful definition of Froude number, ,which includes vapor and liquid density factors.
Expressed in this manner and put into the context of a
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 2, 1981
304
10 8 7 b
0.6
5
4
:I+ -
1 ,L
0.5 2
I1 F
Y
/ ,
.*e
a -
P-
u
n.
1 08
&z
m i d and Sarwnt 1 1 9 6 6 )
0.4-
0.3-
1
E 0
002
004
006
01
02
04
-
Tr
06 .08
/'-
0.2 -
Fr lAdAB1-o 6 2 5
.
-J
Figure 7. Froth density correlation.
.
Data References
distillation tray, the Froude number expresses a measure of the ratio of kinetic energy of the vapor to the potential energy of the liquid holdup. Thus, any directional change which increases this value would be expected to create a less dense dispersion on a tray. A threefold range in vapor density in the froth density data used justifies including the density factors in the Froude number. In addition to the Froude number, the analysis shows another significant parameter affecting I] to be the hole to bubble area ratio, A,/AB. Additional slight dependencies on hole diameter and weir height were detected statistically; however, these were deleted from the final analysis since they offered no significant improvement to the correlation's accuracy. Equation 3 expresses the final form of the froth density correlation. 1
A
4 '
0 .! 1
'
0.2 !
!
'
0.3
1 I
!
0.4
)
l
I
0.5
!
0.b
FROTH D E N S I T Y , M E A S U R E 0
Figure 8. Parity plot. Froth density; data used to test correlation. 100 90
80
70
