Liquid Capacity of Bubble Cap Plates A. J. GOOD, M. H. HUTCHINSON, AND W. C. ROUSSEAU E. B. Badger & Sons Company, Boston, Mass.
In large-diameter bubble cap towers, or even moderate-size towers carrying high liquid loads, the hydraulic gradient set up between upstream and downstream ends of a plate becomes an important factor in determining the maximum liquid load the plate can handle and still maintain uniform distribution of vapor over the plate. This gradient has been measured under varying conditions on an experimental plate, and data for one type of bubble cap are given as a function of liquid rate, vapor rate, liquid depth above slots, and certain structural characteristics. Charts can be constructed to enable quick checking of allowable liquid rates. HE amount of liquid which can be handled by a bubble plate is a function of the driving force and the resistance to flow across the plate. The resistance to liquid flow is created by the bubbling caps in its path, and the necessary head across the caps to overcome this resistance appears as’a kind of hydraulic gradient, called “liquid build-up” in this paper. Although reference to such a gradient or build-up has been made by Chillas and Weir (g), Carey (I), and others, little definite information concerning the variables which affect its magnitude has been published. Some time ago it was found that the available information on entrainment, pressure drop through caps, downpipe capacity, etc., ww not sufficient to permit the design of large towers or of smaller towers having high liquid loads. Studies on the operation of certain towers indicated low efficiencies which could be due only to highly irregular distribution of vapor and liquid cawed by build-up of liquid above that allowed for in the design calculations. I n order to obtain information on flow of liquid across plates and the factors affccting distribution of liquid and vapor, work was carried out on the various types of bubble caps and plates in commercial use by this company. Data are for 3-inch-diameter caps spaced with centers on 41/4-in~hequilateral triangles. This cap is used primarily for vacuum towers where it is desirable to keep pressure drop a t a minimum. Required liouid rates for this service are usuallv comp t k i v e l y low and, as might be exGected, liquid-carrying capacity for this type of cap is correspondingly low. This cap was chosen for initial presentation primarily be-
T
cause it has a relatively high build-up and the effect of variables is pronounced. Stable plate operation is shown in Figure 1. I n general, the difficulties which arise from excessive build-up and result in bad distribution of vapor and liquid are illustrated in Figures 2A and B and 3B. The build-up is such that some of the caps are not bubbling and others are badly overloaded with respect to vapor. I n a large tower the area of blankedoff or inactive caps may shift from side t o side; hence the term “unstable” has been applied to a plate on which some of the caps may be inactive. The degree of instability varies, depending upon relative vapor and liquid rates. The case shown in Figure 3B is quite severe, with four out of twelve rows blanked off. Figure 2B shows a less severe case with only‘one row blanked off. I n a severe case, such as that of Figure 3B, liquid may run down the chimneys of the upstream rows and thus by-pass the plate. This can be serious, especially if the tower is of the cross-flow type with liquid flowing from side to side in opposite directions on alternate plates. In this case liquid running through the chimneys may essentially by-pass two plates. While it is possible to have practically any unstable plate condition operate without liquid running down the chimneys by using caps having sufficient chimney overlap (Figure 4), it is impossible with the usual designs of caps to have liquid flow down the chimneys when a plate is stable. Thus, a design which will guarantee stability will automatically guarantee that liquid will not flow down the chimneys.
Experimental Procedure The construction of the experimental unit is illustrated by Figure 5. Two removable rectangular plate sections appro=mately 5 feet long and 2 feet wide were used for this ca ; one had chimneys 2 inches high, the other, 3l/2 inches hipi. Water, measured by an orifice, was pumped across the plate; air, measured by a Pitot tube or orifice and controlled by a damper on the suction of the blower, was blown into the space below the
FIGUREl. TYPICAL “STABLE” PLATE
---
Skirt clearance = 1 inch 1000 gal. per hr./ft. Liquid rate sa, 1 inoh U ( P P 0.81
1445
Vol. 34, No. 12
INDUSTRIAL AND ENGINEERING CHEMISTRY
1446
to error, especially when some value of flow per square foot is taken as a maximum. To illustrate the fallacy, let us use a maximum loading figure, as is often done, and apply it to 2- and 4-foot-diameter columns. The area of the latter would be four times the former, so the “allowable” flow would be assumed to be four times as great. A flow rate based on width or some average of diameter would be more nearly true since it would be directly proportional to the liquid velocity across the plate for constant depth. The plate width in these tests was uniform, but on a circular tower it is necessary to take an average. It is recommended that the arithmetic average of the width of the plate at the shortest and longest rows of caps be used with these charts. Hydraulic gradient or build-up may be defined as the driving force, in terms of hydrostatic head, which must exist in order to overcome the resistance to flow of liquid across a bubbling plate or part of plate. On the laboratory plate, upstream and downstream calming sections were made free enough from turbulence and aeration to provide direct measurement of build-up across the bubbling portion of the plate in terms of head of clear mater a t atmospheric temperature. Although the effect of vapor density on liquid build-up has not been determined in these investigations, all vapor rates are expressed as U ( ~ ) O . ~ , where p is the density and u is the linear velocity of the vapor passing through the superficial cross section; in the experimental apparatus the area of the FIGURE 3. EFFECT OF LIQUID RATE OF VAPORRATE FIGURE 2. EFFECT
Skirt clearance = 3/s inch Liquid rate = 1385 gal. per hr./ft. SW = 1 inch A . u(p)@.5 = 0.33 B. u ( p ) @ . 5 = 0.58
c.
u(p)0.5
* 0 91
plate. Up t o twelve rows of caps were used, each row suspended by trolley bars which were well above the plate to prevent interference with liquid flow. Adjustment of seal was made by a threaded pipe which served as part of the downpipe. Readings by means of gage glasses were taken of the liquid height at downstream and upstream ends of the plate, and build-up was taken as the difference in these readings. I t was important that the gage glass taps be well away from the agitated mass; otherwise, disturbance would result in incorrect readings. At first a perforated plate was used just beneath the bubble plate to guarantee that all air entered the plate from below in one direction, but it was soon demonstrated that the screen had no detectable effect and it was eliminated.
Variables Liquid rate is expressed as gallons per hour per linear foot of plate width normal to liquid flow. Often in the past liquid rate has been based on cross-sectional area instead of plate width. This method can lead
Skirt clearance
Sa.
= 3/8 inch = 1 inch 0.77 Liquid rate = 1000 gal. per hr./ft. Liquid rate = 3000 gal. per hr./ft.
1C(p)@.5
A.
B.
P
December, 1942
TABLE I. ORIQINAL DATAWITH MINIMUM SEALCOXSTANT AT Run No.
Skirt
ClearLnce,
1447
INDUSTRIAL AND ENGINEERING CHEMISTRY
Liquid Rate
Gal./Hr.)Ft.
83A
500
83B
1000
83C
1385
84A
500
84B
1000
84C
1385
84D
2365
84E
3365
94A
500
94B
1000
94c
1385
94D
2365
94E
3365
97A
500
97B
1000
97c
1385
97D
2365
97E
3365
?I?
t4P)O.S
0.36 0.66 0.98 1.26 0.34 0.67 0.90 1.27 0.35 0.73 1.08 1.32 0.35 0.61 0.95 1.12 0.35 0.56
0.97 1.23 0.37 0.67 1.06 1.20 0.35 0.64 0.96 1.2 0.35 0.60 1.02 1.20 0.36 0.63 0.95 1.38 0.36 0.58 0.91 1.25 0.43 0.89 1.3 0.40 0.80 1.27 0.39 0.80 1.20 0.37 0.80 1.25 0.36 0.91 0.96 1.19 0.38 0.82 1.24 0.36 0.85 1.24 0.36 0.87 1.30
Water 0.30 0.45 0.58 0.75 0.66 0.90 1.05 1.35 1.10 1.40 1.65 1.80 0.19 0.24 0.30 0.35 0.30 0.40 0.55 0.75 0.60 0.72 0.95 1.15 1.40 1.59 1.70 1.85 1.85 2.15 2.60 2.75 0.05 0.11 0.11 0.17 0.11 0.13 0.15 0.25 0.23 0.33 0.46 0.69 0.78 1.03 1.23 1.36 1.53 0.03 0.04 0.05 0.06 0.10 0.11 0.15 0.16 0.20 0.30 0.40 0.45 0.56 0.75 0.83 0.99
APt
No. of
Water
Bubbling 12 12 12 12 11 12 12 12 8 11 12 12 12 12 12 12 12 12 12 12 11 12 12 12 7 9 12 12 8’/n 7Vr 11 12 12 12 12 12 12 12 12 12 12 12 12 1 1I/: 12 12
In.
.. .
1.25 1.65 1.82 1.32 1.52 1.82 2.28 1.39 1.90 2.25 2.52 0.87 1.12 1.55 1.70 1.0 1.2 1.65 2.0 1.1 1.4 1.9 2.2
...
1.75 2.15 2.35 1.7 2.15 2.65 2.8 0.7 1.1 1.45 2.0 0.8 1.0 1.4 1.85 0.95 1.45 2.0 1.15 1.55 2.15 1.3 1.8 2.25 0.75 1.25 1.8 0.75 1.25 1.5 1.8 0.80 1.35 1.85 0.95 1.45 1.9 1.0
1.7
2.15
Row!
Number of rows, as used in the build-up chart or capacity chart, refers to the number of rows of caps which lie across the path of liquid flow. I n some eases of unusual types of flow this number can only be estimated. The term “liquid capacity’’ means the maximum volume rate of liquid flow a t which all upstream caps are active. If this rate is exceeded, caps become inactive as a result of too great liquid build-up. Skirt clearance is the distance between the bottom of the cap and the plate. This distance is measured in inches (Figure 4).
Results Beside liquid and vapor rates, the variables studied were seal and skirt clearance. Table I gives original laboratory data for a series of runs taken a t constant minimum seal. Skirt clearances of s/8, 1, l S / d and 2l/2 inches were studied. Vapor rates were varied between zero and U ( P ) O * ~ = 1.6, and liquid rates up to 3400 gallons per hour/foot were taken. Typical plots of build-up, Ah, against vapor rate, U ( ~ ) O . ~ , are shown in Figure 7. Numerals beside points indicate the number of rows out of twelve that are not bubbling. Figure 2 shows qualitatively the effect of an increase in vapor rate. A comparison of curves a t different seals indicates that Ah is less a t higher seals. This is especiallynoticeable a t the lower skirt clearances where the percentage change in pool depth is greatest for a small change in seal. Since minimum seal applies only to the downstream end of a plate because of build-up, some kind of average seal should be used in a correlation. A simple arithmetic average, SO” =
sm
+ Ah2-
8Vl
12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 11 12 12
cross section is taken as 9.25 square feet. This product is the simplified form of the term generally recommended for expressing maximum vapor load in a tower as determined by entrainment. It does not seem unreasonable to expect that vapor resistance to liquid flow should be a function of vapor “impact head”, which is proportional to u2p. Since all runs were made using air, conversion of this factor to velocity above for the data presented can be made by multiplying by l / ( p ) O e 5 or by 3.6. Seal is used here as the depth of liquid, in terms of clear liquid, above the top of the slots. Figure 6, which is an idealized sketch, helps to illustrate the concept of seal and the relation of build-up to it. On an actual plate, liquid is in such a state of turbulence and aeration that minimum seal, is tangible only by reference to the depth of cannot be clear liqbid a t the downpipe, and average seal, Sa,, visualized except by its mathematical definition.
s,,
FIGURE 4. BUBBLE CAPASSEMBLY
1448
INDUSTRIAL AND ENGINEERING CHEMISTRY
DATAWITH AVERAGE SEALCOXSTANT TABLE11. ORIGINAL Run NO.
Skirt Clearance, In.
lOOA
'/n
1OOB lOOD 1OlA l0lC lOlD 102A 102B 102c 103A 117A
1
118A
Liquid Av. Rate. Seal, Gal./Hr./ In. Ft. 2.0 1000
1/11
2.0
1385
"/a
2.0
2365
*/S
2.0 =/a
3365 500
1
=/a
1000
ll9A
1
1/1
1385
117C
1
2
500
118C
1
2
1000
1190
1
2
1385
12oc
1
2
1875
121c
1
2
2365
122c
1
2
3365
u ( P ) 0.5 0.33 0.68 1.31 0.34 0.90 1.23 0.92 1.20 1.50 1.52 0.32 0.92 1.52 0.31 0.91 1.52 0.30 0.91 1.53 0.31 0.92 1.53 0.30 0.93 1.52 0.29 0.92 1.52 0.28 0.93 1.52 0.28 0.92 1.52 0.28 0.92 1.62
Ahs In. Water
0.56 0.69 0.88 0.77 1.15 1.20 2.06 2.33 2.42 3.40 0.26 0.40 0.66 0.36 0.64 1.21 0.63 1.15 1.83 0.32 0.31 0.5 0.40 0.55 0.80 0.49 0.71 1.04 0.68 1.00 1.39 0.87 1.35 1.65 1.09 2.04 2.44
AP,
In. Water 2.1 2.3 2.7 2.2 2.4 2.7 2.7 2.95 3.1 3.65 1.04 1.66 2.29 0.96 1.60 2.40 1.10 1.68 2.46 2.32 2.72 3.25 2.20 2.69 3.28 2.34 2.76 8.30 2.29 2.74 3.33 2.30 2.76 3.35 1.93 2.65 3.20
No. of Rows Bubbling 8'/1
12 12 8 12 12
81/1
12 12
..
12 12 12 11 12 12 11 12 12 11 12 12 8 12 12
8
12 12
7 12 12 6 11 12 5 9 12
as illustrated by Figure 6, was found t o be a reasonably reliable expression of seal as it affects build-up, and another series of runs was made in which this average seal was kept constant as vapor rate was increased. Representative data for these average seal runs are given ir, Table 11. Some of these are shown by Figure 8. The constant seal curves of Ah os. U ( ~ ) O . ~are somewhat steeper than the corresponding curves for constant minimum seal. The effect of liquid rate on build-up is shown in Figure 9. This is a cross plot derived from plots of the original data by letting lines of constant vapor rate intersect the smoothed curves. Points enclosed in parentheses are for unstable regions. It is apparent that build-up is roughly proportional to liquid rate for rates up to about 1500 gallons per hour/foot. Above this rate the curves based on average seal swing upward, especially for lower seals. Fimre 3 shows qualitatively the
l'igure 11 is a condensea representation of all build-up data.
Vol. 34, No. 12
Data taken at constant minimum seals were interpolated for constant average seals, and the best straight lines drawn to represent Ah data up t o 1500 gallons per hour/foot. Intersection of lines by the 1000-gallon abscissa gives the ordinate 4 h l in Figure 11, an averaged build-up based on 1000 gallons per hour/foot and tnelve rows; the pronounced effect of skirt clearance on build-up is illustrated. By applying the proportionality shown below, this chart can be used for different numbers of rows and different liquid rates. For average seals of less than 1.5 inches, however, the curves give values of a h , which are too lorn if applied t o liquid rates greater than 1500 gallons per hour/foot. The factor 7.14/N is included in the abscissa to permit a correction to laboratory conditions of a plate on which N,the total number of caps divided by the area upon which u is based, differs from the value of 7.14 used for these measurements. The following equation may then be used t o estimate build-up from Figure 11,subject t o the limitations discussed earlier: (1)
Since average seal is a function of Ah, trial and error procedure is necessary a t the lower skirt clearances. Although a series of runs with soapy water has confirmed the applicability of this build-up data to liquids of different foaming properties, the effects of liquid specific gravities and of viscosity have not been established. It is suggested, however, that the curves be considered as representing for other liquids an approximation of build-up in terms of a given pressure unit-e. g., inches of water (provided average seal is taken in terms of the existing specific gravity). This figure in inches of water as computed by Equation 1 can be converted into inches of liquid flowing by dividing by its specific gravity.
Stability For any given liquid rate across a plate there is a definite vapor rate, all else being constant, below which the plate is unstable. At high liquid rates this critical vapor rate is higher than a t lorn liquid rates. As an approach to the relation between liquid and vapor rate, consider the simplified representation of a plate just barely stable, shown in Figure 6. Let one cap in the last row downstream be indicated by A and one cap in the first row upstream by B. The bubbling a t B is supposedly so slight that negligible vapor passes through, and therefore pressure drop of vapor, A P E , across the plate a t B is made up of hydrostatic head alone, the sum of some function of 8, and of 4 h . On the other hand, the total pressure drop across the plate a t A , A ~ Ais, made up
~~
FIGURE 5. LABOR.ATORY UNIT
’
December, 1942
C H E M ISTR Y I N D U S T R I A L A N D E N G IN E E R IN G,
marked difference in the proportion of vapor passing through each end of the plate.
LIQUID FLOW
{
Atl
sov
Capacity Charts
-.
i -L---J-
The foregoing section demonstrated how probable stability can be predicted for a definite set of conditions. It involves individual determination of Ah and Apo. It is convenient to have a chart which will permit a quick check of liquid carrying capacity in order that unstable arrangements
I
s,
’MINIMUM
SEAL
S,
:AVERAGE
SEAL
1449
OF PLATE IN OPERATION FIGURE 6. DIAGRAM
largely of vapor losses (contraction, expansion, and friction) as well as hydrostatic head, the latter composed of some function of S , and some function of slot opening. It is obvious that A ~ = B Apa. If it can be assumed that the effect of 8, is the same a t both A and B, then there should be a relation between Ah and the pressure drop a t A up to the , Ah is expressed in the same point of zero seal ( A p o ) ~when pressure unit as Apo, The present data give both Ah and Apo in inches of water. It would be difficult to determine (Ap0)n or to estimate the exact relation of vapor rate a t A to the over-all, or average vapor rate. However, pressure drop a t zero seal-i. e., with liquid level (in terms of clear liquid a t the down pipe) just equivalent to the top of the slots-has been measured over a wide range of vapor rates a t a liquid rate so low that Ah was negligible. A plot of these values, Apo, is shown in Figure 12. The data given here were taken a t 1-inch skirt clearance with chimneys 2 inches high, but these agree with corresponding data for other skirt clearances. No attempt was made to adjust vapor rate to the point of bare stability for each run, However, a rough check of the relation between Ah and Apo close to the critical state can be shown by Figure 13, in which Ah is plotted against Apo for the first recorded vapor rate after all rows have started bubbling. The values of Ap, are read from the curve of Figure 12 for a uniform plate, a t corresponding values of average vapor rate entering the plate, and can be expected to apply to the plate with build-up only a t the row where the actual vapor rate is equal to the average. In some cases the conditions are further from the critical than in others but a fair relationship exists, and a t values of Apo below 1 inch of water the best representation is the line of Ah = Apo. The conclusion can be drawn that a plate is stable provided Apo based on average vapor rate is greater than Ah, both Apo and Ah being expressed in the same pressure unit. Since a t higher values of Ape, most of the points fall above the line of Ah = Apo, it can be concluded that, as Ah increases, stability is possible even when Apo is less than Ah. An explanation of the upward trend of the points may be found by considering Figure 6 in connection with the foregoing analysis. Higher Ah means less uniform vapor distribution with a corresponding increase in the ratio ( A p o ) ~ / A p o . It is significant that the points are independent of skirt clearance but tend to be lower for the higher values of minimum seal. This latter fact means that the assumption of equal effects of S, a t the extreme ends of the plate is not strictly true. One point which must be stressed is that a plate is not always operating a t high efficiency simply because it is stable. The build-up might be of such magnitude that too great a proportion of the vapor is passing through the downstream rows, and excessive entrainment might occur there. Figure 2C shows a stable plate, and it is obvious that there is a
G.RH~FI:
;
,;
SKIR-- CLEARA MIN. S E A L CON
I -0 I
x
0
0
QP
0.4
0.6
0.8
LO
1.2
1.4
6
0.2
0.4
0.6
0.8
10 .
1.2
1.4
6
I
5
1
0
us. VAPORRATE.~AT FIGURIG 7. ORIQINALDATAFOR BUILD-UP CONSTANT MINIMUM S~AL
1450
11
INDUSTRIAL AND ENGINEERING CHEMISTRY x
-
I,
i
n
;'5 0'.
ah
(o,
,y,
1.0" sw. 2.0"Sa,
0.0
SKIRT CLEARANCE = AVERAGE SEALS CONSTANT
M
ah
U ( p P . 5 = 0.9
-----
3
2
e
Vol. 34, No. 12
I
I'
I
l
e '0
1490 0.2
0.4
a6 4 6
0.8
1.0
1.2
1.4
e f e3 0 0.8 0
P a
t?
0.6
c 0.4
0.2
0
2
10
12
NUMBER OF ROWS
FIGURE 8. ORIGINAL DATAFOR BUILD-UP us. VAPOR RATEAT CONSTANT AVERAGE SEAL
FIGURE9 (Above). EFFECT OF LIQUID RATE ON BUILD-UP FIGURE 10 (Below). EFFECTOF Rows ON BUILD-UP
can be eliminated quickly from further consideration. Such a chart is shown in Figure 14. The basis of this chart is the chart is demonstrated by Table 111. For a given vapor rate, straight line of Figure 13 and the premise that a plate is stable Ap0 is read from Figure 12. By the relation Ah = Apo, if Ah is not greater than Apo taken a t the corresponding value S,, can be computed by adding A p 0 / 2 t o 8,. Knowing S,,, of u(p)o.6 (7.14/N). The further assumption is made that it is possible to interpolate for Ah on Figure 14,and by the Apo and Ah are functions of the same expression of vapor rate. expressed in Equation 1, the product of rows , The Apo is represented fairly well by relating it to ~ ( p ) ~ . ~proportionality and liquid rate can be computed which will make Ah = Apo. especially a t the higher vapor rates where the major comIn using this capacity chart, it should be remembered that ponent is pressure drop through the chimney and dry parts the build-up chart on which it is based applies to liquid rates of the cap. At the lower vapor rates, pressure drop through under 1500 gallons per hour/foot and that erroneous conthe slots becomes a major component of Apo, and since slot clusions may result a t much higher liquid rates if the average pressure drop is a function of liquid specific gravity as well as seal is less than 1.5 inches. vapor velocity and density (S), the values based on air and EXAMPLE. An 8-foot-diameter tower is designed to absorb water used in the preparation of Figure 14 are not applicable ethyl alcohol from a dilute mixture of air and alcohol vapor, to all systems. using water as absorbing medium. Each plate is to have 350 The ordinate is proportional to what might be called a "capacity product"-i. e., the product of r o w times maximum liquid rate, The liquid rate below which all rows will be bubbling can easily be computed from the known values TABLE 111. SAMPLE CALCULATION OF A CAPACITY CHARTWITH SKIRTCLEARANCE AND S , OF 1 INCH of vapor rate (corrected for the number of caps per square foot), skirt clearance, and minimum seal. The more convenient minimum seal is used on the capacity chart, but in constructing the chart average seal is taken into considera0.42 12,600 0.44 1.22 0.30 0.47 14,000 0.55 1.28 0.46 tion. This is made possible by the stipulation that for the 0.51 16,700 0.71 1.36 0.60 condition of bare stability, Ah = Ap0 and thus S,, is fixed for 0.64 20,200 0.91 1.46 0.73 a given point. The procedure followed in making up the
1451
INDUSTRIAL AND ENGINEERING CHEMISTRY
December, 1942
caps with dimensions as shown in Figure 4. The caps are to be placed on 4l/rinch equilateral centere, providing staggered flow, and to have a skirt clearance of 1 inch. The following characteristics apply: Vapor rate, u(p)o*r Total liquid load, gal. per hr. Plate width at ahort row of caps, ft. Plate width at wide row of oaps, ft. Averane d a t e width. ft. .~ Minimum seal, in. ' Number of rows
Check the original assumption of Sao:
S,, = 1
+ 0.72'
1.39 instead of 1.5 inch
0.65 7000 6.5
a
7.25 1.0 19
7000 Actual liquid rate = - = 965 gal. per hr./ft. 7.25 N -
350
(8)* X 0.785
u(P)"5
=
6.95
( y ) 0.65 ( 7.147) 0.67 6 95 =
=
Capacity. From Figure 14 for skirt clearance = 1 inch, S, = 1 inch, and
U(~)OJ
(gal. per hr./ft.)(No. of rows) = 19 1000 allowable rate =
'Oo0 19 .
= 1000 gal. per hr./ft.
Since actual liquid rate is 965 gal. per hr./ft., the plate should be stable.
BuiZ&up. First assume Sa, = 1.5 inches. From Figure 11 for Sa. = 1.5 inches. skirt clearance = 1 inch, and u(p)Os6 .. = 0.67:
f$)
Ahi =
id
0.51 inch
Ah = 0.51
'0
(E)(") looo 12 = 0.78inch
a2
OA
as
FIGURE12 (Top).
QIL
1.0
LZ
14 .
1.6
IS
PRESSURE DROP AT ZEROSEAL
FIGURE13 (Center). BUILD-UPus. APO, FROM FIRST RUN AFTER ALLRows HAVEBECOME ACTIVE FIGURE11. BUILD-UP CHART,BASEDON TWELVE Rows 1000 GALLONS PER HOUR/FOOT
AND
CAPACITY CHART FIQURE 14 (Bottom). LIQUID
1452
INDUSTRIAL AND ENGINEERING CHEMISTRY
Assume S,, = 1.4 inch. From Figure 11 for Sa, = 1.4, 7 14 skirt clearance = 1 inch, and z ~ ( p ) " . ~ ( + ) = 0.67: Ahl = 0.52 inch Ah = 0.52
(go)(;) O.8Oinch =
0.80
Sa,= 1 + = 1.4inches 2 which checks the assumption. Therefore the build-up across the plate is 0.80 inch of water.
Conclusions I n order that liquid may flow across a bubble cap plate of the usual design, it is necessary that a hydrostatic head be set up between upstream and downstream ends of the plate. This differential of level can be so great that some upstream rows of caps are rendered inactive; all vapor is thus required to pass through the fewer caps which remain. Such an effect can lead to high pressure drop of vapor, bad entrainment, danger of flooding, and low efficiency. Hydraulic gradient, or build-up, is shown t o increase rapidly with liquid rate, expressed as volume per unit of time per unit of plate width. It is higher a t low skirt clearance and low seal, and increases with increasing vapor rate. For the caps discussed in the present paper, build-up is proportional to the number of rows normal to liquid flow and, therefore, increases with tower diameter. There is a definite relation between vapor rate and amount of liquid a plate can handle with all caps bubbling. If build-up is no greater than its equivalent in pressure drop up t o zero seal, it can be expected that all caps will be active. As Ap, exceeds one inch of water, the ratio Ah/Ap, can be greater than unity with safety. This criterion makes possible the prediction of plate stability if the separate values of Ah and of Apo (average for the plate) can be estimated. It can be concluded that plate design should involve keeping build-up at a minimum, and that when high liquid rates are to be handled on a large-diameter plate, caps should be a t a, sufficient height above the plate. Also if vapor rate is so low that Ap, is low, it may be advantageous to use fewer caps on wider spacing. This has the twofold advantage of reducing resistance to liquid flow as well as increasing a p ~ . The determination of stability should not be regarded as a substitute for other methods of establishing an optimum design. However, it is an important supplementary determination without which the usual calculations of pressure drop, entrainment, and plate spacing may have little value, since these usually assume a uniform plate. It is obvious that the use of the capacity chart alone could lead to serious overloading of a tower from the point of view of pressure drop, entrainment, and efficiency, since the provision for stability alone often permits extremely high liquid rates a t sufficiently high vapor rates. Even a stable plate can have such a high build-up a t higher vapor rates that distribution of vapor is poor enough to cause bad entrainment and poor conditions for vapor-liquid contact.
Acknowledgment The authors wish t o express their indebtedness to W. A. Peters, Jr., of E. B. Badger 8: Sons Company, for his suggestions during the progress of the work reported in this paper.
Nomenclature Ah = build-up or hydraulic gradient, in. of water N = number of caps per sq. ft,. of area upon which u is based
( N = 7.14 for exptl. plate)
Vol. 34, No. 12
A p = total pressure drop through plate, in. of water
pressure drop up t o zero seal or total pressure drop corrected for head of liquid above top of slots, based on average vapor rate through caps, in. of water S, = minimum seal, difference between level of clear liquid at downpipe and level of top of slots, in. A h / 2 in which Ah is exSa, = average seal, defined as S , pressed in inches of the liquid flowing, in. u = linear velocity of vapor based on superficial cross section of tower, ft./sec. p = density of vapor, lb./cu. ft. Apo =
+
Literature Cited (1) Carey, J . S., Chem. & M e t . Eng., 46, 314 (1939). ( 2 ) Chillas, R. B., a n d II'eir, H. M., Trans. Am. Inst. Chem. Engrs., 22, 79 (1929). (3) Rogers, M. and Thiele, E. IF'., IXD. ENG.CXEM., 2 6 , 5 2 4 (1934).
c.,
PRESENTED before the Division of Petroleum Chemistry at the 104th Meeting of the ERICAN AN CHEMICALSOCIETY. Buffalo, s.Y.
Effect of ALBERT LIGHTBODY AND D. H. DAWSON,
WHITE paint depends upon the white pigment in its composition not only for its whiteness but also for its opacity or obscuring power. The effect of the vehicle on hiding power has been generally disregarded, since the refractive indices of the suitable binder solids differ only slightly. The fact that dark colored vehicles give higher hiding has been noted (9),and the variation of hiding with brightness has been shown in several instances (2, 6, 8, 10). The fact that the hiding power of pigments is dependent upon their concentration in the binder has been pointed out by Sawyer ( I f l ) , Jacobsen and Reynolds ( 8 ) , and others ( 1 ) . It has been shown in this laboratory and has been recognized by others that enamels made with certain types of binders give greater hiding or greater coverage a t a given hiding level than with other vehicles. The factors that cause these differences between binders and their individual importance in influencing these hiding power variations are the subjects of this study.
A
Method The method employed for the determination of hiding power is an incomplete dry hiding method adapted from the photometric method of the National Bureau of Standards (3, 4). The paint films were laid down over black and white lacquered paper, carefully dried or baked, and photometered by the Hunter reflectometer (7); and a definite area of film was stripped from the paper and ashed. From the weight of ash, the composition of the paint, and the area stripped, the wet film thickness and spreading rate per gallon of paint can be calculated. The contrast ratio was determined from the Hunter readings over the black and white areas. Throughout this study the doctor blade method of laying down films was used. This method makes possible films which are quite uniform in thickness and also allows handling of paints too thick to be applied by brushing, spinning, or similar methods. These doctor blades had clearances varying by 0.002 inch from 0.002 to 0.012 inch.
