n
n
Performance
tative and quantitative behavior of such phenomena, the present investigation has been carried out experimentally in a 12-inch i. d. column equipped with a 12 X 24-inch visible glass section.
of
Apparatus and Procedure The laboratory column with its auxiliary parts is shown in Figure 1. With the exception of the visible glass section a t the top of the tower, the apparatus is essentially the same assembly used in previous work in these laboratories ( 1 , 3 ) . A detailed sketch of the glass section with its auxiliary parts and supporting flange is shown in Figure 2. Table I includes the tower and plate dimensions, and Table I1 gives the physical properties of the liquids used. A rotary pump circulated liquid from the base of the column over the top of the visible section. The air supply entered the tower about three feet from the base. The temperature of the circulating liquid was controlled manually within * 2" F. by means of a steam coil located in the kettle a t the base of the column. The higher froth heights could readily be observed with the increase in air velocities.
Bubble-Plate Columns Froth Heights and Pressure Differentials
Original data have been obtained on froth heights and pressure differentials in a bubble-plate column, by observing the performance of air-kerosene and aiplubricating oil systems in a visible glass section (12 inches i. d. x 24 inches). The pressure drop through the bubble plate seems to be influenced largely by the head of fluid (probably a mixture of liquid and vapor) which is required to pass the liquid into the downspout. The experimental results may be explained qualitatively if it be postulated that the downspout operates under three distinct conditions of fluid head. These are: (1) at low heads, operating as a weir; (2) at intermediate heads, operating as a free-running orifice taking a froth mixture of liquid and vapor, but with sufficient vortex area to allow free separation of the vapor from the liquid; and (3) at high heads, operating as an orifice running full and with capacity diminished by disengagement of vapor from the froth mixture within the orifice.
MOTT SOUDERS, Jr., Yale University, New Haven, Conn., R. L. HUNTINGTON, H. G. CORNEIL,l AND F. L. EMERT,* University of Oklahoma, Norman, Okla.
T
HE capacity of a fractionating column may be limited by the maximum quantity of liquid that can be passed
downward or by the maximum quantity of vapor that can be passed upward, per unit time, without upsetting the normal functioning of the column. These maximum quantities of liquid and vapor are not usually definitely fixed by mechanical design and the properties of the fluids flowing in the column, but are mutually interdependent qualities. That is, a change in liquid throughput affects the maximum vapor throughput, and a change in the vapor throughput affects the maximum liquid throughput. Designers of bubble-plate absorbers and fractionators recognize that the capacity of a column may be overtaxed as a result of one or more of three separate effects: 1. Entrainment or the mechanical carrying of liquid droplets from one tray to another due to inadequate tray spacing or t o
excessive vapor velocities. 2. Priming or the building up of a pressure differentialthrough the bubble caps greater than the equivalent head of liquid between plates. 3. Flooding or the overtaxing of the liquid capacity of a downspout or weir due t o excessive liquid overflow.
Results have been published recently (1-6) on entrainment, especially in its relation to mass velocity, tray spacing, and the reduction of plate efficiency. Little data are available, however, in the literature on the interaction of liquid and vapor in the column on the nature of the fluids (froths and foams) which are formed above the trays, and the pressure differentials existing between adjacent bubble plates. I n order to gain a better insight into the quali1 2
The effect of temperature on froth height is shown in Figure 3 both for kerosene-air and a light lubricating oil-air system. The oil has a much greater tendency to form froth than the kerosene. Figure 4 shows that the froth causes a greater pressure differential between adjacent plates, as evidenced by the greater resistance to flow set up by the lubricating oil with increasing temperatures. Table I11 gives the data from which Figures 3 and 4 were made.
Present address, Humble Oil end Refining Company, Bayton. Texas. Present address, Phillips Petroleum Company, Borger, Texas.
86
JANUARY, 1938
INDUSTRIAL -4ND ENGINEERING CHEMISTRY
TABLE 111. ORIGINALDATAON LIGHTLUBEOIL ASD KEROSENE
A N D PLATE DIMENSIOSS TABLE 1. TOWER
12.5 2
Inner diameter of tower, in. Number of chimneys in plate Chimney (round in shape): Inner diameter, in. Outer diameter, in. Height from bottom of plate, in. Ratio. cross-sectional area of chimnevs to that of tower
2 2.375 2.25 0.051 2 3 625 X 3 625 4 0 X 4.0 32 1 0 0 1875 12 0 0 0975
tal area of tower
2.0 2.375 26.0 2.0 2.0 1.0
External diameter, in. Length in Height'of downspout above bottom of plate, in. Height of liquid seal above bottom, in. Height from top of slots to top of downspout, in.
87
Air Mass Velocity, 302 Lb./Hr./ Sq. Ft.; Liquid Rate, 10 Gal./ Min.; Barometer, 14.3; Air Temp., 78.5' F. Froth Pressure height drop Run Liquid on through No. temp. plate plate F. In. In. of oil 6 3.45 284 79 285 96 9 4.75 9 4.70 286 104 287 116 10 5.15 288 128 11 5.50 289 143 13 5.75 291 167 17 7.50 292 179 20 8.40 293 195 23 8.40 294 199 9.00
Liquid Rate, 7.9 Gal./.Min.; Air Mass Velocity, 402 Lb./Hr./ Sq. Ft.; Barometer, 14.3; Air Temp., 68.5' F. Froth Differential height pressure Run Liquid on through No. temp. plate plate F In. In. of keroeene 253 70 14 5.7 254 80 14 5.7 255 90 14 5.7 256 100 14 5.7 257 110 14 5.7 258 120 14 5.7 259 130 14 5.7
..
TABLE11. PHYSICAL PROPERTIES OF LICKrIDS Water : Viscosity, centipoises Surface tension, dynes/cm. Kerosene: Specific gravity Viscosity centipoises Surface tknsion, dynes/cm. Texaco light lubricating oil: Specific gravity Viscosity, centipoises Surface tension, dynes/cm.
80" F.
100'F.
120' F.
0.85 71.8
0.68
70.2
0.56 68.2
0.817 1.8 30.8
0.809 1.7 29.6
0.802 1.6 28.4
0.884 30.7 32.4
0.877 17.7 31.5
0.870 12.1 30.8
Kerosene-Air System At 5 gallons per minute of liquid, the differential pressure increases with the vapor velocity in proportion to the increase in the vapor friction loss (Figure 5 and Table IV). At 9 gallons per minute of liquid, the differential pressure increases with the vapor velocity to a greater extent than does the vapor friction loss (Figure 5 and Table V),
SEc T I o N MANOMETERS
FIGURE 1.
DI.4GRAM O F LABoR.4TORY C O L U M N
''A'--A
LAYOUT AT BASE FIGURE 2. BUBBLE-TRAY OF
GLASSSECTION
At 9 gallons per minute of liquid, the froth height increases with the vapor velocity according to two separate functions, one function for vapor velocities below 320-360 pounds per square foot per hour and the other function for yelocities above this velocity (Figure 6). The curves for differential pressure (Figure 5 ) similarly indicate two functions and a critical v e locity. At 5 gallons per minute of liquid, no such critical velocity is observed (Figure 6). With a constant vapor velocity, both froth height and differential pressure increase more rapidly as the liquid rate increases until a liquid rate of about 8 gallons per minute is reached (Figures 7 and 8). These experimental observations seem to show that the pressure drop through the bubble plate is influenced largely by the head of fluid (probably a mixture of liquid and vapor) required to pass the liquid into the downspout. This fluid head appears to be a function of both vapor and liquid throughput.
88
INDUSTRIAL AND ENGINEERING CHEMISTRY
*
d 4
d0
d,
l!Z
I
I28
0
1 4!
VOL. 30, NO. 1
KERO5ENE
LUBE
LIGHT
160
TEMPERATURE - *L
176
OIL
192
Zd8
FIGURE3. EFFECTOF TEMPERATURE o s FROTHHEIGHT
I 0
I 80
I
I
I
I
160
240
320
400
A
I 480
560
L40
~
720
T
FIGCRE5. EFFECTOF AIR VELOCITYO N PRESSERE DROP THROUGH PLATE the liquid; and (3) a t high heads, operating as an orifice running full and with capacity diminished by disengagement of vapor from the froth mixture within the orifice. On this basis the standard (Francis) weir equation should be applicable a t low heads, with this particular column up to about 5 gallons per minute liquid throughput. For a circular weir of 2.0-inch diameter, the discharge formula is, Q where Q
HL
18.9H~312
= liquid, gal./min. = head, in inches of
(1)
liquid over weir (HL < D / 4 )
For intermediate fluid heads, the equation for a free-running orifice of 2-inch diameter and with a discharge coefficient of 0.5 should apply: Q = 11.3H~$/~
n-here Q = froth mixture, gal./min. HF = head, in inches of froth over orifice ( 3 D / 2 D/2
L '64
80
96
112
128
id4
-=
:60
TEMP€RATURE
176
142
Zb8
FIGURE4. EFFECTOF TEMPERATURE ox PRESSURE DROP THROUGH PLATE
Performance of Downspout The experimental results may be explained qualitatively if
it be postulated that the downspout operates under three distinct conditions of fluid head : (1) a t low heads, operating as a weir; (2) at intermediate heads, operating as a free-running orifice taking a froth mixture of liquid and vapor, but with sufficient vortex area to allow free separation of the vapor from
(2)
> HF >
For high fluid heads, the same orifice equation should apply with the insertion of a constant factor to provide for the diminished discharge caused by separation of vapor within the orifice. At some critical point the vortex of the orifice thus becomes too small for the free separation of vapor, and the orifice becomes choked with vapor so that a much higher fluid head is required. This mechanism appears to account for the curve> of Figures 7 and 8. To compare the experimental data with the three postulated conditions of downspout operation requires the estimation of the friction loss from the vapor flowing through the bubble caps and the density of the fluid head over the downspout. The frictional resistance of the vapor flowing through the caps is estimated by the equation: Hj = 0.533 u.'dv/dL
(3)
JANUARY, 1938
'
INDUSTRIAL AND ENGINEERING CHEMISTRY
A I R MA55 V E L O C I T Y
-
89
L05/HB/SQ,FT
OF AIR VELOCITYON FROTH HEIGHT FIGURE6. EFFECT
LlQUiD
RATE
- G
PM
FIGURE 8. EFFECTOF LIQUID RATEON PRESSURE DROPTHROCGH PLATE (Constant mass velocity of air, 502 Ib./hr./sq. ture, 100' F.i
ft : tempera-
. DRV PLATE -
LIQUID R A T €
-G
0
WATER
0
LIGHT LUeE - 5 G
3 G P M PM
PM
FIGURE 7. EFFECT OF LIQUID RATEON FROTH HEIGHT (Constant mass veloclty of air, 502 lb./hr./sq. ft.; ture, 100' F.)
tempera-
0
200
400
600
V-CT IY
FIGTRE 9. EFFECT OF AIR VELOCITY
frictional resistance, m. of liqutd on plate velocity of vapor in chlmney, ft./sec. density of vapor dL = density of liquid
800
1000
- LBS/HR/SQFT
ON PRESSURE
DROPTHROUGH
PL.4TE
mThere H,
= u, = dv =
The constant 0.533 is the average value of Table for Pressure drop of vapor floning through a Plate with no liquid on it.
Calculation of Froth Density The density of the fluid head over the downspout is assumed to be the average density of the froth on the bubble plate.
There is a possibility of rather large errors in this assumption since the froth is probably not of uniform density. Since there appears t o be no other convenient means for estimating the density of the fluid head, the assumed equivalent average density is used. This density, relative to the density of the liquid, is obtained from the equation: P - Hj
dF/dL
HF - S/2
(4)
INDUSTRIAL AND EN
90
TABLEIV. AIR-KEROSENE SYSTEM
NEERING CHEMISTRY TABLEVI.
Air a t 72' F. and 14.36 lb./sq. in. abs ' 5 gal./min. of kerosene a t 120° F.: d v = 0.0725 lb./cu. ft.;"dL = 49.48 lb./cu. ft. Pressure -CalculatedAir Drop Froth Hf1 AP = Run Mass across Height friction 1 0.4 f No. Velocity ,Ll?ii Plate on Plate loss" HI '. In. of I n . of L b . / h r . / s q . ft. kerosene In. kerosene 186 2.6 187 2.6 188 3.0 3.5 189 0:07 1 :50 4.0 190 0.21 1.60 191 4.0 0.28 1.70 192 4.25 0.44 1.80 193 4.50 0.77 2.20 194 4.75 1.15 2.45 195 5.0 1.80 3.20 196 5.0 2.02 3.40 197 6.0 2.63 4.00 198 6.0 2.37 3.80 199 6.0 2.10 3.50 200 6.0 1.57 3.00 201 5.0 1.26 2.70 202 5.0 2.10 0 67 203 4.5 2.30 0.93 204 5.0 2.40 0.99 205 2.80 1.37 206 3.40 2.02 207 6.0 3.70 2.30 208 2.35 6.0 3.75 6.0 3.95 209 2.55 4.25 210 6.0 2.85 211 7.0 4.95 3.55 212 4.6 3.2 7.0 213 5.3 7.0 3.9
TABLEV.
AIR-KEROSENE SYSTEM
.
Air, 78' F. and 14 2 lb /sq. in dsir = 0.0715 lb./cu. ft.; kerosene, 9 gal./ min. ad 80' F.': dkerosene = 50.83 Ib./cu. f t . mass = 0.0715 X 3600 X 0.051 0.0761 X mass velocity, (lb./hr./sq. ft.) Friction drop, Hj = 0.533 (dv/dL)uZ = in. kerosene = 0 . 0 0 0 7 4 9 ~ ~ AP - Hf Air u, Run Mass Chimney Froth HF - 0 5 Froth No. Velocitv Velocitv Heiaht 4P fff Ca1cd.a Volume Gal./ Lb./hr.) mrn. sq. ft. Ft./sec. In. I n . a / kerosene .. 3.0 132 0 ; 2 5 . . 3.0 0 133 1.7 .. 0:69 13:5 3.2 5.4 71 134 3.5 1.8 14.1 0.64 8.1 136 106.5 2.0 0.54 o:i 4.0 16.7 13.24 136 174 2 . 0 20 0 . 4 5 0 . 2 4 . 5 15.30 20 1 137 0.3 3.5 19.5 0.46 7.5 20.62 271 138 0.28 3.1 20.9 0.43 7.0 19.56 257 139 0.2 5.5 2.5 19.5 0.46 17.88 235 140 20 0.45 0.3 6.5 2.9 19.18 252 141 20.4 0.44 0.39 4.8 22.68 10.5 142 298 0.3 3.1 20.9 0.43 7.0 19.94 143 262 0.3 3.5 20.9 0.43 8.0 20.62 144 271 3.9 21.9 0.41 0.4 9.0 21.92 288 145 4.9 20.9 0.43 0.4 11.0 22.91 301 146 20.4 0.44 5.7 .4 12.5 22.83 300 147 0.43 19.5 0.46 6.2 23.51 13.0 148 309 0.45 6.3 20.9 0.43 14.0 23.8 149 313 22.5 0.82 0.40 6.8 15.5 432 32.9 150 23.7 0.96 0.38 16 6.8 34 446 151 23.1 0.39 1.0 16 7.0 36.4 478 152 25 0.36 1.5 9.7 23 45.4 596 153 25 1.5 0.36 9.6 23 44.7 154 588 25.7 1.1 0.35 6.8 17 505 38.4 155 7. . 7. 25.7 0.35 1.2 19 39.6 521 156 25.7 0.35 1.2 18 7.4 39.4 518 157 25.7 0.35 1.3 22 8.9 42.1 553 158 23.7 0.38 1.3 22 9.4 42,l 553 159 0.38 1.4 .. 23 9.7 43.2 568 160 24 .. .. 601 45.7 1R1 162 635 48.3 Air velocity in chimney =
... ...
~~~
5
From Equation 4, ratio of froth density to kerosene density.
where dp
= av. density of froth P = differential pressure across plate, in. of liquid H p = height of froth above plate, in. S = vapor-filled opening of slot; for velocities greater than 200 lb./sq. ft./hr. the slot is completely open (S = 1)
The quantity of fluid entering the downspout operating as a n orifice is obtained by dividing the liquid throughput by the relative froth density. The head over the downspout orifice
PL.4TE
Flr --,
Run N o .
360 361 362 363 364 365 366 367 368 369 370 371 372 373
~~~
From Equation 3.
DROPWITH KO LIQCIDON
Air a t 72' F. and 14.13 lb./sq. in. abs.: dair = 0.072 lb./cu. Et.; dHrO = 62.29 lb./cu. it.
+
a
PRESSURE
VOL. 30, A-0. 1
Mass Velocity Lb./hr./sq. f t . 206 302 360 400 451 503 490 731 781 837 922 972 1020 1150
Chimney Velocity, u
Ft./sec. 15.6 22.9 27.3 30.3 34.1 38.1 44.7 55.3 59.1 63.4 69.8 73.6 77.2 87.1
Obsvd. ( AP)
(dv/dL)u* from Equation 3
In. water Hf 0.35 0.45 0.60 0.70 0.85 1.00 1.20 1.65 2.00 2.30 2.90 3.50 3.70 6.40
... 0 : 634
0.595 0.519 0.467 0.494 0.494 0.514 0.560 0.537 0,524
TABLEVII. AIR-KEROSENE SYSTEM Air at 502 lb./sq ft /hr 73' F., and 14.15 lb./sq. in.; kerosene, 100' F.; dair = 0.672 L$./cu. ft.; dkeroaene = 50.18 lb./cu. ft. 502 Air velocity in chimney = 0.072 X 3600 X 0.051 = 38 = dv Friction drop HI = 0.533 - u* = 1.1 in. kerosene dr. A p Calcd. Run Froth AP H P - 0.5 Froth So. Kerosene Height Kerosene Calcd." Volume Gal./min. In. In. Gal./min. 17.0 6.60 0.333 54 8.60 25.8 14.0 5.40 0.319 24.8 7.90 55 12.0 5.00 0.339 20.7 7.00 56 2.80 6.5 0.284 22.6 6.50 57 2.00 4.0 18.3 5.30 58 1.95 4.0 14.3 4.10 59 1.70 3.00 4.0 ... .. 60 1.60 3.0 ... 1.90 .. 61 1.50 3.0 ... 1.10 .. 62 1.20 2.5 0 63 2.40 5.80 6.0 0 236 24:6 66 2.70 6.5 6.35 23.8 0.267 67 3.10 25.1 8.0 6.70 0.267 68 3.20 21 7.0 0.323 6.80 69 3.60 24.1 7.10 9.0 0.294 70 5.30 21.7 13.0 7.30 0.336 71 5.40 14.0 7. 2 23 0.326 7.50 4.80 22.6 12.5 0.308 6.95 73 3.10 22.1 6.80 0.308 7.0 74 5.50 23.6 0.326 14.0 7.70 75 5.80 25 0.324 15.0 8.10 76 5.80 24.8 15.0 8.00 0.323 77 6.20 25.2 0.329 16.0 8.30 78 6.60 25.3 0.355 16.0 9.00 79 6.40 25.7 0.342 16.0 8.80 80 28.3 7.00 0.336 18.0 9.50 81 28.5 0.326 18.0 6.80 9.30 82 26.9 7.40 0.360 18.0 9.70 83 29.5 8.10 0.359 20.0 10.60 84 30.1 0.362 19.0 7.80 10.90 85 3 5.1 8 . 6 0 0 , 3 6 5 21.0 12.80 86 35.8 9.70 0.382 23.0 13.70 87
'
:
a
From Equation 4, ratio of froth density t o kerosene density.
is the observed froth height, less 2 inches. Calculated friction loss, and density and volume of froth are given in Tables V and VII. Table IV presents data and calculations for 5 gallons per minute of kerosene and various air velocities. The calculated differential pressure here is the sum of the distance between the top of the slots and the edge of the weir (1inch), the head over the weir required for 5 gallons per minute (0.4 inch), and the friction loss expressed as inches of kerosene. The agreement between the calculated and observed differential pressures is very good. A comparison of the resistance set up by the several different liquids is shown in Figure 9. The linear relation between pressure drop and froth height is clearly brought out in Figure 10, where a large number of runs representing the different liquids under various conditions of flow are plotted. Figure 11 is a plot of observed head over the downspout
JANUARY, 1938
INDUSTRIAL AND ENGINEERING CHEMISTRY
91
24
I
.
X
I-
O
n! 4 o
- LEGEND K E ~ O S E N E80-F E 9~ P
-
- 80.F KEeosENE - 100.F
KEROSENE
s
0
L
DIFF.
2
3
4
PRESSURE
-
5 6 INCHES
M
$ 502 LB/HCL/FT' L
Le /WR /FT'
502
7
8
9
KEROSENE
FIGURE10. RELATIONBETWEEN FROTHHEIGHTAND PRESSURE DROPTHROUGH PLATE
4ENTERING WEIR - G . P M FIGURE 11. FROTH HEIGHTus. CALCULATED VOLUME OF FLUID ENTERINQ DOWNSPOUT 0 Low vapor and liquid rates
against volume of fluid entering the downspout. The individual points are taken from Tables IV, V, and T'II. The solid lines represent the discharge equations for the three different conditions under which the downspout is assumed to operate. Although there is considerable scattering of points, the agreement between the individual points and the theory appears to be good, especially in view of the possible errors in thepbserved froth height and the calculated froth density.
Conclusions The data show clearly the interdependence of downspout size, pressure drop, and entrainment in a bubble-plate column. The hazards attendant upon independent extrapolation of any-one of these factors in column design are obvious. It is recognized that the analysis here presented is inadequate for predicting pressure drop and liquid capacity of columns, except under such conditions as the weir equation may apply. These data and calculations are presented to indicate a method for treating the complex fluid dynamics of fractionating col-
X 502 lb./hr./sq. ft. and various liquid rates (Table VII)
A Kerosene, 9 gal./min. and various mass velocities (Table V)
umns. It is hoped that further experimental data will provide the basis for a more complete and generalized dynamical treatment.
Literature Cited (1) Ashraf, F. A., Cubbage, T. L., and Huntington, R. L., IND.Esa. CHEM.,26, 1068 (1934). (2) Holbrook, G. E., and Baker, E. M., Ibid., 26, 1063 (1934). (3) Pyott, W. T., Jackson, C. A., and Huntington, R. L., Ibid.. 27. 821 (1935). (4) Rogers, M. C., and Thiele, E. W., Ibict., 26, 524 (1934). (5) Sherwood, T. K., and Jenny, F. J., Ibid., 27, 265 (1935). (6) Souders, M o t t , Jr., and Brown, G. G., Ibid.,26, 98 (1934). REcBrvEn December 2, 1937. Presented before the 30th Meeting of the American Institute of Chemical Engineers, St. Louis, IMo., November 15 and 16, 1937. Mott Souders, Jr., is the Sterling Fellow in Chemical Engineering a t Yale University. The data of this paper are the results of work done by H. C. Corneil and F. L. Emert in 1936 for their undergraduate theses in petroleum engineering a t the University of Oklahoma,
