0.8
U DOIUCOYCR
Q3 0.4
Figure 11.
ARC4 1
1
l
I
7.1
I
1
1.5
2
-
I
0.6 08 1.0
3
4
5 6 7 8 9 10
15
20
30
Column pressure drop as function of hole diameter
hole diameter on over-all plate efficiency as a function of the vapor throughput rate (Figure 9) is not clearly defined. T h e fact that the curves with a parameter of hole size are not parallel would seem to indicate that other factors are involved than those maintained constant during this study. Some variation in hole size could result in indefinite conclusions. However, this variation was believed small enough to be considered negligible. T h e results of the 1/16-inch-diameter hole test indicates a much longer throughput range of operation than those
obtained from the larger hole sizes tested. T h e effect of surface tension in preventing the dumping of liquid through the holes would be more pronounced on the hole plates of smaller diameter. Column Relationship. The 1.83-inch and 3-inch columns were compared by operating both columns under the same conditions and using the same mechanical design features. The mechanical design features that varied between the columns were: the plate spacing of 3 and 6 inches, the per cent downcomer area of 1.08 and 3.5570, and the column
diameters of 1.83 and 3 inches. The results of this comparison are shown on Figure IO. T h e two curves of overall plate efficiency as a function of the vapor throughput rate overlap throughout the throughput range of the smaller diameter column. T h e range of the smaller column was shorter because the per cent downcomer area was less. T h e difference in plate spacing does not seem to have a noticeable effect on the over-all plate efficiency in the range of vapor velocities investigated. Pressure Drop. Column pressure drop as a function of the vapor throughput rate is plotted on Figure 11 for the 3-inch column. A single curve was plotted for the ‘/aq, 5/32-, and 3,’~6-inchdiameter hole plates, but the I / L ~ inch hole plate produced a separate pressure drop curve as a function of the vapor throughput rate a t the lower vapor velocities. This curve explains the variation in operating range of the various hole diameters on Figure 9. As the throughput rate was decreased. the plate retained a liquid level (providing a contact medium for the rising vapor) until the dumping point was attained. Then the liquid dropped through the holes in the plate, resulting in a lower pressure drop as well as a lower over-all plate efficiency. T h e ultimate result of the over-all research project, of which this work is a small portion, is to predict efficiencies in distillation columns. A great deal of work, some of which may seem obvious or unimportant, must be done before a project of this type can be completed.
Variables in Perforated Plate Column Efficiency and Pressure Drop
Effect of Plate Thickness and System Properties
I
P. D. JONES1 and MATTHEW VAN WINKLE
F O R evaluation of the effect of plate thickness and system properties of efficiency and pressure drop in a 3-inch-perforated plate distillation column, the column and accessories are shown in Figure 2, with slight modifications in heating provisions, so that throughputs in the neighborhood of 2000 pounds per I Present address, Shell Chemical Co., Deer Park, Tex.
232
hour per square foot of free cross-sectional area could be attained. T h e plates were made of brass and were machined to the exact thickness required: 0.054, 0.083, 0.125 (‘/a), 0.1875 (31’18), and 0.250 inch (l/4), varying at the most ~ k 0 . 0 0 2 inch. Thickness-hole diameter ratios ( 7 / ’ D ) were, respectively, 0.46, 0.66, 1.0, 1.5, and 2.0. Seventy-two l/*-inch holes totaling 12.5yG free area were drilled,
INDUSTRIAL AND ENGINEERING CHEMISTRY
as shown in Figure 12, using triangular pitch of ‘14 inch for a pitch-hole diameter ratio of 2. Holes were drilled from the bottom side of the plate, so that the sharpest edge of the orifice formed would face the vapor flow direction. Downcomers were made of ‘j2-inch hard-drawn copper tubing and totaled 7.1y0 free area. They were soldered to the plate, forming I-inch over-flow weirs which extended to within 3/a inch of the
V A R I A B L E S IN PERFORATED PLATE C O L U M N EFFICIENCY A N D PRESSURE D R O P Procedure
1 ~i~~~~12.
~~l~ pattern for
-
pressure drop plate studies Plate cross-sectional area, sq. inches Downcomer crosssectional area, sq.
efficiency
7.06 0.50 (71%) 12.5
inch
% free area
T h e test procedure followed was essentially that described above. T h e reboiler composition was maintained within a definite range, in order to eliminate the effect of composition on efficiency which was observed by Umholtz and by Wijk (28). Reboiler composition ranges used are listed in Table 111. Approximately 3 hours were required for the column to reach equilibrium, before data were taken. Test data included temperatures in the tops, bottoms, and reflux plus the rotameter and pressure manometer readings. Physical properties used in the evaluation of pressure drop and efficiency were the arithmetic average properties a t the
I00
plate below. No seal pots or baffles were used, in order to eliminate the effect of these variables on plate operation. Results obtained were reproducible.
90
eo
v)
W
I-
a 2
70
a
Y)
k.
0
Materials
W
T h e materials used in the evaluation of over-all plate efficiency and pressure drop are listed in Table 11. Relative volatilities for the n-octane-toluene binary were obtained from data of Berg and Popovac ( 4 ) . Relative volatility of the n-heptane-methylcyclohexane binary were taken as constant a t 1.075, as indicated by Bromiley and Quiggle ( 5 ) and by Wijk (28). Relative volatilities for carbon tetrachloride-benzene binary were calculated from data of Rosanoff and Easley (24). T h e values vary linearly from 1.137 a t 56 mole 7 0 carbon tetrachloride to 1.092 for 76.6 mole % carbon tetrachloride, the average being approximately 1.125 for the range used. Densities for the liquid mixtures were taken for heating and cooling runs, using standard liquid hydrometers at the temperature of the reflux. Data were accurate within f 0 . 0 0 2 and were within the accuracy of rotameter corrections for density and viscosity (negligible).
Table II. Observed Material n-Octane Toluene %-Heptane Methylcyclohexana Carbon tetrachloride
Benzene
SO
W
a > a
40
\ 1
8
30
> 0
z !!!
0
k w,
20
W
I-
a -I n -I
A
a
V. FREE AREA
t> O
12.5
I
IO )O
I I
300 400 SO0 600 G - SUPERFICIAL MASS VAPOR VELOCITY LB./ I I 1 1 I I I 0 . 0 8 0.10 0.15 0.2 0.3 0.4 I F - FACTOR (FT./SEC) (LB. / FT3) T I I I I I I 1 1 IS 2 3 4 S 6 7 8 HOLE VELOCITY, FT./SEC. 200
Figure 13.
800
1000
HR.- SQ.FT. I 0.5
1 0.6
I
I
l
l
0.7 0.8 0.S 1.0
1 1 9 1 0
I IS
I le
Effect of plate thickness on efficiency
System, n-Heptane-methylcyclohexane.
Atmospheric pressure. Total reflux
Materials Used in Evaluation of Over-all Plate Efficiency Literature
n "g
n
1.39510
1.39508
(86)
1.49413
1.49413
(86)
1.38784
1.38764
I .42325
1.42312
(86) (96)
1.45732
1.45737
($4)
Source of Material Phillips, 99 mole yo,gallons Cosden Oil Co., barrel Phillips, 9 9 mole yo,redistilled Unknown Adamson and Baker reagent, ACS Code
1.49743
1.49290
(26)
Adamson and Baker reagent, ACS Co6e
1554 1442
VOL. 49, NO. 2
FEBRUARY 1957
233
10 9
4
8
vihtOSPHERlC PRESSURE e
Figure 14. Effect o f plate thickness on pressure drop
5
4
3
2
,
I
I
l
con
l
oi
,
02
CIS
I
too
2
04
,
I
,
I
90
k
lFT./SEO ( L e . /FT.sI
0.46
0.003.
0.66
m
0 12s.
1.0
0
0 . 1015'
1.5
,
I
I
SYSTEM
10
,
I
l
' 07
I
06
I
I
-
overhead and bottom condition of the column. Results
2000
T h e variables were boil-up rate at total reflux, for three different binary systems and five plate thicknesses per system. Figures 13, 15, and 17 show plots of over-all plate efficiency us. G, the mass velocity, with a scale for F factor and velocity V superimposed upon the G scale. Figures 14, 16, and 18 show the pressure drop us. G corresponding to the efficiency curves. I n all cases velocities are for data "as taken." As cold reflux was used in all cases, data may be corrected to column conditions by a simple multiplying factor listed in Table
I l l 0L10010
l
5
6 7 8 9 1 0 FT./ SEC.
3 4 5 HOLE VELOCITY,
2
,
I
03
F - FACTOR
m f
0 059.
0
230 300 400 500 6 0 0 m m 1000 0 - SUPERFICIAL MASS VAPOR VELOCITY ( L E . / HR:SQ.FT.I
00
I
0
I
I
I
? -OCTANE I TOLUENE
:
ATMOSPHERIC PRESSURE TOTAL REFLUX
70
0
$
60
Y
- 5 0 Y
z 2
40
\
s = Y
L
Y
w
20
f
2 _1
2
5 IO
m
200
5
L
I
01
-
$00 400 500 600 a00 I000 SUPERFICIAL MASS VELOCITY, L&"R%.FT. I I I I I I I I 06 07oa 02 03 0 4
ILB. /FW
F - ~ C T O R ( FTJSEC) ~ 1
,3
2
I
I
t
4
5
I
3
8
HOLE VELOCITY,
7
t
I
1
I
9
1
I 10
I5
0
Figure 15. Effect of plate thickness on efficiency
I
I
I
1
i
2000
10
FT./KC.
t
COLUMN D I A M E T E R
3"
NUMBER OFPLATES
5
i 1
PLATE
0 054'
t
STATIC S E A L
n.
HOLE DIAMETER
'A F R E E AREA
B 200
6
L
-
01
2000
SUPERFICIAL MASS VELOCITY (LB/HR.-SO.FT.) I I I I I I I I 0: OS 04 05 06 0 7 0 1 F-FACTOR
I
Figure 16.
' t
I
a
I
I
CFT/SECr I
,
I
l
5 e ? a 9 1 0 H O L E VELOCITY, FT./ SEC,
4
I$
G
20
'
I
3
Figure 17.
Effect o f plate thickness on pressure drop
System.
INDUSTRIAL AND ENGINEERING CHEMISTRY
SUPERFICIAL M A S S VELOCITY j LB/HR.I
02
reflux
234
-
I
I
l
2.0
i
1
I
I
12 5
0 250"
10
40
ILB./FT?Ii
0. 1875"
b
PITCH /DIAMETER
a 100
T/D
THICKNESS
Y
I
4
SQ.FT.1 1
!
03 04 F-FACTOR r
I
0 5
08 0706
(FT/SEC) ,
,
5 6 1 0 9 H O L E VELOCITY,
I O
I 3
(iB./FT?)i
,
,
1
0
IS
20
I
FT./SEC.
Effect of plate thickness on efficiency
Carbon tetrachloride-benzene.
Atmospheric pressure.
Total
V A R I A B L E S I N PERFORATED PLATE C O L U M N EFFICIENCY A N D PRESSURE D R O P IV. This multiplying factor assumes average column conditions of composition and physical properties for all runs. For all three binaries, pressure drop and efficiency curves show inflection points (weep points) below which the plates ceased to operate. Figure 19 shows that the velocities are the same a t inflection points for both pressure drop and efficiency curves. Both curves show that higher velocities are required when thicker plates are used. Efficiency curves show a characteristic rise in efficiency for lower velocities, which has been reported by Umholtz and by Wijk (28). T h e increase in efficiency for lower velocities appears to be the effect of optimum time, bubble size, and time of rise of the bubble through the liquid and froth on the plate. Also at higher velocities entrainment may be encountered because of the low (6-inch) plate spacing. Efficiencies appear to be the same for all plate thicknesses, while pressure drop is slightly less as plate thickness increases. T h e pressure difference is of the order of 0.054 to 0.250 inch. Data obtained here indicate that composition affected the fall-off point. Figures 20 and 21 show the effect for a carbon tetrachloride-benzene system. For an 0.083-inch of plate, as the reboiler composition was lowered from 6870 to 62.870, the velocity required to make the plate operable became less. No detectable change in efficiency could be observed once normal plate operation was attained, and no effect on pressure drop could be detected. A check was made to see if the change in surface tension or density could account for the phenomena. T h e change in composition was approximately 670 in each case. This corresponds to approximately 0.1 dyne per cm. or 0.0025 inch of water (for five plates). T h e change in density of the mixture could account for a difference in pressure drop corresponding to 0.07 inch of water in the case of the 0.1875-inch plate, and 0.02 inch of water for the 0.083-inch plate.
v" for
2g
five plates is approximately 0.1 inch of water. T h e precision of the data is not great enough to evaluate these small differences. T h e relation between fall off and composition is not apparent. Explanation for the trends of the data obtained was sought in the differences of basic physical properties of the binary mixtures and in phenomena of flow of fluids. Table IV shows the average properties of all three binaries a t the av. erage column conditions for each binary. All average properties except viscosity are weighted averages based upon mole per cent of each binary component. Viscosities of the mixtures are weight
IO0
I
so
SYSTEM
in
f
I
I
00
*0'
70
n 00
a
PLATE
-
0
0.054'
0 46
%
0
0.083'
0.66
0
0.125'
1.0
0
0.1875'
I .s
0
0.250'
2.0
40
W 0. X
z
30
n'
I
I I
0
n a W
2
1
l
I
-
1l 1l
I
I
I
I
I
TfD
IICKNESS
$ 5 0
Y)
l
CARBON TETRACHLORIDE B E N Z E N E ATM 0 S PH ERIC PRESS UR E TOTAL REFLUX
I
COLUMN DIAMETER
3"
NUMBER OF PLATES
s
PLATE SPACING
6. I.
WEIR H E I G H T
6
Y. DOWNCOYER AREA
20
Y) Y)
7.1
-s
STATIC S E A L
a
HOLE DIAMETER
f
A
PITCH /DIAMETER
2
2w
Y. FREE AREA
.
10
5
100 6 0 0 (100 1000 2000 G SUPERFICIAL MASS VELOCITY (LB./HR.-SQ.FT.)
400
I
I
I
I
0.6
(Fl./SEC)
I
1 5
I 4
I
0.5
I
0.3 0.4 F-FACTOR
l 7
6
l 8
H O L E VELOCITY,
Figure 18.
I
I
I
07 00
f
(LB./FT.3)
I
1
1.0
I3
IS
1
FT./SEC.
Effect of plate thickness on pressure drop
Table 111. Reboiler Composition Ranges Compn., % Component
System
4000
1
I 20
I
l l 910
12.5
3000
-
0 2
-
5 ' 3
w
0
-
n-Heptane-MCH n-Octane-toluene CCL-benzene
53-55 45-49 66-69
Figure 13,14 15,16 17,18
n-Cr Toluene CCla
10
9
8 Lo
E7
9
n \ 5
K e W % 4 Lr 0 in
I
? 3
I
I
I
l
I
1
l
0
r
--PLATE
THICKNESS
0
0.054'
0.46
0
0.083"
0.66
2 in
0
0.121'
1.0
W
Q
o.ie7s.
1.5
0
0.250-
2.0
' a
0
E 2 W
K
In a. K
T/D
-
I
300
400
SO0
600 7 0 4 0 0
IO00
G-SUPERFICIAL MASS VAPOR VELOCITY
Figure 19.
2000
LB.
/ HR.-
3000
ScI.FT.
Efficiency and pressure drop at fall-off point VOL. 49, NO. 2
FEBRUARY 1957
235
Table IV.
Physical Data for Binary Systems a t Average Column Conditions Av.O
L.b
Column Ta Compn. Reflux Mole Mole Wt. F. C. Wt. % %
T G
Column Compn. ‘C. F. N-Cs 238 115 138 59 Toluene
pL
at T,, Cp.
O
Av? 238 115 138 59
N-C7
211 100 115 46 MCH A v . ~ 211 100 115 46 CCL 170 78 107 42 CeHe Av.* 170 78 107 42
114 92 103 100 98 99 154 78 133
37 63 58 42 73 27
6‘ at T,, Cp V” at T = , B t . u / at T ~ .at T ~ Dynes/ Hr./Sq. B.t.u./ Cc./ Cm. Ft./’F. Lb./” F. Mole 12.6 0.0775 0.473 184 19.2 0.082 0.351 118 16.8 0.080 142 0.379 13.0 0.077 0.474 164 15.2 0.344 141 13.8 0.419 154 20.3 0.0902 0.23 104 21.6 95.7 0.083 0.49 20.7 0.089 0.296 102
42 58
0.228 0.249 0.238 58 0.208 42 0.30 0.246 84.5 0.49 15.5 0.318 0.454
LHV
PL
at , T“, G./
Cc.
at T ~ ,Cc, ps, ea at B.t.u./ Lb. fit at T,, T, Lb. Lb. Ro c p .
0.662 0.778 0.719 1.64 0.612 0.698
0.650 1.47 0.815 1.30
1.015 1.12
130 156 146 136 139 137 84 169 106
P P
at T a . Lb./ Cu.Ft.
0.007 0.0077 1.26 0.0073 0.204 0.0071 0.0093 1.29 0.0078 0.202 0.0125 0* 0088 1.175 0.0118 0.290
Calculated. Estimated. C . Correction factor for cold reflux. References for pure component properties (2, 7, f4,20,26).
a
~
~
Plate
Go
Table V. Tabulated Data on Fail-Off Point APa, v h Vh’, AP. Inch Ft./ sq. Ft./ Vh2, Inch H10 See. See. 2g Hz0 I
3
DVHP,
HzO
Lb.
P
1.42 X 10-3 lb./ft. (20.8 cp.) 0.52 0.17 3.30 0.22 3.27 0.52 0.52 0.33 3.27 0.49 3.31 0.52 0.74 3.37 0.52
2.78 2.75 2.75 2.79 2.85
9.0 8.9 8.9 9.0 9.2
2400 2600 2600 4080 4900
0.42 0.42 0.42 0.42 0.42
1.94 1.93 1.93 1.95 1.92
8.7 8.7 8.7 8.7 8.6
1740 2100 2500 3700 4530
n-Heptane-methglcyclohexane, 6 = 895 X 10-3 Ib./ft. (13.8 cp.) 0.03 1.57 0.35 1.60 3.08 9.5 0.04 3.62 13.1 1.59 0.35 1.63 4.45 19.8 0.06 1.68 1.62 0.35 0.20 1.82 0.35 2-02 8.05 65.0 0.30 2.0 0.35 2.33 10.1 100
1.22 1.24 1.28 1.47 1.65
6.6 6.6 6.9 8.0 8.9
1230 1460 1780 3200 4060
0.053 0,083 0.125 0.1875 0.250
0.46 0.66 1.0 1.5 2.0
825 920 1120 1400 1700
69 68 64 61 58
3.47 3.49 3.60 3.80 4.11
0.053 0.083 0.125 0.1875 0.250
0.46 0.66 1.0 1.5 2.0
370 435 530 800 960
52 49 44 42
2.41 2.42 2.45 2.55 2.67
0.053 0.083 0.125 0.1875 0.250
0.46 0.66 1.0 1.5 2.0
280 330 405 730 920
78 77.5 76.5 65 62
%
APL,
Hz0
T/D
Carbon tetrachloride-benzene, 6 6.30 7.05 8.60 10.7 13.0
=
39.6 49.6 75.0 114 169
Inch
APL,
sq. Ft./
Inch
Eo,
AP6,
Inch
Lb./Hr./ Sq. Ft.
T,
n-Octane-toluene, 6 = 1.16 X 10-8 Ib./ft. (16.8 cp.) 51
averages. Table V lists pressure drops, efficiencies? and fall-off points for each binary system and each plate thickness. An investigation into the flow of a gas through orifices appears to explain the trends observed. Perry (23) notes for single tubes that flow of gas phenomena are similar to those of a “Borda tube” or, more nearly. a “standard short tube.” In either case the edge is sharp and behavior is often erratic. in that it may “run free” when the minimum cross-sectional area of the jet does not touch the walls of the tube, or it may “run full“ when the minimum cross section of the jet touches the walls of the tube. Estimated coefficients of C,’C, for liquids are0.53 for running free and up to 0.91 for running full. For submerged discharge C,’C, of 0.72 is estimated. For a short tube, when running full, C,’C, is estimated to be 0.82. Buckingham’s work (6)on orifice meters and the
236
4.02 4.75 5.75 8.70 10.4
16.2 22.5 33.0 76 108
0.05 0.07 0.10 0.23 0.33
2.36 2.35 2.35 2.37 2.34
expansion factor of gases indicates that the vena contractu moves downstream as the velocity through the hole is raised. In addition, as the freearea approaches 5070, the static pressure in the region of the jet becomes less uniform (free area here = 0.2 in the hole zone area). Baines and Peterson (3) in their investigation of flow through screens, and thick plates and screens, observed that for low velocities and low free area ratios, each jet remains a stable entity until diffusion is complcte. For higher velocities with higher free area ratios, the pressure variation causes jets to diverge laterally or to coalesce, causing unstable plate operation with alternate zones of high and low pressure. In addition, as plates become thicker, the minimum cross section of the jet approaches the wall of the tube, and a constant CO of 1. A short tube effect results. The experimental results may be ex-
INDUSTRIAL A N D ENGINEERING CHEMISTRY
plained on the basis of information in the above section. The varying fall-off points and the pressure drop variation stem from the fact that as the plate thickness increases, the areas of the minimum cross section of the jet stream increases and approaches the area of the perforation as a limit. For any given velocity, since the energy balance a t an\- cross section of the strram must be constant, the higher forms of enerqv (momentum. etc.) per unit cross-scctional area of jet-which must support the “clear liquid head ’ on the plate-are less as the plate thickness increases. The result is a draining of liquid through the plate until equilibrium is re-established. For perforations of very small diameter. it is possible that surface tension and flow phenomena combine to extend operation to low velocities Similarly. the evidence that the minimum diameter of the jet approaches the wall of the prr-
V A R I A B L E S IN PERFORATED PLATE C O L U M N EFFICIENCY A N D PRESSURE D R O P foration implies that the constant CO of the orifice equation approaches 1 as a limit. T h e orifice equation in its simplest form states
100
In 90 w
80
I-
3 a
70
v)
u.
60
0
where V = velocity of gas through the orifice, feet per second C" = orifice coefficient, dimensionless Ha = pressure loss in orifice, feet of gas g = acceleration due to gravity, feet per sec.l
w
50
0 4
K
w
-E.
40
30
Hence, from the orifice equation, an increase in COwith plate thickness permits a decrease in H for the same velocity V,. This trend will eventually be reversed with the increased plate thickness when internal fluid friction due to the thickness of the perforation becomes the predominant loss and reverses this trend. Kamei (76, 77) shows this reversal to be at approximately thicknessdiameter, T i D = 2 . The lack of correlation of plate thickness with velocity is also partially explained. Two effects oppose each other; (1) a t constant velocity, the increase with plate thickness of the minimum crosssectional area of the jet, and (2) with increased vapor velocity, the shifting of the jet downstream. For low velocities where the velocity effect on the minimum cross-sectional area of the jet is small, it is reasonable to find that V,Z (velocity through holes)2 can be predicted if Vhz and T / D (thicknessdiameter) are known for any plate thickness u p to and including the diameter of the hole ( T / D = 1). Above this thickness of the diameter of the hole, the higher velocities for plate operation combined with properties of the system (at present unknown) to produce erratic behavior associated with a short tube or a Borda tube. T h e fact that efficiencies remain the same for the plate thicknesses observed, would seem to support the supposition that bubble formation should be similar for these plate thicknesses. Evidence to support this statement includes observations of Baines and Peterson (3)that the jets should retain their identity until diffused, and by recent pictures by Groothuis and Kraniers (72), who studied the reverse process of gas absorption in a liquid during drop formation. T h e accuracy of efficiencies calculated will not permit positive conclusions to be drawn a t the present time.
z !!!
0 u.
-
COLUMN DIAMETER NUMBEROFPLATES PLATE SPACING WEIR HEIGHT
3'
5
s
-I
a
2 1 4
c
f .I"
PITCH /DIAMETER
2
6
12.5
>
0
IO
Figure 20. System.
Effect of system composition on efficiency and fall-off point Carbon-tetrachloride-benzene.
Atmospheric pressure.
Total reflux
M W I L E R COUP NUYBER OF PLATES PLATE SPACINB WEIR HEIGHT
% DOWNCOYER AREA STATIC SEAL MOLE DIAYETER
PITCW/DIA.YETER */, FREE AREA
I.
200
300
2 IS 5
400
so0 0 0 0 000 moo 2ooo SUPERFICIAL YASS VELOCITY I LWHR.-scl.FT.)
G
I
03
L
I 4
I
s HOLE
Figure 2 1 . System.
I
Q
00
(FTJSEG I
1
1
1
0.7 0.0
1
l
1.0
4000
1
I1
(LB./FTP)~
I
7
l
1
0.5
0.4
F-FACTOR
Correlations
3Ooo
-
I
0.2
Attempts a t correlating over-all efficiency and pressure drop as a function of the variables studied was unsuccessful. However, a tentative correlation relating
s 0'
7.1
HOLE DIAMETER
% FREE AREA
d: W
a
I"
- STATIC SEAL
w w
c
o-w
6'
7. DOWNCOMER AREA
u.
-4
--
I
9
VELOCITY,
I
1
0
I
IS
I
20
,
FZ/SEC.
Effect of system composition on pressure drop and fall-off point Carbon tetrachloride-benzene.
Atmospheric pressure.
VOL. 49, NO. 2
Total reflux
FEBRUARY 1957
237
to the vapor velocity through the holes a t the fall-off point in terms of surface tension, density of vapor and liquid, hole diameter, and “clear liquid head” on the plate was developed. I t was assumed that the total pressure drop was composed of that caused by clear liquid head, velocity head through the holes, and surface tension equivalent head (for bubble formation).
Thus
HtA
( u j * ’ 3 ( D n ) ” 3 ( p~ pv)’l3
where
3
6 Dh p ~ PG,
Thus A P = APL
+ A P v + APs
Pressure drop a t the fall-off point may be correlated by the grouping
=
= = = =
head of liquid on plate constant surface tension hole diameter densities of liquid and vapor
(3) Then
and (4)
I n terms of hole velocity the following relation results
and APs
=
46 Dh
(5)
where = pa, p~ = g = 6 = Vh
Dh
=
velocity through holes densities of vapor and liquid gravitational constant surface tension diameter of holes
T h e evaluation of APS is the same as that used by Kamei and associates (77) a n d Geddes ( 7 7 ) . Clear liquid head may be considered as such or as any froth plus liquid on the plate. I n general, when APL is evaluated from Equation 3, its value is constant a t the fall-off point for the same system for any plate thickness tested. However, for the thicker plates the A P L a t the fall-off point for the n-heptanemethylcyclohexane system varied somewhat from that determined for the thinner plates. This was attributed to operation difficulties and not considered significant in the light of the other data. T h e constancy of APL tends to indicate nearly constant aeration a t the falloff point (or slightly above) and nearly ideal bubble formation on the plate. By considering the mechanics of bubble formation and the force balances a t the point of break-off of the bubble from the plate it was possible to arrive a t a grouping of variables which serves as a correlating factor for pressure drop a t the fall off point. T h e following were assumed :
1. T h e bubbles are spheres or nearly so.
2. They can be considered packed on perpendicular axes when bubbling is vigorous with practically all holes operating. 3. T h e net volume of clear liquid on the plate varies as Da3. 4. T h e maximum number of bubbles any distance L above the hole (assuming no lateral mixing) equals C’-,L
Da
5. T h e clear liquid on the plate is inversely proportional to maximum No. of bubbles X bubble volume x density of liquid.
238
For head loss expressed in terms head of water where
This also assumes the specific gravity is constant, the viscosity effect is small, and the function factor is approximately constant.
Further work with different mechanical properties is needed to extend the relation and establish constants involved. Literature Cited
American Petroleum Institute Project 44, Carnegie Press, Pittsburgh, Pa., 1953. Arnold, D. S . , Schoenborn, E. M., Chem. Eng. Progr. 48, 633-42 (1952). Baines, W.D., Peterson, E;. G., Trans. iMech. Engrs. 73, 467 (1951). A m . SOC. Berg, L., Popovac, D., Chem. Eng. Progr. 45, 683 (1949). Bromiley, E., Quiggle, D., IND.ENG. CHEM.25, 1136-8 (1933). Buckingham, E., J . Research n h t l . Bur. Standards 9, 61 (1932). Dow Chemical Co.. Midland, htich., “Physical Properties of Chemical Compounds,” 1955. Drickamer, H. G., Bradford, R., Jr., Trans. A m . Inst. Chem. Engrs. 39, 319 (1943). Edmister, W. C., Petroleum Engr. 21C, 45 (January 1949). Fenske, 11. R., IND.ENG.CHEW24, 482 (1932). Geddes. R . L.. Trans. A m . Inst. Chem. Engry, 42, 79 (1946). Groothuis, H., Kraniers, H., Chem. Eng. Sei. 4, 17 (1955). Gunness, R. C., Baker, J. C., Trans. A m . Inst. Chem. Eners. 34, 707 (1938). Hodgeman, D. D., “Handbook of Chemistry and Physics,” p. 1762, Chemical Rubber Publishing Co., Cleveland, Ohio, 1950. Jones, J. B., Pyle, C., Chem. Eng. Progr. 51, 424 (1955). Kamei, S., Chem. Eng. ( J a p a n ) 18, 307 (1954). lbid.: p. 467. Karim, B., Nandi, S. K., J . Indian Chem. SOC.,Ind. and A’ews Ed. 11, 3 (1948). Kirschbaum, Emil, “Distillation and Rectification,” p. 265, Chemical Publishing Co., New York, 1948. Maxwell, J. B., “Data Book on Hydrocarbons,” pp. 161-2, Van Nostrand New York, 1950. Mayfield, D. F., Church, W. Id., Green, A. C., Lee, D. C., Jr., Rasmussen. R. W..IND.ENG. CHEM. 44,2238 (1952): O’Connell, H. E., Trans. A m . Inst. Chem. Engrs. 42, 741 (1946). Perry, J. H., “Chemical Engineers’ Handbook,” pp. 404, 615, 3rd ed., McGraw-Hill, New York, 1950. Rosanoff. M. A,, Easley, C. W., J . A m , Chem. Soc. 31, 9:1-87 (1909). Rossini, F. D., others, SeIected Values of Physical and Thermodynamic Properties of Hydrocarbons and Related Compounds,” Carnegie Press, Pittsburgh, Pa.. 1950. (26) Timmermans, J. R., “Physical Constants of Pure Organic Compounds,” Elsevier, New York, 1950. (27) Umholtz, C. L., Van Winkle, M., Petroleum Refiner 34, No. 7 , 114 (1955). (28) Wijk, W. R. van, Thijssen, H. A. C., Chem. Eng. Sci. 3, 153-60 (1954). ~
I
Conclusions T h e conclusions are based upon a single composition per system and a 1-inch weir height in a 3-inch-diameter column. No detectable change in over-all efficiency was attributable to plate thickness. Pressure drop and corresponding efficiency curves have the same vapor velocities a t inflection points. Inflection points, which correspond to the falloff points, occur a t higher velocities for thicker plates. For very thick plates ( T / D > 2), this effect is reversed. T h e fall-off point, in terms of the square of the hole velocity Vh2,for any plate thickness from T / D = 0.46 up to and including T / D = 1, may be predicted from a known T / D and fall-off point (Vh2) by dividing by the known T / D and multiplying by the unknown T j D . Liquid composition and plate mechanical features must be constant. Minimum velocities for satisfactory plate operation vary with the physical properties of the system, and with the change in position and minimum crosssectional area of the vapor jet through the perforation. For this same reason pressure drop for a given velocity is less for increased plate thickness with the value of COof the orifice equation changing toward the value of 1 as a limit. For thick plates a short tube effect reverses this effect.
INDUSTRIAL AND ENGINEERING CHEMISTRY
RECEIVED for review November 25, 1955 ACCEPTED August 24, 1956
