PULSATION AND VIBRATION section required is reduced as much as three times when the column liquids are pulsed. 2. Optimum operating conditions can be obtained b y varying both frequency and amplitude of pulse. 3. Greater efficiency can be obtained with the proper low amplitude a t high frequencies than is possible a t low frequencies. 4. T h e maximum throughput is reduced slightly ( 5 t o 1 O o J ~ ) when the column is pulsed. 5 . Changes in feed rates have less effect on the efficiency when pulsation is used than with the usual packed column operation. Sieve-Plate Column 1. Average plate efficiencies as high as 70% can be obtained in pulsed sieve-plate columns. 2. High throughput rates compared t o packed column capacity may be used with high efficiency. 3. Smaller perforations are more efficient but more a p t to corrode and clog, and have reduced capacity.
Gallo, S. G., and Hartvigsen, B. (to Standard Oil Development Co.), U. S. Patent 2,562,783 (July 31, 1951). Gilbert, T. E., and Huntress, A. R., “Pulsation in a Packed Liquid-Liquid Extraction Column,” Senior Project Report, Cornell University, June 1953. Goundry, P. C., and Romero, V. M., “Effect of Agitation on Liquid-Liquid Extraction in a Packed Column,” Senior Project Report, Cornell University, Feb. 1950. Hunter, T. G., and Nash, A. W., J . SOC.Chem. Ind., 53, 95T (1934).
I. G. Farben, British Patent 457,552 (Nov. 25, 1936). Marsland, D. B., and Buckner, L. R., Jr., “Effect of Agitation on Liquid-Liquid Extraction in a Packed Column,” Senior Project Report, Cornell University, June 1951. Maycock, R. L. (to Shell Development Co.), U. S. Patent 2,474,007 (June 21, 1949). Morello, V. S., and Poffenberger, N., IND. ENG.CREM.,42, 1021 (1 950).
Ney, W. O., and Lochte, H. L., Ibid., 33, 825 (1941). Oldshue, J. Y . ,and Rushton, J. H., Chem. Eng.Progr., 48, No. 0, 297 (1952).
Literature Cited
Benedict, iM., IND. ENQ.CEIEM.,45, 2372 (1953). Callahan, E. W., and Geyh, C. A., “Effect of Pulsation on 8 Sieve-Plate Extraction Column,” Senior Project Report. Cornell University, June 1953. Chantry, W. A., “Application of Pulsation to Liquid-Liquid Extraction,” Ph.D. Thesis, Cornell University, June 1953. Chem. Eng.,61, No. 6, 282 (1954). Chem. Eng. News, 32, 350 (1954). Chemical Week, 69, No. 24, 32 (Dec. 15, 1951). Cohen, R. M., and Beyer, G. H., Chem. Eng. Progr., 49, 279 (1953).
Coinish: R. E., Archibald, R. C., Murphy, E. A., and Evans, H. M., IND. ENG.CHEM.,26, 397 (1934). Davis, M. W., Jr., Hicks, T. E., and Vermeulen, T., Chem. Eng. Progr., 50, 188 (1954). Feick, G., and Anderson, H. M., IND.ENG. CHEM.,44, 404 (1952).
Rich, W., Ross, K., and Mehler, G., “Agitation in a LiquidLiquid Extraction Column,” Senior Project Report, Cornell University, June 1952. Robinson, J., U. S. Patent 2,072,382 (March 2, 1937). Scheibel, E. G., Chem. Eng. Progr., 44, 681, 771 (1948). Scheibel, E. G., IND. ENG.CHEM.,42, 1497 (1950). Scheibel, E. G., and Karr, A. E., Ibid., 42, 1043 (1950). Sege, G., and Woodfield, F. M., Chem. Eng. Progr., 50, 396 (1954).
Sherwood, T. K., Evans, J. E., and Longcor, J. V., IND.ENQ. CHEM.,31, 1144 (1939). Smith, H. M., and Caplan, R. H., “Effect of Agitation on LiquidLiquid Extraction in a Sieve-Plate Column,” Senior Project Report, Cornell University, June 1951. Treybal, R. E., IND.ENG.CHEM.,45, 50 (1953). Van Dijck, W. J. D., U. 9. Patent 2,011,186 (August 13, 1935). Von Berg, R. L., and Wiegandt, H. F., Chem. Eng., 59, No. 6, 189 (1952). RBCEIVED for review December 20, 1954.
ACCEPTED March 28, 1956.
Power Requirements for Pulse Generation in Pulse Columns A. CARLETON JEALOUS O a k Ridge Nafional laborafory, O a k Ridge, Tenn.
HOMER
F. JOHNSON
Deparfmenf o f Chemical Engineering, Universify o f Tennessee, Knoxville, Tenn.
The power required to pulse a liquid-liquid extraction column is determined by the static head of the liquid system, the acceleration and deceleration forces on the liquid system, and the friction losses. The theoretical total power that must be applied to the liquid-liquid system b y the pulser i s given by the equation
where the equation for y defines the cyclic motion imparted to the liquid system by the pulse generator. Power input data obtained on a 50-foot pulse column 24 inches in diameter are presented, as well as information on development of the power formula and the means of experimentally evaluating the formula.
T
HE use of pulsed towers in continuous, countercurrent liquidliquid extraction frequently leads to improved performance over conventional types of towers such as the packed tower. The pulse action is provided by aome sort of mechanical pulse generator, usually a reciprocating piston-type unit. Pulsing June 1955
the fluid in the tower has the effect of putting energy into the liquid-liquid system beyond that which is due solely to the action of gravity on the dispersed phase particles. This additional energy probably benefits performance by increasing effective interfacial area as well as increasing turbulence in the system.
INDUSTRIAL AND ENGINEERING CHEMISTRY
1159
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT near-sine wave operation, and advantages, if any, need to be investigated further. Pulsing a liquid-liquid tower may be accomplished by use of a reciprocating piston (Figure 1) or a reciprocating action applied to a bellows or diaphragm, the pulse action being transmitted to the liquid system in the main column in either case through a pipe connection a t the base of the tower. The piston is a reliable, well tested means of obtaining pulse action, but requires provision for process fluid leakage past the piston (a particular problem where the fluid may be radioactive) and is subject to abrasion problems if solid particles are present. Both of the latter problems have been handily overcome in practice. On the other hand, the bellows or diaphragm eliminates the leakage and abrasion problems, but the longevity of either bellows or diaphragm is not as certain as the piston. Teflon bellows, although not promising where radiation exposure would be significantly high, appear to be otherwise suitable for pulsing solvent extraction towers and may prove upon further testing to have a very satisfactory longevity-almost certainly significantly greater than metallic bellows. Teflon bellows evidently
3 SEGMENTS - L A P JOINTS 0.005-in.
M A X . CLEARANCE
GRAPHITAR S E A L RING
18-in IPS PIPE
b
SEAL
RING
EXPANDER
~
DIA MUST BE ROUND WITHIN 0005-in TIR BACK-UP RING
Figure 1.
Pulser cylinder and piston, 12 inches in diameter, including piston rings
The effect of pulse frequency and amplitude on tower performance has been discussed ( I , 2 ) . The present paper presents methods for calculating pulse generator power requirements in sieve-plate columns as a function of pulse amplitude and frequency, physical properties of the system, and tower design. The methods are tested by comparison with experimental data from a tower 24 inches in diameter, operated with a fixed amplitude but having varied frequency. Several types of pulse generators are briefly described.
Types of Pulse Generators Pulse generators have generally been built to provide what is essentially a sine wave pulse action, but some significant increase in mass transfer or tower throughput may be found in applying other pulse wave shapes approaching, for instance, a saw-tooth or square shape. However, it is not yet clear that such advantages will lead to any significant over-all economic savings over
1160
Figure 2. Mechanical drive pulse generator coupled to bottom end of pulse column
can withstand mechanical actuation very much better than metal bellows; the latter proved to have a very short life (about 1,000,000 cycles) under mechanical actuation. However, for metallic bellows, hydraulic actuation (thus balancing the forces uniformly over the bellows surface) increased bellows life considerably-possibly up to 30,000,000 cycles or more. The reciprocating action for either bellows or piston may be provided by either a mechanical or hydraulic system (Figures 2 and 3). The mechanical system may be either some form of conventional eccentric movement for a near-sine wave action, or a
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 47, No. 6
PULSATION AND VIBRATION special cam-type movement for sawtooth or square-type pulse actions. The hydraulic system incorporates a hydraulic pressure circuit which actuates a hydraulic motor in the form of a doubleacting piston controlled by a pilot unit for alternately pressuring one side of the piston and then the other. A drive shaft extending from the hydraulic motor connects directly to the pulse piston or bellows. The hydraulic system is much more readily adjustable for varying the shape of the pulse wave.
PILOT VALVE.
n i o i valve operating
F o r Flow Diagram
(Rrgu'ste by adjustiiig c o l u m nstroke) Amp
PRLSSURE. RLTURN
I
Hgdraulic Puiser D r i v e Cylinder
RF-MOTL PRESSURE. RLLlLF
Cylinder Support.
Theory
-
I n the following treatment, uniform velocity throughout the column at any instant is assumed. This assumption is obviously not correct; however, empiri-
DIRECTIONAL CONTROL
Pulser P Cylinder
VALVE.
-4
WAY
lot Choke Adjustment
cal corrections to allow for it are attempted later in this article. I n order to provide pulsing action to the fluid in the column, force must be provided to overcome three effects: static head, inertia, and friction.
Pilot Pressure L i n e Main Pm>sune Line
outlet f o r secoitd
pro-ure
Pressure Rolie
R o t u r n Line
A diagram of a column and pulse line is shown in Figure 4, a. The main column is L1 in length and 81 in crosssectional area. The effective density in Figure 3. Hydraulically actuated pulse generator with feedback pulse this section is p1 ( a mean density if two fluids are used). Pressure a t the top of amplitude control the column, assumed constant, is Pa. Interrupted lines denote intermittent flow Pressure a t the bottom of the column is P I . The total length of pulse line from the main column to some point where pressure, Pz,is to be calculat,ed is Lz. Cross-sectional area and pressure difference in the pulse line by of the pulse line is X B and density of the fluid in this line (the continuous phase fluid if the light phase is dispersed) is p z . Eleva- pzLag tion of the point of PZrelative to the bottom of the column is La. (Pz - P l ) s t s t i c = (2) 8. y represents the vertical distance of some parbicle of fluid above a reference plane. It is further assumed that there is no net flow of fluid in the main column or in the pulse line. This assumption should be a fairly sound one, because superficial velocities of flow in extraction columns are generally small relative to velocities of the fluid bulk generated by pulsing. g. is the conversion factor from gravitational to absolute units. n is the number of screens in the column, and y is the fractional free cross-sectional area of the screens. I Static Head. Pressure difference in the main column due to static head is given by
(P: -
Pa)etatic
P1LlL-l = __ gc
(1) DISPLACEMENT
Figure 5.
ANGLE,
315
DEGREES
Velocity function
1.0
0.5
LI
LENGTH FROM THIS POINT TO COLUMN = La
N c
-0.5
PI
( a ) COLUMN AND PULSE TRANSFER PIPE
!b) PULSE GENERATOR DRIVE
-1.0
90
Figure 4.
lune 1955
Diagrammatic representation of equipment
135
iao 225 DISPLACEMENT ANGLE, DEGREES
Figure 6.
270
315
Acceleration function
INDUSTRIAL AND ENGINEERING CHEMISTRY
1161
ENGINEERING. DESIGN. AND PROCESS DEVELOPMENT 10
1
I 1 90
I 180
I
135
I 225
DISPLACEMENT
Figure 7.
Figure 8.
ANGLE,
I
2m
315
OEGREES
Friction function
Total pressure and components
145.3 CYCLES/ MIN 1/4 INCH AMPLITUDE /-
I
145 3 CYCLES/ MIN 5L 114 INCH AMPLITUDE 4
3
2
=6 'I
Q
a.
L
90
1
I
2 70 DISPLACEMENT ANGLE,
I80
360
0
J
450
OEGREES
Figure 9. Total pressure difference at 145.3 cycles per minute
1162
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 47, No. 6
PULSATION AND VIBRATION
Figure 1 2. Figure 1 1.
Sanborn direct-writing recorder
Statham low pressure differential transducer
for a screen of the same fractional free cross-sectional area it is 1 dY equal to - X Y dt Taking Co as 0.6, one can obtain for n screens
-.
The absolute value of one of the derivatives is indicated because the sign of ( P I
- Pa)friotion must
be the same as that of
z.
dY
The only friction effect of any significance in the pulse line is assumed to be due to contraction or expansion a t the connection between the pulse line and the column.
The sum of Equations 9 and 10 is Figure
Again treating Equations 9 and 10 as 1 and 2 were previously treated, (Power )friction *
2g,
[
s~(PZ-
~
~
)
(2) ~
~
t
~
l
where y represents pulse shaft movement. If motion of a particle of fluid in the column is desired, Equation 14 need merely be multiplied by h / R where h is amplitude in the column (one half of total distance traveled by the fluid particle). Thus for the column,
(13)
The sign of power indicates the direction of energy flow. Negative power means that the system is driving the pulser and positive power means that the pulser is driving the fluid. Cyclic Motion of Fluid. A frequently used pulse generator scheme is represented in Figure 4,b. A wheel of radius R turning a t constant angular velocity has a connecting rod of length L attached to a point on its periphery. The other end of the rod moves along a straight line which would pass through the center of the wheel. The motion of point q is related directly to motion in the column by a constant factor. Take as a reference point the position of p half way between its two extreme positions. June 1955
The position of p relative to the reference point is y, a function of the angle e, which is measured counterclockwise from the horizontal radius as shown in Figure 4,b. From the geometry of the system, y is related to e by
0.36~~
Total Power. The total pressure difference, P I -Pa,is given by adding Equations 1 , 5, and 9. The total pressure difference, Pz - Pa,is obtained by adding Equations 3, 7, and 11. The total instantaneous power that must be supplied at the point of Pp is given by Power =
13. Transducer, recorder, and several traces
where y represents liquid displacement in the column: the position of a liquid particle relative to its reference point which is halfway between the two extreme positions of the particle. The term under the radical can be written as a series by use of the binomial theorem, Combining this expression with the remainder of Equation 15 - 1 cos6
e
-
INDUSTRIAL AND ENGINEERING CHEMISTRY
7 c 0 s ~ 8-
(g)'
. . . . . . . . . .]
(16)
1163
ENGINEERING. DESIGN. AND PROCESS DEVELOPMENT L1 = 43.5 feet 22 12
LZ = - = 1.833 feet L8 = 0 n = 450 screen plates -1
= 0.40 free area of screens
R = 0.1212 L For the above value of
-
"I
L' dt
h ( 2 4 has been computed as a
functionof Oandplotted in Figure 5. Velocity for simple harmonic motion ( R / L = 0) has been plotted for comparison, and
""/ R/ at2
[-h(2~f)*] has been plotted as a function of e in Figure 6 for L = 0.1212and R / L = 0. The difference between the two cases is somewhat greater for acceleration than for velocity; thus i t would appear that including the correction for nonharmonic motion is worth while. Use of the first correction term alone was sufficient.
($)'($)'/[h2(2~f)2]has also been plotted in
R,fL
= 0.1212 and
(Pp -
(P, -
=
Po)atatio may
Pa)statio
0.
be computed from Equation 3 ,
[(50.1)(43.5) - 01 (32.12) = (32.12) 2180 pounds per square foot
This value is shown as a horizontal line, 1, on Figure 8 or 15.18 pounds per square inch. Equation 7 can be rewritten
Figure 14. Typical trace of pulse pressure wave obtained at bottom of pulse column From 50-foot pulse column
RIL
Figure 7 for
24 inches in diameter
The displacement angle, e, may be written in terms of frequency, f (or rotation rate of wheel), and time, t,
e
= 2Tfi
(17)
From Equations 16 and 17 it can be shown that
ir
+ R cos e sin e + ( 5 ) cos3 e sin e + cos'esin e + . . . . . ] (18) cos5 e sin e + 16 ( E )
= h(aTj) [cos
.-
s(E)
e
-
and dt2 4 sin2 0 ) -
( ~ ) ' c o s 4 0 (1 - 6 sin2 0 ) COSBe(l
-
1"6
();:
- 8sin28) - . . . .
.A
[19)
The case of simple harmonic motion (obtainable by use of a simple cam action) comes out of Equations 16, 18, and 19 if R / L approaches zero. I n the case of an eccentric and connecting rod herein considered, only one correction term is significant. Sample Calculations. In the test on the 2-foot diameter column containing a single fluid, kerosine, pressure was measured a t a point in the horizontal portion of the pulse line 22 inches from the column.
XI =
G
1/4 INCH AMPLITUDE
0 w
3.1416 sq. feet
= 1.77
PI = P Z =
50.1 pounds per cubic foot
h
0 25 = = 0.02082 foot 12
f
= -145'3 -
1164
18 95 9 CYCLES/MIN
E
60
-
I80
2.42 cycles per second
Figure 16.
450
270 360 DISPLACEMENT ANGLE, DEGREES
Total pressure difference at per minute
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
95.9
cycles
Vol. 47, No. 6
PULSATION AND VIBRATION
pi^ +
2)
=/
0.0338 inch, The total open area of the screen (uncorrected for weave characteristics) was about 40%. The pulse generator for the column consisted of a stainless steel 1 [ -h(2rf)‘] = - _ - [(50.1)(43.5) (50.1)(1.833)(1.77)] pulse piston 12 inches in diameter with four Graphitar seal rings 32.16 (U. S. Graphite Co.) plus one Graphitar wear ring installed in a [0.02082(2* 2.42)’l [ - h ( 2 ~ f ) ~ ] smooth-walled stainless steel cylinder 12 inches in diameter. Graphitar has excellent wear and lubricating qualities for this application. The piston was driven by an electric motor variable[ -h(2d?1 pounds Per square foot (Pz- P a ) i n e r t i a = - 382 speed unit through a variable eccentric drive head. The variablespeed unit provided a range of 60- to 200-cycles-per-minute pulse frequency and the variable eccentric drive head provided a 0- t o pounds per square inch. 2-inch maximum piston stroke-hence a 0- t o 0.5-inch maximum pulse travel per cycle in the column. A time-displacement’ trace be a sine Wave. of the piston movement Values from Figure 6 multiplied by -2.66 yield points plotted Instrumentaticn: The pressure wave sensing and recording as curve 2 of Figure 8. Equation 11 may be rewritten were accomplished by use of a Statham low pressure differential transducer (Figure 11) in conjunction with a Sanborn direct-writ1 n-~ (1 - y2) ing recorder (Figure 12). The pressure transducer is a strain (Pz - P a ) f F i c t i o n = gage-type unit, in which the pressure to be measured is applied 2g, 0.36~~ + to a bellows or diaphragm. The latter in turn actuates a standard four-element resistance bridge 450(1 - 0.16) based on the unbonded strain wire principle. Pres50,1 sure applied t o the bellows is translated into an exact) electrical equivalent by means of this full bridge transducer. This transducing element is claimed to (1.77 - 1)2(50.1)] [(0.02082)z(2,2.42)z] (2~f)z] be the lowest mechanical energy system of the strain gage type as no associated cantilever beams are required to be stressed with the strain-sensitive wires. An ac= 511 b p ( 2 ~ f ) zpounds ] per square feet curacy and linearity of 1% of full scale or better and a resolution of 0.1% of full scale are claimed for this method of translation. The unit used in this study had a natural frequency of 1300 cycles per second-over 1000 times the pulse frequencies [h2(2iif)z] pounds per square inch or 3.55 of normal interest. The Sanborn strain gage amplifier-recorder is a direct-writing Values from Figure 7 multiplied by 3.55 lead to curve 3 of vacuum tube recording system capable of reproducing on rectangular coordinates any phenomena involved in measurements of Figure 8. Curve 4 of Figure 8 is obtained by adding curves 1, 2, stress, strain, pressure, temperature, etc. The TT7riting arm with and 3. curve 5 is the experimental curve transcribed from the attached stylus is driven by a d’Arsonva1 moving coil galvanomrecorder chart. The disagreement between curves 4 and 5 i5 eter. A4Nichrome stylus ribbon is welded to the top of the arm, probably due largely to the assumption of uniform velocity throughout the column a t any instant. An attempt has been 24 made t,o obtain better agreement empirically by shifting curve 3 176 4 CYCLES/ MIN. 1/4 INCH AMPLITUDE relat’ive to curve 2. Results of this shift are shown for the case of 145.3 cycles per minute in Figure 9. As curve 3 is shifted to the left (designated as lag in the figures) the maximum (Pz - Pa)increases and the minimum value decreases. The best single fit of maximum and minimum points (magnitude fit, not displacement fit) appears to be a t a lag of approximately 10’. Power to the fluid a t the point of Pz may be computed from (Pz- Pa)curves, calculated or experimental, by Equation 13. (PZ
-
= -
Pa)inertia
1
-
sc
P 2 ~ 2
[h(2rf)21
d2Y
+
(2
[
’)’”1
(2) (f)
+
[Az
($) (%)i / (2;) (f) 1 / ~
~
(Power)tOt,l = 3.1416 (Pz - Pa)d y X dt
144 -
550
0.8225
=
2
(Pz-
where ( P , - Pa)iotal is in pounds per square inch.
Pa)totai H
P
2 can be ob690
Figure
June 1955
180
270
DISPLACEMENT
360
ANGLE, DEGREES
450
17. Total pressure difference at 176.5 cycles per minute
Experimental Equipment
The pulse column in which the pulse power input tests reported in this paper were made consisted of a tower 24 inches in inside diameter incorporating a 40-foot contacting section containing 450 20 X 20 mesh stainless steel screen plates on approximately l’/s-inch spacings. A bottom end section 24 inches in inside diameter accommodated various external connections including a horizontal pulse transfer pipe 18 inches in diameter. The top of the column consisted of a dome 35 inches in inside diameter, which was connected by a short truncated cone to the main column section and which accommodated various external connections. The system is simply illustrated in Figure 2. The 20 X 20 mesh screen plates were made of Type 304 stainless steel wire of 0.0162-inch diameter and with a screen opening of
I
1
WY
tained from Figure 5. Results of the power calculations based on curves 4 and 5 of Figure 8 are plotted in Figure 10 as “0 friction lag” and “experimental” curves, respectively. Other curves of Figure 10 were computed in the same manner from the other curves (different friction lags) of Figure 9. 2
0
= I E
w
Po0
I
-2 DISPLACEMENT
Figure 18.
ANGLE,
0
DEGREES
Total power at 67.4 cycles per minute
INDUSTRIAL AND ENGINEERING CHEMISTRY
1165
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT 8
'
EXPERII
C M114 CIC INCH L E SAMPLITUDE IMIN
1
I
180
Figure 19.
1764 CYCLES/MIN 1/4 INCH AMPLITUDE
I
270 DISPLACEMENT ANGLE, DEGREES
360
40 h
Total power at 95.9 cycles per minute Figure 20.
and the stylus is electrically heated. The stylus marks on a plastic-coated heat-sensitive, pressure-insensitive printed chart paper. The action of the heated stylus wiping over the paper as it is pulled across a knife edge results in the inkless rectangular coordinate tracings (see Figure 13) over a 5-cm. chart width. The paper speed for the unit used in this work was 25 mm. per second. By means of a microswitch contact adjacent to the pulser drive, an additional mark was made on the chart to indicate the end point of the piston upstroke, TDC in Figure 14. Liquid System. The liquid system for the power tests was simply kerosine. Later tests are expected to be made on a twophase system. Procedure. The column was filled with kerosine and this body of liquid was pulsed without either dispersing another, immiscible phase in the kerosine or providing any net flow through the tower. These simplifying conditions probably do not affect the pulse power requirements significantly, but they are expected to be checked in subsequent tests. The column was filled with kerosine through a bottom inlet until a liquid level was established in the top dome. The liquid was pulsed until no further gassing was noted a t the liquid surface and a constant kerosine leakage rate (about 50 cc. per minute) was obtained a t the pulse piston, denoting that air in the column had been flushed out. The pressure wave recorder was turned on and a series of traces was obtained for a range of frequencies from 67 to 176 cycles per minute, after the pulser had been in opeSation for 2 or 3 hours (see Figure 14).
Results I n the design of pulse columns knowledge of maximum and minimum pressures in the column and pulse line is important. Mechanically, the equipment must be designed to withstand maximum pressures. If the minimum pressures go lower than the vapor pressure of the fluid, cavitation will result and pulsing will become ineffective. Comparisons of calculated and experimental pressure differences for four different frequencies are shown in Figures 9, 15, 16, and 17. The friction lags giving best single fits of maximum and minimum points appear to be approximately as follows: Cycles/Rlin. 67 4 95 9 145.3 176 4
Friction Lag 40'
30'
10: 20
The trend is b y no means consistent; more experimental data need to be analyzed to learn whether the friction lag concept has any merit. However, the work to date indicates that best agreement is obtained with some friction lag. Power requirements are also obviously important in pulse column requirements. Comparisons of calculated and experimental power requirements for the four different frequencies studied are shown in Figures 10, 18, 19, 20. Because the pulse generator must be able to supply the maximum power requirement, this
1166
I
I
I
I
180
270
360
450
DISPLACEMENT ANGLE, DEGREES
Total power at 176.4 cycles per minute
value would appear to be the most important. The result of shifting the friction effect has little effect on the magnitude of maximum power and agreement of calculated values and experimental ones is good. Agreement between calculated and experimental values of minimum power requirements (or maximum power provided by fluid on pulser) is very poor for all cases of friction lag. I n the event that a pulser were to be designed equipped with a flywheel t o act as an energy reservoir, the power required to operate the system would be equal t o J(power)dt t
over one complete cycle. Thus instantaneous power over the whole cycle would have to be known accurately. Operation with a flywheel would cut down considerably on power requirement t o the drive, as power is negative over one half of the cycle. Theoretically the only power that would have to be supplied would be that to overcome friction. So far, flywheels have not been used extensively in conjunction with pulse generators.
Nomenclature Co = orifice coefficient
f g
a
= = = =
L
= = Lz = LB = n = R =
LI
P, = PI = PP
=
S i Sz
= = = = =
1 y p1 p~
e
y
= = =
frequency of pulse generator cycle, cycles per second acceleration due to gravity, feet per sec.2 conversion factor lb. mass-ft./lb. force-sec.2 amplitude of pulse motion in column, one half of total displacement distance, feet length of connecting rod on pulser drive, feet effective height of column, feet total length of pulse line from column to point of Pz,feet elevation of point of Ps above bottom of column, feet number of screen trays in column radius of pulse generator drive wheel, feet pressure a t top of column, pounds per square foot (pounds per square inch for special cases) pressure at bottom of column, pounds per square foot (pounds per square inch for special cases) pressure a t a point in pulse line, pounds per square foot (pounds per square inch for special cases) cross-sectional area of column, square feet cross-sectional area of pulse line, square feet time, seconds fractional free cross-sectional area of screens effective density of fluid in column, pounds per cubic foot density of fluid in pulse line, pounds per cubic foot displacement angle, degrees ( " ) linear displacement of pulser rod or liquid in column, f t .
Literature Cited (1) Sege, G., and Woodfield, F. W., Chem. Eng. Progr., 50, 396-402 (1954). (2) Weigandt, H. F., and Berg, R. L. van, Chem. Eng., 61, 183-8 (July 1954).
RECEIVED for review January 24, 1955.
INDUSTRIAL AND ENGINEERING CHEMISTRY
ACCEPTEDNIarch 31, 1055.
Vol. 47,No. 6
*
