ENGINEERING AND PROCESS DEVELOPMENT
Flow of liquids through Perforated-Plate liquid Extraction Towers ROBERT J. BUSSOLARI', SEYMOUR SCHIFF2,
AND
ROBERT E. TREYBAL
New York University, New York 53, N. Y.
S
+
4
'
IEVE-tray or perforated plate towers for countercurrent liquid extraction operations have now become well established as devices capable of high flow capacities and extraction efficiency (8). This paper presents d a t a leading t o a design procedure for calculating some of the conditions t h a t limit flow rates through such equipment. Consider a perforated plate extraction tower arranged for operation with light liquid dispersed, of conventional design such &s that used in this study (Figure 1). The heavy liquid flows generally downward through such a tower, horizontally across each tray, and through t h e downspouts from tray t o tray. The insoluble light liquid issues from the perforations in each tray in the form of bubbles or jets, rises through the heavy liquid, and coalesce8 into a layer of light liquid which accumulates immediately beneath each tray. For cases where the heavy liquid is dispersed, the tower of Figure 1 is turned upside down; the heavy liquid collects upon each tray and flows downward through the perforations, while t h e light liquid flows u p the passages from tray t o tray and across each tray. This discussion is presented with the former arrangement in mind, but i t is directly applicable t o the latter in all respects with only obvious changes in notation. The vertical thickness of the light liquid collecting beneath each tray (in the case of light liquid dispersed) will be sufficient t o provide the necessary buoyant force t o overcome the various resistances t o flow experienced by the liquids in passing each tray. The thickness will increase with flow rate of eachliquid, as the resistances t o flow are thereby increased. It is necessary to be able t o compute the thickness t o be expected in order t o be certain that ( a )the remaining vertical distance between the undersurface of the light liquid layer (interface) and the tray below is sufficient for flow of the heavy liquid, and sufficient for formation and rise of the bubbles of light liquid issuing from the perforations; and ( b ) the downspout extends adequately below the interface, thereby ensuring t h a t light liquid will not enter the downspout. This study was planned t o establish a method of making this computation. Only three previous investigations of any magnitude into these matters have been published (3, 9, 1 1 ) ; two of these have left unanswered at least some questions respecting the influence of interfacial tension on the thickness of the liquid layer, and the other was done in very small equipment.
The sides were made of flat, transparent Plexiglas, a n acrylic plastic, cemented together with a glue of Plexiglas dissolved i n glacial acetic acid, The plates were of 0.25-inch-thick brass, and the several plates and sections were held together i n leakproof fashion by tie rods extending from the top t o the bottom of the tower, with cork gaskets 0.125 inch thick. Two complete plates were provided a t a spacing of 6 inches, and the top and bottom end sections were 1 foot tall. The downspouts were made by soldering 0.0667-inch-thick brass plates extending the full width of the tower t o each perforated plate and sealing them t o the plastic tower walls with the plastic glue. Two downspout widths were used. The perforations in the plates were drilled on a pattern of equilateral triangular centers, 0.5 inch apart as in Figure 1. Only alternate rows were drilled for the measurements of series 1through 6, every row for series 7 t o 9. The liquids were pumped from their storage vessels and entered the tower to flow countercurrently. Light liquid entered at the bottom through a perforated pipe to distribute the liquid evenly under the lower plate, while heavy liquid was introduced into a downspout before entering the top tray. The top tray was thus
IOWNSPOUT L R E S 8,9
XRlES 1-7
I
I/ * HOLE
PATTERN SERIES I - 6
HOLE PATTERN SERIES ?-9
PLASTIC,
SIDES
?TIE-ROD
\
HOHIZONTAL SECTION
0.05-IN.
Experimental Work Provides Data on Operating Conditions
The tower used in this work was rectangular in cross section, and the essential dimensions are shown in Figure 1. 1 2
Present address, E. I. du Pont de Nemoura & Co., Wilmington, Del. Present address, National Lead Co., New York, N. Y .
November 1953
VERTICAL SECTION
Figure 1.
Perforated Plate Tower
INDUSTRIAL AND ENGINEERING CHEMISTRY
2413
ENGINEERING AND PROCESS DEVELOPMENT osine does not preferentially wet brass and did not. flow through the perforations until a sufficient depth had accumulated Series 1 2 3 4 5 6 7 8 9 below the plate to overcome interfacial Perforations 0 . 1 2 8 0 , 1 2 8 0 . 1 2 8 0 . 1 2 8 0 . 1 2 8 0 . 1 2 8 0 . 1 2 8 0.128 0,180 Diameter, inch tension. At lox velocities, kerosine 216 216 216 216 216 216 423 423 423 hTumber passed through some of the perforations, Downspout width, inch 1 . 3 7 5 1 . 3 7 5 1 . 3 7 5 1 . 3 7 5 1 . 3 7 5 1 . 3 7 5 1 . 3 7 5 0 750 0 . 7 5 0 t,he bubbles forming directly at, the surDispersed liquid face of the plate. d s the rate of flow Viscosity cp. 1.489 1.489 1.489 1.489 1.435 1 4 3 5 1 4 3 5 1.435 1.436 50.4 50.4 51.1 51.1 51.1 511 51.1 50.4 50.4 Density, ib./cu. foot vias increased, more and more perforaContinuous liquid tions passed kerosine until event,ua.lljI .20 1.20 1.20 2.58 7 . 6 1 0.801 0.801 0.801 Viscosity c p . 1.20 62.4 62.4 62.4 62.4 70.0 75.6 6 2 . 0 6 2 . 0 62.0 Density, ib./eu. foot all operated. At still higher velocities 22.6 38.1 38.0 32.7 33.2 40.5 4 0 . 5 40 5 Interfacial tension, dynes/cm. 41.2 the bubbles of kerosine did not form Range of flow rates directly a t the surface of the plate, but 0-60 0-107 0-89 0-101 0-101 0-114 0-ZG 0-78 0-106 Vdidiap feet/hour instead jets of kerosine extended :is 0 0-117 0-120 0-161 0-137 0-141 0-191 0 0-131 T7c0n;, feet/hour much as 2 inches from the perforations upward into the continuous liquid, and these bloke into,bubbles. This Eondition free of entrance effects. The heavy liquid leaving a t the bottom is later called streaming. Coalescence of the bubbles into a clear flowed through a n adjustable leg which permitted control of the liquid layer beneath the plate took place over a vertical depth of position of the principal interface in the top section of the t,ower, from 0.2 t o 0.5 inch a t low velorities and as much as 2 inches a t and then t o the storage vessel. The light liquid left the top of high velocities. This made for some uncertainty as t o the actual the tower to flow directly to storage. The exit lines were of 2thickness of the layer, but the lowest level of the mass of coinch pipe, amply large in order t o ensure that these would not limit the capacity of the tower. Orifices weye used in the inlet alesciug bubbles was assumed, €or practical purposes, to be t h e lines to set flow rates and to ensure steadiness of flow during position of the inteiface. runs, but the final rate measurements for each run were made The general behavior seemed t o he independent of the flow rate by diverting the exit liquids into tared receivers for a measured of continuous liquid, except that a t inrreasingly high rates of the time and weighing the collect~edliquid. latter the jets of kerosine were broken off into bubbles at (lisThe thickness of the light liquid layer was measured with the tances nearer the plat? from which theg- rose, waves of increasing help of 20-to-the-inch graph paper strips glued to the outside of the tower below the top plate. Several measwenwits a t various amplitude developed i n the interface which made its location tiif: positions on the t o r e r periphery were averaged. ficult, and eventually bubbles of kerosine were carried t o the The light liquid was kerosine, and t,wo batches of slightly difdownspout to be recirculated around the plate. ferent characteristics were used. The heavy liquid was either water or aqueous solutions of cane sugar of various concentrations. The interfacial tension was varied by adding minute Dispersed and Continuous liquids Contribute amounts of Alkaterge C: to the kerosine, which did not affect its Independently to Depth of liquid on Plates density or viscosity. Density and viscosity of the liquids were measured in conventional fashion; interfacial tension was measThe observations made indicate that the depth of light liquid ured by a drop-volume technique ( 4 ) . below the top surface oi the plate, h, is made up of the separate effects for the dispersed and continuous liquids taken independTable I lists the circumstances for the several series of measure ently: ments.
Table I.
Systems Studied and Operating Conditions
The behavior of the light dispersed liquid in flowing through the perforations was similar tlothat previously observed ( 5 ) . Ker-
=
hdiap
-t homt
(I?
Dispersed Liquid Effects. Thrse were determined bv oDeratinn v it11 zero flow rate of the continuous liquid. Typical of the data for siich conditions are those shown in Figure 2. The "head" necessary for flow throuyli the perforations is that required t o overconie interfacial tension, h,, w hicli predominates a t low velocities, and orifice effects, ho,which predominate at high velocities: "
4.0
2.0
1.0
I
I
0.8 kdiep
0.6 v)
Y
fho
(2)
The depth of diqiersed liquid c!oi'responding to h o is given by the standard orifice equation,
0.4
,F T / S E C . Depth of Liquid for Stationary Continuous Liquid U,
Figure 2. 2414
= hr
where COis the usual orifice coefficieiit. At high rates of flow, the data of series 1 through 4, Figure 2, show that interfacial tension effects are entirely unimportant, and that the data follow Equation 3 n i t h CO = 0.0'7 (line AB, Figure 2 ) . This is the value observed before ( 3 ,
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 45, No. 11
ENGINEERING AND PROCESS DEVELOPMENT 9) at high rates of flow in extraction towers, and is substantially the same as t h a t for flow of air through a perforated plate (7).
h,
3.0
20 "STREAMING" BEGINS
LO 0.8 0.6
0.4
Uo
Figure 3.
,F V S E C .
Depth of Liquid for Stationary Continuous Liquid
T h e excess pressure at a n y time owing t o surface tension in a spherical bubble forming at a small perforation, expressed in terms of the depth of light liquid below the plate, is ( 1 )
h
w
- -d4a Ap
(4)
where d is the instantaneous diameter of the bubble. If the perforation diameter &, is substituted in Equation 4, the value of hq so calculated is t h a t required t o initiate flow, but at finite rates of flow the bubble diameter is appropriate. The bubbles form intermittently and at different times from the various perforations, so that a time-average bubble diameter is required. This may be estimated approximately in the manner of Eversole et al. (2). Assuming that the volume of a bubble increases from zero 4: t o its final value linearly with time when the rate of liquid flow is constant, and t h a t the bubble is always spherical,
=
6u -
(7)
dbAp
This is, of course, a much simplified picture of the situation, as the bubbles are not spherical; neither does the interfacial surface exposed a t a perforation vary exactly in the manner assumed. Nevertheless within the accuracy of the data and the limitations of the prediction of bubble diameter i t describes the results. Figure 3 shows the data for series 4,5 , and 6, representing variations in fluid properties which most greatly influence bubble diameter. The curves marked h , were computed by means of Equation 7 , using the previously developed correlation for estimating bubble diameter (6). At values of U Oin excess of 0.33 foot per second (10 cm. per second), the bubble diameters are not uniform ( 5 ) ,but the calculated h, follows the data within the limits of error in locating the interface for values of Uo up t o 0.5 foot per second, where streaming begins. The lines AB on this figure correspond t o Equation 3 with the previously determined orifice coefficient. For these series, the orifice effect IS unimportant up t o UOof 0.5 foot per second. It is therefore suggested t h a t hdiap be computed by Equations 2, 3, and 7 up to U Ocorresponding t o streaming, by Equation 7 a t higher velocities, and smoothing the juncture of the two curves on logarithmic plots such a s Figure 3 by free-hand curves. This was done for all thc data, arid the errors arc plotted in Figure 4. They are well within the limits of err& in locating the interface. This is believed t o be an improvement over the previously suggested alternatives (3, 9, 11), which describe all or part of kdlsp by means of varying orifice coefficients, since these will require extensive complications of coefficients to account for the diverse bubbling characteristics of different liquid systems and perforation diameters. It is probably for this reason that the orifice coefficients of two of the previous investigations (3, 9 ) arc so considerably a t variance at low ratcs of flow of dispersed liquid. Continuous Liquid. The depth of dispersed liquid required t o overcome the frictional effects of flow of continuous liquid, hoont,can be considered as kont
=
hc
f /LE
+ h~ $.
(8)
hF
where hc and h~ are, respectively, the contraction and expansion losses as the liquid enters and leaves the downspout, and h B is the loss owing t o changes in direction. In this investigation k p , the friction in the downspout, was entirely negligible, as it wilI ordinarily he. The values of hoont were determined by subtracting from the observed h the values a t zero rate for the continuous liquid. The differences for series 8 and 9 were most consistent and these n e r e used to establish h ~ .The velocitj- in the downspout for moqt of these r u m corresponds t o turbulent flow, and the contraction and
.$
(w) 0
e! = da
1/3
(5)
where d is the bubble diameter a t time e and da the uItimate diameter a t the time of breaking away from the perforation, Ob. The time-average value of h , is then
November 1953
0.01 Figure
0.02
4.
0.04 0.06
0.1 0.2 l&, F T / S E C .
0.4
0.6
1.0
2
Comparison of Computed and Observed Values of hdirp
INDUSTRIAL AND ENGINEERING CHEMISTRY
2415
ENGINEERING AND PROCESS DEVELOPMENT 2.c
Table II.
Flow Rates, Gal./Min. hobavd, hcaicd. hobsvd - h c a l e d , Butanol Water Inch Inch Inch Series 3. 1.5-Inch Plate Spacing, Perforation Area = 10.5% of Tower
I. 0
2.98 2.0 0.33 0.267 +0.063 1.98 0.375 0.290 f0.085 2.35 3.00 Flooded 0.479 ..... 2.05 2.50 0.25 0.359 -0.109 2.60 2.50 0 38 0.359 -0.021 3.00 2.50 0.25 0.362 -0.112 Series 5 . 2.5-Inch Plate Spacing, Perforation Area = 15.0% of Tow-er 1.95 1.95 0.104 0.255 -0.151 2 0 0.323 0.267 3.0 f0.056 4.0 2.0 0 389 0 314 +0.075 5.0 2.0 0.729 0.302 f0.427 2.0 1.0 0.063 0 115 -0.052 2.0 2.5 0.340 0 379 -0.039 1.9.5 3.0 0.483 0.510 -0.027 1.95 3.6 0.883 0.675 f0.208
0.8
4 00
0.6
o)
xI
-
0.4
m
-e
5 I1
Comparison of Observed and Computed Data of Tepe and Woods (77)
0.2
-2
‘u c 1.s P -r
-e
-
0.1
0.08 0.06
0.04
‘R~,=2000 0.c3~.~
1 0.2
4000
0.4
0.6
0.8 I
expansion losses were calculated by means of the standard expressions for these quantities:
where K is a quantity dependent upon the ratio of cross-sectional areas of downspout and tower (8). The use of St t o establish the lower velocity is somewhat arbitrary, but use of any other reasonable value such as the cross section between and perpendicular t o the plates does not influence the sum of hc and h~ significantly. The sums of hc and h~ were subtracted from hoont. The residuals, ha, are plotted in Figure 5 , where they are seen t o be very consistent despite their small size. The equation of line CD is
U, ,FTJSEC.
Figure 6.
Comparison of Computed and Observed Values
of corresponding to 2.93/2 or 1.47 “velocity heads” for each abrupt change in direction on entering and leaving the downspout. This is a little larger than the losses t o be expected for aright-angle bend in a closed duct a t fully developed turbulent flow, which are variously stated t o be from 1.1 (10) t o 1.3 (8) velocity heads. This may be due t o the fact t h a t Equations 9 and 10 are really applicable only at fully developed turbulence, and the losses are indefinitely larger for laminar flow. For most of the remaining runs, flow through the downspouts was laminar. The losses comprising hcont as found by the differences of h and hdisp for these are plotted in Figure 6, with the inclusion of A p / p c in the ordinate t o account for the various den, sities in these series. Line EF represents the sum of hc, h ~and hg as computed by Equations 9 through 11. These data are not 2416
hcont
so consistent as those of series 8 and 9, and it is evident that the points are largely above the line. This may be the result of the laminar flow prevailing. Xevertheless the maximum discrepancy between the plotted points and line EF, which occurs for one point a t nearly the highest continuous liquid rate, represents a 0.54-inch error in the light liquid depth, in turn less than the amplitude of the waves in the interface a t these velocities. Eight pc.1 cent of the points represent errors in hcont between 0.3 and 0.4 inch (all at conditions corresponding t o large interface Traves), 9% between 0.2 and 0.3 inch, 23% between 0.1 and 0.2 inch, and 60% less than 0.1 inch. It is concluded therefore that Equations 8 through 11 satisfactorily represent the effects of the continuous liquid flow. d s an example of the ability of these expressions to predict be-
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 45, No. l l
ENGINEERING AND PROCESS DEVELOPMENT havior under conditions very far removed from those prevailing in this study, they were used t o compute some of the results of Tepe and Woods (11) (Table 11). For these measurements a circular tower 8.5 inches in diameter was employed, with very small plate spacings, and 0.1 1-inch perforations. The domnspouts were circular, 2 inches in diameter. The dispersed liquid was isobutyl alcohol, and the continuous liquid was water, both mutually saturated solutions, u i t h u = 2.5 dynes per cm. With two exceptions the data are predicted very well.
vdisp
= superficial velocity of dispersed liquid, based on Sc,
6
= differential operator = time, seconds
feet per hour
8 eb
= time for bubble formation, seconds
pc PD
= density of continuous liquid, pounds per cubic foot = density of dispersed liquid, pounds per cubic foot
Ap
= difference i n liquid densities, pounds per cubic foot
U
e
= interfacial tension, pounds per foot ( = dynes per cm.
6.85 x 10-5).
x
Literature Cited Nomenclature 4
CO
= = = = = =
d
db
do gc *
h
hs = he = hoont = hdiaD
=
h~ hp ho h,
=
K Reo SO SO St
UD UO
= = = = = = = =
= =
Voont =
(1) Adam, N. K., “Physics and Chemistry of Surfaces,” p. 11, Ox-
orifice coefficient, dimensionless diameter of bubble a t time e, feet ultimate bubble diameter, feet perforation diameter, feet 32.2 Ib. mass feet/lb. force sec.2 total thickness of coalesced dispersed liquid below top surface of plate, feet thickness of layer owing t o change of flow direction, feet thickness of layer owing t o contraction, feet thickness of layer owing to continuous liquid flow, feet thickness of layer owing to dispersed liquid flow, feet thickness of layer owing to expansion, feet thickness of layer owing t o friction in downspout, feet thickness of layer owing to orifice effect, feet thickness of layer owing to interfacial tension, feet contraction coefficient, dimensionless Reynolds number for flow in downspout, dimensionless cross-sectional area of downspout, square feet area of all perforations, square feet cross-sectional area of tower, square feet superficial velocity in downspout, based on SD,feet per second superficial velocity through perforations, based on SO, feet per second su erficial velocity of continuous liquid, based on St, feet per hour
ford. Eneland. Clarendon Press. 1938. (2) Eversole, W.G., Wagner, G. H., and Stackhouse, E., IND. ENO. CHEM., 33,1459 (1941). (3) Fujita, S., Tanizawa, E., and Chung-gyu, K., Chem. Eng. (Jaguan),17, hTo.3, 111 (1953). (4) Harkins, W. D.. in “Physical Methods of Organic Chemistry.” Vol. 1, A. Weissberper, ed., New York, In6rscience Publishers, 1945. ( 5 ) Hayworth, C. B., and Treybal, R. E., IND.ENG.CHEW,42, 1174 (1950). (6) Mayfield, F. D., and Church, W. L., Ibid., 44, 2253 (1952). (7) Mayfield, F. D., Church, W. L., Green, A. C., Lee, D. C., and Rassmussen, R. W., Ibid.,44,2238 (1952). (8) Perry, J. H., ed., “Chemical Engineers’ Handbook,” 3rd ed.. pp. 388-90, New York, McGraw-Hill Book Co., 1950. (9) Pyle, C., Colburn, A. P., and Duffey, H. R., IND. ENG.C H ~ M . , 42,1042 (1950). (10) Rouse, H., ed., “Engineering Hydraulics,” p. 422, New York, John Wiley & Sons, 1950. (11) Tepe, J. B., and Woods, W. K., Atomic Energy Commission, AECD-2864 (1943). RECEIYED for review May 12, 1953. ACCEPTEDJuly 31, 1953. An adaptation of the theses of R. J. Bussolari and Seymour Schiff, submitted in partial fulfillment of the requirements for the degree of M.Ch.E. at New York University.
Semiempirical Equation of Electrostatic Precipitation ERIC A. WALKER, Pennsylvania Stafe College, Stafe College, Pa. JOHN E. COOLIDGE, Borg- Warner Central Research Laboratory, Bellwood,
w
T
HE design of electrostatic precipitators for the separation of dust particles must, even after more than 40 years of com-
mercial experience, still be classed as an art. The majority of the large electrostatic precipitators for cleaning gas with heavy dust loadings have, in this county, been made by three companies. Each has gradually built up a body of design data as precipitators with larger capacities, higher dust loadings, shorter influence time, etc., have been designed and constructed. New ground has been broken by extrapolating from tested units and occasionally an uncertain but usually successful step has been taken from one type of aerosol t o another. European companies have concentrated on smaller and usually more efficient precipitators; and there have been some communication and transfer of design data between European and American manufacturers. However, t o step out and t r y t o precipitate entirely new aerosols at different dust loadings has always been fraught with danger; and, even when it has been thought t h a t conditions were
November 1953
111.
well understood and the solution was straightforward, “queer resultsJ’have occasionally been obtained, requiring the use of inelegant procedures, much like using rubber gloves as a cure for leaking fountain pens. A thorough study of the field, going more into the basic aspects than is usually done by design engineers, and more into design and practice than the theoretical investigator usually touches, is now in order. Such a program has been undertaken at the Pennsylvania State College with four main objectives: (1) t o survey the available knowledge, both theoretical and operational; ( 2 ) t o collect operational d a t a on as many existing commercial installations as possible; (3) t o make a laboratory study of the more fundamental processes involved in electrostatic precipitation; and (4) t o study the possibility of extrapolating, from small scale laboratory operation t o full scale commercial precipitators. T h e results of the literature survey, along with some initial results of the laboratory study, were reported in a previous paper (6). The
INDUSTRIAL AND ENGINEERING CHEMISTRY
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