ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT
Continuous Settling and Thickenin E . W . C O M I N G S ' , C. E. P R U I S S P ,A N D C. D E B O R D ~ P U R D U E U N I V E R S I T Y , W E S T LAFAYETTE, I N D . , A N D U N I V E R S I T Y O F ILLINOIS,U R B A N A . ILL.
Borosilicate glass cylinders, 3 inches a n d 8 inches in diameter, a n d a copper sheet cylinder, 14 inches in diameter, were operated continuously, a n d t h e l i m i t i n g conditions of sedimentat i o n a n d t h i c k e n i n g were determined. T h e slurries were made f r o m multisized particles of a l u m i n u m oxide, glass, c a l c i u m carbonate, a n d t w o clays in water. T h e mechanism of cont i n u o u s sedimentation was investigated t o explain t h e behavior observed in experimental thickeners. T h e f o u r zones observed when solids settle in a c o n t i n u o u s thickener are described. T h e settling capacity f o r a specified c l a r i t y of overflow isdetermined by t h e rate a t w h i c h solids w i l l settle t h r o u g h one of these zones. B y extending t h e basic assumptions of Stokes, a general expression f o r s e t t l i n g nonflocculent slurries under hindered settling cond i t i o n s is developed a n d used t o calculate t h e m a x i m u m settling capacity f r o m measured settling rates a n d s l u r r y properties. T h e m e t h o d provides a qualitative explanation f o r t h e settling of flocculent slurries. T w o experimental u n i t s have been operated w i t h slurries of t h r e e materials t o determine t h e effects of d e p t h of compression zone, t i m e of detention in t h e compression zone, a n d rake action o n t h e underflow concentration. All three of these variables are shown t o be of importance. B a t c h settling tests w i t h a n d w i t h o u t slow s t i r r i n g indicate t h a t t h e mechanism of s e t t l i n g in these tests m a y differ appreciably in t h e t w o cases. These results indicate t h a t published procedures f o r t h e design of thickeners based on batch settling tests are empirical, a n d t h e i r use should be associated w i t h extensive experience in t h e a r t .
T
HE batch sett'ling of a suspension of solid particles has been
described by Coe and Clevenger (6) and by Comings ( 7 ) . When the suspension is placed in a vertical glass cylinder, and t,he per cent solid is above a minimum value, a dist,inct line forins near the upper surface. The liquid above this line is clear, and the liquid below contains a per cent solids near that of the suspension a t the start of sett'ling. The solid particles settle to the bottom and form a dense layer of increasing depth. The solid, settling through the cylinder, displaces 11 ater which rises. When coarse sands are present these settle rapidly, but the major part of t,he solid settles as a coherent floc. In a continuous thickener the clear liquid at the top overflows, while the dense layer is pumped from the bot,tom. The feed slurry is introduced to a feed n-ell in the center, as shoivn in Figure 1, and discharges into the thickener a t a level some distance below the liquid surface. The behavior of the feed a t this point depends on the design of t'he feed well. The concentrated slurry on the bottom is moved gently to a central discharge by a rake on a radial arm. The arm nioves slowly around the tank. The rake increases the per cent solids in the underflow slurry. It disturbs archlike structures of solid particles and permits these t o collapse. The a-eight of solid above squeezes out the Riater. The thickener may be divided into four horizontal zones one above the other ( 7 ) . Zone 1 is the region through which the rake moves and is the zone of rake action. Zone 2 is above this and extends to the top of the denser layer of solid particles. Zones 1and 2 comprise the compression zone. The per cent solids increases with the distance down from the top of this zone. Zone 3 extends from the top of the compression zone to t,he level where the feed is introduced a t the bottom of the feed well. The feed well in all the experimental thickeners used in this invest,igation permitted dilution of the feed slurry. The well was designed
so that discharge of diluted feed caused a minimum disturbance. The solids in the feed set,tle through zone 3 to the compression zone. Zone 4 extends from the feed level t o the overflow level and is the clarification zone. During steady state operation the larger part of the liquid in the feed rises through the clarification zone and overflows. The rest of the liquid and all the solid move doivnmrd and arc diw-, charged through the bot,tom. Once established, the concentration gradient down through zones 3, 2, and 1 remain fixed and no liquid is displaced upivard from these zones. The only net upward flow occurs in zone 4. Concentration gradients in a radial direction are small. This is evident since a variation in density at a given level would result, in hydroat,atic pressure gradients in a radial direction. These gradients n-ould cause a flow that would equalize the concentration at that level. The concentration in zone 3, the sedimentation zone, is nearly constant with vertical distance. The concentration in this zone depends on the rate a t nrhich solids are introduced in the feed. At low rates of feed the solid settles readily, and the concentration in zone 3 is very lorn. When the feed rate is increased and approaches the settling capacity of this zone, the concentration rises to a definite value, and this concentration is maintained as the feed rate is increased. Solids fed in excess of the settling capacity leave in the overflow. Continuous thickeners are nov designed from batch settling data and from empirical rules and experience ( 1 , 4, fi). While theae methods satisfy those with considerable expericncc in the art, they do not interpret t,he procees eo it is generally undcist,ood. Several series of experiments were carried out to obstve the behavior in the conipression and settling zones and to relate t,he behavior to the controlling factors. COMPRESSION ZONE
Present address, Purdue University. Present address, Engineering Department, Solvay Process Division, Allied ChemiCal & Dye Gorp., Syracuse, N. Y . a Present address, The Dow Co., Midland, hlich. 1 8
1164
The compression zones presented several problems:
1. Is the underflow concentration appreciably affected by the
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 46, No. 6
FLOW THROUGH POROUS MEDIA action of the rake? What is the effect of increasing the depth of the rake action zone? 2. I n addition to the action of the rake, two other factors were thought to be important in determining the underflow concentration. According to one concept water is pressed from the lower layers by the Ryeight of the solid above. (The weight of the water is balanced hydrostatically and has no compressing effect.) The concentration a t any layer, according to this concept, quickly reaches equilibrium and is determined by the force gradient acting on it. A second concept proposes that the weight of the solid in each layer is sufficient to squeeze out the water. The resistance to flow through the interstices between the solid particles controls the flow of water from the layer. The concentration is then determined by the time available for this flow to occur. This is the time of detention in the compression zones. 3. Since all the earlier measurements of concentration distribution were made on ralcium carbonate slurry, similar information was desired on other solids. 4. Do the previous results apply to thickeners of larger diameter. The solutions of these prokilems are discussed but not in the order listed above. A 7.62-inch diameter by 4-ft. high vertical glass thickener was used, This has already been described ( 7 ) . It was equipped with rotary-type slurry pumps made of rubber tubing, a feed ring, overflow weir, and a rake. Samples were removed from several points a t different levels and analyzed for per cent solids. Calcium carbonate slurry was thickened to determine the effect of solid detention time in zones 1 and 2 on the underflow concentration. Three runs were made (11) with the same depth of compression zone but with different feed and underflow rates. By this means the solid was held in the compression zone for 1500, 2650, and 4800 minutes. The under-flow concentration in these three runs was 340, 429, and 512 grams per liter. This variation in underflow concentration may be attributed to the difference in detention time since the depth of the compression zone was the same in each case. The concentration versus height in the compression zone curvet; for these three runs are shown in Figure 2. FEED
WELL,
CLARIFICATION
J
OVERFIBW
FEED
\
ZONE I
SETTLING
UPPER
I
ZONE
COMPRESSION
ZONE
3
. -
I
e
The data from 12 runs are listed in Table I. These have been plotted in Figure 3 as depth of compression zone versus detection time a t several values of the feed rate. The same data are shown in Figure 4 as underflow concentration versus depth of the compression zone. The lines representing constant detention time and constant feed rate are also shown in this figure. The measurements are not of a high order of consistency, and this makes the position of these lines somewhat uncertain. Nevertheless,
Or
CONCENTRATION
OF CA GO3
GRAMS/ LITER
Figure2. Effect of Time Detention i n Compression Zone on Underflow Concentration of Calcium Carbonate
with the depth of the compression zone constant the underflow eoncentration increases as the time of detention increases. On the other hand, for a constant detention time, the underflow concentration decreases as the depth of the compression zone increases. This latter result was not expected since it was anticipated that the added weight of solid in the greater depths of compression zone would squeeze out more water in a given time. The added solid also increases resistance to the flow of water from the greater depth of solid, and a greater retention time is necessary because of the increased resistance. At a given feed rate, both increased depth of compression zone and increased time of detention are necessary to attain higher concentrations in the underflow. However, any given underflow concentration is attained fastest by using a shallow compression zone depth, but the amount of slurry that can be thickened is less for a given thickener area. Greater depths require greater detention times. As an example, a feed rate of 40 grams per minute produces an underflow concentration of 400 grams per liter with a 10-inch compression zone. If the underflow concentration depended only on the detention time, it would be possible, approximately, to increase the feed rate to 50 grams per minute and the height to 16 inches. The underflow concentration should remain the same. However, Figure 4 shows that the height must be increased to 26 inches and the time of detention doubled to maintain an underflow concentration of 400 grams per liter. A slurry prepared with 45 grams of Mississippi pot clay and 1.5 grams of aluminum sulfate per kilogram of slurry was thickened in the 7.62-inch diameter glass thickener. This clay had a finer particle size than the calcium carbonate used previously and settled more slowly. It was expected to be more compressible. The feed rate was constant a t about 15 grams per minute, and the Underflow rate was adjusted to obtain compression zone depths of 15, 30, and 45 inches. Five runs were made (IS) as shown in Table 11. The same general shape of concentration
a I
RAKE
COMPRESSION
PCTION
i
UNDERFLOW
Figure 1.
ZONE
i
REVOLVING
RAKE
Four Zones i n Continuous Thickener
Other runs ( 3 , 9 ) were made to dettrmine the effect of variation in the depth of the compression zone when the time of detention is held constant. This was more difficult since there was no means for controlling the detent~ontime at a fixed value and varying the depth of the compression zone. The detention time is determined from the concentration versus height curve in the compression zone after the run has been completed and after samples from several levels h w e been analyzed. Detention time = area under curve, C us. h rate of solids entering compression zone June 1954
_ - 4d2
LhCCdh
7r
F CJ
(18)
INDUSTRIAL AND ENGINEERING CHEMISTRY
1165
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT versus height in the compression zone curve was found. The results from three of these runs are shown in Figure 5 . The thickening effect of the rake is evident in the lower few inches, and the concentration of the underflow increases with depth of the compression zone. C U W CU(B0IIATE CONSTANT FEED RATES
Figure 9. The concentration increases rapidly with depth near the top of the compression zone and increases rapidly again near the bottom of the thickener. The increase near the bottom cannot be attributed to the action of the rake since the pickets have been effective throughout the compression zone. This increase is attributed to the larger particles, present in this and not in the other slurries, which settle through the rest of the slurry and accumulate a t the bottom where they raise the solids concentration. No effect was observed because of the nearly twofold increase in diameter. S E T T L I N G ZONE
The solids entering the compression zone pass through the settling zone or zone 3. Bond ( 5 ) states
-
0 COMINGS
4 - GRlFFlTH 0
0
1000
2000 TOTAL TIME
Figure 3.
3000
-
DEBORD EELTER
4000
5000
OF DETENTION I N MINUTES
Detention T i m e Versus Compression Zone Depth
A commeicial size of thickener was not available for testing. A thickener with a diameter somewhat larger than that previ-
When a suspension of finely divided solid particles in water: is allowed partially t o settle in a beaker. and a fresh pulp suspension is added to the supernatant water from a pipet, it is observed that the new feed flows downward in a channel, or stream, through the water, and does not spread out appreciably until it enters a layer of pulp of approximately its own specific gravity. The entering stream flows as a heavier liquid would flow- in the water, and there is little separation of the solid particles in the feed until after the pulp level has been reached.
-
ously used was built with a deep zone of rake action. It consisted of a copper sheet tank 14 inches in diameter and 60 inches high, equipped with long narrow glass rrindows placed vertically. 40 There m-ere three of these windows extending the length of the tank. The tank was provided with a feed ring, overflow weir a t the top, and a picket-type rake. This rake is shown in Figure 6. 30 It consists of a row of blades across one diameter a t the bottom 0 for moving the thickened solids at the bottom to the cential Y eo discharge. Above this is an arrangement of lengths of angle iron. These revolve slowly through the compression zone and serve t o prevent the thickening solids from forming a network 0 of arches with a low concentration of solids. The complete apparatus is shown in Figure 7 and consists of the thickenei in the 0 center, the feed and discharge rubber tube pumps on the floor, ROO 300 400 50 0 UhiDERFLOW CONCENTRATION (GRLYS / L I T E R ) the agitated feed tank on the right, and the tank to receive the underflow streams on the left. Figure 4. Underflow Concentration as Function of Mississippi pot clay and a diaspore clay were used to prepare Compression Zone Depth When Thickening Calcium slurrys for thickening in this apparatus. The diaspore clay Carbonate Slurry was more granular, contained large particles in a range of sizes, and settled more rapidly than the calcium carbonate of the MisThis type behavior was not observed in these experiments, sissippi pot clay. Five runs (8, 19) were made on the Mississippi possibly because the feed was introduced in a feed well or on a pot clay and the conditions for these runs are listed in Table 111. feed plate which stopped its downward velocity. The slurry In Figure 8 three of these runs are shown compared with two discharging from the bottom of the feed well spread out uniformly runs in the 7.62-inch thickener with the same compression zone across the cylinder and the Eolids settled through zone 3. No depth. The effect of the picket arrangement extending through the compression zone is evident. There is no break i n t h e concentration-height curve, and the concent'ration increases more uniformly in the run with a 15-inch compression zone depth. The Table I . Thickening of Calcium Carbonate Slurry (Peed concentration approximately 45 g./l.) two runs with a 30-inch depth appear t o have Rate, G./fi'Iin. Under Compression Detention reached a limiting concentration a t some distance Run UnderConcn. Zone Capacity Time, Tfmp., above the bottom of the thickener so that the conNo. Feed flow G./L.' Depth, Inches G./Min.' Min. C. centration increases very little in the lower 4 to A19e 61 7.9 423 48.4 2.67 3840 23.0 8.5 377 27.2 2.72 1960 27.5 6 inches. The pickets do not have as beneficial A9EC 62 9.6 310 23.0 2.63 1460 26.0 A17a 60 an effect in this region as they would if the concenA15a 59 11.6 258 9 4 2.59 467 26.5 25.0 1.06 4800 26.8 trat,ing action extended to the bottom. The rake 15.5 1.77 1790 28.5 without pickets is effective in a narrower zone C2; 40.6 4.80 504 37.0 1.78 4960 28.5 c3 39.9 5.0 475 28.8 1.75 3600 28.5 than is the picket arrangement. Dld 49.4 8.24 310 13.5 2.18 1002 28.7 D2d 49.9 6.36 456 39.25 2.19 4015 28.7 Six runs (f7) were made in the 14inch diamD3d 7 , 6o 374 28.40 2.19 2620 28.5 eter thickener with the diaspore clay. The conD4d 24.1 4.10 435 11.83 1.06 2300 28.5 ditions for tbese runs are given in Table IV and a Comings. Q Griffith. C DeBord. d Belter. the concentration-height curves are shown in
g:: i;:;
1166
!:E:
zii
INDUSTRIAL A N D ENGINEERING CHEMISTRY
Vol. 46, No. 8
FLOW THROUGH POROUS MEDIA Table I I .
Thickening Mississippi Pot Clay Slurry (13)
(Glass thickener, 7.6-inch diam., equipped with rake operating at 1.1 r.p.m.) Feed Depth Underflow Zones Concn., 8. Run clay/1000 g. Rate, Rate Concn., 1, 2 NO. slurry g./min. g./min. g./lOOO g. Inchks M1 45.60 14.18 3.44 194.0 31 L M2 43.60 14.57 3.18 196.0 31 M3 46.20 14.10 3.87 15.2 M4 44.80 14.85 3.84 iii 15 R.15 40.7 15.60 3.06 204 45.2
-
Table 1 1 1 .
Thickening Mississippi Pot Clay Slurry (8, 19)
(Thickener, 14-inch diam., with picket-type rake operated at 0.35 r.p.m.) Underflow Time Column Feed Rate Concn., Detention, Rate Concn., Run Height, &/mid. g./kg. Min. g./kg. No. Inches g./min. Y1a 31 52.9 41.9 8.8 240.1 7050 25 53.8 38.9 8.9 227 5820 Y2a 4500 20 55.7 36.3 9.4 209 Y35 1Ab 15 59.2 37.0 10.5 195 2710 2b 31 52.7 41.5 8.7 222 6470 4
b
Yehling. DeBord.
Table IV.
5
OO
Thickening Diaspore Clay Slurry (17) rake operated at 0.35 r.p.m.) Underflow Time Detention, Rate Concn. illin. g./min. g./kg. 27.0 312.3 2030 33.5 265.5 1115 35.8 238.5 827 46.2 167.0 438 42.5 189.5 595 52.6 119.0 396
experiments were made with the feed introduced as a solid stream with no obstruction. There are unanswered questions concerning the behavior in this zone. What is the maximum rate that solids will settle through this zone? What is the concentration in this zone a t the maximum settling rate? What is the effect on this zone when more solid is introduced in the feed than can settle through the zone? 1 The behavior when the feed rate is in excess of the settling capacity of zone 3 i s illustrated by two series of experiments. One series was made by Griffith (11). This was carried out in the 7.62-inch inside diameter by 4ft. high glass thickener. Calcium carbonate slurry containing 45 grams of solid per liter was fed to the thickener a t four rates, each of which exceeded the settling capacity of the unit. The concentration distribution through the unit is shown in Figure 10. The concentration in zone 3 is constant for each run in a narrow range from 67.0 to 72.2 grams of solid per liter. Zone 3 accepted a certain amount of the solid and the rest passed out in the overflow where the concentration increased from 2.27 to 30.0 grams per liter as the feed rate was increased. The rate a t which the solid settled to the bottom was nearly constant in the range from 3.05 to 3.41 grams per minute. When the concentration in the feed is less than a critical concentration, the concentration in zone 3 does not exceed this critical concentration as the feed rate is increased. When solids are settling through zone 3 a t the maximum possible rate, the concentration in this zone will have its maximum value. If solids are fed in excess of this rate, the excess will not settle through zone 3 but will be eliminated in the overflow. The maximum sedimentation rate may be estimated from batch settling tests by the method described by Coe and Clevenger (6). This method assumes that settling in zone 3 is the flocculent-type of settling observed in batch settling teste. Actually, the feed t o the continuous thickener is diluted in the feed I’
40
80
CLAY
I
Figure 5.
(Thickener, 14-inch diam., with picket Column Feed Rate Concn.; Run Height, No. Inches g./mih. g./kg. 59.7 €31 30.0 152.5 58.9 S2 20.0 155 58.0 S3 15.0 152 55.0 S4 16.0 146 58.0 S5 27.0 142 44.3 S6 16.0 145.7
June 1954
“
Run No.
M-2 M-4 M-5
SLURRY
120
160
200
CONCENTRATION
(C. SOLID / KO. OF SLURRY 1 Solids Concentration Versus Height When Thickening Mississippi Pot Clay Feed Concn., g./kg. Rate, g./rnin. 43.6 14.6 44.8 14.8 40.7 15.6
Underflow Rate, G./Mln. 3.1 8 3.84 3.06
well and reconcentrated in zone 3. The opportunity for settling in a different particle structure or as separate particles is increased. The second series was by Price and Kanitz (14) who inveetigated the behavior in zone 3 when a thickener is fed a t a rate that exceeds its capacity. Calcium carbonate slurries were used in a 4ft. high borosilicate glass cylinder 3 inches in diameter. The feed was introduced and the underflow was removed by the rotary-type slurry pumps made of rubber tubing used with the 7.62-inch diameter thickener. At concentrations of solid in the feed below 60 grams per liter, a constant composition of about 62 grams of solid per liter was established in zone 3. At concentration in the feed greater than 65 grams of solid per liter, the concentration in zone 3 was no longer 62 grams per liter but approached that of the feed. Under the latter conditions the settling capacity of zone 3 increased in the order of 25 to 50%. The factors that determine the maximum settling capacity or settling rate are not self evident. Neither the maximum settling rate nor the corresponding concentration in the settling zone are evident from batch settling tests on the feed slurry. A rational explanation is desired as t o why a certain characteristic concen-
Figure 6.
Rake and Picket Assembly Used in 14-Inch Diameter Thickener
INDUSTRIAL A N D ENGINEERING CHEMISTRY
1167
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT
Figure 7.
Continuous Thickener, 14-Inch Diameter, Equipped w i t h PicketType Rake
eliminated in the overflow. This was the masinium settling capacity of the cylinder, and under these conditions, the volume fraction of solids -fC was constant down through the settling z o n e . S o l i d s accumulated in the bottom of the cylinder but no measurements were made in this region. Samples were removed from the conetant composition zone and y e deteimined from the solids content. The values of F , yf, and -,c are given in Table V. Both y c and the maximum feed rate varied with the feed concentration. The following analysis applies to nonflocculcnt slurries of the type used by Pruiss (15). It explains qualitatively the behavior of flocculent types of slurry such as those used by Griffith (11) and by Price and Kanitz (14). In steady state operation a total slurry volume balance over the whole thickener is expressed by
Agitated feed t a n k is o n right, and t a n k t o receive underflow and overflow streams is o n left w i t h rubber tube pumps for feed a n d underflow o n floor
tration is reached in the settling zone a t the maximum capacity. A thickener would normally be operated a t a lower feed rate, and the condition is not to be expected in the normal operation. It is one of the limits in the operation and is important for that reason. A reasonable quantitative analysis is piesented. The experiments by Griffith ( 1 1 ) and by Price and Kanitz ( 1 4 ) demonstrated the presence of a constant concentration zone. No attempt n a s made by these investigators t o adjust the feed rate to correspond to the mavimum settling capacity where no solide are carried out in the overflow. Pruiss ( 1 5 ) performed experiments in which this n-as done. The measurements were made on slurries of tivo sizes of aluniinum oxide abrasive and one size of glass spheres. The solids Jyere 600 mesh Aloyite, 325 mesh Aloxite and 3L1 Scotchlite beads. Each of these contained a range of particle sizes. They settled with little tendency to flocculate. The viscosity ( 2 ) of several slurries of each material was mcasured in a modified Stormer viscometer that was calibrated against standard solutions of aluminum sulfate. The relation betwern volume fraction of solid and viscosity relativc to water is shown in Figure 11. Similar curves for tm.0 sizes of calcium carbonate are given by Brown ( 4 ) and \T7ard and Xammermeyer (18). Continuous sedimentation esperimcnts (15) were conducted in the apparatus shown in Figure 12. This consisted of a glass cylinder 3 inches inside dianic'tpr by 4 feet long and was fed by a Schaar Sigmamotor slurry pump. This pump contains a number of fingers that exert pressure on rubber tubing and squeeze the slurry along thiough the tubing. A range of pumping rates was obtained by using six sizes of rubber tubing and a variable speed motor controlled by a variable transformer. Solids fiom the bottom and clear overflow were mixed and returned to the feed tank. The per cent solids was determined in samples withdrawn from several levels in the tube. I n the series of runs to be described no underflow stream was removed but a 1.5-liter vessel was attached to the bottom of the cylinder to collect the solids during each run. Slurry containing a volume fraction of solids y/ was fed continuously to the feed plate below the surface of the fluid in the cylinder. The solid materials had previously been washed free of a small percentage of very fine particles. The experiments were made with a clear overflow. The feed rate was adjusted until a slight increase in feed rate would have caused solids to be
1168
while a volume of solids balance is
F r f = 0% -b DYd
(2)
When the volume of solids in the overflow is negligible
F r j = Dyd
(3)
For a very dilute slurry of spherical particles, the particles settle according to Stokes law. This is expressed as
(49 Robinson (16) modified this equation for the more concentrated slurries and hindered settling by Eubstituting the density of the slurry p' for the density of the fluid and the viscosity of the slurry p' for the viscosity of the fluid. A shape factor is also needed since the particles are not usually spheres, or the equivalent diameter d,, may be used. A hindered settling factor k, niay be defined so that the eettling velocity of a particle undergoing hindered settling is given by the product of k , and the settling velocity calculated from Stokes law thus
v = k, Tis
(5)
The density of the slurry is related to the volume fraction of solids by the equation PF =
Y(PS
-
P)
+
P
(63
then by definition
From Equation 6
According to Equation 8, the ratio betmen the settling vc,locity for a particle in the slurry and the settling velocity for the same particle settling freely, as given by Stokes law, is independent of the particle diameter. This ratio depends only on the volume fraction of solids in the slurry since the viscosity depends on y.
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 46, No. 6
FLOW THROUGH POROUS MEDIA 32
2
RUN BY YMUM
Table V.
RUN BY C€BORD RUN BY MYERS
Run
Settling of Aluminum Oxide and Glass Bead Slurries F
Cc./lSlin.
NO.
1 2 3 4
82
5 6
110
65 70 75
Y
120
7
126
8 9 10
230 210 208 235
11
-/f
kc
ye
VL~
vm Tiam cm./Sec. ~ m . / ~ k cCm./Sec. .
600 Mesh Aloxite 0.949 0,050 0,0528 0,0301 0.035 0.862 0.040 0.0465 0,0238 0.0275 0.893 0,043 0,0483 0.0266 0.0185 0.925 0 046 0.0498 0,0275 0.0494 Av. 325 Mesh Aloxite 0.062 0.0110 0.955 0 , 2 2 8 0,239 0,0404 0.047 0.0080 0.965 0 258 0.268 0.0440 0.033 0.0070 0.967 0.200 0,207 0.0461 0.238Av. 3M Sootohlite Beads 0.0662 0.00915 0.968 0.600 0.620 0.0845 0.0991 0.0118 0.960 0.645 0,671 0.077 0,140 0.0180 0.940 0.694 0,633 0.0764 0.032 0.0040 0.987 0.690 0,700 0.0862 0 656 Av. 0.010 0.059 0.046 0.031
0.006
When there are solids in the overflow and an appreciable downward velocity below the feed exists, the expression is
SLURRY
Figure 8.
CONCENTRATION
(a. CLAY/KQ
SLURRY)
The mean Stokes law settling velocity V S , is defined b s the equation
Comparison of Thickening with Picket Rake and Standard Rake
A method for calculating the maximum settling velocity will be described for the case when the separate particles in the Blurry settle a t different velocities. All settling velocities are relative to the fluid rather than the vessel walls. The velocity V, is defined as .P bulk solid settling velocity. If all particles settled with this velocity, the same volume of solids will settle per unit time as, under actual conditions, where each size of particle settles with a different velocity. When all the solids in the feed are removed in the underflow, and when the bulk fluid velocity down the thickener is negligible, relative to the solid settling velocity, V , is defined by the equation
Vsm = V m / &
(10)
The mean Stokes law settling velocity Vs, is a characteristic of a given slurry and is independent of slurry concentration. This value was calculated for the three solids used by Pruiss (15). From Figure 11 values of k , may be determined as a function of the volume fraction of solids. These curves are shown in Figure 13 together with a curve for calcium carbonate. Values of k,, V,, Vsm,and VA are given in Table V. The conditions for the maximum settling rate will be analyzed by describing two idealized cases A and B. Case h represents a close approximation to the nonflocculent settling observed in the 3-inch inside diameter continuous settler and may be extended in a qualitative way to explain the flocculent settling behavior observed in the 7.5-inch inside diameter thickener. Case B represents an approximation to nonflocculent settling in commercial settlers of large diameter. Case A. Consider the situation shown in Figure 14 where the feed spreads out from the bottom of the feed well in a thin uniform layer a t the boundary between zones 3 and 4 shown by a-a. The
o1
EFFECT OF FEED RATE ON
CONCENTRATION GRADIENTS
OVERFLOW
CLOUDY RUN FEED NO. R A E
0 81 10
0
50
100
200
I50
SLURRY OONCENTRATION
250
300
June 1954
867
OVER CONC. 4/L 23 8 0
CAP
vu
305 3.41
400
200
350 SLURRY
IO. CLAY / K L SLURRY)
Figure 10. Figure 9.
I00
82
rn 713
Thickening of Diaspore Clay with Picket Rake
CONCENTRATION
GJLITCR
Solids Concentration Versus Height When Thickening Calcium Carbonate
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
1169
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT overflow fluid sepaI2 11rates a t this plane and flovis upward IO.. with the velocity ; 3 O / A . The solids 8 08settle downward as 07individual particles. The settling veloc06ity of the smallest particles to be excluded from the + 3 M GLASS BEADS 0 325 MESH ALOXITE overflow is critical. A 600 MESH bLOXlTE The settling veloc01 ! I , ! ity of these in zone 10 I1 I2 13 14 IS 3 is designated Ti’. SPECIFIC VISCOSITY OF SLURRY The concentration in 3 is y c and Figure 11. Effective Viscosities of Aluminum Oxide and Glass Bead V’ = k, V $where k, Slurries is evaluated a t y c . If the feed rate is at its maximum allowable value, a slight increase will cause these smallest particles to be carried upxard in the overflow. The upward velocity would then exceed T i . At the maximum feed rate OIA = .1 ;’ The tests were carried out at the maximum settling rate, and the observed values of V6 are included in Table V. Tismand Vi each fall in a narrow range, and average values may be used to predict the maximum settling rate for considerable range of feed concentrations.
and from Equation 12
Eliminating FIA from Equations 11 and 13
1’
a
I
1
The value of F / $ may be determined from Equation 13 and the product y c k , may be evaluated from Equation 11 or 14. A plot of yc t s . y e k c is prepared from Figure 13 and the value of y o is read from this using the calculated value of yokc. This case also applies t o the settling of flocculent solids. When large floes are present there is little or no claesification, but the size of the floes changes with concentration and previous treatment. The method Rould require modification to allow for these variations. Nevertheless, it provides a qualitative explanation of the behavior observed by Griffith ( 1 1 ) and by Price and Xanitz (14). Case B. I n case A, the feed slu spreads over the area of the settler before appreciable solid settles from it. Kow conqidcr the case of a commercial settler of large diameter with a nonflocculent feed slurry. As the feed slurry flows radially a t the approximate level, a-a, in Figure 14, the larger diameter particles, with a greater settling velocity, Eeparate from the smaller. The distribution of particle size thus varies with radial distance in zone 3. The smallest particles predominate near the periphery. At the maximum feed rate these must settle before the flow reaches the discharge lveir. If the flow is assumed to have a un form upward velocity component O / A , this must not exceed Vi I n this respect cases A and B are similar. In case B, the concentration in zone 3 may be expected t o vary with iadial distance. No experiments applying to case B viere conducted. In large commercial settling and clarifying tanks the radial flow patterns have an appreciable effect on the clarifying and settling zones. Factors such as the design of the feed inlet, temperature gradients, and wind blowing across the surface are important. The radial velocity may be high near the surface with a relatively stagnant mass of liquid further down. Model experiments were carried out by Hubbel ( I d ) using dye and floats to explore the hydraulic character.os [ istics of various circular settling 08 tanks. Cases A and B represent ALOXITE ideal situations. 07 -
1
Figure 12.
Continuous 3-Inch Settling Column
I. Agitator 2. 3. 4.
Feed t a n k Schaar Sigmamotor p u m p Feed ring
5. 6. 7.
Glass column Overflow weir Storage t a n k
8
BATCH SETTLING
.06-
This prediction is carried out in the following manner. Given the feed slurry concentration, the relation b e h e e n solid concentration and viscosity, the average values of Vsm and Vi, and the desired underflow concentrations, y d , the maximum feed rate per unit area of settler may be determined. From Equation 9 the feed rate per unit area is
From Equations 1 and 3 and for the smallest particles t o settle into zone 3 and thus t o avoid cariying these particles in the overflow (12)
1170
il I’
L
L
.g
.os-
+
-
z : 04
4 -
03-
)o^
.02-
I’
1.00
I
0.90
0.80
0.79
0.60
1
b
Figure 13. Hindered Settling Correction Factor as Function of Volume Fraction of Solids
INDUSTRIAL AND ENGINEERING CHEMISTRY
T h e use of batch s e t t l i n g data for the design of continuous t h i c k e n e r s involves the following assumptions which are implicit in the method of making the calculations. The concentration is unifoim in the d i f f e r e n t lagers e n o o u n tered in the batch settling test. The floc structure
Vol. 46, No. 6
FLOW THROUGH POROUS MEDIA and settling behavior are the same in batch and continuous settling. The underflow concentration from the continuous thickener is predictable from the average concentrations found in the shallow compression zone depths encountered in the batch tests.
FEED WELL .
0.-
I
OVERFLOW
.
---
ZONE 4
-_ _ t
ZONE 3
SOLIDS SETTLE DOWN Figure 14. Solids Separate from Feed and Settle Downward ; Clear Liquid Flows Upward
Two series of batch settling tests mere performed to determine the distribution of concentration with and without stirring. These series (IO) were performed on slurries of Mississippi pot clay in glass cylinders 2.5 inches in diameter by 48 inches high. The cylinders were fitted with stirrers consisting of a heavy brass rod, The rod was bent a t right angles a number of times to form about 4-inch vertical lengths, on alternate sides of the axis, connected by horizontal portions of the rod. The stirrer revolved at 1.7 r.p.m. and served only to disturb the slurry. It did not agitate or mix it. Initial concentrations of 25 to 50 grams of clay per liter were used. Aluminum sulfate was used to control the hydrogen ion concentration. The slurry was added t o the cylinder, and after the upper line of demarcation had settled to a given level, samples were removed progressively from several levels below this line. In this manner the concentration throughout the slurry was explored after it had settled to several levels. The concentration versus height curve for each level is shown in Figure 15 for the runs without stirring and in Figure 16 for the runs with stirring.
after prolonged settling there is a pronounced concentration gradient through the layer of solids. The average solids concentration is determined for this layer by calculating the ratio of the total solids in the initial slurry to the volume of the solids layer a t the ultimate height. In this case the maximum concentration a t the bottom of the layer is 24% greater than the average concentration, The curves obtained with stirring present a different picture. The concentration varies with height shortly after settling starts, and there is no clearly defined pile at the bottom of the cylinder. Instead the concentration increases continuously as the bottom is approached. Considerably higher concentrations are attained a t the bottom of the cylinder both during settling and after the ultimate height is reached. This indicates that the gentle stirring breaks up the floc structure, permits the particles to settle separately, and promotes classification. It also permits more water to escape from the lower layers of solid, and a higher solids concentration is attained.
"t f H E M 1 OF L I N E 0
f
D
a
x ULTIMATE
CONCENTRATION
Figure 16.
H E M T OF LINE OF DEMARCATION 40:
0
3s + 30" 0 25" b 20' 0 15" 0 8.3 WLT1MATEl 0
*
n
CONCENTRATION
Figure 15.
,
I60
,
,
, ,
I80
200
,
,\
220
14
IGRAMSILITER)
Batch Settling of Mississippi Pot Clay without Stirring
The curves without stirring are similar to those reported for calcium carbonate slurry ( 7 ) . A slight decrease in concentration is evident near the line of demarcation, but for the most part, the concentration of the initial slurry is maintained through most of the region below this line. This indicates that the solid settles as a coherent floc without classification. Kear the bottom the solid piles up in a Compression zone. At the ultimate height lune 1954
C%
DEMARCATION:
40' 35'
30'* 25'* 20" 15"
HEIGHT
5:75*
(ORAMS / LITER 1
Batch Settling of Mississippi Pot Clay with Stirring a t 1.7 R.P.M.
Concentrations are not uniform throughout the various layers in batch settling tests. The floc structure is altered by stirring in the batch tests and by dilution a t the feed well in continuous tests. There is slight assurance that water will flow from the interstices between the solid paiticles a t the same rate in the compression zones in batch and in continuous tests. The forces acting on a given layer of solid differ considerably in the two case8. The resistance to the flow of liquid from the solid and the time available for this flow t o occur are also different. There is little rational basis for the design of continuous thickeners on the basis of batch settling data. Design based on batch settling tests using empirical rules and sufficient experience is satisfactory. ACKNOWLEDGMENT
C. E. Pruiss and Carl DeBord carried out master of science theses on the subject of this paper. P. A. Belter, H. A. Dick, E. H. Engquist, J. S. Griffith, E. H. Kanitz, N. W. Myers, F. L. Price, W. A. Schaffer,and G. C. Yehling, Jr., contributed bachelor of science theses and deserved to be included as coauthors. The latter have not been included to avoid listing 13 authors. The contribution of each is acknowledged by reference to Literature Cited.
INDUSTRIAL AND ENGINEERING CHEMISTRY
1171
ENGINEERING. DESIGN, AND PROCESS DEVELOPMENT NOMENCLATURE
A
c
=
= =
= = = =
Y h
= =
kc 0
= = =
r-
= =
=
=
T-6
=
= = =
= = =
=
LITERATURE CITED
cross-sectional area of settler: sq. em. ratio of weight of solid to g./cc. volume of slurry (subscriptfrefers to feed) volume rate of underflow diameter of thickener (cylindrical), em. particle diameter, em. diameter of single sphere wit'h the same settling velocity as an actual particle, equivalent diameter, cm./sec. volume rate of feed acceleration of gravity, 980.1 cm./sec.2 height from bottom of compression zone, em. hindered settling correction factor defined by Equation 5 volume rate of overflow set'tling velocity of each solid particle, cm./sec. settling velocity of equivalent single spherical particle in laminar flow range (Stokes law settling) cm./sec. observed mean set'tling velocity of all particles defined so that V,yA is the volume of solids settling relative t o the liquid per unit t,ime average Stokes law settling velocity for all particles, defined by Equation 10, cm./sec. settling velocity of smallest part,icle to be kept out of the overflow when settling through a suspension containing a volume fract'ion of solids, y e , cm./sec. settling velocity of the smallest part'icle to be kept out of the overflow when settling alone, cm./eec. volume fraction of solids in slurry; subscripts J,, 0, and d refer t o feed, overflow, and discharge, respectively volume fraction of solids where composition is constant in zone 3 density of the liquid (without suspended solid) g./cc. density of solid, g./cc. density of slurry g./,cc. viscosity of the liquid g./cc. viscosity of the slurq- g./cc.
(1j Anable, Anthony, "Chemical Engineer's Handbook," .J. 1-1. Perry, Editor, 3rd edition, p. 937, Keiv T o r k , McGrarv-Hill Co., 1950. (2) B a b b i t t , H. E., a n d Caldwell, D . H., Cnic. ITlinois E n g . Expt Sta. Bull., Ser., KO.319, 37, No. 12 (1939). (3) Belter, P. A,, "Continuous Thickening of Slurries." B.S. t h e & University of Illinois (1942). (4) Brown, G. G., and associates, "TTnit Operations," Kea. York J o h n Wiley & Sons, Inc., 1950. (5) Bond, F. C., Can. Inst. Mining M e t . , 49, 546 (1946). (6) Coe, H. S.,and Clevenger, G. E l . , Trans. Ani. I m t . M m i n y N P : .
Enyrs., 55, 356 (1916). (7) Comings, E. W., IND. ERG.CHEA~., 32, 663 (1940). (8) DeBord, C. D., "Settling and Thickening of 81urrie6," 3I.F. thesis University of Illinois (19433. (9) DeRord, C. D., "Thickening of Slurries," 13,s.thesis, University
of Illinois (1941). ect of Stirring o n Settling (10) Dick, H. d.,and Engquist, E. H . , R a t e , " B.9. thesis University of Illinois (19413). (11) Griffith, J. 3., "Continuous Thickening of Calcium Cailmiiate Slurries," B.B. thesis University of Illinois (1940). (12) T-Iuhbel, G. E., J . A m . TVatei W o r k s Assnc., 30, 33.5 (1938,. (13) Myers, S . W.,"Thickening Clay Slurries," B.8. thesis Uni1-ersity of Illinois (1943). (14) Price, F. L., and Kanitz, E. H., "Limiting Rates of (,'ontinuow Settling," B.S. thesis, University of Illinois (1943). (15) I'iuiss, C. E., " I I a x i m u m Rates of Clarification," 3I.S. the+ Purdue University (1953). (16) liobinson. C . S..IXD.ERG.CHEX. 18.. 869 .I19261. , il7) Schaffer, W.A.; "Continuous Thickening of Granular Slurry." B.9. thesis, University of Illinois (1948). (18) W a r d , H. T., and Kammermeyer, IC, IN). Ex:. CHFX.. 32, 622-6 (1940). (10) I'chling, G. C., Jr., "Continuous Thickening of Clay Slurries,'' B.S.thesis University of Il~nioi5(19413).
RCCEIVED for review November 19, 1953.
ACCEPTED April 0, 1 9 j 4
Effect of Ultrasonic Energy on of Solids in Phosphate Tailing DUDLEY T H O M P S O N
AND
F. C.V I L B R A N D T
VIRGINIA POLYTECHNIC INSTITUTE, B L A C K S B U R G , VA.
B e n e f i c i a t i o n of TVA phosphate ore by washing produced a -10-micron suspension of clayd quartz, a n d phosphate m i n e r a l , called phosphate t a i l i n g , t h a t was strongly t h i x o t r o p i c in n a t u r e a n d retained approximately 3 parts water per 1 p a r t solids even a f t e r 2 years of settling. Usual methods of i m p r o v e m e n t in s e t t l i n g pond operation a n d mechanical separation of solids d i d n o t provide a satisfactory solution. T h e effect of ultrasonic energy o n t h e settling characteristics of solids in t h e t a i l i n g suspension was investigated. For suspensions near t h e isoelectric p o i n t , m i l d i n t e n s i t y (below a cavitation level of 0.3 volt-ampere per sq. cm.) insonation increased by a t least five t i m e s t h e coagulation a n d subsequent settling rate of solids in t h e insonated sample over t h a t of t h e control, d u r i n g hindered settling, Intense insonation (above cavitation level) disrupted a n d dispersed t h e loose agglomerates of clay thereby increasing t h e effective n u m b e r of charged particles in suspension. These, in turn, increased a n d emphasized t h e effect of t h e t h i x o t r o p i c gel s t r u c t u r e w h i c h retarded settling. T h i s effect was shown t o be inversely proportional t o t h e intensity.
W
ASHIKG was employed by the Tennessee T'alley Authority, during the gears folloxing the close of IYorld War 11, as a means of beneficiat,ing the ore from it,s phosphate deposits in the Tennessee Valley (61). The clay fraction of t'hk sedimentary de-, posit (Figure 1) was removed by this rrashing. Along with clay, particles of which were essentially smaller than 10 microns in average diameter, quartz and phosphate mineral in the size 1172
range of the clay were removed from suspension. This - 10micron suspension of clay, quartz, and phosphate mineral was called phosphate tailing and was the suhiect of this investigation, -4s R matter of fact, the phosphat,e ore that, is being mined by the TVA today does riot respond well to washing (OR) and is handled by other means. However, results obtained in t h k investigation focus attent,ion on the effect of ult'rasonic energy on
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 46, No. 6
