The Design of Intermittently Fed Thickeners BRYANT FlTCH theoretically based design procedures for DorrA11type thickeners (7,2,6, 9, IO,72, 14, 15) assume that the unit in the plant will run a t steady state. I n practice, almost no thickener operates this way. Both rate and consistency of feed vary from hour to hour. I t is recognized in industrial practice, however, that thickeners have the capacity to absorb surges of short duration and to even out variations in flow. They are consequently usually designed on the basis of average flow, or of tons of solids to be handled per day. Not infrequently, however, thickeners operate while accepting a high input for several hours during a day, and little or no feed the rest of the time. For example, a thickener in a coal washer may receive fine wastes during one shift operation and none the remainder of the day. Again, a tailings dump may be reclaimed by hydraulic mining one shift per day, and the solids, stored in a thickener, may be continuously fed from it to a processing plant. I t is apparent that the surge capacity of a thickener is not boundless. At some point design will have to be based on the high, intermittent feed rate, rather than upon the long-term average. Difference in thickener size between the two design bases may be substantial. I t is worth knowing if and when the larger, more costly installation is needed. This paper gives a design basis for thickeners fed intermittently. I t should be applicable for all pulps to which the classical Coe and Clevenger design procedure is suited. I n steady-state operation concentrations are normally distributed as shown in Figure 1. The tank contains compacting or compressing slurry to some level a. Above a, except near the feedwell, it is filled with clear supernatant. New feed, entering at the feedwell, plunges as a submerged waterfall (13) or density current (5) to its level of hydrostatic balance, and there spreads out. This occurs a t a stratum in the thickener where the pulp specific gravity is the same as that of new feed. Inherent hydrostatic stability of suspension systems stratified with higher concentrations below precludes any substantial recirculation or gross mixing of feed pulp back up into the supernatant ( I 7). 8
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
Thus, new feed flows into a position above layers of compacting pulp, but below clear supernatant. When a feed surge occurs, the excess of solids over that which can be transmitted to the underflow by settling backs u p above the compacting solids as a pulp zone, displacing clear supernatant into the overflow. Solids do not overflow until the pulp zone builds up to overflow level. The surge capacity of a thickener depends upon how long it takes this zone to reach overflow. We will, therefore, be concerned with how fast the pulp level rises when a thickener is overfed. A procedure for determining it is given first. An example of its use is given in a second section. I t is derived and justified in a final section. Procedure
The procedure makes use of a Kynch-type (7) plot of solids settling flux, RC us. concentration C, such as shown in Figure 2a. Determine batch settling rate R as a function of concentration C for a number of concentrations between that of feed and underflow, by the standard Coe and Clevenger method (7)) preferably using settling columns three feet or more in height. Plot RC us. C for the concentration range above C., This is shown in Figure 2a as curve f-a-e. Choose the desired underflow concentration C,. Plot its value on the C axis of Figure 2a. Draw an operating line through this point, to as high a value G, on the RC axis as possible, without cutting through the This line will usually be tangent settling flux plot f-a-c. to the plot at some point a. I n rare cases it will pass through point f. G, then represents the maximum solids flux which will pass through the thickener to an underflow at concentration C,. G, is (underflow solids rate)/ (thickener area). The desired solids rate is specified, so the necessary thickener area can be found. (This is the standard Yoshioka construction for determining limiting solids flux for steady-state operation.) Determine the instantaneous or surge value of solids flux G,. Plot this point on the RC or flux axis, and draw on a construction line to the largest possible value Cext
Surges in continuous thickener throughput need not always necessitate overdesign t o accommodate the occasional peak flow. This analysis will help
I
determine whether extra capacity should be provided to handle a surge of given size and extent
.~
rWu1-u
1.
Solids concentratior, 11). Rake Drive Superstructure
e-
erflow . .
..I
I
^ .-I
t
Feed In
I
a
a
Solids Out
If G is given in tons/ft‘/day R is given in ft/hr C is given in g/l.
t
Y
G
C-
Multiply G, and G, in tons/ft’/day by 1.3 X 1P to get values for use on a plot of RC VS. C. Safety factors. It is suggested that at least 20% should be added to thickener area as a safety factor. This will also add 20% to the surge volume. The procedure given is b a d upon current thickening theory, which derives largely from Kynch (7). This theory assumes that the settling rate of solids in a thickener, at least at the concentration of “critical” pulp zona which may build up in a surge-fed thickener, will be a function of concentration only. The classical Coe and Clevenger (7) method made the same assumption. Modern treatment goes on to deduce mathematically many implications or consequences of the assumption. The assumption, however, is far from precisely valid for many industrial pulps. The practicing engineer should not be misled by the mathematical elegance of current theorv into ascribine imoroved validity to it, or into abandoning generous safety factors. Under0ow recirculPrion. The design procedure is based on a limiting condition. If the actual underflow flux is less than the limiting amount for any reason-as for example, application of safety factors on areas or underflow change in the nature of the solid-then concentration will not be p d y C. as selected. Speciiicallv. Some DU~US ,-it mav be considerablv , hieher. are capable of thickening to a concentration at which they are not pumpable. To avoid this, it may sometimes he necessary to withdraw more underflow than
-~
_ -
10
I N D U S T R I A L AND ENGINEERING CHEMISTRY
0.5
1
m
1
1
400
1
1
6m
1
800
1
1
1
1
1
1ooo1200
cowtorrunow, 111 . Figulr 3. &lot
-
of s a t t h g ro& 01. commtr&n data
would correspond to average feed and to recirculate the exeess back into the thickener. Use is made of this technique in the example which follows, and it is discussed in
the Derivation scction. 'J'he problem. A sulfuric acid plant was to operate on SOrobtaind by roasting a by-product pyrite flotation concentrate. Narmally the matuial would be received continuously, in suspension at about 195 g/l. bolids. i t would be sent to a thickener whose underflow fed acid plant During mill shutdowns, however, it was pmpokd to supply the acid plant from a pyrite tailings pile. Material would be recovered by hydraulic mining six hours per day, at abaut 390 g/l. solids, and at a rate mch that sufficient pyrite w& be stored in the thickmcr to feed the acid plant continuously. Thua the thickener surge feed while recovQing tailings would be four time the daily average feed rate. Could the thickener be designed on the basia of the daily average feed rate, or would it have to be tour times a8 big to handle rate? or would the proper size lie between tt2 ' 'anntprir. The following subsidence rates were reporb3 from the laboratory, based on standard Coe ;adUcvengawne settling tests:
*
asallw& 811. d J d 5
&ding rate, j f / b
W 254
5.23 4.53
290
3.79
338 457
3.12
511 580
205 1.52 1.074 0.572
683 816
904 IMO 1158 1383 1.531
Initial plotting of settling rate us. concentration indicated that these data have considerable scatter, which is not unusual. Therefore, they are replotted (8) in the form: (settling rate) cxp (E/4.65) vs. concentration, as in Figurc 3. This give a reasonably linear plot up to a concentration of about 820 g/1. and a straight line drawn through the points seems a reasonable representation of the relationship between R and Cup to this point. At about 280 g/1. there is an obvious change in settling mechanism. The Coe and CleMlger batch subsidence rate becomes nearly independent of concentration up through the point at 1158 g/1. Over this range a zone of concentration lower than the initial test concentration teeters off the top of subsiding pulp solids. Surface sula9idence rate observed in Coe and Clevenga tests then measures settling rate at this lower concentration, rather than that at initial test concentration. The higher concentration material settlcs more rapidly. We athibute this to phase settling (2,3). A flux plot, RC us. C, constructed fiom the bold linc of Figure 26 is shown in Figure 4. There is little positive curvature below the critical point 6. It appears that about as soon as positive curvature permits, zone settling braalrs up into phaae settling. By Kynch analysis this yields a typical Coe and %levmger Typc 1 batch Bettling curve. Pulp interface subsides at agentially a constant rate until it collapses into compression.
267
0.548 0.509 0.547 0.321
V O L 6 0 NO. 7 J U L Y 1 9 6 8
11
It was decided that the underflow would be taken at . of about 2090 g/1. solids. Higher cona value of C centrations could be reached, but were not pumpable. The maximum pnmissible underflow flux, G., in steady-state operation is found by the Yoshioka (76) construction to be about 740 graph units (g/l. times ftb) which is equivalent to 740/1.3 X l V or 0.57 ton/day/ .'tf Point 6 obviously defines the controlling zone. At surge feed, the flux G, will be four times this,or 2960 graph units per day. The surge feed construction line passes through feed point f and gives a value for,C of 648 g/l. Since it paws through point f, a zone of feed concentmtion will back up in the thickener. When we apply Equation 1
2960
U P = - - -648
-
740 2090
3.22 ft/hr
The one to be followed does not correct for the ineruue in C, and thus is in mvr, bbt on the CarrmcfVBtive side. (Soiutions for rdrculation arc discuascd later.) Net valuca of Cs and (Ps arc marked with primca. K is the ratio: (net surge feed) I- (net u n d d o w to process), and in this example has a value of 4. We want a d G, to be 1850 graph units, G. is 740 grauh units. Then the net underflow flux will be:
and we find that during surge feed the pulp level will back up 3.22 ft/hr, or a total of 19.3 ft for the 6 hr of redaim operation. An unusually dcep thickener would thereforebe needed to contain the surge. Themetically there is nofhing wmng with a thickener perhaps 25 ft deep (to allow for 19.3 ft of 8urgc above normaloperating Ievd). The practicing e n g i n e might be concerned with what would happen if there were a power failure when the thickener was full of pulp. The &ids could settle and form a compacted bed that might be thicker than the rake lift mechanism could dear. For a practically important reason, one might desire to spnad = 370 graph units out the stored solids in a shallower unit. The corresponding net thickener discharge flux is A p o d compromise design might be found by drawing 370/1.3 X 10' = 0.285 ton solids/M/day. With a the surge construction line through points f and e. Up 20% d e t y factor this drops to 0.237 Qn/ft'/day. to this point, the change in slope is obtained by rotating Thus we condude that, as one reawnable design fiaure, aruund pointf. Beyond it, the line rotate around point the thickener should allow a "unit area" of 1/0.237 or e, and further dccrcascs in Cy/&, arc obtained with a 4.22 ft'/ton solids to process per day. It should have much larger sacrifice in G, The new surge line dotted about 9 ft of extra depth over normal design to handle in Figure 4 gives a dope GY/G-, of 1.72 and, by 4 u a surge feed. tion I, a pulp level rise rate, u, of 1.37 ft/hr or 8.2 ft for The above data relate to a rcal problem. Unforhlthe mlrgc period. nately, we cannot report on continuow thickening reWe arrive at such conditions through an appropriate sults, since the project has not yet been executed. increase in thickener area. However, since thickener BM will be i n d , the flow of solids thmugh the Dohotion limiting zone wiU also increase. To maintain the deFirst, the upward velocity of the interface between &ed u n d d o w concentration, more underflow must be pulp and supapatant is calculated for a thickener column didprgd. T h e exis recycled to the thickener feed. T h ~ . ~ ~ r i ~ t u a l t h i & ~ ~ W , G ~ , w i l l b e g r ewithout a t e r unddow. Then the general d o n caused by withdrawal of underflow is determined and superposed than the RCW or net surge feed, G,', by thin amount. to give net i n t u k e velocity. It wfU also be of higher concentration, because it conPropagation of pulp level in eolrunn without some underflow. CbeyFtiOns for exact d@iolM underflow. New feed enters in a thin sheet or lamina involve trial and mmr, and arc probably not warranted.
* 12
1NDUSTIIAL
A N D ENQINCE1INO C H E M I S T R Y
into the interface, a t a rate corresponding to a solids flux G,. Let concentration just below the feed zone be C, and its settling rate be R,. The propagation of the pulp level in the direction of settling is taken as 6. Then flux out of the feed lamina must equal that into it, or :
(Re - S)C, = G I 6 5
(RC),
- Gf
C,
And if Cext is defined as the intersection of line G, z extended, with the C axis, then it is apparent (Figure 5) that:
-
(3) The zone yielding the greatest rate of upward propagation will overrun all others. Therefore, a zone of concentration C, that leads to the largest value of G,/C,,t will be just below the feed lamina. This concentration will be defined by the construction line from G, through whichever of the possible points on the RC curve gives the minimum value of Cext. We now have to define what points on the RC curve are possible. No zone of concentration lower than that of feed can form, because if it did, new feed would flow in beneath it as a density current. Since it is then no longer being fed, it collapses. Only zones of higher concentration are possible. (Behavior of the flux plot at concentrations lower than C, is not relevant to thickener operation.) Limiting zone at feed concentration. If the construction line from G, through point f gives a lower value of Cext than is obtained from any other point on the RC plot (Figure 2a), then a zone of feed concentration will form just below the feed lamina, and will increase in thickness. T h e discontinuity between supernatant and feed concentration is propagating upward faster than any higher concentration zone. (In such a case the thickener is often thought of as being “overflow rate-controlled.”) Limiting zone at “critical” concentration. If minimum Cextis not given by a construction line through point f, it will be determined by one through some tangent point b (Figure 26). I n this case, by Kynch analysis, a zone of concentration cb will propagate up-
AUTHOR Bryant Fitch is Technical Adviser with the Dorrco Division of Dorr-Oliver Inc., Stamford, Conn.
ward more rapidly than one of feed concentration, and will appear just below the feed lamina. Such zones are commonly called “critical.” I n this case variations in feed dilution, and the resulting changes in overflow rate, do not affect thickener solids handling capacity, over whatever range leaves cb the controlling concentration. Effect of compression on CeXt.The above assumes that pulp is in zone settling (2, 4) at whatever concentration on the flux plot determines Cext. If instead it is in compression, settling rate R will not be a function of C only, but will depend also upon the amount of mechanical support transmitted through the layers of pulp solids. Over the compression concentration range, the flux plot does not have a fixed location ( 3 ) ,and the constructions of Figure 2b cannot, in principle, be made. Practically, there will be compensating errors between Coe and Clevenger tests defining R, and thickener operation, so that the constructions should give useful figures even when Cbis somewhat within the compression regime. Effect of underflow on pulp level propagation. Underflow is being discharged at some concentration C, and volumetric rate Q,. Solids are thus being discharged a t a rate C,Qu, and the solids flux to the unO n a Kynch-type plot of flux derflow, G, = Q,C,/A. us. concentration, it may be represented by some operating line G, - C, (Figure 2 a ) . T h e slope of the line is - G,/C,, but since G, = C,Q,/A, it is also equal to -Q,/A. This is equal to the rate a t which pulp as a whole is moving downward through the thickener, but is opposite in sign. Previously, the rate at which pulp level rises with respect to the pulp as a whole (zero total flux) was found to be G,/Cext. Superimposing the movement of the pulp as a whole as derived above, the net upward velocity of the pulp-supernatant interface in a thickener is: u p
=
GJCext
Gu/Cu
(1)
Underflow flux C,. To use Equation 1, a value for G, must be found. Values of C, and G, are not independent of one another. At a given underflow concentration C,, the underflow flux cannot be arbitrarily assigned a value, but will be’ determined by operating conditions. I t will ultimately be determined either by free settling limitations or by compression (2). If determined by free settling limitations, G, will have the value established by the construction of Figure 2a. An operating line, drawn through any value of C, and tangent to the underside of the flux plot at some point a, will intersect the RC axis at the corresponding value of G,. (In this case the pulp interface rise velocity, up, will be constant for given values of G, and G,.) VOL. 6 0
NO. 7 J U L Y 1 9 6 8
13
If G, is controlled by conlpression conditions, it will increase as compression depth increases during a surge of feed. And the flux plot, as determined from Coe and Clevenger batch settling tests, will not be single-valued in the range of tangent point a. However, if the batch tests are made in columns with substantial initial depth, the RC plot will represent essentially free-settling or limiting values of settling flux (2). G , cannot then have a value significantly higher than that determined by the construction of Figure 5 . The pulp buildup speed, u p , will not be faster than predicted on the basis of this construction. Therefore, the value it gives is safe for design purposes. Thus, Equation 1 gives an upper bound and a reasonable design value for the upward propagation of pulp level in a thickener during surge feed. Recirculation of underflow. I t will be apparent that the construction line G, - C, can be drawn with either G, or C, specified, and will serve to determine the value of the other. Thus, if G, is decreased, C, must increase. Usually this will be acceptable, but in some cases the underflow can become so thick that it cannot be pumped. I n such a case, as in the illustrative one in the example, G, must be maintained high enough to give a pumpable underflow, and the excess recirculated. There are two possibilities for recirculation. First, the excess underflow may be mixed into the new feed, and this was the procedure contemplated in the example. Second, the excess underflow may be recycled separately back into the compaction zone of the thickener. I n the latter case, a certain amount of intermixing between the recirculated underflow and partially compacted solids must be effected in the thickener. I n the first case, underflow concentration C, is governed by flux through the critical zone. I n the latter, it is governed by the rate at which the final phases of compaction take place. For the first case, there is a net flux G,‘ corresponding to the flow of solids advanced to process, equal to Q ’C,/A. The difference between actual and net underflow flux (G, - G,’) is recirculated to feed. There is also a net surge flux G,’ which is some known factor K times the net underflow flux. G’,
=
KG,’
(4)
Total surge flux is equal to net surge flux plus recirculated flux.
G,
=
GI’
+ (G, - G u t )
(5)
And the new surge feed concentration is determined from total material balance :
C,
Constructions must be made by trial and error, so that Equations 4 through 6 are satisfied, and point f on the flux curve is located at concentration C,. 14
INDUSTRIAL AND E N G I N E E R I N G CHEMISTRY
It will be apparent from Figure 4 that, in this case, if point f is moved along the flux plot from the concentration of new or net feed to that of true thickener feed including recycle, the slope of line G, - Cextwill not change greatly. I t will therefore (Equation 1) not significantly change the propagation velocity u p . I n such cases C, may be taken as equal to C,’, particularly in view of the only approximate validity of the thcory. Eliminating GI’between Equations 4 and 5 :
Recirculation of underflow back to the compaction zone is effected by feeding in a well or location separate from the new feed. The recirculated underflow plunges to its density level with a limited amount of mixing. If there were no mixing it would plunge directly to the underflow, and build u p an ever-increasing recirculation. With a controlled amount of remixing, it, in effect, keeps the compaction zone agitated and causes it to build up. The excess solids inventory then is stored in the compaction zone instead of in a critical zone. I n this case, the recirculated underflow solids do not have to settle through the critical zone. So G, = G,’, but G, > G,‘. Therefore, such recirculation decreases the critical zone propagation velocity u p . As such recirculation is increased, however, the compaction zone would at some point build u p faster than the (‘critical” zone, and would overrun it. Recirculation in this manner is still an art, and will not be discussed further here. NOMENCLATURE A = area of thickener C = solids concentration, wt/vol Celt = concentration defined by intersection of construction line from GIwith C axis C, = solids concentration in actual thickener feed C,‘ = solids concentration in net or new thickener feed C, = solids concentration in thickener underflow G = solids flux, wt/area-time G, = feed solids flux G, ’ = G, minus flux due to recirculated underflow solids G,, = underflow solids flux G,’ = G, minus flux due to recirculated underflow solids K = G,,’/G,’ Q, = thckener underflow, vol/time R = settling or subsidence rate in batch test, lengthjtime = duration of feed surge t, uz, = upward propagation velocity of pulp-supernatant interface = downward propagation velocity of discontinuity (Kynch) 6 REFERENCES (1) Coe, H. S., and Clevenger, C . H., Trons. A I M E , 55,356 (1916). (2) Fitch, E. B., IND.ENO.CHEM.,58 (lo), 18 (1966). (3) Fitch, E. B., IND. ENO.CHEM.FUNDAMENTALS, 5, 129 (1966). (4) Fitch, E. B., Tranr. A I M E , 223, 129 (1962). (5) Fitch, E. B., and Lutz, W. H., J. Water Pollution Control Fedaration, 32, 147 (1960). (6) Hassett, N. J., Znd. Chemist, 34, 116, 169, 489, (1958); 37, 25 (1961); 40, 25 (1964). (7) Kynch, G. J., Trans. Faraday Soc., 48, 166 (1952). (8) Michaels, A. S., and Bolger, J. C., IND.ENS. CHEM. FUNDAMENTALS, 1, 2 4 (1962). (9) Moncriefl, A. G., Trans. Inrl. Mining .Met. 73, 729 (1964). (10) Porter, J. L., and Scandrett, H. F., Ext. M e t . Aluminum, 1, 24 (1962). (11) Roberts,E. J., andFitch, E.B., Tranr. A I M E , 2 0 5 , 1113 (1956). (12) Robins, W. H. M., Trans. Inrt. Chem. Engrs., 42, T 158 (1964). (13) Sawyer, C. N “Biological Treatment of“ Sewage and Industrial Wastes,” Vol. 1, p. 328, Rk)inhold, 1956. (14) Shannon, P. T., and Tory, E. M., IND.ENO.CHEM.,5 7 (2), 1 8 (1965). (15) Talmage, W.P., and Fitch, E.B,ibid.,47,38 (1955). (16) Yoshioka, X., Hotta, Y . , Tanaka, S., Naito, S., Tsugami, S., Kagoku Kagaku, 19, 616 (1955).
