Document 99DKnBaD5qONb76ndmE22kn5R

BIRO MACHINI COMPANY INCn SO. WALPOLI, MASS. 0*071 Plcosv reply loi 7 Pm*woody Pork, Swtto 129, Atlanta, Oewgio 30341 404-439-7421 Ttiai 542370 November 14, 1972 DOW CHEMICAL USA P. o. Drawer K Freeport, Texas 77541 Attn: Mr. Mauldin Gentlemen: This is to report that we have finished our preliminary evalua tion tests on your dilute asbestos slurry and wish to report as follows. This would not be a good vacuum filter application. Flow rate specified of 1,500 GPM at the low feed concentration produces cakes which cannot be handled without precoat and, therefore, are not dischargeable. This material is amenable to being handled in a Solid Bawl Centrifuge, however, at limited solids recovery of approximately 80%. Even assuming that a solids recovery of approximately 80% were acceptable, you would require on this basis, we estimate, three or four of our larger centrifuges amounting to several hundred thousand dollars. At this point, our recommendation would be, although it might be undesirable for labor and maintenance reasons, a batch pressure filter probably with precoat to handle this stream. We would like to suggest that some means could be devised to reduce the total incoming flow and raise the concentration of the asbestos fiber, it then would make economic sense to con sider a centrifuge. This possibly could be done in a device like a hydrocyclone and you might be interested in exploring this avenue. If results were favorable, we could re-evaluate on a pilot plant test basis the concentrated slurry and give you a more realistic centrifuge approach for final concentra tion. 2 N. M.W. PARK RfDGt, ILL 10041 7 OuAmtfy Mr*. ATLANTA. GA. 30UI 4415 1W. Canyo* Coert. P0*TUM0. 04C. *7721 P 0, 0o 494. OUflftAA, W. VA. 25094 >445 Co*# Cits Way. UfAtOTi. ' M t bird MAOHINI COMPANY -15- Dow Chemical USA Freeport, Texas Page 2 We certainly appreciate your contacting us regarding this problem and we are sorry that we cannot give you any more practical and affirmative answer. Very truly yours, 6 C lM 3 1 5 s h . a . uaiier Sales Engineer Centrifugal and Filtration Equipment Process Equipment Division HAB/pjh k..O..- . -i-: - - TT Mi i.-1 m: ,: ij';H JMCMWaatWO, DESIGN, AMP PROCESS DEVELOPMENT . _________ . ^M Determining Thickener Unit Areas .W; P. TAIMAGE and E. B. RTCH At Dtir Ca., Wmtpeif, Cm. i 9 PKKATTON of Dorr-tvpe thickener* was analyzed by Coo Kynch started from the postulate that the settling velocity, V, 0 and Clevenger (?) in 1!)18. They showed hoar to predict of a particle ia a function only of the local solids concentration, C, thickener capacity from hatch settling test*. The method out around the particle, or mathematically, V -- ff,C\ The function lined in their planer paper hat l>een u*cd aithotrt eignificarrt im U not defined and may change in any manner as the concentration provement to thie time (11. change*. This will be recognized as the tome assumption Coe ami A irrmt paper (.1) hv K.vnvh presents a mathematical analyeia Clevenger made for the free settling regime. of hatch settling tests that supplements the original picture sup In a batch test starting at uniform concentration, all the solid* plied hr One and Clevenger. Application of the Kynch mathe- start settling at uniform velocity since V /(C). Aa the settling matir* to thirkening problem* makes it possible to simplify the solids begin to collapse against the bottom of the vemel, they experimental procedures and interpretation of results. must pen through all concentrations between starting concentra tion and that of the deposited iblids. If, at any of these inter Simple Geometrical Constructions Aid Direct Determination of Unit Area Requirement* mediate concentrations, the solids-handling capacity is Ices than that at the lower concentration occurring immediately above it in Kynch does not analyze the relationship between batch set tling testa and continuous thickeners. In order to apply the KvncH analysis, it will Ih> useful to review that part of the mech anism of continuous thickening pertinent to the problem. Ac cording to Coe and Clevenger (?) there may be several regimes or tones in a thickener but the thickenerarea required is determined the vessel, a zone of such intermediate concentration must sinr: building up, since the solids cannot pa through it as fast as they are settling down into it. Kyach showed that the rate of upward propagation of each such constant concentration zone is constant. Consider the in finite!}* thin layer at the upper boundary of such a zone, having a by conditions in what they designate as free settling zones. These concentration, C. originating at the bottom at aero time and mov arc defined as zones iu which the doe* are falling through the liquid without pressing on layers of rioe below. In a free settling ing upward at a velocity of C feet per second. The solids set tling into this layer come from a litw having a concentration of regime, the quantity of solids which can settle through a tail cross section in unit time is equal to the product of the settling rate and the solids concentration. Coe aod Clevenger tacitly as (C -- rfC) poundj per cubic foot and n sat tting velocity with re spect to the veeeei of (F -r dV) feet per second bat with respect to the layer of (F + dV V) feet per second. The concentration sumed that, under the operating conditions, the settling rate would bo a function solely of the solids concentration. Therefore, the solide-handling capacity of any layer u a function only of its of solids settling out of this layer will be C with a eettling velocity of F with respect to the vessel and (I* 4- V) with respect to the layer. Since the concentration of the layer ia constant, the concentration. In a cor.f.r.uous thickener, the solids must be quantity of solids settling into the layer most equal the quantity ablo to suhsi.ic through any concentration l.r-vrs between the of solids settling out of the layer and a material balance ean there concentrations of tost and ur.dirdow a: least ...- rapidly as they fore be made. are fed lo the ur.it. Otherwise. a layer or zone of whatever coneeutration limits the sol:ds-hand!L-.g capioity v.il form, and act as (C - dO At (F -r dl*+ T) - CAi(V + V) (1) a barrier. If insuiccicr.t area is present to handle "he soiid*. such a barrier layer would rtttlJ up and all solids iu ev-ess of the amount which could subside through this sor.e would erentuaily By simplifying and solving for V, dropping out infinitesimals of the second order. have to oerniew the t hickener. Therefore, a thickener must base at least enough area to allow the sodd* to subside through which V-C^L Ldc <2; ever oon*niraUnn layer would have the least solids-hasdUpg capacity. The method Coe and Clevenger used for determining the Since, according to the Kynch postulate V - /(O, it follows that thickener stroa needed seas to make a series nf hatch settling testa on the pulp at various concentration* and lo determine trie area <fF se ~r{C) required to handle unit flow of solids for each lowsatniwa. The maximum unit area thus determinsd was used a* a hasis of thick ener desicn. u-cno-no IV Coe and Clevenger rsalired that in a tottling test, concentration Since Ciamnriaatfcwthalsytriaq--tiua./TCI and/*(C;iuTr layers of lower solids handling rapacity than savers of initial eoo- fined vulnee and therefore U oaatalso bo constant. .vniration. if tltoy potentially ovist, must propagate up from the The constancy e# C may now be naed to determine the soGdi bottom of the vnaaal and appear eventually at the upper bound iwlniiie of thelnyor at trie apper boundary i Ilia settling ary nf the settling pulp. They applied this coaoept te onrianaos pulp. Let C| aad be the initial coacealrariaa and height, re- settling lv hut did not develop it to explain the srer-derwnaeiag speetzrelr, of e eokznmedpri^p in a belsri settling teto. The total w ttlirig rate they observed in the transition beiwe-tt ir-v settling weight of soSda ia thie palp (sin ia then CJ1*4- When any av.d oomprveaton rondrtior.s in a hatch test. eapacsty-finritiag mi--diatiso ispr nailiss the pulp-water In Kv-rt.th showed how the settling rate and ooDcentrsuon of assy terface aU eahda ia the aahaaa not hqaa paaed Ihzongh H asoa rapacity-hmiung ooncontration layer which may far can be de ----- j--rr--*1 ~T *~r~n tfw hittoni id Ika n ilaMi Dtheeon- termined from the variation in s-nling rate ot-served in s single ftrstjm if this lays is C, nl jtimha tri litnti ns at iin*. ;mv r. settling test. It, erica the qnasdihf of alri iiqhg pajoad *--/! this layer, / AS IH DU S TP 1 A L AND IHGIWirWBTWrz pbsutovsv 1I I * 1 9 2 0 1 * * : v-r- r --" . .__ d(Ft + Tf), must equal tbs ti>taT weight ca-solids In the The total quantity of solids in batch teat la CaHaA and it lmo. -I V- would take time U for thia quantity of solids to subside past a /tontine than* axpranriom layer of concentration Ct in a continuous thickener. Therefore, the quantity of solids that could be brought through layer con CaBU -CwUrfF,* UO (4) centration per unit time ia CaHaA/U. "Unit area" of a layer is, by definition, the area required to allow 1 ton of solids to subside f Ht represents tha height of th* interfae* at time, W, and ainea through the layer concentration in 1 day. ns been proved that the upward velocity i any specifie layer ooatant. 0a-& Is () Unit t square feet/ton solkls/day CHt (10) In order to obtain unit area in the kibstituting in Equation 4 and simplifying specified units of C, - CJI. Ht+ FA (#) square feet per ton per day, it ia neces sary in Equation 'i ia equal to dH/dt at the point on a plot of H versus t(Figure it which the layer having a concentration of Ct cornea to the face of the pulp. Ft ia then the alope of the tangent to the ve at (If*, It). It follow* mathematically that the intercept of i tangent on the if aria ia if* + FA (ahown aa Hi). By aub.uting Hi for Ht + FA in Equation 0, it ia ahown that CJHi " /*. From thia it followa that ifi ia the height the pulp would upy if all the aolida prevent were at the aame concentration aa layer at the pulp-water interface. For any arbitrarily eboaen ue of Ci the corresponding value of Hi may be calculated. V, i then be determined aa the alope of the line drawn through at Hi and tangent to the settling curve, and a complete aet of a showing F aa /(C) can therefore be developed from one aetig teat. n order to specify the area requirement of a thickener, the iccntration layer requiring the marimum area to paaa a unit ;ght of aolida must be determined. Thia may be done by calating the unit area required for a eeriea of concentrations, og the data showing V as/(O developed in the previous para ph and substituting in tha Coe and Clevenger formula (k ~ ) Unit -----------v-- 10 to express H, and C in units of days, feet, and tons per cubic foot, re spectively. How ever, it will usually be convenient to construct the set tling curve and carry out the graphical construc tions in terms of more conventional Figure 1. Typical Pulp Height vs. Time Relationship for Batch Settling Test units, using an ap propriate conver sion factor to con vert unit area into the specified units. Tbs'method for determining the unit area corresponding to any pulp concentration C in tha free settling range is therefore aa follows: 1. Determine ifi and Hm from the following material balances: point Hi corresponding to on arbitrarily selected concentra tion, Ct C,ff. - CiHi - CJf. lichcver concentration layer gives the largest value of unit area 'hen used aa a design basis With Figure 1, a simple geomet- il construction may be used to obtain the unit areas directly. U time h the aolida in tha layer existing nt the surface of the !p are settling at a linear rate of Hi -- HxJU. If the aolida of 2. Draw an "underflow" line parallel to the time axis at H * H. on s plot of pulp height versus time, aa shown in Figure 1. 3. Draw a tangent to the settling curve through point Hi on the H axis. 4. Read i, at the intersection of the tangent and.the underflow s layer are assumed aa a datum, water ia p"iwng the solids at a ik rate of A(Hi -- Ht)/t%. In a continuous thickener, the ids in any sons do not have to settle past all of the water in the ie, since part of this water will accompany the aolida to the derflow. Tbe amount of water they must settle past is equal .her to the amount which would be released in bringing aolida m layer concentration to underflow concentration. The eor- 5. Calculate unit area from Equation 10. a When the underflow line, H,, intersects the settling curve above the {mint where the layer at the surface of the pulp goes into com pression, the time, f, corresponding to maximum unit area will be the coordinate of the intersection since uny other tangent will in tersect the underflow line at a lesser value of U- When the under ponding quantity of water for the aolida present in the batch t would be A{Hi -- HJ), since Hi ia the height the pulp would upy if all solids present in the batch test were at layer eoneention and If, ia the height the pulp would occupy if all solids sent in the batch test warn at the thickener underflow concen- flow line intersects tlio settling curve below the point where the layer at the surface of the pulp goes into compression, tbe tangent giving marimum unit area will be drawn through this compres sion point, since this tangent gives the highest value of t, in the free settling range and only free .settling xones govern the unit tion. Tbe time that would be inquired to release A(Hi -- H,) ter through a layer of concentration C, would then be l' -- MDOUP* of water to eliminate _ A(Hi -- Hm) eliminating water _ A(Ht -- Botch Settling Testa Demonstrate Validity of Kynch Analysis *' It is implicitly assumed in Coe and Clevenger's treatment that solids in frvesettiing pui|* will olwy Kynch's basic assumption-- I' he., that the settling velocity of a particle is a function only of the H, - H. Hi- Hi ' local concentration. Since the Kynch conclusions, ore mathe By the law of triangles matically certain if the basic assumption is met, the Kynch method for determining behavior of free settling layers must be at least aa (9) valid as tliut of Cue and Clevenger. The Coe and Clevenger teat inaxy 1963 INDUSTRIAL AND INGINXIRING CHIMISTRT m '/ l ij BWMEBUNO, PESK^VNP PROCESS PEVROFMENT m<' ! r.w i'(t .4 *' t ?vjj h* >1 'V * j h"' -A r " 3- 1 COi eo C .EVEN *CR V-- WCTM * <0P 200 300 CD*CtT*ATtO* -Cju M>ufcr>tenl Pulp --J--J-- II I s' c * a-e l{v*OEA \fNC~H ' oo too no CONCCnTRAT ion 4/U Colduia Corbonot* V COC ait CLE' ENOCH fs . yTM< < kvNC* r 30 75 CONCENTRATION - O/u Cmarf Rodk A 3; :s iOL. 31 MATeMriiXk xs' ^ kUlflCL tOO 140 tOQ concentration 3-50gVu Ctmtml Bock i figure 2. Comparison of Coe and Gevengec and Kyndi Methods for Analysis of Batch Settling Tests procedure, however, entails an additional assumption which is not nerreesrily valid and which is not oontained in application of tha Kyneh analysis. The Coe and Clevenger test procedure of ob serving the initial settling rate in a series of batch testa of various . initial concentrations assumes that the settling characteristics of the floe will be independent of the initial solids concentration in the pulp in which they are formed. Roberta (4) indicated that this is not always true, as is also demonstrated in this paper. In order to compare the results of the Coe and Ctevengcr method and tha Kyneh method, batch settling tests were made on the following materials: Metallurgical pulp, specific gravity 4.44--settled fairly rapidly to a high Anal concentration Calcium carbonate (CaCOs), specific gravity 2.63--settled fairly rapidly to an intermediate final concentration Cement rock A, specific gravity 2.56--a highly flocculent, stowsettlicg material which had a low final concentration Cement rock B, specific gravity 2.81--a segregating material which settled slowly to a high final concentration Figure 2 show* tho settling rate versus oocoentrillion as deter-' mined from batch testa on these materials using both the Coe and Clevenger procedure and the Kyneh procedure. The results of the two procedures cheek in tha lower concentration ranges, dem onstrating that the methods sre equivalent in this range. How ever, the results diverge as the concentration increases and this must be due to failure to conform to the additional assumption entailed by the Coe and Clevenger procedure. The settling velocity of a floo may be presumed to be a function of the structure of the floe, as well as of tha solids concentration. In order to obtain an indication of the effect of initial pulp con centration on floe structure, batch tests were made on each of the four materials at a series of different initial concentrations. In each case the solids were allowed to settle until the pulp line re mained at constant height (final concentration). If the structure of the floe were independent of the initial solids concentration, the - tame final concentration should he reached in nil such tests on a given material. The results given in Table I show this is not the casa. The floe structure was apparently affected by this initial concentration, and hence it must be assumed that tha settling rata also would be affected. Therefore, Coe and Clevenger's ad ditional assumption is not necessarily valid. It can be concluded that results of tho Kyneh method will al ways be aa good as those of the Coe and Clevenger method and in many cases the results of the Kyneh procedure should be more valid. However, since settling characteristics mav vary with changing initial pulp concentration, batch testa following the Kyneh procedure should be made on pulp of the expected thick ener feed concentration. deed Cerreiafien Is Obtained with Field Operating finetrite A correlation between batch tests interpreted by the Kyneh procedure and actual field operating results was obtained during a survey of the beet sugar industry. The operation of thickeners in the beot sugar industry is subject to many variables both from plant to plant and from day to day in any ooe plant. Some of the more important variables with respect to thickening area re quirements are tons of beets sliced per day, cubic feet of juice per ton of beets, amount of carbon dioxide gas used, amount of lime added, and quantity and type of flocculating agents added. Tn view of these variables, the checks an unit areas, as determined by the Kyneh procedure and actual operating data, are excel lent. These rreults are presented in Table IL No testa could be made according to the Cos and Clevenger procedure as the floo structure changed radically when tbs matariai was repulped. Thickener unit areas have sometimes been emneoosly based solely on the initial settling rats of a cylinder of pulp at feed con centration. By using this procedure, tha following unit area re quirements in square feet per ton solids per day of the tour beet sugar plants were calculated: Table t. Effect of Initial Concentration oo Ffctal Concentration Coooontratlon. (jnss/Lllw ________ Initial Final Initial Final Initial ' Final Initial Flat! MotaJIarcioal Pulp 197 1083 JW 1170 242 1338 Ciioum CbrbnuU 27.3 701 70. t 794 Cooloot Rook A ! 1 210 14.0 293 Ctmoat Rock B 181 KUO 293 1*73 109 419 334 1*94 - 20! 449 ' 43 9 307 M0 1304 Plant A . Plant B Plant C Plant D ' 2.4 3.4 2.0 ' 2.5 Table II. Thickener Unit Areas at Beet Sugar Plants Deter mined from Operating' Data and Batch Tests by Kyneh . Procedure ' . FUat A B c D. Vr> : V r> ;,'e* Unit Arm. 8q. Ft./ Too SolWPay `ve.r- s.sa ColonSs ' IS.4 Moataaa - ' Y~. ' 4.13 Calibrate..' - . ',4.44 jfraoh a.sa leS.sso 1.33 .1- l M 40 INDUSTRIAL AND ZNGINXXRING CH.TIST*T'->' i **- VoL 47, No. 1 7 *1 1 *1 0 2 0 1 $ . rhe difTereneee between 'thee* values'. and. the ae. value ' ' err:. -- upward layer velocity, ft./da >wn in Table II clearly InrilnatS the baaard of this procedure - - UA -- unit area, sq. ft./ton solids/d.. V .- particle settling velocity, ft-/day 5 !o2$ J indicate the utility af thaKynoh method/y ir ' -* TV a particle settling velocity at eooeentratioo C,( IL/day * mencMwre-i -rv; i.' :; >1:.; ' Acknowledgment oal'araa,an.It. -- concentration, tona/ca^ft tvir'.****? i i tv. j,':. , .:> -- initial concentration, tona/oa. ft. - craoantrataoa of pulp at pulp-water interlace, tona/co. It The author* wish to thank R. H. Van Note of the Don Co., for supplying the thickening data on the sugar beet industry. - concentration of undarfloir, toos/cu. It -- initial height, ft , ... . -- height of intercept of tangent to pout (B%k) and B ana, it. J> r1' " -- pulp height at time It, ft - .> height palp would oeeapy if eolida werw at underflow concentration, ft -- time, daye -- time required to eliminate A{B, -- N.) unite of water, monitor# Otsd (1) Aaabls, A., in Chtmical Enginsers Handbook (J. H. Perry, edi tor), 3rd ed., p. 397, McGraw-Hill, New York, 1950. (3) Coe, EL 8.. and Clevsoasr, G. H.. Tran*. Am. IntU Mining Engrt.. 55. 355 (1910). (3) Kyneh. G. J.. Trans. Faraday Sec., 43, 161 (1953). (4) Roberts. E. J.. Mining Eng., 1, 61 (1949). daya -- time at which pulp height is Ht, daya -- time at intersection of tangent to point (ffijt) and Bm, daya Rscsrras lor rsviow Mar 10. 1*44. Accsrrss Oetoto 4, 1944. Pnaastad bslsrs tha DirUos ol Iadtutrial sad Eadaswiae Chtmisuy si tk I26tk Mt.tisr of th* Aksucjui Ckxxicai. Socistt. New York, N. Y. lynsnic MsMte &lr Drying dttSa Bead-Type Besieearot H. G. GRAYSON Sscosy Vacs-- 05 Co., lac., 36 Irwdwsr, Now York 4, N. Y. lTRIPPED of individual refinements, dynamic gas drying ) units operate on a few basso principles. The air or gas it reed through the bed of desiccant until the bed reaches a certain igree of saturation At this paint the flow is directed to another yd of riariooent while the first bed is being reactivated by tbs apication of beat. The most important properties of a dosiocaat dynamic dehumidiSoation are its moisture adsorption capacity id its ability to lower the dew point of the effluent gas stream. When a humid gas stream pssses through a bed of desiccant, le first gas that comes in contact with the desieeant is dried to re dew point characteristic of the desiccant. The layer of aiecant nearest the hdet becomes saturated rapidly during this base and little or no drying of the gas occurs as it approaches the utiet side of the bod. As further increments of humid gas pass irough the bed, the sons of saturated desiccant progresses steady through the bed, but the dew point of the effluent gaa remains tactically constant. As the sons approaches the outlet side, the sw paint of the effluent gas rises sharply and increases until it quals that of the ineoming gas stream. The bod is completely itorsted at this point, and the amount of moisture adsorbed is nown as the equilibrium capacity. The magnitude of the equilibium capacity depend* on the relative humidity of the incoming as and is affected only slightly by temperature, as shown in Igum 1 for the range 50* to 150* 7. Furthermore, air velocity -nd desiccant bed depth have no effect on this capacity (0). In actual operation, a drying unit is seldom ran so that the dee-' scent reaches its equilibrium capacity. If it were, its drying ffidency would decrease rapidly near the end of the cycle. A yptca! adiabatic drying ran dew point curve (Figure 3) indies las i sharp rise in the dew point venue capacity ourve. The instant >f effluent dew point rim is known as the break point, and the (uantity of moisture adsorbed up to that point is known as the weak point capacity, dry gas capacity, or capacity at maximum ;ffidency. It is the break point capacity that is of greatest im- oortance to the designer and operator of drying units producing /ery low dew paint effluents and not the equilibrium capacity. Much of the data published on ;ur ilrying by solid desiccants have been obtained on laboratory scale equipment operated under isothermal conditions--i.e., the heat of adsorption was removed by proper cooling to maintain a constant temperature (1, t, 8). The equipment used for the studies described in this paper was of semicommercial rise containing 6.5 to 24.5 pounds of desiccant, depending on bed depth, and runs were made under "adiabatic" conditions. In industrial installations truly adiabatic adsorption is never obtained because insulation is not sufficient to suppress heat looses entirely. Consequently, the term "adiabatic" is considered as meaning that no attempt was made to remove the heat of ad sorption, and that the equipment was insulated. Somkommercial Size Drying Tower Is * Operated under Adiabatic Conditions The equipment, as shown in Figure 3, comprised the apparatus uaod for the adsorption and desorption runs. The flow was aa follows: Laboratory air'from a 100-pound main passed through a 0 X 12 inch filter pot filled with a desiccant to remove any entrained compressor oil or moisture, then through s fiberglass filter and strainer to complete the cleanup. The air flow was controlled by a hand-control valve and bypass. The control of the steam, which was injected to regulate the inlet humidity, posed somewhat of a problem, as the amount was as low as 0.04 pound per hour for the low vclocity-low humidity runs. The aouree of steam from the 100-pound main wits wet as the boilers were located several thousand feet away. The steam required not only throttling and accurate control, hut also continuous bleeding to remove auy condensed water. The steam system consisted of a hand-control valve (of the type used in instrument air throt tling), a separator pot with bleed line and pressure gage, a needle valve in the vapor line off the separator, and a restricting orifice just upstream of the steam-air mixing point. The sin of the restricting orifice was determined by trial and error.- Several orifices were drilled; the smallest site was tried first and found to be adequate to luradle the total range of flow* required. Tannery 1933 INDUSTRIAL AND ENGINEERING CHEMISTRY 41 <!! 'fti 41, h> - is -20- Batch Tests Predict Thickener Performance Advantages and limitations of several methods for analyzing thickener criteria provide the basis for optimum design of the equipment. BRYANT FITCH, Dorr-CHIver Inc. A thickener is a sedimentation basin, usually cir cular, provided with a raking mechanism to convey settled solids to a discharge point It is distinguished from other types of sedimentation basins such as clarifiers in that particles suspended in die feed s.uny cohere in some Sort of floe structure. This causes them to separate with a sharp line of de marcation between dear supernatant liquid and set tling solids. In such a case, overflow clarity is not normally a problem, and design is controlled by conditions necessary to deliver settled solids to the underflow at the expected underflow consistency. That is, the con sistency is controlled by the thickening capability of the basin. In normal operation, the bottom part of the thick ener is filled with a layer or bed of thickening pulp that subsides toward the underflow and becomes ever thicker in solids as it approaches the bottom (Fig. 1). The deeper this layer (solids feedrate and other tilings remaining equal), the thicker the underflow. But if you try to get underflow at too high a concentration, the thickening-solids layer will build up to such a depth that it fills the thickener, part of the solids are displaced into the overflow, and tiie thickener fails. Thickeners may fail in another way. New feed, having a higher specific gravity due to its suspended solids, plunges through the lower-gravity supernatant (usually without too much intermixing) and spreads out in a layer just above the thickening solids. The new solids settle into the thickening zone. The remaining supernatant, relieved of solids, is dis placed upward toward the overflow by the contin uing invasion of new feed. But all of the solids may not be able to settle out of the feed layer in the area provided. In this case, a layer of some constant-solids concentration builds up above the layer of thickening pulp (Fig. 2). In time, it reaches the top of the thickener, and the excess solids overflow; and the thickener is now said to fail in "free settling." The design problems are then: 1. How much area is needed for a given feed, to prevent formation and backup of a constant-concen tration or critical zone? 2. How deep must the thickening layer be to give the expected underflow consistency? We can get the necessary design information from laboratory measurements made on a sample of feed pulp. Derivation of Fundamental Equation The fundamental equation (Coe and Clevenger) relating solids flux toward die underflow (solids flow CHEMICAL ENQINEERINQ/AUOUST 23, 1971 CONCENTRATION zones in overloaded condition--Fta 2 THICXENER3 . . . -21- 4 NORMAL batch-settling curve shows two discontinuous regions--Fig. 3 S tfW S tlS a Tima, min. INCREASING RATE section during initial period of batch settling--Fig. 4 . per unit time per unit area) and concentration exist ing at any layer in a thickening or critical zone it as follows: <?------------ ------- A11 C ~ C. (1) where G it solids flux through concentration layer, 5 is flow of solids through thickener, A is area of thickener, R is settling rate of solids with respect to pulp as a whole in die layer, C is solids concen tration in the layer, and C, is solids concentration in the thickener underflow. At every level of settling pulp in a steady-state operation, the solids have two velocity components. First, there is the settling velocity, H, of soHds with respect to the pulp as a whole. Second, there is a doaward component, V, of the pulp as a whole because underflow is being withdrawn at the bottom of the thickener. Total downward velocity of solids is then (A + V), and the total flux of solids is: a - C(R + V) (3) Total underflow rate is AV, so the solids underflow rate is C.AV, and the solids flux through the thickener must then also be: Q - S/A - C^AV/A - C.K (3) Eliminating V between Eq. (2) and (3), we obtain: 11 -"cT which is the same as Eq. (1), the Coe and Clevenger equation. Cm and Clavangar Modal of Thickening In order to use the Coe usd Clevenger equation, we need some model or theory that will relate laboratory data to what happens in thickeners. All cur rent design methods sue based on the thickening beHavior conceived by Coe and Clevenger.1 (The model is Dot completely valid, but we do not as yet have 14 a better one. The problems this creates will be dis cussed later.) In line settling, all particles in a given location may be considered to settle at about the same rate. If they did not, slower se *hng particles would string out behind faster settling ones. Tbe pulp-supernatant boundary would become diffuse, and then would no longer be line settling. Thus, a tingle settling rate can be attributed to all solids in a lamina of pulp. Coe and Clevenger postulated that this settling rate, ft, would he a function of solids concentration, C, only, as long as no mechanical support wen con tributed from layers of pulp below. They called this condition "free settling,** and identified it with the critical zones that can form in overloaded thickeners. As particles pile up from the bottom of a thick ener or settling column, they must at some point start receiving mechanical support and pais Into a "compression zone." Coe and Clevenger defined a compression zone as "that portion of the pulp where the floes (considered as integral bodies) have settled to a point where they rest directly one upon another. After pulp enters the compression zone, further sep aration of liquid must come through liquid pressed out of floes and out of the interstitial spaces between the floes.** In compression, the settling rate, R, should be some function not only of concentration bat also of the depth and concentration distribution In the zone. Coe and Clevenger consequently assumed that the thickening-pulp layer in a thickener would be in compression. One important assumption in the Coe and Clev enger model is that, in "free settling," R is a function of C only. Therefore, for concentrations in the freesettling domain, the settling rate observed in a batch test would be the same as would occur in a critical zone in the continuous thickener. Batch Settling In batch-settling tests, a column of pulp initially at uniform concentration is allowed to settle. The subsidence of the pulp-supernatant Interface is roeas- AUGUST 23. 1971/CHEMICAL ENGINEERING -22- ured as a function of time. Coe and Clevenger dis covered that there might be either one or two sub sidence-rate discontinuities (Fig. 3). Two discontin uities divide the subsidence curve into a constant-rate section, a first falling-rate or transition section, and a second falling-rate section. If only one discontinuity exists, the first falling-cate or transition zone is considered ahsent. They observed extensive channeling in the second falling-rate period. Channels of clear liquid form in the settling pulp, often erupting through the pulp-supernatant interface as miniature volcanoes of fluid. The constant-rate section corresponds to settling of pulp at the initial test concentration. The Coe and Clevenger procedure is to make batch tests at a series of initial concentrations, and to determine free-settling behavior from the constant-rate sections of the batch-settling curves. The first falling-rate period was explained qualita tively by Coe and Clevenger, but it remained for Synch to provide a satisfactory quantitative analysis. As solids collapse against the bottom of the column, there are formed zones of free-settling concentrations that cannot transmit solids at the rate they are settling in from above. Zones of such limiting or critical con centrations back up. During the first falling-rate pe riod, zones of ever more limited solids-fiux capacity are reaching the surface, and the subsidence rate at the interface corresponds to the concentration exist ing there at the moment Synch showed how to deter mine this concentration. This promised (assuming the model is correct) a way of calculating all freesettling behavior necessary for thickener design from the first falling-rate period of a single batch test [There will sometimes also be an initial increasingrate period (not allowed for in the Coe and Clevenger model) before a constant settling rate is reached. (Fig. 4). This is presumably the time taken for the particles to arrange themselves and cohere into what ever sort of floe structure is formed. This period for arrangement and cohesion is ignored in existing design procedures.] Finding the Compression Point Conventional design procedures consider 'free set tling" and 'compression'' independently. They rely heavily upon identifying the "compression point" dis continuity at the start of the second falling-rate period. The average concentration of pulp at this point (weight of solids divided by volume of settled solids) is taken as the dividing line between free-settling and compression domains. Often there is no difficulty in identifying the com pression point on a linear plot of pulp height vs. time, as shown in Fig. 3. But in cases of doubt, a log-log plot may be helpful (Fig. 5), or a Roberts* plot (Fig. 0). In the last, (H--Hao) is plotted on a log scale vs. time on a linear scale. With an appro priate choice for Hao (the height of the settled solids at infinite time), the compression leg of the settling CHEMICAL ENQJNEERINQ/AUCUST 23, 1971 LOO-LOO plot locates compression point--Fig. 5 ROBERTS pfot-locates compression point--Fig. 6 curve will be linear. And the junction between first and second falling-rate sections usually (but not al ways) will become obvious. Determining Needed Thickener Area The Coe and Clevenger model assumes that the most flux-limiting concentration will not lie in the compression range. In principle, we test the fluXhondling capacity for zones of every concentration between that of feed and that of compression, using free-settling data and Eq. (I). (The procedure given by Coe and Clevenger does just this.) The overall solids-haudling capacity of the thickener must then correspond to the most limiting concentration, because it constitutes the bottleneck or throttling point Any excess solids that could reach this concentration could not pass through it so would have to back up above it. If a critical zone formed in the thickener, it would have this concentration. In practice, we now prefer to use the Talmage and Fitch method.* It derives from the Synch analysis of the first falling-rate section of a batch test, and selects the limiting or critical-zone flux directly by graphical means. The mathematics will not be pre sented here, but the procedure is as follows: Make a single batch-settling test, starting at feed concentration, Plot pulp height, H, vs. time, t, as 89 rwcttNEm . . . -23- 4 LOCATINQ umhrllow time when H>H.--FJfl. 7 . .> nr x. rsv. i.1 l*l8 2 0 iS ,, LOCATINQ underflow time when H,<H--Flfl. 8 shown in Fig. 8. Select attainable and acceptable C%: and calculate H%: H. - CM./C. (4) If Hm lies above the compression point on the batch-settling curve, read f at H, on the curve. Therefore: a, - cm./i. () where G, is the mAnmn solids flux that can be passed through the thickener. If Hi lies below the compression point, draw a tangent to the free-settling side of the curve at the compression point (see Fig. 8). Read t. at H. on the tangent line, and calculate by using Eq. (5). If the test is carried out in a liter graduate: where C, is tons solids/(sqdt) (day), W is grams solids in batch test, t. is min., and K is cu.cm./ft. in graduate. Where hatch-test data are scattered, it may be advisable to replot the data as a Roberts curve to determine the compression point The construction to Fig. 9 may then be used in place of Fig. 8 to determine t>. Draw a tangent to the Roberts plot on the free-settling side of the compression point Then: t, L+ HH, - g.) 2MB. - Bm) (7) where t, is time at compression point, min.; H, is pulp height at the compression point, cu.cm.; H% is pulp height st the underflow concentration, cu.cm.; Hao is ultimate pulp height shown in preparing Roberts plot, cu.cm.; and 9 is time interval required for the constructed tangent line to cross one log cycle [Le., from (H - Hao) ~ 1,000 to (H - Hao) = 100, min.]. Example of Test Procedure Actual data from a batch-settling test are given in Fig. 9. Kynch zones were propagating to the surface 88 (first falling-rate period) between points a and c. Note that in the region of compression. Point C, the data points appear to wander a little, but we can still draw a tangent to the left of cusp c with con siderable confidence. Cycle rime 9 is determined from points on the tangent line one log cycle apart. The value for fj at (H -- Hao) = 100 is 108 min.; and for tt at (H -- Woo) = 1,000 is --15 min. Therefore. - 108 - (--15) - 123 min. Additional data for the example are: 1,-79 min. (from Pig. 0) (B. - W) - 172 (from Fi*. 9). iff -- -- 200 (found io constructing Fig. 9). B. - 172 + 200 - 372 B, -- 213 (by choice, from final dilution data). W - 201.3-*. solids in test. K - 850 cu.cm./fL in graduate. Substituting in Eq. (7), we get: I. 123(372 - 213) + 2.3(172) 128 min. Then, substituting in Eq. (8) yields: a, 45(201.2) 128(850) 0.063 tons/(sq.ft)(day) Determining Thickening-Zone Depth Coe and Clevenger observed that subsidence rate in the compression regime was a function of concen tration and also of pulp depth. They also noted that the subsidence rate, R, was augmented in this regime by channeling. This led to the idee that subsidence rates could be increased by increasing pulp depth as much as necessary to make the corresponding fluxes nonlimiting. Therefore, settling rates observed in shallow batch tests for pulp in compression, and the corresponding flux capacities calculated by Eq. (1), could be ignored, if sufficient depth of pulp in compression were provided in the thickener. The design question was only how much compression depth would be needed. Coe and Clevenger further observed for metallurgi cal pulps that batch-subsidence rates in compression were more or less proportional to initial pulp depth. AUGUST 23. 1971/CMEMICAL ENGINEERINQ -24- TANGENT at cofnpreaaion point of Roberta plot enable* computation of underflow time--Fig. 9 This leads mathematically to the idea that, for such pulps, final pulp concentrations should be a function only of time in compression. (They further observed that for chemical pulps, with "a highly viscous homo geneous structure," "the law of compression being a function of time would not bold.') Upon this highly empirical and somewhat dubious foundation, Coe and Clevenger base their "final-dilu tion* test to estimate compression depth needed to attain specified underflow concentration, C,, A cyl inder of pulp is allowed to settle (with very slow, intermittent stirring) for an extended time. Settled pulp heights are read at intervals. After any specified time, t, .In compression, the settled-pulp height is read and the corresponding pulp concentration cal culated. This is taken as thickener underflow concen tration. The average pulp volume over this compres sion time is then determined from a plot of the subsidence curve (Fig. 10). The compression depth (in feet) needed to produce the selected C, may then be calculated from: P4 - 1,333<7#</W (8) where ?t is pulp depth, ft; C, is thickener flux, tons/ (sq.ft.) (day); t is compression time, hr.; o is average pulp volume over compression time, cu.cm, of pulp; and W is weight of solids, g. The stirring referred to in this procedure simulates the action of a thickener rate structure. It prevents bridging of solids in the small-diameter batch test. CHEMICAL ENGINEERING/AUGUST 23, 1971 and in other ways assists compression. A typical stirrer might make one revolution in 10 min., and then be stationary for 10 to 20 min. The "Three-Foot" Rule As noted by Coe and Clevenger, and as observed early in the art chemical pulps in which the compresri/m process continues for a long time do not follow their detention-time law. Darby and Queens* on the basis of laboratory tests and field experience, came up with an empirical 3-ft rule. This rule states that if die pulp depth as calculated by Eq. (8) comes out to be over 3 ft, then thickener area is increased sufficiently (that is, Gt is reduced) to make compression pulp depth equal 3 ft This brought underflow concentration, as observed in the field, more nearly in line with that predicted by the Coe and Clevenger final-dilution or compres sion-test procedure. Undoubtedly this 3-ft. rule has done much to shield design engineers from the limita tions of the Coe and Clevenger model, both with respect to compression and to zone settling. Validity of Design Procedure Dorr-type thickeners have been sized from batch tests, using the Coe and Clevenger model and pro cedures, for over 50 yr. This time-hallowed use, to gether with the fact that most of the thickeners so specified perform adequately, have given the design procedures an aura of unquestioned validity. But they are not that infallible. Usually they work, but in certain cases they can lead to serious underdesign. The reason for this is that pulps do not behave com pletely as in the manner postulated by Coe and Clevenger. While current research is making os ever more aware of deficiencies in the Coe and Clevenger model, we have Dot as yet developed and proved any new design procedure. But the practicing engineer cannot cease specifying thickener size. He must do the best ho can with the information available. And the old 87 d -25- THtCXKNERS . . . procedures are obviously adequate for all but `special" cases, or they would not have survived. In dealing with engineering uncertainty, there is really no substitute for experience and the informed judgment of those `versed in the art.' But the follow ing should give some feel for the nature and scope of the problems in predicting thickener performance. It should be apparent that the Coe and Clevenger procedure for predicting compression depth has no clearly understood theoretical basis, and relies on the roughest sort of empirical correlation. Even Coe and Clevenger ascribed only limited validity to it (u fact quite generally overlooked). It has, however, proved adequate, with the 3-ft. rule, for nearly all practical purposes. There ore several reasons for this: It seems to work pretty well in many cases. A great many pulps, including most metal lurgical ones, thicken readily to concentrations as high as m" be pumped, so compression depth is often not a critical factor. The rate of compression is, in almost all cases, a rapidly diminishing function of time. In normal design, a large error in compression depth will usually lead to only a small change in underflow concentration. Finally, the 3-ft rule ap parently saves the day in many cases. However, if underflow concentration is of critical importance, you should not rely too heavily on the batch procedure--particularly where: Indicated underflow concentrations are low. Say less than 25% solids by volume. Indicated compression times are long. Say over 24 hr. There is no dearly defined `compression point.* Strong channeling is not evident in `compres sion* regime. In such cases, continuous piloting or the semicontinuous procedure to be described later should be used. The Coe and Clevenger procedure for predicting thickener area, on the other hand, was long believed to be completely sound. We took it for granted that in "free settling* ft = ft(C). But if so, the Coe and Clevenger procedure (not described here) that derives free-settling behavior from the constantrate section of batch-settling curves, and the Kynch approach that derives it from the first falling-rate period, should have been equivalent They should have given the same answers. Experimentally, they do not Areas predicted by the Kynch procedure can in rare cases be up to twice those indicated using Coe and Clevenger zone tests. Part of the discrepancy was traced to the fact that a compression zone, building up from the bottom in a batch test, could interfere with some of Kynch's zones in such a way that his analysis would not be completely valid.1 But this explains only part of the discrepancy. Now it appears that columns of freesettling pulp break up into something akin to aggre gative fluidization, starting at the point of inflec tion on a Kynch plot of RC vs. C.* At higher con centrations, even where pulp is still in free settling, ft is not R(C), but increases with column height This channeled free-settling regime has been called phase settling. It is outside the Coe and Clevenger model, and therefore also outside what is accounted for by Kynch. Just what causes phase settling, and how it affects thickener design are still moot questions. They are beyond the scope of this article, but were discussed at some length in a recent paper.4 Current experimental workT indicates that the Kynch approach and the Talmage and Fitch procedure give slightly conservative predictions, while the Coe and Clevenger procedure, not adjusted by the 3-ft. rule, can in certain cases give results 50% lower than actual thickener performance. In case of doubt, it now appears that the Talmage and Fitch procedure is to be preferred. Semicontinuous Test Procedure ' Probably the best method of predicting thickener performance, short of pilot-plant testing, is the semicontinuous procedure suggested by Coe and Clev enger for chemical pulps. It is carried out in a column that is tall enough to provide whatever compression depth will be provided in the thickener. The column is filled with pulp and, at an appropriate time interval, clear supernatant is siphoned or other wise removed from the top, a volume of underflow is removed from the bottom, and feed pulp is added at the top to refill the column. (If the solids are not changed in settling characteristics, the underflow may be repulped and recycled as feed pulp.) This pro cedure is repeated for as many cycles as necessary to achieve a quasi steady-state, after underflow with drawals have been adjusted to yield the desired underflow concentration. The average solids through put is then calculated, and from this and the column area the corresponding average flux, G|. References O(ImMS. )H. . a. and OmnjtT, O. H, Trcnj. AJMt. SJ. 1M DBaotrre-rO. llOve. rU. . us Quwra. B. lataroal eomaiiBlaaUon. Jltofc, B.. Ini. tng. CAral, St, IS (IMS). MItater.nX. B1_STPI.aPperer pprinret MnoM. Tla-Bt -AUJ.34B Canteanlai Wanna Jracn. O V, Tran*, fond** See., it. 1M (1SS2). Bobaru. B. 1.. iriiiia# (nr.. 1. (IMS). TB(1aoSlomStJta,).aXa., Jw.,. Ppr.anaan.dHPuittc. hM, ina.inAa ,MI*ant.i-,. tt-ln,fC.SCS h(e1SaWt, ).VI, SS Meet the Author Bryant Filch <a chief icJantiat tar Dorr-Olivar Inc., Stamford, CT 0490V. Ha Mined tlta firm in 19V4 and has haM various poartMna *rth it Ha has sea- eialttad in physical aeparationa, ion aschango. and fartilliers. Mr. Pitch has a B.S. in chemical engineering tram California Inttraita of Technoloey. and an M.S. in charm ical engineering from tha University at Cennacttcut. Ha la a mam Hr of AlChC. ACS. and tho Amarican Inst of Chemists. la tho hoMar of 14 oatanta and had authored numerous articles. AUGUST 23. 1971/CHEMICAL ENGINEERING