'
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT
Determining Thickener Unit Areas W. P. T A L M A G E
AND
E. B. FITCH
The Dorr Co., Westporf, Conn,
0
PERATION of Dorr-type thickeners was analyzed by C,oe and Clevenger (2) in 1916. They showed how to predict t'hickener capacity from batch settling tests. The method outlined in t,heir classic paper has been used without significant improvement to this time (1). A recent paper (3) by Kynch presents a mathematical analysis of batch settling tests t'hat supplements the original picture supplied by Coe and Clevenger. Application of thc Kynch mathematics to thickening problems makes it possible to simplify t,he experimental procedures and interpretation of results. Simple Geometrical Constructions Aid Direct Determination of Unit Area Requirements
Kynch does not analyze the relationship between batch settling tests and continuous thickeners. In order to apply the Kynch analysis, it will be useful to review that part of the mechanism of continuous t'hickening pertinent to the problem. A c cording to Coe and Clevenger ( 8 ) there may be several regimes or zones in a thickener but the thickener area required is determined by conditions in what they designate as free settling zones. These are defined as zones in which the floes are falling through the liquid without pressing on layers of floc below. I n a free settling regime, the quantity of solids which can settle through a unit cross section in unit time i s equal to the product of bhe settling rate and the solids concentration. Coe and Clevenger tacitly assumed that, under the operating condit'ions, the settling rate would be a function solely of the solids concentration. Therefore, the solids-handling capacit,y of any layer is a function only of its concentration. In a continuous thickener, the solids must, be able to subside through any concentration layers b e t w e n the concentrations of feed and underflow a t least as rapidly as they are fed to the unit,. Othern-ise, a layer or zone of whatever concentrat,ionlimits the solids-handling capacit'y will form and a,ct'as a barrier. If insufficient area is present to handle the solids, such a barrier layer would build up and all solids in excess of the amount which could subside through this zone would eventually have to overflow the thickener. Therefore, a, thickener must' have a t least enough area t o allow the solids to subside through whichever concentration layer would have the least solids-handling capacity. The method Coe and Clevenger used for determining the thickener area needed was to make a series of batch settling tests on the pulp at various concentrations and to deterniirie the area required to handle unit flow of solids for each concentration. The maximum unit area thus determined was used as a basis of thicliener design. Coe and Clevenger realized that in a settling test', concentration Iayers of lower solids handling capacity than layers of initial concentration, if they potentially exist, must propagate up from the bottom of the vessel and appear eventually a t the upper honndarg of the settling pulp. They applied this concept to continuous settling t,ests but did not develop it to explain the ever-decreasing settling rate t,hey observed in the transition between free settling and compression conditions in a batch test. Kgnch showed how the settling rate and concentration of any capacity-limiting concentration layer which may exist can be determined from the variat,ion in setmilingrate observed in a single batch settling test.
38
Kynch started from the postulate t,hat t,he settling velocity, ,T' of a particle is a function only of the local solids concentration, C, around the particle, or mathematically, V = f (C). The funct,ion is not defined and may change in any manner as the concentration changes. This will be recognized as the same assumption Coe and Clevenger made for the free settling regime. In a ba,tch test starting a t uniform concentration, all t,he solids start eettling a t uniform velocity since V = f(C). As the settling solids begin to collapse against, the bottom of the vessel, they must pass through all concentrations between Rtarting concentration and that of the deposited solids. If, a t any of thePe intermediate concentrations, the solids-handling capacity is less than that a t the lower concentration occurring immediately above it in the vessel, a zone of such intermediate concentration must start building up, since the solids cannot pass t,hrough it as fast as they are eettling down into it. Kynch shovied that' the rat,e of upward propagation of each such constant concentration zone is constant. Consider the infinitely thin layer a t the upper boundary of such a zone, having a concent'ration, C, originating a t the bottom at, zero time and moving upward a t a velocity of I-7 feet per second. The solids settling into this layer come from a layer having a concentration of (C - dC)pounds per cubic foot and a settling velocity with respect to the ~ e ~ sofe l( V dT') feet per second but with respect t o the layer of (Ti d V j-U )feet per second. The concentrat'ion of solids settling out, of this layer will he C with a settling velocity of V with respect, to the vessel and (V C ) Kith respect to the layer. Since the concentration of the layer is constant, the quantity of solids settling into the layer must equal the quantity of solids settling out of thc layer and a material balance can therefore be made.
+
+
+
(C
- dC) At
(V
+ d V + L!)
By simplifying and solving €or of the second order,
=
C At ( V
=
(1)
U,dropping out infinitesimals
Since, according to the Kynch postulate that
u
+ U)
Cf'(C) - f ( C )
V
=
f(C), it follows
(3)
Since Cis constant for the layer in question,f( C) andf'(C) have fixcd values and therefore C must also be constant. The constancy of U may now be used to determine the solide concentration of the layer a t the upper boundary of the settling pulp. Let COand Ho be the initial concentration and height, respectively, of a column of pulp in a batch settling test. The total weight of solids in this pulp column is then CoHoA. When any capacity-limiting concentration layer reaches the pulp .water interface, all solids in the column must have passed through it since it was propagated up from the bottom of the column. If the concentration of this layer is C, and it reaches the interface a t time, t., then the quantity of solids having passed through this layer,
INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY
Vol. 47, No. 1
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT
+
C2Atz(Vs U Z ) ,must equal the total weight of solids in the column. Equating these expressions COHd = CzAtz(V2
+ Uz)
(4)
If HZ represents the height of the interface a t time, k, and since it has been proved that the upward velocity of any specific layer is constant,
uz
Hz
t,
=
(5)
The total quantity of solids in the batch test is CJIo.4 and it would take time tu for this quantity of solids to subside past a layer of concentration CZin a continuous thickener. Therefore, the quantity of solids that could be brought through layer concentration per unit time is CoHoA/t,. “Unit area” of a layer is, by definition, the area required to allow 1 ton of solids to subside through the layer concentration in 1 day. Unit area =
A, square feet/ton COHO
solids/day
(10)
I n order to obtain unit area in the specified unit8 of square feet per ton per day, it is necestsary in Equation H: 1 10 to express tu, H , LL and C in units of I days, feet, and tons t per cubic foot, reI 9 spectively. However, it will usually FH2 be convenient t o a construct the set3 tling curve and &H” carry out the graphical construct2 tu tions in terms of TIME - DAYS more conventional Figure 1 . Typical Pulp Height vs. units, using an apTime Relationship for Batch Settling propriate ConverTest sion factor to convert unit area into the specified units. The method for determining the unit area Corresponding t o any pulp concentration C2 in the free settling range is therefore as follows: HO
Substituting in Equation 4 and simplifying
V2 is equal t o dH/dt a t the point on a plot of H versus t (Figure I ) a t which the layer having a concentration of C2 comes to the surface of the pulp. VZ is then the slope of the tangent to the curve a t (Hz, t 2 ) . It follows mathematically that the intercept of this tangent on the H axis is Hz V~tz(shown as HI). By substituting H I for Hz Vdz in Equation 6, it is shown that CzHl = Colla. From this it follows that H1 is the height the pulp would occupy if all the solids present were a t the same concentration as the layer a t the pulp-water interface. For any arbitrarily chosen value of Cz the corresponding value of HI may be calculated. Vz can then be determined as the slope of the line drawn through point H I and tangent to the settling curve, and a complete set of data showing V as f ( C) can therefore be developed from one settling test. I n order to specify the area requirement of a thickener, the concentration layer requiring the maximum area to pass a unit weight of solids must be determined. This may be done by calculating the unit area required for a series of concentrations, using the data showing B a s j ( C ) developed in the previous paragraph and substituting in the Coe and Clevenger formula
+
+
Unit area =
1. Determine H I and H , from the following material balances: point H I corresponding to an arbitrarily selected concentration, C2 COHO= CzHi = CuHu
V
Whichever conrentration lager gives the largest value of unit area is then wed aF a design basis. With Figure 1, a simple geometrical construction may be used to obtain the unit areas directly. At time t2 the solids in the layer existing a t the surface of the pulp are settling a t a linear rate of H I - Hz/tz. If the solids of this layer are assumed as a datum, water is passing the solids a t a bulk rate of A ( H , - Hz)/tz. In a continuous thickener, the solids in any zone do not have to settle past all of the water in the zone, since part of this water will accompany the solids to the underflow. The amount of .ivater they must settle past is equal rather t o the amount which would be released in bringing solids from layer concentration to underflow concentration. The corresponding quantity of water for the solids present in the batch test would be A ( H , - H,)) since Hl is the height the pulp would occupy if all solids present in the batch test were a t layer concentration and Hu is the height the pulp would occupy if all solids present in the batch test were a t the thickener underflow concentration. The time that wodd be required to release A ( H l - H,) water through a layer of concmtration C2‘ would then be
t , -- amount of water to eliminate rate of eliminating water
- A(H1 - H,) - A(H1 - H z )
(7)
t2
By the law of triangles
t‘ January 1955
=i
tu
_I
(9)
2. Draw an “underflow” line parallel to the time axis a t H = H , on a plot of pulp height versus time, as shown in Figure 1. 3. Draw a tangent t o the settling curve through point H I on the H axis. 4. Read t, a t the intersection of the tangent and the underflow line. 5 . Calculate unit area from Equation 10. ’\TJhenthe underflow line, H,, intersects the settling curve above the point wl ere the layer a t the surface of the pulp goes into compression, the time, tu, corresponding to maximum unit area will be the coordinate of the intersection since any other tangent will intersect the underflow line a t a lesser value of I, When the underflow line intersects the settling curve below the point where the layer a t the surface of the pulp goes into compression, the tangent giving maximum unit area will be drawn through this compression point, since this tangent gives the highest value of t, in the free settling range and only free settling zones govern the unit area. Batch Settling Tests Demonstrate Validity of Kynch Analysis
It is implicitly assumed in Coe and Clevenger’s treatment that solids in free settling pulps will obey Kynch’s basic assumptionLe., that the settling velocity of a particle is a function only of the local concentration. Since the Kynch conclusions are mathematically certain if the basic assumption is met, the Kynch method for determining behavior of free settling layers must be a t least as valid a s that of Coe and Clevenger. The Coe and Clevenger test
INDUSTRIAL AND ENGINEERING CHEMISTRY
39
ENGINEERING. DESIGN, AND PROCESS DEVELOPMENT I
CONCLNTSATIOU
Metallurgical Pulp
Figure 2.
Calcium Carbonate
Metallurgical pulp, specific gravity 4.44-settled
fairly rapidly
to a high final concentration Calcium carbonate (CaCOa), specific gravity 2.63--aettled
fairly rapidly to an intermediate final concentration Cement rock A, specific gravity 2.56-a highly flocculent, slowsettling material which had a low final concentration Cement rock B, specific gravity 2.81-a segregating material which settled E ~ O I V ~toJ ~a high final concentration Figure 2 slio~rsthe sett,ling rate versus concentration as determined from batch tests on these materials using both the Coe and Clevenger procedure and the Kynoh procedure. The results of the two procedures check in the lovxx concentration ranges, demonstrating that the methods are equlvalent in this range. Iloxever, the results diverge as the concentration increases and this must be due t o failure to conform to t,he additional assumption entailed by the Coe and Clevenger procedure. The settling velocity of a floc ma) be presumed to be a function of the structure of the floc, as well as of the solids concentration. In order to obtain an indication of the effect of initial pulp concentration on floc structure, batch tests mere made on each of the four materials a t a series of different initial concrntrations. In each case the solids were allon-ed to settle until the pulp line remained at comtant height (final concentration). If the structure of the floc were independent of the initial solids concentrat'ion, the
Cement Rock A
hlctallulgical Pulp 1%: 242 182 1236 1082 iiin
40
B
Plant Plant Plant Plant
27.3 761
16 1 210
70.5
1OR
795
810 35.0 202
151
IO50
A B C D
2.4 3.4 2.0 2.5
338 1295
203 1273
201 859
63 .n 307
Cement R o c b i i B Initial Final
Cement Rock
S,/L.
.1 cor] elation between batch teats interpreted by the K p c h procedure and actual field operating results was obtained during a survey of the beet sugar industry. The operation of thickcncrs in the beet sugar industry is subject to manv variables both from plant t o plant and from day to day in any one plant. Some of the more important variables with respect t o thickening area requirements are tons of beets sliced per day, ciihic feet of juice per ton of beets, amount of carbon d i o d e gas used, amount of lime added, and quantity and type of flocculating agents added. I n viem of these variables, the checks on unit areas, as determined by the Kynch procedure and actual operating data, are eucellrnt. These results are presented in Table II. KO tests could be made according to the Coe and CIevenger procedure as th? floc Etructure changed radically when the material was repulped. Thickener unit areas have sometimes been erroneously based solely on the initial settling rate of a cylinder of pulp a t feed concentration. By using this procedure, the lollowing unit area requirements in pquare feet per ton solids per day of the four beet sugar plant3 were calculated:
Effect of initial Concentration on Final Concentration
Ca1ciL;in Carbonate
Initial Final
-
Good Correlation le Obicained with Field Operating Results
~
Initial Final
450
350
250 COUCE\TRATION
same final concentration should he reached in a11 such tests on a given material. The results given in Table I show this is not the case. The floc structure was apparently affected by this initial concentration, and hence it must he assumed that the settling rate also would be affected. Therefor?, Coe and Clevenger's additional assumption is not necessarily valid. It ram be concluded that results of the Kynch method will alil-ays be as good as those of the Coe and Clevenger method and in many cases the results of the Kynch procedure should be more valid. However, since settling characteristics niny vary with rhanging initial pulp concentration, batch tests fo!lowing the Kx-nch procedure should be made on pulp of the expected thickcaer feed concentration.
Grams/Liter ________Conerntiation, ~Initial Final
G./L
Comparison of Coe and Clevenger and Kynch Methods for Analysis of Batch Settling Tests
procedure, however, entaile an additional assumption vdiich is not necessarily valid and which is not contained in applicat,ion of the Kynch analysis. The Coe and Clevenger test procedure of observing the initial settling rate in a series of batch tests of various initial concentrations assumes that the settling chara,cteristics of the floc will be independent of the initial solids concent>rationin the pulp in which they are formed. Roberts (4)iridicated that this i s not always true, as is also demonstrated in this paper. I n order to compare t.he results of the Coe and Clevengcr method and t'he Kynch method, batch settling teste were made o n the following materials:
Table:l.
-
BFO 1265
Table II. Thickener Unit Areas a t Beet Sugar Plants Determined from Operating Data and Batch Tests by Kynch Procedure Unit 4rea. 8 Ft./ Ton Solids?i)ay Actual Kync!i 6.98 6.88 19.4 16 . .5
____^__
Plant A B C
D
Location Idaho Colorado Montana California
INDUSTRIAL AND ENGINEERING CHEMISTRY
zn
5.23
5
4.64
5.32
Vol. 47, No. P
ENGINEERING. DESIGN. AND PROCESS DEVELOPMENT T h e differences between these values and the actual values shown in Table I1 clearly indicate the hazard of this procedure and indicate the utility of the Kynch method. Nomenclature
Acknowledgment
A
cross-sectional area, sq. ft. Concentration, tons/cu. ft. initial concentration, tons/cu. ft. concentration of pulp at pulp-water interface, tons/cu. ft. C , = concentration of underflow, tons/cu. ft. Ho = initial height, ft. H I = height of intercept of tangent t o point ( H z , ~and ) H axis,
= C = Co = C, =
ft. H z = pulp height at time h, ft. H , = height pulp would occupy if solids were at underflow concentration, It. = time, days = time required
t t’
-
to eliminate A(Hi H,) units of water, days = time at which pulp height is Hz,days = time a t intersection of tangent to point (H2,h) and H., days
tu
U = upward layer velocity, ft./day U A = unit area, sq. ft./ton solids/day V = particle settling velocity, ft./day V2 = particle settling velocity at concentration GI ft./day
T h e authors wish t o thank R. H. Van Note of the Dorr Co., for supplying the thickening data on the sugar beet industry. literature Cited (1) Anable, A., in Chemical Engineers Handbook (J. H. Perry, editor), 3rd ed., p. 397, McGraw-Hill, New York, 1950. (2) Coe, H. S., and Clevenger, G. H., Trans. Am. Inst. Mining Engrs., 55, 356 (1916). (3) Kynch, G. J., Trans. Faraday SOC.,48, 161 (1952). (4) Roberts, E. J., Mining Eng., 1, 61 (1949). RECEIVED for review May 10, 1954. ACCEPTED October 6, 1054. Presented before the Division of Industrial and Engineering Chemistry at the h’ew York, X. Y . 126th Meeting of the AMERICAN CBEMICAL SOCIETY,
Dynamic Adiabatic Air Drying with Bead-Type Desiccant H. G. GRAYSON Socony-Vacuum Oil
s
Co., Inc., 26
Broadwoy, New York
4, N. Y.
TRIPPED of individual refinements, dynamic gas drying
units operate on a few basic principles. The air or gas is forced through t h e bed of desiccant until the bed reaches a certain degree of saturation At this point the flow is directed to another bed of desiccant while t h e first bed is being reactivated by the application of heat. T h e most important properties of a desiccant in dynamic dehumidification are its moisture adsorption capacity and its ability to lower the dew point of the effluent gas stream. When a humid gas stream passes through a bed of desiccant, t h e first gas t h a t comes in contact Fith the desiccant is dried to the dew point characteristic of the desiccant. The layer of desiccant nearest the inlet becomes saturated rapidly during this phase and little or no drying of the gas occurs as it approaches the outlet side of the bed. As further increments of humid gas pass through the bed, the zone of saturated desiccant progresses steadily through the bed, but the dew point of the effluent gas remains practically constant. As the zone approaches the outlet side, the dew point of the effluent gas rises sharply and increases until it equals t h a t of the incoming gas stream. The bed is completely mturated at this point, and the amount of moisture adsorbed is known a8 the equilibrium capacity. The magnitude of the equilibrium capacity depends on the relative humidity of the incoming gas and is affected only slightly by temperature, as shown in Figure 1 for the range 50’ to 150” F Furthermore, air velocity and desiccant bed depth have no effect on this capacity (6). I n actual operation, a drying unit is seldom run so t h a t the desiccant reaches its equilibrium capacity If it were, its drying efficiency would decrease rapidly near the end of the cycle. A typical adiabatic drying run dew point curve (Figure 2) indicates a sharp rise in the dew point versus capacity curve. The instant of eitluent dew point rise is known as t h e break point, and the quantity of moisture adsorbed up t o that point is known as the break point capacity, dry gas capacity, or capacity at maximum efficiency. It is the break point capacity t h a t is of greatest importance to the designer and operator of drying units producing very low dew point effluents and not the equilibrium capacity January 1955
Much of the data published on air drying by solid desiccants have been obtained on laboratory scale equipment operated under isothermal conditions-Le., the heat of adsorption was removed by proper cooling to maintain a constant temperature (1,4, 6). The equipment used for the studies described in this paper was of sdmicommercial size containing 6.5 to 24.5 pounds of desiccant. depending on bed depth, and runs were made under “adiabatic” conditions. I n industrial installations truly adiabatic adsorption is never obtained because insulation is not sufficient to suppress heat losses entirely. Consequently, the term “adiabatic” is considered as meaning t h a t no attempt was made to remove the heat of adsorption, and that the equipment was insulated. Semicommercial Size Drying Tower I s Operated under Adiabatic Conditions
The equipment, as shown in Figure 3, comprised the apparatus used for the adsorption and desorption runs. The flow was as follows: Laboratory air from a 100-pound main passed through a 6 X 12 inch filter pot filled with a desiccant to remove any entrained compressor oil or moisture, then through a fiberglass filter and strainer to complete the cleanup. The air flow was controlled by a hand-control valve and bypass. T h e 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 velocity-low humidity runs. The source of steam from the 100-pound main was wet as the boilers were located several thousand feet away. The steam required not only throttling and accurate control, b u t also continuous bleeding t o remove any condensed water. The eteam system consisted of a hand-control valve (of the type used in instrument air throb 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 size of the restricting orifice was determined by trial and error. Several orifices were drilled; the smallest size was tried first and found to be adequate to handle the total range of flows required.
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