Continuous Thickening of Flocculated Suspensions Comparison with Batch Settling Tests and Effects of Floc Compression Using Pyrophyllite Pulp Keith J. Scott Chemical Engineering Group, S.A. Council for Scientific and Industrial Research, Pretoria, South Africa
Previous postulations on the thickening behavior of flocculated pulps, as related to the floc volume concentration, are confirmed. The correlation between batch settling tests and continuous thickening can be improved b y applying mild stirring in batch settling to prevent channeling and to simulate the dynamic conditions in the thickener. Evidence i s provided for the dewatering of the floc in the lower mud zone in a thickener through mechanical compression caused by the weight of the overlying solids. Such a lower mud zone is present when the underflow density exceeds that of the uncompressed flocs.
THE
OBSERVED continuous thickening behavior of aggregated calcium carbonate suspensions (Scott, 196%) and of a lime-flocculated superfine silica suspension (Scott, 1968b) were found to differ from the behavior predicted for a n ideal pulp in an ideal thickener (Shannon and Tory, 1966). h model that explained the observed behavior of flocculated pulps \vas presented a t the time, but it was speculative in some aspects and direct experimental confirmation was therefore required. Specifically, it was postulated that normal batch settling tests underestimated the required thickener area because under static conditions flocculated pulps of intermediate concentration tended to give rise to enhanced descent rates due to channel formation. I n a n operating thickener channel formation is not possible, because of the presence of mechanical slurry disturbance arising from various causes. Comparative tests on the effect of mild stirring in a batch test were not incorporated in the previous work, however. Furthermore, i t was stated that in flocculated pulps the natural tendency is to produce lorn density sediments and t h a t to obtain a n underflow pulp of high density it was essential that a compaction mud zone should form in the thickener in which "solids pressure" causes dewatering through floc compression. This zone is essentially different from the controlling concentration (minimum combined flux) zone, in t h a t it does not disappear a t throughputs below the maximum loading. No runs a t a sufficiently lorn solids throughput were made at the time, however, to prove the existence of the compaction mud zone under these conditions, and nor was any independent measure of the degree of mechanical compression in this zone obtained. These points have now been investigated using a limeflocculated pyrophyllite as the test pulp. This material was selected for study because it constitutes the second main component, after quartz, in many South African milled gold ores. I n addition, as the proposed model is intended to cover flocculated pulps in general, it was desirable in the present work to test a material different from that used previously.
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Theory
Floc Model. I n flocculated pulps, the primary particles are in a state of aggregation and these aggregates behave as individual sediment'at'ion unit's called flocs. T h e flocs contain primary particles in the form of a loose random structure of l o w density and a relat'ively high proportion of water filling the voids between them (Michaels and Bolger, 1962). This water remains virtually immobilized as i t sediments iyith the floc and while settling i t does not take p a r t in the return flow. It does not contribute t o t h e effective porosity of t h e suspension. Because of the importance of the solids concentration in sediment'ation and thickening, it was post'ulated that the e q u i d e n t , essential feature in flocculated pulps is the volume concentration of the flocs-Le., solids plus enclosed water. B y taking this into account,three distinct concentration regimes can be visualized, each with clearly discernible propert'ies. In the dilute regime the floes are separated from each other and they descend ideally as spherical units (Kynch, 1952) a t a rate which is a function only of concent,rat'ion. Aft'er settling, they form a zone with a floc volume concent'rat'ion in excess of 0.64 (maximum packing densit'y of rigid spheres) , because the floes are nonrigid. The concentrat'ion reached is somewhat less than 1.0, which would correspond to complete exclusion of the water between the flocs (Scott, 196th). I n intermediate pulps there is a degree of interfloc cont'act while settling, with consequent formation of a loose threedimensional structure extending throughout the pulp. Sedimentation rates depend initially solely on concentrat'ion, but in settling test's in a n unstirred cylinder, the escaping water, displaced a t the base of the cylinder, given sufficient time (t,all cylinders), causes the formation and development of short-circuit' return flow channels wit,hin the pulp mass, gradually enhancing the apparent subsidence rate of the slurry. Xaximum sett'ling rates are t'herefore a function of time, pulp height, and absence of slurry disturbance in addition to solids concentration. Concentrated pulps constitute t'he third regime. I n such
pulps the primary particles are packed more closely to each other than in the original floc structure. T o reach this state requires the application of sufficient mechanical force to overcome the frictional resistance of the original interparticle contacts. This can be brought about in sedimentation b y the buildup of the necessary height of overlying solids or b y slowly stirring the compacting layer. Settling rates for such pulps are not constant b u t decrease with time and depend on the total weight of overlying solids and the degree of stirring a s well as solids concentration. If the solids concentration of concentrated pulps is expressed in terms of the original floc volumes, volume “fractions” in excess of 1.0 are obtained. T o avoid possible confusion the term “fraction” is therefore omitted and all concentrations are expressed as floc volume concentrations, C F . For dilute or intermediate pulps, this term is, in fact, the volume fraction of the flocs in the suspension, while for concentrated pulps it represents the degree of dewatering of the original floes. Thus if C p = 0.5, 5Oy0 of the slurry volume consists of free water and 50% of floes (the d r y solids volume fraction being generally much lower than this), while if C F = 2.0, the solids are a t twice the concentration as found xithin the original floc>, total volume of the slurry is now half that of the total volume of original flocs, and hence the original flocs are compressed b y a factor of 2.0. Experimental
Materials. T h e pyrophyllite used was a -400-mesh powder purchased from G. and W.Base Minerals (Pty) L t d . , Johannesburg. A suspension in water, u-hen flocculated with lime a t pH 11.0, was observed t o be fully aggregated, with no evidence of free-settling coarse sandy particles. The size distribution of the primary particles was measured by means of a Sartorius sedimentation balance, their density b y means of a Beckmann air pycnometer, and the specific surface area by means of a Shimadzu air permeasizer. The results are shown in Table I. The pyrophyllite was slurried with mains water and sufficient commercial lime added to cause flocculation. The same decrease in free alkalinity with time was noted as previously (Scott, 1968b), and daily additions of lime were made t o maintain the alkalinity of the overflow liauor between 0.017 and o.023y0 CaO. Equipment. T h e test pulp was fed continuously t o a 6foot-diameter Denver thickener of conventional design equipped with control and measuring instruments a s described previously (Scott, 1968b). Procedure. F o r all runs, t h e feed concentration was maintained between t h e lower and upper conjugate concentrations of Hassett. (1964), while t h e underflow volumetric rate was varied bet’ween runs so as t o yield discharge concentrations below and above t h e floc volume concentration of 1.0. T h e volumetric feed rate was maintained a t t’he maximum allowable level without solids carry-over for six runs and at’ a reduced rate of 80 a n d 50y0of this maximum for one r u n each. For any one run, t’he feed and underflow volumetric rates and concent’rations were maintained steady for 18 to 24 hours before making observat’ions. Thereafter, the solids throughput rate and the underflow concentration were measured and the solids concentration-depth profile of the thickener was determined bot’h by direct sampling followed by oven drying and by means of the [‘superelevat’ion” of dip tubes set a t various dept,hs (Fitch, 1966). Samples of pulp in circuit, were taken a t the completion of each run and used to obtain the following batch settling rate data. Initial constant set,tling rate of various initially homogeneous pulps ranging in concentration from feed to that of the thickest free-settling pulp was measured under both st’atic conditions (Coe and Clevenger, 1916) and in the presence of slow stirring with a bent wire stirrer (Scott, 1 9 6 8 ~ Work ; and Kohler, 1940) a t speeds of between 1 and
Table 1. Density, G/Cc
2.70
Characteristics of Pyrophyllite Powder Particle Size Distribution, Microns
d2s, 3 .O dso, 6 . 5 1 d,S, 1 0 . 2
Specific Surface Area, Ma/G
1.14
4.5 rpm (Yoshioka et al., 1957). The complete subsidence curve of samples of feed pulp was determined and the graphical technique of Talmage and Fitch (1955) applied to obtain settling rates at the various concentrations assumed to be just below the pulp interface at different times. This was done for the free settling phase of the sedimentation curve and, by simple extension, also for the compaction phase following the critical settling point, although this is not recommended b y Talmage and Fitch. KO tangents were drawn to the critical settling point itself, as it is accepted t h a t there is a step change in concentration from free settling to initial compression (Scott, 1967). Resulfs
Normalizing a n d Processing of Data. Changing ambient temperatures, variations in degree of flocculation, a n d effects of pulp aging altered t h e floc characteristics and hence t h e settling rate of t h e pulp from d a y t o day. As this made direct comparisons between lengthy thickening runs extremely difficult, the sedimentation and thickening d a t a were therefore “normalized.” Settling rates, u, were expressed not in absolute units of feet per hour b u t as relative t o t h e Stokes settling velocity of a n average floc at infinite dilution, uo.The product of the normalized settling rate, u/u,, and the corresponding floc volume concentration, C F , is termed the normalized solids flux. These dimensionless values of flux and floc volume concentration are identical to the “reduced” velocities, solids flux values, and concentrations of Shannon et al. (1963), b u t the term “reduced” is avoided because of its ambiguity in this work. Fuller details on the method of converting the raw data to their normalized values have been published (Scott, 1968a). Briefly, it is assumed that for dilute pulps the observed decrease in settling rate with increasing solids concentration follows the equation
u = uo(l -
kc)4*66
observed settling rate at a solids concentration of c. feet per hour u, = Stokes settling velocity of an average individual floc, feet per hour c = d r y solids concentration, pounds per cubic foot of Pub k = volume of floc, cubic feet, produced b y 1 pound of d r y solid kc = total volume of floc, cubic feet per cubic foot of Pulp = floc volume fraction
where u
=
= CF
The values of k and hence C F are obtained b y plotting experimental values of ~ 1 ’ 4 . 6 6 against c and extrapolating the straight line so obtained to find the value of c at which ~ 1 ’ 4 . 6 5 and hence (1 - k c ) becomes zero. The value of u,is obtained b y extrapolating the same straight line to intercept the ordinate a t c = 0. The floc volume concentration, C F , is the product of k and c. The corresponding value of u is normalized b y dividing b y u,. Ind. Eng. Chem. Fundam., Vol. 9, No. 3, 1970
423
I-
LL I
1
t W
W I I : 2’ W Y
f
22 P
0.04
-
B
-
!
0 03
O W lo
0.02
-
0.01
-
IT OF FREE-SETTLING FLUX WUES
3
z
20 CF- FLOC VOLUM CONCENTRATION
-
3.0
Figure 1. Concentration-depth profiles and throughputs for eight steadystate runs A. B.
Depth-Roc volume concentration profiles Solids throughputs and underflow concentrations
The normalized solids flux is then (u/uo)kc,which is equal to the dry solids flux, uc, multiplied by the factor k/u,. This factor was determined a t the completion of every run and was found to vary from day to day, To compare the actual thickener performance with the normalized flux values obtained from batch settling tests, the unit solids throughput was multiplied b y the factor k/u,and the pulp concentratioiis a t various depths by k , as obtained on the same day as the thickener run. Continuous Thickening. T h e normalized throughputs and underflow floc volume concentrations of eight steadystate runs are shown in Figure 1, B. The straight line joining the corresponding values is termed the operating line (Fitch, 1966). Also shown (Figure 1, A ) are the concentration-depth profiles of the eight runs as obtained by means of sampling and oven drying. As all steady-state coiicentrations present in the cylindrical portion of the thickener must lie on the operating line (Fitch, 1966), the normalized gravity flux values of the various concentrations found in the thickener can be deduced and these values represent the ‘(true” gravity flux of the test pulp 424
Ind. Eng. Chem. Fundam., Vol. 9, No.
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under conditions of actual thickening. The values so obtained are shown as thickened sections on the corresporidirlg operating lines. Below C F = 0.9, the values fall on a single curve, assumed to be the free-settling flux curve. When operating a t a reduced throughput such as in runs 6 and 7, the operating lines fall well below the flux curve and,
Table 11. Comparison of Actual Solids Throughputs at Various Discharge Rates with Values Predicted According to the Normal Talmage and Fitch Method for Five Runs for Which Thickener Was Operating at Full l o a d Throughput, Lb/Sq Ft/Hr Predicted
Actual
11.6 13.0 15.6 17.9 18.7
10.2 11.6 13.7 16.3 16.5
Ratio Predicted/Actual
0.88 0.89 0.88 0.91 0.88
0.08
38
Figure 2. Normalized batch settling flux curves obtained under static conditions and in presence of different speeds of stirring
0.04
0 X
A
A
U
CF
0 5 n U M E CONCENTRATION
- FLOC
Static botch tests (Coe and Clevenger) Stirring a t 1 rpm Stirring a t 2 rpm Stirring a t 3 rpm Stirring a t 4.5 rprn
1.0
curve for prediction of thickener throughputs. T h e direct method was used to predict t h e throughputs for various runs and these are compared with t h e actual values in O OB Table 11. X 3 Evidence of Solids Compression. Figure 5 shows t h e LL 0.05 solids-depth profile of a thickener measured both b y 8 sampling followed b y oven drying and b y t h e use of dip tubes. I n t h e absence of solids compression, all t h e solids would be hydraulically borne a n d therefore register in t h e dip tube measurement's as contributing fully t o t h e ( AT "liquid" de1isit.y. T h e experimental values indicate t h a t T OF above a floc volume concentrat,ion of 1.0 t h e dip t u b e -I- I I I I I method yielded increasingly lower values t h a n the solids 1.0 20 actually present and t h e difference is therefore t h e measure CF- F L K VOLUME CONCENTRATION of the quantity of solids resting mechanically upon the flocs Figure 3. Normalized batch settling flux curve obtained below. Figure 5 also shows that not all the solids contribute b y method of Talmage and Fitch and similar construction to the effective compression and therefore the required height applied to compaction region of several subsidence curves of a compaction zone depends upon the degree to which it is hydraulically supported by the return fluid flow. Figure 6 shows the results obtained by means of several :IS exl)ected, the zoiie corresponding to t'he flus curve is absent such comparnt,ive profiles espressed in a different way, the from t h e thickener profile. The flus curve is r e c h w i in Figure results of the sampling analysis being plotted against those 4 (on a differeiit scale). 'The reliability of a n y means of sizing obtained by means of the dip tube technique. thickelms on the basis of batch settliiig tests depends upon U p to a true floc volume concent.ration of 1.1,both methods the accnracy with whicli t,liis ~ u r v can e be simulat,ed. Batch Settling Tests. n I A x i h f u M CONSTANT SETTLING yield similar results, but above this value the results of the RAWOF HOMOGENEOUS PULPS AT VARIOUS CONCENTRATIOAX. dip tube technique, although variable, are consist'ently lower. The variability arises from the fact t h a t in the large number 'L'he iiornialixed flux oElserved iii static and slowly stirred of runs used to obt,aiii the data, the throughput was varied batch set'tiiig tests at different initially uniform coiiceiiover a wide range, including that of zero underflow discharge. t>rationsis sliowii in Figures 2 a i d 4. It was directly observed that sampling in t'he compression (>OhlPLETl? SURSIDENClE OF T E S T P U L P AT FEED COh'CENzone even 6 inches below the surface led to "coning" or crater TRATION. T h e 'l'almagc! a i d Fitch tallgent const,ruct,ion formation. This result'ed in the sample's being obt'ained riot was applied to t8hecolri.plet,e subsidence curve of t h e feed from a layer level with the ent,rance to the sample tube but slurry and t h e flux-coiicentrat,ioii d a t a so obtained were iiomialixed by usiirg t,he 21, and k values ol)taiiied on t,he same from a lower concentration zone above. Direct sampling could t,hus give rise to concentration values which are on the day. The result's of several test's are sho\vir in Figure 3. low side, but this was not, a serious problem in the present The most rollcentrated free-setthg zone was fouiid to be work because of the shape of the solids profiles. The point is C F = 0.65, while floc. buildup zones were found to comnieiice meiit,ioried, ho\vever, as the shape of the permanent steepa t C F = 0.99 (il and B , Figure 3). 111 the proposed model, coirceiit,ratioii zones i i i excess of C F = 0.89 are therefore in sided craters which formed affords additional evidence of the comprwsioii. l'he data from t'he different, test,s sliow a n fact that the flocs in the compression zone behave as solid in the sense t h a t the pulp eshibits a distinct yield value and does u i i c y w t e d scat,ter in t,hc free-settling zone, alt,liough approxiinnt'rly the same bb-eight of solids was u ~ c diu each sett,ling not deform as a free-flowing liquid, as would be the case if the test. 'L'his esplaiiis the relat,ive lack of scatter iii the comprescontained particles were in free suspension. sion zone where set,t'ling rates are st'rongly depeiident on Discussion weight of ovcrlyiirg solidq. 'l'he mean curve is inc.luded in Figure 4. Thickener Profiles. Although compression effects are Direct Prediction of 'Thickener Throughput by Talmage not clearly discernible below C F = 1.1, it will be accepted t'hat pulps a t CF 5 0.9 are in compression, according to the and Fitch Graphical Method. It is not necessary to draw the flux curve in order t,o use t h e subsidence height time Talmage and Fitch data (Figure 3, B ) . The result's of the
f:
d
I
Ind. Eng. Chem. Fundarn., Vol. 9, No. 3, 1970
425
o
-*, \
'\\
RPM .STATIC BATCHTEST(C0E 6 CLEVENGERI
/
\
05 CF
Figure 4.
- FLOC
15
10
VOLUME CONCENTRATION
Solids flux curves determined by various methods
C
0 DIRECT SAMPLING
X DIP-TUBES
IC
It I
c I w
0
20
L
g Y
F
25
30 0
7 Figure 6. 1.0
CF- FLDC
2.0
VOLUME CONEMRATITION
Figure 5. Thickener concentration profile determined by direct sampling and oven drying and by superelevation o> dip tubes
thickening runs shown in Figure 1, A and B, are discussed accordingly. I n run 1, the thickener is accepting the maximum steadystate volume of feed pulp and the solids profile indicates the presenze (below the feed well) of the single uniform controlling concentration as expected from the ideal flux theory (Jernqvist, 1965; Yoshioka et al., 1957). I n the present interpretation the underflow concentration is below CS = 0.9 (Figure 1, B ) and hence floc compression is not necessary and the mud zone at the base of the thickener is absent. I n runs 2 t o 5, a concentrated underflow of increasing density was produced and hence the lower mud zone became a n increasingly important feature of the solids profile. The upper controlling concentration zone continued to exist, because the maximum feed rate was maintained in each case. Above C p = 0.6 this zone became less uniform and this appears to be related to the thickest free-settling pulp being about CF = 0.65 (Figure 3), which is close to the maximum packing density for spheres, 0.64 (Shannon et al., 1963). 426
Ind. Eng. Chem. Fundam., Vol. 9, No. 3, 1970
1.0
2.0
FLOC VOUlME CONCENTRATION BY ELEVATION OF UPTUBES
SUPER-
Floc volume concentration determined by two different methods
The operating lines form a reasonably consistent envelope u p to C F = 0.9. In run 6, the thickener was fed a t a reduced rate of 80% and the operating line fell below this maximum flux "envelope." As expected from the ideal flux theory, the upper controlling concentration disappeared from the profile. This zone has been termed also the upper conjugate concentration b y Hassett (1964) and, as predicted b y him, is replaced in the profile of run 6 b y the lower conjugate concentration because of the reduced throughput. Although the operating line in run 6 lies well below that of run 5 a t all points (Figure 1, B ) , the lower mud zone, unlike the upper controlling concentration zone, persisted in run 6. This confirms that the lower mud zone is esseiitially different from the ideal controlling concentration zones and even when the throughput was reduced to about 50% of the maximum in run 7, the lower mud zone continued to persist. I n run 8, the thickener was again operating a t full load but now in a different sense. The extremely high underflow density produced demanded a correspondingly increased height of compaction mud and for the throughput of run 8 this approached the overflow point. I n the previous runs the
area of the t,hickeiier alone was the limit'ing fact'or, b u t in this case the available thickener depth became a n additional factor. These runs therefore fully confirm the findings of Comings (1940) of two distinct zones in t'he thickener profile and also his conclusions that overloading of a thickener can be due to tv-o distinct (causes-feeding a t a solids rate t h a t exceeds the minimum flux or demanding an excessively high underflow density. The data are also iii agreement with previous findings (Scot,t, 1968b) that the flux curve should consist' of two part's: a single discontinuous curve u p to a conceiit.ration of C F = 0.9, and n series of curves above C F = 0.9, for which both concentration and weight of overlying solids are important variables. Batch Settling Tests. The normalized flus observed in static and s l o ~ l ystirred batch settling tests a t differelit initially uniform concentrations is shown in Figure 2. -1bove C F = 0.3 slow stirring even a t 1 rpm had a profound effect on the shape and position of the flux curve and the speed of stirring was also importantm. Above C F = 0.7, unslirred settling t'ests gave increasingly erratic results, as the maximum subsidence rate of the interface attained before reaching t,he compression point depended strongly on the time of onset, of channel formation aiid this, in turn, became iiicreasiiigly less reproducible as the concentration increased. Nild d r r i n g , on the other hand, prevented the onset of channeling b y breaking u p the potent'ial flow paths, and hence sett'ling rates were lolver and also more reproducible. Below C F = 0.3, the floes are sufficiently separated from each other to preclude channel formation and hence settling rates were unaffected b:i- the presence of s l o ~stirring. This also indicates that' the reduction in settling rate noted for the higher concentrations n-as not caused primarily by undue pulp ag i t a t ion. For pulps in compression, C F > 1.1, stirring had a distinctly beneficial effect upon the rate of descent of the pulp interface as predicted by the compaction model. Comparison of Batch Settling Tests with Thickener Throughput. I n Figure 4, t.he discontinuous flux curve observed in t h e operating thickener is compared wit,h the flux curves obtained b y means of t h e various batch settliiig tests aiid t h e curve for rigid spheres obtained b y Shaiiiion et a l . (1963). Belou- a concentrat'ion of C F = 0.3, all the curve.; agree, be8:ause the floes are independent aiid settle as .separate spheres. -4bov-e this concentration, flocculated pulp^ set'tle faster than individual spheres of equivalent, denqity a i d diameter, mid as substantial nettliiig rates are olitained eT-eii :ibove C F = 0.64, a t which rigid spheres reach their closest packing and caiiiiot subside any further, the reason must lie in the deforniahility of the nonrigid floes. h b o r e C F = 0.4, channeliiig become> increasingly important under static conditions a-nd the fact that slow stirring betn-een 2 aiid 4.5 rpm give. a c1o;er correlation 11-ith the values found in the operating thickener is accepted as indicating the prtdeiice of mechanical disturhaiice similar under both condition\. I n full scale thickener., the mechaniqm of 11~111) disturbances may well be different from that employed in the stirred t e i b ; hence 110 attempt is made to recommend a particular speed for designing t,hiekeners in general. Yoshioka et al. (1957) recommend a method of st'irring in bat,ch tests identical to that employed in the continuous thickener. Compared to batch test. carried out' under various condition.; of mild stirring, the single subsidence curve of Talmage
and Fitch is experimentally more simple and less subject to error. Figure 4 shows that the flux curve so obtained is in fair agreement with practice, although displaced. Table I1 shows that the actual performance of a thickener may exceed the design throughput b y about 10%. These results are somewhat higher than those of Couche and Goldney (1959) who, for flocculated pulps, found that the actual performance of a pilot thickener on two dlfferent materials was 2% higher than predicted using the Talmage and Fitch analysis and higher than the 47, found for silica (Scott, 1968b). The fact, however, that the final design will be slightly conservative is not regarded as a disadvantage. For a nonflocculated pulp, Jeriiqviqt (1966) found an almost perfect comparison between theory and practice. Conclusions
Mild stirring in babch settling tests reduces the onset, of channeling aiid result's in settling rates t'hat agree more closely with t'hose observed in an operating pilot thickener. The Talinage and Fitch test, gives results which are equally reliable and, experimentally, the method is less involved. The second mud zone which appears in the t'hickener profile when operating a t high underflow densities is a true compaction zone in which flocs are in mechanical compression. Settling rates in this zone are virtually zero in the absence of overlying solid and generally increase with increasing depth of the zone. Uiilike the upper zone in fully loaded thickeners, t,he compaction zone does not disappear when the throughput is reduced, nor does it. appear when the thickener produces an underflow pulp less concentrated than the flocs-Le., C F < 1.0. Acknowledgment
The author gratefully thanks Gold Fields of South Africa, Ltd., for their helpful cooperation and for the loan of the test thickener, J. IT.Stander for carrying out the large number of settling tests, and IT.G. B. llandersloot for helpful advice in preparing the paper. literature Cited
Coe, H. S., Clevenger, G. H., Trans. Am. Inst. Mmng Eng. 55, 356 (1916). Comings, E.W., Ind. Eng. Cheni. 32, 663 (1940). Coache, R . A,, Goldney, L. H., Proc. Bust. Inst. Mznzng M e t . No. 191 (1959). Fitch, Biyant, Ind. Eng. Chem. 58, 18 (October 1966). Hasqett, N . J., Trans. Inst. Mznzng M e t . 74,627 (1964-65). Jernqvist, S -H , Sz.Papperstzd. 68, 506, 545, 578 (1965). Jernqvist, 4.S.-H., Se. Papperstzd. 69, 395 (1966). K p c h , G. J., Trans. Faraday SOC.48, 166 (1952). hlichaels, A S..Bolger. - J. C.. IND.E N G CHEW F ~ K D A1.V . 24 (1962). Scott, K. J., IND.ESG. CHEM.FCXDIX. 7, 484 (196%). Scott, K . J., ISD.EYG.CHEM.F T T N D7.~582 V I1965 Scott, K. J., Trans. Inst. Wznt Process
4.
Process Extr. 1Ietall.) 7: CHEM. Shannon, P. T., i FUKDAM. 2. 203 il96$,.' Shannon, P. T . , Tory, E. 11.)Trans. SOC.-1Iinzng Eng. 235, 375 (Dec. 1966). Talmage, W. P., Fitch, E. B., Ind. Eng. Chem. 47,38 (1955). Work, L. T., Kohler, A. S., Ind. Eng. Chem. 32, 1329 (1940). Yoshioka, S., Hotta, Y., Tanaka, S., Naito, S., Tougami, S., Kagaku Kogaku 21, 66 (1957). I
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RECEIVED for revieJY August 15, 1969 ACCEPTEDMay 18, 1970 Ind. Eng. Chem. Fundam., Vol.
9, No. 3, 1970 427
