temperature i: \ \ h i c h \elution \vith L: lvould be saturated t l = temperature of liquid in tubes t, = temperature at inner surface of scale At = total temperature droll from heating to cooling medium c' = over-all coefficient of heat transfer C, = initial IT x = scale thickness
t l ' = hypothetical
temperature change of the liquid through the heat exchanger is small compared with the total temperature drop from the heating or cooling medium to the liquid. This is often the case. T h e relatively simple relationships should prove of value in interpreting experimental d a t a . By proper interpretation the work can be extended to cases of stepwise changes in At and to multiple effect evaporation problems. Nomenclature
GREEKLETTERS p = constant
A
p
= density of solid scale 0 = time All in consistent units
= area
constant b slope of solubility curve c, concentration of liquid cl' h>.pothetical concentration of liquid saturated with sealing component a t t l cs = concentration of saturated liquid a t inner surface of scale h , = film coefficient, inside tubes h, = film coefficient, outside tubes corrected for inside area h , = equivalent coefficient of tube wall corrected for inside area k = combined diffusion-reaction mass transfer coefficient k , = thermal conductivity rn = mass of scale component n = constant exponent s = supersaturation a
= = = =
Literature Cited
(1) Badger, \V, L..Othmer. D. F , , Trnns. A m . Inst. C'heni. Eri,qrs, 16, Part 11. 164 (1924). ( 2 ) Ranchero. .J. T.. Gordon, K. F.; A d r a n . Chern. Ser.. S o . 27, 105 (1 960).
(,., 3 i Rraksorn. S H.. Bri/ Chem
E n p . 38. 838 11960'1 .i. H. 'Perry; ed., 3rd ed.; p. 313, .McGraw-Hill. New York. 1950. (5) Hixson. A. LV.,Knox. K. I... In(/. En-. Cheni. 43, 2144 (1951). (6) McCabe, \V. I.., Robinson. C:. S.. Ibid.. 16, 478 (1924). ~~
~~~~
~
~
(4) Chemical Engineers' Handbook:
liEcEivm
for re\.ie\i July 3. 1963 ACCEPTEDJuly 9 , 1964
PRESSURE AND ADDITIVE EFFECTS ON FLOW OF BULK SOLIDS P F R
. U.
. .
A
,
A
.
U L S A R A , Polytrchnic Iw/i:itte of Brooklyn. B i o o k l ~ n ..\'. 1 ~ ~ ~ a ~RoJyn . Horboi. L. I...V. 1'. Z E N Z , Sqzutps I i ~ / r r t ~ o t i oIric.. . Gnrden City. L . I . . .V. 1.. E C K E R T , : l ~ s o c i ' n t r d . ~ u c i p o n i c sInr.. B
In contrast to the conventional addition of fine anticaking agents to render "sticky" powders free-flowing, the addition of coarse inert particles, in a quantity sufficient to make these the bulk of the mixture, will also result in a free-flowing mass at ambient conditions. Even without the use of any sort of additives, sticky powders can be made to flow b y properly applying pressure differentials or reducing total ambient pressure. The effect of pressure differentials on free-flowing solids i s in accord with the conventional orifice equation.
u
NUMEROVS
po\vder-processing or handling operations it is
I-not 'only desirable but necessary that the powder be freeflo\ving and exhibit no caking or agglomeration. Highly successful conventional practice calls for the addition of small amounts of flo\v-conditioning agents. These conditioners. usually in amounts of less than 1 weight yG,act principally as selective adsorbents for gases o r vapors otherwise adsorbed on the surfaces of the particles of the sticky poLvder. T h e conditioners are usually of submicron particle diameter and thus exhibit an erormous surface area for adsorption. Certain conditioners also promote free flow by dispersing themselves throughout the interstices and particle surfaces of the poLvder. giving a lubricative effect; the effectiveness of some is also attributed to residual electrical charge, which counteracts agglomeration of a po\vder as the particles of the dispersed conditioner repel each other within the bulk mixture. Conventional submicron conditioners have won \vide acceptance because they are effective a t concentrations so low as to have a negligible effect on the functional properties of the po\vder to Lvhich they are added. Many of them are acceptable as additives even to food products and pharma348
I&EC PROCESS DESIGN A N D DEVELOPMENT
ceuticals. I t Ivould. hoivever. in relatively rare instances be desirable to remove all foreign matter from the final product. and in some i:Istances submicron. highly adsorptive solids might be harmful to the product. In such cases it is possible to carry the sticky potvder through various processing phases in admixture with a n inert, free-flou.ing material of coarse particle size. Gravity Flow of Sticky Powders
Coarse Additives, 'To explore the ranges of admixture concentrations \vithin Lvhich coarse plus fines \ \ o d d still exhibit the free-floLv characteristics of the coarse additive. various mixtures of sand and po\vders Lvere made up by stirring lveighed batches in a large pail and pouring them into a cylindrical bin. T h e bin consijred of a 5.625-inch I.D. Lucite tube, 28 inchej high, closed at the bottom Lvith a flat plate. in the center of which a 1-inch hole \vas rapped and fitted \vith bushings, permitting threaded long- and short-tube orifice openings of 0.493- and 0.838-inch I.D. to be inserted. T h e cylinder \vas a small flat-bottomed bin \vith variable discharge porr characteristics. .2 standard 20- to SO-mesh Otto\va sand \vas used as the free-flo\\-ing coarse additive and fly ash and Xficro-Ckl rrprc-
.
sented the sticky powders. T h e fly ash was obtained from a S e w York Consolidated Edison Co. power plant a n d the Micro-Cel from the Johns Manville Co. T h e propcrtics of these solids are summarized in Table I. Figurrs 1 a!id 2 illustrate typical d a t a o n rates of mixture efflux from the bin. When fly ash concentrations exceeded 60% by wei :ht and Micro-Cel concentrations exceeded 9% by weight. the mixtures were no longer free-flowing. As shown in Figures 1 a n d 2 , a decided decline in efflux rates began a t a fly ash concentration of 20y0 a n d a Micro-Cel concentration of 3.6YGby weight. To determine whether the point of decline in efflux rate might be related to inefficiencies in the mixing technique, a comparison was made between measured voids in the sand-powder mixtures a n d theoretical voids calculable for ideal homogeneous mixing. Two-Component Mixing Efficiency. At fines concentrations less than required to saturate the interstices of the coarse sand ideal mixing calculations predict: Fraction voids in bulk mixture
=
At the fines concentration just sufficient to saturate the interstices of the coarse sand: W t . fraction of fines a t satn.
1
=
+
r S- c L1
' I
1
Voliime fraction of coarse a t satn. =
(2)
'CPPIJ
(3)
1c Fraction voids in bulk mixture = e c e I
(4)
At fines concentrations in excess of that necessary to saturate the interstices of the coarse sand :
Table 1.
Physical Properties of Bulk Fly Ash, Sand, and Micro-Cel
Fly .Ish
Sand
Mean partick diarn., D,, inch 0 0282 Particle density, lb./cii. f t . 164 95 2 Bulk dmsity, Ib..!cu. f t . 0 419 Voidage, 6 , cu. ft./cu. ft.
.bfiLro-Cel
0 000755 147
0 000126 141
57
8 4 0 9409
0 612
T h e calculated a n d experimental curves shown in Figures
3 a n d 4 may be interpreted in terms of a n "efficiency" of mixing, though the calculated ideal is never attainable, particularly in the neigborhood of the minimum voidage. unless a n added coarse-surface wall effect is taken into account. Figures 3 a n d 4 indicate that the mixtures were probably uniform a t fines concentrations less than needed to saturate the interstices of the coarse sand. Comparisons between Figures 1 a n d 3 a n d 2 a n d 4 indicate that the decline in efflux rates began when the fines concentrations were just sufficient to saturate the interstices of the coarse sand. At greater concentrations the fines became increasingly the continuous phase until at approximately 3 times the interstitial saturation concentrations the mixtures behaved as though n o coarse additive were present and free gravity discharge ceased. Long-Tube Orifices. T h e threaded hole in the base plate of the test bin permitted the insertion of long tubes in place of the relatively thin orifice plates to explore the degree to which the suction effect of falling powder slugs might d r a w solids out of the bin. Figure 5 shows results obtained with a n 18-inch tube using fly ash-sand mixtures. Efflux rate no longer declined beyond concentrations where the sand interstices were filled with fly ash. T h e effect of such long-tube orifices in increasing efflux of free-flowing sands had been noted by Bingham a n d Wikoff ( 7 ) . Most surprising were the observations t h a t now the non-free-flowing powders alone discharged
Fraction voids in bulk mixture =
Calculatbd
- - - Experimental 0-
I
I
I
60 Wbight % F l y k h
20
40
I
80
C l !O
Figure 1 . Gravity flow of fly ash-sand mixtures through orifices in base of 5.625-inch I.D. bin
Wblght
u
% Micro-CbI
Figure 2. Gravity flow of Micro-Celsand mixtures through orifices in base of 5.625-inch I.D. bin
2o0
20
40
60
80
0
Volume % Sand
Figure 3. VOL. 3
Fly ash-sand mixing curves
N O . 4 OCTOBER 1 9 6 4
349
freely. Efflux of the pure fly ash and Micro-Cel was initiated by corking the bottom end of the tubular orifice extension and gently filling the tube with powder using a small spoon. When the tube was full, it was threaded into the hole in the bottom of the bin and then the bin itself filled with powder. When the cork was pulled out of the bottom of the tube. the powder flowed o u t as though it were being mechanically extruded and resembled the flow of toothpaste squeezed from a tube. When the length of the effluxing core of powder hung about a n inch below the end of the tube, i t sheared off a t some point and fell away. These observations with long-tube orifices are in
agreement with the effects of pressure and sucrion differrntials on bulk solids efflux and under the force of such differentials normally sticky powders brcomr frrc Iiowing. Forced Flow of Sticky and Free-Flowing Powders
Despite such commercial applicarions as thr pressured injection of powdered coal into blast furnacc. ru)-eres ( I ) . pressured unloading of cement and other chemical5 from tank trucks ( 3 ) . po\vdered fuel injection into rocket engines. and design of landing and transportation devices on rhe supposed powdery surface of rhe moon (8).rhere are still surprisingllfew- d a t a in the technical literature on the effect of total or differential pressures on the bulk flow properties of qolids. In order to explore principally the magnitude of such pressure effects (1)the apparatus illustrated in Figure 6 \cas arranged to measure solids efflux through orifices under four basicall>different conditions arbitrarily designated as pressure, suction. gravity, and vacuum.
Pressure Experiments. First the plug valve below the orifice was closed and then the feed bin filled with a batch of solids (usually to a depth of 24 inches). T h e receiver vessel was vented to atmosphere and air from a standard cylinder admitted to the feed bin through a regulator to a prescribed pressure: which was maintained continuously during the run. T h e plug valve was then abruptly opened and the material discharged inro the receiver over a timed interval. \vas collected and kveighed. I n a few instances a rotameter \cas placed in the air line to measure the rate of gas being fed to maintain the feed bin pressure. Suction Experiments. These folio\\ ed a similar procedure. except that the feed bin remained vented to atmosphere
I
Figure 4.
Micro-Cel-sand mix ing curves
Waight
%
Flykh
Figure 5. Grovity flow of fly ash-sand mixtures from 5.625-inch I.D. bin through nozzle 18 inches long, 0.493-inch I.D. 350
l & E C PROCESS D E S I G N A N D D E V E L O P M E N T
Figure 6. Scale drawing of apparatus
during the run and the receiver \vas vented through a vacuum pump. Before the plug valve \cas abruptly opened, the recrivrr \vas evacuated to a prescribed reduced pressure. ‘The capacity of the vacuum p u m p \vas not sufficient to maintain this reduced pressure during the course of the run. so that the solids Ho\v rate undoubtedly decreased as the pressure diff-rrential fell. T h e measured rate therefore represents a n average over the period in which the differential pressure fell irom the prescribed initial to that recorded a t the time the run \\as arbitrarily terminated. Both initial a n d terminal differentials \\-ere recorded in the tabulated d a t a . Gravity Experiments. Both feed bin and receiver vessels were vented to atmosphere. These tests \cere merely run to demonstrate free floiv i ; ~ . non-free-flowing characteristics of the various materials. V a c u u m Experiments. Both feed bin and receiver were \-ented through a common line to the vacuum pump. I n effect these tests constii.uted gravit>-flow measurements under a reduced pressure environment. as though a n open feeder and receiver had been placed inside a large vacuum chamber. T h e properties of the solids investigated in this study are summarized in Table 11. P r e s s u r e Tests. Since many commercial processing interests lie in pressured flow of solids, this aspect of the test program \cas given the most attention. O n l y after completion of the major portion of the \vork. during which only the solids rates \cere measured. \vas it possible. by a trial and error procedure. to devise a flow model dependent on calculation of both gas and solids (efflux rates! as a function of the pressure differential bet\veen the top of the bed and the discharge side of the orifice. Several runs were then carried out measuring both gas a n d solids rates to corroborate the model. Figure 7 illustrates the simple relationships, based on the orifice equation for pure fluids, 1,chich \cere found to represent the recorded d a t a Jvithin reasonable limits of engineering accuracy. T h e equation for the rate of solids efflux is based o n the substitution of gas pressure for equivalent head of fluidized solids in Equationl’ of Zenz (70) (derived from b’ = C o d = ) TL7,,
=
8.04 ,,:(
pBLB’ (for fluidized solids)
Table II.
Principal Characteristics of Solids Investigated under Forced-Flow Conditions
M e a n Dp: Inrh 0.12 0.011 0.0087 0 00236 0.00086
Material TCC beads Sand Saran FCC catalyst Cement BaCO
or M’,
= 8.04
0,000118
C, p B l/(J‘?
Bulk Density, General Grai’ity f;iorr’ L b . l C u . Ft. CfiuractrrzsfiLs 40 Free-flowinq 85.5 Free-flowing 40 Free-Rowing 39 Free-flowing 90 Non-free-fiowinq 62 Non-free-flo\ving
-pIi) 144
(for pressured solids)
which simplifies to : Solids efflux in pounds per minute = 31.4 Cs
pB1’*(P2
- Pz)‘” (Do-
1.5 D,)?
(6)
T h e equation for the rate of gas efflux is similarly based on the orifice equation __ V G ;=~ C ~ d 2 (PP g - Pi) 144/’pG whence the volume of effluxing gas? assuming the entire area of the orifice to be occupied with solids a t their bulk density--e.g., ignoring wall effects a t the orifice periphery-can be represented by :
CFM
= E
=
0.327
(V,,,
t
+ V,)
D O 2 [ ( 9 6 .C5 G d ( P z - Pi) ’ p c ) -l ( Ll’s
:
pB)] (7)
T h e calculation of the pressure, PB,above a bed of solids L feet deep resting on a flat-bottomed bin containing a hole Do inches in diameter, required to induce a n efflux rate of 11pounds per minute of solids to atmosphere is carried out in the following stepwise fashion from bottom to top of Figure 7 : By substitution in Equation 6 the pressure, P 2 , above the orifice m a y be calculated. Substitution in Equation 7 then allows calculation of the gas efflux rate. T h e pressure drop for the quantity of effluxing gas passing through L feet of fixed bed. added to P?,gives pressure Pa,
Figure 7. Model of solids efflux mechanism under applied pressure differential
Since it was not considered feasible to obtain a reliable pressure measurement upstream of the orifice ( a t P2). the treatment of the d a t a via only Equations 6 a n d 7 would involve the determination of cocfficients C, and CG by a trial and error process geared to minimizing the difference between calculaied a n d observed figures. R a t h e r than adopt such a procedure C,$was taken as 0.445 based on the fluid-efflux d a t a of Massimilla ( 7 0 ) . This coefficient in Equation 17 of Zenz’s paper also correlates the more recent fluidized efflux d a t a reported by Massimilla and Volpicelli (7) for orifices u p to nearly 0.8 inch in diameter. Having accepted the coefficient. C,. was determined from a n average of the d a t a for each orifice size. No allowance was made for the effective flow area contraction through the fixed bed above the orifice; the bed cross section for gas do\vnflo\c \cas based on D , all the \vay from P3 to PB. T h e foregoing procedure is adaptable only to materials through which air will permeate uniformly via the intersriccs between the particles. If the gas channels along the wall of VOL. 3
NO. 4
OCTOBER
1964
351
the feed bin bet\vcen bed and bin surface. the results would corrrlate onl? in terLiis or a bed pressure drop defined as a \vall flo\v. I‘hic \vould be a biglily unconventional procedure. since i t \\.odd have n o means for generaiizarion as vesvel diameter changed. I t is also questionable whether such annular \\.all or channeling flow would have an equally efrectivr rrsult on solids efflux. for it i 5 easy to imagine the wall flow to channel benvcen the bottom of the bin and the underside of the bed of solids. ‘I’hus. the gas flow would be going around the bed of coiids rather than directing a pressure force on top of the particles abovr the orifice. I t is difficult to imagine ho\v such a flo\v pattern could be scaled for various feed bin diameteri. since \vith a very large bin a portion of the total gas atrcarn might find a path of equal resistance through some channrl Lvithin the bed of solids and thus. confronted \vith more than o n r path. it becomes nearly impossible to predict \\-hat effective pressures might be exerted above the solid? at the orifice. LVhen Lvorking \vith the non-free-floLving cement and barium carbonate there \vas a noticeable flow of air betkveen the bed and the feed bin Lvall. Tiny rat holes tended to form a t the ~ v a l l sand the flow of air could be detected by careful observation of the occasional motion of grains of cement on the
Table 111. Comparison between Observed Bin Pressures and Pressures Predicted b y the Flow Model of Figure 7 for Pressured Efflux of Free-Flowing Solids Soi2ds Bin Pressurr. P?,P.S.I.G. ( S r r I:i?ure 7) Eflu Y. Deuation Do. Inch Lh. ‘.\fin. Obsd. Cdcd. S4ND
0 125
0 25
0 12.5
0 25
0 50
3 08 3 18 5 35 4 89 6 25 10 0 9 96 1’ 6’ 18 15 26 4 1 69 2 92 3 91 5 96 9 24 9 40 10 44 15 6 16 11 16 62 16 86 34 ’ ’6 2
3
5
10 10 16 3 3 5 6 11
3 4 11 9 15 1 1 5 6 12
86 05 2 41 14 9 9 66 04 66
FCC: CATALYST9 4 45 9 35 10 13 50 14 3 2 86 i 43 5 3 4 95 6 6 14 10 11 47 11 99 10 12 ’5 13 13 15 13 5 5 88 1’ 8 10
29 0 23 0 12 0 6 0 5 8 58 0 58 0 13 0 0 5 15 0 11 7 3 5 8 1 2 14 19 2 1 1’ 1’
2
25 21 21 20 16
0
surfaces of such holcs. These observation\ cause one to ivondrr about many of the p i ure drop measuremenrh reported in the literature for fio\v through fixed beds of very fine. non-freefloiving po\vders. Certainly in an) nontransparent apparatus one might nevcr subpecr that such \vall chatincling \vas taking place. ‘l’herr albo occurs the probahiliry that if the material Lvere densely packed into the tube. the \\.all rflecr could be spread uniformly over the rntirc inner \vaIl surfacc and thus uniform wall channeling could go undctccted ewii in transparent equipment. .4 study of all the fixed bed data in the literature might reveal that much of the disagreement among the data for fine particles could be attributed to .uch ivall flo\v. By means of the mechanism proposed in Figurr - it is possible to predict required bin pressures and then to compare these u i t h observed d a t a . Such a coinpari.con i r preqented for three free-flo\ving solids in Table 111. I n making rhrse calculations C,s~ c g , . the bed level drcrcascd \\.hrii the \t)acc above the \old.; \vas brought u p to ])re.;sure. '1 his c i l r c t \\-a\ least pronounced \vith the frccAorving solid. but ne\ e v ~vould ailcct the hulk density teriii< in the equation \.n in I'iqurc -. 'I'his is a minor source of error. but correction of bed drn.it)- d u e to compre.;\ion under preasure \\-as ignored in the analy\ic of the results. 111 the work rvith criiirnt if the biti \\-as pressured and then partially relieved. prior to opening the plug valve. no flo~v of cement \\.as obtaincd. In other ~ v o r d s . if the bin were tired to 10 p.s,i,g.and the plug valve opened. there Lvould tic an efflux of cement: if the bin \vcrc pressured to 5 p.s.i.g. and the plug valve opened. there Ivould also br a n cfflux of crmc'nt: but if the b i n \cere pressured to 10 1i.s.i.g. and the cxccs\ p r n s u r e bled do\vn to say 8 or 5 p.>.i.g.before opening the plug valve. no efflux of cement occurred. I t \\-auld a p p e a r that compression be>-ond a degree commensuratr xvith a given prcssure level causes the material to bridge. 'I'hough not explored further. their simple observations suggest a itandard procedure for testing 1.ioLvdei-s which might )-ield considerable insight into the forces that create non-free-flo\ving properties a n d might \vel1 complement the procedures developed by Jenikc ( 5 ) . Data of K u w a i
the inci,c,ayc in mlids efflux over that under free gravity discharqe (\\.ithour an applied ~)rc\siircdiiIcrcnrial) a n d is simply \ \ h e r e i q the covificicnt in the gravity flow equation 1
+
[I-
= TPH(l1,,
- 1.5
z)I,)l
rcprcscnt, the applied pressure differential across
+
t h e bed of solids and is plotted as 1 [ J P L ) in order to allow a n intercept a t zcro 1)rc>
Kiiitri~
Ferd bin diamrtrr. inrhv Orific(. diamctrr. inch Particle diameter. inch Frrr-llo\vint. solitis Yon-frrr-flowing solids Gas flow rnraqiired Ilrd hviqhts. inches Particle biilk denqity. Ih. c u ft. Positive air prrssurr. p.s,i.q. Ycqatir-r air prrssure. p.s.i.q. Krdurccl total pressitre. p.s.1.a.
0 '44 to 4 48 0 0788 to 0 1124 0 0054 to 0 0210 Yes
8
44 9 to 171 0 to 1 42
o
j
inch This Study E 0.125 0 0.25
0.0781 A 0.124 x 0.1605 0 0.241
YPS
s0
No 2 l ' t o 5 94
D., Kuwai
YrS I n comr instances) 14 i n 22 a\.rraqr
I O . 5 0
s 0.3124
39 to 90 0 to 16
3
No
Oto -12
NO
4 9to14 5
I! I
I
I
I
2
4
1
I
+ (AP/L)
6
,
,
I
I
8
10
20
Figure 9. Comparison of data for sand, Saran, and FCC catalyst obtained in this study with data of Kuwai VOL. 3
NO. 4
OCTOBER
1964
353
Vacuum Tests
T h e vacuum tests were designed to determine whether the gravity flow of solids would be affected by a reduction in the total pressure of the surrounding air medium (without a pressure differential to induce solids flow). By means of the vacuum p u m p a n equal reduced pressure was drawn in feed bin a n d receiver vessels a n d then with these two vessels vented to each other the plug valve was opened a n d the solids efflux rate recorded. T h e d a t a , summarized in Figure 10, are rather astoundiyg, particularly for the non-free-flowing cement. T h a t simply reducing the total pressure can impart free-flow characteristics so markedly to a material like cement which will ordinarily not even flow through a 6-inch hole, is worthy of some further study. No attempt was made to analyze these results. I n all probability the resolution of the d a t a would be complex, since the effect is most likely related to the particles' capabilities for adsorption of moisture o r other constituents from the air which form surface layers a n d cause particle-toparticle adhesions, thus affecting the flowability. This subject has been treated a t length in the literature (9) for decades a n d has never been fully resolved. T h e d a t a in Figure 10 are subject to iiconsistencies d u e to daily variations in humidity a n d other ambient atmospheric conditions. Suction Tests
T o explore further the soundness of the mechanism proposed in Figure 7, it was suggested that solids efflux rates be measured under negative pressure differentials as well. Thus, with a vacuum drawn below the orifice there would also exist a gas pressure differential (equal to 14.7 minus the pressure in the receiver) across the bed of solids when the plug valve is opened. This situation should lend itself to the same calculation procedure followed in the analysis of the pressure tests. For the sand and Saran this was foun to be the case. I t was also true for nearly all the FCC catalyst runs. with the exception of those conducted under the lowest pressures-e.g., the highest vacuum below the orifices. Here it is suspected that the increased flon rate was a result not ovly of the differential pressure (as in the pressure tests) but also of the lower absolute pressure. T h e solids flow rates through the orifices under the influence of
2
gravity alone (without a pressure differential) were markedly greater as the total pressure of the surrounding medium in feed bin a n d receiver was reduced more a n d more below atmospheric. Since in the suction tests the pressure in the receiver was below atmospheric, it is suspected that this alone increased the solids flowability above that to be anticipated from the pressure differential across the bed. T h a t this would be far more pronounced with F C C catalyst than with sand or Saran was also to be expected, since the vacuum tests had a far greater effect on the flowability of F C C catalyst than on the flowability of sand or Saran. Following the procedure proposed in Figure 7, the vacuums required in the receiver vessel, to obtain the observed solids efflux rates, were calculated and compared with observed differentials as summarized in Table V. I n the suction tests the vacuum initially drawn in the receiver could not be maintained during the course of a test, since the volumetric influx of a i r and solids from the feed bin exceeded the capacity of the vacuum pump. T h e pressure in the receiver therefore rose during the run and consequently the differential pressure between feed bin and receiver continuously decreased. T h e measured solids efflux rates in the suction runs therefore represent a n average over the range of pressure differentials existing between the start and finish of a r u n ; initial and terminal differentials are noted in Table V. Yo absolute comparison between predicted a n d observed differentials is really possible, since not only were the solids rates and differentials changing during the runs but the rates were affected by the reduction in ambient pressure. A point of particular interest in the suction experiments was the observation that the extremely non-free-flowing barium carbonate could be drawn from the feed bin through the '/.l-inch orifice a t rates of the order of 100 pounds per minute with a differential of 10 to 12 p.s.i. across bed a n d Orifice. Using a n equal differential under the pressure tests did not create any solids flow. Thus, barium carbonate could apparently be sucked out but not squeezed out. This again is suggestive of a
100
I
I
0
~
I
FCC
i
?---A \
D. 112.
--
Pressure
Suction
'x
BOCO,, .D I
I
I
I/*'& I/L. I
'
~
Total
~
'
'
10 '
'
I2 '
"
14
'
Pressure, PSlA
Figure 10. EfFect of total pressure on gravity flows of solids in 70" F. air 354
l&EC
PROCESS DESIGN A N D DEVELOPMENT
I
I
, + (AP/L) I
I
I
, , , I 10
e0
Figure 1 1 . Experimental results on efflux of cement under pressure and suction conditions
Table V. Comparison between Observed Pressure Differertials and Those Predicted b y the Flow Model of Figure 7 for Suction Efflux of Free-Flowing Solids \i
no. infii
1 /ti\
Jl'li l)i//,l,!/!,l/
r pIl
If)
(
5,( I
I' i.!/!it
~
11' I' 5
I
71
~
0I, > d
\lit
[ ,I//
ii
0 12.5
0 25
20 2(1 i
1 ' 1 7 ~ ~ 132 1 0 - 1 2 3
7
8 01
-
80
FCC: C i i 91 y.;r 0 12.5
0 25
4 34 3 88 3 43 20 48 20.96 18 I 1- 09
.io
48 6
0.2.5
13 11
0
s \R 11 ('I 1.5 18
0 . SO
5.5 3 48 1 37 9
8 35-11 8 6 89 1 1 8 -5 9 I 1 8 7 3' 12 3 -,3--12 3 5 9-12 3 4 4 1 2 1 . i9 12 3
12 2 1(1 3 86
4 0 2 11 8 3 42 I 1 8 6 88-11 8
9 2 - 4 12 4
5.9c 11 8 3.44 I 1 8 1 9? 1 1 8
11 4 8 84 6 0
12.43 1 1 34 9 44
\4
VOL.
3
NO. 4
OCTOBER 1 9 6 4
355
