INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY
992
L)&
Vol. 43, No. 4
= 44.7
P
(~)""
= 0.0348 foi, ivater :itl~orptioii H,i = Thus Hd for nitrogen dioxide adsorption divided t>>- H , , i.01, water adsorption = 0.610/0.0348 = 17.5.
1
llir
~ v l i t ~ the r c ~ nelv symbols h a w the following significaiiw : /;
=
diffusion coefficient for diffusion of a d s o r h d iiitrogrii diosido \Tithin the gel particle, pounds of gt.1 p~ hour p r foot
EngFnyring process development
Flow Rates through Soybean Flakes I
GRAVITY PERCOLATION OF'HEXANE MISCELLA
DAVID CORNELL', BLAW-KNOX C O . , PITTSBURGH, PA. DONALD L. KATZ, UNIVERSITY OF MICHIGAN, ANN ARBOR, Hexane is used to extract oil from soybean flakes 11) pcrcolation through beds of flakes. This paper prewnts C Y perimental data on rates of percolation f o r hexane rniscella under specified conditions. The data are correlated by the procedure debised 1)) Brownell and Katz for porous beds; this inbolves a lcnowledge of bed porosity, particle diameter and shape, and properties of the miscella. The correlation permits the presentation of charts for predicting hexane miscella percolation rates under conditions for commercial equipment.
MICH.
M
A S Y so!.lieau cstructiou plants u,w cquipiuent i n whicli hrsane is :rllon.rd to percolate by gravity t,hrough a h t l of so?-hean f l d i p i . The flow rat.c at which the liquid w i l l p n s ~ through thew Halw beds is of interest to equipment designer? and plant operators alikc. Kenyan, liruse, and Clark ( 7 ) give operating data for a basket estractor handling 405 tons per d a y of soybean flakes. Their data show that the mass velocit'y of iniseella through the extraction baskets is about 2200 pounds per Jquare foot per hour on t,he count,ercurrent side, and about 1600 pounds per square foot per hour on the concurrent sidc of thi. :
Pi?-ent address. L-niversity of AIichigan, Ann Arbor, Mich.
@""
04,
993
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
April 1951
'
'
Figure 1 .
'
"""'
'"""'I
1.0 ' ' 4 10 REYNOLDS NUMBER
' 3 a i a 1
' ' 1 "
'
' ' '
Re> noldn \tirnher-Friction
1
100
""
that it. antl its coiitents could be weighed a t any time. ,\[iscdla was circulated continuously by a centrifugal pump, B , antl was allowed t,o flow through the bed by gravity percolation. h cooling coil in tank A was used to hold the miscella teniperaturca constant since the liquid was heated by the pump as it was r11circulated. T h e rate of flou- of the miscella was held constant, liy niaintaiiiirig :I coiist:iiit n-eight of liquid in the column which i i i turn g a w n cori?:t:int hcwl. The How rate was measured t)), (dlectiiig, at 0, the niiscella coming from tlic: column over : I irirusured time anti neighing the :tniount collrvtecl. The tetriIwatures of the iiiiiccJlla pntering :md 1c:tvirig thc colunrii \rere ineniui,rd liy tlieriiionietei.:: E aritl F inini dtrennia The, Il:itu n ~ i ' i xt:tlteii in the I'ollowii1g itia1iiit.i':
"'
'
SO
LJ .-
.I n~ig1it.dsample of flake3
F a c t o r Plot
cAstriictor. These n vrlocitic+ :irt' cnlcu1:itcd froiir 1 1 1 ovisi,-:ill material balance, an ence differ Froiii the actuRl itiuss veloc~itie. i n that during operation the liquids are not intrc)tluced contiiiuously hut :tre added at, int als t.o thc estrnctor I,:iskets. Thp purpose of this papel' ir to how the variable?: that govern th(, How rate of hesane niiscelln through beds of ,soyliean flakes antl to provide data for predicting the flow ratr that will occur for given conditions of the hed niid the niiscelln. THEORI
T h e friction factor plot has long been used for the prediction of flow rat,es for a given pressure drop in cylindrical pipes. Modified friction factor curves for porous media x e r e presented t ) y Chilton and Colhurn (4)and Fancher and Lewk ( . 5 ) . By introducing the porosity of the heti :ind a shape factor for the particles, the friction factor plot has been extended hy Brownell and Katz ( 3 ) to the prediction of flow of fluids through porou? media. Their procedure has recently been modified hy Bron-iirll et al. ( 2 ) . T h e final correlation covering a greater range of variables, which appeared in :i T \BIZ book by Brown and associate. (I), was used in obtaining the wsults of this work. For porous beds the Reynolds number m d friction lactor become:
T h e vnlurs of mass velocity were plotted against thc, ratit I vi liquid head t o hed height BP is shown in Figure 4 t,o iiiiilw surf^ that the data m-ere consistent. During the course of the investigation it was found riecessni'!to discard sonic data that were taken when small quantities 01 water were introduced with the recovered solvcnt. Tahlr I I
I. FLOW R.ITE D.ITAT . i K E S
P
Liquid Height; Bed Height 1.46 1.47 1.07 1.03
1.13.; 1.14 2.0i 2.12
1.43 1.49 1.10 1.27
Figure 1 s h o w the friction factor plot. EXPERIMESTAL WORh
Equipment, was constructed for circulating miscella over :I 1)ed of soybean flakes as indi-
3800
1.01 1.31 1 .29
21.2:
3730 +. O ,1170 ,5220 3830 3950
21.2.i
"90
I .28
1.14 I 52 1.08 I 08
1.92 1.g2 1.54 1 . ,j4 .i 14
0 839
AT
1A 7 1.47 1.07 I
n;
85 O F.
Mass Velocity, Bulk Lb./iSq. Density, Ft.) ( H r . ) L h . / C u . Ft. 2310 2 5 , r, 2260 25.5 1313 25.7 1255 2.3 7 3330 26.0 3390 21i 0 637 2G.X 039 2 6 , :3 1333 26.3 1382 26.3 ,5940 2 0 . $2 GO70 20.9 1310 21.1 4930 21.25
1.01
1 .0ti
i0 i
,
Thi.~:,ho\vever, would have been awkward in the experimental equipment, 3s it mas set up, and commercial procedure could not li:ivp lxen duplicated exactly in any case. It is believed that thv only difference resulting from this procedure is one of bulk densit?of the resulting bed which should be accounted for h y the correlation that takes bulk density into consideration. The niiscell:~ to he used n-as then circulated for about 0.5 hour before any d:tt:i were taken; during this time the hed settled about 10% dqimiliiig on the particular flakes used. Red heights of from 12 to l h inches were used. After steady stat,e flow rate conditions had been niaintairietl lor a few minutes the flow measurements were taken. Beforii and after measurement of the mass velocit,y the heights of thi. liquid and the bed in the column and the temperature of the mirwlla entering and leaving were observed. If any of these quantities varied during the measurement of the flow rate the data wert' discarded and the measurement, repeated. Liquid heights ranging from 12 to 24 inches above the bottom of the bed were used. The temperature of the bed was maintained at 85" F. to prevent lops of the solvent (Table I ) .
2.04 2 06
k,ated in Figures 2 and 3 , Thr. flow rates \yere measured in :I vert,ical glass column, D ,3.78 inches inside diameter and 3ti inches high. This insulated column was fitted at the bottom with a wire screen of approsiinatel?: 14 mesh m d was i~eaiiihalance iiiounted on
w a s poured into tiic cu1uni11. I ) .
< 'uninirrcially the flakes and solvent are charged simultaneousl)
IO00
.i330
2180 :3500 3590 8040 3180 83 3 805 512 498
Reynolds NO.
Flake
DGFR~
Sample
P
.I
17.1 16.8
9.7.;
9.8 15.0 2.5.4
i
R
1,023 0.Y9G 2.08 2.16 69.7 ?I.? . I O . ;1
I3
21.2:) 2 I , 2 .-,
R8.2 33 3 3 2 . $1 48.0 43. ti
Friction Factor, L'gcDH l'i,?l'
2 fjY 2.8% 0.07 li ,52 1 74 I .72 31 . o :32 , !4 13 7 IX.O;r
0,781 0.777 1.14 0 951i 1 .3 3 1.40
0.84.; 0 , 929
R
38.3 28.3 29.0 40.5
1.02 1.33 1 ,5!1 I 08
24.3 2 4 , .i 2 4 . ;1 24.5 2 4 .-, 2 4 ,-,
r
3.06 :3.10 2 . 13 2.03 2.26 2.07
2.1 , :3 24 8 '1 5 24 ;I
r
19.6 19.3 31.3 32,l 27.2 28.5 0.747 0.720 0.458 0.446
21.4
21.6 21 .(i " 1 li
40.4
43.3
78.2 82.8
INDUSTRIAL AND ENGINEERING CHEMISTRY
994
Vol. 43 No. 4
8,
Figure 2.
Column Containing Soybean Flakes
'The hulk drriaity 1v:is olit,ained i'i,oni the n-eiplit 01 t l i i , fl:ihc+ c,liargetl to the. colunin and their volume i n tliv coluinii. Thc, (lensit,!- of the unestracted flake material \vas inore clifficult t o iihtnin. According to Horvatli ( 6 ) AIanchurian soyl)ouns have, :in avcwgc, density of 76.4 poundi pcr rul,ir foot, tlic. densit?, i ) f the soybrans vitrj-ing with their qualitj.. h inisturc of hexane : i i r d perchloroc~thylene, i n which the flakes used ill this work \vould rrmuiir .suspended when initially iinrnersecl, \vas found to li:LvtL n density of al)out 74 pounds per cubic f O O t . Shortly after iiiiiirersioii, the flnkes would sink owing to cstrnction oi t h r oil :(ridits replaccJiniwt,kvith the heavier solverit. A s :t clic:ck OII tlik ligure n weighed snmple of flakes was put in a pycmomcter which \\.:LS t,hen filled with mercury and evacuated. JIercury was used l ) v c : ~ u s r it does not m t or affect the flakes. Thv fl:ilres veri^ r i t c s t l J'I,(III~ fioatiiig l i 1)ridgirig ~ ~ :it tlicx neck o f the p j . ~ iionietri.. Thca volume of niercui.- tiispl:iretf Iiy thc f h k e s W:L.Q ilrterniiiicd i)y \vtiighing, and the density of the material bva.. i~iiiil~utc~tl to lie1 i:3 pourids per cuhic foot. Since this value ma! Iw lo\v IicBcausc. of air trapprd Iietneeii the f l : ~ k ~the ~ , density ( 1 1 7 1 pouriel,~pci. w h i r foot \v:w tnkeri its the dr,nsity of the flak(> iixiterial. Thr porosity of tlic l ) t d ' i v : ~thrn roinpritc.tl from t,liii i-:iluc~: ~ n dthe l)ulk (lensit-. III i 1 r ~ l ( t~ oi ~wtim:itc thv y)Iiwit-ity of tlii, fl:tkw i t \v:i$ itswrii(~i1
above bed iminutes LO minute:3O minutes 4.i niiniite.
were used. Table I11 listr the samples used togethe], with the propertirs of t h r fl:tlcri: : u 1 ( 1 t,he bed$. The tliiekriess of the soyIw:t~~ flakes W E taken as the w i t h metic average of thr thirliiiesses of 100 flakes niemurt~il with a micrometcir. The a v e i ~ age diameter of the Hake.
Sainple
1.04 1.04 1,O.l
i.ni
RYlG
877; 877.5
:/-; /'
/
0
B
I
I
I
I
,
I'Llte i'ljr
hcS:tllt'
riiiscella u t 1 2 5 O 1;. 'iras made. Theses calculations w e r e based on the dashed
:/e. '
.
,INSULATION
/
A'
+/"
@/
35
/
/
:
c E
PREDICTION OF FLOW RATES
,
YI
DISTRIBUTOR
STICK
995
*
COLUMN D O N /BEAM BALANCE
y.l w /..' :A
ROTAMETER C ,THERMOMETER
6 TANK A Figure 3.
T.IRI,EI\-. I ~ T E R M I X A T I OOSF AYERAGEDIAMETER
Flow. Rate Apparatns
(Soybean flake; sample C)
I' SS Siei-r S,,.
that they were disks with a diamet,er equal to the average di:tmet,er from Equation 3 and a thickness equal to the averagca flake thickncsp. The sphericity could then I E computed 1,: means of thc following equation: $ =
(1.5 thickness)"3 ( ~ 9 ~ , . . ) 1 , ' ~ Dav. Ithickness
d 1:i a r t i c i l i (Dialnet el Retained. of Fraction). .TI Inch 0 . 074!4
0 . 3 8 10" 0 . 1390 0.1129 0,0799 0,0496 0.0281 0,0198 0.0131 0.0084 0.0064
0,2598 0.1050 i l 1812 0.2210 0.0463 0,0259 0,0139
(5)
0.0050
~
2
0.0030 0.00-10
The exact way of defining the sphericity of a bcd coinposed u i mixed sizes and shapes such as are cncountered here has not yet l m n established. This arbitrary method provides one me:ins o i arriving at a sphericity that can be used for correlation purI m e i The commercial hewne used v a s Pkellysolve B.
'1
llstimnted.
7
8,0001
0.0044"
I1
'
.U'd
ill/dS
0.2:3
0.0363 0 . 00402
2.27 4.46 1.65 1.31 LOG 2.00 0.47 0.91
6; 113 353 1,813 9.090 3,340 6,170 8,510 11,430 4 6 , goo
I 6 0.i
80.81 I
1.63 1 46
0.001436 0.000512 0.000122 0000222 , .76 X 2 . 9 5 x 10-6 0..592 X 0 . 2 6 2 X lo-' 0 o m x 10-6
g.
CORRELATIOh O F 1J.A'I i
The data were used t o calculate Irictioii factors and Reynolds numbers according t,o Equations 1 and 2. H:iniple calculations :Ire given in Table I-,:ind the summarized datu :irid calculations :tre given in Table I. These values are plotted ill Figure 1. .I3 might be expected, the data scatter, and escluding runs made : L t very high miscelh concentrat.ions, the correlation predicted H o n rates about 20% lower than r e r e observed. It, does, however, give results of the right order of magnitude, and the agreement IS good n-hen one considers the vnriable nature of the material used-its fragility, sampling problems, the possibilit,y o f stratification or preferred orientation of the particles, air vhich is possiblv trapped in the bed, and the fact that this is not a case of fully developed flow but one in which the liquid must enter t,he lied. pass through it,, 2nd then run out. Since the data can be correlat,ed by t,he puc-edurc used according to the equation f = 5O/Rr, rather th:ui .i' = 64/Re, it is 1)elievecl t,hat the method takes into consideration all the niajoi variables i n the flon- process as it occurs in i: basket estract>or. These are the average flake diameter, bulk density of the bed, :md the viscosity and density of the niiscella. Flake t,hickness in its commercial ran e of values is not impoltant in itself, although it affects bulk jensity'rhich in turn is important in determining the flow rnte. The bed height, as vell, is not a varisble hecause n change of bed height changes the liquid head proportionally. It can possibly affect the bulk density somewhat, hiit thiF: n-ill nlso he taken cnre of h y the cnrrelation procedure.
h
h I
\
h I
LL. \
6,000 %
5 4,000
sw > @
2,000
Y,
4.
I
I
I
I
I
24 26 2a 30 22 BULK DENSITY L B / CU. FT. Figure 5. Correlation of Rliscella Flow- Rate, Bed Bulk Density, Flake Diameter, and Oil Concentration 20
Flooded flow rates for 0.10-inch thickness flakes of 89'0 content, system a t 12.5' F.
moisture
