FLOW THROUGH POROUS MEDIA
e
= contact angle = sphericity
(4) Brownell, L. E., and Rata, D. L., Chem. Eng. Progr., 43, 537,
fi
= viscosity = density = surface tension
( 5 ) Brownell, L. E., and Kata, D. L., Trans. Am. Inst. C h a . Eng., 43, 10, 537 (1947). Technology of Fine (6) Dallevalle, J. If., “Micromeretics-The
p
y
601, 703 (1947).
LITERATURE CITED (1) Brown, G. G., and Associates, “Unit Operatiom,” New York: John Wiley & Sons, Inc. (1950). (2) Brownell, L. E., Dombrowski, 13. S., and Dickey, C. A., Chem. Eng. Progr., 46, 415 (1950). (3) Brownell, L. E., and Gudz, G. B., Chem. Eng. 56, 112, (1949).
Particles,” 2nd ed., New York, Pittman Publishing, 1948. , H., Trans. Am. Inst. Mining (7) Uren, L. C., and El D i f r a ~A. Met. Engrs., Petr. Div., 70 (1926). (8) Wyckoff, R. D., and Botset, H. G., Physics, 7, 326, (1936). RECEIVED for review November 23, 1953. ACCEPTED April 19, 1954. Abstract of a dissertation submitted by H. S. Dombrowski in partial fulfillment of the requirements for the degree of doctor of philosophy at $he University of Michigan.
Holdup and Residual Saturation of Hexane in Gravity-Drained Soybean Flake Beds BABUR M . KOCATAS UNIVERSITY
AND
DAVID CORNELL
O F TEXAS, AUSTIN 12, TEX.
Soybean o i l is extracted f r o m soybean flakes by using hexane as t h e solvent. A t t h e end of t h e extraction period hexane is allowed t o drain f r o m t h e bed of soybean flakes. The hexane remaining in t h e bed m u s t be removed by application of heat in a desolventizer. This study was undertaken t o determine t h e effect of t h e various bed properties on t h e solvent holdup for conditions of industrial significance. Factors t h a t tend t o increase t h e permeability of the bed were found t o decrease t h e holdup. Increases In b u l k density due t o flake preparat i o n decreased the holdup, whereas increases in b u l k density due t o bed settling tended t o increase t h e holdup. Increases in flake thickness and average diameter were accompanied by a decrease in holdup. Large saturation gradients in t h e column were observed. Although t h e high saturation a t t h e bottom of t h e bed i s partly due t o capillary end effects, t h e very slow rate of flow of hexane liquid films is believed t o be t h e major factor in determining t h e saturation gradient for drainage periods of commercial importance. The relationship between t h e dynamic and capillary effects is shown by comparison of beds of different heights.
1
N T H E solvent extraction process for recovery of oil from soy-
bean flakes, information is iieeded for predicting the flow rate of solvent through the flakes, extraction rate of the oil, and the holdup of solvent in the extracted flakes after a given draining period. Although studies of the flow rates and extraction rates have been made, information was not available concerning the effect of the preparation procedure and bed properties on the total holdup of solvent and the distribution of the liquid in the bed, Since the amount of holdup determines the quantity of heat necessary for desolventizing the extracted flakes, it is an important economic factor in the selection of the correct heat transfer area and steam requirements of the desolventizer. Furthermore, since several existing extractor designs use bed heights ranging from 6 inches to 4 feet, some means of evaluating the effect of bed height was desired. This paper presents the results of an experimental study of the effect of the bed properties on the holdup of solvent in the bed and the nature of the draining mechanism and resultant saturation gradients in the bed. Theory
Two aspects of the problem of gravity drainage in soybean flakes are the dynamic unsteady state flow of the liquid as it drains down through the bed and the static equilibrium saturation in the bed after a long period of draining. Both of these aspects are important in determining the average holdup and the distribution of liquid in the bed after draining periods of industrial significance, The bed properties and the bed height lune 1954
determine which of these two aspects will be most important in each individual case. Draining Period
The dynamic flow period may be divided into three parts: (1) Viscous flow down through the entire bed with a visible liquid-vapor interface moving down the column; (2) viscous flow through liquid filled flow paths; and (3) viscous flow of films downward over the surface of the particles making up the bed. Since the initial and highest rate of flow is known to be viscous (I),all these flow processes are probably viscous flow. All three mechanisms will occur simultaneously during the draining period but will predominate in the order shown. In steady state drainage through liquid-filled capillaries Equation l for viscous flow through porous media. applies.
In gravity drainage, Equation 1 simplifies t o
The holdup, defined as the pounds of total solution remaining in the bed per pound of oil-free and moisture-free flakes, is inversely proportional to the mass velocity with which the liquid leavee the bed. Although Equation 2 is limited to steady state flow,
INDUSTRIAL AND ENGINEERING CHEMISTRY
1219
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT in determining the effect of change? of fluid properties on the dynamic holdup a t a given time. The holdup is proportional to p / p 2 in film drainage as well as in flow through liquid-filled capillaries. Residual Saturation
When all movement of the liquid in t'he bed ceases: t,he solvent remaining in the bed will be distributed according to some residual saturation curve. The interstitial pore space a t the bottom of the bed will be nearly completely filled with liquid because of capillary end effects (4). At distances high above the bottom of the bed an equilibrium residual saturation will be reached. Equilibrium residual saturation, SO!is defined as the percentage of interstitial void space in the bed that is filled with liquid in the portion of the bed that is free from end effects. It is the net result of the gravitational and capillary forces acting on the liquid. The increased saturation a t the bottom of the bed is due to the discontinuity of the bed and is referred to as the "end effect." Brownell and Iiat'z ( I ) , Dombrowski (3), and othcrs have correlated residual sat'uration with the capillarj- number. Dombrowski also presented a method for handling t,he end effect region. From a practical standpoint it' is desirable t,o know the effect of bulk density, particle diameter, and flake thickness on thr holdup of solvent in the bed. These variables together determine the permeability of the bed (1). The bed permeability appears in the capillary number with ivhich residual saturation is corrplated.
The permeability is determined experimentall>,from Lquation 7 in n hich GI is the flooding mass velocity.
For gravity-drained beds, the capillary number becomec
Figure 1.
Apparatus for Drainage and Holdup Measurements
it is useful in making viscosity a i d delisit>-corrections since the holdup is proportional to ( p ) i ( p * ) for this type of drainage. Following the capillar3- drainage periods, drainage through films of liquid on the surface of the particles is believed to occur. For viscous, unidirectional, steady state, vertical flox by gravity drainage the Savier-Stokes equations reduce t o (3)
For the boundary condition, r = 1, the film thickness, 6vj6x = 0, Equation 3 can be integrated to give Equation 4 for the point velocity in xvhich the constant of integration is zero because the bed is stationary.
The minimum holdup can be calculated from the equilibrium residual saturation which is determined from a coriclation of So( 1 j ivith the capillary number determined by Equation 8 based on an experimental or calculated value of the permeability for soybean flake beds of any bulk density, flake thickness, and average particle diameter. Experimental Work
Unextracted soybean flakes weie obtained in three flake thicknesses. The average flake thicknesscs vere determined with a micrometer and the average diameters by a sievc analysis. The moisture contents mere analyzed by toluene distillation in the Dean-Stark apparatus, and the oil content of both fresh and extracted flakes was determined by a 2-hour extraction with petroleum ether in a Soxhlet extractor. The properties of the flake samples as received are summarized in Table I.
Table I.
The film thickness in terms of thr averago v e l ~ c i t vclan be obtained by integrating Equation 4
Soybean Flake Properties
Property Average diam., inch Average thickness, inch Noisture content ("as is" basis),
1220
Sample 2
0.0138 0.0080
Sample 3 0,0110 0.0057
%
7.3
8 6
6.6
%
21.5 26.2
21.9 21.8
20.7 24.8
Oil content (moisture-free basis),
Equations 2 and 5 represent the two probable steady state mechanisms of drainage from the bed. These equations are useful
Sample 1 0.0140 0.0107
Average bulk density, lb./cu. it. Average permeability, (cu. ft.) (lb. mass)/(sq. hr.) (lb. force)
INDUSTRIAL AND ENGINEERING CHEMISTRY
1,63
1.72
0.82
Vol. 46, No. 6
FLOW THROUGH POROUS MEDIA 1.2
y
prene hose to the drain line. The column assembly was placed ' on a1 balance-type scale and balanced by counterweights. B t
-~-
10
ISAht!LE
[RUN
-_.__
3 71 0 53 364
-@-
---I
maximum load the scale was sensitive to 1/8-ounce weight increments. All metal equipment was electrically grounded as a safety precaution.
I 8 E D I ~ ~ G C T . FT.
3
P 3 0
-+-
0 i
-
I
041
lgoo
Figure 2.
TIME,
-"1
I
3,000
2,000 SECONDS
Drainage Curves for Several Samples and Bed Heights
!I +-
2.0
I I
l i
-OBSERVED AVG HOLDUP
A weighed quantity of flalcee was charged to the column and extracted with commercial n-hexane using three 5-gallon washes, allowing 1 hour for soaking and '/z hour for draining each wash. After extraction, fresh hexane \vas circulated through the column to establish a uniform oil concentration in the solution and to complete the extraction as nearly as possible. The column was then filled with liquid slowly from the bottom t o prevent entrapping of air between the flakes. The flooded flow rate and temperature of the bed were determined in order to establish the permeability of the bed. Then the bed was allowed to drain for about 15 minutes. The weight of the bed was recorded during the draining period in order to obtain the drainage curve. At the end of the draining period the drain valve was closed and the column was disassembled a t the flanges. The contents of the column over 6-inch sections were sealed in gallon cans thus giving five samples over the height of the column. A sample of the liquid was taken to determine oil content and density of the solution. The sealed cans were weighed, then the contents were removed. desolventixed in air, and replaced in the cans which were rewighed. The amount of solution holdup was calculated from the decrease in weight, and known oil content of the solution. and the oil-, moisture-free weight of the flakes. Table I1 summarizes the permeability and liquid distribution data taken on the three flake samples. Experimental Results
Typical drainage curves are given in Figure 2. The solution holdup expressed as pounds of solution per pound of oil- and moisture-free flakes a t any time is inveisely proportional to the permeability of the bed High holdup values are expected for low permeability beds because the drainage rate is low and also because the residual saturation is high Short beds (Figure 2) have a high initial drainage rate. At long draining times, however, the high beds drain more completely than the short beds because the end effect, which is analogous to capillary rise in
I
I !
0
I
,
l
l
l
'
I
I
I
Figure 3. Final Distribution of Holdup i n ColumnSample 1, Run 2
The apparatus for drainage and permeability measurements is shown in Figure 1. A 4-foot, 5.72-inch internal diameter cylindrical column made of Lucite was built of three 1-foot and two 1/2-foot sections flanged together so that the column could be taken apart for sampling a t the end of the drainage period. A wire screen was placed aero68 the bottom of the column to support the bed of soybean flakes. A m e t a l c o n e w a s attached to the bottom of the column leading to a 3/4-in~h drain pipe with a fast-closing valve draining into a surge tank. An air vent valve was put just below the level of the screen to avoid suction on the bed due to the head of liquid in the drainpipe. A centrifugal pump was used to circulate the solution back to the column, which could be filled either from the top or the bottom by connecting a XeoJune 1954
Table II.
Holdup and Saturation Data for Soybean Flake Beds a t End of Draining Period
Run No. Bed height. f t . Bulk density, lb./cu. i t . Temp., O F. Oil content of solution, % Average holdup, (lb. solution)/(lb. flakesc) Flooding mass velocity (Gf), lb,/(sq. ft.j(hr.1 Draining period, see. Holdup, (lb. solution)/(lb. flakesQ)for heights above bottom of bed, f t . 3 . 0 to 3 . 5 2 . 0 io 2 . 5 1 . 0 io 1 . 5 0.5 to 1 . 0 0 too5 Fractional saturation of voids between flakes for heights above bottom of bed, f t . 3 . 0 to 3 . 5 2 . 0 to 2 . 5 1 . 0 to 1 . 5 0 . 5 to 1 . 0 0 to0.5 Predicted residual saturation for high beds a Oil-free, moisture-free.
4.0 27.2 83 2.09
Sample 1 2 1 75 25.3 77 2.09
0,545
0.540
0.492
0.574
2963
4110 1175
4247 1670
0.430 0.474 0.525 0 502
0,149
1
, . .
900
900
n.102
...
0.461
0:443 0 445 0.603
0.145 0.170 o 203 0.188 0.211
o:iii4
0.120
0.437 0.483
0.490
...
3 3 96
26.0
83 0.87
0.670
Sample 4 3.69 23.8 85 0.78
2 5 3.71 25.8 95 0.44
Sample 3 _____ 6 3.92 24.1 84 0.44
7 3 62
0.486
0.687
0 724
3640 900
1540 920
1280 900
0 415 0.510 0.526 0.545 0.750
0.484 0.536 0.616
0.470 0.602
0.679 0.899
0.533 0.656 0,778 0.903 1.052
0,128 0.184
25.6 97 0.30
0.682
0.847 0.994
0.164 0.334
0.191 0.226 0.210 0.332
0.195
0.205 0.327
0.190 0.225 0.279 0.322 0 470
0,222 0.302 0.381 0.461 0.557
0.192 0.283 0.339 0.452 0.554
0.126
0.122
0.120
0.121
0.162
0.160
INDUSTRIAL AND ENGINEERING CHEMISTRY
1221
ENGINEERING. DESIGN. AND PROCESS DEVELOPMENT
\
n W
m LL
0
z
0 II0
m 0 5 U a IU W a 2
z v) a U
0
z
11
I-
5 2 0
I I
)
Figure 4.
0.45 HOLDUP,
I I
l
l
I
!
I
a5 5
0.50 LBS. SOLUTION
/
L B . 0.F.M.E
I
I
I
0.6 5
0860 FLAKES
Final Distribution of Holdup i n ColumnSample 1, Run 3
the same flake sample after a slightly longer draining period (Figure 4 ) shows that the bed has not reached equilibrium as completely as the short bed. However, since the end effect increases the holdup in a smaller fraction of the 4-fOOt bed, the over-all saturation is about the same as that for the 21-inch bed. For every flake bed and drainage time there will be an optimum height for minimum holdup. While values of holdup are important in practical calculations, the fraction of the interstitial void space filled with solution, teimed saturation, is usually correlated because saturation is independent of particle density and for porous materials, such aa soybean flakes, is also independent of internal porosity of the solids. Figures 5 and 6 show typical saturation distribution curves for two of the same runs shown in Figures 1 through 4. Figures 5 and 6 also shov the values of the residual saturation of the bed free of end effects (So) calculated from the correlation of So with capillary number given by Brownell and Katz (1). The Brownell and Katz correlation was used in this case because it gives conservative results and because there does appear to be a variation in residual saturation with capillary number. If furthe1 work establishes the DombroM ski correlation for beds of mixed particle shapes and sizes, these residual saturation curves should be revked downward. The values of the capillary number were calculated from the experimentally determined flooding velocity, the surface tension measured with a du S o u y tensiometer, and the viscosity and densitv of the solution (6). The surface tension of the solutions compared closely v,+th those for pure hexane (4). Since unextracted soybean flakes were charged to the column, it x a s necessary to estimate the replacement of oil by the solution before conveiting holdup to saturation. It was aaeumed, therefor?, that the oil extracted mas replaced by solution. Thie amount of solution was subtracted from the total holdup to find the interstitial solution. The intcrstitial porosity of the bed
small diameter tubing, increaws the over-all average holdup more in a short bed than in a long bed. Typical curves for the distribution of the solution holdup ovei the height of the column are shown in Figures 3 and 4 foi beds 21 inches and 4 feet high. The existence of a very high holdup zone a t the bottom of the short bed in Figure 3 is due to the capillary end effect. The distribution of holdup in the 4-foot bed of
c - t m
811 0
w-
'I I
I
,
t
.
(
,
:
0 02 0 4 U O UCI I" SATVQATION, FRACTI3N oi VOID SPACE BETWEEN TYE FLAKES
Figure 5. Final Saturation Distribution in ColumnSample 1, R u n 2
1222
W 0
m 0 U
a
B 0
m
z ( L.r
I-' LL
w
a 2 vf ii
0
z
0 a
0
0 J
SATURATION, FRACTION OF VOID SPACE BETWEEN THE R A K E S
Figure 6.
Final Saturation Distribution i n ColumnSample 1, Run 3
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 46, No. 8
FLOW THROUGH POROUS MEDIA
86 S.
AVERAGE 'TEMPERATURE
0 300
SECONDS D R A N
e
~ O O S E C O N D S DRAIN 0 900 SECONDS WAIN
0.41 0.005
1
I
I
I 0.008
I
0.007
0.006 AVERAGE
FLAKE
I
I
I
I
0.009
THICKNESS,
,
0x)IO
INCHES
Figure 7. Correlation of Holdup w i t h Average Flake Thickness for &Foot Deep, Gravity-Drained Beds of Soybean Flakes
was calculated from the bulk density of the bed and a density of the flake material of 74 pounds per cubic foot ( d ) . Saturation values were then calculated from the porosity and the interstitial holdup. The average holdup for &foot beds after 300, 600, and 900 seconds of draining a t an average temperature of 86" F. is plob ted as a function of average diameter, flake thickness, and bulk density in Figures 7 , 8, and 9. These curves do not isolate the effects of the individual variables; however, they do show the trends that may be expected when flake preparation conditions are changed. In general, changes in bed properties that increase the permeability decrease the solvent holdup. Since the bulk density can be changed either by changing the flaking procedure or by packing the bed more tightly or loosely, an increase in bulk density can be accompanied by either an increase or decrease in permeability and holdup. If thin flakes are made, a low bulk density bed is obtained. At the same time enough additional fines may be produced to cause the permeability to decrease. Consequently, an increased holdup might be obtained for a low bulk density bed. If the decrease in bulk density is due to looser packing of the bed, however, a decreased holdup might be expected. Both of these cases are shown in Figure 9. Figure 10 shows the holdup correlated with the capillary number. The minimum holdup for an infinite draining period and no capillary end effect was calculated from the residual saturation curve of Brownell and Kat2 (1). Since Figure 10 is based on the capillary number, changes in the bed permeability and solution surface tension are considered. However, the effect of changes in temperature on the drainage rate necessitate a correction to Figure 10 for temperatures other than 86" F. Since holdup is inversely proportional to the mass velocity, Equations 2 and 5 show that the temperature correction for Figure 10 should be proportional to ( g ) / ( p 2 ) . Figure 11 gives
I
0 300 0 600 8 900
I
1 ' 1 ' 1 ' AVERAGE TEMPERATURE 86°F.
86'6
AVERAGE TEMPERATURE
-'WERAIL EFFECT OF BULK DENSITY CHANGES DUE TO CHANGES IN F L A K E PREPARATION
SECONDS DRAIN
0 300 S E C O N D S DRAIN e 600 S E C q t i D S DRA.74 0 900 S E C C N D S WAN
S E C O N D S ORAN SECONDS DRAW
1
-EFFECT OF CHANGES IN BULK DENSITY ONLY, FOR THE SAME SAMPLES
'3
''
300 SECONDS oR4M
0.5
'
0 . 4 1 '
O.C"l0
1
0.011
1
AVERAGE
1
1
1
0.013
0.012 FLAKE
1
DIAMETER.
1
0.014
1
I
0.015
I 0.4
1
23
,
1
24
BUCK
Figure 8. Correlation of Holdup w i t h Average Flake Diameter for &Foot Deep, Gravity-Drained Beds of Soybean Flakes June 1954
>
25
I
l
26
l
,
27
l
,
INCHES DENSITY,
L B S / FT'
Figure 9. Correlation of Holdup w i t h Bulk Density for &Foot Deep, Gravity-Drained Beds of Soybean Flakes
INDUSTRIAL AND ENGINEERING CHEMISTRY
1223
ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT correction factors t,hat may be used to find t,lie holdup a t any temperature from the holdup values of Figure 10. Holdup and residual saturation nieasurements made in this 1%-orkdo not represent an act,ual equilibrium by a dynamic approach to equilibrium. Drainage to equilibrium Ti-ill require much longer times than the practical limit in actual plant operation. Equation 5 shon-s that the drainage rate during the filmtype draining period is proportional to the film thickness Fqiuired.
AVERAGE TEMERPTURE 86 'c.
I
,
,
cc
L23
0tP.T
Figure 11. Correction Chart for Calculating Woldup a t Any TemperatuPe from Holdup e t $6" &.
Aftrr a i'apid initial draining period which reduces thc holdup io about 0.5 pound of solution per pound of oil- and moi5turo-frcc flakes. depending on the temperature and bed properties. thc approach to equilibrium lieconies V P Y slou-. ~ I t is bc~lieved.t h a t the draining takcs place enriiely by viscous flon-. I t that the ultimate equilibrium holdup n-ill he about 0,:l t o 0 pound of solution per pound The saturation distriliutio fialre samples taken from t,he 115- disassembling the column shon-ed a nide variation i n saturation from the top to the bottom of the column. dlthough tho saturation gradient is part,ially due t o the capillary clnd effect, the major reason for the large saturntioil gradient in high beds is the ~ l o vapproach to equilibrium. Sho1.t bcds have a initial draining rate by a higher ultimate holdup than because of the importance of the end eflcct. The choim of hcd height for niiniinum holdup depend. 011. the permeability of the bed and t,he length of draining time involved. CAPILLARY
NUMBER,
Acknowledgment
%Pa
Figure I O . Correlation of Holdup w i t h Capillary Number for &Foot Deep, Gravity-Drained Beds of Soybean Flakes
For values of the film thickness less than 0.01 inch the drainage rates become very small. It is believed, therefore, that, the observed saturation gradients are primarily clue to the Ion. rates a t IThich equilibrium is approached. Calculations of the end eff wt based on t,he Doinbrowski correlation (S),n-hile not espect,ed to give quantihtive results for the beds studied because of the range of particle sizesand unusual shapes involved, indicated that the end-effect region would comprise only the bottom 3 to 5 inches of the bed. Good agreement wa9 found with the short bed shown in Figure 3, but the end effect in the higher beds was considerably greater than n-ould be expected on the basis of the capillary end effect alone. Conclusions
The effect, of variations of average diamet,er, flake thickness, and bulk density on the holdup of hexane in soybean flake liecis has been determined for three samples of soybean flakes with a range of properties covering the commercial limits. Changes in holdup due to changes in these variables vary inversely with the resultant permeability changes.
1224
The SOT bean flake samplcs u d in this work \yere supplictl h y the Central Soya Co., Decntur, Ind. Nomenclature = gc = GI = IC = g
L P
So
t u
= = = =
p
= = = =
7
=
2
acceleration due t o gravity, Er./sq. see. conversion factor, 32.17 (11~.niaFs,(i't.) I(1b. forcc)(sq. flooding mass -velocity. (lb.)/(sq. ft.)(eec.) permeability, cu. ft./sq. sec. bed height, ft. pressure, (lb. force)/sq. it. fractional residual saturation film thickness, f t . velocit,)-, ft./sec. coordinate direction, ft. viscosit,y, Ib./(ft.)(sec.) density, lb./cu. it. surface tension, (Ib. force)/ft. Literature Cited
(1) Brox-iiell, L. E.. and Kate. D. L., C'hcm. E r r g . Prog,.., 43, 601
(1947). ( 2 ) Cornell, D.. and I i a t z , D. L., Ixun. ENG.CHEW.43, 992 (1951).
(3) DombroTTski. H. S., Ph.D. thesis, Vniversity of Michigan, 1952. (4) "I-Iandbook of Chornistry," ( N . A. Lango, editor), 8th ed., p. 1690, Gandusky, Ohio, Handbook Publishers, Inc., 1952. (,5) N a p n e . F. D., and Skrtu, E. L., Ixn. EXG,CHE?rf.. 37, 1097 (1945). RECEII'ED for review November 23, 19.53.
INDUSTRIAL AND ENGINEERING CHEMISTRY
AccCPi'7:u l p r i l 8 , 105-4.
Vol. 46, No. 6
