COEFFICIENT OF KINETIC FRICTION FOR DOWEX 50 ION EXCHANGE RESIN MOVING DOWN A GLASS COLUMN.
Compacted Bed
N I E L H E R S H E Y , L'niuersity of Cincinnati, Cincinnati, Ohio F R E D N. P E E B L E S , C'niuersity of Tennessee, Knoxuille, Tenn. DA
For Dowex 50 ion exchange resin, coefficient of kinetic friction data were obtained from the movement of a compacted bed down a glass column through countercurrently flowing water. A variable-weight piston forced the resin down the column. Coefficient of friction values ranged from 0.01 1 to 0.048.
Iix
THE operation of continuous, countercurrent dense bed ion exchange columns, one of the major limitations is the low fluidization velocity of the ion exchange bed. To circumvent this draxvback, various designs have been evolved. One design \vas a dense bed continuous column developed by Stanton (70). \vho used a pair of rotating plug-type valves for transferring incremental quantities of resin from the bottom of the column to the top. Higgins and Roberts (3) developed a semicontinuous system with a rising resin bed propelled in slug flow by hydraulic impulses applied at the base of the resin bed. The designs of Hiester, Phillips, and Cohen (2), McIlhenny and McConnel ( 6 ) , Mihara and Terasaki (7): Selke and Muendel (81,McCormack and Howard (5),and Jury (4) had utility under some operating conditions. One of the factors tending to upset the dense bed slug flo\v of resin against a countercurrent liquid flow is the energy dissipated as friction a t the column wall-resin interface as the resin moves down the column. I n the investigation of column performance. it becomes essential to know the coefficient of friction for the resin moving past the retaining wall. An analysis of the dynamic frictional effects based on a force balance around a differential slug of dense bed resin allows the extraction of values of the coefficient of friction.
sented here, the hydraulic effect was negligibly small and the coefficient of friction values lvere not significantly affected. Therefore in considering what is the normal force, the surface area is assumed to be P DdL, where D is the column diameter. For the differential length of resin, the normal pressure acting against the wall - assumed to have its point of application at the center of the resin disk-is given by
If this element is thin enough, dPR dL dPL z X - - 2, - dL X -
dL 2
and
are negligible with respect to PR and P,. frictional force, dF', is expressed as dF' =
(P)
Therefore, the
+ PL)
( T O d L ) (PR
(2)
A force balance around the disk yields Derivation of Force Balance Equation
Consider a n elemental disk of resin of thickness dL, moving down the column, as in Figure 1. The resin pressure above and belov this disk of resin is (PR dPR) and PR, respectively. (Resin pressure is the force per unit cross-sectional area exerted on the resin because of the weight of the resin or through the transmission of a n external force by the resin.) Similarly. the liquid piessure above and below is represented bv (P, dP,) and P,. The resin movement down the column is opposed by a frictional force. F'. where F' = pAl' = coefficient of kinetic friction multiplied b\ the normal force acting against the wall. It \+as assumed that the resin particles were capable of deformation and. at the wall, the resin-wall "point" of contact Mas some finite area. If now this compacted and deformed slug of resin is forced to slide over a resisting surface. it will be assumed that there is no intervening liquid film between the resin and this resisting surface - the liquid has been effectively squeezed out. Thus not only the resin pressure but also the hydraulic pressure could be transmitted to the wall. I n some nonpressurized SL stems it is desirable to assume a n intervening liquid film and, in these cases, elementary hydraulic analysis leads to the conclusion that the system behavior should be independent of the hydraulic pressure. For the results pre-
+
+
P, + dP,
P,
+ dP,
-L + d L F'
t
1 L
-L
-L', PR , P; Figure 1. Force balance around a differential slug of resin moving countercurrent to a liquid flow VOL. 3
NO.
1
JANUARY 1964
1
v
Liquid n - . -n7 ,
m
I;
I
I
1
I
0.060.05
0.03 0.02
Resin Dowex-50
0.01
(840-1100
microntl
.e*
0
0
.
1000
2000
3000 Flow
Figure 2. friction
Equipment for measuring coefficient of kinetic
Figure 3.
Role,
4000
5000
6000
73:3
cc/rin
Coefficient of kinetic friction vs. flow rate
dPL. channeling, ~is constant for a given flow rate and dL
meq. per gram of dr)- resin and the density \vas 1.3177 grams per cc., in the hydrogen form and wet ( 7 ) . Xinety-five per cent of the resin was in the 840- to 1100-micron range (wet analysis). The remainder of the resin was fine particles less than 840 microns in diameter. The liquid was ordinary city water.
Xvhere PL'refers to the liquid pressure a t a point, L = L'. L is greater than L'. Since pm and p are also assumed constant. Equation 4 is a linear differential equation of the form
Results
If the resin bed is assumed to be uniformly packed with no
with C constant. The solution of Equation 6 with the boundary conditions (PR:L) and (P, , L') is
PR
=
-[L
- L ' ) dP 2+ dL
Equation friction.
7
(4':) ( p m c- +)
x
sc
\vas used to Calculate the coefficient of kinetic
Experimental Apparatus
The apparatus was set up as illustrated in Figure 2. ;Z 4-inch glass column 30 inches high had provisions for a liquid feed stream to enter 10 inches above the bottom, then leave the column through a n outlet located near the top of the column. A reinforced wire mesh piston was attached to a metal rod which extended outside the column. Weights were added to the rod to provide the load on the resin bed. The liquid feed rate was set above the fluidization velocity, causing a demarcation in the bed, with the bulk of the bed above the feed inlet rising as a slug of dense bed resin. The slug ceased to rise at a point where all the vertical component forces were balanced. The wire mesh piston was lowered onto the top of this slug and weights were added until the force exerted was sufficient to overcome the frictional force maintaining the force balance at the set liquid feed rate. The piston load was then decreased gradually until the minimum load was determined \\;hich maintained the slug in downward motion. For the pressure drop data, the dense bed was loaded sufficiently to ensure that there would be no fluidization of the bed as the liquid feed rates were raised above the fluidization velocity. Manometers were used to determine pressure drop. Thus with the values for the resin pressure at various flow rates and with the pressure drop, hydraulic head, diameter of the column, and average density of the resin known, it was possible to calculate the coefficient of kinetic friction from the derived equation. The ion exchange resin was Dowex 50 W (8% cross-linkages) supplied by the Dow Chemical Co. and screened by the Illinois Water Treating Co. Maximum exchange capacity was 3.93 2
l & E C PROCESS D E S I G N A N D D E V E L O P M E N T
Tl'ith water floxv rates varied from 1010 to 6480 ml. per minute in the 4-inch glass column, the piston load was found to vary from 3.10 to I'.O pounds for a slug length of 5.1 inches and at a constant liquid head of 1.45 p.s.i. at the top of the resin slug. The minimum flow required to maintain the slup. of resin was determined to be about 900 ml. per minute. Figure 3 sh0n.s the variation of the coefficient of kinetic friction \vith floiv rate. Discussion. The coefficient of kinetic friction by the piston loading method rose from 0.011 a t 1000 to 0.048 at 5500 ml. per minute, and remained constant thereafter. Since, by definition, p = F' .V. a change in fi is indicarive of a change in the F"-V ratio. Above 5500 ml. per minute. \\;here p ivas constant! an increase in the piston load on the resin did not affect the F','AV ratio. It was deduced that apparently the slug of resin \vas capable of being compressed, but that abo\Te i500 ml. per minute. the slug was compressed to its limit and \vas essentially incompressible. The effect of the increased resin load was not reflected in the normal force. Compared to the value of 0.048 for the coefficient of kinetic friction for the resin-glass wall interface for a compacted bed. Jury (4)reported a n estimated value of 0.06 for the dry DoM-es 50: 20-mesh system. For a slug flow of dry polymer particles past a smooth wall. Spencer, Gilmore. and Wiley ( 9 ) reported a value of 0.08 for the coefficient of static friction if lubricatins oil was added to the walls. Toor and Eagleton ( 7 7 ) reported no difference in the static and kinetic coefixients of friction for the dry polymer particles. It'ith the tube Tvalls heavily lubricated before making a run: they found the coefficient of friction to be equal to 0.047. and, for a dry bed of particles moving past an unlubricated wall, approximately equal to 0.2 to 0.3. Nomenclature
D
= column diameter, it.
F'
=
j
= local acceleration due to gravity, ft./sec.* = proportionality constant in Neivton's second
friction force, lb., lb., ft. /sec. 1b.l
law-,
L L’
= length of resin column, ft.
h’
= normal force, Ib., = resin pressure, Ib. flsq. ft. = liquid pressure, Ib. f/sq. ft.
PR PL
= generalized distance above reference line, ft.
EL= total
pressure differential betbveen two elevations in column, lb. ,/cu. ft.
dL
=
mean density of resin bed. Ib.
cu. ft.
= coefficient of friction = subscript denoting force
p f
literature Cited
(1) Drake, G. M., “Experimental Study of the Performance Characteristics of a Continuous Countercurrent Ion Exchange Column,” M. S. thesis, LJniversityof Tennessee, 1957. ( 2 ) Hiester, N. K . , Phillips, R. C., Cohen, R. K., Chem. Eng. Progr. Symp. Set.. 50, No. 14, 51-72 (1954).
(3) Higgins, I. R., Roberts, T. J., Ibzd., p. 87. (4) Jury, S. H., “Theory and Some Applications of the Hydraulic Ram as Applied to Countercurrent Ion Exchange,” U. S. At. Energy Comm. ORNL CF-56-6-74 (1956). (5) McCormack, R. H., Howard, J. F., Chem. Eng. Progr. 49, 401 (19 53). (6) McIlhenny, \V. F., McConnel, V. O., U. S. Patent 2,617,714 (1954). (7) Mihara, S., Terasaki, Y . , Japan Patent 2223 (1951). (8) Selke, W. A., Muendel, C. H., “Continuous Ion Exchange with a Cotton Belt,” U. S. At. Energy Comm., Doc. NYO-962 (1953). (9) Spencer, R. S..Gilmore, G. B., Wiley, R. M., J . Appl. Phys. 21. 527 11950). (IOj’Stantbn, L. S., “Continuous Separation by Ion Exchange,” M. S. thesis, University of Washington, 1950. (11) Toor. H. L., Eagleton, S. D., Ind. Eng. Chem. 48, 1825 (1956). RECEIVED for rr\iew November 23, 1962 ACCEPTED July 31, 1963
COEFFICIENT OF KINETIC FRICTION FOR DOWEX 50 ION EXCHANGE RESIN MOVING DOWN A G LASS CO LU M N.
Noncompacted Bed
, PEEB LES,
DA N I EL H E RS H EY
FR ED N
.
University of Cincinnati, Cincinnati, Ohio Cniversity of
Tennesser, Knour~ilie, Tenti.
For Dowex 50 ion exchange resin, coefficient of kinetic friction values were obtained from measurements of the drag force on a thin-walled smooth metal cylinder supported from a spring scale. The noncompacted b e d of resin moved downward, past the cylinder, and was subjected to a countercurrent water feed stream. The coefficient values ranged from 0.0026 a t fluidization to 0.0068.
has been derived and experiments have been ( 7 ) whereby it is possible to obtain values for the coefficient of kinetic friction for the Dowex-glass interface. The resin was in a noncompacted, dense bed condition and moved do\vn past an up\\-ard-floiving water stream. I n the investigation reported here: coefficient of kinetic friction values \vere obtained from measurements of the drag force o n a thin-walled smooth metal cylinder supported from a spring scale. The noncompacted bed of resin moved doivnward, past the cylinder, and \vas subjected to a countercurrent Lvater feed stream.
u
EQUATION
A-conducted
hydrostatic head could be maintained. Spring scale readings were taken with (1) no resin flow (static conditions) and (2) resin flow \vith a “balanced” column. A balanced column was attained when the U-tube manometer across the isolation zone indicated the same differential pressure as in the no-flou static condition. When balanced. there was no flow through Air
spring
Chamber
Scole
i t
L i q u i d Outlet
10
I+’’ Glass
Description of Experiment
I
Pipe,
The system consisted of a 4-inch glass column 4 feet high ivith a 1-foot section of column added on top to house the spring scale. T h e section housing the spring scale was kept dry bv being filled lvith air during operation. Suspended from the spring scale into the resin bed was a thin-walled smooth metal tube. Water was available for flow through the jet lift a t the bottom of the column, conveying resin from the bottom of the column to the top. This water and the liquid feed rising through the bed left through the liquid outlet. The liquid outlet \vas located above the column so that a constant
-1
S t a i n l e s s Steel Tube
The equipment shown schematically in Figure 1 was used in determining the variation of the coefficient of kinetic friction from the unpacked, normal dense bed condition to the ‘.loose” condition of the bed near fluidization.
3” 2;”
0.0. 1.0.
6” L e n g t h
~
L i q u i d Feed
&
Water Jet
Figure 1. friction
~
lift
U
Equipment for measuring coefficient of kinetic
VOL. 3
NO. 1
JANUARY 1 9 6 4
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