Clogging of Filter Media

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plugging) of the filter medium. Clogging of filter media is a particularly severe problem in the paper industry, where the expense of time and material in changing ...
estimate will give the maximum discrepancy between the two cases for inputs of very low frequency. A proper formulation of the design problem should include a description of the disturbances and the control system should be designed simultaneously with the process equipment. This leads to a problem in variational calculus, which can be attacked using the methods described by Horn (3, 4) for periodic processes. Nomenclature

A! A ,

reactor composition and feed composition, respectively, lb. mole/cu. ft. a = dimensionless amplitude of feed composition disturbance b = dimensionless amplitude of flow rate disturbance Cr, Cv,C, = total cost, cost of reactor volume, and raw material cost, respectively G = production rate, lb. mole/hr. k = reaction rate constant, (cu. ft.)/(lb. mole)(hr.) ml,m2,m3,m4,r n j = constants defined by Equation 51 = see Equation 5 Q = flow rate, cu. ft./hr. q r = reaction rate, lb. mole/(cu. ft.)(hr.) T = period of operation t = time, hr. V = see Equation 5 = reactor volume, cu. ft. VR x> XI = dimensionless reactor composition and feed Composition, respectively Y = deviation from dimensionless steady-state reactor composition =

.YO, YI,

y~

= components of y, see Equation 27

GREEKLETTERS see Equation 25 phase angle between feed composition and flow rate disturbances small parameter, see Equations 26 and 27 dimensionless time, see Equation 23 frequencies of feed composition and flow rate disturbances, respectively, radians/hr. w, Wlr w2 = dimensionless frequencies of disturbances, see Equations 23 and 38 SUBSCRIPTS av - average - steady state S literature Cited

(1) Blum, E. W., il.Z.Ch.E. J . 11, 532 (1965). (2) Douglas, J. M., Rippin, D. W. T., Chem. Eng. Sci. 21, 305 (1966). ( 3 ) Horn, F., 56th National Meeting, A.I.Ch.E., San Francisco, Calif., Mav 1965. ( 4 ) Horn, F., Division of Industrial and Engineering Chemistry, 151st Meeting, ACS, Pittsburgh, Pa., March 1966. ( 5 ) Levenspiel, O., “Chemical Reaction Engineering,” Chap. 6, Wiley, New York, 1962. (6) Minorsky, N., “Nonlinear Oscillations,” Chap. 9, Van Nostrand, New York, 1962.

RECEIVED for review May 2, 1966 ACCEPTED November 9, 1966 Presented in part at Division of Industrial and Engineering Chemistry, 151st Meeting, ACS, Pittsburgh, Pa., March 1966.

END OF SYMPOSIUM

CLOGGING OF FILTER MEDIA EPHRAIM KEHAT, ARIEH L I N , AND ABRAHAM KAPLAN Department of Chemical Engineering, Technion-Zsrael Institute of Technology, Haifa, Israel

A simple relationship was derived for the effective resistance of a partly clogged filter medium and the resistance of the filter medium a t the beginning of a filtration cycle. This relationship holds for both complete blocking and standard blocking mechanisms and was verified b y experimental work. Five woven wool filter cloths were tested a t constant low pressures, 1 1.2 to 61.2 cm. of water, and feed concentrations of 2 to 10 grams per liter of ground polystyrene in water. The effective resistance of open filter cloths increased to a relatively low constant value. The effective resistance of tight filter cloths was independent o f pressure and feed concentration, for the range of variables in this work, and increased from cycle to cycle. A simple correction to the classical filtration theory that includes the effect of clogging of filter media i s suggested. HE object of this work was to develop a correction to the Tbasic filtration equations far the increase of the resistance of the filter medium because of clogging (also called blinding or plugging) of the filter medium. Clogging of filter media is a particularly severe problem in the paper industry, where the expense of time and material in changing a clogged “felt” in a paper machine is considerable. Hermans and Bredte (4)were the first to study this problem. They suggested two possible mechanisms for clogging of filter media : complete blocking, in which single particles, some\chat larger than the holes in the filter medium, plug u p individual holes; and standard blocking, also called semiblocking ( 7 , 6) or depth filtration (5),in which particles, smaller than the holes, are attached to the fibers along or within holes, or to other particles previously retained. They showed that for

48

I & E C PROCESS D E S I G N A N D D E V E L O P M E N T

constant pressure filtration, the inverse of the flow rate of the filtrate was proportional to the volume of the filtrate raised by an exponent. The exponent for complete blocking was 2, for standard blocking was 1.5, and for cake filtration was 1. They used the values of these exponents to determine the mechanism of clogging of filter media and suggested that standard blocking is more likely to dominate than complete blocking for most media. Heertjes and Haas (3) derived a rate equation for complete blocking and experimentally found that the exponent in the Hermans and Bredte equations can have any value between 2 and l-i.e., between complete blocking and cake filtrationand is a function of the concentration of the suspension. Grace (2) studied the increase of the resistance of a variety of types of filter media for very low concentrations of solids

in the feed (0.18 gram per liter). His results showed that standard blocking could account for the clogging of the filter media in his work. T h e flow through a filter medium can be interyarn and intrayarn for multifilament yarns generally used for filter media. Smith (8) found that for close-woven fabrics with low twist yarns 95 to 98% of the filtrate passed through the yarn strands, with only 2 to 5y0of the filtrate passing through the apertures betLveen the yarn.. For high twist yarns these proportions were reversed and most of the filtrate passed through the apertures. Since the filter medium incorporates both small and large holes and tbe filtered suspension may be composed of a wide range of particle sizes, mechanisms of both complete blocking and standard blocking probably take place simultaneously. I t is likely that the mechanism of complete blocking dominates the clogging of the small passages between filaments, while the mechanism of standard blocking dominates the clogging of the large passages between the yarns. T h e porosity and the twist of the yarns and the size distribution of the solid particles undergoing filtration probably determine what fraction of the filter medium is clogged by complete blocking and what fraction is clogged by standard blocking. T h e exact mechanism of clogging is more complicated, be, cause in the first cycles before many passages are clogged, bleeding of particles through large and small holes takes place. Concurrent with the clogging of the passages in the filter medium, bridging of particles on the surface of the filter medium takes place. Most of the filtered particles are used for bridging and only a small fraction of the particles is used for clogging. When bridging is completed, no more clogging occurs and cake filtration begins. The theoretical part of this paper shows that a similar relationship can be obtained by both mechanisms, complete blocking and standard blocking, between the effective resistance after clogging takes place and the resistance a t the beginning of the filtration cycle. T h e experimental work substantiates this relationship and shows that both mechanisms can take place simultaneously. Experimental

Figure 1 is a schematic drawing of the experimental equipment. T h e test filter was a short section of Plexiglas piping, 8.9 cm. in external diameter, held vertically. T h e tested filter cloth was supported on a n 8-mesh screen between two Plexiglas flanges, a t the bottorn of the piping section. T h e filtering cross section was circular, with an effective filtering area of 62.2 f 0.7 sq. cm. T h e feed tank capacity was 300 liters and two mixers were used to keep the suspension uniform. T h e piping diameter was 1 inch and the valves were 1-inch diaphragm valves. T h e recirculation system ensured that even a t low feed rates, the velocity in the main line was high enough to prevent settling of particles in the line. T h e head of the suspension above the filter was controlled manually, within zk0.5 cm., by means of a diaphragm valve in the feed line and was kept within +0.5 cm. even a t the beginning of a filtration cycle. T h e feed was a suspension of ground polystyrene ( p . = 1.02 grams per cc.) in water. T h e small difference of densities between solids and fluid helped to keep the suspension uniform. T h e pressure of the suspension on the filter was equal, in the concentration range of this work, to the pressure of water a t the same head. The filter cake was not compressible in the pressure range of this work. New pieces of filter cloth were used for each series of filtration cycles. T h e new piece of filter cloth was soaked in water for a week and was installed wet in the filter. I t was kept under water in the filt.er before the start of each run, to minimize the possibility of interference of air bubbles within the filter cloth.

filter cloth

4

Figure 1 .

Schematic drawing of experimental equipment

T h e resistance of the filter cloth a t the beginning of a cycle was determined by measuring the rate of flow of water through the filter cloth under the same head as in the series of filtration tests, using a graduate and a stop watch. T h e feed suspension was then introduced under the same head for 5 to 10 minutes, and the filtrate volume as a function of time was measured by means of a graduate and a watch. T h e accuracy of the flow measurements is estimated as flyo for low flow rates and f3y0for high flow rates. T h e flange assembly was dismantled a t the end of the filtration cycle and the filter cloth was inverted. Most of the cake fell off and was collected. T h e filter cloth was then soaked in quiescent water for about 5 minutes. Most of the residual cake generally fell off. T h e cake was dried and weighed. T h e concentration of the feed was calculated, after suitable correction for the material in the head of suspension a t the end of the run was made. After a few cycles the cake was returned to the feed tank and a n equivalent amount of water was added. This caused occasional fluctuations in the feed concentration, but this effect was negligible. T h e filter cloth was then replaced in the flange assembly, and the next cycle was started, by measuring the rate of flow of water through the filter cloth. Four to 10 consecutive cycles were made for each filter cloth. T h e values of K for duplicate series of cycles, for two samples of the same filter cloth, under the same operating conditions, varied between 2 and 8%. Range of Variables. T h e five filter cloths tested were obtained from the American-Israeli Paper Mills, Ltd., Hadera, Israel. They were types commonly used as the “felt” in paper machines. They were all woven from wool, with sateen weave, and weights of 27.5 to 28.5 ounces per sq. yard. Other pertinent data for the cloths are given in Table I. Three wide and three narrow particle size distributions of the ground polystyrene were used (Table 11). T h e concentration range of the suspension was 2 to 10 grams per liter. T h e range of head of water was 11.2 to 61.2 cm. of water. T h e odd numbers resulted from the use of round values of the head above the flange. Subsequent to finding that the results are independent of pressure in this range, a head of 21.2 cm. of water was used. T h e use of low pressures in this work resulted in relatively long times for clogging, which enhanced the accuracy of the data. VOL. 6

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49

Table I. Characteristics of Filter Cloths Tested Thickness,

No. 1 2 3 4 5

Cm.

Class&ation

Open Open Intermediate Tight Tight

Count

0.75 0.35 0.50 0.20 0.18

18 23 18 23 23

Ply

X 18 1 X X 23 1 X X 18 2 X X 19 1 X X 23 1 X

1 1 2 2 2

Twist

Nap

Low Low

High High Hinh Low

High Hiih High

Low

~~

Table II.

Screen Mesh 18 25 35 45

60 80 100 120 140 170 200 230

Particle Size Distributions of Ground Polystyrene Opening,

M ~ ,

1 0.707 0.500 0.354 0.250 0 177 0.149 0.125 0.105 0.088 0.074 0.063

Particle Size Distribution A B c Cumu latiue Fraction Passing through Screen 100 97.5 87.1 68.4 45.7 36.3 16.9 8.0 4.0

100 99.6 85.7 59.6 42.2 39.1 20.4

Two types of experimental curves were obtained (Figure 2). The upper curve of Figure 2 is typical for runs where no bleed of particles through the filter cloth took place. The rate of flow decreased while clogging occurred. After V I liters of filtrate had passed through the filter, cake filtration began. The rate of flow continued to decrease, but a t a lower rate. T h e lower curve of Figure 2 is typical for the runs where bleeding of particles through the filter cloth took place. In these cases the flow rate decrease was slower during the clogging, bridging, and bleeding stage than during the subsequent cake filtration stage, since V I in this case was much larger than in the upper curve because of the extra filtrate volume that came through with the bleed. In practice rl6100 and r0/6100 were used instead of r and yo, since

100 99.2 83.0 53.8 10.9 0.4 r Ah t ' 6100 -= 1 (F)

D. -20 +25 mesh, 0.707-0.845 mm. E. F.

(5)

-35 +40 mesh, 0.4204.500 mm. -70 +80 mesh, 0.177-0.210 mm.

6100

p

Results

Effective Resistance. The effective resistance of the filter medium, r, was determined by extrapolation of the inverse filtrate flow rate as a function of the filtrate volume, during the cake filtration stage, to zero filtrate volume (Figure 2). In all cases a straight line was obtained on these plots for cake filtration, as expected from the classical filtration theory (7) :

At the beginning of the cycle, clogging of the filter cloth and bridging of cake over the filter cloth take place. After bridging is completed, no further clogging takes place and cake filtration begins. The effective resistance is defined as the resistance of the clogged filter cloth for the cake filtration stage. Extrapolation to V = 0 gives ( t / V )' and

Figure 3, for filter cloth 4 and particle size distribution A , shows that for this type of cloth and in the range of pressure and concentration of this work, pressure or concentration has no effect on the effective resistance. Figure 4 shows the effect of wide feed particle size distribution on the effective resistance of filter cloths 3, 4, and 5 . T h e data for filter cloth 4 and size distribution A incorporate all the data from Figure 3. Each of the other curves represents one series of successive cycles under a head of 21.2 cm. of water. Figure 5 shows the effect of particle size, for narrow particle size distributions, on the effective resistance of filter cloths 3 and 4, under a head of 21.2 cm. of water. T h e relationship between the effective resistance and the resistance a t the beginning of a filtration cycle is derived

where k is a constant for a series of filtration cycles, made a t the same temperature and with the same head. Extrapolation to Y = 0, in order to obtain r, implies that all the clogging occurs in a very short time, relative to the time that cake filtration takes place. Since the amount of particles used for clogging is only a small fraction of the particles used for bridging, this is a n acceptable assumption. T h e resistance of the filter medium a t the beginning of the cycle, T O , was determined from the water flow rate data, (Vlt),,,without filtration:

F

I

I

I

I

e

I

I

I

1

filter cloth no.4 without bleed

c

:100 0

P

80L

LC

0

2 40 (3) since r and ro were determined under the same head. If washing of the filter medium removes all the cake and none of the clogging particles, ro should be equal to the effective resistance of the previous cycle. Values of ro a t the start of subsequent filtration cycles were, in most cases, within 15% of the values of r for the previous cycle. 50

I & E C PROCESS D E S I G N A N D DEVELOPMENT

filter cloth no, I with bleed

:

I

0 Figure 2. bleed

I

1

I

I

I

2.0 2.5 3.0 3.5 V - total volume of filtrate liters Samples of original data with and without 0.5

1.0

1.5

-

-

0 7

r0/6100 400 800 1200 1600 2000

1

I

I

I

I

T h e probability that a particle clogs a hole, p, is proportional to the concentration of holes in the surface (No):

I

p=aN,

(7)

Taking into account the bleed, the number of holes that will be plugged a t any moment is: ._ L

A-612

2000 0

2

160C

?!

120c

filter cloth no 4 size distribution A

5

80C

head 21.2 cm. water conc. V -2+2.7g/l.

.4-

0)

From

N/N, = 1

-

c’(v - Vb)a

dV - --

u)

2

dt C

400 800 1200 1600 2000 2400 2800 3200 - res,istonce at the beginning of o cycle (crn?)

r0/6100

Figure 3. Effect of cwessure and concentration on effective resistance of filter clotlh 4

below for the mechanisms of complete and standard blocking. Complete Blocking Model. It is assumed that the apertures in the filter medium are cylindrical holes, that part of the particles are in a size range that will block individual holes by single particles, and that probability of a particle clogging a hole is proportional to the total surface of the filter medium and not to the number of empty holes. The last assumption is partly justified because clogging and bridging occur simultaneously and the fraction of holes clogged during one cycle is small.

(9)

mA

The flow through the filter medium is related to the number of empty holes by the Hagen-Poiseuille equation (8):

/

40C

- V&a

The rest of the particles will be used up in bridging. Equation 8 :

m

0)

.-c

C’(V

(8)

=

0

+ ln ._ ln

P=

No



L

- V,)

C’(V

A(N0 - A’)

iz

A A P g , RO4 N

(10)

8PL

Neglecting the resistance of the cake at this stage, and since all the other terms in Equation 10 do not vary during a run:

”/ (z) dt

0

=

N/No

and from Equation 9

[l -

dv =

o)!!(

dt

1

c’(v- Vb)a mA

(12)

The boundary condition for this differential equation is the transition to cake filtration at time t l and volume of filtrate VI (Figure 2). At time 11 the surface of the filter is bridged completely and no more clogging takes place. At this time the number of particles on the filter is:

r0/6100

A o

x

r0/6100

-

size distribution A size distribution B size distribution C

resistance at the beginning

of a cycle (cm:l)

Figure 4. Effect of wide Particle size distributions on effective resistance of filter cloths 3,41, and 5 VOL. 6

NO. 1

JANUARY 1 9 6 7

51

I

-

350

'E

-.-5 300 V

.

50

100

150

I

I

I

L

250

size distribution

A

size distribution E 0.425+0.08mm.

m

size distribution F 0.194 2 0.017 rnm.

Filter cloth no.3

.E

300

D 0.78+0.18rnrn.

o

d

/

m

E"

250

200

2

/

7

'c 'c

O

3000

2000

200

0 V

K

O c

.% 2

15C

no.4

0) .->

c

g 100

1000

'c

0)

0

g

5c

5

0

0

I

I

1000

2000

I

0

30C

r0/6100 resistance at the beginning of a cycle (cm:') Effect of narrow particle size distributions on effective resistance of filter cloths 3

Figure 5. and 4

b is a geometrical proportionality factor, related to the shape of particles and filter surface and to the size distributions of holes and particles, and is assumed to be constant for each series of filtration cycles. Integrating Equation 12 between V = 0 and V = VI and introducing the value of ( V I - V,) from Equation 13 and the definition :

or

where

K

=

1 -In

B

1

-

(20)

1-B

result in :

Vl

1 - - (1 In - l)]

-In -

B

1-B

Vi B

1-B

(15)

-

Since 1/B In 1/(1 B)is always larger than unity, the effect of the bleed, the term with vb, is to reduce the inverse flow rate at the transition point to cake filtration, as was shown experimentally in Figure 2. The ratio of C' to C is independent of the concentration. Equation 14 shows that B should be independent of pressure and concentration. B is always smaller than unity. Since the rate of flow of water through the filter cloth is constant, when no filtration takes place: =

O)$(

!-Lac v*

' +

2 A2 A P g ,

Combining Equations 2, 3, 15, and 17: 52

K a s a Function of 6

B K

0 1

0.2 1.12

0.4 1.29

0.5 1.39

0.6 1.53

0.7 1.72

0.8 2.02

(;)O

From Equations 1 and 2 and since tl/VI, VI is also a point on the cake filtration line,

Vl

and ro reduce the effective resistance, as they represent particles that were used for bleeding and bridging, and not used in clogging holes. When K = 1, rb = 0 and the bleed should have no effect on the effective resistance. Comparison of Equations 2 and 22 shows that rc would generally be much smaller than r . rb

I&EC PROCESS DESIGN AND DEVELOPMENT

Standard Blocking Model. It is assumed that the apertures in the filter medium are cylindrical holes, that the particles are all much smaller than the holes, that small particles gradually build up annular restrictions within the holes, and that a constant fraction of the particles is used for clogging. The flow through the empty center of the holes follows the Hagen-Poiseuille equation (8) and the flow through the

annular sections follows the Kozeny-Carman equation (7), taking a value of 5 for the Kozeny constant. The combined flow rate is :

(23) T h e first term on the right side of Equation 23 for the first cycle is (dV/dt),. Since

V

- R,2 - R2

(24)

RO'

V1

by the assumption that a constant fraction of particles is used for clogging,

where

p = -8

€3

5 (1

- E)'

So2R,'

is proportional to t:he ratio of particle to hole cross-section areas. Integration of Equation 25 gives:

where

T h e integration of Equation 28 gives:

13

2

4 Gp - G2 F

1

I a s a Function of (3 p

0

I

m

0.2 3.1

0.5 1.8

0.7 1.40

1.0

1.2

1.2 1.08

1.3 1.03

1.37 1.00

Since (V/t)' is alwa.ys smaller than (V/t)" when no bleed occurs:

I> 1 Other practical limits are: 0 5 V / V , 5 1 for the clogging stage. T h e mathematical limits of p are: 0 5 13 5 4 from Equation 29. However, for I > 1, (3 < 1.37. I is a function of p only and hence only of particle properties and hole size. By introducing Equations 2 and 3 into Equation 27: Y

=

IYO

(30)

T h e accuracy of this derivation beyond the first cycle is only approximate. T h e practical values of are rather small and therefore the values of I should be much larger than the experimental values of the slopes of the lines of Y us. Yo. Since r b and r c are in general small relative to r , Equation 30 is similar to Equation I 9 for complete blocking.

T h e validity of the two theoretical Expressions 19 and 30, despite the many assumptions used in the derivations, is shown by the experimental results. Since clogging of the filaments within the yarns probably follows Equation 19 and clogging of the apertures between yarns probably follows Equation 30, the similar forms of the two expressions make possible the correlation of the results, irrespective of the actual mechanism. O p e n Filter Cloths. Filter cloths 1 and 2 were classified as open cloths. These two materials had a low total count (count X ply), low twist, and high nap. Examination of the experimental data for these cloths showed that bleeding of particles took place in the first two or three cycles and Y O was larger than r . In subsequent cycles the bleeding stopped with r = r o = constant, K = 1. There were slight variations which were due to the irreproducibility of cake removal. After the first two or three cycles no further clogging took place and the effective resistance stabilized, at about twice the initial resistance. A similar behavior was noted by Wrotnowski ( g ) , who ran a series of seven cycles each on four unwoven filter media, in a small plate and frame filter press. Between cycles, the cake was removed and the filter medium was flushed. For all the filter media he tested, the resistance of the recycled filtered cloth leveled a t approximately three times the initial value after the first few cycles. For his materials and the open filter cloths tested in this work, a t some particular pressure level, no further clogging occurs beyond the first few cycles. Unfortunately, this type of behavior is not the rule for filter media. I n this work these results were due to the presence of a high nap. At low pressures the particles did not go far into the nap and were easily washed out by soaking. Tight Filter Cloths and Wide Particle Size Distributions. Filter cloths 4 and 5 were defined as tight cloths, with a high total count, high twist, and low nap. Filter cloth 3 had intermediate properties between open and tight cloths, but its behavior was closer to that of tight cloths. For all the tests with these cloths, a straight line could be drawn through the experimental points, of the form: r = Kro

(31)

indicating that Y b and y C were negligible. The effective resistance continued to rise in each cycle and Y O for a subsequent cycle was close to r of the previous cycle. Visual and microscopic observations of these cloths showed that soaking removed most of the cake from the surface. For the range of concentration and the low pressure used in this work, no effects of pressure or concentration on the effective resistance were noted, as predicted by the independence of B, as defined by Equation 14, of pressure and concentration, for the same particle size distribution. The effect of the particle size distribution was more complicated and can be understood by the values of K and B, calculated from the slopes of the Y us. ro lines (Table 111). B, as defined in Equation 14, decreases with increasing average size of particles and increases with increase of the concentration of particles in the size range that will clog the holes. For filter cloths 3 and 4, B decreased for particle size distribution B compared with size distribution A . For cloth 4, no difference was noted in the value of B between particle size distributions B and C. For filter cloth 5 no difference was obtained in the value of B between particle size distributions A and B. Apparently, in the last two cases, the increased concentration of the size range that can clog these cloths compensated for the decreased average size from particle size distributions C to B and from A to B, respectively. VOL. 6

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53

Table 111.

Initial resistance of new cloth, r0/6100 crn.-l Particle size distribution A B

K B K B K B K B K B K B rbl6100

C

D E F

Experimental Values of 7

2

63.6

139 1 0

1 0

1

(32)

From Equation 31, when bleeding is negligible: r, = 54

Kr,'

I & E C PROCESS D E S I G N A N D D E V E L O P M E N T

Filter Cloth 3

(33)

5

4

129-195 1.5 0.59 1.1 0.17

344-786 1.6 0.65 1.2 0.30 1.2 0.30 1.125 0.21 1.20 0.313 1.57 0.63 170

1.14 0.22 1.18 0.27 1.26 0.37 22

Values of K in Table I11 are in the range expected from the theoretical derivations. The values of K were reduced from 1.5 to 1.6 for particle size distribution A to 1.1 to 1.5 for particle size distributions B and C. The limiting value of unity was not reached for tight cloths with the tested particle size distributions. The probable ratio of C'/C was low and the values of B were low. Values of K close to unity could be expected if only complete blocking took place. T h e contribution of the mechanism of standard blocking with low values of 6 and high values of I, resulted in the experimental values of r/ro in the range of 1.1 to 1.6, for these cloths. Both mechanisms of complete blocking and standard blocking probably took place simultaneously. Tight Filter Cloths and Narrow Size Distributions. Size distributions D and E were in the size range where only complete blocking can take place in filter cloths 3, 4, and 5. Microscopic observations of these cloths showed that the diameters of the few largest passages in these cloths were of the order of 0.2 to 0.3 mm. No significant difference was obtained between the values of K for these particle size distributions and filter cloths 3, 4, and 5. I n all these runs plots of r us. ro gave straight lines, starting from the origin, and low values of K and B that were expected if the mechanism of complete blocking dominated the clogging of the filter media. T h e smaller size range, size distribution F, was in the size range of the few largest passages in filter cloths 3 and 4 and bleeding occurred in all the filtration cycles with size distribution F. Therefore, positive values of r b , about 15% of the maximum value of r for filter cloth 3 and about 5% for filter cloth 4, were obtained. T h e values of K and B were larger than those obtained for size distributions D and E and were larger for filter cloth 4 than for filter cloth 3, indicating that possibly for filter cloth 3, and more likely for filter cloth 4, some of the clogging was due to the mechanism of standard blocking. Inclusion of Effect of Clogging in Classical Filtration Equations. Standard cake removal techniques remove the cake but have very little effect on the clogging particles. When the clogging particles are not removed and if n is the number of the cycle: r," = r, -

K and B

690-882 1.5 0.59 1.5 0.59

1.14 0.22

and therefore :

r, = Knrl

(34)

where r l is the resistance of the cloth a t the beginning of the first filtration cycle. Substituting rn for r in Equation 1 results in : (35)

K can be determined from the inverse flow rate-time curves for a number of cycles. Cleaning of Clogged Filter Media. SOAKING.Ideal soaking removes only the cake from the filter surface. In practice, however, soaking also removes some of the clogging particles. If is the soaking factor as defined by Equation 36, rnO = q

(36)

r,-1

Then

r, =

qn-l

K"

(37)

r1

7 is equal to unity when no clogging particles are removed and smaller than unity when some of the clogging particles are removed. The soaking factor was calculated for the data of filter cloth 4 and particle size distribution A.

Cycle Soaking factor

1

. . ,

2 0.89

3 0.88

4 0.86

5 0.83

Av. 0.86

COUNTERCURRENT WASHING. Countercurrent washing, between cycles, of filter cloths l and 4 and particle size distribution A, a t various pressures, completely removed the clogging particles and successive cycles were closely reproducible. Conclusions

For open filter cloths some bleeding occurs initially. However, after bridging is established, the effective resistance stabilizes a t a relatively low value, if the cake is completely removed between cycles. For tight filter cloths the effective resistance is independent of pressure and concentration for the concentration range and the low pressure range of this work. The rate of clogging is related to the concentration of the size fractions that takes part in the clogging by mechanisms of both complete blocking and standard blocking.

Countercurrent washing or drying and shaking completely removes the clogging particles. The substitution of l P r for the filter resistance, in the classical filtration equation. includes the effect of the clogging of filter media in the clacssical equations. This correction is independent of the mechanism of clogging. I t is probable that the correlation of the effective resistance is valid a t higher pressures. This postulate will be tested in the near future. Acknowledgment

The help of Y . Gad and M. Cohen in obtaining some of the experimental data is gratefully acknowledged. Nomenclature = constant in Equation 7 , sq. cm. = effective filtration area, sq. cm. A b = geometrical Igctor in Equation 13 = dimensionless parameter, defined by Equation 14 B = concentration of feed suspension, g./liter C = concentration of particles that can clog holes by C’ complete blocking, g./liter = gravitation conversion factor, 980 g. cm./g. force, sc sec.2 Ah = head of water on filter, cm. = integral function of p, defined by Equation 29 I k = constant in E;quations 2 and 3 = ratio of r / r o K = thickness of filter medium, cm. L = average mas:, of single particle, g . m n = number of cycles = number of unclogged holes per unit area of filter, A T cm.? = number of initial holes per unit area of filter, cm.-2 A’, = probability clf particle clogging hole pap = pressure differential across filter and cake, g. force/ sq. cm. 7 = effective resistance of filter cloth during cake filtration, cm.? ra = effective resistance of filter cloth a t beginning of filtration cycle, cm.?

reduction in 7, caused by bleeding, cm.-l reduction in 7, caused by bridging, cm.-’ resistance of filter cloth a t beginning of first filtrarl tion cycle, cm.? R = free radius of partly clogged hole, cm. = radius of hole, cm. R, = average radius of particle, cm. R, = number of layers of particles required for complete S bridging SO = specific surface of particles, sq. cm./cc. t = time from start of filtration cycle, sec. tl = time of beginning of cake filtration, sec. V = total volume of filtrate a t time t , liters VI = total volume of filtrate a t time tl liters V, = volume of filtrate equivalent to bleed, liters ( t / V ) O = inverse of flow rate a t beginning of cycle, sec./liter ( t / V ) ’ = extrapolation of inverse of flow rate for cake filtration. to zero filtrate volume, sec./liter = = =

fo

TC

U

GREEKLETTERS ff

=

p

=

E

cc

= = =

Ps

=

?1

specific resistance of cake, cm./g. dimensionless parameter, defined by Equation 26 porosity of cake within holes soaking factor, defined by Equation 36 viscosity of water a t the operating temperature, centipoise density of particles, g./cc.

literature Cited

(1) Dickey, G. D., “Filtration,” pp. 30, 32, Reinhold, New York, 1961. ( 2 ) Grace, H. P., A.2.Ch.E. J . 2, 307 (1956). (3) Heertjes, P. M., Haas, H.v.d., Rec. Trau. Chim. 68,361 (1949). (4) Hermans, P. H., BredCe, H. L., J . Soc. Chem. Ind. 55T, 1

,- ,--,.

(IC)?&)

( 5 ) Jahreis, C. A., Chem. Eng. 70 (23), 237 (1963). (6) Miller, S. A,, Chem. Eng. Progr. 47, 497 (1951). (7) Perry, J. H., ed., “Chemical Engineers’ Handbook,” 4th ed., McGraw-Hill, New York, 1963. ( 8 ) Smith, E. G., Chem. Eng. Progr. 47, 545 (1951). (9) Wrotnowski, A. C., Zbid., 53, 313 (1957). RECEIVED for review August 4, 1965 ACCEPTED July 28, 1966

ION EXCLUSION EQUILIBRIA IN THE SYSTEM SU CROSE-POTASSI U M CH LORID EWATER-DOWEX 5 0 W X 4 General Correlation of Ion Exclusion Data WALTER

MEYER,’

R I C H A R D S. OLSEN, AND S. L. KALWANI2

Chemical Engineering Department, Oregon State University, Coruallis, Ore.

Wheaton ancl Bauman (77) introduced the principle of ion exclusion, they examined the possible application of the process to sugar purification. However, early attempts failed because of mutual exclusion of both sucrose and salt (NaC1) from the ion exchange resin. T h e process was later re-examined by Asher (2) who, using chromatographic columns, noted the effect of liquid flow rate, resin particle size, feed volume, column temperature, and degree of resin crossHEN

1 Present address, Nuclear Engineering Department, Kansas State University, Manhattan, Kan. 2 Present address, Chemical Engineering Department, Washington State University, Pullman, Wash.

linkage on the separation of sugar and salt. With a suitable choice of these variables, a well defined chromatographic separation was achieved. O n the basis of Asher’s work plus continued work by the Sugar Beet Laboratory, Western Regional Laboratory, U. 3. Department of Agriculture (75), 50- to 100-mesh (U. S. screen size) Dowex 50W X4 (a cation exchange resin of moderate crosslinkage) was shown to produce satisfactory separations of salt and sucrose in fixed bed ion exclusion columns. I t has also been suggested (75) that KCl is the simple salt most representative of the salts present in commercial sugar beet VOL. 6

NO. 1

JANUARY 1 9 6 7

55