708
INDUSTRIAL AND ENGINEERING CHEMlSTRY
given furnish reasonably substantial evidence for the views of Depew and Ruby and of Green regarding the relation of flocculation to the reinforcing effect of carbon black in vulcanized rubber.
Acknowledgment The writers wish to thank the Firestone Tire & Rubber Company for kind permission to publish this work.
Literature Cited (1) Allen, R. P., IND.ENQ.CHEM.,Anal. Ed., 2, 311 (1930). (2) Busse, W . F., and Davies, J. M., paper presented before Div. of Rubber Chemistry at 86th Meeting of Am. Chem. SOC.. Chicago, Ill., Sept. 10 to 15, 1933.
VOL. 30, NO. 6
(3) Dannenberg, H., Kautschuk, 2, 276 (1926). (4) Depew, H. A., and Ruby, I. R., J. IND. ENQ.CHEM.,12, 1156 (1920). (5) Dillon, J. H., Physics, 4, 225-35 (1933). (6) Goodwin, N., and Park, C. R., IND. ENQ.CHEM.,20, 621 (1928). (7) Green, H., Chem. & Met. Eng., 28, 53 (1923). ( 8 ) Green, H., IND. ENQ.CHEM.,15, 122 (1923). (9) Grenguist, E. A., Ibid., 20, 1073 (1928); 21, 665 (1929). (10) Menadue, F. B., I n d i a Rubber J.,85, 689,717; 8 6 , 2 3 , 5 3 (1933). (11) Park, C. R., and Morris, V. N., IND. ENO.CHEM.,27,582 (1935). (12) Roninger, F. H., IND. ENQ.CHEM.,Anal. Ed., 5, 251 (1933). (13) Stamberger, P., “Colloid Chemistry of Rubber,” Oxford Univ. Press, 1929. RECEIVED April 2, 1938. Presented before the meeting of the Division of Rubber Chemistry of the American Chemioal Soeiety, Detroit. Mich., March 28 and 29, 1938.
FILTRATION Accuracy of Prediction of Plant Operation from Test Data E. L. McMILLEN AND H. A. WEBBER Iowa State College, Ames, Iowa
D
’
URING the past three years a rather comprehensive investigation of the accuracy with which large-scale filter operations may be predicted from test filtration data by means of the new Ruth filtration equations (8) has been carried out in the chemical engineering laboratories of Iowa State College. Predictions of larger scale operation secured previous to this time when utilizing the Lewis equations (14) were not satisfactory. Likewise, Irvin (6‘) in 1934 stated: “Mathematical theory can be employed only to a limited extent in explaining or predicting the results obtained”; Badger and McCabe (2) in 1931 stated that “in spite of much careful investigation, complete answers to these questions (amount of filtration to be expected in a definite time, rate, and efficiency of washings) cannot be given.” This situation was due to the variety of equations suggested by Lewis for different conditions, some of which neglected septum resistance, and to the various methods used for plotting test filtration data. The confusion which resulted is best illustrated by Badger and McCabe’s use (3) of the logarithmic plot intended for nonhomogeneous sludges for data secured upon a homogeneous sludge of chromium hydroxide (1). I n addition, the use of fractional exponents, three of which may occur in the same equation, renders the calculations needlessly difficult by means of the Lewis equations. The Ruth constant-pressure filtration equation (9) is similar to that proposed by Sperry (IS)in 1916, but a more tangible meaning has been given to the constants employed than was the case in the Sperry equation. A single parabolic equation is applicable to constant-pressure filtration of any type of sludge (homogeneous or nonhomogeneous, compressible or noncompressible) :
- (v+ cp = K (e + e,)
(1)
The differential form of Equation 1, when plotted as inverted rate of flow, dO/dV, against quantity of filtrate, V , yields a
means of evaluating the two constants, K and C, since it is a straight line of slope 2 / K and negative intercept upon the V axis of C:
The slope, 2 / K , is a measure of filter cake resistance; intercept C is a measure of filter cloth resistance during the filtration under the conditions that the cloth is used. Probably the chief contribution of Ruth to constant-pressure filtration is this new method of analyzing test filtration data to show its parabolic nature and readily yield constants representing cake and cloth resistance. Consequently it is not surprising to find that the authors of the recent (1937) edition of “Principles of Chemical Engineering” (16)have entirely discarded their earlier methods of plotting test fltration data in order to adopt a method essentially similar to Ruth’s inverted rate plot. The similarity between the newer Lewis plot and the Ruth plot is brought out in Figure 1 for the parabola, 1 1 2 = lo(e e,)
(v+
+
for the condition that P and A are unity. Provided time measurement and filtrate collection begin simultaneously, the plotting of this rearranged Lewis equation does yield a measure of both filter cake and cloth resistance, which was not accomplished by their earlier methods of plotting data. When filtrate collection is delayed until the filtrate outlet pipes become full, the Lewis plot is no longer a straight line as is shown in b, Figure 1, while the Ruth plot, d, remains a straight line; the latter is displaced parallel to itself sufficiently to make intercept C larger by the amount of filtrate necessary to fill outlet pipes. The newer Lewis equations retain the scouring coefficient, t, as applied to nonhomogeneous sludges, in spite of the admission (16) that “the available laboratory data on the filtration
JUNE, 1938
INDUSTRIAL AND ENGINEERING CHEMISTRY
709
of nonhomogeneous compressible sludges indicate that t is approximately zero and that equations (for homogeneous sludges) apply to this type of sludge as well as to homogeneous sludges." It is generally admitted that strictly noncompressible sludges are rarely, if ever, encountered in industrial filtration. Thus we have essential agreement that a single constant-pressure filtration equation is applicable to all types of sludges, and basically the Ruth, Lewis, and Sperry equations are similar. The apparent difference between the Ruth and Lewis equations lies in the fact that the Lewis equation includes the change in resistance of cake and cloth due to compression with increasing pressure as power functions of the pressure; Ruth prefers to treat variation of specific cake and cloth resistance in auxiliary equations. The chief defect of the Lewis exponential treatment is that it requires the cake resistance to approach zero as pressure of filtration is decreased to zero. Actually most semicompressible filter cakes do not behave this way, and the Ruth treat" ment is hence to be preferred. An additional advantage of 0 2 4v6 8 IO" the Ruth equation is that the parameter of the parabola, K , contains the necessary variables for relating volume of filtrate FIGURE1. COMPARISON OF RUTH'SMETHOD OF PLOTTING TEST FILTRATION DATA WITH to amount of filter cake formed when sludge concentration is THAT OF WALKER,LEWIS, MCADAMS,AND changed. Walker, Lewis, McAdams, and Gilliland's latest GILLILAND picture of pressure and stress distribution through a filter Walker Lewis, MoAdams, and Gilliland plots: ((I) V = cake (16) is similar to that first proposed by Bloomfield (6) 0 whed 0 = 0: ( b ) filtrate collection delayed at start of test in 1925 and later elaborated upon by Ruth, Montillon, and Ruth plots: ( q ) V = 0 when 0 = 0. (d) filtrate oolMontonna (11). The simplicity of calculations when using leotion delayed at start o! test the new Ruth equations should lead to their universal use by chemical engineers. secured upon a weight basis. A procedure was also adopted Although Ruth (12) utilized various automatic devices to for starting a constant-pressure test filtration in a,small platerecord filtrate volume, he concludes that the use of elaborate and-frame press which allows filtration, filtrate collection, measuring devices is unnecessary for results of accuracy exand time measurement to start simultaneouslv. This Droceceeding- engineering requirements. Using data secured from dure also illows fullAfiltraautomatic recording detion pressure to be secured vices, Ruth (12) plotted almost immediately and filtrate volume against eliminates several other time in order to secure, u n d e s i r a b l e factors (8) from the parabola obHeretofore, prediction of plant filter which affect the observatained, values of time a t operation from test filtration data has tion of the initial stages of equal intervals of filtrate not been considered entirely reliable. the filtration. This results volume. From these data I n the present investigation small-scale, in a more accurate detera second plot of inverted mination of constant C, rate against amount of constant-pressure, test filtration data since the first points obf i l t r a t e was m a d e a n d have been converted into constants repretained in the inverted rate constants K and C were senting filter cake and cloth resistances plot lie upon the straight evaluated. By obtaining by utilizing the new filtration equations line fixed by later points. our original data a t equal of Ruth. This knowledge of cake and Without this precaution it i n t e r v a l s of f i l t r a t e is usual for the first point volume, we are able to cloth resistances is used to predict capacior two to deviate somec o n s t r u c t t h e inverted ties of a variety of larger filters under what from the straight line rate plot a t once; in fact, various conditions of temperature, sludge and thus render its locawhen using intervals of 1, concentration, and pressure (or vacuum) tion uncertain. The true 2, 5, or 10 pounds of filof filtration. Actual results using these value of C is secured trate, not even slide rule directly without the necalculations are necessary. larger filters are found to parallel prediccessity of s u b t r a c t i n g Ruth (10) suggested that tions remarkably well in the majority of amount of filtrate passv o l u m e o r w e i g h t of cases. Observed capacities less than preages. Although approxieither filtrate or sludge dicted are usually the result of poor filter mately correct values of C may be used as a measure operating conditions, rather than of may be obtained in startof amount of cake formaing a test filtration in the tion and recommended as defective filtration theory or equations. usual way in a plate-andto hoF his equations may It is believed that the new filtration equaframe press, the new probe adapted to the particutions of Ruth are entirely reliable and cedure is more satisfactory. lar variable that is measfurnish a means of determining whether In this work the nomenured. Since weight of filplant filtration equipment is operating clature used by Ruth and trate is much more easily eo-workers (8, IO) has been measured b y ordinary at its maximum capacity. adhered to as nearly as equipment than volume, possible. The symbol, p, t h e p r e s e n t data were
INDUSTRIAL AND ENGINEERING CHEMISTRY
710
has been used for viscosity rather than %, in conformity with the usage in Perry’s handbook (7) where the former is used as symbol for viscosity in absolute English units. Working entirely in the English system as is done in other chemical engineering work, it is possible to show in the list of nomenclature the dimensions in which each quantity is expressed. I n test filtrations time is usually measured in seconds or minutes. It is desirable to express a, specific cake resistance, in hourly units and thus obtain values of reasonable magnitude. Hence the hour is used as the basic unit of time. Quantities involving time on a minute basis are primed (e’, etc.), and on a second basis, double-primed (k”,etc.) to distinguish them. Capital letters represent total quantities; small letters represent quantities per unit filter cloth area.
Constant-Pressure Filtration Equations The present investigation was confined to constant-pressure filtration of insoluble solid from solute-free water. Equations for this case only will be given. The following equations, which are all adaptations of those of Ruth (8, 10) to present needs, are valid when the particular quantity indicated is used as a measure of amount of filtration accomplished. Total volume of filtrate,
Volume of filtrate per unit filter cloth area, (3)
(4)
Total weight of filtrate,
Weight of filtrate per unit filter cloth area, (w,
+
kw =
+ eo)
W J ~ = k,(e ZPp(1 - ms)
VOL. 30, NO. 6
Equation 9, obtained by differentiation of Equation 7, was used as the basis for the inverted rate plot:
With d91dwf as ordinate and w, as abscissa, a slope of 2 / k , and negative intercept of w. upon the abscissa are obtained. From the slope of this plot specific cake resistance, CY, may be calculated from Equation 10:
The intercept, wc,a measure of cloth resistance in terms of pounds of filtrate per square foot to produce cake equal in resistance to the cloth, will vary in size as the proportion of solids in the sludge varies and also as the specific resistance of the solids varies. Change in filtration pressure may also produce change in cloth resistance. To determine whether cloth resistance is constant or varies with pressure, Equation 11 is useful in eliminating effect of variation in sludge concentration and cake resistance from wc: 7-1
=
woas 1 - ms
If the filter cloth is truly noncompressible, r1 will remain constant with increase in filtration pressure; i. e., with no change in sludge concentration, s, the product of intercept, wc,and specific cake resistance, a, will remain practically constant. Most cloths are nearly noncompressible (at least in the higher pressure range above 10 pounds per square inch), and variation of cloth resistance with age and condition of previous use are much greater than pressure effects. Dry filter cake density, 6, may be computed (8) from the following equation, provided sludge density, u, and filtrate density are known:
Direct washing will take place a t the same rate as final filtrate flow and can be computed by inverting Equation 9. Thorough washing taking place through twice the thickness of cake and one-half the area will be one-quarter as rapid, as shown in Equation 13:
-Ws
Since the test filtrations were carried out in two frames of a 6 X 6 inch plate-and-frame filter press, and the four cloths possessed a filtering area of 1 square foot, Equations 7 and 8
were utilized. Incidentally, in calculating capacity of any larger filter or the size filter necessary for a given output, it is simpler to use these equations based upon unit cloth area and to reserve the transposition to the larger area for the last step. Quantities m and s in Equations 2 , 4,6, and 8 are dimensionless; they represent the ratio of wet-cake weight to dry-cake weight (both solute-free), and weight fraction of solids in the sludge, respectively. Thus 1 pound of sludge contains s pounds of dry solid, yields ms pounds of wet filter cake, and (1 - ms) pounds of filtrate. The ratio (1 - ms)/s which occurs in these equations is the ratio of pounds of filtrate produced per pound of dry solid left behind in the filter cake; its variation with pressure of filtration depends upon change in m with pressure. Only a slight decrease in moisture content, m, is necessary to bring about large increase in specific filter cake resistance, a. In these tests m was determined by weighing a complete filter cake 2 inches thick immediately after filtration ceased and again after drying (any smaller amount representative of the entire cake thickness could be used).
The final seven equations (7 to 13) were used in this work and suffice for evaluation of specific cake resistance, CY, and cloth resistance, T I , from experimental constant-pressure test filtration data and prediction of filter capacity and washing rate, employing any concentration of the same sludge in any type of plant filtration equipment utilizing the same filter cloth.
Test Filtration Procedure A sludge composed of calcium carbonate in water was utilized for the greater portion of this work; some few tests were performed upon a sludge of indefinite composition obtained from the neutralization of crude phosphoric acid with soda ash in the manufacture of trisodium phosphate from phosphate rock. Approximately half a ton of calcium carbonate was present in a large mixing tank and thickener system which was operated in conjunction with these filtration experiments. Sludge for test filtrations and large-scale filter operation was withdrawn from this system. Thus t h e sludge which was later filtered in the rotary filters and the larger plate-and-frame press was identical with that used in the test filtrations. During test filtrations
JUNE, 1938
INDUSTRIAL AND ENGINEERING CHEMISTRY
length of 3/s-inch standard pipe as possible. Without stopping the the times for sive I-, 2-, or £ increments of filtrate to be delivered were noted. A moving stop watch cannot be read more accurately than one-half second; usually results were reported only to the nearest second which was found to be sufficiently accurate for the purpose. Additional dat,a secured for each test included pressure of filtration and weight of one entire filter cake when wet and again after drying. Also during each series of tests a liter sample of sludge was filtered, and the solid was weighed after drying to determine independently the weight fraction of solids in the sludge.
T~BLE 1. IXVERTED RATE DETERMINED FROM TEST FILTRATION DATA Lb./Sq. In.----lS
-5
Lb./Sq. In.---
e' 0 1 2
.
3 4 5 6 7
8
9 10
11 12
13
14
15 16 17 18
wj
0
24 .. 71
. 146 244 372 324
690 888 lis8
0
12' 23:s
37:s 49, , .. 64 76' .. 83 .. 99 110'
,-30
Lb./Sq. In.-
AO"
At?"
2.5 5 7.5
8" 0
..
50
io
is1
15 17.5 20 22.5 25
385 660
12.5
27.5 30 32.5 35
1009 1443 2ii7
Awf
..
10
26:2 46:8 55. , 8618 146:8
..
Lb./Sq. In.-
A0 "
11
"7 0 2.5
5 7.5 10 12.5 15 17.5 20
6918
--50
4e
22.5
25
27.5 30 32.5 35
8"
wf
Awf
0 ,
26
0 2.5 5 7,5
5:2
1i:4
98
555 788
io83
30. , 38:s 46:6 .. 59 ..
..
TABLE11. DETERMINATION OF CAKE DENSITY, CAKE RESISTANCE, AND CLOTHRESISTANCE CONSTANT P filtration pressure,* lb./sq. in. 51 , 0 9 3 151 , 0 9 3 301 , 0 9 3 50 Sb. gr. of sludgea Temp. of sludge,a O F. 77 80 81 Wet cake weight a grams 1183" 1997 2059 2064 Dry cake weight,'a grams 745 1352 1397 1406 m, wt. ratio wet to dry cake a , w t . fraction solids in sludge 1 -ms filtrate perlb sludge lb. 0.779 0.795 0.795 0.796 p viscbsity of filtrate lb./ft: hr. 2,085 2.17 2.085 2.05 p:density of filtrate, ib./cu. ft. 62.2 62.2 62.2 62.2 2/12,", slope of inverted rate plot, 6 , 29 3 , o6 1 ,62 1, sec./lb.2 U I ~ intercept , of invertedrate plot, lb. 0,85 0,70 1.20 1.10 6,obsvd. drycakedensity,lb./cu.ft. 71.5 73.8 74.3 6 , dry cake density calcd. from Equation 12, lb./cu. f t . 63.5 72.9 72.9 73.5 r,, cloth resistance constant, calcd. fromEquation ll,lb.Z/sq. ft. 31.2b 35.6b 7 3 . 9 ~ 72.7c a, sp. cake resistance calcd. from Equation 10, hr.*/lb. 210 300 352 379
:;A
a
b c
:;:A
A U ~
0
3:s
..
i18
19
,,
10 68 12.5 . . 15 1 7 . 5 142 20 241 22.5 25 368 27.5 . . 30 524 32.5 . . 35 702
22:6
211 361
e"
:;A
Observed experimental data. 24-ounce cotton twill filter cloth (new). 14-ounce cotton duck filter cloth (previously used for some time).
711
14:s '9"
2i:4 3i:2
Test Filtration Data
35:6 ..
Experimental time us. weight of filtrate data, together with the reciprocal rate of filtrate flow calculated from it, are shown for a series of constant-pressure filtrations in Table I. I n plotting these data use is made of the fact t h a t for any parabola the slope of a chord, AO/Awf, is identical with t h e exact slope of t h e parabola, dfl/dwf, a t t h e mid-point of t h e interval of the variable, w ,which is squared. The d a t a of Table I are plotted in Figure 2 . Table I1 includes additional experimental d a t a secured during these same tests, together with slope and intercept of curves in Figure 2. From these are calculated a number of other quantities, including t h e calculated (Equation 12) and observed dry cake densities, cloth resistance constant (Equation ll),and specific filter cake resistance (Equation 10). I n Figure 3 the variation of specific filter cake resistance, a, with pressure of filtration is plotted. In case the weight ratio of wet t o dry cake, m, and cloth resistance constant, r1, appear t o vary regularly with pressure, they m a y also be included in Figure 3. From this plot t h e proper value of filter cake resistance, a,t o use i n calculation of capacity of any type of filter a t any filtration pressure (or vacuum) may be secured.
P
a large sludge supply was maintained in a 120-gallon tank from the conical bottom of which it was drawn off by a centrifugal pump capable of circulating 40 gallons per minute; it was then returned to two different levels in the tank, thus stirring the sludge to prevent settling. The tank was also equipped with air agitation to keep the solid in suspension when the pump was not in use. To be sure that settling in the sludge supply was not influencing results, weight fraction of solid in the sludge was determined from a sample of sludge withdrawn from the sludge supply line just before it entered the press during each test. Since the ,sludge supply was large, its temperature remained fairly constant during the time required to perform a series of test filtrations a t different pressures. During each test, temperature of filtrate was measured. The pressure gage was located as close to the press as possible, and all piping was of generous size so that practically no resistance to flow other than that due to cloth and filter cake was present. Two types of filter cloth were used-a 14-ounce cotton duck and a 24-ounce cotton twill. The duck was identical with filter cloth later used on the larger plate-andframe press and the Oliver rotary vacuum filter; the twill was used as representative of the 18-ouncetwill cloth supplied with the American leaf filter. All test filtrations were performed in a 6-inch iron, closeddelivery, washing-type, plate-and-frame filter press, using two (usually 2-inch) frames with an active filter cloth area of 1 square foot. These frames were equipped with pet cocks a t the top. The pres6 and filtrate piping were completely filled with water previous t o the start of a test. With the filtrate outlet then closed and pet cocks on frames opened, the water within the frames was completely displaced by sludge. The pressure upon the sludge supply (either a blow case or centrifugal pump) had been previously adjusted to the desired value, so that the filtration could be immediately started by closing the pet cocks and opening filtrateoutlet and sludge-supply valves simultaneously with the start of the stop watch. This procedure ensured that the zero of time and filtrate measurement coincided and that full tiltration pressure was obtained from the start. The filtrate was delivered into a 5-gallon container resting upon a scale through as short a
IO0
80 A 8" w
60
40
20
~
O
O
10
20
30
u.'f
FIGURE 2. INVERTED RATEPLOTS FROM CONSTANTPRESSURE TEST FILTRATIONS
INDUSTRIAL AND ENGINEERING CHEMISTRY
712
TIMEAND WASH1[NG TABLE 111. CALCULATION OF FILTRATION FILTERPRESS RATE IN LARGE PLATE-AND-FRAM~ A filter cloth area sq. ft. Pi filtration pressdre, Ib./sq. in. S gr. of sludge emp. of sludge, ' F. a, wt. fraction of solids in sludge na, predicted wt. ratio of wet to dry cake 1 -naa,,filtrate per lb. sludge, lb. 0 . densitv of filtrate. lb./cu. ft. b, viscosity of filtrate, lb./ft. hr. a,predicted filter oake resistance, hr.s/lb. T i , predicted cloth resistance constant, hr.*/sq. ft. a, predicted dry cake density, lb./cu. ft.
3.16 25 1.091 84 0.138 1.47 0.797 62.2 1.985 340 73.9 73.0
r".
Nominal 1.50 4.56 26.35 1.33 27.68 1.065 722 1.7 720 686
Cake thickness, in. Dry solid per sq. f t . of cloth to fill press, lb. w j filtrate per sq. f t . of cloth to fill press, lb. W C : filtrate per sq. ft. equivalent to cloth resistance, lb.
eo", kec. B o , predicted filtering time, sec. e", obsvd filtering time a sec. '
... ...
Predicted washing rate 'lb./min. Obsvd. washing rate, ld./min. a
Wt. of Filtrate,
Lb.
Actual 1.625 4.95 28.6 1.33 29.93 1.065 83 5 1.7 833 803 0.91 0.71
CONSTANT-PRESSURE FILTRATION IN LARGE PLATE-
AND-FRAME FILTERPRESS
Time, See.
w e . of Filtrate, Lb.
Time, Sec.
wt. of Filtrate, Lb.
Time, Sec.
30, NO. 6
filter and a 4-foot American rotary vacuum filter. I n the filter press the thickness of the cake and hence the amount of filtrate, wf,that will flow before the press becomes filled are known, but in the rotary filter the cake thickness t o be expected is unknown. However, the length of time, 8, during which suction is applied to the submerged section of the filter cloth, is easily determined for any speed of rotation, and this determines how thick a cake shall be formed. The same equations (7 to 13) that were used for pressure filter calculations also suffice for rotary filter calculations. The usual
From data of Table IV and Figure 4.
TABLE Iv.
VOL.
'0
-20
40
wf 60
60
FIGURE4. WALKER,LEWIS, McADAMS, AND GILL~LAND PLOT OF CONSTANT-PRESSURE FILTRATION IN
Predicted us. Observed Filter Press Behavior I n Table I11 the above results are applied to the prediction of filtering time and washing rate, under the conditions indicated, in a 12-inch, hard-lead, plate-and-frame filter press.
20
P
40
FIGURE3. \'ARIATION O F SPECIFIC FILTERCAKE RESISTANCE, CY, WITH PRESSURE, P
Actual filtration result2 under these conditions in the larger press are given in Table IV. These data are plotted according to the new method suggested by Walker, Lewis, McAdams, and Gilliland in Figure 4 to aid in determining when the 83 and 90 pounds of filtrate corresponding to the nominal (1.5-inch) and actual (1.63-inch) cake thickness, respectively, were reached. The observed time of filtration agrees closely with that predicted. Washing rate was only 78 per cent of the predicted value, which seems to be a common occurrence.
Predicted us. Observed Rotary Filter Behavior These same test filtration data were used as the basis for prediction of capacity of a 1 x 1 foot Oliver rotary vacuum
12-INCH
P L A T E- A N D - F R A M E
PRESS
procedure was to evaluate w e by means of Equation 11, IC, by means of Equation 8, Bo from the relationship wO2= k , eo, and finally wf by means of Equation 7 ; wf is the amount of filtrate to be obtained per square foot of filter cloth during filtration time 8. Weight of dry solid per square foot of filter cloth per revolution is obtained by multiplying wf by the ratio s / ( l - ms). Finally, weight of dry solid filtered per revolution may be secured by multiplying by the entire filter cloth area. This procedure avoids the use of the somewhat complicated special equations developed by Ruth and Kempe (10)for rotary filters and is accurate as long as the filter cloth is submerged during the entire time suction is applied to it. This condition was easily met upon the Oliver filter which filtered during 110" of rotation; since it had twelve sections of 30" each, it required a submergence of only 140" of the drum. The American filter, consisting of eight leaves, had suction applied for 154" of rotation as shown in Figure 5 . Suction was applied to each leaf as it came into position 1 and continued until the dotted position was reached. Part of the leaf, a, was submerged during the entire suction period; other portions, 6 , were submerged for as little as 120" of the suction period. Thus the average time that the filter cloth was both under suction and submerged was undoubtedly less than the 154" used in these calculations (probably in the neighborhood of 140"). I n order to secure proper operation of this filter, some suction was usually applied during the washing portion of the cycle immediately following the filtration port. This resulted in filtration continuing in that portion of the leaf still below the sludge level. It should also be pointed out that a low sludge level will result in lessened filtration time. In some of these tests difficulty was experienced in maintaining the sludge level. This can be readily understood when the capacity of the thickener supplying thick sludge to this filter (4tons of solids per day) is contrasted with the filter capacity .when a feed is used containing 50 per cent solids (15 tons of solids per day). A considerable reserve of thick sludge was usually built up before its filtra-
INDUSTRIAL AND ENGINEERING CHEMISTRY
JUNE, 1938
I n Table V the observed data upon filtration of thin and thickened sludges of calcium carbonate in both rotary filters are given, together with the calculations of filter capacity from the test filtration data. T h e last two figures a t the bottom of each column give the comparison between
OF ROTARY FILTERCAPACITY TABLEV. CALCULATION
-Oliver Observed data: A , filter cloth area, sq. ft. Sp. gr. of sludge Temp. of sludge, O F . s, wt. fraction of solid in sludge Vacuum, in. of Hg P , vacuum, lb./sq. in. Time of 1 revolution, see. Time of cake collection, see. Wet cake w t . , lb. Dry cake wt., lb. Predicted from test data: a. filter cake resistance, hr.*/lb. v3; cloth resistance constant, hr.a/sq. ft. m, wt. ratio of wet to dry cake Calculated data: 1 - ms filtrate per lb. sludge, lb. p deniity of filtrate, lb./ou. f t . p: viscosity of filtrate, lb./ft. hr.
Filter-
-American
Filter-
18.0 3.2 3.2 18.0 1,120 1.430 1.098 1.430 78 110 95 74 0.156 0.477 0.176 0.476 13.5 14.5 20.0 19.0 7.11 6.64 9.8 9.3 114 114 105 105 114 57 360 195 15.75 27.0 8.0 18.0 10.87 20.0 0.5 12.9 245 73.0 1.52 0.732 62.0 1.74 0.473 1.240 3.25 32.10 35.35
k"
E?,, O", filtryFon time, see. e" + eo wf,filtrate per sq. f t . per revolution, lb.
Dr solid per sq. f t . per revolution,
lt. Dry solid per revolution, Ib. Observeddry solid per revolution, Ib.
243 73.0 1.52
226
0.277 62.2 2.25 0.0493 0.175 0.62 32.10 32.72
0.758 0.260 61.9 62.0 1.49 2.13 0.509 0.0386 0.716 0.083 1.01 0.176 48.80 48.80 49.81 48.98
2.85
1.095
0.685 2.19 1.90
1.885 6.04 6.95
713
220
33.4 1.55
4.31
33.4 1.55
1.294
0.889 2.375 16.0 42.8 10.87 40.0
~
FIGURE5. AMERICAN ROTARY LEAF FILTER
tion was attempted. A low sludge level i n the American filter in some tests and lack of submergence of the entire filter leaf during the entire period of suction serve to explain the tendency for actual capacity to be somewhat less than predicted. Nevertheless in a good many tests remarkably good agreement was secured. Both rotary filters were operated using a dilute (15 per cent) and a concentrated (50 per cent) feed under the maximum possible vacuum attainable. The time of revolution was the same in all cases-105 seconds for the Oliver and 114 seconds for the American filter. Since air pressure is necessary to secure removal of the cake from the filter cloth by the doctor blade of the American filter and this air must be removed from the interior of each leaf as it enters the filtration cycle, a momentary drop of suction from about 15 inches of mercury to zero occurred. This effect may also play some part in lowering the capacity of this filter.
TABLEVI.
Group NO.
Weight Fraction of Solid in Sludge, S
V
XIIIa
ip XI1 XIV XV XVI
pi1 XXI
{ "Xp::1
0.102 0.035
10 54 2680
Pressure, lb./sq. in.: 20 40 60 62 58 59 3870 5675 7310 Pressure, lb./sq. in.: 15 30
123 136 121 137 147 206 133 179 129 148 146 189 93 122 iis.149.... 153
106 100 114
...
106 127 110 109 120 110 128 177 160 210 235 259
:;;
I;:( 230 229 300 288 317 270
270 275 352 362 343 321
50
153 138 201 183 163 198 136 191 188 218 215 286 307 379 390 401 365
Test Filtration Results A summary of all test filtration results is given in Table An attempt is made to indicate the type and approximate condition of filter cloths used. The variation of specific filter cake resistance, a,with pressure for these various tests is plotted in Figure 6. Group V (1935) filtered the whiting as it was received in bags from the manufacturer; it was practically noncompressible, which was probably due to a
VI.
TESTFILTRATION RESULTS Cloth Resistance Constant, 71, Hr.Z/Sq. Ft.
.
I
Slud e from trisodium phosphate manufacture. b Old iuck filter cloth. 0 New duck filter c!oth. d Press and filter piping not filled before test. 8 New twill filter cloth.
5
OF
Sp. Filter Cake Resistance, a,Hr.*/Lb.
5 0.131 0.155 0.115 0.125 0.108 0.125 0.109 0.117 0.146 0.141 0.110 0.130 0.113 0.139 0.148 0.122 0.141
SUMMARY
calculated and observed weight of dry filter cake per revolution, and show reasonably good agreement in all cases except for the dilute sludge on the American filter. This filter usually gave some trouble with removal of cake when cake thickness was too small, which may account for a general tendency for lowered capacity when using a thin sludge.
Wt. Ratio, Wet to Dry Cake, m
7
10 40.5 25.8 5 67.0; 30.9 41.O C
...
53.5 58.2d
46.20 71.0d 25.0 43.0b 43.9: 25.6 42.3: 31.2 15.4e 30.16
..
Pressure, lb./sq. in.: 20 40 20.4 42.6
..*
...
Pressure, lb./sq. in.: 15 30
71.5b 63.0b 37.3C 42.10 19.3C 37.50 30.8C 36.5C 37.0 15.9 57.5d 68.2d 36.10 28.4C . . . . 79,od. . . . . 38.0 34.8 109.lb 79.6h 61.06 67.0: 57.9C 34.6 46.9c 45.4C 35.6e 73.9b 60.46 47.5 28.06 30.6 49.68 29.40
60 43.3
...
10 1.71 4.48
50
5
57.8: 42.4 36.4C 36.5C 82.5
1.57 1.61 1.60
66.62
34.3 60.Od 31.1 88.0b 70.0b 38.4C 42.1C 72.76 52.8 59.5 18.8C
Pressure, lb./sq. in.: 20 40 1.70 1.70 4.32 4.03 Pressure, lb./aq. in.: 15 30
...
1.56 1.58 1.55 1.64 1.55 1.50 1.62.
1.55 1.56 1.52 1.56 1.55 1.49 1.47
1.60
1.61 1.55 1.69 1.67 1.53 1.47 1.47 1.48 1.51
1.57 1.43 1.54 1.62 1.50 1.47 1.47 1.47 1.48
1.69 1.60 1.70 1.64 1.66 1.50 1.58 1.95 1.59 1.59 1.52
. . . . I .57 . . . .
GO 1.69 3.69 50 1.55 1.57 1.56 1.50 1.53 1.46 1.58 1.55 1.53 1.44 1.53 1.62 1.49 1.47 1.47 1.47 1.48
INDUSTRIAL AND ENGINEERING CHEMISTRY
714
large uniform particle size. Groups VI to XI1 and XIV to XV (1936) filtered calcium carbonate sludge withdrawn from the thickener system, to which new solids were frequently added to make up for losses. This mixture, while kept fairly constant, was not of uniform particle size and exhibited moderate compressibility and somewhat higher resistance than the new material used by group V. Groups XVI to X X I I (1937) utilized sludge from the thickener system to which no additions of new solids were made. The gradual
0
"0
P
t>
20
p
40
60
FIGURE6. VARIATION OF SPECIFIC RESISTANCE, CY, OB CALCIUM CARBONATE WITH FILTRATION PRESSURE AND NATURE OF PRECIPITATE
increase in resistance is due to reduced particle size from the continual re-use of this material in the thickening and filtration experiments. Some fresh calcium carbonate was added to the system before group XXIII performed their tests, and a lowered filter cake resistance was the result. Each two groups in Table VI were entirely finished with their test and large-scale filtrations before the next two groups began. In Figure 6 specific cake resistances calculated from the data of Ruth (4) are included to show that the limit of resistance possible with this material has by no means been reached. The data on cloth constant r1 in Table VI show that a fairly constant value is obtained for the three higher pressures (groups VII, IX, XVII, XIX). In quite a few cases lower cloth resistance is indicated for the 5 pounds per square inch filtration (groups VII, XV, XVI, XVII, XVIII). The test filtrations a t 15 or 20 pounds per square inch were usually performed first in the series of tests. When previously used cloth was employed, an abnormally high cloth resistance was usually noted in this first test even though the cloths were previously wetted (groups VI, XIV, XVI, XVIII). In other cases when new cloth was used from which sizing had been soaked, low values of cloth resistance were noted in this first test a t 15 pounds per square inch pressure (groups V, VIII, IX). In other cases the cloth resistance data seem entirely erratic (group X) which may be due to poor experimental technic or to changing filter cloths during the series of tests. These data give some idea of the range of resistance to be
VOL. 30, NO. 6
expected from the types of filter cloths used, although it should be pointed out that extremely old impervious cloths were not used in any tests and in reality no upper limit of resistance for these cloths has been established. Occasionally a filter cloth after long use will lose the loose ends of fibers which project from the main threads and help to bridge over the openings during filtration. Such a cloth possesses less resistance than a new one and tends to allow cloudy filtrate to flow a t the start. The weight ratio of wet to dry cake, m, varies only slightly with pressure. The uniform large-particle-size material of group V produced a wetter or more porous cake with less variation in m than the finer, less uniform material used by later groups. Thus compressibility or increased a values are associated with decreasing m values as the pressure of filtration mounts. Values of m greater than 2 were secured by others (4) working with a calcium carbonate sludge. When tests a t low pressure were stopped before the press was completely filled, a somewhat higher m value was usually observed (group XVIII a t 5 pounds per square inch). It is not definitely known whether this was due to excess moisture being secured with the sample of cake dried or is a real effect resulting when the continued application of pressure compacted the cake still further after the press was first filled. This behavior is being studied more completely. The latter theory is probably correct since cessation of filtrate flow, except in the case of group V and earlier groups dealing with relatively noncompressible material, was not a sharp break but a gradual decrease. However, these values of m secured upon the completed filter cake enabled reasonably accurate prediction of rotary filter capacity; in a good many cases they checked closely with observed m values on the rotary vacuum filters, where such a compression effect, due to the frame becoming completely filled, cannot occur. In other cases, values of m on the rotary filters deviated because of blowback of filtrate within the filter leaf or continued suction during the washing portion of the cycle. It is believed that the m values of Table VI represent fairly closely the moisture content and porosity of a filter cake during filtration in any type of filter, since in reality all filtrations are carried out under pressure. In the rotary vacuum types the atmosphere obligingly furnishes the pressure needed.
Results in Larger Plate-and-Frame Filter Press A summary of filtration results in the larger (12 x 12 inch) plate-and-frame filter press is given in Table VII. Observed filtration time agrees reasonably well with that predicted, under filtration pressures of 20 to 50 pounds per square inch and with sludge concentrations from 2 to 15 per cent solids. Observed filtration time was taken as that time when the expected amount of filtrate was secured or when the filtrate rate was decreased markedly (indicating a full press); whichever occurred first was considered to be filtration time. The first five groups, using fairly noncompressible material of low resistance, observed that actual washing rates were nearly as great as predicted values (81 to 92 per cent). Later groups, using a more resistant and more compressible calcium carbonate sludge, found washing rates to be as low as 70 per cent of the predicted values. Some groups observed a gradually decreasing washing rate as washing progressed. This effect seems to be associated with the compacting of the filter cake a t the end of filtration, which was previously discussed in connection with m values observed in test filtration. It is interesting to note that group XIII, working with the highly compressible material of high resistance from trisodium phosphate manufacture, was able to predict filtration time accurately in the larger press. In connection with this com-
INDUSTRIAL AND ENGINEERING CHEMISTRY
JUNE, 1938
715
drum not removed by the doctor blade. The effect of this variable cloth resistance and thin solid layer is greatest when a thin sludge is filtered, since only a small cake thickness reFiltraWt. sults. Consequently, when using thin sludge in the Oliver tion Fraction Filtration Time Washing R a t e Group Pres- of Solids PrePrefilter, a t times we find the observed capacity practically equal No. Date sure in Sludge dicted Obsvd. dicted Obsvd. to that predicted and in other cases observed capacities as LbJsq. in. Minutes Lb./minute low as 30 per cent of that predicted. When filtering thick .... 10 6 .. 8.3 I Nov., 1935 .. 5.45 4:82 36.5 .... 35 0 .. I1 Nov., 1935 sludge the effect of this uncertainty in filter base resistance is 4.29 3.62 12 4 12.1 .... .. 111 Nov., 1935 less since it comprises only a small portion of the total resist8.00 8.73 .... 4.55 6 0 Nov., 1935 118.5 8.50 10 6.9 50 0.0217 v Dec., 1935 ance during the major portion of the filtration cycle. Con5.69 6 16 0.125 VI Oct. 15,1936 20 1:50 20 5.77 7 07 2 : 0 6 0.125 VI1 Ool;. 16,1936 sequently, observed weight of dry solid filtered per revolution 2.08 .. 40 0.0485 16.38 16 60 v111 Oot. 27,1936 checked more closely with that predicted from the test filtra10.98 9 3 0.102 Oct,. 27,1936 20 1.84 1:31 6 47 0.120 6.35 20 IX Oct. 28,1936 tions when filtering thick sludge upon the Oliver filter. The 7 62 1.49 1.33 0,115 7.95 20 x N o v . 6,1936 2.38 0.030 25.41 26 80 Nov. 7,1936 40 XI few cases where observed capacity was decidedly below that 2:73 13.35 13 80 2.91 0.044 XI1 Nov. 25,1936 40 expected may have been due to a low sludge level or settling 21 1 0.0317 22.0 50 XIII" Nov. 28,1936 xx Nov. 1, 1937 25 0.138 13.9 13 4 0 :91 0:71 of the solid away from the drum. One of the chief criticisms 0.150 10.62 12 0 25 NQV.2,1937 XXI 32 4 34.8 0.090 X X I I Nov. 19,1937 25 of using pressure filtration tests to predict vacuum filter operation is that in the plate-and-frame filter settling is not a Residue from trisodium phosphate manufacture. particularly objectionable and may even result in faster cake formation, whereas in the vacuum filters settling is objectionable and results in less cake formation. In both the test filtrations and the rotary vacuum filter operation every effort pressible material it might be well to point out a misconcepwas made to avoid settling; under these conditions low-prestion prevalent in chemical engineering texts that compressible sure test filtrations should furnish a reliable basis for accurate sludges possess a critical pressure above which an increase in pressure results in an actual decrease in filtration rate. 4- vacuum filter predictions. In some tests more than the predicted amount of filter cake was formed. This was probably though this phenomenon remains a possibility, the authors due to error in either sludge concentration measurement, s, are aware of no published data showing that compressible or weight ratio of wet to dry cake, m, used in the calculations. materials more than double in resistance when filtration presWhen dealing with sludges consisting of more than 50 per sure is doubled. The curvature in the plot of specific recent solid by weight, $he amount of filtrate flow necessary to sistance vs. pressure is in the reverse direction to that which deposit 1 pound of solid in the filter cake, (1 - ms)/s, varies would make this phenomenon possible, and even compressgreatly with small changes in the m value. For example, a ible materials seem to increase in resistance a t a decreasing 54 per cent sludge with an m value of 1.55 would require 0.3 rate as pressure mounts. pound of filtrate flow to deposit one pound of solid in the cake; with an m value of 1.65 only 0.2 pound would be reResults in Rotary Vacuum Filters quired. Since predicted amount of cake formed is based upon calculated filtrate flow, the latter case would represent a A summary of predicted and observed capacities of the 50 per cent greater predicted capacity than the former. Thus Oliver and American rotary vacuum filters is presented in when calculating the output of a rotary filter with a thick Table VIII. These predictions were based upon the cake feed, it becomes necessary to have accurate knowledge of the and cloth resistances observed in test filtrations a t pressures value of m. As pointed out previously in the discussion of corresponding to the vacuum used on the rotary filters. m values obtained in test filtrations, it would be desirable to Several times in the course of this work the cloth upon the secure m values from a partially completed cake rather than Oliver filter was replaced. I n the test filtrations it was obfrom a completely filled frame as was done in these tests. served that cloth resistance constant r l varied threefold, deThe fact that, in the major portion of these filtrations of pending upon the age of the cloth. Obviously, then, some thick sludge upon the Oliver filter, observed capacities within groups based their predictions upon a cloth resistance less 15 per cent of those predicted were secured, serves to confirm than that of the cloth upon the Oliver filter while other groups the usefulness of the Ruth filtration equations for rotary did the reverse. Furthermore, the cloth upon the Oliver filter calculations. drum was held in place by a fine wire wound upon the drum, On the American filter, groups previous to and including which tended to produce a thin cake permanently upon the
TABLEVII.
CONSTANT-PRESSURE FILTRATIONS IK LARGE PLATE-AND-FRAME FILTER PRESS
I
TA4BLEVIII.
PREDICTED AND OBSERVED CAPACITIES O F
Oliver Filter-
Group
-Thin Sludge Lb. dry sohd/revolution Calcd. Obsvd.
No.
S
VI VI1 VI11 IX X XI XI1 XI11 XIV XVI XVII XVIII
0.124 0.108 0.109 0.068 0.089 0.125
1.60 1.98 1.68 1.21 1.38 1.94
1.57 1.50 0.80 0.59 0.65 1.75
0 :097
1.85 1.40 3.06 2.58 2.36 2.2s 2.09 2.88 1.65 1.51
1.35 0.93 2.14 1.34 0.87 0.70 1.90 0.73 1.15 0.74
xrx xx
XXI XXII XXIII
0.091 0.146 0.153 0.134 0.112 0.176 0.264 0.150 0.107
...
...
.-
8
0.530 0,520 0.395 0.518 0.360 0.603 0.481 0.470 0.462 0.506
0,515 0.542 0.398 0.476 0.498 0,632 0.527
-Thick SludgeLb. dry solid/revolution Calcd. Obsvd.
11.50 11.61 5.95 13.6 6,22 9.57 10.9 9.89 8.09 10.17 10,oo 17.2 8.9 6.04 6.68
7.13 7.97
8.60 4.50 6.80 15.3 4.70 13.25 12.55 13.12 9.08 9.99 11.25 15.8 7.74 6.95 7.44 9.70 8.50
ROTARY VACCUM FILTERS
--
S
0.112 0.073 0.108 0.109 0.117 0.117 0.112 0.136 O.OS3 0.156 0.148 0.126 0.112 0.156 0.207 0.206 0.101
American Filter -Thin Sludge--. Lb. dry solid/revolution Calcd. Obsvd. S
13.7 17.7 12.3 16.1 13.65 14.90 17.0 19.2 9.34 19.8 15.5 15.4 14.0 16.0 13.5 19.65 8.68
3.7 3.8 2.0 6.5 9.64 9 30 10.0 9.92 4.66 12.5 10.25 7.2 7.0 10.87 5.25 6.80
4.2
Thick Sludge-----, Lb. dry solid/revolution Calcd. Obsvd.
0.530 0.480 0.360 0.511 0.366 0,512 0.480 0.474 0.454 0.318 0.485 0.473 0.454 0.477 0.446 0.450 0,462
90.5 74.0 39.2 110 36.8 80 79.8 76.1 54.4 35.7 62.7 69.3 52.0 42.8 34.1 33.6 38.6
64.2 65.0 17.6 54 38.4 33.8 41.4 49.7 44.9 33.7 49.0 53.9 46.0 40.0 25.5 33.5 23.7
INDUSTRIAL AND ENGINEERING CHEMISTRY
716
group IX did not secure satisfactory performance because of the presence of a series of wire fingers attached to the doctor blade which were intended to break u p the cake as it was removed. Actually this arrangement prevented efficient cake removal; this was especially noticeable when filtering thin sludge where as low as 16 per cent of predicted capacity was observed in some cases. This wire cake-breaking arrangement was removed, and the doctor blades were adjusted closer to the filter cloth for subsequent filtrations. Although cake removal never became entirely satisfactory when filtering thin sludges, this adjustment did serve to bring observed capacities up in the range from 35 to 70 per cent of capacities predicted from test filtrations. When filtering thick sludge upon the American filter, much better cake removal was secured. A majority of those groups working subsequent to the alterations in the doctor blade secured actual capacities in the range from 78 to 104 per cent of predicted values, again illustrating the applicability of the Ruth equations to the rotary filter calculations. Observed capacities lower than predicted may have been due to low sludge level and to the fact that even with the maximum possible submergence the filter leaf was not entirely submerged for the entire suction period of 154” used in the calculation of predicted capacity. Taken as a whole, these rotary filter experiments bring out the unsatisfactory operating characteristics of rotary vacuum filters when filtering sludge low in solid content and the fact that almost theoretical capacity is attained when filtering thick sludge. They also serve to emphasize the vastly greater capacity of such equipment when using a thicker sludge. The calculation from test filtration datri of the expected capacity of the American filter soon led to the observation that it was not performing up to its possibilities and suggested improvements in the doctor arrangement and valve adjustment. This seems to be one of the chief justifications for making test filtrations under ideal conditions as a basis for calculation of plant filtration behavior, and it should bring out whether or not the plant equipment is operating a t its maximum theoretical capacity.
and rotary vacuum filters. In order to secure accurate predictions when filtering thick sludges, exact knowledge of the value of the weight ratio of wet to dry cake, m, is necessary since slight variation in m leads to considerable change in the ratio, (1 - ms)/s, the pounds of filtrate per pound of dry solids deposited. There are indications that the value of m secured from a full frame may be slightly lower than the value secured from a cake still in the process of formation. The use of test filtrations as a basis for calculation of theoretical capacity of plant filter equipment is shown to be a valuable means of determining whether existing plant equipment is operating a t its maximum possible output.
Nomenclature
Constant-pressure test filtrations in a small plate-andframe filter press were found to be a suitable basis for accurate prediction of capacity of larger plant-scale filtration equipment, including both the pressure and rotary vacuum types. The new Ruth filtration equations adequately represented the test data and were used in making the calculations of predicted capacities of the larger filters. Test filtrations upon calcium carbonate sludge were made in the concentration range of 10 to 15 per cent solids, a t temperatures between 60” and 100” F. and a t a series of pressures between 5 and 60 pounds per square inch. The larger scale filtrations were performed at pressures intermediate to those used in the test filtrations, a t sludge concentrations ranging from 2 to 54 per cent solids and at temperatures ranging from 60’ to 150’ F. Not only are the Ruth equations capable of predicting largescale filter operation when pressure, temperature, and concentration of sludge are identical with those used in test filtrations, but, when all of these conditions differ from those used in the test filtrations, accurate predictions are still possible. Accurate predictions of large-scale operation were secured both with a fairly noncompressible sludge of calcium carbonate and with a highly compressible sludge resulting from the neutralization of crude phosphoric acid with soda ash. Only relatively few constant-pressure atration equations are necessary in order to calculate plant filtration capacity, and these few equations apply equally well to filter presses
total vol. of filtrate delivered, cu. ft.
V v
=
c
= vol. of filtrate delivered per sq. ft. of filter area, cu. ft. = vol. of filtrate t o roduce cake equal in resistance to the
c
= vol. of filtrate per sq. f t . of filter area to produce cake
K k
= constant in total-vol. equation, ft.f/hr. = constant in vo1.-per-unit-area equation, ft. s/hr.
0
=
00
P
A
m s a!
p p
W! wf
W,
wc K, k, TI
u
Summary
VOL. 30, NO. 6
6
filter cloth, cu. ft.
equal in resistance to cloth, cu. f t .
time of filtration, hr.
= theoretical time to form cake of resistance equal to cloth
resistance present at start of filtration, hr. filtration pressure, lb./sq. ft. filtering (cloth) area, sq. ft. = ratio of wet to dry cake weights (solute-free) = weight fraction of solids in sludge = av. sp. resistance of 1 lb. of dry solid deposited upon 1 sq. f t . of filtering area, hr.2/lb. = filtrate density, lb./cu. f t . = filtrate viscosity, lb./ft. hr. = total weight of filtrate, lb. = weight of filtrate per sq. f t . of filter area, Ib. = total weight of filtrate to produce cake equal in resistance to filter cloth, lb. = weight of filtrate per unit cloth area to produce cake equal in resistance t o filter cloth, Ib. = constant in equation for total weight of filtrate, lb.%/hr. = a constant in equation for weight per unit area of filter cloth, lb.2/hr. = constant representing cloth resistance per unit area, hr.l/sq. ft. = sludge density, lb./cu. ft. = dry cake density, Ib./cu. ft. = =
Literature Cited (1) Almy, C., and Lewis, W. K., J. IND. ENQ.CHEM.,4 , 528 (1912). (2) Badger, W. L., and McCabe, W. L., “Elements of Chemical Engineering,” 1st ed., p. 456, New York, McGraw-Hill Book Co., 1931. (3) Ibid., 1st ed., pp. 461-2. (4) Ibid., 2nd ed., p. 509, 1936. (6) Bloomfield, A. L., Trans. Inst. Chem. Engrs. (London), 3, 38 (1925). (6) Irvin, D. F., Chemical Engineers’ Handbook, p. 1381, New York, MoGraw-Hill Book Co., 1934. (7) Perry, Ibid., p. 673. (8) Ruth, B. F., IND.ENG.CHEM.,27, 708 (1935). (9) Ibid., 27, 806 (1935). (10) Ruth, B. F., and Kempe, L. L., Trans. Am. Inst. Chem. Engrs., 33, 34 (1937). (11) Ruth, B. F., Montillon, G. H., and Montonna, R. E., IND. ENG. CHEM.,25, 76 (1933). (12) Ibid., 25, 153 (1933). (13) Sperry, D. R., Met. & Chem. Eng., 15, 198 (1916). (14) Walker, W. H., Lewis, W. K . , and McAdams, W. H., “Principles of Chemical Engineering,” 2nd ed., pp. 366 and 372, New York, McGraw-Hill Book Co., 1927. (15) Walker, W. H., Lewis, W. K., McAdams, W. H., and Gilliland, E. R., “Principles of Chemical Engineering,” 3rd ed., p. 344, New York, McGraw-Hill Book Go., 1937. (16) Ibid., pp. 347-50. RECB~IVED M a y 2, 1938. Presented before the meeting of the American Institute of Chemical Engineers, White Sulphur Springs, W. Vs., May 9 to 11, 1938.
