INDUSTRIAL A N D ENGINEERING CHEJIISTRY
890
T’ol. 20, s o 9
Effect of Pressure on Fundamental Filtration Equation when Solids Are Non-Rigid or Deformable’ D. R. Sperry 119 htCKlr. ST
I
N A previous article2 the fundamental 1a.m governiog tho phenomena of constant-pressure filtration, whore the solids are rigid and of constant shape, were foilnd
to be:
where Q and “represent a point on a filtration time-discharge curve and Q, and T, represent another point 011 the same curve WIICE T,> T. The symbol Rf = Q,& or tlic ratio of the 62‘s. I n deriving this forinuia t,he fscior N was not nerrlectrd hut was eliminated by algebraic means. By meiins of this expression an analysis can be made of a const,antpressure filtrat,ion timedischarge curve for the 117‘ value, by merely knowing the time and discharge value of two points thereon and the p r e s s u r e . A)foreover, as explained in a previous article,‘tbe:malyxis pennids theexclusion of initial irregularities, such as lowered pressure and leakage t h r o u g h cIot,l1s. To dettwnine the exponent of P a n o t h e r Figure 2 curve is needed made under a different nressure, other conditions being held constant. ~
P T
R
K
Rm or
= = = = = =
pressure (a constant) time resistance of solids to flow rate of deposition per cent of solids in mixture resiqtance of filter bastQ = v%’PT N2-N
+
].,;.!!.>p FiBure 1
If bhe factor N be neglected Q = m T Under this condition the pressure is a coirstaiit and the rate of flow a variable. The w e a is taken as unitg. If a symbol A for area is used, it. should be placed immediately before the radical. I n mother article3 the equation for flow, where the Aow is constant and t,he pressure a variable, is dwived as folloirs: Q = -P w 2M where M = constant rate of flow
By algebraic means an expression described as a “mathematical t,ool” was derived4 as follows: WP
=
Qz’-ReQ T,-R*T ~
(1)
1 Received March 29. 1928. Presented at the Round-Table Discussion ”Filtration” before the Division of Industrial and Eogineetiog Chemistry at the 75th Meeting of the American Chemical Soeicty. SL.Louis. Mo.. April 16 to 19, 1928. 2 Sperry, Mcf. Chem. Eng., 16, 198 (1915). Sperry. I. Inn. ENO.CHGY., IS, 985 (1921). 4 Sperry, Met. Chem. En#., 17, 151 (1917).
on
Method
The method employed was to take a certain mixture a i d obtain timedischarge curves Eroin it for several different pressures, each one representing a different constant-pressure eiin’e. These curves were made on a inechanical filtration recording device as described in a previous The 1VP value for eacli of these curves was rompuled by means 01 equation 1. If the solids were rigid and undeformable, t,he curve obt.ained by plot,t.ing these IVP values for each pressure on logarithmic cross-section paper would be a straight line making ari angle of 45 degrees with the preisure rnijrdinates, corresponding to an expimential value for P of unity. If, on the other hand, the solids are not rigid. or are deformable, the curve will be citiier a line that is not straight or one that is straight and makes an angle OS.T less than 45 degrees. If the line is not straight, tlieu certain factors other t.han the pressure enter into the A proposition; but if thelineis straight, the tangent of the ., HOU 5 angle which it makes with the pressure axis is equal to Figure 3-Representative Curve the exponent of P.
~,
Apparatus
Figure 1 shows B dingram and Figure 2 a photographic view of the apparatus as actually employed. It will be noted ‘Sperry, INn. END. CHsm.. IS, 276 (1926).
September, 1928
INDUSTRIAL A S D EAL-GI.VEERISG CHEMISTRY
that the montejus is a closed pressure vessel. The mixture h i r pressure is to be filtered is cont,ained in this introduced as shown in Figure 1. The air pipe reaches to the bottom of the vessel. The air bubbling from this pipe acts to a certain extent as an agitator. As the air pressure above the liquid increases 1,he mixture is displaced into the filter press. The filter chamber and the
893
4-After a careful check-up of all valves, the predetermined air pressure was admitted to the montejus and kept constant by manipulation of the air and vent valves. Occasionally the plunger agitator was operated during the run, &When the run was completed the time-discharge curve was removed from the recorder and the apparatus prepared for might be. thenext run Or for shutting down as the 6-Thv time-discharge curve was filed for later analysis, care being taken to mark on the curve such data as would make its identification positive. M e t h o d of Analysis
Two points on the time-discharge curre were chosen-one near the high end of t h e c u r v e a n d the other a short distance f r o m t h e low end. These TT-ere points QI, TI and Q, T , respectively, and their v. a. .l u~e s were substituted in equation 1, viz. : ~~
Test 22323A--1.406 kg.,per sq. cm. Test 22428-2.812 kg. per sq. cm. Test 22328-0.703 kg. per sq. cm. (40 Ibr. per sq. in.) (LO Ibs. per sq. in ) (10 lbs. per sq i n . ) Figure 4-Time-Discharge Curves for S t a r c h (3.85 Per Centj
Test 31527B-0.321 kg. per sq. cm. (4.57 Ibs. per sq. in.)
Test 3 5 2 7 4 . 7 0 3 kg. per sq. cm. (10 Ibs. per sq. in.)
Test 3527A-1.406 kg. per sq. cm. (20 lbs. per sq. in.)
Test 3527B-2.812 kg. per sq. cm. (40 Ibs. per sq. in.)
Figure 5--Time-Discharge Curves for Kieselguhr
two filter bases are used in a horizontal position. This is done to minimize the effects of sedimentation, the idea being that sedimentation would affect the lower filter surface to somewhat the same extent that it affects the upper surface but in opposite directions, each error tending to nullif] the other. Experimental basis for this conclusion was given in a previous article.4 To insure agitation previous to and occasionally during runs a plunger agitator was provided. This consists of raising and lowering a perforated, loosely fitted disk. A very efficient churning agitation is produced. Procedure
Figure 3 shows a curve with the two points indicated. In cases where there are liable to be errors caused by unstable conditions a t the commencement of a run a new base line may be selected4 above the old one, as at -A, Figure 3. When the two points and the base line are determined the values of Q1, T I , Q, and T are entered on a computation sheet containing 16 lines. The items as listed are especially arranged so that the computations are easily carried out. It is a very simple matter to compute the value of TTP ' . The TYP values are then p!otted as determined for each of the
Each mixture was carefully prepared by weighing the solids and measuring the mater a t the temperature as drawn from the tap. Each run mas made from freshly prepared mixtures-that is, more than one run was not made from the same batch-in order to eliminate effects due to possible physical changes in the solids which are dependent on a time factor. The actual steps xere approximately as follows: 1-The filter was assembled and closed using No 10 duck as the filter-base. 2-The recorder was provided with a paper, the pen inked, the base line drawn, and the clock mechanism set in motion. 3-The mixture was prepared by putting into the montejus the calculated weight of solids plus the requisite water. The mass was then thoroughly mixed by hand with a paddle (through the hand-hole of the montejus) followed by a vigorous mixing with the plunger agitator. The vessel was then closed.
--
RED COLOR ( ? %)
J
0703 KG/5Q CM.
0.1 H O U K t ,
0.1 HOURS
0.1HOURS Figure 6-Time-Discharge
Curves for a Red Color
Eh, 4\\ "\
Vol. 20, No. 9
INDUSTRIAL A N D ENGINEERING CHEMISTRY
894
-
7.9
t4
_I
0 I HOUR
I
Test 51027-0.703 kg. Test 5927-1.406 kg. per sq. cm. (10 lbs. per per,sq. cm. (20 lbs. per sq. in.) sq. In )
HOUR
Test 5927A-2 812 kg. per sq cm. (40 Ibs. per sq. in )
Remarks
The 'determination of the TVP value from a filtration time-discharge curve by use of equation (1) is not SO tedious as it may seem. The writer has repeatedly analyzed recorder filtration curves for the W P value in only 15 minutes. The determination of W P from commercial-sized units by means of equation 1 is easily accomplished, since the only data needed are two readings of the total discharge (which may be obtained by measuring the ievel of the filtrate in receiving tank) together With the elapsed time from the commencement of the
{h,$h, $3 Figure 7-Time-Discharge
Curves for Masons' L i m e (3.85 Per C e n t )
,-g
A
Test 3 2 5 2 7 4 . 7 0 3 kg. per sq. cm. (10 lbs. per sq. in.)
Test 42027-2.109 kg. per sq. cm. Test 32527A--1.406 kg.,per sq. cm. (30 Ibs. per sq. in.) (20 Ibs. per sq. in.) Figure I-Time-Discharge Curves f o r Fuller's Earth (1.43 Per C e n t )
different pressure curves for a given mixture, on logarithmic cross-section paper. If the curve is straight, the tangent of the angle which it makes with the pressure axis is found. This is the value of the exponent of P. Data
The time-discharge curves (Figures 4 to 8, inclusive), the computation tables, and the logarithmic curves (Figures 9 and 10) for five different substances are attached. The computations all show t h a t f o r each s u b s t a n c e the logar i t h m i c c u r v e s for the W P v a l u e s are straight lines, indicatSTARCH ing that the effect of pressure on non-rigid TAN A = 0.87 or deformable solids is to modify the ex07 1 2 3 4 ponentofP, the pressure. The value of C of this exponent of P was found to be as follows: 3527 A starch 0.87, kieselguhr 0.82, a red color 0.70, 3527 m a s o n s ' lime 0.525,
///
31527B
T/N A=082
'
0 I HOURS
0 I HOURS
0 I HOURS
0 I HOURS
'
' O e Figure 9-Logarithmic Curves for S t a r c h a n d Kieselguhr
Test 42227-2.812 kg. Per sq. em. (40 lbs. per sq. in.)
run to the two discharge readings, the pressure during the run to be kept constant. More accurate data could be secured by means of a float in the receiving tank which actuates a pen or a recorder, such as was used in preparing this paper. Attention is called to the varying effect of pressure when filtering different substances. As shown by the curves for fuller's earth, all that was gained in output by increasing the pressure fourfold was 11 per cent, while in the case of kieselguhr the increase caused by increasing the pressure the same amount is 244 per cent. I n a subsequent paper the practical application of these filtration laws will be described. The accuracy of the computations is that of a 20-inch slide rule with the exc e p t i o n of t h e f r a c t i o n a l expo- 7 nential values of the pressure which 4 RED COLOR were c o m p u t e d .,13 from a six-place T A N 4 = 0.7 logarithmic table. Other efforts to 07 1 determine the effects of pressure on the phenomena 7 of filtration have 5 . 3 been made by MA50NZ L I V E Lewis and Almy,6 ".% T A N A = 0 525 Baker,'and Weber and H e r s h e y . * T h e s e investigaPRESSURE K G / S Q C M 0 7 1 2 3 tors found that the
-
.-g ."
.
f i l t r a t i o n equation then becomes:
42227
as an exponent of the pressure. 25
or in its approximate form: Ad/WP.T (for constant pressure conditions) Pc w or Q = - (for constant rate of flow conditions) 2M Q
=
IND. ENG. CHEM, 4, 528 (1912). 7 I b i d . , lS, 6 1 0 , 8 J
'Ibid., (1926).
8
FULLERS E A V I I
2
TAN A = O
115
PRESSURE KG/SQ CM
F i g u r e 10-Logarithmic Curves f o r m e d Color, Masons' L i m e , a n d Fuller's Earth
INDUSTRIAL A N D ENGINEERING CHEXISTRY
September, 1928
895
Computation Tables Test Pressure, kg. per sq. c.m. T , hours 0 , liters per sq. m. 01, liters per sq. m. Rq
02 QIZ
RnQz Q I ~ - RnQz T I ,hours RqT Ti-RqT WP Po
' U
STARCH 22328 0.703(10) 0.1 186.2 450 2,415 34,700 202,500 83,800 118,700 0.45 0.2415 0.2085 569,000 0.7361 773,000 C = 0.87
22328A 1.406(20) 0.1 201.5 546 2.68 40,600 298,000 108,800 189,200 n.. 4~. 5 0.268 0.182 1,040,000 1.345 773,000
22428 2.812(40) 0.1 328.5 639 1,944 107,800 408,200 209,600 198,700 0.30 0,1944 0.1056 1,880,000 2.402 773,000
KIZSELGUHR Test 31527B Pressure, kg. per sq. cm. 0.321 (4.57) T , hours 0.1 0, liters per sq. m. 86.9 Qi. liters per sq. m. 236.0 2,715 Rq 7,550 55,700 Kq02 20.770 34,930 Q12-RqQP 0.50 Ti, hours 0.2715 RQT Ti - RqT 0.2286 W P 153,300 P c0.3936 W 389,500
%
Test Pressure, kg. per s q . cm. T . hours Q, liters per sq. m. Q I , liters per sq. m. Rq
52526
3527 0 . i03(10)
0.1 136.5 306.0 2.24 18,650 93,600 41,800 51,800 0.40 0,274 0.176 294,000 0.7477 392,500 C = 0.82
3527A
3527B
1.406!20) 0.1
2 812(40)
0 1
195.5
174.0
391.0 2.00 38,200 152,700 76,400 76,300 0.35 0.20 0.15 509,000 1.322 384,500
385 0 2 21 30,300 148,200 66,900 81,300 0 2 0 1105 0 0895 909,000 2 333 390,000
Q12- RnQa T i , hours RaT Ti - RgT WP Pc W
0.703(10) 0.1
40.3
55.6
80.6 2.0
108.5 1.95
RnQ2
012-Rn02 T I ,hours RqT T I - RnT U'P Pc
iv
Test Pressure, per sq. T , hours Q , liters sa. m. 01, 'liters sq. m.
RqQ2
1.406(20) 0.1
2 812(40) 0 1
Ti, hours RqT T I- RqT WP PO
71.3 158.1 2.218
rv
FULLER'S EARTH 32527A 42027
32527 kg. cm.
0 1 4
22526C
62.00
51027 5927 1 406(20) 0 7 0 3 ~ ') 0 02 0 05 117 8 96.1 296 0 260 5 2 51 2 71 13,850 9230 87,600 67,820 34,800 25,000 52,800 42,820 0 225 0 25 0 1265 0 1355 0 0985 0 1145 536,000 374,000 1 196 0 831 448.200 450,000 c = 0,525
Q2 QiZ
52526B
130 2 2.1
3845 16,950 7880 9070 0.4 0.21 0.19 47,700 1.27 37.540
5080 25,030 11,260 13,770 0.4 0.2218 0.1782 77,200 2,062 37.950
MASONS' LIME
012-
0.322(4.67) 0.1
3090 11,670 5940 5730 0.4 0.195 0.205 27,900 0 783 35.700 C = 0.7
-
Test Pressure, kg. per sq. cm. T , hours Q , liters per sq. m. 01, liters per sq. m. Rq
;:
R E D COLOR 525268
1623 6490 3246 3253 n~ ". 0.2 0.2 16,260 0.4496 36,200
kiQ2
RgOl
per per
0.703(10) 0 1
1.406(20) 0.1
2.109(30) 0.1
130.2
155
297 2.28 16,950 88,200 38,660 49,650 0.4 0.228 0.172 288,000 0.9605 301,000
331.5 301 2.14 2.068 24,100 21,200 109,900 90,600 51,600 43,800 58,300 46,800 0.4 0.35 0,214 0,2068 0.186 0.1432 313,500 326,500 1.04 1.09 301,500 298,200 c = 0.115
145.6
5927.'' 2 812(401 0.05 151.8 390 5 2 575 23,000 152,300 59,200 93,100 0 25 0 1288 0 1212 768 000 1 721 449,000
42227 2.812 (401 0.1 148.9 341 2 29 22,000 116,200 50,400 65,800 0.425 0.229 0.196 33 1,000 1.126 294,000
Abrasion Tests of Rubber Stocks Containing Various Types of Carbon Black' W. B. Plummer and D. J. Beaver COXBVST:OXDTILITIES CORPORATIOK,
HIS paper presents certain interesting results obtained during the course of a general study on the abrasion resistance of rubber stocks compounded with various types of carbon black. All tests have been carried out using the Grasselli abrasion tester as described by Williarn~,~ since this method measures the actual power consunied per unit of material abraded. and hence eliminates some of the uncertainties inherent in other abrasion test devices. Vogt3 has tested seven redaim stocks by this method as well as with four other devices, all designed to measure or take account of the power consumed during abrasion. Averaging the results of three of his methods, the fourth being definitely discordant with the others, the relative abrasion resistances for the various stocks were 100-95-91-83-80-74-71, whereas with the Grasselli abrasion machine the results were 100-9189-83-77-72-67. The concordance between these results is very close. In his second paper Vogt discusses certain differences between the results of his "angle abrasion" machine
T
L
Presented before the Division of Rubber Chemistry a t the 75th Meeting of the American Chemical Society, S t . Louis, Mo., April 16 t o 19, 1028. IND. ENG.CHRM.,19, 674 (1927). * Zbid., 20, 140, 302 (1928).
LONGISLAND CITY,
S . E'.
and the Williams machine, to which further reference nil1 be made later. In the present tests with the Grasselli machine the standard procedure outlined by Killiams has been used except that round blocks are used instead of square ones. This simplifies the construction of molds very greatly and permits test blocks to be made by rolling up narrow strips of the raw stock, which completely eliminates any possible effect of calendar grain on the test results and in general gives a more satisfactory test block. Check determinations have shown no difference in results between round or square blocks. The average deviation of test results for a given stock by this method has been found in general to be less than 3 per cent, although occasionally a given test will give obviously discordant results, ordinarily in the direction of OW abrasion loss. A priori this might result from changes in the motor speed (line voltage), in the size of the abrasive, or in the condition of the abrading or abraded surface. KO detectable differences in speed haie been observed during tests,and although the abrasive siae is important, as discussed later, it cannot account for the occasional erratic results. Such results are attributable only to the condition of the surface involved, and hence in routine testing special atten-
