STUDIES OF FILTRATION

THESIS FOR THE DEGREE m? m. s.

HERBERT T. WALWORTH
1933

 

OF FILTRATION

0)
:3.
L4
If)
H
M
U)

Thesis
Submitted to the Faculty
of

Xichigan State College

In Partial Fulfillment
of the
Requirements for a Degree
of

Easter of Science

Herbert To Walworth

Hay 27, 1933

9 fil"~T/‘\ "7 *fl {\7 ".."T
I‘LI V .II L1! -- J T

Q --A'1 v - . .3-"

The writer is indebted to Professor H. 8-

Reed for suggestions and assistance iven in

Cl
C.

connection with this study.

Part I
Part II
Part III

Part IV.

Part VI

Part VII

Part VIII

Part X
Part X1

Table of Contents.
Introduction.
Laboratory Experiment.
Derivation of Equation of Walker, Lewis and Kc-
Adams and Badger and LcCabeo
Application of equations of "Elements of Chemi-
cal Engéneering" by Badger and MoCabe to the
filter press, suction filter and leaf filter and
comparing the values of the filter constants.
Testing the Validity of Filtration Equations of
Badger and HcCabeo
First Attempt to Develope a more Accurate Equation
for Predicting Filtering Times.
Development of Final Equation for Predicting the
Filtering Times at a Certain Pressure.
Comparison of the Rate of Filtration, Using the
Several Different Kinds of Filter Cloth of the
Edward H. Best Co.
Investigation of the Washing Characteristics of
Different Slurries.
Conclusions.

Bibliography

I. Introduction.

Filtration is tne process of separating the solids from
a mixture of solids and liquids. This is done by allowing the
liquid to flow through a porous mednum whose orfices are not
large enough to allow the passage of the solids. There must
be some device to support the medium as well as a difference
in pressure between the two surfaces so as to force the liqui
through.

The most common of the various ty es, is the filter

press. There are two general types of the filter press, the

recesse7, and the plate and frame press. The pla e and frame
press (fig. 1) which is the more comzon of the two types con-
sists of a series of plates, (fig. 2), which are ribbed in

one way or another and support the filter medium; and freres

which are hollow and afford space in which the cake builds up.

I)

These plates and frame. are so arranged that the feed channels
on all frames are placed in the same line and the discharge
channel of the plates are placed in line diagonally opposite
the feed channels. One cloth is placed on each plate surface
and holes are cut in the filler cloths corresponding to tie
feed and discharge channels. The slurry comes in the feed
and the filtrate leaves through the discharge channels, the
percipitate collecting on the filter cloth.

Other common types of filters are the centrifuge and
suction filters (fig.3). Suction filters are of the filter

bed, leaf, (fig.4) and rotary types and their various modi-

fications.

The selection of any type depends upon the VHLIZCt of
the slurry to be filtered. Only crystalline solids can be

ndled efficiently in centrifuyal machines. Very collodial

precipitates filter most readily on gjr avity filters, etc.

Generally soealiing, slurries which filter at a high rate
are filtered in large chambers. That is, the ratio of slurry
to filter area is large. Where slurries are hard to filter
the char.oe1 s are not thicker than or.e inch. That is, the
ratio of slurry to filter area is small.

washing of the filtered cake is also a big problem.

“asiing is carried on for two reasons, either to recover a

)—

yaluable liquor from the solid particle s which retai in it or
to free the p1recipita te of the mother liquor or of impurities
in the mother liquor. here are two generil methods of mesh-

ing the direct wash and the counter flow sash. The direct

wasi consists of forcing the wash water through the feed chan-

nel. The dis a6vantage of this method of washing is danger of
channeling, thus learing parts of the cake th at are not pro-

perly rashed- In host cases the counter flow wash is useo;
out with so e cakes t-ere is danie r os incomplete peei'
to cracking of the cake. The success in washing a crhe pro-
per rly depends greatly upon the filtration technic ue.

"Given the filtration conditions and the design of a
filter what volume of filtrate can he obtains” in a definite
lené th of timel?""

L

"What volume of we n water can be passed throu5h tie

1 A

e in a definite lengtn 0: time? .Ynat will be the relation-

7

1

G)

c
ship between concentration of recovered material in tLe wash
water and tLe amount of wash water used?"

"Theoritical solution of these questions is retarded by
the fa cts the t different sludges vary g1 e"ttly in characterist—
ics and the resistance to flow of any of its extremely sensi-
tive to temlerature, method of prepar- ion, and a“e. It is
very difficult, especially with collodial slud5es, to dueli-
cate results nitlin several hundred per cent, even wlen diff-
erent batches are prepared under apparently identical condi-
tions."

These statements are taren from Elements of Chemical
Engineering by Bad5e and icCabe (8). However, I am in—
clined to believe that results can be made to check if the
filtration cycle is properly carried out. Filtration re-
quires great care; and the temperature, pressure, and plac-
ing of filter ed a should be carefully regulated.

In industrial practice the method of preparation of a
slurry and age, in most cases is a minor problem in filtrat-
ion. It is true that the characteristics of some sludges vayy
some from time to time. However, these slurries are a part
of a certain chemical process which is carried on in a cer-
tain way from day to day under the same conditions, thus the
variation in character should be very slight. Age does have
a great effect upon filtration but industrally, the time slur-

ries stand before filtering is generally about t11e same, from

day to day.

If filtration is properly carried out it should not be
haid to c1eck results much closer than several hundred per
cent.

The slurries used in this work were selected as repre-
sentative slurries of the compressible non-homoheiieous tyre.
These slurries were made up in snall batches of about fifteen
gallons. Althou5h the quantity maze rather small, I was forced
to do so because of my inability to check results where large
quantities were tade up, and one slgrry stood longer than
another.

All of this work pertaining to~filt ration theory has been
done in connection with the equations of Walker, Lewis and X
Adams (1) and Badger and thabe (2). It has been nv on
show the inefficiencies of these equations as well as the ex-
tent of involved theory whichtthey embody. It is almost imposs-
ible to get a thorough understanding of these equations with-
out an unusual theoritical mind.

The real iztportance of a filtration equation is in afford-
ing a means of determining the area of filter surface reotired
for any definite amount of sludge and the time required to
carry out the filtration cycle. Although I realize that fees
equitions could give a rouxh estimate in predicting filtering
times, they do not meet the eQLireiwnts of ordinary indust-
rial practice- It is with this in mind that I have developed
the equations which will follow in one of the chapters of this

thesis.

II. Laboratory Experiment.

A. Preparation of Slurries.

The first slurry usediin his work and one which repre~
sents the non-homogeneous class of sludges, consisted of cal-
cium carbonate and aluminum hydoxide.

This slurry was made by dissolving 12' calcium chlo-

ride and 3.3 aluminum chloride in 48.7 of water and aCdin

(T1 3

this solution to a solution of 10.95 sodium carbonate in
53.1 of water. However, he calcium chloride used were not

pure material and the slurry was made up according to the

 

 

 

 

Table I
Solution A Parts of Actual Wt.
Pure Compounds. in Pounds.

Calcium Chlordde 10.0 12.6
Aluminum Chloride 1.82 3.3
Water 48.7 48.7
Solution B
Sodium Carbonate 10.95 10.95
Water 53.1 53.1

Total Weight 128.65

 

 

Solution A was slowly added to solution B with constant stir-
ring. The resulting slurry was allowed to stand for at least
twelve hours before using. After the slurry stood for this

length of time, more uniform r sults could be obtained, upon

filtering.

When ever possible or advisible simultaneous experiments
were run with a second slurry. Slurry no. II consisted of
sodium carbonate only as the precipitate, which represents the
homogeneous class of slurries. This slurry was made up in a

similar manner to that of slurry , as follows:

 

 

 

Table II-
Solution A Parts of Actual Wt.
Pure Compounds. in Pounds.
Calcium Chloride 10.0 12.6
Water ' 45.0 45.0
Solution B
Sodium Carbonate 9.6 9.6
water . 50.4 50.4
Total Weight 117.6

 

 

 

 

In the eXperiments which are to follow these slurries

will be ref rred to as slurry I and slurry II.

B. Sonstituents of each slurry.
1. Calculated
Sl‘rry I
(l) Caclg + NaBCO5 ZNacl + 08003
110 106 116 100
(2) 313512003 + 2A1013 + sage 2A1(0H)3 + 6NaCl + 3002
264 156 348
a. Per cent Solids.
From equation (1)

110:100

1000:X

x 9.1 03003

From equation (2)

1264:156 = 1.62:X

x = 0.96 A1(0H)3
Total Solids 9.1 + 9.6 = 10-06
Total Wt. of Slurry = 128.6
(10.06 : 128.6) x 100 = 7.87049
Solids
Per cent Sodium Chloride

From equation (1)

110:116

10:1
x = 10.5 Naol.
From equation (2)

264:348

1062:}:

x 2.13 Nacl
Total Wt. of Slurry = 128.6

Per cent of Nacl

12.63 : 128.6 X 100 9.98°

Slurry II

a.

Per Cent Solids
From equation (1)

110:100

10:x

x 9.1 Ca003
Total Wt. of Slurry = 117.6
Per cent Solids

9.1 : 117.6 x loo = 7.87°/o

C. Per Cent Sodium Chloride
From equation (1)
110:116 = 10:x

x = 10.5 Nacl

Total Wt. of Slurry = 117.6
Per cent Nacl
10.5 : 117.6 X 100 = 9.l°/o

Actual

Slurry I

a. gel; _C_ent_Sg_li_d§ _
Wt. of Sample as taken = 9.219 Gms.
Wt. of Sample Dry = 0.7089
Per cent Solids
0.7089 : 9.219 X 100 = 7.69 °/o

b. Per Cent Sodium Chloride
AgNOS Solution N/10
92.? cc AgNO3 N/lo neutralized a 500 sample
of filtrate.
Specific gravity of filtrate = 1.08
1 cc of N/10 AgNO3 will neutralize .0058 grams
of Nacl, therefore,
92.7 X .0058 = 0.53766 gr. Nacl
0.53766 : 5 = 0.10753 gms. Nacl in loo
0.10753 : 1.08 X 100 = 9.95°{° Nacl.

Slurry II
a. Per cent Solids.

Wt. of Sample taken 8.29

Wt. of sample dry = .6234
Per cent Solids =
.6234 : 8.29 X 100 = 7.5 °/o
b. Per Cent Sodium Chloride
Agl‘IO:5 Solution N/lO
86.3 cc A52303 Neutralized a 5 cc sanple of
filtrate.
Specific gravity of filtrate = 1.08
1 cc of N/lo AgNO3 will neutralize .0058 gas.
of Nacl, therefore,
86.3 X .0058 = .49054 gms. Nacl
.4905 : 5 = 0.0981 gms. Nacl in 1 cc.
.0981 : 1.08 X 100 = 9.08 °/o

 

 

Table III
Per Cents Per Cents
Calculated Actual
Slurry I
Solids 7.87 7.69
Sodium Chloride 9.98 9.95
Slurry II
SGlids 7.87 . 7.5
Sodium Chloride 9.10 9.08

 

 

 

Co EXperimenta.
Test l---Dewatering by continuous vacuum filtration.
Conditions---Using slurry I with 9.95 °/o Nacl and 7.69‘
°/¢ solids. Filtration carried on in a 6 inch bushner

funnel with a two liter suction flask.

10

 

 

 

 

Table IV

Volume of Feed 1200 1000 750 500
Fozrming Time- Min. 23.75 17.75 11 5.25
Fozrming vacuum- in Hg. 25 25 25 25‘
Drgring time- min. 4 3.75 4 2.75
Drgring vacuum- in H5. 20 20 20 20
Calce Thickness- inches. 3/4 5/8 7/16 5/16
Wei: Cake- Gms/ 339 272 163.5 128
Per? Cent Water 060.6 60.3 56.5 59.2
Dryr Cake Gms. 135. 108 80.5 52
To ta]. Cycle- Minutes 27.75 21.5 15 7.75
Calpacity- /Sg.ft./24 hs. 175.2 182.8 193.7 262.8

Test 2. Washing on continuous vacuum filters.

Problem: To determine the displacement of Nacl by wash

valter, using slurry I.

Procedure: The filter used ‘38 a 6' buohner funnel (.088
Sq. ft.) with a two liter suction flask. The suction flask was
minnected to the vacuum line and 1000 cc of the slurry poured
itho the bashner funnel over filter cloth as the filter medium.

The vacuum was built up to 25 inches of mercury and con-
tiINled until the cake was formed. That is, until all the water
WlSt diaap eared above the cake. The filtrate was then removed
and.neasured. wash water was then poured over the cake and
Vacuum.built up to 24 inches of mercury. The washing was con-
tinued until all the water had passed throught the cake.

Table V.

¥

11

 

 

 

 

 

 

’ Test No. 1 2 3
Volume of Feed cc 1000 1000 1000
Fozrming time, min. 16.75 17.5 17.75
Fozrming vacuum, inches Hg. 25 25 25
cc wash Water 100 200 350
cc Filtrate 117 208 297
I%11310 of wash water to dry solids 1:1 2.2:1‘ 2.7:1
'Wasshing time, din. 6 11.75 12.75
Wasshing vacuum, inches Hg. 24 24 24
Calms thickness, inches 5/8 5/8 5/6
We1: cake in grams 276 266 269
°/o Water in cake 63.5 65.9 66.3
Dry cake in grams 100.5 90.5 90.5
Total.cycle, Kin. 27.75 34.5 35.5
Gapacity, /sq. ft./ 24 hrs. 132 93 96
Gms. Nacl in cake after wash 10.3 3.04 0.01
Gale. gms. Nacl in cake before
Washing 21.0 23.61 24.0
°/o Displacement 51.0 87.1 99.96
Drying time, Minutes 5 5.25 5

 

 

Test 3. Washing intermittently.
Procedure: This test was carried out with slurry I. A

liter of the slurry was poured into the bucdner funnel and de-
watered as in test 1. After the filtrate was measured, 100 cc
0f wash water was poured over the cake and filtered through.

AS near as possible, the last 10 cc of filtrate was collected

and tested for Nacl. This was then repeated until 600 cc of

wash water had been added.

 

 

 

Results. Table VI
Time cc Wash Water Titration°
0 00 185.4
5 101 183.0
10 203 112.9
15 301 2.7
20 404 0.8
25 504 0.45
30 606 0.00

 

 

 

 

 

° Note: Titration is empressed in cc N/lO AgNOS Per 10 cc

of Wash Water.

Discussion.

By referring to table III it is seen that the calculated
per cents of solids and Nacl are practically the same as the
actual. Any variation would be due to some of the nateriels
used not being pure.

The use of a small laboratory apparatus for determining
rate of filtration would not be accurate but an idea of a cer-
tain slurry's behavior could be observed. By referrizg to

able IV a good comparison of the different rates of filtrat-
ion using different cake thicknesses is found. According to
these results the capacity increases as the cake thickness de-

creases. This does not necessarially mean that with a thinner

cake more material could be filtered per twenty four hours,

because of the time required to clean and recharge the filter.

14

III. Derivation of equations of Walker, Lewis, and hcAdam
and Badger and KcCabe.
A. DiScussion.

The equations which are to follow have been worked out
for the most part by Walker, Lewis, and McAdams and Badger and
McCabe. The books "Principles of Chemical Engineering“ by
Walker, Lewis, and hcAdams and "Elements of Chemical Engineer-
ing" by Badger and HcCabe, have been used as reference and
the e;uation numbers will be the same as those in the respect—
ive books.

Although these equations have been derived by these res-
pective authors, they have not given complete derivations of
the fundamental filtration equations. In the following pages,
I have attempted to bring out all the points in the derivation
of these equations; especially those points which were not tak-
en up by the respective authors.

3. Derivation of Filtration Equations.

The filter cake may be sonsidered as equivalent to a
series of capulary tubes. he passing of a liquid through a
capillary tube is given by Poiseuilltb equation:

P=32IULCL
g

'where, P = pressure dr0p
,Ll= absolute viscosity of liquid .

L = length of tube.
6‘: linear velocity of tube.

D = diameter of capillary

15

For a filter cake of thickness L and area A with k capillaries,

 

P = SaAZL LC
gD2
01‘ (.62?ng
SBZZL
However, , the velocity is equivalent to volume of filtrate

per unit of time.

 

Then dv/de = k gk n3 D2 PA
“I'x BZAQ'L
or, = k k D4 ng A

 

128.6(L
”Although the filtration equations cannot by derived dir-
ectly from this equation, it helps to eXplain certain things in

developing~a workable filtration equationl."

 

1 Walker, Lewis, and chdams--Principles of Chemical Engineer-
inge--Bage 861.

The eiuation suggests that providing you have an incom-
pressable sludge, the rate of flor is diredtly proportional to
the pressure. It also suggests that for compressible cakes a
direct proportion between pressure and rate of flow does not
exist. The equation also suggests that the rate of flow of
filtrate decreases with the increased thickness of cake.

Differential Equations for Incogpressible Horogeneous
Sludges.

"Since the pressure drop through a cake is proportional
to the velocity of flow, we may consider filtration rate as

equal to driving force. That is, pressure divided by resist-

18

 

 

1 Principles of Cherical Engineering by Walker, Lewis, and
Kcidams---Page 581.
Nomenclature for following equations.
A = Total area of filt;“ing surface in sq. ft.
V = Total volume of filtrate in cu. ft.
v = Volume of cake as it collects on cloth, in cu. ft.
per unit volume of filtrate.
P = Pressure drop through cake.
Pi = Pressure drop hrough cake, filter, medium, press
channels.
8 = Total time of operation.
R = Total resistance of cake.
r = Specific resistance of cake.
r' = Coefficient in equation: r = r'PS
' r!‘ = Coefficient in equation: r = r"PS(dv/de)t
P/A = nesistance of press channels.
L = Thickness of cake at variable time.
S = Coefficient of compressibility.
t = Coefficient of velocity effect.

(Scouring effect.) Zero for homogeneous sludyes.

From above,

 

91. _ Pt ( 1 - p-363 - Wo,L., and T.)
d .—
9 n+P/A

In most cases the resistance of filter cloth and pure channels

can be disregarded, then,
(iv _ Z (13- " p.362 " 40,130, cad ,1.)
d9 B

17

Since resistance is proportional to lengtli “to l :oly pro-
portional to the ere» of a conductor, R = r L , and since,

the volume of a cake is LA, while sludge brought in by liquor

is vV, we have,

 

Substituting,

R = rv V

 

t1ien equation la becomes,

dv P ‘2 (3a - p.232 - V-,L-, and M-)

55" er

Differential Ecuaticns for Contoressi ble, Honoceneous

Sludges.

Substituting in 2a,

 

dv _ Pl-B A2 (3 - p.264 - W.,L., and m+>

 

 

 

 

 

a r'v V
Differential Equations for Comore sible, Eon—Ho WO' reous

Sludges.

R = rL/A (p.363 - W-,L-, and Lo)
and L = vV/A or dL = v dV/A
then R = 1‘ V (W

‘2
but r = r"PS(dV/Ade)t (p.36 5 - W. ,L., and r.)
8.10 Sit tutiixl Yv’e 1-C-Ve,
R = r"vPS g1, t EV
Ag+t d9

but, dV/de = P/R

18

substituting,

dV _
09 r" av t @v

 

dv -8 Af
65' ’
r" P‘ (%f dv

Integrated Eeuations.

 

 

Homogeneous Sludges.

Constant Pressure

 

y? _ 2 91‘s 9 (3a- w.L.&r.)
A2 r v.

Constant Rate
QX_ _ X; Constant = P1”8 A2 (3b)
d6 _ 9 I'V'V

Constant pressure Gradient through cake:

= Const. = r' V1+8 (30)

V A2 9 (1+8)

Sludges wi+ h Filter aids or equivelents.

Constant Pressure-

 

®v t dV Pl's A2+t
d§' = r" (dV/d9¥7

differentiate relative to Vo

(dV/de}t = P1"8 A8+t d(dV/dG)/dv
r"v (dV/de)2

Solve for dV

dV = P1“8 A2+t dinvzuel
r"V (dV/de)3+t
Integrate,
r"v (1+t) dV/de

 

19

Solve for dV/de,

 

91. = l+t Pl‘s A2+t 1
d9 r"'v(l+t). vI7I+f
Integrate,
3+t Pl‘s + t e l + t (4a)

H T.\')

r"(l+t)V' + t

I.
A
Derivetionlgf eguation 27 o Badger and EcCabe.
I.
A

 

2+t _ P1‘3 2 + t e 1 + t
‘ r"(l+t)V l + t

 

 

Taking logarithms,
2+t log V/A = l-s log P - log r"(l+t) + 1 + t log
(2+t/l+t) + 1 + t log 9 '

Dividing both sides od equation by l + t,

 

2+t los’E, = 1-8 log P - 10s r"(1+t) + log 2+t
1+5 A 1+? l+t ITIETZ'
+ log 9
taking the anti-10g,
2+t l-g
II” = PI“ 2+t lr"(l+t)vll+te

A (iii72'
If log 9 be plotted against 105 V, we will obtain a straight
line with a slope of (2+t/1+t). (2+t/l+t) is a constant and
for simplicity we may substitute m. In a similar manner if
we plot log 9 against log P we will have a straight line those
slope is (l-s/l+t). For (l-B/l+t) we may substitute n.

The value of 2 + t [I"(1+t)‘7ll+t is also a con-
(1+t)2

stant and k may be substituted in its place.
Then with these new constants, equation 4a becomes,

1_m _ Pn k e . (27s - s. a n.)
A _

C. Conslusions:

The derivations of the above equations are very diffi-
cult and beyond the comprehension of the ordinary student.
The application of such equations would then be difficult
without some understanting of their origin.

The sonstant k cannot have any physical significance
because it depends upon so many factors. The constant k
which equals 2 + l lr"(l+t)'v|l+t. k is therefore

(1+t)2
dependent upon t, the coefficient of velocity effect,v the
volume of cake as it collects upon the filter in cu. ft. per

unit volume of filtrate and r" which is a coefficien in

equation r = IH P8 (dV/Ade).

IV. Application of equations of "Elements of Chemical Enri-
neering" by Badger and McCabe, to the Filter press, Suction
Filter and L =af Filter and comparing the value of the con—

stants.

A. Slurry I.

'I I

Procedure: The apparatus used in his work is shown in :1 g's.

q

ess coisists of plat er a frames

H

1, 2, 3, and 4. The filter p"
and a filter medium. Two presses were used in my work. The
larger press having fromes 8.5" X 8.5", or a filter area of

134 square inches. The other press is smaller having a filter
area of 32 sq. in. (tr 0 surfaces). The auxillary eeuip21ent to
the press, consists of a blow tank equipped with an air line,
water line, steam line and a vacuum.line for filling.

'The filter press, (fie. 1), was first fitted with a filt-
er cloth (one frame being used) and then the slurry to be filt—
ered was drav n into the blow tank thr ugh the flexible rubber
hose, by means of vacuum. It will be noticed that the air line
extends nearly to the bottom of the blow tank, to keep the
slurry aggitated during the filtrations.

A set of Toledo scales, which weigh accurately to 1/4 of
an ounce, were set in such a position that the filtrate was
allowed to run from the press into a cents; ner on th: scales.

his made it possible to record the exact quantity of filtrate
at any given time.
he air in the blow tank was then turned on and tne ee-

1red pressure regulated by means of the felief cock, When

t5 ('-
(g1;

the desired pressure was obtained the value into the press

was opened, the pressure being kept constant by regulating the

relief cock.

‘5)

The filtration cvcle was divided into periods ,nd at the
J -

flu

end of each perio , the exact weipht of filtrate was recorded.

1. Filter Press-

 

 

 

Data: Table VIII

Period Time(Sec.) Filtrate(lgL.) Total FiltratePressure
1 240 4 11/16 4 11/16 25

2 480 2 13/16 6 14/16 :5

5 720 1 7/16 8 5/16 25

4 1280 1 15/16 10 4/16 25

1 240 5 7/16 5 7/16 35

2 480 2 7/16 7 14/16 35

3 720 1 12/16 9 10/16 ‘ 35

4 1280 2 2/16 11 12/16 55

 

 

 

 

 

Calculations:
a. Determination of filter constants:
(if = kPne Where,
A .
V = lbs. of Filtrate

A

in sq. inches.
0 = in seconds-
The value of m may be obtained by plotting log 9 vs. log V

for a y given run and observing the slope of the line- (Fig. §)

 

”'0‘." ‘4'.»

,‘r..
l
1
4
I
r
I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table IX

Data for fig. 5

7X)

()3

 

 

 

 

 

 

 

Point 9 V Log 9 Log V

1 240 4.688 2.3802 0.6710
2 480 6.876 2.6812 0.8374
3 720 8.312 2.8573 0.9157
4 1280 10.250 3.1072 1.0107
5 240 5.438 2.3802 0.7355
6 480 7.876 2.6812 0.8963
7 720 9.625 2.8573 0.9884
8 1280 11.750 3.1072 1.0700

 

The slope of line =

Now we have,

-/14= 10857 =m

1.857
Gflgé) = k F“ = 9

Applying this equation to the two runs for a convenient value

 

 

 

 

 

 

 

of V and choosing as this value of V whose log 0.9. V =
7.944 1.857
'jfifi:> = k Pn e = .00485

Where 9 is the time at which V = 7.944

The value of e at which log V = 0.9 are:
Table X Data for figure 6

Run Press Log P Log 6 at log V = 0.9 e in sec.

1 25 1.3979 2.81 646

, 2 35 1.5441 2.69 490

 

Plotting 10g 6 vs. log P of table X we have,

 

 

-e6

.'1 "111

'1

. ..!-II‘ I. Apt-1..

. 1‘..- -Adnt ax

 

 

 

 

a
Icy/D mum

IJ

A5“

 

lnti... a iimllllmb
a. a

s
2

‘
eméduvh k, htsk g

 

 

 

 

 

 

 

 

24

n = slope of line = l5/19.5 = .77
Choosing convenient values of log P and log 6, fig. 6: log P
= 1.3979 , log 6 = 2.81. Substituting these values,
Log .00485 = 1.3979 X 77 + 2.81
___1?__

k = 000485
LOg 3.885

 

7670

k = 0000000637

Rewriting equations,

(h??”857 = .oooooossv P°77 o

A

Changing to engineering units

Units Used Eng. Units Factor

V Filtrate Cu. ft. 64.5

A Sq. in. Sq. ft. 144

9 Seconds hours 3600

P /Sq0/ino /sq.in. 1
108.)? 64.5 1.857

(E) - ‘11:” = .ooooooss7 P’77 3600 9
1.857 or

_ 0006495

(X) = - 25 P‘77 9
1.857

C§> = .010185 P'77 e

2. Calculation of filtering times:-

For 1" frame

1.857
17- 77
A = .010185 P' 9

1.857
(1%? .—. .010185 (25)“779

25

.1218 G

.0314

9 .258 hours
9 = 15.5 minutes.
For 2” frames.

Calculations same as for 1" frame.

.142 x 2.125 1 _
1.125 = '643

- 1.857
(’43-?) = .1218 9

9 = .903 hours

 

e = 55 minutes.
For 3” frames.

9 a 1.69 hours

9 = 102 minutes
For 4“ frames-
2.85 hours

9
9

172 minutes.

2. Suction Filter
Procedure:

1e apparatus used in this case is shown in fir. 3

\J 9

which is an ordinarr suction filter havi.5 a filter area of
154 sq. in.
The method of taking samples, using the suction filter
is not as accurate as that used in the case of the filter press.
The outside diameter of the drain cock of the filter is

about 1 1/4" and was fitted with a rubber stopper. A four

26

liter bottle was attached to .he stopper and supuorted to
prevent its falling off the stopper under the Wei ht of the
filtrate. A second hole was put in the stopper in which res
inserted a piece of ordinary glass tubing. This was then con-'
nected to the vacuum line on the Opposite side of the
by means of rubber tubing. This arraniement equilized the
pressure in the bottle and filter after the bottle had been
remoVed and put in position again. A pinch clamp was used on
the rubber tubing when the bottle was removed, to prevent los-
ing the vacuum. .

The vacuum was built up in the vacuum line and tTe slurry
poured over the filter cloth. The vacuum was then turned on
and the drain cock on the filter opened. With tie pressure
equalized the filtrate runs directly into the bottle-

At the end of a certain period of time the drain valve
was closed, the receiving bottle emoved and filtrate weighed
an‘ the receiving bottle placed in position again. This pro-
cess was repeated until the filtration cycle was completed.

Although this rethod is not as accurate as the sampling

method of the filter press, satisfactory results may be obtain-

 

 

ed after some practice.
Data: Table XI _
Run I Per sq. ft. area ure

Period Time(seco) Filtrate(lbs) Total Filtrate(lbs.) Press-

 

 

1 120 4 1/16 4.06 12.5
2 240 1 15/16 5.02 12.5
360 1 9/15 7.58 12.

01

5
720 3 15/16 11.50 12.5

VP.

 

 

 

 

 

 

27

 

 

 

 

 

 

 

 

 

 

 

 

Table¥X1 (Gontinued)

, Per sq. ft. Area
Period[Time(sec) Filtrate(lbs) Total Filtrate(1b J Pressure
1 147 3 13/15 380 7.32
2 300 2 1/13 5.89 7.32
3 450 1 8/18 7.41 7.32
4 1080 4 10/18 12.00 7.32
1 200 3 12/18 3.75 4.9
2 400- 1 12/16 5.50 4.9
3 600 1 7/16 6.91 4.9
4 1200 3 12/16 10.70 4.9
Weight of slurry charged. 20*
°/° Water in cake 63 °/°
Filtef Area (sq. in.) 154
Cake thickness (in.) 5/4
Volume of cake (cu. in.) 106
Temperature 19° C
Calculations:

All calculations same as in (1) above.

1. Det. of filter constants.

 

 

 

Table XII m,= slope = 1.75
V 9 Log V Log 9
4.06 120 0.6085 2.0795
8.02 240 0.7800 . 2.3805
7.58 560 0.8800 2.5550
11.50 720 1.0810 2.8750

 

 

 

 

 

 

o I I . -- nulllio-'llll..o It. I

 

 

u
_.
rll‘I'lI I. II ‘ .II I '. I'Il II Iii‘..l 'I’I'li'll I

r—--- I

i, l 'l ' I'- I l'!' I .I. I'll I- .'.'.'I ' I ". .

.| ‘ii'l".l' 0‘

 

 

 

   

   

.
R

up.

 

 

 

 

 

 

 

 

 

 

 

 

 

......

 

.1’._

 

 

+~ "-1-

 

 

 

 

 

 

 

 

a9 abfl

mic/immu- .4»

I
o

escalates-a?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

k Pn 9

Table ill (Continued)
V 9 Log V Log 9
p3.s 147* 0.5800 2.1575
5.89 300 0.7705 2.4775
7.41 450 0.8700 2.5555
12.00 1080 0.7950 5.0355
3.75 200 0.5705 2.3150 7
5.50 400 0.7595 2.8205
8.91 800 0.8595 2.7785
10.70 1200 1.0295 5.0795
M = sIOpe = 1.75
Data. Det. of n. ‘
Table XIII n = slope = 0.741

Run Pressure LOg P Log 9 at log V = 8.31 9 in sec.
1 12.5 1.097 2.41 257
2 7.82 0.884 2.545 550
3 4.90 0.890 2.700 501

m = 1.75

n = 0.741

= .072 (Pressure = 12.5 / sq. in.)
2. Calculation 6f filter times.
For 1" cake V = 18.00 #
A = 154 sq. in.
P = 12.5 / sq. in.

2.1 igM-dr'e 8

 

 

 

 

—'—1 “A“
I

 

 

 

 

_... .-~‘--._

 

 

 

a4! a: as a7 08 a9 10 n a: 2.! M!
£0} ’47- xax'eosam //7 @m f‘

O

I

 

 

 

 

 

 

288 1.75 ,
6757-) = .078 X (12.5)07‘1-1 e
(.2sa)1'75 = .072 x 5.5 e

9 = .214 hours

9 = 13 minutes.

For 2” cakes.

V = 028 .. = .541

K
.60

 

8 X 2.125
lol

9 = .848 hours

39 minutes.

(I)
II

For 3" cakes.

V = .288 X 3-125

1.125
.80 1075
(To)

9

= .80

.072 X 6.5 X 9

1.29 hours

9 77 minutes.

For 4” cakes.

V = 0288 x 40125
1.125

 

= 04875 9
e = 2.1 hours

9 = 127 minutes.

3. Leaf Filter
Procedure:

The apparatus used in this eXperiment is shown in fig. 4.

30

The apparatus consists of a filtrate tank which is con-
n3cted to the vacuum line and to the air line, and a frame
which supports a filter cloth. The frame is a g" pipe, welded
in the shape of a square, 12" on a side, with holes on the in-
side of the pipe, through which the filtrate passes. Two
pieces of 1/4" mesh wire screen are place between the filter
clothes as a sup: JOIt to then. This prevents the cloths being
pulled together and sriutt in:; of the vacuum.

The slurry to be filtered was placed in a 15 gallon
crock on a large set of Toledo scales. A perforated pipe, 1/8"
in diameter was laid in the bottom of the crock and connected
to the compressed air line. The air was turned on a: c the pre-
cipi mt te vas kept in sus1s._on during the filtration c; cle.

+1.:

The vacuum was then turned on in bus filtra

(1*

e tar 1: and the leaf
placed in the crock. The scales were t1en be elanceda the
vacuum in the leaf turn d on, the time being not d at
stance.

he less in wei-

01

At the end of a certain perio of time th

{(1)

ght of slurry was noted an; ulated. This was repeated 1 -

Q

til four losses in weight had been recorded.

Data: Table XIV -

 

Period Time(sec) Filtrate(lbs) TOtal Tiltrate(lbs) Pressure

 

 

1 240 10 10 11

2 480 4.5 14.75 11
3 720 3.5 18.25 11
4 1080 4.75 23 11

 

 

 

 

 

 

31

 

 

 

 

 

 

 

 

Table XIV Continued)
Period Time(sec) Filtrate(lbs) Total Filtrate(lbs) Pressure
1 240 9.25 9.25 64
2 480 4.5 13.75 84
3 720 3.5 17.25 EA
4 1200 5.5 22.75 EA
Temperature 20° 0.
Cake thickness 2.25"
0/o Water in cake 63°/o
Filter area Sq. in. 288

Calculations:

All calculations same as for filter press.

 

 

 

 

 

 

 

 

 

 

 

1. Det. of filter constants.
Data for Det. of m
Table XV
Point 9 v loge 109; v ‘fi
1 240 10.0 2.5802 1.0050
2 480 14.75 2.8812 1.1888
5 720 18.25 2.8572 1.2815
4 1080 23.00 3.0534 1.3817
5 240 8.25 2.5802 0.9881
8 480 15.75 2.8812 1.1380
7. 720 17.25 2.8572 1.2388
3 1200 22.75 3.0792 1.5588
m = slope = 1.84 (fig. 8)

 

ire 9

3131

 

 

 

.- 31w»: '3: ~

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Data for Det. of n

 

 

 

 

 

 

 

 

Table XVI
Run Pressure Log P Log 9 at log V = 1.5817 8 in sec.
1 11 1.0414 5.0354 1080
2 8.4 0.8082 3 5.085 1218
n = slope = .241 (fig. 10)

m = 1.84

n = .241

k = .0778

2. Calculations of the filtering times same as for filter

press.

For 1" cake

(11m

=kPn9

V 0-368 cu.

A 2 sq. ft.

.94
.388 .941
“'2“ = .0775 (11) “' e

O
(D
.p
I

— .272 9

For 2" cake.

 

e = .182 hours
9 = 10 minutes
V = .5881¥l§élg§_ = 0.895

1 1.34
6.55.3.4) = .272 9

ft.

11 pounds /sq. in.

 

71

3
Ho

jjur'e 10

-PI‘I~. '. 1'." I

 

 

 

 

$50

39‘

1:

'4'

€~77aun&can(v
‘4 °' "' I:
‘ bl

t’

2.6

 

 

 

1%

z 03 0? 0.5 0.6 ~é‘1*'-'b'e' a9 40 1:1 /2
(gyro—Wart»? -.-..~ 1%um6'

A! (-

 

 

 

 

 

 

 

 

 

 

00

.143 = .272 9
9 = .528 hours

9 = 32 311111113880

For 5" cakes.

i3) = 1002 0110 ft.

For 4“ cakes.

 

1.78 hours

(I)
ll

9 = 101 minutes.

Table XVII Comparison of filter constants.

 

 

 

Filter m n k
Filter press 1.85 .77 .01018
Suction Filter 1.75 .741 .072
Leaf Filter 1.84 .241 .0776

 

 

 

 

 

Bo' Slurry II
Procedure: The prodedure using slurry II was exactly the same
as that of slurry I. The apparatus was also the same, except

that with slutty II the leaf filter was not used.

1. Filter Press.

.34

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Data: Table XVIII
Period Time(sec) Filtrate(lbs) Total Filtrate(1bs) Pressure
1 60 11 15/18 11 13/18 35
2 120 5 13/18 17 10/18 55
3 240 4 8/18 22 35
1 70 9 1/18 9 1/18 25
2 140 4 15/18 15 14/18 25
3 300 6 14/18 20 12/18 25
0 Run I Run II
Average Pressure 35 85
Wet Cake (51118.) 1840 1922
Cake Thickness 1.575 1.57V
Filter Area (sq. in.) 154 134
Temperature of slurry 19° 0 19° C
°/o Water 41.0 48.5
Calculations:

I- Bet. of filter constants.

(1)2 = 1

' 9

II

20075 = O

2. Bet. of filtering times.

constant 25 / sq.

552

0110

in.

ft.

 

35

Fpr 1" frame
6 = 5 minutes.

For 2“ frame

 

 

 

 

V = .332 X 20125 = 0628
1.125
.828 3 = 1.58 x e
.924
9 = 18 minutes.
For 3" frame
v = .332 X 3.125 = .924
1.125
.814 3 = 1.56 e
.924
e = 38 minutes.
For 4" frame
V = 332 X 4.125 = 1.32
1.125 '
10222 = 1056 8
.924 ,
1074: = 1056 9
e = 87 minutes

2. Suction Filter

 

 

 

 

Data: Table XIX

Period Time(sec) Filtrate(lbs) Total Filtrate(lbs) Pressure
1 60 7 4 ’ 7 4 9.82

2 120 8 9/18 14 4 1 9.82

2 180 8 5/18 20 6/18 9.82

4 240 6 26 6/15 9.82

5 375 8 7/18 _ 34 13/18 9.82

 

 

 

 

 

 

Table KlK (Continued)

 

 

 

 

 

 

 

 

 

 

Period Time(sec) Filtrate(1bs) Total Filtrate(lbs) Pressure
1 75 8 8/16 8 8/18 7.85
2 150 8 8/18 18 14/18 7.85
3 225 7 2/18 24 7.85
4 300 4 8/18 28 8/18 7.85
5 455 8 8/18 54 12/18 7/85
Run I Run II
Volume of feed (cuff) 0.72 0.72
°/o Water 43 45
Filter Area 154 154
Cake Thickness 15/16 15/16

 

 

 

Calculati

0118:

Calculations same as in (l) for filter press.

10 Deto
k =
2. Det.

For

For

For

of constant.

2063 V =

of filtering times.

1“ cake

9 = 13 minutes.

2" cake
9 = 38 minutes.
3" cake
9 = 76 minutes.
4" cake

6 = 128 minutes.

54.75 at 15/18" cake

 

V Testing the Validity of Filtration equations of Badger and

McCabe.

Procedure:

the filter press in part IV sec.

made instead of two.

After the data had been taken and the Value of

ermined,

the value of n was determined for three values.

The procedure in this case was the same as that for

'1, except that four runs were

:11 VIE—S det-

This

was done by drawing a line through any three points as shown

in figure 12.

 

 

 

 

 

 

 

Data: Tablexx

Period Time(sec) Filtrate(1bn) Total (lbs)thta1 F11. Press-
Filtrate Per sq. ure.

1 250 4 15/18 4 15/18 5.51 15

2 500 2 5/18 7 4/18 7.80 15

5 750 1 14/16 9 2/18 9.82 15

4 1080 1 12/18 10 14/18 11.70 15

1 240 5 9/18 5 9/18 6.00 20

2 480 2 8/18 8 1/16 8.87 20

5 720 1 12/18 9 15/18 10.55 20

4 1080 1. 5/16 11 13/16 13.40 30

1 250 5 12/18 5 12/18 8.18 25

2 480 2 11/18 8 7/18 9.18 25

5 890 1 11/18 10 2/18 10.90 25

4 960 1 15/18 12 1/18 12.95 25

 

 

 

 

 

 

 

17w

 

88

 

 

 

 

 

 

 

 

 

 

Table 11 Continued)

Period Time(sec) Filtrate<lbs) Total(1bs) Total Filt. Press-

' ‘ Filtrate Per sq. ft. ure
1 50 2 8/16 2 8/18 2.69 52
2 155 2 8/16 5 5.57 32
3 525 2 8/18 7 8/18 8.06 52
4 555 2 8/18 10 10.75 52
5 900 2 4/16 12 4/16 13.28 52
Filter Area (sq. in.) 134
Temperature 18° C
Calculations:

(§)m = k Pn 9
Where, = Filtrate in pounds.

mon. and k =

V
A = Area in sq. in.
P
9.

Time in seconds.

Press. in /sq. in.

constants.

The value of m is obtained by plotting log 9 vs. log V

and observing the slope of line. (fig. 11)

 

 

 

Table XXI
Point 9 V Log 9 Log V
1 250 5.51 2.5979 0.7251
2 500 7.80 2.8990 0.8921
3 750 9.82 2.8751 0.9921
4 1080 11.70 5.0554 1.0882

 

 

 

 

 

 

 

 

Figure 11

 

 

 

 

 

E

3 «Run».
”.3. u

9

222 .22 .
22,222“

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table ifil (Dentinned)

 

 

 

 

 

 

 

 

 

Point 8 ; v. Log 8 Log v
5 240 8.00 2.5802 0.7782
8 480 8.89 2.8812 0.9590
7 720 10.55 2.8575 1.0252
8 '1080 12.40 5.0554 1.0954
9 . 250 8.18 2.5817 0.7910
10 480 9.18 2.8828 0.9819
11 890 10.90 2.8588 1.0574
12 980 12.95 2.9825 1.1122
15 50 2.89 1.8990 0.4298
14 155 5.57 2.1905 0.7500
15 525 8.08 2.5119 0.9085
18 555 10.75 2.7445 1.0514
17 900 15.28 2.9542 1.1214

 

 

 

 

 

Plotting and observing slope, (fig.ll) m
. A 1085
we now nave, (%) = k Pn 6

Applying this equation to the four runs for a convenient

value of V, and choosing as this

V = 5.31. Then,

value of V whose log = 0.8;

 

8031 1085
3 = k Pn 9 = 000035

where 9 is the time at which V = 6.51 . The value of 9 for

the different pressures may be taken from fig. 11.

.32‘ i 5113 'e 1 2

 

 

 

.0.

 

 

 

9
/
d m
\\ 7
/
h x
.. w. a
e.
.2 , 2
.\ ..
x .r.\ ¥
.4. /
x
k J
\ x
x
. u M
o
/
.0
/
6
p. a 3 2 2 2 2 / I
.1 .3ka !- QWOV

 

Zc‘yP-ansure ‘ If} [dbl/”d!

 

 

 

 

 

 

40

Table XXII

 

 

 

Run Pressure Log P Log 9 at log V: 0.8 9 in sec.
1 15 1.1761 2.525 555
2 20 1.5010 2.420 285
3 25 1.5979 2.570 253
4 52 1.5051 2.515 207

 

 

 

 

 

Plotting log 9 against log P (fig. 12)1 n = slope of line
. = 0533

 

1Note: By referring to fig. 12 it may be seen that all the
points do not fall in a straight line. If only three runs had
been made the value of n might have been either of two other

values, as illustrated.

By combining runs 1, 2, and 5, n .425
By combining runs 2, 5, and 4, n = .682
Choosing convenient values of log P and log 9 from fig. 12
log P = 1.5979; log 8 = 2.570.
Substituting these values of log P and log 8 we have,
.0055 = k(25)'533 254.
Rearranging and taking logs we have,
2.57 = -.555(l.5979) + .0055/k
2.57 = -.746 + .0055/k

k = 00035 = 00035 = 000000268

Changing to engineering units

 

Units use Eng. units. Factor
v of filtrate cu. ft. 82.5
A Sq. in. sq. ft. 144
9 in seconds hours 5800
P /sq. in. /sq. in. 1

.00000288 p'533 e 5800

A K “1:2”

(%)fi.85 =

A

.009648 _
(.454)l.85

.533

 

8

.0448 P°553 8

By substituting the two other values of n in the equation a

different value of k is obtained for each value of n. The
ultimate results are exactly the 8528, however, because n and

k vary directly with each other.

 

 

Table XXIII
m n k
1.85 . .555 0.0448
1.85 .425 0.0845
1.85 .882 0.0272

 

 

 

 

 

2. Calculation of filtering times.

V = 12-00
P = 25
A = .924 sq. ft.

For 1" frames

.1921085_
7924. ' —

)‘533 = 5.88

A
to
(fl

.055 = .0448 X 5.83 e

e = 0.218 hours

8 15 minutes.
For 2" frames

V = .792 X 2.125 '= .363 cu. ft.
1.125

0363 1085
.92 4) = .0448 X 5.65 G

.183 = .0448 X 5.65 9

 

e = 0.725 hours
9 = 45 minutes.
For 5" frames.

v = .192 x 5.125 = .555 cu. ft.
1.125

1.85
(§§§§> = .0848 x 5.88 8

0362 = 0252 e

 

e 1.45 hours

9 = 87 minutes.

V = .192 X 4.135 = .705 cu. ft.

 

1.125
.7 5 1.85
.808 = 0.252 8

9 = 2.41 hours
9 = 145 minutes.
Table XXXIV

Comparison of actual and calculated filtering times.

Units use Eng. units. Factor
V of filtrate cu. ft. 82.5
A Sq. in. sq. ft. 144
9 in seconds hours 5800
P /sq. in. /sq. in. l

1’85 ' 1085 .
(F. x <§§j§> - .00000288 P'553 8 5800

A
(91°85 1992.842. _ P233 9
A " (.454)1.85
1.85 ,
(LE. = .0448 13.5.33 9

By substituting the two other values of n in the equation a
different value of k is obtained for each value of n. The
ultimate results are exactly the same, however, because n and

k vary directly with each other.

 

 

Table XXIII
m n k
1.85 , .555 0.0448
1.85 .425 0.0845
1.85 .882 0.0272

 

 

 

 

 

2. Calculation of filtering times.
V = 12°00
P = 25
A = .924 sq. ft.

For 1" frames

.192 1'85 _-
1'52: - = '0”

(25).533 = 5065
.055 = .0448 X 5.85 e
9 0.218 hours

9

15 minutes-

For 2" frames

v = 079

 

20125 '= 0363 C“. ft-
5

0363 1085
.924) '— 00448 X 5.88 9

0182 = 00448 x 5063 9

e = 0.725 hours
9 = 45 minutes.

For 5" frames.

 

V = .193 X 5.125 = .555 cu. ft.
1.125
1.85
<§g§g> = 00946 X 5066 9
0362 = 0252 e
9 = 1.45 hours

9 = 87 minutes.

For 4" frame.

 

 

v = 0192 X 40135 = .705 cu. ft.
1.125
07 5 1’85
(fig-7;) = .0448 x 5.88 8
0606 = 00252 e

9 = 2.41 hours
9 = 145 minutes.
Table XXXIV

Comparison of actual and calculated filtering times.

43

 

 

 

 

 

 

 

Cake thickness Calculated Actual °/° Variation
Filtering T. Filter. To from actual
1.375 13 16 18.75
2.375 43 54 20.40
. 3.575 87 100.5 13.40
4.575 145 185 21.65
Discussion:

 

According to Badger and HcCabe (2) the values of the

constants in heir equation for non-homogeneous sludges, (278)1

 

1 Elements of Chem. Eng. b1_Badfier and HcCabe.

have a definite relation to the character of the slud;e. "Since
the value of m is not quite 8.0, the sludge is not quite homo-
geneous, but nearly so. On the other hand, n is far from 1.0,

. . .. . . 2
and nence the sludge 18 very nignly compressible."

 

E_£1ements of Chem. Eng. page 464

The value of tnese constants (m and n) do not seem to give
one and idea as to tie character of the sludge according to my
work. By referring to fié. 11, it may be seen that the value
of m equals 1.84, and since the slurry was made up to be non-
homogeneous here is agreement with the equation of Badger and
KcCabe (2). However, suppose instead of limiting the amount of
collodial material, as was the case here, we increase it to
say fifty per cent of the total solids.

In this case the filtration will be much more difficult

and the time required to obtain a definite amount of filtrate,

 

44

J

will be greater than was the time raquired for the same amount

of filtrate, using slurry I. In other words the lines of the
graph (fig. 11) will approach the vertical position with the

rester amount of collodial material. Then th value of m

be

would be greater than 2, (providing enough A1(OH)3 had been
used) which according to Badger and IcCabe (2) would make the
sludge homogeneous, although the slurry was originally made so
as to be non-homogeneous.

On the other hand, when you do have a homogeneous sludge,
it is true, except incnse of collodial or finely divided part-
icles, the rate of filtration is greater tlan in nest eases of
non-homogeneous sludges. According to this reasoning more
filtrate will be obtained per unit time. The lines in LL€
graph (fig- 11) will then flatten out and the value of m will
become less. This will tend to show that the sludge is non-
homogeneous. This is exactly what happened in the case of
slurry II.

The value of n also apparently fails to ascertain the
character of the sludge. Supposedly the closer the value of
n approaches 1.0, the less compressible is the sludge. By
referrinq to the graph (fig. 12) it may be seen that n may
have different values for the same sludge. In this case the

values of n vary from about 0.4 to nearly 0.7. It would be

w
0
H,
:3
’—
O
H

possible to even have greater variation in the valua
the same sludge.
This could be done by making a greater number 0

ahing different combinations of points. These

Bi ‘u‘r'e 12

 

 

 

 

 

h.c_.._.

.-

N
'f

h
'fi

. -m ch / 0‘ ~

[0 0
N yin
(a f

22

2/

l9

 

{-0 '
‘3 7 z ”(I)“:
- ‘ i
n /
. Q. -
‘\ 7“
K ‘\
x 'i
K‘
C \
. \_£'\ .
.\ x ‘\.
\ \\_ _
“u \ \
\
i
x \
\
‘\

 

"lead: 419

/0

l/ [.2 I! [4'

Aqu~ansure ://7 fibofldl

/..5' K‘ [7

A!

1
Q

/9

 

 

 

 

 

 

4O

 

 

able XXII
Run Pressure Log P Log 9 at log V: 0.8 e in sec.
1 15 1.1761 2.525 335
2 20 1.3010 2.420 263
3 25 1.3979 2.370 233
4 32 1.5051 2.315 207

 

 

 

 

 

 

Plotting log 8 against log P (f’g. 12)1 n = slope of line

II

.533

 

1Note: By referring to fig. 12 it may be seen that all the
points do not fall in a straight line. If only three runs had

been made the value of n might have been either of two other

values, as illustrated.

By combining runs 1, 2, and 3, n = .425
By combining runs 2, 3, and 4, n = .682

Choosing convenient values of log P and log 9 from fig. 12
log P = 1.3979; log 9 = 2.370.
Substituting these values of log P and log 9 we have,
.0035 = 1:(25)°533 234.
Rearranging and taking logs we have,
2.37 = —.533(1.3979) + .O 35/k
2.37

-.746 + .0035/k

00035 = 00035 = 000000868
30:10 1305

Changing to engineering units

k

 

Units use

V of filtrate
A Sq. in.

9 in seconds

P

/sq. in.

2.1. .85 62.5 1.85
A X “TEE
((7)1085
1.85
(1:)

Eng- units.
cu. ft.
sq. ft.
hours

/sq. in.

o00000268 P'533 e 3600

(,434)1.85

.009648 .533 e

.0446 P°533 9

By substituting the twO otlzer values of n in t1 e

equation a

different value of k is obtained for each value of n. The

ultimate results are exactly the same, however,

k vary directly with

each other.

because n and

 

 

 

 

Table XXIII
m n k
1.85 .533 0.0446
1.85 .425 0.0845
1.85 .682 0.0272

 

 

 

2. Calculation of filtering times.

For 1" frames

<§%§§)1.85=

12.00
25
.924 sq. ft.

(25)°533 = 5.66

.055 = .0448 X 5.63 e
9 = 13 minutes.

For 2" frames

V

.363 1'85
71'). 2 .0446 x 5.66 e

.0446 X 5.63 9

 

o
*4
C0
[0
II

0.723 hours

G)
H

9 = 43 minutes.
For 3" frames.

V = .192 X 3-125 = .533 cu. ft.
1.125

 

1.
(Eggg' = 00946 X 5066 9

.382 = .252 e
9 = 1.43 hours
9 = 87 minutes.

For 4" frame.

 

V = 0192 X 401245 = 0705 C110 ft.
1.125
. 1.85
(7%,?) = .0446 x 5.86 e
0606 = 00252 9

9 = 2.41 hours
9 = 145 minutes.
Table XXXIV

Comparison of actual and calculated filtering times.

43

 

 

 

 

 

 

 

Cake thickness Calculated Actual °/o Variation
Filtering To Filter. T- fram actual
1.375 13 16 18.75
2.375 43 54 20.40
. 3.375 87 100.5 13.40
4.375 145 185 21.65
T‘iscussion:

 

According to Badger and "cCa—be (2) th is values of the

constants in their equation for non-homogeneous sludges, (278)1

 

1 Elements of Chem. Eng, b1_B- -d;; or and thabe.

have a definite relation to the character of he slud3e. "Since
the value of m is not quite 2.0, the slud3e is not quite homo-
geneous, but nearly so. On the other hand, n is far from 1.0,

q

an. hence the sludge is very highly compressible."

 

Elements of Chemo Eng3_paee 464

The value of these constants (m and n) do not seem to give
one and idea as to the character of the slud3r e ac cording to my
work. By referrin3 to fi3. 11, it may be seen that the value
of m equals 1.84, and since the slurry was made up to be non-
horao3eneous there is a3reerent nit h the equation of Badger and
thabe (2). However, suppose instead of limiting ne amount of
collodial materia , as was the case here, we increa.se it to
say fifty per cent of the total solids

on will be much rore di““icult

H

In this case the filt

.nc the time required to obtain a definite amount of filtrate,

 

44

will be greater t?_:an was the time r wq ired for the. sage amount
of filtrate, using slurry I. In other words the lines of the
3 aph (fi3. 11) will approach the vertical position vith the

raster amelnt of collodial mater‘al. Th n the v31ue of m
would be greater than 2, (providing enough Al(OH)3 had been
used) which Hccordl ~ to Badger and KcCabe (2) would malce the
sludge hono.;wene01s, althou3h the slurrv was ori3inelly made so
as to be non-hom03eneous.

On tile other hand, when you do have a homogeneous slud3e,
it is true, except incnse of 0011061 31 or fine ly divided part-
icles, the rate of filtration is greater tLan in nest cases of
non-hom03eneous slud3es- According to this reasoning more
filtrate will be obtained per unit time. The lines in tle

(fig. 11) will then flatten out and the value of m will
become less. This will tend to show that the slud3e is non-
homogeneous. This is exactly what happened in t e case of
slurry II.

The value of n also apparently fails to ascertain the

cha acter of t? -e slud; e. Supposedly the closer the value of

preaches 1.0, the less compressible is the sludge. By

L

n ap
referring to the graph (£13. 12) it may be seen that n ma"
have different values for the say e sluc 38. In this case the
values of n v; I} from about 0.4 to nearly 0.7. It would be
possible to even have 3reater variation in the value of n for
the same slud3e.

This could be done by makin a greater number of runs and

Jin3 different com inations of points- These points of the

v.5
(1"!

gr aph (fig. 12) do not lie in a straight line because tLe posi-

tion of the points depend upon the distance apart of tie lines

n graph (fig. ll). The position of these lines deie-d upon

Po

the difference in pressures of tLe two runs. The ;re:t;r t: e
distance oett een these lines t11e greater the irregularity ofi
the points in fig. 12.

As far as the different values of n are concerned they will
not affect the workibility of the equation. The value of n and
k are directly proportional to each other and as n and k vary
the values of P and 9 remain the same for a particular run.

‘I

1 . 1 . 1 .. . 0
Tue ult1mate results oota1ned Dy tnis equation are not

 

°1. Eq. 278 Elements of Che :3. End. by Badger and IcCabe-

very satisfactory. By referring to table XXIII it may be seen
that the calculatéd filtering ti1res va ry from the actual filt-
ering tines all tLe way from 18.75 °/° to 26.85 °/o- The varia-

tion being greater with the increased thickness of cake.

N

VI. First attempt to develOpe a more accarate equation for

predicting filtration times.

Procedure:

The equation which is to follow was not worked out from a
mathematical standpoint but from actual experiments carried out
in the laboratory. These equations hate no theoritical backing
but check up fairly well with actual eXperimental data. They
check at least as good, and better inlmost cases, as the results
obtained when applied to the equations of Walker, Lewis, and
KcAdams (l) as Badger and EcCebe (2).

I first drew a picture of a 1, 2, S, and 4 inch cake (fig.

13). The 2, 3, and 4 inch shes being drawn representin- cakes

(w-
Cf.

1nd been filtered except for the final one inch in tle

r-1

‘V
C 1.

Fl.

nh
center of the cake. The total time to filter a one inch cake
was accurately determined. Then the time to filter a two inch
cake will be equal to the time to filter a one inch cake plus
the time to filter an additional one inch cake. Tne time to
filter this final one inch cake will take longer than the first

one inch cake because of the increased resistance due to the

r ° 4. a. u.- ‘- at: i 1, a ‘m ~_ r
assage of filtrate t :oh n that care thicn nus alIQLQJ been

’0

filtered. To illustrate by referring to fir. 13 the time to

filter II will be the time to filter a'+ b' + c'. But the time

required to filter a'b' is the same as the time to filter a+b.
Then the time required to filter c' is dependent upon some

‘

power of the thickness. From many actual filtrations runs tnis

JV ' r A:

-lh-l‘.

Figure 15

 

 

 

l/ ,'( I)

4’
L..J

. 44{.1. ‘

 

arIIII |.I

 

 

 

 

 

 

 

 

47

power was observed to be tne first. Then the time to filter II
will be,

9 = 91 + n X 91 (l)

8
where, 9“ = time to filter II
9 = time to filter
n = thickness of II
The same thing holds for the 3 and 4 inch cakes. The time

to filter a" + b" is the same as the time to filter a' + b' +
c' and the time to filter a"' + b"' is the sane as the time to
filter a'! + b" + c*'. Also, the time required to filter 0H

+ c"' is dependent upon the first power of the thickness.

9 =19 + n X e

3 2 3 1
94 = 93 + n4 X 91
where, 93: time to filter a three inch cake

94: time to filter a four inch cake
n3: 3.125'
n4: 4.125.

To test the workability of these equations, reference will

be made to the data of part IV- The data for the :5 pressure

run will be recepied for simplicity.

 

 

 

Table XXV
Period Time(sec) Filtrate(lbs) Total Filtrate Pressure
1 240 4 11/16 4 ll/16 25
2 480 2 13/16 6 14/15 25
3 720 1 7/16 8 5/15 25
4 1280 1 15/16 10 4/15 25

 

 

 

 

 

 

 

B' refer‘inn to fig. 5 it will be noted that the frsne
C‘ r .

i’

is full when l_g V = 0.95 or V = 8.9 . This point is deter-
mined by the sudden curvature of the line upward. That is, the
amount of filtrate decreases per unit time. Then the cake
builds up on each cloth the frame gradually fills and finally
the cakes build up to the point when they touch. The filter
area is immediately reduced and it is at this point that the
lines in the graph turn upward. The time at which this occurs
is the time required to fill the cake. It was this time that
was used as a basis for the following calculations, and found
to be 16 minutes.
A. Application of equation to Slurry I-

Calculations:

9L = e L-l + nL X 61 (l)

61 = 16 minutes.
6

= Time reg'd to filter the next less
L-l
hickness of cake.

n = Thickness of cake being filtered.

(D
II

Filtering time.

For 2" frames.
92 = 91 + n2 X 91
92 = 16 + 2.125 X 18

9 = 50 minutes.

For 3" frames.

93=92+n3X91

93 = 50 + 3.125 X 16
63 = 99 minutes.
For 4" frames.
94 = 83 + n4 X 91
94 = 99 + 4.l25 X 16
64 = 166 minutes.

‘13
(D

As a matter of comparison the following table was arrang-

ed-

HcCabe were taken from part IV above.

The values of calculated times by equation of Badger and

The actual filtration

times were arrived at by actual filtration.

being the same as in other runs with filter press

runs were made for each size frame up to the 4 inches.

actual thickne

.0 1w .n ~.
SS OJ. 06.5.8 “at

thickness nlus 0.125”.

L

measured and found to be

The technique

The

frame

xcept that

 

 

 

 

 

 

 

 

 

Table xxvrl
Cake Thick- Badger &ICCabe Formula $1) Actual
ness Inches Formula Filter.v Derived imes Filter Times
Times. min. Kin. HIn.
1.125 15.5 16 16
~2.125 55 50 49
3.125 102 99 92.5
4.125 172 .1 165 150
°/. Variation from °/° Variation from Pressure
Actual of Bdm for. Actual for For. (1)
3.3 O 25
12.2 2.0 25

 

 

 

 

50

Table IXVl (continued)

 

 

 

°/° Variation from °/° Variation from Pressur
Actual of B&M For. Actual for For. (1)
10.3 7.0 ‘ 25
14.7 10.0 25

 

 

 

 

 

It will be noted t1 at the values of actual filtering time
and calculatei tizxe of this table vary greatly from the same
values of table XXIII. This is due to t e fact the the slurry
used in previous work was made up with ch e:rically pur meter-
ials, while the slurry of the latter work was made up with
connercial material. Althouj n the slurries were nade up ex-
actly the same, they gave different results upon filtering.

Due to the fact that we were unable to ootai the C.P.
materials, the commercia TiatGTL als had to be uS3d. In as
much as comgarative re ults were ohtained, the co :m3rcial

arterials were satisfactorY°

B. Application of eoula tion (1) to Slurry II-
Procedure:

In using slurry II the same procedure was used as was used
in the case of slurry I. The time to filter a 1" cake mas acc-
urately determined first. The times for filtering a 2", 8", and
4" frame were also determined by carrying out the filtration
and found to be 4, 11%, 22%, 67 1/6 minutes respectively.

As a ratter of comparison the filtering timi as calculated

in part II sec. Bo will be tabulatgd in the table which is to

follow.

Calculations;

9L = eL_1 + nL x 91 (1)

91 = 4: 1111111113880
GL_1 = Time required to filter the next
less thickness of cake.

n = Thickness of cake being filtered.

L
For 2" frames.
92 = 81 + n2 X 91
9 = 4 + 2.135 X 4

93 = 12.5 minutes.

For 3" frames

93 = 92 + n2 X 91

9

12.5 + 3.125 X 4

63 = 5 minutes.
For 4" frames.

94=e3+n4xel
9 = 25 + 4.135 X 4

94 = 41.5 minutes.
Table XXVII

Comparison of calculated and actual filtering times.

 

 

 

 

Cake thick- Badger&KcCabe Derived For. Actual T.
ness Inches- Formuaa Time (1) Min. in hin.
in minutes.
1.125 5 4 4

2.125 16 12.5 11.5

 

 

 

 

 

52

Table KKVll (Continued)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Cake thick— Badgerarccabe Derived For. fictual
ness Inches. Formula Time (1) Min. i'ilter.
in minutes T. Kin.
3.125 38 25 22 3
4.125 67 41.5 ‘ 37 1/6
°/° Variation from ° Variation from Pressure
Actual B & M For. Actual of For. (1)
25 O 25
39.1 8.7 25
69 11.1 25
53.8 10.8 25
Discussion:

By referring to tables XXVI and XXVII a very good compari-
COn of the calculated filtering times by the equation of Badger
and Eccabe (2) and of the equation (1) above, is shown. In
the case of slurry I the e uations of Badger and thpbe hold
fairly well, but in no case areethe results as good as the cal-
culated filtering times by equation (1).

When slurry II is used (table XXVII) neither equation
holds as good as they do with slurry I (table XXVI). Inweither
case it may be noted that equation (1) holds closer to the
actual than does the equations of Badger and McCabe. Then too
the per cent variation from actual of equation (1) is practi-
cally the same in either case and does not vary more than 11
°/oo These calculated values are greater than actual values
in both cases. If these calculated values by equation (1)

always give values greater than the actual times, regardless

of the slurry used, and always by a certain per cent, and in
this work all results tend to prove this, then a correction

to

(D

factor could be used which rould give values V63? 0105

"J

ctual filtration values.

54

VII. Development of final equation for predictin. the filt-

ering times of a certain slurry for a certain constant ress-

y-

urea

A. Derivation of equation.
Prccédure:

All the preliminary filtrations pretaining to this equat—
ion were carried on with slurry I. The first steo in the pro-

edur was to determine the exact time at which a frame use

0

(D

J

H)

ille“ when filtering at a constant pressure of 85 /sq. in.
using slurry I. The slurry was made up according to specifi-
cations and placed in the blow tank (fig. 1). The pressure
was raised to Esdrin the blow tank and filtration started. The
filtrate was collected as in part IV, sec. A. That is, by
allowing the filtrate to run in a container balanced on a Tol-
edo scale.

The filtration cycle was divided into six periods and the
weight of filtrate at the end of each of the periods was noted.
Tnis data is given in table XXVIII below.

Table XXVIII

 

 

 

Period Time(sec) Filtrate(lbs) Total Filtrate ressure
1 240 1 12/15 1 12/16 25
2 480 A 12/5/16 2 8.5/16 25
5 720 10.5/15 3 3/16 25
4 1080 10/18 :3 e/is 25
5 1500 7/15 4 4/15 25
e 2100 5/16 4 9/16 as

 

 

 

 

 

 

.o,“\

¢~r

‘ ng‘i‘

1+"

 

 

 

   

{max/02164 aw :

 

 

JJ

00

00/ uqsarairacdr

 

-d/

«Jun

!

197’— film. m

 

.321
J]
50

 

(g

 

 

 

 

 

 

Table KKK (Continuedl

 

 

 

Time (Kin) Wt. 0f ’iltrate Cake Thickness Pressure
4e 4 5.97 2.125 25

so ' 8.78 5.125 2

147 11.50 4.125 ' 2

 

 

 

 

By plotting log of thickness against 105 of tige it is
seen that all tLe points follow the course of a straight line
(fig. 15).

fable xxxr

Data for fig. 15

 

 

 

9 L Log 9 Log L
14.5 1.125 1.1395 0.207
46.5 2.185 1.2980 0.395
90 3.125 1.7950 0.758
147 4.125 2.1405 1.131

 

 

 

 

 

3

With all the points of the above drapn (fir. l") falling

'C: C

on a straight line, only two oints would be necessary to

D("

draw the line. After the line had been deterrined, then the
time for filtering any thickness etke could be determined from
the graph.
The equation of a straight line is,
'y = mx + k
Then the equation of line of fig. 15 is,

(l)

y = mlx + k1

Where,

y = L03 L vake thickness in inches.

 

‘J'm“-‘ I

.'s

a can ’Iiaa'!i ‘1' VI\.-‘0 a

e 15

igur

,1
d

"I 5.7.1:. ..

.!"‘ ‘I.~".‘lw‘.l .0; ‘v'l.‘ Q-F‘L

.pl

0 1".

hi: .

I.‘

191;, 1 H

.n.

4.x

1
it
i
f
I
I
E
3
I

i

l

i

I
I
1
1
l

o

k:»~~.-...».n¢.*. MVMWM—qbd .v- .._ ~ —-,--.

i

.rl'nl‘ I. u

 

 

 

 

 

 
   
  
 

+191 1030 01/72 62:0ij

0 ‘ - r
a ,
_ , ——o—— [g1 igé) (were Ac/w/ 16,9“
‘

 

 

.’ 3G - ‘
T“ {to 1/ /.z [.7 [9' I: [a /.7 AD-
.$ ".1 - -- . .; ‘ .-

l

I

 

 

 

 

57

x = log 9 Time to filter cake in minutes.
M1 = slope of line.
kl = constant.

But it is desired to get a relation between cake thickness,
filtering time and pounds of filtrate. Then it will be nec-
essary to plot log of pounds of filtrate and 103 of time.

(fig. 15)

 

 

 

Table XXXII
e V LOg 9 Log V
14.5 _ 3.15 1.1562 0.500
46.5 5.9? 1.868 0.776
90.0 8.76 1.954 0.943
147.0 11.60 2.168 1.065

 

 

 

 

Equation of line, fig. 16,

y=l£2x+k2 ------------------------- (2:)
where,
y = Log V Filtrate in pounds.
x = Log 9 Filtering time in minutes.
M2 = slope of line.
k = consta t.
2 n
By substituting in (l), we have,
Leg L = M1 L0g e + L0g k1
Transposing,
M1L0g9_ k
7351?“ ”Ma 1

Removing the log, we have,

 

 

 

 

 

 

/.8

£75

£6

[.5

(1‘

1.2!

1.!

1.0

 

[W'hnm
Q 8 8 9.8:

E

 

 

 

/.l /2 /.3' "'9‘ 15’ x'6 A7 /6’ [9 .20 1!

1030 77mg ”7 ”mu/rs

 

 

 

 

 

 

 

LOg V - V

— m2 LOg e + L0g k
Transposing,

2
" 0
M2 L g 9 = - log k2
Log V
M
or, 'g 2 —
v 2

(4)
Multiplying (3) and (4), we have,
m + K
9 l 2

VL = R1 k2

By combining the sloyes of t

 

he two lines of fig. 15 (21) and
fig. 16 (M2) into a single lepe E and the eonstants hi and
k2 into a single constant k, we have,
v
6“ = k
VL
rearranging,
e:L = kVL ---------------------------------- (5)
B. Application of eq ation (5) to Slurr, I.
Procedure:
In as much as the testing when a one inch frame was fill-
ed; had been determined previousl , (fig.
necessary to repeat it.

14) it will not be
The one

inch frame was inserted in the press and filtra—
tion started at 25*

per. sq. in. pressure. When the required
amount of filtrate was obt ined the time was taken. This was
then repeated for a two inch cake.

Data:

 

 

 

 

 

 

 

 

 

Table XXXIII
Run Time(minutes)- Wt. of Filt. in Cake Thick- Pressure
pounds. ness in in.
1’ 15 5.15 1.125 25
2 49 5.97 2.125 25
Temperature of slurry 19°C.
Calculations:
eLi = L v k

Apply this equation to the two runs at the constant
pressure, by plotting log L vs. 10g 9 and observing the slope
of the line (fig. 15).

Table XXXIV

 

 

 

 

 

 

 

 

 

 

 

 

Run . 9 L Log 9 Log L
1 16 1.125 1.204 0.051
2 49 2.125 1.690 0.328
This line shown in fig. 15.

M1 = slope of line = §%€%_ = .580
Plotting 10g V vs. log 9 and observing the slope of line.
(fig. 15)

Table XXXV

Run 9 V Log 9 Log V
l 16 3.16 1.204 0.580
2 49 5.97 1.590 0.775

 

 

 

 

 

 

In as much as the data

of

this table

and that of table

50 i

XXXII are practically identical, the slope of tie line of
fig. 16 will be taken as tTe actual slope.

M2 = 810pe of line = 47/83 = .57

1+M2= .58+ .57: 1.15

Applying this equation to run 1, we have,

" I
M = 5

51°15 = L v k
Substituting we have,
(15)1°15 = 1.125 ' 5.15 - k
24.3 = 5
k = 6.64
Calculation of filtering times:
For 2" fra es.
(e)1°15 = 5.54 - 5.97 . 2.125
(5)1'15 = 54.4

l‘15r’54.4

9 = 47-5 minutes.

(D
H

For 3" frames.

(6)1015 = 6064 o 8078 o 5.125

(9)1'15 = 152.
e = 1'15" 152.
9 = 92.5 minutes.

For 4" frames.
(5)1'15 = 5.54 ° 11.5 - 4.125
(e)1°15 = 515.

9 = 1.15, 3180

9 = 150 minutes

Table XXXVI

61

Comparison of Filtering Times.

 

Cake Thick- Badger & ICCabe Form. (5) F. Actual T.

 

ness inches. Form. T. in Lin. T. in Kin. in min.
1.125 15.5 16 16
2.125 55 47.5 46.5

3.125 102 92.5 90
4.185 172 150.0 147.

 

 

 

 

 

°/° Variation from actual °/o Variation from Actual
of Badger & Mccabe Form. of Formual (5)

 

 

3.3 0.

18.5 2.15
13.3 2578

17.0 2600

 

 

 

Discussion:

The application of the aoove equation (5) as shown, is
comparatively simple. It merely consists of making a run with
a one inch cake, drawing a graph which is either a V2 - e or
log V - 10g 9 graph, to determine the point at which the frame
is filled« After the pounds of filtrate have been determined
for the one inch cake , the pounds of filtrate for a 2", 5",
and 4" cake are determined. A second run is tL—n made, filt-
ering a two inch cake, the time being noted when the required
amount of filtrate has been obtained.

With this data a log 9 - log L and a log 9 log V graph is
'constructed and the slopes of the lines noted. Using tze data
the one inch cake, the values of V, L, and e are substituted

in the equation-

O 2
m

v 3'
es = k L V
the value of K being equal to the combined slopes of the two

determined. After k has

I"!
F“
0)

lines. From this the value of 1

5

been calculated, the filterin;

r+
H.
is
(a

for any thickness cake
may be determined.

The results obtained 3:33 this :cua.tion depend greatly
upon the accurateness of the initial run. That is, the run
Where the time and filtrate of a one inch cake are aster~“nedo
Great care should be taken, then, in deter: lull V and G for
the one inch oak

By referring to table XXXVI it may be seen that the equa-
tion holds fairly well. It is seen that by equation (5) the
calculated values va ry onl y fro n O to 2.78 °/o from the act—
ual filtration values. However, the filtration times as cal-
culated from formula of Badger and X00 63be vary from 3.5 to
18.5 °/°.

The correct method to use, in deter ining when the cake
is filled, depends upon the slurry oeins filtered. If the
slurry is filtered bery easily, probably tne best nethod would
be the V2 - 9 graph. However, if the slurry is collodial or
otherwise difficult to filter, it is best to use the log V -
log 9 graph. When interpreting these graphs, it rust be under-
stood tLat when the line starts to curve that tie cake is not
necessarially entirely filled. It does mean, however, that

the half cakes on each fi.lt er cloth have touched each other

F4,

illed.

an

5').
(I)

the caLe is n wly

If the graphs are read correctly a short time will be

allowed for a complete filli“" of the frame. The time allow-

~e

ed depending upon the total time of tte cycle. In en" case

U~Au

the time allowed will not be

greater than one ninute and in

I

most cases not more than thirt ee

(3

on

ES.

(3

K:

64

VIII. Comparison of the rate of filtration, using the seve-

ral different kinds of filter cloths of Edward H. Best & Co.

Procedure:

Nine sets of filter cloths of the Edward H. Best & Co.
were cut for use on the filter press. The same procedure was
used in connection with the filter press as described in part
III sec. A. Slurry I was filtered under the sate conditions,

with only the filter medium being changed. Filtration was

5'

qd'

 

 

 

 

 

 

 

 

 

carried on at a constant pressure of 52 per. sq. in.
Data:

Table XXXVII
Period Time(sec)) Filtrste(lbs) Total Filtrate(lbs) Pressure
1 5O 2 § 2 1/4 32
2 155 2 5 5 - 32
3 325 2 fi- 7 fi 32
4 555 2 g 10 32
5 900 2 1/4 12 1/4 ' 32
Regulg;_2uck Cloth
1 55 2 § 2 § 32
2 160 2 fi 5 32
3 330 2 fit 7 § 32
4 530 2 fi- 10' 32
5 905 2 1/4 12 1/4 32

 

 

 

 

 

 

Cloth No. 3565--- dward . est 0.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table TKKVll (Continn 1)

Period Time(sec) Filtrate(los) Total Filtrete(lbs) Pressure
1 5o 2 g 2 4 32
2 150 2 4 5 32
3 320 2 4 7 4- 32
4 570 2 g 10 32
5 920 2 4 12 4 32
Cloth o. 5 85--—Edward fl. Begtééggo.

1 47 2 .4 2 g 32
2 150 2 5 5 32
3 345 2 4 7 4 32
4 600 2 4 10 32
5 930 2 1/8 12 1/8 32
gloth No. 8367---Edward H. Begidg Co.

1 2o 2 4 i 2 4 32
2 5o 2 4 5 32
3 75 2 4 7 4 32
4 180 2 4 10 32
5 525 4 ' 14 32
Cloth Ho. 1642-—-Edward H. Best 0.

1 42 2 4 2 g 32
2 135 2 4 5 32
3 300 2 4 7 t 32
4 540 2 4 10 32
5 '900 2 1/4 12 1/4 32

 

 

Heavy Weave Cloth---§dwerd Ho Best & Co.

 

 

 

 

 

Period Time(sec) Filtrate(lbs) Total Filtrate(lbs) Pressure
1 47 2 4 2 4 32
2 150 2 4 5 _ 32
3 320 2 4. 7 4 32
4 550 2 4 10 32
5 900 2 1/4 12 1/4 32

 

 

 

 

 

.Cloth N0. lCfiQ--—Edward H. Best & Co;

 

 

1 47 2 4 2 4 32
2 155 2 4 5 32
3 340 2 4. 7 4 32
4 595 2 4. 10 32
5 910 2. 1/4 12 1/4 32

 

 

 

 

 

Cloth N0. 4555--:§dward H- Best & C0.

 

 

 

Temperature of slurry 19° 0.

 

Results: - -
- Table XXXIII

Comparison of filtration rates of several kinds of filter cloths.

 

 

 

Cloth No. - Filtrate ‘** Filtrate Time(sec)
Reg. Duck Clear 12 1/4 900
3565 ClOUdy at start. 12 1/4 905
5085 C 'Clear 12 4 920
8367 ' Cloudy ar strrt. 12 1/8 930
1642 Very cloudy. 14 y ‘ 525
Heavy Weave Clear 12 1/4 900
1030 Clear 12 1/4 900
‘4555 Clear 12 1/4 910

 

 

 

 

 

67

Conclusions:

The idea in choosing a filter cloth is to select one
which will allow the Ftreetest amount of filtrate to pass thro—
ugh and at the same time be able to stahd up under the chemi-
ca action of the filtrate and precipitate. The function of a
filter cloth plays a very small part in the actual filtration
cycle. The cloth affect enters only in the initial stages of
filtration. he precipitate at the beginning of the cycle cab-
lects on the cloth and after a small amount has built up the
precipitate acts as its own filter medium. The filter cloth
is necessary throu4 h- ut the filtration cycle, however, because
it holds the precipitate in the chamber.

Concluding from table XXXVIII, we may say that the rate d
filtration is a- ffected very little by filter cloth used. In
other words more attention could be spent to controling temp-
erature and pressure than in selecting tle filter medium. How-
ever, when the precipitate or filt rate affect the cloth chemi-

election cf the

(f)

cally, then great Cure should be tahen in the

proper medium.

In only one case in the above tebhe did the tire v21;
:rcEtly from the other filtering tires. In this etse tfe filt-
er cloth was v ry porous and nuch of the precipitate passed

through the cloth. It will be seen froxn table XXXVII the
during the initial staQes of filtration the filtering times
varied somewhat. However, after tle cake built up to where it
was serving as the medium, filtration retained constant thr-

ourhout the remainder of therun.

Probably the greatest variations occur, not beceu

the filter cloth, but because of Slight differences ir

ure er teuperature control-

68

C‘.
(0

IX. Investiyations of the washing dharacteristics of differ-

ent slurries.

.A. Slurry I.
Filter Press.

Procedure:

In carrying our the washing of a cake the filtration cycle
was carried on as in all cases using the filter press (Part IV
Sec. A). When the filtration cycle had been completed the val-
ues on the water line were regulated so that the water was app-
lied to one filter surface at the same pressure as that used
in filtering. The water passed through the cake and filter
cloths and into the grooves of the plate on the opposite side

of the cake. The wash water then left the press tirOURh the

discharge channel. At definite intervals of time samples of
the wash water were taken and analyzed for NaCl. After the Na
Cl had been reduced to 1 cc N/lO Ag N03 per 10 cc of wash water
the valves were closed. '

Due to the crack'ng of these cakes, repeat runs were made,
where, on the final few minutes of filtration the pressure was
increased to 701?. Washing was then carried on a the same
pressure as before.

Direct washing was also carried out, with apparently bet-
ter results than those obtained by the counter flow wash. Aft

ter the filtration cycle was complete the wash water was forced

'through the feed channel. samples were taken as before.

70

Data:
Table XXXIX

Counter Fbow Wash.

 

 

 

 

 

Time (EInutes) cc AgNOs per 10 cc of filtrate
O 194.
0.5 V . 125.0
1.0 111.8
2 53.1
3 '42.5
4 35.7
5 58.5
16 28.1
15 21.9
30 18.1
25 17.0
30 14.5
40 . 3.1
50 1.25
Temperature of water 19° 0.
Weight of wash water 33 4’
Weight of cake 3 12/16#
Pr e 5 sure 321%51- ”7°
9/0 water 65 °/°

 

 

Plot time in minutes vs. cc N/lO AgKCS per 10 cc of wash water.
(fig. 17)
Table XL

a) .0... 19'5’4 0!... ...

l7

' l ["311 1‘3

‘3

 

 

 

 

.Ill. ml? .

a

, ‘L‘Lvr .I‘léJb/Iy

w

llllllnuhlfi. “11.5% -

m

m .i

\uxflx «x3: Bold. 3.3%» M _,

 

/ozo.sv/u"avcoma95p

 

I

l

77.»? If} :MflU/GJ ’ -

 

 

 

 

 

 

 

 

71

Counter Flow Wash

 

 

 

 

Time (Minutes) cc AgNoéper 10 00 water.
0 184
5 105
10 73
15 61.0
20 43.0
85 37.5
30 35.0
40 28.5
50 19.0
to 14.23
70 9.0
80 6.8
90 5.8
100 4.3
110 3.7
150 ’ 1.0
Temperature of water 19° C.
Weight of wash water 28 7/165r
Weight of cake , 3 113/161;
Pressure 32 4"75.7",”
°/o Water 62 °/°

 

 

 

Last five minutes of filtering cycle, tn, was raised

m
*d
H
w
m
m
L
H
m

to 60 per. sq. in.

Pigure lo

 

 

 

 

 

”bub/”y Car-re
fi/fcl' Pies:

 

”wan/wm/w'fimm-

 

 

00

Tim: III 'flmfic

 

 

 

 

 

 

 

 

 

 

 

 

 

TLe data of table XXXVIII was then plotted. Time in Linutes
vs. ccAgros per cc 10 of wash water.
Table XLI Direct Washing
Time (minutes) cc ASNOB per 10 cc Water
0 195
0.5 194
l 181
2 124
5 107
4 99
5 87
10 58
15 14
80 6.0
25 3.6
50 1.5
35 0.5
Temperature of water 18 ° C.
Weight of rash water ZOTF
Weight of cake 3 12/164F
Pressure -#/sq. in. 52
°/¢ Water 65 °/°
The data in table XLI was t1en plotted, time in minutes

vs. cc N/lO AgNOS per 10 cc of wash no

ter. (fig. 19)

v.1

.‘gg’.

igure 19

 

 

 

kl-
§

 

Arna- Mal/lb
1

«gm

3

 

,5:

/<!f

/0

x-

D/recf him/wry

M n A

1

20 “J5 60
77mg #7 Alma/ea

 

 

 

 

 

 

 

 

73

Suction Filter;

.0

The procedure in filtering with a suction filter is des-

q!

cribed in part IV - sec. B. After the washing cycle was com—

d

Plated, a large Quantity of rash water was poured over the

v

cake an

r

r the vacuum kept the same as was used in filtering.

H
b

At regular inta vals of time the bottle which was attached to

F

the drain valve was rexoved and mesh rater dunoed. The bottle
was immediately replaced, valved tarned to take sagple, renov-
ed and another bottle put in its place.

Taking samples in this way is rather inaccurate in as
much as the pressure is affected by the removal of the bottle
because the pressure has to be built up in the bottle each
time it is removed. Then too, the samples collected nill~not
be truly samples at the moment. Due to the time elapsed bet-
ween the time of dumpiru the sash rater and t kin; sfrrles, thh
samples will be a little cumulative. However, for ordinary

practice satisfactory results can be obtained.

a.

Table XLII

 

Time(minutes) cc AgNOg N/lO per 10 cc Water

 

O 197
197
191.5
190.5

01¢.me

lane
10 179.5

 

 

 

 

ure 20

no
.1
1‘

.5

 

 

 

.L

w"..-

 

 

 

 

 

 

 

 

Table XLII Continuted

 

Time (minutes) cc Agfios per 10 cc of Water

 

 

15 4O
20 16
25 10

C» J
0
IO

30 ' ~ ,

0

Cr]
\1
U".

40

50
60

h)

70

O H H N r?-
O
(D (I)
01 CO

0
L0
(II

80

 

Temperature of water 19° 0

. . - - , n, 0a?
Welgnt or ween water as l/o
Csk thickness 3/4"

Weight of ceke 5

°/° water 53 °/°

 

 

 

The data of tsble XLII was then, plotted; time in rinutes
vs. cc AgNOS per 10 cc of wssh water. (fig. 70)
B. Slurry II
Filter Press.
Procedure:
slurry II was o :ziec out

'y— 1’.‘ -. 4? c. '1 ~f‘.,r" Q :n
flusning or a liltei Cunt usin

in the same ‘5;:;-::; as 171.6311 slurry I
l

of this part. The sane difficu ties were also encountered in
J.
.1. LI-L

O
e
U)
t
b

“CShinS: slurry II being almost impossible t

cracking.

"2
(I)

 

 

 

 

 

 

Dc ts;
Table XLIII Counter Flow Wash
Time (minutes) ‘ cc AgNOS per cc (10% wash
0 185.0
Oo5 82.5
1 75.5
2 78.5
3 71.0
4 88.0
5 58.0
10 2.9
15 , 1.0
Temperature of slurry 19° c.
Weisht of ca}: V 3 3/44;
Weight of wash water 14 5/154’
Pressure Ski/59’“
°/o Water I 41.4 0/a

 

Plotting time in minutes vs. cc N/lO AgNOS oer 10 cc
of wesh water. (fig. 31)
Suction Filter.

The procedure in this case is the same as in section A

of this part.
Data:
Table XLIV Continuous Washing
Time (minutes) 00 N/lO AgHOs per 10 cc of wesh

0 193.5

21

igure

(1
fl

V; \,‘.| u

21

bigure

 

 

 

‘

>
s >
a
u >

1. A w 513‘st SWIG. in“.

. _

a

 

l0

6’

I:
Malay 77m M Mam

 

 

 

 

 

 

 

 

 

 

Tab'e XLIV

4

 

Time (minutes) cc N/lO Agfloa per 10 cc of Wash

 

1 46.0

2 12.0
3
4 7.0
5

10 1-0

 

 

 

Temperature of Wash 18° C

. . n . . . 4*
Weight or cage in pounds 7 3/4
1 ',1 4? ,— ‘ ,- '_ "f
flei nt 0; WuSfl water in pounds. 43

Pressure 9.8#/5j'”7'

°/o Water _ 43.3

 

 

Plotting time in minutes vs. cc N/lO AgNOs per 10 cc of

wash water. (fig. 22)

Discussion:

It was almost impossible to
the counter flow method of Wishing, using the fi
This is not surprising, however, because when the oils is being

filtered tie coke ouil

Q4
U)
{.3
L;
O
U
(U
S
O
’—
s
C’)

~ide, from tha center.
When washing is started tne flow of water throught half of the

cake is in the opposite direction, thus there is a wrest strain

d-

uoon that half of he cake. Unless the cake is quite solid

n

and uniform this halr of the cake is very likely to orach, al-
lowing 'he water to reach the center of the cake and only pro-

perly rushing one half of the cake. That is, the half throughh

F igure 2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

which the wash water passes in the srne directitn as did the
filtrate.
to fig. 17 it will be seen that this very
tiny haopened. Xhen tie water was first turned on the ceke
crscreu and t4€ filtrate in the pours of the Opposite half of
the cake was forced out. Hotever, at the end of about five
minutes the water seems to be graduilly absorbinj the Heel
from the cracked cake and the line flattered out some vict. It

’ Q

.A 5‘ . .- .C‘ .C‘ . 5’} .C‘ ‘. — A . 1.. r‘ 3 r~. .- - . .- o ‘0.
tie absorornb of filtrate -ron the cries“; nu I Can: 1-1Cu

H.

L‘

prevents tie graoh fron followin: LQQ course of th3 dottcC line.
Finally 81 of the N801 has removed-

Cakes washed as renresented in fig. 17 were tion tested
for Kacl. In all cases very little racl was left in the cake.
Although all the Nacl as; us removed, it does not roan tltt

" '1

sati era ctory resui have been obtained. us a cunt 0: test
he weshin; time are increased-

In an attempt to overcome this Crackin: of the cake many
exteriments mere run. Host of these trials were tri:e by diff-
erences in pressure of filtering and washing. Finally satis-
feotory results were obtained oy incrcasing tie OISSSCIG dur-

& the last five minutes of the filtering cycle to BO‘k/sq.in.
Wasliing of the cake was the carried on a Bo to as . .

Raising; of the filteri n: 1338: sure. to 60" packed t‘qe c“ 1re

so that it was more or less uni orm tLIDU;_LOUto’ When the washn

water was gradually acolied to t;e kae, dis :1“C‘1€“t grtdually

took place, which gave a very smooth curve. (fig. 13) A;

t' ‘ '~ n..-” ° .1“ .3“, .0 .. 4.: -qo ~_ I": i
this methoo of mu: in, Is 10: from satisfactory as “111 be

fl “‘0 1

5’

order to flesh tLe Cele to 1 cc of N/lO

0)
FJ .
k
r

seen in ;

A K05 per 10 cc of meter 145 minutes are recnired. The
pours of the cake ere ref”Cfd in si: e 3? t13 incr31see gress-
are of filtration and the tesning rate is c creased.

There ere also disadv: te;es in direct neshinjo Thet is,

.n. I..- .o . ‘.— - r w. :3 .- .1 I
tnronsn the lees channel. Wnen a case 1; irlttrec, tnat

(1'

no inlet forms lest. Then it is rea—
sonab e to expect that t33 o‘ce rill oe less 03m not in this

corner. When the wash ester is turned on
ency for the wash tat er to pass tnrougn this corner of t:e CSke.

If the weter finds no difficulty in pessiig tire: h tnis port-

H

I: K c ' x I‘- F : ' Q- . “R J- .v 4'" ‘3‘ ‘ A . ~ v ' ’,‘. (a ‘ A ~ .? ""
ien Oi tnc Cfihe, it L111 not eon tie on Oblfd corie*s or tie

n v- --‘. ' T- n »‘ -- ,n ‘.'\ ‘..‘ ~.- '15 -.
Cone MHICLL are £13.18 (3031300130 In Ct- :33: WOIIS, Cl;3.-1.iC_...Lng_ OCCUI‘S

neference to fig. 13 shows peculiarities, which are pro-

:3
.3
0
U
(U
C')
I):
O
:3
H
(D
I

bebl y dae to ch“nnelin . The line of th:

)

m
C)
(J
5.:
d-
c1-
E
C
:23
C'
d
(D
m
0

rularally, which shows proper nesEing for

At this point the line tehes a retler sharp jog unicn indicates

~ ~- . ru -, ' .. A vs "h A. -'r-. ~,n: "1 4"" ’1" ‘ “‘1 ‘ ‘~ r
cnanneliné. Tnat 18, meter seems to es coming .ii,.:n t1; Cake

\

some 9180 which does not tame up any 3301. If c=

(D

not taken place, the curve would have bzen more rerulsr like
tIL’t of fig. 20.

Table XLV Comparison of Washing tines

AA

 

Type of Weshinr Wt- of Wash Water(lbs) Wash Time(min.)

 

 

Counter Flow 28 g 55

 

Counter Flow (special wash) 33 150

 

 

Direct Flow 1 20 ~ 35

 

\T
((1

Washing with the suction filter is a such easier Opera-
tion then that of the filter press, especially with tfis type
of slurry (slurryl) The cake is Wisled in 80 minutes at a
much lower pressure tLan that used with tle filter nress. The
wesling approaches that o: ideal washing, as shown in fig. 20.

In general, wasting consists of two onerations, narelv
first replacing filtrate from the pours of the cake end sec-
ond, gradual elimination of absorbed chloride fron the cake

1

eurin; the last portion of tne tisn. This is illustrated
very well in fig. 20. The Nacl is being removed from the pours
of the cake for tn: first twenty or twenty two minutes. At
en’s point the Neel-in tne pours nas been removed and tLe re—
nainder of the rash water is spent in absorbinx the Nacl from
the cake.

The results obtained from slurry II were similar to those
of slurry Io However, I Wes unable to obtain satisfactory data

with the filter press on a cake which did not crack,

Xo Conclusions:

Up to the present ti re, wit?

’-

C};
O
(f)
(O
F]
CI
3.4
‘64
O
H
,.)
(D
C)
O
(u
d-
i. 1
C)
*1
V

there is no netnecaticul eeue ion for treating filter date
whicn is set; Mf story for industrial practice. This one
Lossiole excegtion is the vork "Studies ifi Filtri
B. F. Ruth which is not 3st entii el 3 published. Of tLe york
which has been published (4),(5) I have been unable to mrke
a thoroutb enve sti ation.

'1

Types of experiments to be carried out in filtration

deyends greatly upon the type of slurry. The Gene rel sehe'ior

C

.1

of a certain slurry n-33 be determine c with an oriinery lebor-
story suction filter. However, it would not be Wise to base

"i

calculations ujson such data because of the smallness c: equip-

ment and small quantit* of slurry, tLere is great chance for
error.
uenerellv accented filtration equations tOdfiV are

The 5 3 3 5 ,
tLose proposed by Lewis (1), (2). However, D- R. Sperry has

presented efiuations which constitute another group sf filtra-

tion equations (3). and differ from the equations of Lewis
only in the manner in wzich tne filter base resistance is
treated. Sm) rrr's trectue nt lee to a nore formidable equa-
tion then does Lewis'.

By referrin5 to part II of tLis thesis it is seen that
the equations of Lewis are very difficult to understand, and
their derivations very complicated.

The validity of these ecusticns is ill streted in pert v

81

above. The filtering tires as calculated cy t3: e ungions
vary from 18 °/o to 21 °/o from the ectuel filtering times.
Great care being used in carrying out t-e filtration while
data was being collected. An equation to be of industrial

use should not show calculated resu ts vqr*in as much as

20 °/o from tLe actual 'elues.

(0

Of the two ecuations I nev su5gested (pert VI and part

I
L

H

e setis:sctoryo inflation (1)

VII) probably tLe latter is mo

h I

of part VI seems to hold fairly well ror the slurries used in
this work, but which mi ht not hold Ior otner slurries. The

,.
..
_.

V

derivation of his ecueti n is not based on matnciit“c l cel-

r0

b eff on observations end results I

U)

culations. Ratzer it i
J- .L.

nave oota ine«i in my work. In all uses I observed test the

Fny liefnec" coke ver—

Pb

time to filter the final one inch 0

.‘

iec as the first poser of ,he thickness.

Equation (5) of part VIIn proves very satisfactory. The
celculeted values by this scintion.veryin3 only iron 2 °/° to
nearly 3 °/o (table 38). This variation could easily be wit

in exoerimente 1 error-

filter medium is not so much

9’

The problem of selecting
selecting one vhich will allow the f51":ntes st azount of filtrate

1

to pess throuih, but how lon; will 9 certein medium stand up

D

usin5 a particular slurry. The filter medium proolen varies,
however, depending u_on the slurry being filtered.

Washigg of a filter cake is a greater problem then is
ly believed. Tne was in; technique changes cvezy time

'I.

l
”e filtering technique changes. Cracking of CCLG is 3 common

diffi ulty in nasLin5, as is channelin5 of a cake. Enetler

or not counter flow r ect v enin5 is used, degenis ugon

tuo factors. When crackin5 occurs direct rangin, is some times
used. However, in ccse Cnannelin; occurs with direct reeling

the cake is com ressei by Special ecuinment, and tlen washed

Filtiation as Q‘Ullxu to mos st sluiries is a large nrob-

g

lem. There age so many variables involved tnat results vlich
cleck are difficult to obtain. For excel imental wor: the
technique of filte rin can be de vo loned 11*] practice 5nd

great care.

6.
7.

10-

11.
12.

Biblio5raphy

Walker, Lewis and HcAdams.--Principles of Chenical
Engineerin5.---Pages 341-387

Badge and flcCabe--Elements of Chemical Engineering.
Pages 424-475

D. R. Sperry--Chem. and Met. En5.---15,198(1916)
B. F. Ruth with G. H. montillon and R. E- Kontanna
J. Ind. and Eng. Chem.---25, 76-82 (1953)
B. F. Ruth with G. Ho hontillon and R. E. hontanna
J. Ind. and Eng. Chem.---25, 153—61 (1933)
Eryden and Dickey--Filtration---Pages 1—85

B. R. Sperry---J. Ind. and Eng. Chem.---15,1133—4
(1381)

F. P. Baker-—J. Ind. and Eng. Chem.---13, 610-12
(1921)

W. Go Weber and R- L. Hershey-~J. Ind. and Eng.
Chem.---18, 341-4 (1923)

J. H. Hinchley, 3- Go Ure and Bo Jo Clarke-~ J.
Soc. Chem. Ind.---45, 1-1or (1926)

H. B. Faber-—Chem. Met. En5.---22, 17-19 (1980)
Almy and Lewis--J. Ind. and Eng. Chem.---4, 528

(1912)

 

.v~llflf
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