FILTRATION
Introduction
Filtration may be defined as the separation of
solids from liquids by passing a suspension through a
permeable medium which retains the particles.
Figure 1. Schematic diagram of filtration system
The fine apertures necessary for filtration are
provided
 by fabric filter cloths,
 by meshes and screens of plastics or metals,
 by beds of solid particles.
In some cases, a thin preliminary coat of cake, or of
other fine particles, is put on the cloth prior to the
main filtration process.
Types of filtration
1.
Surface filters
2.
Depth filters
1.Surface filters
used for cake filtration in which the solids are
deposited in the form of a cake on the up-stream side
of a relatively thin filter medium.
Figure2. Mechanism of cake filtration
2.Depth filters
used for deep bed filtration in which particle
deposition takes place inside the medium and cake
deposition on the surface is undesirable.
Figure 3. Mechanism of deep bed filtration
The fluid passes through the filter medium, which
offers resistance to its passage, under the influence
of a force which is the pressure differential across
the filter.
rate of filtration = driving force/resistance
The filter-cake resistance is obtained by multiplying
the specific resistance of the filter cake, that is its
resistance per unit thickness, by the thickness of the
cake.

The resistances of the filter material and pre-coat
are combined into a single resistance called the filter
resistance.

It is convenient to express the filter resistance in terms
of a fictitious thickness of filter cake.

This thickness is multiplied by the specific resistance
of the filter cake to give the filter resistance.

Factor affected on filtration






Pressure drop ( ∆P )
Area of filtering surface ( A )
Viscosity of filtrate ( v )
Resistance of filter cake ( α )
Resistance of filter medium ( Rm )
Properties of slurry ( μ , ฯลฯ )
-(P) or
Pressure
drop
rate of filtration = driving force/resistance
Filter cake ()
Filter medium (Rm)
Viscosity ()
Filtration Equation


Flow of fluid through packed bed : Application of Carmankozeny’s equation
Pc
k1 v (1   ) 2 s 02


L
3
k1
โดย

v

L
S0
Pc
=
constant = 4.17 for particles with
definite size and shape
=
viscosity of filtrate (Pa.s)
=
linear velocity based on filter area (m/s)
=
void fraction หรือ porosity of cake
=
thickness of cake (m)
=
specific surface area of particle area per
volume of solid particle (m2/m3)
=
pressure drop in cake (N/m2)

Substitute v in term of volume (V)
dV dt
v 
A
A
V
L
Cs
P
= filter area (m2)
= volume of filtrate at t sec
= thickness of filter cake
= kg of solid/m3 of filtrate
= density of solid particle in cake (kg/m3)

Substitute L in term of height of cake (L)
C sV
L 

A (1   )  p
Obtain:
1 dV

A dt

 P
  CsV


 Rm 
 A

Specific cake resistance ()
 
โดย

S0
f ( , S 0 , Pressure)
=
Void fraction
=
specific surface area of
particle (m2)
  0 (P)n


  0 1   (P)
n

Specific cake resistance; 
Their specific resistance change with pressure drop
across the cake ∆pc. In such cases, an average specific
cake resistance av should can be determine from
If the function  = (∆pc) is known from pilot filtration
tests, bomb filter test or from the use of a
compressibility cell.
An experimental empirical relationship can be used
over a limit pressure range
   0 ( p ) n
c
Where
0 : the resistance at unit applied pressure drop
n : a compressibility index obtained from
experiments
(n = 0 for incompressible substance)


  0 1   ( Pc)
n

Filter medium resistance; R
Normally be constant but may vary with time (as a
result of some penetration of solid into the medium)
and sometimes may also change with applied
pressure (because of the compression of fiber in the
medium).
As the overall pressure drop across an installed
filter include losses not only in the medium but also in
the associated piping and in the inlet and outlet ports

It is convenient in practice to include all these extra
resistances in the value of the medium resistance R.

Constant pressure filtration



Equation is useful because it covers a situation that is
frequently found in a practical filtration plant.
We could predict the performance of filtration plant on
the basis of experimental results.
If a test is carried out using constant pressure, collecting
and measuring the filtrate at measured time intervals
Filtration Equations for
Constant – Pressure Filtration
At
At tt == tt sec
sec
t
Cs V Rm


V / A 2 P  A  P 
Determine  and Rm
Filtration equation for
Constant rate Filtration
For incompresible cake: Kv and C are
constant
Slope
Y-intercept
P
dV/dt = constant = V/t
t

From constant rate equation the pressure drop
required for any desired flow rate can be found.
Also, if a series of runs is carried out under different
pressures, the results can be used to determine the
resistance of the filter cake.
Ex1. Constant pressure
Filtration area
=
0.01 m2
A
Solution density
=
1,062 kg/m2

Solution viscosity
=
1.610-3 Pa.s

Filtration pressure
=
200 kPa
P
Solid concentration
=
3 kg/m3
Cs
Determine specific filter cake resistance and filter medium
resistance
Time (sec)
Volume (cm3)
0
0
14
400
32
800
55
1200
80
1600
107
2000
The solution
Y = aX + C
Y axis = tA/V
X axis = V/A
Slope = Cs/2P
Y intercept
= Rm/P
Time (sec)
Volume (cm3) Volume (m3)
tA/V
V/A
0
0
0
0
0
14
400
0.0004
350
0.04
32
800
0.0008
400
0.08
55
1200
0.0012
458.33
0.12
80
1600
0.0016
500
0.16
107
2000
0.0020
535
0.20
600
500
tA/V
400
y = 1175x + 307.67
2
R = 0.9912
300
200
100
0
0
0.05
0.1
0.15
V/A
0.2
0.25
Cs
Slope 
2P
(1.6 10 3 ) (3)
2  (200 103 )

y int ercept

1175

1175

9.792 1010
m / kg

Rm
307.67
(1.6 10 3 ) Rm

3
200 10
Rm

P

307.67
3.845 1010
1/ m
Ex2. Constant rate
A slurry containing 25.7 kg dry solids/m3 of filtrate across the
filter medium area 2.15 m2 at a constant rate of 0.00118
m3/s. If the pressure drop was observed 4,000 and 8,500 Pa
after 150 and 450 seconds of filtration, respectively. The
viscosity of filtrate was 0.001 Pa.s
Determine the specific cake resistance and filter medium
resistance.
The solution
dV
AP

 Cons tan t
V
dt Cs  Rm
A




AP
  dt
 dV  
V

Cs
 Rm 

A


P
(Pa)
t (sec)
Slope 
Cs  V 
2
 
A t 
Rm  V 
y int ercept 
 
A t 
2




AP
t
V 
V
 Cs  Rm 


A


CsV 2 RmV
P 

2
At
At
(1)
(2)
(3)
Cs  V 
Rm  V 
P 
.
t

 
 
A2  t 
A t 
2
(4)
P (Pa)
P (Pa)
t (sec)
4,000
150
8,500
450
9000
8000
7000
6000
5000
y = 15x + 1750
2
R =1
4000
3000
2000
1000
0
0
100
200
300
t (sec)
400
500
Slope 
Cs  V 

15

15


1.938 109
Rm  V 

1750

1750

3.189 109
 
A t 
(0.001) (25.7)(0.00118) 2
2.152
y int ercept 
2
2
 
A t 
(0.001) Rm (0.00118)
2.15
Rm
m / kg
1/ m
Filtration Equipment
The basic requirements for filtration equipment are:
 mechanical
support for the filter medium
 flow accesses to and from the filter medium
 provision for removing excess filter cake.


In some instances, washing of the filter cake to
remove traces of the solution may be necessary.
Pressure can be provided on the upstream side of
the filter, or a vacuum can be drawn downstream, or
both can be used to drive the wash fluid through.
Filtration equipment: (a) plate and frame press (b) rotary
vacuum filter (c) centrifugal filter

1.Plate and frame filter press


In the plate and frame filter press, a cloth or mesh is
spread out over plates which support the cloth along
ridges but at the same time leave a free area, as
large as possible, below the cloth for flow of the
filtrate.
The plates with their filter cloths may be horizontal,
but they are more usually hung vertically with a
number of plates operated in parallel to give
sufficient area.



In the early stages of the filtration cycle, the pressure
drop across the cloth is small and filtration proceeds
at more or less a constant rate.
As the cake increases, the process becomes more and
more a constant-pressure one and this is the case
throughout most of the cycle.
When the available space between successive frames
is filled with cake, the press has to be dismantled and
the cake scraped off and cleaned, after which a
further cycle can be initiated.


The plate and frame filter press is cheap but it is
difficult to mechanize to any great extent.
Filtration can be done under pressure or vacuum.
The advantage of vacuum filtration is that the pressure drop
can be maintained whilst the cake is still under atmospheric
pressure and so can be removed easily.
 The disadvantages are the greater costs of maintaining a
given pressure drop by applying a vacuum and the limitation
on the vacuum to about 80 kPa maximum.
 In pressure filtration, the pressure driving force is limited only
by the economics of attaining the pressure and by the
mechanical strength of the equipment

BAS stainless steel plate and frame filter press
2.Rotary filters


In rotary filters, the flow passes through a rotating
cylindrical cloth from which the filter cake can be
continuously scraped.
Either pressure or vacuum can provide the driving
force, but a particularly useful form is the rotary
vacuum filter.
The rotary vacuum drum filter


A suitable bearing applies the vacuum at the stage
where the actual filtration commences and breaks the
vacuum at the stage where the cake is being scraped
off after filtration. Filtrate is removed through trunnion
bearings.
Rotary vacuum filters are expensive, but they do
provide a considerable degree of mechanization and
convenience.
3.Centrifugal filters



Centrifugal force is used to provide the driving force in
some filters.
These machines are really centrifuges fitted with a
perforated bowl that may also have filter cloth on it.
Liquid is fed into the interior of the bowl and under the
centrifugal forces, it passes out through the filter
material.
Centrifugal filters
4.Air filters



Filters are used quite extensively to remove
suspended dust or particles from air streams.
The air or gas moves through a fabric and the dust is
left behind. These filters are particularly useful for
the removal of fine particles.
The air passing through the bags in parallel. Air
bearing the dust enters the bags, usually at the
bottom and the air passes out through the cloth

A familiar example of a bag filter for dust is to be
found in the domestic vacuum cleaner. Some designs of
bag filters provide for the mechanical removal of the
accumulated dust.