Filtration
Learning objectives
• Explain the basic types and mechanisms
of filtration
• Exploit the Darcy’s Law equation in
order to solve problems for conventional
and constant pressure cake filtration
• Select filtration media and equipment to
meet bioproduct processing requirement
Introduction
• Filtration is a solid-liquid separation where the
liquid passes through a porous medium to remove
fine suspended solids.
• The main objective of filtration is to produce highquality drinking water (surface water) or highquality effluent (wastewater) and also for
biopharmaceutical products
Figure 1 Schematic diagrams for dead-end or
conventional filtration. For dead-end filtration the
thickness of the solids buildup increases and the
permeate flux decreases with time, ultimately
reaching zero.
Filtration
Filters use a filter cloth or some porous material along with
applied pressure to push smaller particles through the filter,
thus separating elements of the solution based on size.
Filtration for biological materials is generally completed using
batch filtration, rotary drum filtration, or ultrafiltration
methods.
Batch Filtration
• Usually performed under constant pressure with a pump that
moves the broth or liquor through the filter
• Filter cake will build-up as filtration proceeds and resistance to
broth flow will increase
• The filter press is the typical industrial version of a batch
vacuum filter, using a plate and frame arrangement
• Can be used to remove cells, but does not work particularly
well for animal cell debris or plant seed debris
Filtration
Rotary Drum Filtration
• Solution is vacuumed upward where it crosses a filter
septum removed by a positive displacement pump
• Filter cake is removed after each rotation to give a fresh
surface for filtration
• Rotary vacuum filters can be used to efficiently remove
mycelia, cells, proteins, and enzymes, though a filter aid
or precoat of the septum may be necessary
Ultrafiltration
• Utilizes a membrane to separate particles that are much
larger than the solvent used
• Successful removal occurs in the partical size range of
10 solvent molecular diameters to 0.5 μ
Filtration Principles
• When a slurry containing suspended solids flow
against a filter medium by the application of a
pressure gradient across the medium, solids begin to
build up on the filter medium
• The buildup of solids on the filter medium is called a
cake
• This type of filtration is sometimes referred to as
“dead-end” filtration”
• Darcy’s law describes the flow of liquid through a
porous bed of solids and can be written as follows:
(1)
V: volume of filtrate, t: time, A: cross-sectional
area of exposed lilter medium, Δp: the pressure
drop through the bed of solids (medium plus cake)
µ0: the viscosity of the filtrate, R: resistance of
the porous bed.
Filtration Principles
• In this case, R is a combination of the resistance Rm of
the filter medium and the resistance Rc of the cake
solids:
(2)
• It is convenient to write the cake resistance Rc in
terms of specific cake resistance α as follows:
(3)
ρc: mass of dry cake solids per volume of filtrate.
• Thus, the resistance increases with the volume filtered
• Combining Eq. (1), (2) and (3), we obtain
(4)
Filtration Principles
• For the case of zero filtrate at time zero, integration of
this equation yields:
(5)
• The pressure drop is influence by α, the specific cake
resistance
• α can be increased if the cake is compressed
• Cakes are typically compressible when cells and other
biological materials are being filtered
• The specific resistance of the cake is directly affected
by Δpc, the pressure drops across the cake
Filtration Principles
• Studies have shown that the relationship
between specific resistance and pressure drop
commonly takes the form:
(6)
• where α’ and s are empirical constants.
• The power s has been called the “cake
compressibility factor” and has been found to
range from zero for incompressible cakes such
as sand and diatomite to near unity for highly
compressible cakes
Filtration Principles
Figure 2 Filtration data for Streptomyces
griseus broth with Δp = 2.0 bar. The filter
medium was of cotton cloth, and
diatomaceous earth filter aid was added
to the broth. (Data from S. Shirato and S.
Esumi, “Filtration of a culture broth of
Streptomyces griseus” J. Ferment,
Technol. (Japan), vol. 41, p. 87, 1963.)
;1]
Example 1
Batch Filtration
A Buchner funnel 8 cm in diameter is available for testing the
filtration of a cell culture suspension, which has a viscosity of 3.0
cp. The data in Table E1 were obtained with a vacuum pressure
of 600 mm Hg applied to the Buchner funnel. The cell solids on
the filter at the end of filtration were dried and found to weigh
14.0 g. Determine the specific cake resistance α and the medium
Resistance Rm. Then estimate how long it would take to obtain
10,000 liters of filtrate from this cell broth on a filter with a surface
area of 10 m2 and vacuum pressure of 500 mm Hg.
Example 1
TABLE E1
Example 1
Solution
According to Equation (5), we can plot t/(V/A) versus V/A and
obtain α from the slope and Rm from the intercept. We see that the
data are reasonably close to a straight line.
Figure E1 Plot of batch filtration data for the determination of α and Rm.
Example 1
A linear regression of the data in this plot gives the
following results (Figure E1):
Example 1
From these values, we can calculate α and Rm:
This is a typical value of Rm for a large-pore
(micrometer-sized) filter.
Example 1
To determine the time required to obtain 10,000 liters of filtrate
using a filter with an area of 10 m2, we must make the assumption
that α does not change at the new pressure drop of 500 mm Hg.
We use Equation (5) and solve for time:
We calculate the two components of this equation as follows:
and finally
Example 1
Thus, this filter is probably undersized for the
volume to be filtered. In addition, from this
calculation we see that at the end of the filtration,
Therefore, the filter medium is contributing very
little of the resistance to filtration, a typical
situation in a lengthy dead-end filtration.
Filtration Principles
• For products that are recovered in the filtrate, it is often
necessary to wash the filter cake with water or a salt solution to
maximize the removal of dissolved product from the cake.
• Frequently, the wash must be done with more than the volume
of the liquid in the cake
• This is because some of the product is in stagnant zones of the
cake, and transfer into the wash liquid from these zones occurs
by diffusion, which takes place at a slower rate than the
convective flow of wash through the cake
• Data for the washing of the filter cakes has been correlated by
Choudhary and Dahlstrom using the following equation:
(7)
R’: weight fraction of solute remaining in the cake
after washing (on the basis that R’ = 1.0 prior to
washing), E: percentage wash efficiency, and
N: volume of wash liquid per volume of liquid in
the unwashed cake.
Filtration Principles
• Assuming that the liquid viscosity and the pressure
drop through the bed solids are the same during the
filtration of the solids, the washing rate per crosssectional area can be found from the filtrate flow rate
per unit area given in Equation (4) at the end of the
filtration
• Thus, for negligible filter medium resistance for filtrate
volume Vf at the end of time tf to form the cake, this
yields
(8)
Filtration Principles
• If Vw is the volume of wash liquid applied in time tw, then
(9)
• Using the definition of (dv/dt)V=Vf from Eq. (8), we obtain
(10)
• At the end of filtration, the integrated form of the filtration
equation (Eq. 5), with Rm neglected, can be written
(11)
• Substituting this expression for Vf/A in Eq. (10) and simplifying
gives
(12)
Filtration Principles
• From Eq. (11) and (12), the ration of tw to tf is
(13)
• It is helpful to write tw/tf in terms of n, the ration of the volume Vw
of wash liquid to the volume Vr of residual liquid in the cake:
(14)
• where f is the ratio of Vr to the volume Vf of filtrate at the end of
filtration.
• The ratio f can be determined by a material balance
• Thus, for a given cake formation time tf, a plot of wash time tw
versus wash ratio n will be a straight line
Example 2
Rotary Vacuum Filtration
It is desired to filter a cell broth at a rate of 2000 liters/h
on a rotary vacuum filter at a vacuum pressure of 70
kPa. The cycle time for the drum will be 60 s, and the
cake formation time (filtering time) will be 15 s. The broth
to be filtered has a viscosity of 2.0 cp and a cake solids
(dry basis) per volume of filtrate of 10 g/liter. From
laboratory tests,the specific cake resistance has been
determined to be 9 x 10 cm/g. Determine the area
of the filter that is required. The resistance of the filter
medium can be neglected.
Example 2
Solution
We can use the integrated form of the filtration equation, Equation
(5), with Rm = 0:
We solve for A2 to obtain
In applying this equation, it is helpful to focus on the area of the
drum that is submerged, which is where the cake is being formed
and where filtrate is being obtained. Thus, A is the area of that
part of the drum that is submerged. We can calculate the volume
of filtrate that needs to be collected during the cake formation time
of 15 s:
Example 2
We use this volume of filtrate with t = 15 s in the equation for A2 to
obtain
The area A’ of the entire rotary vacuum filter can be calculated
from the cake formation time and the total cycle time as
This is a medium-sized rotary vacuum filter, with possible
dimensions of 1.0 m diameter by 1.0 m long.
Example 3
Washing of a Rotary Vacuum
Filter Cake
For the filtration in Example 2, it is
desired to wash a product antibiotic out
of the cake so that only 5% of the
antibiotic in the cake is left after
washing. We expect the washing
efficiency to be 50%. Estimate the
washing time per cycle that would be
required.
Solution
Example 3
From Equation (7) for the washing efficiency of a filter cake
where R’ is the weight fraction of solute remaining in the cake
after washing (on the basis of R’ = 1.0 before washing), E is the
percentage wash efficiency, and n is the volume of wash liquid
per volume of liquid in the unwashed cake. Substituting R’ =
0.05 and E = 50% into this equation gives
From Equation (14), the relationship between the washing time
tw, and the cake formation time tf is given by
where f is the ratio of volume Vr of residual liquid in the cake to
the volume of filtrate Vf after time tf.
Example 3
Thus, we need to estimate the volume of residual liquid in the filter
cake to determine tw. At the end of the 15 s cake formation time,
Assuming the cake is 70 wt% water, which is typical for filter
cakes, we find
Thus,
From this result, the estimated washing time is 20% of the cake
formation time.
Filter Media and Filter Aids
1. Filter media
• The filter media must remove the solids to be filtered
from the slurry and give a clear filtrate
• The pores should not become plugged so that the rate
of filtration becomes too slow
• The filter medium must allow the filter cake to be
removed easily and cleanly
• Some widely used filter media are woven fabrics (e.g.
woven heavy cloth, glass cloth, etc, no leaching of
components are allowed, size of particle trapped: 10
μm), metal fabrics or screens (e.g. nickel,copper, etc,
good resistance to leachingand corrosion required,
size of particle trapped: 5 μm), and rigid porous media
(e.g. sintered stainless steel, silica, pocelain, etc)
• For sterile filtration, commonly used are asymmetric
membrane filter (cellulose esters or other polymers,
pore size: 0.22-0.45 μm)
Filter Media and Filter Aids
• 2.Filter aids
• Certain filters aids may be used to aid filtration
• Can be either added directly to the feed or applied to the
filtration equipment
• These are often diatomaceous earth or kieselguhr and
perlite which is composed primarily of silica.
• Also used are wood cellulose and other inert porous solids
• Can be use as a precoat before the slurry is filtered to
prevent gelatinous-type solids from plugging the filter
medium and also give clearer filtration
• Can also be added to the cake during filtration to increases
the porosity of the cake and reduces resistance of the cake
during filtration
Types of Filtration Equipment
1. Plate-and-frame filter presses
•
•
•
•
Consist of plates and frames assembled alternately with a
filter cloth over each side of the plates
The plates have channels cut in them so that clear filtrate
liquid can drain down along each plate
The feed slurry is pumped into the press and flows through
the duct into each of the open frames so that slurry fills the
frames
The filtrate flows through the filter cloth and the solids build
up as a cake on the frame side of the cloth
Types of Filtration Equipment
2. Leaf filters
• Developed for larger volumes of slurry and more efficient
washing
• Each leaf is a hollow wire framework covered by a sack of filter
cloth
• The slurry enters the tank and is forced under pressure through
the filter cloth, where the cake deposits on the outside of the
leaf
• The wash liquid follows the same path as the slurry. Hence, the
washing is more efficient than the through wishing in plate-andframe filter presses
Types of Filtration Equipment
3. Continuous rotary filters
(a) continuous rotary vacuum-dryer filter
• Filters, washes and discharges the cake in continuous,
repeating sequence
• covered with a suitable filtering medium
• rotates and an automatic valve in the center serves to activate
the filtering, drying, washing, and cake-discharge functions in
the cycle
• The filtrate leaves through the axle of the filter
(b) continuous rotary disk filter
• consist of concentric vertical disks mounted on a horizontal
rotating shaft
• operates on the same principle as the vacuum rotary-drum
filter
• Each disk is hollow and covered with a filter cloth and is partly
submerged in the slurry
• The cake is washed, dried and scraped off when the disk is in
the upper half of its rotation
Types of Filtration Equipment
(c) continuous rotary horizontal filter
• This type is a vacuum filter with the rotating
annular filtering surface divided into sectors
• As the horizontal filter rotates, it successively
receives slurry, is washed, is dried and the cake
is scraped off