1. Filtration

2. 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 high-quality drinking water (surface water) or high-quality effluent (wastewater)
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.

3. 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

4. Filtration Rotary Drum Filtration Ultrafiltration
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

5. 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:
where V is the volume of filtrate, t is time, A is the cross-sectional area of exposed lilter medium, Δp is the pressure drop through the bed of solids (medium plus cake), µ0 is the viscosity of the filtrate, and R is the resistance of the porous bed. In this case, R is a combination of the resistance Rm of the filter medium and the resistance Rc of the cake solids:
It is convenient to write the cake resistance Rc in terms of specific cake resistance α as follows:
where ρc is the 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
(1)
(2)
(3)
(4)

6. Filtration Principles
For the case of zero filtrate at time zero, integration of this equation yields
This is a convenient form of the integrated equation
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
Studies have shown that the relationship between specific resistance and pressure drop commonly takes the form:
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
(5)
(6)

7. 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]

8. 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.
TABLE E1

9. 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.
A linear regression of the data in this plot gives the following results (Figure E1):
Figure E1 Plot of batch filtration data for the determination of α and Rm.

10. 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.
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:

11. Example 1
We calculate the two components of this equation as follows:
and finally
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.

12. 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 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:
where R’ is the weight fraction of solute remaining in the cake after washing (on the basis that R’ = 1.0 prior to washing), E is the percentage wash efficiency, and n is the volume of wash liquid per volume of liquid in the unwashed cake.
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 cross-sectional 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
(7)
(8)

13. Filtration Principles
If Vw is the volume of wash liquid applied in time tw, then
Using the definition of (dv/dt)V=Vf from Eq. (8), we obtain
At the end of filtration, the integrated form of the filtration equation (Eq. 5), with Rm neglected, can be written
Substituting this expression for Vf/A in Eq. (10) and simplifying gives
(9)
(10)
(11)
(12)

14. Filtration Principles
From Eq. (11) and (12), the ration of tw to tf is
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:
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
(13)
(14)

15. Example 2 Rotary Vacuum Filtration Solution
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.
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:

16. 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.

17. Example 3 Washing of a Rotary Vacuum Filter Cake Solution
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
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

18. Example 3
where f is the ratio of volume Vr of residual liquid in the cake to the volume of filtrate Vf
after time tf. 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.

19. Filter Media and Filter Aids
The filter media must fulfill a number of requirements
First and foremost, it must remove the solids to be filtered from the slurry and give a clear filtrate
Also, 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 twill or duckweave heavy cloth, other types ot woven heavy cloth, wooded cloth, paper, felted pads of cellulose, metal cloth, nylon cloth, dacron cloth, and other synthetic cloths
2.Filter aids
Certain filters aids may be used to aid filtration
These are often diatomaceous earth or kieselguhr 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

20. Types of Filtration Equipment
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
The filtrate flows between the filter cloth and the face of the plate though the channels of the outlet
The filtration proceeds until the frames are completely filled with solids

21. Types of Filtration Equipment
2. Leaf filters
The leaf filter was developed for larger volumes of slurry and more efficient washing
Each leaf is a hollow wire framework covered by a sack of filter cloth
A number of these leaves are hung in parallel in a closed tank
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 filtrate flows inside the hollow framework and out a header
The wash liquid follows the same path as the slurry. Hence, the washing is more efficient than the through wishing in plate-and-frame filter presses

22. Types of Filtration Equipment
3. Continuous rotary filters
(a) continuous rotary vacuum-dryer filter
This filter, filters, washes and discharges the cake in continuous, repeating sequence
The drum is covered with a suitable filtering medium
The drum 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
This filter consist of concentric vertical disks mounted on a horizontal rotating shaft
The filter 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
(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

23. Types of Filtration Equipment