ERT 313 :

BIOSEPARATION ENGINEERING

Mechanical - Physical Separation Process

Students should be able to;

APPLY and CALCULATE based on

filtration principles; ANALYZE cake

filtration, Constant Pressure Filtration,

Continuous Filtration and Constant Rate

Filtration.

Introduction

• Filtration is a solid-liquid separation where the

liquid passes through a porous medium to remove

fine suspended solids according to the size by

flowing under a pressure differential.

• The main objective of filtration is to produce high-

quality drinking water (surface water) or high-

quality effluent (wastewater)

2 categories of filtration, which differ according to the

direction of the fluid feed in relation to the filter

medium.

Results in a cake of solids depositing on the filter medium

Minimize buildup of solids on the filter medium

Application of Filtration in

Bio-industry

Recovery of crystalline solids

Recovery of cells from fermentation medium

Clarification of liquid and gasses

Sterilization of liquid for heat sensitive compound

Filtration Equipment

Filtration for biological materials is generally completed using batch filtration, rotary drum filtration, or ultrafiltration methods.

1. 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

Cont….Filtration Equipment

2. Rotary Drum 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

3. 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

Filter Media • To act as an impermeable barrier for particulate matter.

• Filtration media for cross-flow filtration are generally referred as “MEMBRANE”

• 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 (for conventional filtration) like filter paper, ceramics, synthetic membrane, sinterd & perforated glass, woven materials (woven polymer fiber).

Filter Aids

• Substance (solid powder)that are mixed with the feed for creating very porous cakes ( increase filtration rate very significantly)

• Can be added to the cake during filtration to increases the porosity of the cake and reduces resistance of the cake during filtration

• Can also be added directly to the feed to:

i) maintain the pores in the filter cake open

ii) Make the cake less compressible

iii)Provide faster filtration

• Common types of filter aid is diatomite (types of algae) and perlite.

The structure of diatomite particles gives them a high intrinsic permeability

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)

• For the case of zero filtrate at time zero (before start an exp), integration of this equation yields

• where and

(can determine specific cake resistance,α and medium resistance, Rm by plotting the graph)

In a cake filtration process where a significant amount of cake is allowed to accumulate, the medium resistance, Rm become neglegible compare witn the cake resistance. (Rm=0). So,

Incompressible Cake

(5)

BA

VK

V

At

PK o

2

P

RB m

CmXY

2

2

A

V

Pt o

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

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):

Example 1

Figure E1

Plot of batch

filtration data

for the

determination

of α and Rm.

(5)

BA

VK

V

At

CmXY

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:

Example 1

(5)

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.

Example 1 (5)

• Almost all cakes formed for biological material are compressible.

• As these cake compressed, filtration rate drop (flow become relatively more difficult as pressure increase)

• The pressure drop is influence by α, the specific cake resistance

• α can be increased if the cake is compressed

• 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”. (for incompressible cake, s=0 and for compressible cake, s=0.1-0.8)

Compressible Cake

(6)

Cake Washing

• After filtration, the cake contains a significant amount of solute-rich liquid broth that usually removed by washing the cake

• 2 function of washing:

A) displaces the solute-rich broth trapped in pores in the cake

B) allows diffusion of solute out of the biomass in the cake(enhance recovery if the desired product is in the biomass)

• 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)

• 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

Filtration Principles

(9)

(10)

(11)

(12)

• 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

Filtration Principles

(13)

(14)

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.

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, which is where the cake is being formed and where filtrate is being obtained.

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 (15s) and the total cycle time (60s) as

This is a medium-sized rotary vacuum filter, with possible dimensions of 1.0 m diameter by 1.0 m long.

Thus, A is the area of that part of the drum. We can calculate the volume of filtrate that needs to be collected during the cake formation time of 15 s:

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; 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. 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,

Cake solids per volume of filtrate

Volume of filtrate need to be collected during the cake formation time of 15s

llg

gmV

soV

m

194.0/1000

194

,

Crossflow filtration

as for conventional filtration, scale up of crossflow requires data from laboratory or pilot-scale units

the determination of the size of a plant unit can be done by a direct scaleup of the filtration area based on the feed or output flow rate

continued

for this scaleup, however, it is important that the following variables be kept constant:

inlet and outlet pressures

crossflow (or tangential) velocity

flow channel sizes (height and width)

Feed stream properties – test slurries should be representative of the actual process streams

Membrane type and configuration – test data from one design cannot directly be used to design another geometry

four basic modes of operation of CFF: batch concentration, diafiltration, purification and complete recycle (figure 3.11)

Figure 3.11: The four basic modes of operation of C/flow filtration (CF=crossflow filter)

continued

Mode Description

Batch

concentration

The retained stream containing the product suspended

particles or dissolved macromolecules is reduced in vol.

Diafiltration The vol. of the retained stream is maintained constant by the

continuous addition of water or buffer which results in the

removal of low MW solutes into the permeate

Commonly used when salt removal or exchange is desired

Purification A low MW product passes into the permeate and is thus

separated from higher MW impurities or

The product can be retained and impurities removed in the

filtrate

Complete

recycle

Both the retained stream and the permeate are returned to the

feed tank

Systems may be operated in complete recycle at start-up to

reach steady state, saturate the membranes, test for leaks and

blockage and adjust the feed rate

continued

in designing a diafiltration process, a decision must be made about the concentration of retained product at which to operate

as this concentration is increased, the filtration flux will decrease according to eqn. (3.16), and

the total vol. of filtrate will decrease for the removal of a given percentage of a low MW solute

this leads to an optimum concentration to minimize the time required which can be determined mathematically if the relation between filtrate flux and concentration in the bulk fluid (cb) is known

continued

the basic components in the design of a c/flow filtration sys. are shown in figure 3.12

a pump flows the feed through the filtration module to give a permeate and a retentate or retained stream

the pump needs to be sized to provide the desired flow velocity and pressure

the TMP is controlled by a back-pressure valve on the retentate stream exiting from the filtration module

thus the TMP drop is estimated by

pi pppPTM 02

1(3.28)

continued

where pi and po are the retentate pressures in and out of the module respectively and

pp = the pressure of the outlet permeate

in designing a CFF system – important to minimize the occurrence of gas-liquid interfaces, since bioproduct denaturation, especially of proteins, can occur at these interfaces in the presence of mechanical shear and turbulent flow

continued

Figure 3.13: Comparison of (a) batch and (b) single-stage continuous (feed-and-bleed) crossflow filtration systems

Figure 3.12:Basic components of a crossflow filtration system.

continued

CFF systems : operate in batch or the continuous mode (Figure 3.13)

batch system : feed is pumped through the filtration module and then back to the feed tank

variation mode (semibatch) for diafiltration: fluid is continuously added to the feed tank to keep the feed volume constant (3.11b)

continuous mode of operation (“feed-and-bleed” or “retentate bleed”): feed is added to a recirculation loop by the feed pump, and concentrate exiting in the retained stream is withdrawn from the system so that the concentration factor is at the desired value

continued

* concentration factor : i.e. conc. in the retentate divided by the conc. in the feed)

when steady state – achieved, the concentrate will be at its max. conc.- means that the filtration flux will be at a min. throughout the run

generally, more economical to use a multistage system in a continuous process (Figure 5.14)

continued

Figure 5.14: Multistage CFF system using the retentate bleed mode

continued

as more stages are added, the ave. filtration flux approaches that for a batch sys., thus the total filtration area decreases

refer to table 3.2 – batch UF operation is compared with continuous operation using one, two, three and five stages

continuous operation : economical – reduced tankage – preferable to batch operation for most large –scale UF operations

another advantage: it permits the minimization of the residence time of the product in the CFF unit (important for products that are sensitive to heat or shear)

Table 3.2: Comparison of Batch and Continuous UF System

b System design for 10x conc. factor and feed rate of 5000liters/h .Flux from J = 20ln(30/cb)

System b Flux (litersm-2h-1) Total area (m2)

Batch

Continuous

One-stage

Two-stage

Three-stage

Five-stage

33.1 (average)

8.1

31.1

8.1

38.7

23.4

8.1

44.7

35.6

26.4

17.3

8.1

136

555

243

194

165

Biotechnological products produced by different

types of cells can be intracellular or extracellular.

If these are intracellular (inside the cell), the cells

have to be disrupted to release these products

before further separation can take place.

Cell disruption / lysis is a method or process for

releasing biological molecules from inside a cell

(breaking / lysing cells and tissues)

Types of Cell Need to Disruption

Bacteria ( gram +ve @ gram –ve)

Yeast

Culture (plant culture @ animal culture)

Ease

of cell

breaks

Gram-positive Gram-negative

Thick wall No wall (got multilayer

enveloped)

Some Elements of Cell Structure

Prokaryotic Cells

• Cells that do not contain a membrane-enclosed

nucleus.

• The bacteria cell envelope consists of an inner plasma

membrane that separates all contents of the cell from

the outside world, a peptidoglycan cell wall, and outer

membrane

• Bacteria cells with a very thick cell wall stain with

crystal violet (Gram stain) and are called “Gram

positive”, while those with thin cell wall stain very

weakly – “Gram negative”

Eukaryotic cells

• Eukaryotic cells (cells with nuclei and internal

organelles) are considerably more complicated than

prokaryotic cells, and bioproducts may have to

released from intracellular particles that are

themselves coated with membranes and/or consist

of large macromolecular aggregates

• The eukraryotes includes fungi, and, of course, the

higher plants and animals

• The cell membrane of animal cells is easily broken,

whereas the cell wall of plants is strong and

relatively difficult to break

Some Elements of Cell Structure

Figure : Eukaryotic cells. Simplified diagrammatic representation of

an animal cell and a plant cell.

Different cell disruption techniques are used. These

include:

Physical methods

•Disruption in ball mill or pebble mill

•Disruption using a colloid mill

•Disruption using French press

•Disruption using ultrasonic vibrations

Chemical methods

•Disruption using detergents

•Disruption using enzymes e.g. lysozyme

•Combination of detergent and enzyme

•Disruption using solvents

Mechanical Methods for Cell Lysis

• Sonication

• Ball milling

• Pestle homogenization

• Shearing devices

(blender)

• High pressure

homogenizers

• Bead mills

Bead mill

Cascading

beads

Cells being

disrupted

Rolling

beads

• Disruption takes place due to the grinding action of the

rolling beads and the impact resulting from the cascading ones

• Bead milling can generate substantial heat

• Application: Yeast, animal and plant tissue

• Small scale: Few kilograms of yeast cells per hour

• Large scale: Hundreds of kilograms per hour.

ERT 313/4 BIOSEPARATION ENGINEERING

SEM 2 (2010/2011)

ERT 313/4 BIOSEPARATION ENGINEERING

SEM 2 (2010/2011)

Colloid mill

Cell

suspension

Rotor

Stator

Disrupted

cells

• Typical rotation speeds: 10,000 to 50,000 rpm

• Mechanism of cell disruption: High shear and turbulence

• Application: Tissue based material

• Single or multi-pass operation

Separation of cells and medium

• Recovery of cells and/or medium

(clarification)

– For intracellular enzyme, the cell

fraction is required

– For extracellular enzymes, the culture

medium is required

• On an industrial scale, cell/medium

separation is almost always

performed by centrifugation

– Industrial scale centrifuges may be

batch, continuous, or continuous with

desludging

CENTRIF UGATION

A centrifuge is used for separating particles from a

solution according to their size, shape, density and

viscosity of the medium by the application of an

artificially induced gravitational field.

In bioprocesses, these particles could be cells, sub

cellular components, viruses and precipitated forms

of proteins and nucleic acids.

Centrifugation can be used to separate cells

from a culture liquid, cell debris from a broth, and a

group of precipitates.

Centrifugation may be classified into two types:

•Analytical centrifugation

•Preparative Centrifugation

Tubular Bowl Centrifuge

• Most useful for solid-liquid separation with enzymatic isolation

• Can achieve excellent separation of microbial cells and animal, plant, and most microbial cell debris in solution

Disc Bowl Centrifuge

• Widely used for removing cells and animal debris

• Can partially recover microbial cell debris and protein precipitates

Industrial centrifuges

Perforate Bowl Basket Centrifuge

• Exception at separation of adsorbents,

such as cellulose and agarose

Zonal Ultracentrifuge

• Applied in the vaccine industry

because it can easily remove cell debris

from viruses

• Can collect fine protein precipitates

• Has been used experimentally to purify

RNA polymerase and very fine debris

in enzymes

Properties of industrial centrifuges

• Tube

– High centrifugal force

– Good dewatering

– Easy to clean

• Chamber

– Large solids capacity

– Good dewatering

– Bowl cooling possible

• Disc type

– Solids discharge

– No foaming

– Bowl cooling possible

– Limited solids capacity

– Difficult to recover protein

– No solids discharge

– Cleaning difficult

– Solids recovery difficult

– Poor dewatering

– Difficult to clean

Centrifugation properties of different cell types

• Bacteria

– Small cell size

– Resilient

• Yeast cells

– Large cells

– Resilient

• Filamentous fungi

– Mycelial

– Resilient

• Cultured animal cells

– Large cells

– Very fragile

– High speed required

– Low cell damage

– Lower speed required

– Low cell damage

– Lower speed required

– High water retention in pellet

– Very susceptible to damage

Forced Developed in Centrifugal Separation

1. Introductions

• Centrifugal separators use the common principal

that an object whirled about an axis or center

point a constant radial distance from the point is

acted on by a force

• The object is constantly changing direction and is

thus accelerating, even though the rotational

speed is constant

• This centripetal force acts in a direction toward

the center of rotation

3.2. Sedimentation in a centrifugal field

3.2.1.1 Centrifugal settling or sedimentation Use of centrifuges increases the forces on particles manyfold. Hence, particles that will not settle readily or at all in gravity settlers can often be separated from fluids by centrifugal force. These high centrifugal forces do not change the relative settling velocities of small particles, but these forces do overcome the disturbing effects of Brownian motion and free convection currents. Sometimes gravity separation may be too slow because of the closeness of the densities of the particles and the fluid, or because of association forces holding the components together as in emulsions.

continued

gravity and centrifugal sedimentation of a single particle are illustrated in Figure 3.9

Figure 3.9: Gravity and centrifuge sedimentation of a single particle. Angular speed (ω); distance of particle to axis of rotation (r), m = mass, g = gravity

continued

An example in the dairy industry is the separation of cream from whole milk, giving skim milk.

Gravity separation takes hours, while centrifugal separation is accomplished in minutes in a cream separator.

Centrifugal settling or separation is employed in many food industries, such as breweries, vegetable-oil processing, fish-protein-concentrate processing, fruit juice processing to remove cellular materials, and so on.

Centrifugal separation is also used in drying crystals and for separating emulsions into their constituent liquids or solid—liquid

continued

3.2.1.2 Centrifugal filtration Centrifuges are also used in centrifugal filtration, where a centrifugal force is used instead of a pressure difference to cause the flow of slurry in a filter where a cake of solids builds up on a screen. The cake of granular solids from the slurry is deposited on a filter medium held in a rotating basket, washed, and then spun ‘dry.’ Centrifuges and ordinary filters are competitive in most solid—liquid separation problems.

If the object being rotated is a cylindrical container, the contents of fluid and solids exert an equal and opposite force, called centrifugal force, outward to the walls of the container. This is the force that causes settling or sedimentation of particles through a layer of liquid or filtration of a liquid through a bed of filter cake held inside a perforated rotating chamber In Fig. 3.10a cylindrical bowl is shown rotating, with a slurry feed of solid particles and liquid being admitted at the center

3.2.2 Forces developed in centrifugal separation

Figure 3.10: Sketch of centrifugal separation: (a) initial slurry feed entering. (b) settling of solids from a liquid, (c) separation of two liquid fraction.

continued

The feed enters and is immediately thrown outward to the walls of the container, as in Fig. 3.10b. The liquid and solids are now acted upon by the vertical gravitational force and the horizontal centrifugal force. The centrifugal force is usually so large that the force of gravity may he neglected. The liquid layer then assumes the equilibrium position, with the surface almost vertical. The particles settle horizontally out ward and press against the vertical bowl wall. in Fig. 3.10c two liquids having different densities are being separated by the centrifuge. The denser fluid will occupy the outer periphery since the centrifugal force on it is greater.

3.2.2.1 Equations for centrifugal force

In Fig 3.11 a schematic of a tubular-bowl centrifuge is shown. The feed enters at the bottom, and it is assumed that all the liquid moves upward at a uniform velocity carrying solid particles with it. The particle is assumed to be moving radially at its terminal settling velocity υt. The trajectory or path of the particle is shown in Fig. 3.10. A particle of a given size is removed from the liquid if sufficient residence time is available for the particle to reach the wall of the bowl where it is held. The length of the bowl is b m. At the end of the residence time of the particle in the fluid, the particle is at a distance rB m from the axis of rotation. If rB < r2, then the particle leaves the bowl with the fluid.

Figure 3.11: Particle settling in sedimenting tubular-bowl centrifuge.

continued

If rB = r2 , it is deposited on the wall of the bowl and effectively removed from the liquid.

In circular motion the acceleration due to the centrifugal force is where ae is the acceleration from a centrifugal force in m/s2 (ft/s2), r is radial distance from the center of rotation in m (ft), and ω is angular velocity in rad/s The centrifugal force Fc in N (lbf) acting on the particle is given by

Where gc= 32.174lbm.ft/lbf.s

2

2rae E3.19

2mrmaF ec

c

cg

mrF

2 E3.20 (SI) (English)

continued

r

m

rmrFc

22

Since ω = υ/r, where υ = the tangential velocity of the particle in m/s Often rotational speeds are given as N rev/min and

E3.21

60

2 N

rN

2

60 E3.22

continued

For settling in the Stokes’ law range, the terminal settling velocity at a radius r is obtained by substituting eqn. (3.19) for the acceleration g into eqn. (3.8): where υt = settling velocity in the radial direction (m/s) Dp = particle diameter (m) ρp = particle density kg/m3 ρ = liquid density in kg/m3 and μ = liquid viscosity in Pa s,

18

22

pp

t

rD E3.23

continued

If hindered settling occurs, Since υt = dr/dt, Eqn. (3.23) becomes Integrating between the limits r = r1 at t = 0 and r = r2 at t = tT

p

pp

t

gD

2

2

18

E3.24

r

dr

Ddt

pp

22

18

1

2

22ln

18

r

r

Dt

pp

T

E3.25

E3.26

continued

V = πb (r22 – r1

2) , thus, the feed volumetric flow rate Q in m3/s is

2

1

2

2

1

2

22

1

2

22

ln18ln18

rrb

rr

DV

rr

DQ

pppp

E3.27

Particles having diameters smaller than that calculated from eqn. ( 3.27) will not reach the wall of the bowl and will go out with the exit liquid. Larger particles will reach the wall and be removed from the liquid.

Notes:

centrifugation is most effective when the particles to be separated are large, the liquid viscosity is low and the density difference between particles and fluid is great

it is also assisted by large centrifuge radius and high rotational speed

in centrifugation of biological solids such as cells, the particles are very small, the viscosity of the medium can be relatively high and the particle density is very similar to the suspending fluid. These disadvantages – easily overcome in the lab with small centrifuges operated at high speed

continued

however, problems arise in industrial centrifugation

when large quantities of material must be treated

centrifuge capacity cannot be increased by simply increasing the size of equipment without limit; mechanical stress in centrifuges increases in proportion to (radius)2 so that safe operating speeds are substantially lower in large equipment

the need for continuous throughput of material in industrial applications also restricts practical operating speeds

to overcome these difficulties, a range of centrifuges has been developed for bioprocessing industry

3.2.2.2 Sigma Analysis & Scale up

commonly used analysis in industry is “sigma analysis” which uses the operation constant Σ to characterize a centrifuge into which feed flows at volumetric flow rate Q

Estimation of Q the followed equation can be used:

Q = {υg} [Σ] where υt = the sedimentation velocity at 1 x g, namely

and Σ represents the geometry and speed of centrifuge and as the cross-sectional area equivalent of the centrifuge with units of length squared

E3.28

E3.29

18

2

pp

t

gD

continued

therefore, in eqn. (3.28) the accolades { } indicate properties of the particle to be separated and of the fluid in which separation is occurring and the brackets [ ] indicate properties of the centrifuge

if two centrifuges perform with equal effectiveness:

where subscripts 1 and 2 denote the two centrifuges

the above equation can be used to scale-up centrifuge equipment

equations for evaluating Σ depend on the centrifuge design

2

2

1

1

QQ

continued

the above equations for Σ are based on ideal operating conditions

Because different types of centrifuge deviate to varying degrees from ideal operation that equation cannot generally be used to compare different centrifuge configurations

performance of any centrifuge can deviate from theoretical production due to factors such as

Particle shape and size distribution

Aggregation of particles

Non-uniform flow distribution in the centrifuge and

Interaction between particles during sedimentation

Experimental tests must be performed to account for these factors

Figure 3.12: Common types of production centrifuge: (a) tubular bowl (b) Multichamber, (c) disk, nozzle (d) disk, intermittent discharge, (e) scroll and (f) basket. Arrows indicate the path of the liquid phase; dashed lines show where the solids accumulate

3.2.3 Centrifuge Equipment

The Operation Steps of Centrifuge Equipment

Tubular-

bowl

centrifuge

the simplest configuration

widely employed in the food and pharmaceutical industries

Feed enters under pressure through a nozzle at the bottom,

is accelerated to rotor speed and moves upwards through the

cylindrical bowl

As the bowl rotates, particles are traveling upward are spun

out and collide with the walls of the bowl as illustrated

schematically in Figure 3.13

Solids are removed from the liquid if they move with

sufficient velocity to reach the wall of the bowl within the

residence time of liquid in the machine

As the feed rate is increased the liquid layer moving up the

wall of the centrifuge becomes thicker;

this reduces performance of the centrifuge by increasing the

distance a particle must travel to reach the wall

Centrifuge equipment is classified according to internal structure

continued

Figure 3.13: Separation of solids in a tubular-bowl centrifuge

= R1

= R0

continued

liquid from the feed spills over a weir at the top of the bowl;

solids which have collided with the walls are collected

separately

when the thickness of sediment collecting in the bowl reaches

the position of the liquid-overflow weir, separation efficiency

declines rapidly.This limits the capacity of the centrifuge

applied mainly for difficult separations requiring high

centrifugal forces

solids in tubular centrifuges are accelerated by forces between

13 000 and 16 000 times the force of gravity

continued

then in the axial direction, due only to pumped flow, Q

where A = the cross-sectional area for liquid flow in the centrifuge. These equations of motion are combined to give the trajectory equation

2

1

2

0 RR

Q

A

Q

dt

dz

(E3.30)

dz

dR

dt

dzdt

dR

(E3.31)

The equations of motion that give the trajectory of sedimented particles - in the radial direction from equation (E3.23)

18

22

pp

t

rD

dt

dR

(E3.32)

continued

substituting equation (E3.30) and (E3.31) into this ratio (E3.32), integrating dR between r1 and r2 and integrating dz between 0 and b and solving for Q gives

the first factor in equation (3.33) can be multiplied by g while the second is divided by g to give, again, equation (E3.28) for Σ analysis:

Q ={υg}[Σ]

(E3.33)

(E3.28)

1

2

22

1

2

2

2

ln18r

r

rrbDQ

pp

continued

where for a tubular bowl centrifuge,

1

2

22

1

2

2

lnr

rg

rrb (E3.34)

Example 3.5: Complete recovery of bacterial cells in a

tubular bowl centrifuge

It is desired to achieve complete recovery of bacterial cells from a fermentation broth with a pilot plant scale tubular centrifuge. It has been already determined that the cells are approximately spherical with a radius of 0.5μm and have a density of 1.10g/cm3. The speed of the centrifuge is 5000rpm, the bowl diameter is 10cm, the bowl length is 100cm and the outlet opening of the bowl has a diameter of 4cm. Estimate the maximum flow rate of the fermentation broth that can be attained.

Solution

continued

Ultracentrifuge

(A type of

narrow tubular-

bowl centrifuge)

Used for

recovery of fine precipitates from high-density solutions,

breaking down emulsions

separation of colloidal particles such as ribosomes and

mitochondria

produces centrifugal forces 105-106 times the force of gravity

the bowl is usually air-driven and operated at low pressure or in

an atmosphere of nitrogen to reduce generation of frictional heat

a typical ultracentrifuge operates discontinuously so its

processing capacity is restricted by the need to empty the bowl

manually

continuous ultracentrifuge are available commercially

continued

Disc-stack

bowl

centrifuge

many types of disc centrifuge; the principal difference between them

is the method used to discharge the accumulated solid

In simple disc centrifuges, solids must be removed periodically by

hand

Continuous or intermittent discharge of solids is possible in a variety

of disc centrifuges without reducing the bowl speed

Some centrifuges are equipped with peripheral nozzles for continuous

solids removal; others have valves for intermittent discharge

Another method is to concentrate the solids in the periphery of the

bowl and then discharge them at the top of the centrifuge using a paring

device; figure (3.14)

A disadvantage of centrifuge with automatic discharge of solids is that

the solids must remain sufficiently wet to flow through the machine

Extra nozzles may be provided for cleaning the bowl should blockages

of the system occur

continued

Figure 3.14: Disc-stack bowl centrifuge with continuous discharge of solids

continued

Contain conical sheets of metal called discs - stacked one on

top of the other with clearances as small as 0.3 mm

The discs rotate with the bowl and their function is to split the

liquid into thin layers

As shown in figure (3.15), the feed is released near the bottom

of the centrifuge and travels upward through matching holes in

the discs

Between the disc, heavy components of the feed are thrown

outward under the influence of centrifugal forces as lighter liquid

is displaced towards the center of the bowl

As they are flung out, the solids strike the undersides of the

discs and slide down to the bottom edge of the bowl

At the same time, the lighter liquid flows in and over the upper

surfaces of the discs to be discharged from the top of the bowl

Heavier liquid containing solids can be discharged either at the

top of the centrifuge or through nozzles around the periphery of

the bowl

continued

Figure 3.15: Mechanism of solids separations in a disc-stack bowl centrifuge

continued

therefore, in a sensitivity analysis, ∑ factor depends on

the cube of the bowl radius,

the cotangent of the disk acute angle,

the number of disks in the stack and

as in the tubular centrifuge, the square of the rotor speed

the disk acute angle θ made by the conical disks is typically between 35 and 45 degrees

g

RRngaQ

3

cot)(2

9

2 3

1

3

0

2

0

2

(E3.35)

Q ={υg}[Σ]

System Advantages Disadvantages

Tubular bowl a)High centrifugal force

b)Good dewatering

c)Easy to clean

d)Simple dismantling of bowl

a)Limited solids capacity

b)Foaming unless special

skimming or centrifugal pump

used

c)Recovery of solids difficult

Chamber

bowl

a)Clarification efficiency remains

constant until sludge space full

b)Large solids holding capacity

c)Good dewatering

d)Bowl cooling possible

a)No solids discharge

b)Cleaning more difficult than

tubular bowl

c)Solids recovery difficult

Disk

centrifuge

a)Solids discharge possible

b)Liquid discharge under pressure

eliminates foaming

c)Bowl cooling possible

a)Poor dewatering

b)Difficult to clean

A comparison of the advantages and disadvantages of the different centrifuge designs is given in table (3.2.1)

continued

System Advantages Disadvantages

Scroll or

decanter

centrifuge

a)Continuous solids discharge

b)High feed solids concentration

a)Low centrifugal force

b)Turbulence created by scroll

Basket

centrifuge

a)Solids can be washed well

b)Good dewatering

c)Large solids holding capacity

a)Not suitable for soft biological

solids

b)No solids discharge

c)Recovery of solids difficult

Table 3.2.2: Capabilities of tubular and disk centrifuges

Type Bowl dia.(mm)

Speed (rpm)

Max. dimensionless acceleration G, ω2R/g

Throughput (liters/min)

Tubular bowl

44

105

127

50,000

15,000

15,000

61,400

13,200

16,000

0.2-1.0

0.4-38

0.8-75

Disk with nozzle discharge

254

406

686

762

10,000

6,250

4,200

3,300

14,200

8,850

6,760

4,630

40-150

100-570

150-1500

150-1500