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Centrifugation When a solid-liquid suspension is rotated in a

cylindrical container (bowl) the suspension issubject to a centrifugal force in the radialdirection.

Centrifugation is a process by which solidparticles are sedimented and separated from aliquid using centrifugal force as a driving force.

Depending on the rotational speed and distance

from the axis of rotation, the centrifugal forcecan be many times greater than the force ofgravity, allowing even very small particles orparticles slightly denser than the fluid to settle.

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Sludge Thickening and Dewatering

In wastewater treatment, sludge is producedfrom a number of operations such as primarysettling, coagulation and flocculation, andbiological activated sludge processes.

The sludge produced in these processes mayvary greatly in concentration, but it is typicallyof the order of 1%.

Sludge concentration, typically conducted in

stages, is a common way to reduce the amountof sludge to be eventually disposed of.Thickening and dewatering are commonoperations to concentrate sludges.

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Sludge Thickening

Sludge thickening consists of increasing theconcentration of a sludge from its originalvalue (typically about 1%) to between 2 and10%.

Physical methods are typically used, includingsedimentation, flotation, centrifugation andcake filtration.

The thickened sludge still contains a

significant amount of water and can bepumped.

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Sludge Dewatering

Thickened sludge still contains too muchwater to be economically transported anddisposed of.

Sludge dewatering is an operation throughwhich a significant portion of the sludgemoisture is removed to produce a semidrycake typically containing solids inconcentration ranging between 10 and 40%.

Operations such as cake filtration,centrifugation, and bed drying are commonlyemployed for this purpose.

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Application of Centrifugation toWaste and Wastewater TreatmentCentrifugation has two main applications, namely:

Thickening of sludges and especially activated

sludges and chemical slurries. In these casesthe sludge produced during primary orsecondary treatments is concentrated in itssolids content (typically up to 2-10%).

Dewatering of sludges from primary andsecondary treatments. In these applicationswater is removed from sludges that have beenalready thickened, producing cakes having 15-20% (or even higher) solids concentration.

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Thickening and Dewatering of Sludgesvia Centrifugation

Most centrifugation processes for wastewatertreatment operate in a continuous mode.

The performance of centrifuges as sludgethickeners (in which both the clarified liquidand the thickened sludge are fluids) is moreeasily predicted and quantified than whencentrifuges are used as sludge dewatering

devices (in which a moist solid or cake mustbe effectively moved out of the centrifuge as itis formed).

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Centrifuges

Centrifuges are sedimentation devices inwhich suspended solids are separated from aliquid under the action of centrifugal forcesgenerated by spinning the internal bowl of the

centrifuge.

The resulting settling velocities of the solidscan be significantly higher than thosegenerated by gravity forces.

Centrifuges can be thought of assedimentation vessels operating under highgravitational forces.

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Types of Centrifuges Used inWastewater and Sludge Applications

Solid bowl centrifuges (decanters)

Basket centrifuges

- Perforated basket centrifuges

- Imperforated basket centrifuges

Disk bowl centrifuges

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Solid Bowl Decanter

Motor

Liquid DischargeSolid Discharge

SolidsLiquidHelicalScroll

RotatingBowl

Feed

Cover

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Solid Bowl Centrifuge (or Decanter) A solid bowl centrifuge (or decanter) consists

of an elongated cylindrical rotating bowlhaving a tapered conical end

The bowl length-to-diameter ratio is typically in

the range 2.5:1 to 4:1

The suspension is continuously introduced atone end of the bowl and travels parallel to thebowl axis. The clarified liquid is collected at

the end of the cylindrical section of the bowl

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Solid Bowl Centrifuge (or Decanter)(continued)

The solids are collected at the end of thetapered section of the centrifuge where thecentrifuge forms a dewatering beach.

The solids move typically countercurrent to theliquid. Co-current centrifuges are also used.

A helical scroll rotating at a slightly differentspeed than the bowl is used to move the solidstoward the tapered end where they arecontinuously removed through ports.

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Perforated Basket Centrifuge

Solids Liquid

Feed

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Perforated Basket Centrifuge This type of centrifuge is provided with a

rotating perforated basket, which allows acake of solids to build inside the basket whileallowing the liquid to pass through the

cylindrical wall of the basket (centrifugalfiltration)

The clarified liquid is continuously removed asit emerges from the basket

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Perforated Basket Centrifuge(continued)

The solid is intermittently removed with a knife(not rotating with the basket) placed inside thebasket, and collected in a vertical chute

Drier cakes are obtained with this type ofcentrifuge than with other types. Thereforethis type of centrifuge is used when therecovery of solids is desirable

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Imperforated Basket Centrifuge

Liquid

Cake

Feed

Knife

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Imperforated Basket Centrifuge This centrifuge consists of an imperforated

(solid) basket spinning vertically

The feed is continuously introduced into thecentrifuge while the liquid (centrate) is

continuously removed from an overflow weirinside the centrifuge

Solids build up during centrifugation forming acake that must be periodically discharged

After the basket becomes filled with solids thecentrifuge slows down and "skimming" (theremoval of the top semi-liquid soft cake layer)takes place

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Imperforated Basket Centrifuge(continued)

Skimming typically removes 5 to 15% of thebowl solid volume

The bulk of the cake is discharged using aplowing knife moving into the slowly rotatingcake

The solid is discharged centrally at the bottomof the centrifuge

Solid accumulation is typically up to 60 to 85%of the maximum available depth

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Disk Bowl Centrifuge

Liquid

SolidsSolids

Feed

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Disk Bowl Centrifuge In order to leave the centrifuge the liquid must

pass between conical plates where the solidscan separate after impacting on the plates

The clarified liquid is continuously fed and

removed from the center of the centrifuge

The solid cake (thickened sludge) iscontinuously or intermittently removed fromthe side of the centrifuge

Only degritted suspension can be fed to thistype of centrifuge in order to minimizeproblems associated with plugging

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Chemical Additions DuringCentrifugation Operations

In sludge thickening operations chemicalconditioners (especially polyelectrolytes) areoften added to the sludge before feeding it tothe centrifuge or directly in the centrifuge.

The additives promote the ability of thesuspended particles to flocculate and settleinside the centrifuge, thus increasing solid

removal. Chemical additions promote the removal of

fine solids.

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Chemical Additions DuringCentrifugation Operations

Chemical additives can also be used topromote sludge dewatering. However, this is amuch more difficult process to describe andpredict. Hence, the effectiveness of chemicaladdition in dewatering processes must betested in pilot plant experiments.

Cakes with a higher water content are obtained

if chemical additions are made duringdewatering processes.

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Typical Levels of Polymer Additionsfor Thickening of Sludges

Amount of Polymer Addition(lb dry polymer/ton dry solids)

Type of Sludge Dissolved

Air Flotation

Solid Bowl

Centrifuge

Basket

Centrifuge

Gravity Belt

Filter

WasteActivated

4-10 0-8 2-6 6-14

AnaerobicallyDigested

8-16

AerobicallyDigested

8-16

After Metcalf and Eddy, Wastewater Engineering, 1991, p. 262

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Centrifuge Operations inWastewater and Sludge Applications

Batch

- Perforated basket centrifuge

- Imperforated basket centrifuges

Continuous

- Solid bowl centrifuges (decanters)

- Disk bowl centrifuges

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Centrifuges vs. Vacuum FiltersCentrifuges and vacuum filters are often used forthe same sludge treatment purposes.

Advantages of centrifuges over vacuum filters:

Lower capital costs; Lower space requirements;

Capability of treating suspension with poorfiltration capability.

Advantages of vacuum filters over centrifuges:

Higher solid concentration in the cake;

Lower solid concentration in the effluent.

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Analysis of CentrifugePerformance

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Process Variables AffectingCentrifugation

Type of slurry and solid particles contained init:

- Liquid viscosity- Liquid density

- Solids concentration

- Particle size distribution

- Surface charge of particles

- Type and/or shape or particles

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Process Variables AffectingCentrifugation (continued)

Feed rate of slurry

Agitation speed

Size of centrifuge (distance from rotation axis) Height of cake

Allowable pressure drop across cake

Mode of operation (batch vs. continuous) Time at full speed

Depth of skimming

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Possible Cases to Be Examined Batch centrifugation (e.g., with imperforated

basket centrifuges)

Continuous centrifugation (e.g., with solidbowl centrifuges)*

Batch centrifugal filtration (e.g., withperforated basket centrifuges)*

(Semi-)Continuous centrifugal filtration (e.g.,with perforated basket centrifuges)

(*) Cases that will be examined here

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Alternative Expression for theCentrifugal Force

The relationship between the rotational speed, N

expressed in rpm, and the angular velocity, , is:

=2

60N

If the rotational speed is expressed in rpm thenthe centrifugal force is:

F m a m r N e e= = 260

2

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Centrifugal AccelerationThe acceleration due to the centrifugal force isgiven by:

a re = 2

or

a r Ne =

2

60

2

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Relationship Between Centrifugal and

Gravity Accelerations: The g-FactorThe g factor is defined as the ratio of thecentrifugal force to the gravity force:

g ag

FF

rg

rg

Ne eg

= = = = factor 2 2

2

60

ga

g

F

Fr Ne e

g

= = =factor 0 001118 2. (SI units)

ga

g

F

Fr Ne e

g

= =factor = 0 000341 2. (English units)

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Settling Velocity of Particles

Subject to Centrifugal ForceThe terminal velocity, vp, of a spherical particle of

diameter Dp and density s located in a rotatingfluid at a distance r from the rotation axis and

moving in laminar flow is:

( )v

r Dp

p s L=

2 2

18

where: = fluid viscosity

L = fluid density

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Analysis of Continuous Centrifugation

in a Solid Bowl Centrifuge

Liquid DischargeSolid Discharge

Feed

R r RL

Suspension

Solid Movement

Liquid Movement

b

w

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Nomenclature for Solid Bowl

Centrifugesb length of the cylindrical part of the centrifuge

r generic distance from the axis of rotation

RC radial distance from the axis of rotation tothe top layer of the cake

RL radial distance from the axis of rotation tothe liquid pool

RW radial distance from the axis of rotation tothe centrifuge wall

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Assumptions Made to Model Continuous

Centrifugation in a Solid Bowl Centrifuge The feed (suspension) enters at the end of the

cylindrical wall of the centrifuge bowl near thetapered end and travels across the centrifuge

If a particles reaches the bowl wall is consideredsettled

The settled solid particles and the cleared liquidmove countercurrent with respect to each other

The settled particles and the cleared liquid arecontinuously removed at opposite ends of thecentrifuge

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Assumptions Made to Model Continuous

Centrifugation in a Solid Bowl Centrifuge The particles are assumed to settle

independently of each other (Type 1 settling)following Stokes law

Each liquid element remains in the centrifuge fora time equal to the residence time. Hence, theresidence time is the time available for theparticles to settle

All the particles that have not reached thecentrifuge wall within the residence time will exitwith the clarified liquid

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Settling Velocity of a Particle Inside a

Continuous Solid Bowl CentrifugeA particle settling inside the bowl centrifuge willhave a settling (radial) velocity given by:

( ) ( )v r d rd t

r Dp

p s L= =

2 2

18

where RL

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Relationship Between Time and

Distance Traveled by a Particle Insidea Continuous Solid Bowl Centrifuge

The radial distance, dr, traveled by a particle

during an infinitesimal time interval, dt, is:

( )( )

dr v r dt r D

dtpp s L= =

2 2

18

This expression can be rearranged and integrated

to give:

( )18

2 2

1

2

1

2

r Dd r dt

p s Lr

r

t

t

=

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Relationship Between Time and

Distance Traveled by a Particle Insidea Continuous Solid Bowl Centrifuge

Upon integration it is:

( )18

2 2

2

1

2 1

Drr

t tp s L

= ln

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Residence Time of the Liquid Inside

the Continuous Solid Bowl CentrifugeThe residence time, to, of the liquid in the bowl isthe time an average element of fluid will spend inthe centrifuge at steady state conditions:

tV

Qo =

where: V = volume of centrifuge available toliquid

Q = volumetric flow rate of liquidthrough centrifuge

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Liquid Volume in a CentrifugeThe liquid volume in the centrifuge is determinedby the height of the weir over which the liquid isdischarged:

( )V b R R w L= 2 2

Hence:

( )t

b R R

Qo

w L= 2 2

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Critical Particle Diameter for Settling

in a Continuous Solid Bowl CentrifugeIn order for the particle to settle it will have totravel a distance (Rw- RL), i.e., the distancebetween the surface of the liquid (where the

suspension is added) and the bowl wall, and to doso in the time interval to.

Only particles having a diameter larger than acertain critical diameter will be able to cover this

distance during the time interval to.

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in a Continuous Solid Bowl CentrifugeUpon substitution of:

t1 with 0 r1 with RL

t2with to r2with Rw

one gets:

( )

( )182 2

2 2

D

R

Rt

b R R

Qp s L

w

L

o

w L

= =

ln

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in a Continuous Solid Bowl CentrifugeFrom the previous equation the critical particlediameter, Dpo, can be found to be:

( ) ( )D Q

b R RRR

po

w L s L

w

L

=

2 2 2

18 ln

Particles larger than Dpo will settle during to,particles smaller than Dpowill not.

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Generalized Design Equation for

Continuous Solid Bowl CentrifugesThe following equation can be derived from theprevious equations, and used as the main designequation for solid bowl centrifuges:

( ) ( )( )

QD b R R

R

p s L w L

L

=

2 2 2 2

18 ln Rw

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Simplified Design Equation for

Continuous Solid Bowl CentrifugesThe previous equation can be simplified if oneassumes that the distance traveled by the particlein order to settle (equal to the liquid radial height)

is small in comparison to the bowl radius, Rw, i.e.:R R R R w L L w

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Simplified Design Equation for

Continuous Solid Bowl CentrifugesAssuming that:

lnR

R

R R

Rw

L

w L

w

and R R Rw L w+ 2

the equation:

( ) ( )( )

QD b R R

R R

p s L w L

w L

=

2 2 2 2

18 ln

becomes:( )( )[ ]

( )Q

Db R R R

b R Dp s Lw w L

w p s L

+

2 2 2 2 2

18 9

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Centrifuge Scale-up: the Sigma ValueThe design equation:

( ) ( )( )

QD b R R

R R

p s L w L

w L

=

2 2 2 2

18 ln

can be rewritten as:

( ) ( )( )

QD g

g

b R R

R Rv

p s L w L

w L

p=

=218 2

2 2 2 2

ln

where the parameter (Sigma value), defined as:

( )( )

= 2 2 2

2gb R R

R R

w L

w L

ln

is independent of the particle type and size.

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Centrifuge Scale-up: the Sigma ValueFor two geometrically similar centrifuges ofdifferent sizes (1 and 2) separating the same solidparticles from the same fluid it will be:

Q v Q v p p1 1 2 2= = and

To scale up experimental results from alaboratory centrifuge one can use the followingscale-up rule:

Q

Q

v

v

p

p

1

2

1

2

1

2= =

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Simplified Expression for the

Sigma Value: Simplified Scale-upAssuming that:

lnR

R

R R

Rw

L

w L

w

and R R Rw L w+ 2

then the Sigma value can be rewritten as:

2 2b R

gw

i.e.:

Q

Q

b R

b Rw

w

1

2

1

2

1

2

1 1

2

2

2

2 2

2=

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Solid Movement Inside a Continuous

Solid Bowl Centrifuge In a continuous solid bowl centrifuge both

clarification of the suspension and removal ofsolids occur simultaneously.

If the settled solids are not transported out at asufficient rate the pool inside the bowl fills upwith solids and no separation occurs.

The settled solids are transported out of acontinuous solid bowl centrifuge by the actionof a helical screw (scroll) rotating at a slightlydifferent velocity than the bowl.

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Scale-up of Continuous Solid Bowl Centrifuges

Based on Solid Throughput: the Beta ValueIf two centrifuges (labeled 1 and 2) are comparedin terms of solids removal the followingrelationship between the mass flow rate of solidscan be obtained:

( )( )

W

W

R R R Z N

R R R Z N

s

s

w w L s s s

w w L s s s

2

1

2 2 2 2 2 2 2

1 1 1 1 1 1 1

2

2=

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Scale-up of Continuous Solid Bowl Centrifuges

Based on Solid Throughput: the Beta ValueAssuming that the fraction of solids is the same in

both centrifuges (i.e., s1 = s2) and that the solids

fraction is also equal (i.e., s1 = s2), then:

( )( )

WW

R R R Z N R R R Z N

s

s

w w L s

w w L s

c

c

2

1

2 2 2 2 2

1 1 1 1 1

2

1

=

=

This equation defines a second scale-up methodbased on the beta value, i.e., the ratio of solids

throughputs for two centrifuges of two differentsizes. This method is important to determine thesolids removal in full-scale centrifuges based onthe results of pilot tests.

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Effect of Bowl Diameter Size on Solids

Separation Larger bowl diameters (while maintaining the

same centrifugal force by slowing down themachine rotation) result in longer retention

time within the centrifuge.

This results in higher solids recovery and awetter cake (i.e., having a lower concentrationof solids).

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Effect of Pool Depth on Solids

Separation The pool depth is the height of the liquid

annulus in the centrifuge.

The pool depth can be adjusted in mostcentrifuges, even when the centrifuge is inoperation.

An increase in the pool depth will result inhigher solids recovery (because of the

increased residence time), and a wetter cake

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Effect of Feeding Point on Solids

Separation The incoming sludge can be fed (at least in

some centrifuges) at different points along theaxis of the centrifuge.

When the feeding point is closer to the beach awetter cake will be produced, but the solidscontent in the centrate will be lower (highersolids recovery) because of the longer timeavailable for solids separation.

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Performance of Solid Bowl CentrifugesType ofSludge

Concentrationof Solids in

Cake (%)

Solid Recovery[No ChemicalAddition] (%)

Solid Recovery[Chemical

Addition] (%)

Primary 20-40 70-90 75-98

Primary &Activated

15-30 50-80 75-98

Activated 5-15 65-90 85-95

DigestedActivated

15-25 70-90 85-95

LimeSoftening 35-60 70-90 85-95

After Sundstrom and Klei, Wastewater Treatment, 1979, p. 238

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Characteristics of

Solid Bowl Centrifuges Feed rate range: 1.5-12 L/s (25-200 gal/min). Specific flow rate range: 3.5-15 m3/(d KW) (0.5-

2 gal/(min hp)).

Rotational speed: 1000-6000 rpm. g factor (ratio of centrifugal force to gravity

force): 2000-3000.

Centrifuges with larger pool volumes are moreeffective at dewatering sludges.

Pool depth (radial height of liquid) can beadjusted in most centrifuges.

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Analysis of Semi-Batch Centrifugal

Filtration in a Perforated Centrifuge

Solids Liquid

Feed

R

RL

w

Cake Liquid

Rc

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Filtration in a Perforated CentrifugeAssuming that the cake is not compressible (i.e.,

is independent of P) the pressure drop acrossthe cake at any given time is given by:

( )( )( )

( )P tX V t AR

AQ t

s F m

F=+

2

where XsVF(t) is the amount of solids that have

been deposited up to time t, and that have formedthe cake.

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Filtration in a Perforated CentrifugeThe pressure drop across the cake has to beovercome by the hydraulic head of liquid abovethe cake. Similarly to the differential pressure

head in a gravitational field given by:

dP g d =

the differential pressure head in a centrifugal fieldis

dP r dr = 2

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Filtration in a Perforated CentrifugeThe pressure head available to overcome thepressure drop can be obtained from integrationbetween the radial liquid height, RL and the

distance of the vessel wall from the rotation axis:

dP r dr P

LR

R

L

w

0

2

=

i.e.:

( )P

R RL

w L=

22 2

2

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Filtration in a Perforated CentrifugeCombining the expressions for the pressure dropand the available pressure head one gets:

( ) ( ) ( )( ) ( )P t R R X V t AR AQ tL

w L s F mF= = + 2

2 2

22

i.e.:

( )

( )( )( )Q t

A R R

X V t AR F

L w L

s F m=

+

2 2 2 2

2

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Filtration in a Perforated CentrifugeNote that the area A in:

( )( )

( )( )Q t

A R R

X V t AR F

L w L

s F m

=

+

2 2 2 2

2

is a function of the radii Rw, RL and Rc.

In addition, this equation is valid only for a givenmass of solids in the cake at a given time. This

equation is not in the integral form, i.e., it cannotbe used to describe the entire centrifugal filtrationprocess.

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Filtration in a Perforated CentrifugeIf the filtration area A varies significantly with theradius then it can be shown that the flow rate Qcan be expressed as:

( ) ( )( )

Q tR R

X V t

A A

R

A

F

L w L

s F

L a

m

w

=

+

2 2 2

2

where: ( ) ( )[ ]( )

A b R R R R

A b R R

A b R

L w C w C

a w C

w w

=

= +

=

2

2

ln

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Additional Information and Examples on

CentrifugationAdditional information and examples on can be found in thefollowing references:

Corbitt, R. A. 1990, The Standard Handbook of EnvironmentalEngineering, McGraw-Hill, New York, pp. 5.138-5.139; 6.210-

6.211; 6.223-6.229; 9.32-9.34.

Droste, R. L., Theory and Practice of Water and WastewaterTreatment, John Wiley & Sons, New York, 1997, pp. 732-735.

Geankoplis, C. J., Transport Processes and Unit Operations,3rd Edition, 1993, Allyn and Bacon, Boston, pp. 828-838.

Haas, C. N. and Vamos, R. J., 1995, Hazardous and IndustrialWaste Treatment, Prentice Hall, Englewood Cliffs, NJ, pp. 67-69.

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Additional Information and Examples on

Centrifugation Metcalf & Eddy, 1991, Wastewater Engineering: Treatment,

Disposal, and Reuse, McGraw-Hill, New York, pp. 805-806; 860-864.

Sundstrom, D. W. and Klei, H. E., 1979, Wastewater Treatment,Prentice Hall, Englewood Cliffs, NJ, pp. 234-238.

Vesilind, P. A., 1979, Treatment and Disposal of WastewaterSludges, Ann Arbor Science, Ann Arbor, MI, pp. 161-200.

Wentz, C. W., 1995, Hazardous Waste Management, SecondEdition, McGraw-Hill, New York. pp. 193-194.

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