Decanter Theory

Separationby

Centrifugation

Vanderbeken Enterprises Ltd.15525 Cliff Avenue, White Rock (B.C.), V4B 1V8, CANADA

[email protected]

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02 Vanderbeken Enterprises Ltd

Vanderbeken Enterprises Ltd 03

C E N T R I F U G A L F O R C E

The maximum centrifugal acceleration, developed inside a bowl with a radius “r” androtating at the angular speed of “ ω” is:

The G factor is in this

r = bowl inner radius (meters)ϖ = angular speed (radian/sec)*g = acceleration (9.81 m/sec2)n = bowl speed (RPM)

note: 1 radian = 57.3o

360°°°°= 6.287 radian

The term G- force or G- value is frequently used instead of acceleration. The G-force isdefined as the multiple of the gravitational constant that is obtained in the centrifuge.

An approximate formula for calculation the G-force at the bowl periphery is:

n = bowl speed (RPM)φ = bowl max inner dia. (meters)

Consequently the centrifugal acceleration or G-value will increase with the bowldiameter and bowl speed.

2

602

ng

rG

== πϖ

gr. 2

2rã ϖ=

1800

2φnG =


S L I P P A G E F O R C E

When solids are transported along the beach of a decanter, there is a force acting onthe solids in the direction of the liquid pool, named the SLIPPAGE FORCE (S).This force depends on the value of the difference in between the specific gravity of thesolid and the surrounding medium.

This means that the slippage force increases considerably when the solids pass out ofthe liquid pool onto the beach where they are surrounded by air.

As specified before, the centrifugal force is:

or simply

r = bowl inner radius (meters)ϖ = angular speed (radian/sec)*g = acceleration (9.81 m/sec2 )n = bowl speed (RPM)

note: 1 radian = 57.3°°°°360°°°°= 6.287 radian

The SLIPPAGE FORCE (S) : S = Sin αααα x G

#####n RPM

S G

αααα**

** note: Pieralisi α = 8030’ Others 80 200

22

60

2

== n

g

r

g

rG

πϖ

1800

2φnG =


E Q U I V A L E N T S U R F A C E ( S IG M A V A L U E )

∑ = sigma value (sq. m)n = bowl speed (RPM)

cylL = length cyl. section in meters

r = ½ bowl diameter in meters

Is the equivalent surface in sq. m of a static flotation tank to produce the samesolid / liquid separation result.

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Σ = 1 x 3200 2 x 1.230 x 0.235 2 = 4347 sq. m 160

22

160

1rLn cyl=∑


D E W A T E R I N G S U R F A C E

The dewatering surface in sq.m is the surface of the bowl cylindrical section that mayvary according to different decanter manufacturers.

Or

ncA , = wet dewatering (liquid) surface of decanter in sq. m

Σ = sigma value (sq m) – (equiv. surface)G = centrifugal force (G- force G- value)D = bowl inner diameter in meters

cylL = length cyl. section in meters

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A c, n

= 3.14 x 0.47 x 1.230 = 1.82 sq. m *

or

A c, n

= 4347 = 1.61 sq.m *2700

* the above results difference are related to the bowl RPM and G- force generated.

cylnc DLA π=, GA nc

∑=,


D E W A T E R I N G V O L U M E

The dewatering volume of a decanter is to be considered as the total content of theliquid zone in the cylindrical part of the bowl.

This volume may change in relation to the “weir plate” diameter. For the PieralisiJumbo 3 decanter, weir plates standard diameters are: 310, 300, 285, 280, 273 mm

re r i

Lcyl

#####weir plates

To calculate the dewatering volume cylindrical part take into a consideration the

cylindrical length L (in m) only, the bowl inner radius re ( in m

) and the r

i ( in m ).

The ri is approx = 60% of

re

as for the weir plates.

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D max = 470 mm

r max = 0.235 m (re)

ri = 60% of 0.235 = 0.141 m Lcyl = 1.23 m

The related dewatering volume will be:

( π x re

2 x Lcyl ) - ( π x ri 2

x Lcyl )

( 3.14 x 0.235 2 x 1.23 ) - (3.14 x 0.141 2

x 1.23 ) = 137 l


R E T E N T I O N T I M E

R t = 3600 (sec) x bowl total dewatering volume

(sec) Q input

Q = effluent input (l / h)btdw = bowl total dewatering volume (l)

The retention time is the standing time of the liquid in the bowl before discharge.

Retention time depends on characteristics of effluent input: e.g.

specific weight of solidviscosity of liquid phasequantity of polymer (if needed)

For a giver input Q, and no change of scroll rpm, the retention time will changewhen the weir plates diameter is modified to change the dewatering volume.

1RWH=1RWH=1RWH=1RWH= a smaller weir plate diameter will increase the retention time

When retention time is longer, more efficient solid / liquid separation will be achieved.

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Q = 22 m3 / h

Dewatering volume = 146 l ( based on 310 mm dia. weir plates )(total bowl liquid content)

R t = 3600 x 146 = 24 sec

22000


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Q = 22 m3

/ hDewatering volume = 179 l ( based on 273 mm dia. weir plates )(total bowl liquid content)

R t = 3600 x 179 = 29 sec

22000

A simple explanation about the importance of the retention time will be given using forexample a static settling tank 200 m (600 ft.) long as shown the following sketch.Note that the efficiency of process separation is related to the settling time allowed aswell as to a bigger settling surface.

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@450ft(150m)@ 300ft(100m)


In a decanter, the settling time will be related to the retention time provided and theapplied G - force).

Larger settling area will result in shorter separation time. However, one of the negativeaspects will be explained by the following example.

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We note that at the same Q effluent input, the settling time will be proportional to thetank surface ( less time in tank B ), …… in tank A we may observe a betterseparation layer.

Time required for separation to occur depends on the speed of descent and on thedistance the particles must travel. A shorter distance results in quicker separation.

According to what has been previously stated, we may conclude that a larger decanter(if compared to a settling tank), will provide a better separation efficiency; in themeantime, we noted that with settling surface, a better separation result will beattained because the clearest separation layers are achieved.

However, when a decanter is used in a separation process, it is important to rememberthat a bigger decanter will run at less RPM and develop a lesser centrifugal force, Gthan a smaller one.

In other words, the centrifugal force is very influential during any solid / liquidseparation process where different chemical and physical factors may contribute to theprocess results.


R E T E N T I O N A F F E C T E D B Y ∆∆∆∆n V A R I A T I O N

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100 cm

123 cmlength cyl. part

A to B = distance covered by the liquid through the bowl before the exit, will beequivalent to:

@ ∆n = 0 100 / 13 x 3.14 x 0.47 = 11 m

@ ∆n = 10 11 + ( 10 x 3.14 x 0.47 ) = 25 m

It is evident that the length, 11m or 25m, is the distance A to B travelled by the liquidthrough the bowl due to the turning effect of the scroll, creating an opposite liquid flowin the bowl until discharged at the weir plates.

127(=127(=127(=127(=In some cases (for example PAINT effluent separation), decreasing ∆n will create aturbulent effect that prevents the required separation.

PIERALISI JUMBO 3Total bowl content = 146 l( based on 310 mm dia weir plate)RETENTION TIME = 1 minute

22 m3 / h inputSludge feeding point@ 100 cm from theliquid outlet

A B


Efficiency in separation may be obtained by the ∆n variation.(∆n = differential speed between bowl and scroll)

if a decanter runs with ∆n = 10weir plates 310 mm diameterseparation efficiency = 95%polymer consumption = 12 Kg / h

and Customer needs separation efficiency = 98%polymer consumption = 12 Kg / h

If the decanter used in this operation is a Pieralisi Jumbo 3, it is necessary to

reduce the weir plates diameter from 310 mm down to 273 mm (resulting inlarger volume

or

increase the ∆n from 10 up to 12 or more (resulting in slower scroll rpm).

According to the following illustration we may note how ∆n affects the retention time:

When ∆n is decreased, (the scroll will turn faster) RETENTION time for separation inthe liquid phase will be reduced.


T H E R E T E N T I O N T I M E S L U D G E O N D R Y B E A C H

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############# 200 mm dewatering zone

1230 mm cyl. part length 768 mmseparation zone con. part length

1998 mmtotal bowl length

Assume that with ∆n = 10 and feedrate, Q = 22 m3 / h, the RETENTION time of liquidfor solids separation is 24 seconds, Example a), page 8 then

Calculate the RETENTION TIME SLUDGE ON DRY BEACH, length = 200 mm

∆∆∆∆n = 10 rpmPitch = 13 cmDry L = 20 cm

Ratio of material transport to dry beach length, 10 x 13 = 130 / 20 = 6.5

Time available on dry beach for material, 60 (sec ) / 6.5 = 9.2 sec

Rt (sludge dry beach) in seconds = 60 x dewatering zone length (cm)

∆∆∆∆n x scroll pitch (cm)

Effluent input22 m3 / h

Weir Plates310 mm dia


S L U D G E D E C A N T E R C O M P A R I S O N

Sometimes manufacturers offer decanters with unrealistic capacity or dewateringvolume .

It is necessary to have a common denominator to compare costs and capacities.Following example shows how to compare two centrifuges:

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Manufacturer Machine type Capacity m3 /h Price (comparison units)

PIERALISI PIERALISI JUMBO 3 25 100,000Westfalia CA 450 25 85,000

Manufacturer Cyl. part lengthmm

Con. part lengthmm

Bowl diametermm

Slender’ns RatioTotal length / Dia

PIERALISI 1230 768 470 4.25Westfalia 705 745 458 3.16

Dewatering volume cylindrical part calculation: (60% bowl dia. weir plates)

Pieralisi 3.14 x 0.235 x 0.235 x 1.23 = 213 liters3.14 x 0.141 x 0.141 x 1.23 = 76 litersDewatering volume cyl. parts = 137 liters

Westfalia 3.14 x 0.229 x 0.229 x 0.705 = 116 liters3.14 x 0.1374 x 0.1374 x 0.705 = 40 litersDewatering volume cyl. parts = 76 liters

Pieralisi Dewatering volume cyl. parts = 137 liters

Westfalia Dewatering volume cyl. parts = 76 liters

Difference = 61 liters

Pieralisi PIERALISI JUMBO 3 decanter dewatering volume over Westfalia 80%

Pieralisi decanter selling price = 100,000 CU / 137 liters = 730 CU / literWestfalia decanter selling price = 85,000 CU / 76 liters = 1,118 CU/ liter


If dewatering volume = 25,000 liters / h

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Rt (seconds)

= 3600 x bowl dewatering volume (liters)

Q input

Pieralisi Rt = 3600 x 137 / 25.000 = 19.7 seconds

Westfalia Rt = 3600 x 76 / 25.000 = 10.9 seconds

Westfalia RETENTION time 55 % shorter than Pieralisi decanter

Polymer consumption

If poly consumption for Pieralisi decanter is 5 Kgs / Ton DS (dry solid)

Westfalia will need a quantity equivalent to 5 / 0.55 = 9.1 Kgs / Ton DS

It is evident that the polymer consumption is related to the retention timedue to the time needed for floculation.(the G – force ialso influences over consumption)


T E C H N I C A L I N F O ’ S Q U I C K R E F E R E N C EF O R M U L A S

C E N T R I F U G A LF O R C E

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The term G- force or G- value is frequentlyused instead of acceleration due to Gravity.The G-force is defined as the multiple of thegravitational constant that is obtained in thecentrifuge. The centrifugal acceleration or G-value will increase with the bowl diameter andbowl speed.

n = bowl speed (RPM) Φ = bowl max. inside dia. in meters

When the solids are transported along thedry beach of a decanter, there is a forceacting on the solids in the direction of theliquid pool, named the SLIPPAGE FORCE(S).This force is affected by the value of thedifference in between the specific gravity ofthe solid and the surrounding medium.This means that the slippage forceincreases considerably when the solidspass out of the liquid pool onto the beachwhere they are surrounded by air.

Note: Pieralisi α = 8030’ Others 80 @ 200

Is the equivalent surface in sq.mof a static flotation tank toprovide the same result for solidsseparation from the feed slurry.

Σ = sigma value, sq.mn = bowl speed, RPML cyl = length cyl. section, m r = ½ bowl diameter, m


D E W A T E R I N GS U R F A C E ( s q . m )

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The dewatering surface in sq.m is thesurface of the bowl cylindrical sectionthat may vary according to differentdecanter manufacturers.

D = bowl inner diameter, mL cyl = length cyl. Section, mA

c, n = wet dewatering (liquid) surface of

Decanter, sq.mΣ = sigma value, (equiv. surface), sq. mG= centrifugal force (G- force, G- value)

The dewatering volume will be as thetotal content liquid zone of the bowlcylindrical part.This volume will change in relation tothe “weir plates” diameter.For the Pieralisi Jumbo 3 decanter theweir plates std. Diameters are: 310,300, 285, 280, 273 mmTo calculate the dewatering valuecylindrical part consider only thecylindrical length L in m, the bowlinside radius re ( in mts ) and the ri ( in mts ).The ri

is approx = 60% of re as for

the weir plates.


R E T E N T I O NT I M E ( s e c )

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R E T E N T I O N T I M EA F F E C T E D B Y ∆n V A R I A T I O N

T H E R E T E N T I O N T I M ES L U D G E O N D R Y B E A C H

The retention time is the time liquid remains inthe bowl before being discharged.Retention time depends on characteristics ofthe feed slurry, e.g.specific weight of solidviscosity of liquid phasequantity of polymer ( if needed)

At a given Q input the retention time will changeeach time we modify the weir plates diameter(dewatering volume change).Longer retention time will result in more efficientsolid / liquid separation.

Q = Slurry feed rate, (l / h) btdw = bowl total dewatering volume, (l)

see details on page 10

see details on page 13


D E C A N T E R I N IN D U S T R I A L A P P L I C A T I O N

Construction main data and differences per unit (sheet 1)

TYPEApplication

DFAsludge

DDBdistillery

DET*C

a

tartrate

DAGcitrus

DPOtomato

DENwine

Bowl with liner X X X

Bowl with grooves X X X

Liquid phase overflowby weir plates X X X X X

Liquid phase overflowby centripetal pump X

Scroll edge hard surfacing X X X X X

Scroll face hard surfacing X X X X X

Scroll shaft with diffuser X

Normal gaskets X

Viton Gaskets X X X X X

Decreased bowl speed X

Increased bowl speed X X X

Oversized main motor X

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#D E C A N T E R I N IN D U S T R I A L A P P L I C A T I O NConstruction main data and differences per unit (sheet 2)

TYPEApplication

DFAsludge

DDBdistillery

DETCatartrate

DAGcitrus

DPOtomato

DENwine

D

D=clearancedistance

<[email protected]

<[email protected]

= 0.5bowlwithgrooves



stellite(tungstencarbide)


All wetareas,sedimentand effluentchambers incontact withproduct arelined withstainlesssteel



no protectionfor specialuse

MATERIALS BOWL - F 51 (ex AISI 304) austenitic iron , plastic, corrosionresistantSCROLL – AISI 304

bowl and scroll in AISI 316 if required

Scrollprotection

Decanter Theory

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