Filtration

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FILTRATION

Removal of solid particles from a

Removal of solid particles from a fluidfluid by passing theby passing the

fluid through a f

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MECHANSIMS OF FILTRATION

(a) Clarifiers (a) Clarifiers

*

* Also known as “deepAlso known as “deep--bed filters”.bed filters”.

*

* The particles The particles of solid arof solid aree trappedtrapped inside the filt inside the filterer

medium.

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* A typic

* A typical cartridge al cartridge filter:filter:

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(b) Cake filters

*

* The filter The filter medium ismedium is relatively thinrelatively thin, compared with that, compared with that of a clarifying filter.

of a clarifying filter. *

* After the After the initial period,initial period, the cake of solids does thethe cake of solids does the filtration,

filtration, not the septum not the septum.. *

* A A visible cake of appreciable thickness builds up on visible cake of appreciable thickness builds up on thethe

surface

surface and must and must be periodically removed.be periodically removed.

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EQUIPMENT FOR CONVENTIONAL FILTRATION

(1) Plate and

(1) Plate and Frame Filter PresFrame Filter Presss

*

* The most common typeThe most common type,, but less common forbut less common for

bioseparations.

* Used where

* Used where a relatively dry cake dischargea relatively dry cake discharge is desired. is desired. * Cake removal:

* Cake removal: open the whole assemblyopen the whole assembly Should not be used

Should not be used where there arwhere there are toxic fumes oe toxic fumes orr biohazards.

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(2) Horizontal Plate Filter:

*

* Filtration Filtration occursoccurs from the top of each platefrom the top of each plate.. *

* Cake rCake removal: emoval: removed removed with with a sluicing a sluicing nozzle nozzle oror discharged by rapidly rotating the leaves.

discharged by rapidly rotating the leaves. EQUI

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(3) V

(3) Verticaertical Leal Leaf Ff Filter ailter and nd Candle Candle TType Vype Verticaertical Tl Tankank

Filter:

EQUI

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(3) V

(3) Vertical ertical Leaf Leaf Filter anFilter and Cand Candle Tdle Type Vype Vertical Tertical Tank ank FilterFilter (2/2)(2/2)::

* Have a relatively

* Have a relatively high filtration area per volumehigh filtration area per volume.. Require only a small

Require only a small floor area.floor area. * Filter cake is formed

* Filter cake is formed on the external surfaceon the external surface of the tubes. of the tubes. * The tubes a

* The tubes arere cleaned by backwashingcleaned by backwashing..

EQUI

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(4) Rotary Vacuum Filter:

* Rotate

* Rotate at a low speedat a low speed during the operation. during the operation. * Pressure inside the drum is a

* Pressure inside the drum is a partial vacuumpartial vacuum.. Liquid is sucked through the filter cloth

Liquid is sucked through the filter cloth and solids and solids are retained on the surface of the

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*

* Three chThree chief steps of the filtration ief steps of the filtration cycle:cycle: (1) cake formation

(1) cake formation

(2) cake washing

(2) cake washing (to (to remove either valuable or unwantedremove either valuable or unwanted solutes)

solutes)

(3) cake discharge

(3) cake discharge EQUI

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*

* The wThe workhorse of biorkhorse of bioseparations.oseparations. *

* Common for Common for large-scale operationslarge-scale operations whenever the solidswhenever the solids

are difficult to filter.

* Being automated.

Have a lower labor cost. Have a lower labor cost.

EQUI

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PRETREATMENT OF FILTRATION

Filtration is

Filtration is a straightforward a straightforward procedurproceduree

for well-defined crystals for well-defined crystals.”.” *

* Fermentation beers and other Fermentation beers and other biological solutions arbiological solutions aree notoriously hard

notoriously hard to filterto filter, because of:, because of: (1) high, non-(1) high,

non-newtonian viscosity,

newtonian viscosity, and and (2) highly (2) highly compressiblcompressible filter cakes.e filter cakes.

Conventional filtration is often

Conventional filtration is often too slow to be practicaltoo slow to be practical.. The filtration

The filtration requirrequireses pretreatmentpretreatment: heating,: heating, coagulation and flocculation, or

coagulation and flocculation, or adsorption onadsorption on

filter aid

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A. Heating

*

* TTo impo improve the rove the feed’sfeed’s handling characteristicshandling characteristics..

(Thinking of filtering a dilution solution of egg white.) (Thinking of filtering a dilution solution of egg white.) *

* The simplest The simplest pretrpretreatmenteatment (and the least expensive). (and the least expensive). * Chief constraint:

* Chief constraint: thermal stabilitythermal stability of the of the product.product.

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B. Coagulation and Flocculation

* Through the

* Through the addition of electrolytesaddition of electrolytes.. * Types of coagulants:

* Types of coagulants: (1)

(1) Simple electrolytesSimple electrolytes (such as ferric chloride, (such as ferric chloride, alumalum,, or acids and bases)

or acids and bases) (2)

(2) Synthetic polyelectrolytesSynthetic polyelectrolytes PR

PRETREATMETREATM ENT OF FENT OF F II LTLT RARATITI ON (ON (3/3/1212))

coagulation

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*

* Action of Action of simple electrsimple electrolytes:olytes: reduce the electrostaticreduce the electrostatic

repulsion existing between colloidal particles

repulsion existing between colloidal particles..

*

* Action of Action of synthetic polyelectrsynthetic polyelectrolytes:olytes: (1) Reduce

(1) Reduce electrostatic repelectrostatic repulsionulsion (2)

(2) Adsorb on adjacent particlesAdsorb on adjacent particles

*

* Commercially available polyelectrolytesCommercially available polyelectrolytes (can be anionic, (can be anionic, cationic, or nonionic): polyacrylamides, polyethylenimines, cationic, or nonionic): polyacrylamides, polyethylenimines, and polyamine derivatives.

and polyamine derivatives.

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* The effect of

pH

pH onon filtratefiltrate

volume

volume for for

Streptomyces Streptomyces griseus

griseus ::

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C. Adsorption on

C. Adsorption on Filter

Filter Aids

Aids

* Why filter-aid filtration?

Two major problems can be reduced: Two major problems can be reduced:

(1) High compressibility of the accumulated

biomass

(2) Penetration of small particles into the filter

medium

Lengthen the filtration cycle; improve Lengthen the filtration cycle; improve the quality of the filtered liquor.

the quality of the filtered liquor.

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* The effect of * The effect of filter aid filter aid onon filtrate volume filtrate volume for

for StreptomycesStreptomyces griseus

griseus ::

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* The effect of

* The effect of pH pH andand filter aidfilter aid on filtrate volume foron filtrate volume for

S

Strtr eeptomptomyceyces gs grr iisseeuus s ::

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* How does

* How does the filter-aid help?the filter-aid help?

(1) Give porosity to the filter cake.

Solids

Solids to to be be filtered filtered PorosityPorosity Hard spheres of the same size

Hard spheres of the same size 0.45 0.45 General

General cases cases 0.20.2

Compress

Compressible ible solidssolids 0 0 Diatomaceous silica

Diatomaceous silica (( 0.9 0.9

(2) Create a very large surface to trap t

(2) Create a very large surface to trap the gelatinoushe gelatinous

precipitate.

Allow much more filtrate to be

Allow much more filtrate to be obtainedobtained beforebefore eventually clogging up

eventually clogging up..

PR

PRETREATMETREATM ENT OF FENT OF F II LTRATILTRATI ON (ON (99/1/122))

0.3 0.3

矽藻矽藻 ))

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- Protect the filter medium from fouling. - Protect the filter medium from fouling. - Provide a finer matrix to

- Provide a finer matrix to exclude particlesexclude particles from the filtrate.

from the filtrate. * How to use

* How to use filter-aidfilter-aid?? (1) Precoat

(1) Precoat — — a thin layer (0.1 to 0.2 lb/fta thin layer (0.1 to 0.2 lb/ft22) of filter aid is) of filter aid is deposited on the filt

deposited on the filter mediumer medium prior toprior to introducing introducing the filter feed to the system

the filter feed to the system

(2) Body

(2) Body feedfeed — add the filter aid — add the filter aid to the filter feedto the filter feed PR

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---PR

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*

* The use of filterThe use of filter-aid is main-aid is mainlyly for removing smallfor removing small

amounts of unwanted particulate material

amounts of unwanted particulate material..

It cannot deal with large quantities of precipitate It cannot deal with large quantities of precipitate successfully.

successfully. * T

* Types of ypes of filter-aid (the most effective):filter-aid (the most effective):

(1) Diatomaceous earths such as

(1) Diatomaceous earths such as CeliteCelite (consisting mainly of SiO (consisting mainly of SiO₂₂)) (2)

(2) PerlitesPerlites (volcanic rock processed to yield an expanded form) (volcanic rock processed to yield an expanded form)

Note: some products like

Note: some products like the aminoglycoside antibioticsthe aminoglycoside antibiotics may

may irreversiblirreversibly bind y bind toto diatomaceous earth. diatomaceous earth. PR

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GENERAL THEORY FOR FILTRATION

Darcy’s law

Darcy’s law — — relaterelate the flow rate through a porous bed ofthe flow rate through a porous bed of

solids

solids to the pressure drop causing that flow. to the pressure drop causing that flow.

    P P k k v v





v

v = velocity of the liquid = velocity of the liquid

of thickness of thickness ℓ ℓ

= viscosity of the liquid = viscosity of the liquid

k

k = permeability of the bed, a proportionality = permeability of the bed, a proportionality constant (dimension: L

constant (dimension: L22)) *

* Like Like Ohm’s lawOhm’s law,, ℓ ℓ //k k is the resistance of filtration is the resistance of filtration..

P

P = pressure drop acros = pressure drop across the bed s the bed

P

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Strictly speaking,

Strictly speaking, Darcy’s law holds only whenDarcy’s law holds only when

5 5 )) 1 1 (( --        vd vd where

where d d is the particle size of the fi is the particle size of the filter cake,lter cake, is the is the liquid density, and

liquid density, and is the void fraction in the is the void fraction in the cake.cake. * Biological separations

* Biological separations almost alwaysalmost always obey this inequality. obey this inequality. For a

For a batch filtrationbatch filtration,,

dt dt dV dV A A v v  11     P P k k dt dt dV dV A A     1 1   where

where V V is the total volume of filtrate is the total volume of filtrate,, AA is the filter is the filter area, and

area, and t t is the time. is the time.

GENERAL TH

GENERAL TH EOREORY Y FF OR OR FF II LTLT RARATITI ON (2ON (2/5/5) )

    P P k k v v   Darcy’s law: Darcy’s law:

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T

Two contributions wo contributions to tto the filtration he filtration resistance:resistance:

C C M M RR R R k k     where

where R R _M_M is is the resistance of the filter mediumthe resistance of the filter medium (constant), (constant), and

and R R _C_C is is the resistance of the cakethe resistance of the cake (varies with (varies with V V ).). The basic differential equation

The basic differential equation for filtration at constant for filtration at constant pressur

pressure drop can thus e drop can thus be obtained as:be obtained as:

)) (( 1 1 C C M M RR R R P P dt dt dV dV A A







      P P k k dt dt dV dV A A     1 1 GENERAL TH

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Incompressible Cakes

= specific cake resistance, cm/g

0

0 = mass of cake solids per volume of filtrate = mass of cake solids per volume of filtrate

)) (( 1 1 C C M M RR R R P P dt dt dV dV A A        ]] )) // (( [[ 1 1 0 0 V V A A R RM M P P dt dt dV dV A A







a a      (I.C.:(I.C.: t t = 0, = 0, V V = 0) = 0)               A A V V R R_C_C aa  ₀₀ B B A A V V K K P P R R A A V V P P V V A At t _M_M __                               aa    2 2 0 0 GENERAL TH

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Plot Plot













V

At

versus versus













A A V V   Slope =Slope = P P K K





2

0 0



a

a



Known

Known ,, ₀₀,, can can be be determined.determined. * Often, the

* Often, the medium resistancemedium resistance R R _M_M is insignificant, is insignificant, B B = 0. = 0. 2 2 0 0 2 2

















A A V V P P t t aa  B B A A V V K K P P R R A A V V P P V V A At t _M_M __                               a a   2 2 0 0 GENERAL TH

GENERAL TH EOREORY Y FF OR OR FF II LTLT RARATITI ON (5ON (5/5/5) )

P

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[Example]

[Example] A A suspensiosuspension n contaicontainingning 225 g225 g of carbonyl iron of carbonyl iron powder

powder, Gr, Grade E,ade E, per literper liter of a solution of 0.01 of a solution of 0.01 N N NaOH is NaOH is to be filtered, using a leaf filter.

to be filtered, using a leaf filter. Estimate the size (area) ofEstimate the size (area) of

the filter needed

the filter needed to obtain to obtain 100 lb100 lb of dry cake in of dry cake in 1 h1 h of of filtration at a

filtration at a constant pressurconstant pressure drop ofe drop of 20 psi20 psi. . The The cake cake isis incompress

incompressible. ible. The speciThe specific cake fic cake resistance resistance isis 10101111 ft/lb ft/lb.. The resistance of the medium is taken

The resistance of the medium is taken asas 0.1 in0.1 in

P P R R A A V V P P V V A At t _M_M                   aa    2 2 0 0 Solution: Solution: 3 3 3 3 0 0 1414..00 lb/ftlb/ft g g 453.6 453.6 llbb ft ft L L 32 32 .. 28 28 L L g g 22 2255 filtrate filtrate of of volume volume solid solid cake cake of of mass mass __                 3 3 3 3 77..11 ftft lb/ft lb/ft 14.0 14.0 llbb 10 1000 filtrate filtrate of of volume volume     V V (To b

(To b ontionti d)d) 1

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[Example]

[Example] A A suspension containingsuspension containing 225 g225 g of car of carbonyl iron powderbonyl iron powder, Grade E,, Grade E, perper

liter

liter of a solution of 0.01 of a solution of 0.01 N N NaOH is NaOH is to be filtered, using a to be filtered, using a leaf filterleaf filter.. Estimate theEstimate the size (area) of the filter needed

size (area) of the filter needed to obtain to obtain 100 lb100 lb of dry cake in 1 h of dry cake in 1 h of filtration at a of filtration at a constant pressure drop of

constant pressure drop of 20 psi20 psi. . The The cake cake is is incompressible. incompressible. The The specific specific cakecake resistance is

resistance is 10101111_ft/lb_ft/lb_._{. The resistance}_{The resistance of the medium}_{of the medium is taken as}_{is taken as 0.1 in}_{0.1 in}-1-1_..

P P R R A A V V P P V V A At t _M_M                   aa    2 2 0 0 Solution (cont Solution (cont’d):’d): t

t = filtration time = 1 h = filtration time = 1 h

                       2 2 2 2 2 2 2 2 f f 2 2 f f 3 3 h h ss )) 3600 3600 (( ss --llbb ft ft --llbb 2 2 .. 32 32 psi psi 14.7 14.7 /f /ftt llbb 1 100 1 11616 .. 2 2 psi psi 2 200 P P = 1.2 = 1.2

= specific cake resistance = 10

= specific cake resistance = 101111_ft/lb_ft/lb

R

R _M_M = resistance of the medium = 0.1 in = resistance of the medium = 0.1 in

= viscosity of the liquid = 1 cp = 2.42 lb/ft-h

= viscosity of the liquid = 1 cp = 2.42 lb/ft-h (assumed)(assumed)

(To b

(To b ontionti d)d)

10

101212_lb/ft-h_lb/ft-h22

1

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Solution (con Solution (cont’d):t’d): P P R R A A V V P P V V A At t _M_M                   a a   2 2 0 0 12 12 12 12 11 11 10 10 2 2 .. 1 1 )) 2 2 .. 1 1 )( )( 42 42 .. 2 2 (( 1 1 .. 7 7 )) 10 10 2 2 .. 1 1 (( 2 2 )) 0 0 .. 14 14 )( )( 10 10 )( )( 42 42 .. 2 2 (( 1 1 .. 7 7 )) 1 1 ((         A A A A A A22 1.7 1.7 71.2 71.2 = = 00 A A = 8.4 ft = 8.4 ft22 # # [Example]

[Example] A A suspension containingsuspension containing 225 g225 g of car of carbonyl iron powderbonyl iron powder, Grade E,, Grade E, perper

liter

liter of a solution of 0.01 of a solution of 0.01 N N NaOH is NaOH is to be filtered, using a to be filtered, using a leaf filterleaf filter.. Estimate theEstimate the size (area) of the filter needed

size (area) of the filter needed to obtain to obtain 100 lb100 lb of dry cake in 1 h of dry cake in 1 h of filtration at a of filtration at a constant pressure drop of

constant pressure drop of 20 psi20 psi. . The The cake cake is is incompressible. incompressible. The The specific specific cakecake resistance is

resistance is 10101111_ft/lb_ft/lb_._{. The resistance}_{The resistance of the medium}_{of the medium is taken as}_{is taken as 0.1 in}_{0.1 in}-1-1_..

10

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[Example]

[Example] Streptomyces Streptomyces Filtration frFiltration from an om an Erythromycin Erythromycin Broth.Broth. Using a test filter, we find the following data for a broth

Using a test filter, we find the following data for a broth

containing the antibiotic erythromycin and added filter aid: containing the antibiotic erythromycin and added filter aid:

The filter leaf has a total area of

The filter leaf has a total area of 0.1 ft0.1 ft22_{and the filtrate has a}_{and the filtrate has a}

viscosity of

viscosity of 1.1 cp1.1 cp. . The The pressure pressure drop drop isis 20 in. of 20 in. of mercurymercury and and the feed contains

the feed contains 0.015 kg dry cake per liter0.015 kg dry cake per liter.. Determine theDetermine the

specific

specific cake cake resistance resistance and and the the medium medium resistanceresistance R R _M_M..

P P R R A A V V P P V V A At t _M_M





















aa    2 2 0 0 Solution: Solution: (To b

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Example: Streptomyces Filtration from an Erythrom

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Example: Streptomyces Filtration from an Erythrom

Example: Streptomyces Filtration from an Erythromycin Broth (cont’d)ycin Broth (cont’d)

P P R R A A V V P P V V A At t _M_M                   aa    2 2 0 0

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[Example]

[Example] WWe have filtered e have filtered a slurry of sitostera slurry of sitosterol at constantol at constant pressur

pressure through a e through a filtration medium consisting of filtration medium consisting of a screena screen support mounted across the

support mounted across the end of end of a Pyrex a Pyrex pipe. pipe. WWe finde find that the resis

that the resistance of the filtration medtance of the filtration medium is negligible. ium is negligible. WWee also find the following data in a laboratory test:

also find the following data in a laboratory test:

On the basis of this laboratory

On the basis of this laboratory test,test, predict the number ofpredict the number of

frames (30 in

frames (30 in 30 in 30 in

frame press.

frame press. Estimate the time required for filtering a 63 kgEstimate the time required for filtering a 63 kg

batch of steroid.

batch of steroid. In these In these calculations, calculations, assume that assume that the feedthe feed pump will deliver

pump will deliver 10 psi10 psi and that and that the filtrate from the pressthe filtrate from the press must be raised against the equivalent of

must be raised against the equivalent of 15 ft15 ft head. head.

(To b

(To b ontionti d)d)

1 in thick) needed for a

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plate-and-Ex

Ex ampample: fle: f ilil teterr inin g a sg a sll urur ry of ry of ssitositosteterr olol

Solution (cont

Solution (cont’d):’d):

(a) Predict the number of frames needed

3 3 3 3 00..242455 g/cmg/cm cm cm 3 3 .. 25 2533 g g 62 62 density density Cake Cake   Cake volume of 63 kg

Cake volume of 63 kg steroid =steroid = 33 55 33 3 3 cm cm 10 10 57 57 .. 2 2 g/cm g/cm 0.245 0.245 g g 10 10 63 63 __ __

Number of frames needed =

Number of frames needed = 1177..44

cm cm 2.54 2.54 iinn iinn 1 1 3 300 3 300 cm cm 1 100 5 577 .. 2 2 33 3 3 3 3 5 5            

18 frames are needed.

(To b

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(b) Time r

(b) Time required for filtering a 63 kg batch equired for filtering a 63 kg batch of steroidof steroid

Solution (cont

Solution (cont’d):’d):

For incompress

For incompressible cake with ible cake with a negligible filtera negligible filter medium resistance, medium resistance, 2 2 0 0 0 0 2 2 0 0 11 2 2 or or 2 2                            A A V V P P t t A A V V P P t t     a a a a 

In the laboratory test: In the laboratory test:

2 2 2 2 0 0 ₍₍₅₅_..₀₈₀₈_cm)_cm) 4 4 g g 62 62 ps psii)) 15 15 (( 2 2 min min 16 1633                    a a 2 2 4 4 0 0 gg cm cm -- ps psii --m miinn 26 2611 2 2     a a Ex

(To b

(38)

(b) Time requir

(b) Time required for filtering a 63 ed for filtering a 63 kg batch of kg batch of steroid (cont’d)steroid (cont’d) Solution:

Solution:

In the large-scale operation: In the large-scale operation:

2 2 5 5 2 2 2 2 cm cm 10 10 09 09 .. 2 2 iinn cm cm 54 54 .. 2 2 iinn )) 30 30 30 30 (( 2 2 18 18   _ _     A A ps psii 5 5 .. 3 3 (water) (water) head head ft ft 33.9 33.9 ps psii 7 7 .. 14 14 head head ft ft 15 15 ps psii 10 10 _       -   _P_P m miinn 8 8 .. 6 6 10 10 09 09 .. 2 2 00 0000 ,, 63 63 5 5 .. 3 3 1 1 26 2611 1 1 2 2 2 2 5 5 2 2 0 0 0 0                                   A A V V P P t t     a a Ex

# #

In the laboratory test:

In the laboratory test: ₂₂

4 4 0 0 gg cm cm -- ps psii --m miinn 26 2611 2 2     a a

(39)

Compressible Cakes

Almost all cakes formed of

Almost all cakes formed of biological materials arebiological materials are

compressible.

compressible. As these cakes compress, filtrationAs these cakes compress, filtration

rates drop.”

To estimate the effects of compressibility, we assume that To estimate the effects of compressibility, we assume that the

the cake cake resistance resistance is is a a function function of of the the pressurpressure e dropdrop..

s s

P

))

((

''





_a

a

where

where ’ ’ = a constant related largely to the size and shape = a constant related largely to the size and shape of the particles forming the cake

of the particles forming the cake

s

s = the = the cake compressibilitycake compressibility GEN

GEN ERAERA L TL T HH EORY EORY FF OR FIOR FI LL TRATITRATI ON: ON: CompComprr eessssii ble ble CakeCakes s (1/3(1/3))

            A A V V R R_C_C aa  ₀₀ Recall: Recall:

(40)

s s

P

))

((

''





_a

a

llog

og

a



llog

og

a

''



s

llog

og



P

Plot

Plot log log versusversus log log s s ,, intercept = logintercept = log ’.’. GEN

P

(41)

s s

P

))

((

''





_a

a

For a r

For a rigid, incomprigid, incompressible cake,essible cake, s s = 0. = 0.

For a

For a highly comprhighly compressible essible cake,cake, s s

the feed with filt

the feed with filter aids.er aids.

GEN

            A A V V R R_C_C aa  ₀₀ Recall: Recall: 1. 1. In practice,

In practice, s s ranges from 0.1 ranges from 0.1 0.8.0.8. When values of

(42)

[Example]

[Example] Filtration of Beer Containing Filtration of Beer Containing Protease.Protease. WWe e have have aa suspension of

suspension of BacBaciillllus us ssubtilubtil iis s fermented to produce the enzyme fermented to produce the enzyme protease.

protease. TTo separate the o separate the biomass, we have added biomass, we have added 1.3 times the1.3 times the biomass of a Celatom filter aid, yielding a beer containing 3.6 biomass of a Celatom filter aid, yielding a beer containing 3.6 wt% solid, with a viscosity of 6.6

wt% solid, with a viscosity of 6.6 cp.cp. With a Buchner funnel 5With a Buchner funnel 5 cm in diameter attached to an aspirator

cm in diameter attached to an aspirator, we have found that we, we have found that we can filter

can filter 100 cm100 cm33 of this beer in 24 min of this beer in 24 min. . HoweverHowever, , previousprevious studies with this type

studies with this type of beer have had of beer have had a compressible cake witha compressible cake with

s

s equal to 2/3 equal to 2/3..

We now need to

We now need to filter filter 3000 L3000 L of this material in a pilot of this material in a pilot plant’s plate

plant’s plate-and-frame -and-frame press. press. This This press press hashas 15 frames, each15 frames, each of area 3520 cm

of area 3520 cm22. . The spThe spacing betweacing between these en these frames frames can becan be made large, so that we can

made large, so that we can filter all the beer in one single run.filter all the beer in one single run. The resistance of the filter medium is much smaller than the The resistance of the filter medium is much smaller than the filter cake, and the total

filter cake, and the total pressurpressure drop that can e drop that can be used is 65 be used is 65 psi.psi. How long will it take to

How long will it take to filter this beer filter this beer at 50 psi?at 50 psi?

(To b

(43)

Ex

Ex ampample: Fle: F ilil tratitrati on of Bon of B eeeer r ContaContaii nini ng Proteng Proteasasee

Solution (cont Solution (cont’d)’d):: Negligible Negligible R R _M_M 2 2 0 0 2 2              A A V V P P t t aa  Compress

Compressible ible cake,cake, a a



a a ''((



P P )) s s

2 2 1 1 0 0 2 2 ''

















_- - A A V V P P t t a a   _s_s Laboratory test: Laboratory test: P

P = = 14.7 psi14.7 psi (a Buchner funnel attached to an aspirator) (a Buchner funnel attached to an aspirator)

A A = = 22 ;;V V = 100 cm = 100 cm33_;; _t_t_{= 24 min;}_{= 24 min;} _s_s_{= 2/3}_{= 2/3} )) cm cm 5 5 (( 4 4   2 2 2 2 3 3 3 3 // 1 1 0 0 )) cm cm 5 5 (( 4 4 cm cm 10 1000 )) ps psii 7 7 .. 14 14 (( 2 2 '' min min 24 24                    a a ’

(44)

2 2 1 1 0 0 2 2 ''

















_- - A A V V P P

t t a a   _s_s ’ ’ ₀₀ = 4.53 min psi = 4.53 min psi1/31/3 _cm_cm

Pilot-plant operation: Pilot-plant operation: V V = 3000 L = 3 = 3000 L = 3 A A = 15 = 15 22 frame.) frame.) 2 2 6 6 3 3 // 1 1 2 2 1 1 0 0

3520

2

1

15

5

1

10

0

3

3 ))

5

50

0 ((

2

5

53

3 ..

4

2

2 ''

































_-

- A

A

V

P

t



a

a



_s_s ;; = 496 min = 8.3 h = 496 min = 8.3 h Ex

Ex ampample: Fle: F ilil tratitrati on of Bon of B eeeer r ContaContaii nini ng Proteng Proteasasee

Solution (cont Solution (cont’d)’d):: # # 2 2 10 1066_cm_cm33 3520 cm

(45)

ANALYSIS OF CONTINUOUS ROTARY

VACUUM FILTERS

There are three There are three

stages involved in the stages involved in the operation: operation: (1) cake formation (1) cake formation (2) cake washing (2) cake washing (3) cake discharge (3) cake discharge (not affecting (not affecting the filter size the filter size and the cycle and the cycle time)

(46)

Cake Formation

For compressible cake and

For compressible cake and negligible medium resistancenegligible medium resistance,,

2 2 1 1 0 0 2 2 1 1 0 0 2 2 '' or or 2 2 ''                             _-_- _- - A A V V P P t t A A V V P P t

t a a   _s_s _f_f a a   _s_s f f

where

where t t _f_f= cake formation time= cake formation time

V

V _f_f= volume of filtrate collected during the period= volume of filtrate collected during the period

of

of t t _f_f

A

A = filtration area (submerged area of filter) = filtration area (submerged area of filter)

AN

(47)

Cake Formation (cont’d) Cake Formation (cont’d)

2 2 1 1 0 0 2 2 ''

















_- - A A V V P P t t _f_f a a   _s_s f f Let

Let t t _f_f = = t t _c_candand AA = = AA_T_T

2 2 1 1 0 0 2 2 ''

















-T T f f s s c c A A V V P P t t b b    a a b b where

where t t _c_c = cycle time = cycle time

A

A_T_T = tot = total filter areaal filter area

= fraction of the drum submerged

= fraction of the drum submerged AN

(48)

Cake W

Cake Washing

ashing

T

Two factors involved wo factors involved in the stage of in the stage of cake washing:cake washing: (1) The fraction of soluble

(1) The fraction of soluble material remained after the washmaterial remained after the wash Governing the volume of

Governing the volume of wash liquid required.wash liquid required.

(2) The rate of wash liquid passes through the cake (2) The rate of wash liquid passes through the cake

Controlling the fraction of cycle time for cake

washing.

washing. AN

(49)

An empirical equation for the fraction of soluble material An empirical equation for the fraction of soluble material remained: remained: n n r r



((

1

1 -

-



))

where

where r r = = ratio of ratio of soluble soluble material material remained remained after after thethe

wash to that originally present in the cake

n

n = volume of wash = volume of wash liquid divided by the volumeliquid divided by the volume of retained liquid

of retained liquid

= washing efficiency of the cake = washing efficiency of the cake

T

Two factors involved in the wo factors involved in the stage of cake stage of cake washing:washing:

(1) The fraction of soluble material remained after the wash (1) The fraction of soluble material remained after the wash

Governing the volume of wash

Governing the volume of wash liquid requiredliquid required.. AN

(50)

The wash liquid contains no additional

solids.

(1) The cake thickness is constant. (1) The cake thickness is constant.

T

Two factors involved in the wo factors involved in the stage of cake stage of cake washing:washing: (2) The rate of wash liquid passes through the cake (2) The rate of wash liquid passes through the cake

Controlling the fraction of cycle time for cake washing. Controlling the fraction of cycle time for cake washing.

(2) Wash rate (2) Wash rate

= filtration rate at the end of cake formation

The flow of wash liquid is The flow of wash liquid is constant.

constant.

AN

(51)

w w w w w w At At V V dt dt dV dV A A



11 rate rate Wash Wash where

where V V _w_w = volume of wash water required, = volume of wash water required, andand t t _w_w= time= time

required for washing.

Filtration rate at the end of cak

Filtration rate at the end of cake formation =e formation =

f f t t t t dt dt dV dV A A  1 1 2 2 // 1 1 0 0 1 1 2 2 1 1 0 0 '' )) (( 2 2 or or 2 2 ''                        -    a a   a a P P t t A A V V A A V V P P t t s s s s 2 2 // 1 1 0 0 1 1 '' 2 2 )) (( 1 1 rate rate Wash Wash                          -    _f_f s s t t t t t t t t t t P P A A V V dt dt d d dt dt dV dV A A f f f f a a   2 2 // 1 1 0 0 1 1 '' 2 2 )) ((











 







- f f s s w w w w t t P P At At V V    a a AN

(52)

A useful expression: A useful expression: 2 2 // 1 1 0 0 1 1 2 2 // 1 1 0 0 1 1 '' )) (( 2 2 an andd '' 2 2 )) ((











 















 





- f f s s f f f f f f s s w w w w t t P P At At V V t t P P At At V V    a a    a a nf nf V V V V V V V V V V V V t t t t f f r r r r w w f f w w f f w w 2 2 2 2 2 2     2 2 // 1 1 1 1 0 0 2 2 // 1 1 1 1 0 0 )) (( 2 2 '' an andd )) (( '' 2 2                     _-_- _- -ss f f f f f f s s f f w w w w P P t t A A V V t t P P t t A A V V t

t a a   a a  

where

where V V _r_r= volume of liquid retained= volume of liquid retained

f

f = ratio of the = ratio of the volume of retained liquid (volume of retained liquid (V V _r_r) to) to

the volume of filtrate (

the volume of filtrate (V V _f_f))

AN

(53)

[Example]

[Example] It is desirIt is desired to filter ed to filter a cell ba cell broth at roth at a rate ofa rate of 2000 L/h

2000 L/h on a on a rotary vacuum filter at a vacuum pressure ofrotary vacuum filter at a vacuum pressure of 70 kPa

70 kPa. . The cycle The cycle time for time for the drum the drum isis 60 s60 s, and the cake, and the cake formation time is

formation time is 15 s15 s. . The brThe broth to be oth to be filtered filtered has ahas a viscosity of

viscosity of 2.0 cp2.0 cp and a cake solid per volume of filtrate of and a cake solid per volume of filtrate of 10 g/L

10 g/L. . From From laboratory tests, laboratory tests, the specific the specific cake rcake resistanceesistance has been determined to be

has been determined to be 99 .. Determine theDetermine the

area of the

area of the filter that is filter that is requirrequired.ed.

Solution:

For incompressible cake, For incompressible cake,

P P t t V V A A A A V V P P t t f f f f f f f f   __              2 2 or or 2 2 2 2 0 0 2 2 2 2 0 0 a a  a a (To b

(To b ontionti d)d)

10

(54)

Ex

Ex ampleample: D: D eeteterr mimi ne ne the the area area of a rotarof a rotar y vy vacuum facuum f iillteterr

Solution (con Solution (cont’d):t’d): ss --cm cm g g 0.02 0.02 cp cp 2 2      g g cm cm 1 100 9 9 1010   a a 33 3 3 0 0 cm cm g g 10 10 10 10 L L g g 10 10   - -    ;; ;; 3 3 3 3 3 3 cm cm 8333 8333 ss 3600 3600 h h s) s) 1 155 (( h h cm cm 1 100 2000 2000 _ _ _               f f V V 2 2 5 5 2 2 2 2 3 3 ss --cm cm g g 10 10 0 0 .. 7 7 cm cm 10 1000 m m kg kg g g 1000 1000 ss -- N N m m --kg kg m m N N 10 10 70 70 kPa kPa 70 70 _ _ _                   _P_P 4 4 7 7 5 5 2 2 3 3 10 10 2 2 0 0 2 2 cm cm 1 100 9 955 .. 5 5 )) 1 100 0 0 .. 7 7 )( )( 1 155 (( 2 2 )) 8333 8333 )( )( 1 100 1 100 )( )( 1 100 9 9 )( )( 0 022 .. 0 0 (( 2 2              - P P t t V V A A f f f f a a  A A = 7715 cm = 7715 cm22_{= 0.7715 m}_{= 0.7715 m}22 2 2 T T 33..0909 mm 15 15 60 60 7715 7715 .. 0 0         f f c c t t t t A A A A # #

(55)

[Example]

[Example] WWe e want to want to filterfilter 15,000 L/h15,000 L/h of a beer containing of a beer containing erythromycin using a rotary vacuum filter originally

erythromycin using a rotary vacuum filter originally purchased for

purchased for another product. another product. Our Our filter has filter has a cycle a cycle timetime of

of 50 s50 s and an area of 37.2 m and an area of 37.2 m22_._{. It}_{It operates}_{operates under}_{under a}_{a vacuum}_vacuum

of 20 in Hg.

of 20 in Hg. The prThe pretreated betreated broth forms roth forms an incompran incompressibleessible cake with the resistance:

cake with the resistance:

2 2 0 0 ₂₉₂₉ _s/cm_s/cm 2 2 P P   aa  W

We want to e want to wash the cake wash the cake until onlyuntil only 1%1% of t of the retainedhe retained solubles is left, and we expect that the washing

solubles is left, and we expect that the washing efficiencyefficiency will be

will be 70%70% and that and that 1%1% of of the filtrate is retained.the filtrate is retained. (a)(a)

Calculate the filtration time per cycle.

Calculate the filtration time per cycle. (b) Find the washing(b) Find the washing

time.

Solution

Solution ::

2 2 0 0 2 2                   T T f f c c f f A A V V P P t t t t b b  aa  b b

(56)

Example

Example: : FF ilil tration of tration of eerythromyrythromycin ucin u ssinin g rotag rotary vacry vacuum uum fifi ltelterr

Solution (con

Solution (cont’d)t’d)::

2 2 0 0 2 2                   T T f f c c f f A A V V P P t t t t b b  aa  b b t t _c_c = 50 s = 50 s A A_T_T = 37.2 m = 37.2 m22_{= 37.2}_{= 37.2} 2 2 0 0 ₂₉₂₉ _s/cm_s/cm 2 2



P P



 aa  3 3 3 3 cm cm 10 10 20 2088 L L 20 2088 ss 3600 3600 h h )) ss 50 50 (( )) L L/h/h 00 0000 ,, 15 15 ((   _ _      _b_b _b_b _b_b f f V V ss 1 1 .. 9 9 10 10 2 2 .. 37 37 1 100 20 2088 2 299 2 2 44 3 3 2 2 0 0                                  b b b b b b a a  T T f f f f A A V V P P t t (To b

(To b ontionti d)d)

10

(57)

Solution (cont Solution (cont’d):’d): n n f f w w r r nf nf t t t t )) 1 1 (( an andd 2 2



-

 



Fraction of retained solubles,

Fraction of retained solubles, r r = 0.01 = 0.01 Washing efficiency,

Washing efficiency, = 0.7 = 0.7 Fraction of f

Fraction of filtrate retained,iltrate retained, f f = 0.01 = 0.01

r

r = = 0.01 0.01 = = (1 (1 0.7)0.7)n n _n_n_{= 3.82}_{= 3.82}

t

t _w_w = 2 = 2nnff

Example

Example: : FF ilil tration of tration of eerythromyrythromycin ucin u ssinin g rotag rotary vacry vacuum uum fifi ltelterr (b) Find the washing time.

(b) Find the washing time.

# #

t

(58)

Application of Rotary Vacuum Filter

*

* It is commonIt is commonly used to ly used to recoverrecover yeast and myceliayeast and mycelia.. * Filtration of

* Filtration of bacterial fermentation brothbacterial fermentation broth will usually will usually require a precoat of filter aid

require a precoat of filter aid..

* The separation of

* The separation of cell debriscell debris is performed by adding is performed by adding filter aid to the feed liquor.

(59)

CENTRIFUGAL

FILTRATION

* A combination of a * A combination of a

centrifuge and a filter.

* Accumulated solids * Accumulated solids

can be washed. can be washed.

(60)

CENTR

(61)

Hydrostatic Equilibriu

m in a

Centrifugal Field

In a rotating centrifuge,

In a rotating centrifuge, a layer of liquid is a layer of liquid is thrown outwardthrown outward

from the axis of rotation and

from the axis of rotation and is held against the wallis held against the wall of the of the bowl by centrifugal force.

bowl by centrifugal force.

CENTR

(62)

Consider a volume element of

thickness

thickness dr dr at a radius at a radius r r ,,

dm

r

dF



  22 ;; _dm_dm



_

₍₍

₂

_

_rrh_h

₎₎

_dr_dr dF

dF = centrifugal force = centrifugal force

dm

dm = mass of liquid in the element = mass of liquid in the element

=

= angular velocityangular velocity

= density of the liquid = density of the liquid

h

h = height of the ring = height of the ring

rrdr dr rrhh dF dF dP dP dr dr r r h h dF dF 22 22 22 2 2 an andd 2 2         --       Integration Integration (( )) 2 2 1 1 ₂₂ 1 1 2 2 2 2 2 2 2 2 1 1 P P P P r r r r P P

-



-





 

-

-CENTR

(63)

Principles of Centrifugal Filtration

R

R ₁₁ = radius of the = radius of the surface of feedsurface of feed

solution

R

R _cc = radius of the cake’s interface= radius of the cake’s interface

Darcy’s law: Darcy’s law: v v k k P P P P k k v v     1 1 or or           Set Set 00 1 1 a a 



k k vv P P 0 0  aa 





 

For centrifugal filtration, the

pressure drop varies with the

radius,

radius, thus thus

v v dr dr dP dP 0 0  aa 



-CENTR

(64)

v v dr dr dP dP 0 0  aa    -The

The total volumetric flow ratetotal volumetric flow rate,, Q Q = (2 = (2 rr h h ))v v ; or; or

rrhh Q Q v v   2 2



(Note:

(Note: v v varies with varies with r r .).)

            -  rrhh Q Q dr dr dP dP    a a 2 2 0 0 Integration Integration c c R R R R h h Q Q P P ₀₀ llnn 00 2 2

















-   a a

The pressure drop (

the liquid. the liquid. )) (( 2 2 1 1 ₂₂ 1 1 2 2 0 0 2 2 R R R R P P



-

-



--

__

))

//

lln(

n(

))

((

0 0 2 2 1 1 2 2 0 0 0 0 2 2 c c R R R R R R R R h h Q Q



-

-

a

a







* Note:

* Note: R R _c_cis a function of time, and so is a function of time, and so isis Q Q ;; however,however, Q Q is is

not a function of

not a function of r r ..

CENTR

CENTRII FF UGAL FUGAL F II LTRALTRATITI ON (ON (66/8/8))

P

(65)

)) // lln(n( )) (( 0 0 2 2 1 1 2 2 0 0 0 0 2 2 cc R R R R R R R R h h Q Q



-

- aa     

Mass balance for the solids:

h h R R R R V V _cc

((

₀₀22 _cc22

))

0 0







-

- 



(where(where _c_c = cake density) = cake density)

)) // lln(n( )) (( )) 2 2 (( 0 0 2 2 1 1 2 2 0 0 0 0 2 2 0 0 cc c c c c c c R R R R R R R R h h dt dt dR dR R R h h dt dt dV dV Q Q



-



-

- aa           

))

//

lln(

n(

1

2

2 ))

((

0 0 2 2 1 1 2 2 0 0 2 2 c c c c c c c c

R

dt

dR



a

a





-

-



-I. C.: I. C.: t t = 0, = 0, R R _c_c = = R R ₀₀ CENTR

(66)

)) // lln(n( 1 1 2 2 )) (( 0 0 2 2 1 1 2 2 0 0 2 2 c c c c c c c c R R R R R R R R R R dt dt dR dR  a a     - -  -I. C.: I. C.: t t = 0, = 0, R R _cc = = R R ₀₀

The integrated expression is complex,

and can be approximated as:

























-











-



c c c c c c c c R R R R R R R R R R R R R R t t 00 2 2 0 0 2 2 1 1 2 2 0 0 2 2 2 2 llnn 2 2 1 1 )) (( 2 2    a a

This is the desired result

This is the desired result to find the time needed to find the time needed forfor obtaining

obtaining a cake of thickness (a cake of thickness (R R ₀₀ R R _c_c).).

* Recalling that

* Recalling that for a flat cakefor a flat cake,,

2 2 0 0 2 2

















A A V V P P t t a a CENTR

(67)

[Exampl

[Example] e] WWe e can filter can filter 250 cm250 cm33 of of a slurrya slurry, containing, containing 0.016 g

0.016 g progesterprogesteroneone (( Our Our filterfilter

has a surface area of 8.3 cm

has a surface area of 8.3 cm22, a pressure drop of 1 atm, and, a pressure drop of 1 atm, and a filter

a filter medium of medium of negligible rnegligible resistance. esistance. The solids The solids in thein the cake have a density of

cake have a density of 1.09 g/cm1.09 g/cm33, and the slurry density is, and the slurry density is that of water.

that of water. W

We want to e want to use this experiment to estimate the use this experiment to estimate the time totime to filter

filter 1,600 liters1,600 liters of this slurry through a centrifugal filter. of this slurry through a centrifugal filter. The filter has a basket of

The filter has a basket of 51 cm radius51 cm radius and and 45 cm height45 cm height. It. It rotates at

rotates at 530 rpm530 rpm. . When When it it is is spinning,spinning, the liquid and cakethe liquid and cake

together are

together are 5.5 cm thick 5.5 cm thick .. How long will this filtration take?How long will this filtration take?

Solution: Solution:                   -          -  c c c c c c c c R R R R R R R R R R R R R R t t 00 2 2 0 0 2 2 1 1 2 2 0 0 2 2 2 2 llnn 2 2 1 1 )) (( 2 2    aa  Need data of

Need data of andand R R _c_c..

(To b

(To b ontionti d)d)

黃體激素

(68)

[Exampl

[Example] e] WWe e can filter can filter 250 cm250 cm33_{of a slurry, containing}_{of a slurry, containing 0.016 g}_{0.016 g}

progesterone

progesterone ( ( Our Our filter filter has a surfhas a surfaceace area of 8.3 cm

area of 8.3 cm22_{, a pressure drop of 1}_{, a pressure drop of 1 atm, and a}_{atm, and a filter medium of}_{filter medium of}

negligible r

negligible resistance. esistance. The solids in the cake have The solids in the cake have a density ofa density of 1.09 g/cm1.09 g/cm33_,,

and the

and the slurry density is slurry density is that of waterthat of water.. Ex

Ex ampleample: f: f iill trtr ation of pration of pr ogeogessteterr one one (2/3)(2/3)

Solution (cont’d

Solution (cont’d):):

In the laboratory test,

2 2 0 0 2 2              A A V V P P t t aa  t t = 32 min = 1920 s; = 32 min = 1920 s; ₀₀ = 0.016 g/cm = 0.016 g/cm33 2 2 6 6 2 2 2 2 6 6 ss --cm cm g g 10 10 01 01 .. 1 1 dyne dyne cm/s cm/s --g g at atmm dyne/cm dyne/cm 10 10 01 01 .. 1 1 at atmm 1 1 _                  _P_P V V = 250 cm = 250 cm33;; AA = 8.3 cm = 8.3 cm22 2 2 6 6 ₈₈_..₃₃ 25 2500 )) 10 10 (1.01 (1.01 2 2 )) 01 0166 .. 0 0 (( 1920 1920               a a _{= 2.67}_{= 2.67} 黃體激素

黃體激素)) per cmper cm33_{, in}_{, in 32 min.}_{32 min.}

10

(69)

Using centrifugal filtration,

                  -          -  c c c c c c c c R R R R R R R R R R R R R R t t 00 2 2 0 0 2 2 1 1 2 2 0 0 2 2 2 2 llnn 2 2 1 1 )) (( 2 2    a a = 2.67 = 2.67 ; ; _cc = 1.09 g/cm = 1.09 g/cm33_;_; _{= 1.0 g/cm}_{= 1.0 g/cm}33 = 530 rpm = 55.47 s = 530 rpm = 55.47 s-1-1 ; ; R R ₀₀ = 51 cm ; = 51 cm ; R R ₁₁ = = 51 51 5.5 5.5 = = 45.5 45.5 cmcm Mass balance for solids:

Mass balance for solids:   ₀₀V V



  _cc  (( R R₀₀22

-

R R_cc22))hh (0.016)(1,600 (0.016)(1,600 [(51)[(51)22 _R_R cc22](45)](45) R R _c_c = 49.3 cm= 49.3 cm ss 46 4666 3 3 .. 49 49 51 51 llnn 2 2 1 1 3 3 .. 49 49 51 51 )) 5 5 .. 4 455 51 51 (( )) 47 47 .. 55 55 )( )( 0 0 .. 1 1 (( 2 2 )) 3 3 .. 49 49 )( )( 09 09 .. 1 1 )( )( 10 10 6 677 .. 2 2 (( 22 2 2 2 2 2 2 2 2 8 8                     -          -      _t_t Solution (co Solution (cont’d):nt’d): # # Ex

Ex ampleample: f: f iill trtr ation of pration of pr ogeogessteterr one one (3/3)(3/3)

10

1088_s_s-1-1

10

(70)