5 Filtration

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FiltrationChapter 4 in Fundamentals

Professor Richard Holdich

[email protected]

Course details:

Particle Technology,

module code: CGB019 and CGB919,2nd year of study.

Watch this lecture at

http://www.vimeo.com/10201620

Visit

http://www.midlandit.co.uk/particletechnology.htm

for further resources.
mailto:[email protected]://www.vimeo.com/10201620http://www.midlandit.co.uk/particletechnology.htmhttp://www.midlandit.co.uk/particletechnology.htmhttp://www.vimeo.com/10201620mailto:[email protected]


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Filtration

Types

Cake filtration mechanism

Modification of Darcy's law

Constant pressure filtration

Constant rate filtration

Variable rate & pressure filtration

Industrial equipment


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Types of filtration

Normally batch (in duplicate)but some continuous ones:

Deep bed -clarification

Image supplied by DynaSand and Hydro International (Wastewater) Ltd.


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Types - membrane

Clarification on filtering membranes


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Types - Clarification

Cartridge and candle filtration


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Multifilament filter cloth p. 40


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Monofilament filter cloth


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Monofilament open filter cloth/mesh


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p.31

Why cant we simply measureRm

for each medium?

Ideal

Filtrate

Bridgingover pores

Filter medium

Filter cake

sharp interface medium/cake - uniform spheresin cake easy to model


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reality p 41

Why cant we simply measureRm

for each medium?

Real

Filter cake

Filter medium

i.e.Rm = f(material to be filtered)


11/42

Modification of Darcy's law Porosity or voidage

and Concentration

dV

dt

1

A

Porous media

void + solid = unity

fraction fraction

Volume fractions:

U =o

Uo

U

Superficial velocity:

+ C = 1


12/42

Modification of Darcy's lawDarcys law:

At

V

kL

P 1

d

d

Kozeny-Carman equation:

AtVS

LP v 1

dd)1(5 3

22

Pressure/L

Flow rate

xSv

/6

use:


13/42

Modification of Darcy's lawDarcys law/Kozeny:

At

V

kL

P 1

d

d

Pressure/L

Flow rate

What do the graphs tell us about these equations?

How will this vary for filtration?

Think about a given material and filter in these equationswhat is constant, what varies, look at the graph

What are the independent and dependent variables?

A

QSv

3

22)1(5

Time

Volume

liquid


14/42

Modification of Darcy's law p.29

Darcys law:

At

V

kL

P 1

d

d

Q is constant

- permeation

Time

Filtrate

volumeQ decreases- filtration

At constant pressure drop:


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Modification of Darcy's law p. 32Build up of incompressible filter cake:

Filter medium

Filter cakeformation


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20 kPa

P = dV 1L k dt A

1.5 V

V = R I

0.75 V10 kPa

0 kPa 0 V


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Modification of Darcy's lawPressure drops are additive:

Pcake

Pmedium

AtV

kL

1

d

d

At

V

k

L

m

m 1

d

d


18/42

Modification of Darcy's lawPressure drops are additive:

PAt

V

k

L 1

d

d

At

VRm

1

d

d

00

Gradient:

Ca

kevolum

e

Filtrate volume

= LAV

Ratio:

cake volume:filtrate = constant =

PARV

kCC

PAVt m

s

s

2

d

d

PA

RV

PA

c

V

t m

2

d

d


19/42


00

Gradient:

Ca

kevolum

e

Filtrate volume

= LAV

Ratio:

cake volume:filtrate = constant =

1

sC

What does

Represent in English,see the graph

skC

1

What does

Represent in English


20/42

Modification of Darcy's law p.36where cis the dry cake mass per unit volume of filtrate:

and is the specific resistance to filtration (m/kg).

smsc

1

sis feed slurry mass fraction andmis the moisture ratio of thecake (mass cake wet/mass cake dry - or sample). In someinstances one can assume m=1; i.e. neglect liquid in cake.


21/42


p.36

AQRRP mc /)(

w

Rc

alpha =Rc/w

ConsideringRc& alpha some more:

w is dry mass/unit area solids:

A

cVw

so:

AQR

A

cVP m /)(


22/42

Modification of Darcy's law equation (4.11)

sm

sc

1

PARV

PAc

Vt m

2

dd

General filtration equation:


23/42

Constant pressure filtrationConstant P filtration - integrate general equation:

to give:

PA

RV

PA

c

V

t m

2

d

d

PA

RV

PA

c

V

t m

2

2

baVV

t

i.e:

Time over filtratevolume

Filtrate volume

b

a


24/42

Constant pressure filtrationsummary: Need to know:

PA

RV

PA

c

V

t m

2

2

viscosity, pressure,and filter area

& slurry massfraction, liquiddensity (and cakemoisture - if poss.)

Time over filtratevolume

Filtrate volume

b

a

Need to calculate:

c then

andRm


25/42

Constant pressure filtration General filtration equation:

Constant pressure:

PARV

PAc

Vt m

2

2

PA

RV

PA

c

V

t m

2

d

d

y = m x + c


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Constant pressure filtration Filtration Testing in the Laboratory:

effect of pressure,

different cloths or media,

slurry agitation, filter aids and flocculants

effect of slurry pre-concentration

High permeability: vacuum leaf Low permeability: pressure bomb

Tests:


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specific resistance - possibly as f(pressure),

medium resistance

cake concentration - possibly as f(pressure)or moisture ratio


To obtain values of:


28/42


Liquid viscosity

filtration pressure

filter area


Also required for scale-up or simulation:

Slurry mass fraction

liquid density

solid density - if cakeheight is required


29/42

Constant pressure filtrationp. 41 vacuum filter leafTo vacuum

pump

Calibrated

filtratereceiver

Drain

Leaf or

Mechanical

agitation

Vent

Valve - fully open in test

Slurry tank

Filtering side

Buchner

Stirrer

funnel

Experimental characterisation


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Constant rate filtration p. 36

Constant rate:

General filtration equation:

PA

RV

PA

c

V

t m

2

d

d

t

V

A

RV

t

V

A

cP m

2

V

t

t

V

d

d

Filtrationpressure

Filtrate volume

b

a


32/42

Variable rate & pressurefiltration General filtration equation:

Variable pressure and rate equation:

PA

RV

PA

c

V

t m

2

d

d

A

RV

A

c

Q

P m

2

plot numerical integration of:V

Q&

1

QV

td


33/42

Industrial equipment p. 35Rotary vacuum filter (continuous)

Stages cake formation in slurrytank (F)

drying and/or washing

(D and W)

discharge - then back toformation (D & Di)

F

D

W

D & Di


34/42

Industrial equipment Constant pressure:

PA

RV

PA

c

V

t m

2

2

Rearrange for a quadratic:

02

2

2

tV

PA

RV

PA

c m


35/42

Industrial equipment p. 36 Simulation of Rotary Vacuum Filter:

02

2

2

tV

PA

RV

PA

c m

i.e. aV2 + bV- t= 0

a

atbb

V 2

42

where form timet = F/n(submergence/speed)


36/42

Industrial equipment per cycle of drum:

Mass dry cake deposited = cV(kg) Mass wet cake deposited = mcV (kg)

mass slurry filtered = mcV+ V (kg)

a

atbbV

2

42

Calculate volume, hence:

All above is per cycle, hence 3600/tfor output per hour.


37/42

Industrial equipmentVacuum belt filter (continuous)

Image appearscourtesy ofPolyfilters UKLimitedwww.polyfilters.com
http://www.polyfilters.com/http://www.polyfilters.com/


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Vacuum belt

filter(continuous)

Image supplied courteousy of BHS-Sonthofen GmbH, Germany www.bhs-sonthofen.de
http://www.bhs-sonthofen.de/http://www.bhs-sonthofen.de/http://www.bhs-sonthofen.de/http://www.bhs-sonthofen.de/


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Industrial equipmentVacuum disc filter (continuous)

Image courtesy of FLSmidth, Inc.


40/42

Industrial equipmentTube pressure filter (batch)

Image courtesy of Mesto Minerals (Sala) AB


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Filtration

Types




Constant rate filtration

Variable rate & pressure filtration



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This resource was created by Loughborough University and released as an open educational resource through the Open EngineeringResources project of the HE Academy Engineering Subject Centre. The Open Engineering Resources project was funded by HEFCEand part of the JISC/HE Academy UKOER programme.

Slide 3. Image of a DynaSand is provided courtesy of Hydro International (wastewater) Limited. See http://www.hydro-international.biz/irl/wastewater/dynasand.php formore details.

Slide 37. The image of a vacuum belt filter (continuous is provided with the permission of Polyfilters (UK) Limited. See http://www.polyfilters.com/process.html for moredetails.

Slide 38. Image provided courtesy of BHS-Sonthofen GmbH. See www.bhs-sonthofen.de for more details.

Slide 39. Image provided courtesy of FLSmidth Inc. Seehttp://www.flsmidthminerals.com/Products/Filtration/Vacuum+Filtration/Vacuum+Disc+Filters/Agidisc+Vacuum+Filters/Agidisc+Vacuum+Filters.htm for more details.

Slide 40. Image of a tube press discharge, provided courtesy of Mesto Minerals (Sala) AB. Seehttp://www.metso.com/miningandconstruction/MaTobox7.nsf/DocsByID/C44A6B216E52C95142256AF6002D6148/$File/Tube_Press_ES.pdf for more details.

2009 Loughborough University

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The JISC logo is licensed under the terms of the Creative Commons Attribution-Non-Commercial-No Derivative Works 2.0 UK: England & Wales Licence. Allreproductions must comply with the terms of that licence.

The HEA logo is owned by the Higher Education Academy Limited may be freely distributed and copied for educational purposes only, provided that appropriateacknowledgement is given to the Higher Education Academy as the copyright holder and original publisher.
http://www.hydro-international.biz/irl/wastewater/dynasand.phphttp://www.polyfilters.com/process.htmlhttp://www.bhs-sonthofen.de/http://www.flsmidthminerals.com/Products/Filtration/Vacuum+Filtration/Vacuum+Disc+Filters/Agidisc+Vacuum+Filters/Agidisc+Vacuum+Filters.htmhttp://www.metso.com/miningandconstruction/MaTobox7.nsf/DocsByID/C44A6B216E52C95142256AF6002D6148/$File/Tube_Press_ES.pdfhttp://creativecommons.org/licenses/by/2.0/uk/http://creativecommons.org/licenses/by/2.0/uk/http://www.metso.com/miningandconstruction/MaTobox7.nsf/DocsByID/C44A6B216E52C95142256AF6002D6148/$File/Tube_Press_ES.pdfhttp://www.flsmidthminerals.com/Products/Filtration/Vacuum+Filtration/Vacuum+Disc+Filters/Agidisc+Vacuum+Filters/Agidisc+Vacuum+Filters.htmhttp://www.flsmidthminerals.com/Products/Filtration/Vacuum+Filtration/Vacuum+Disc+Filters/Agidisc+Vacuum+Filters/Agidisc+Vacuum+Filters.htmhttp://www.flsmidthminerals.com/Products/Filtration/Vacuum+Filtration/Vacuum+Disc+Filters/Agidisc+Vacuum+Filters/Agidisc+Vacuum+Filters.htmhttp://www.bhs-sonthofen.de/http://www.bhs-sonthofen.de/http://www.bhs-sonthofen.de/http://www.polyfilters.com/process.htmlhttp://www.hydro-international.biz/irl/wastewater/dynasand.phphttp://www.hydro-international.biz/irl/wastewater/dynasand.phphttp://www.hydro-international.biz/irl/wastewater/dynasand.phphttp://creativecommons.org/licenses/by/2.0/uk/http://engsc.ac.uk/an/oer-project/oer-project.asphttp://www.jisc.ac.uk/http://engsc.ac.uk/

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