Particle Technology- Filtration

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]

http://www.vimeo.com/10201620

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

Filtration

Types Cake filtration mechanism Modification of Darcy's law Constant pressure filtration Constant rate filtration Variable rate & pressure

filtration Industrial equipment

Types of filtration

Normally batch (in duplicate) but some continuous ones:

Deep bed - clarification

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

Types - membrane

Clarification on filtering membranes

Types - Clarification

Cartridge and candle filtration

Cake filtration mechanism

Multifilament filter cloth p. 40


Monofilament filter cloth


Monofilament open filter cloth/mesh

Cake filtration mechanism p.31

Why can’t we simply measure Rm for each medium?Ideal

Filtrate

Bridgingover pores

Filter m edium

Filter cake

sharp interface m edium /cake - uniform spheresin cake easy to m odel

Cake filtration mechanism – reality p 41

Why can’t we simply measure Rm for each medium?

RealFilter cake

Filter m edium

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

Modification of Darcy's law

Porosity or voidage

and Concentration

dV

dt

1

A

Porous m edia

void + solid = unityfraction fraction

Volum e fractions:

U =o

U o

U

Superficial velocity:

+ C = 1


Darcy’s law:

At

V

kL

P 1

d

d

Kozeny-Carman equation:

At

VS

L

P v 1

d

d)1(53

22

Pressure/L

Flow rate

xSv /6use:


Darcy’s 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 equations – what is constant, what varies, look at the graph…

What are the independent and dependent variables?

A

QSv

3

22)1(5

Time

Volume liquid

Modification of Darcy's law – p.29

Darcy’s law:

At

V

kL

P 1

d

d

Q is constant - permeation

Time

Filtrate volume

Q decreases - filtration

At constant pressure drop:

Modification of Darcy's law – p. 32

Build up of incompressible filter cake:

Filter medium

Filter cakeformation


20 kPa

P = dV 1 L k dt A

1.5 V

V = R I

0.75 V10 kPa

0 kPa 0 V


Pressure drops are additive:

Pcake

Pmedium

At

V

k

L 1

d

d

At

V

k

L

m

m 1

d

d


Pressure drops are additive:

PAt

V

k

L 1

d

d

At

VRm

1

d

d

00

G rad ie n t:

Cak

e vo

lum

e

F iltra te v o lu m e

= L A V

Ratio: cake volume:filtrate = constant =

PA

RV

kC

C

PAV

t m

s

s

2d

d

PA

RV

PA

c

V

t m

2d

d


00

G rad ie n t:

Cak

e vo

lum

e

F iltra te v o lu m e

= L A V

Ratio: cake volume:filtrate = constant =

1sC

What does

Represent – in English, see the graph…

skC1

What does

Represent – in English


where c is the dry cake mass per unit volume of filtrate:

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

sm

sc

1

s is feed slurry mass fraction and m is the moisture ratio of the cake (mass cake wet/mass cake dry - or sample). In some instances one can assume m=1; i.e. neglect liquid in cake.


AQRRP mc /)(

w

Rc alpha = Rc/w

Considering Rc & alpha some more:

w is dry mass/unit area solids:

A

cVw

so:

AQRA

cVP m /)(

Modification of Darcy's law – equation (4.11)

sm

sc

1

PA

RV

PA

c

V

t m

2d

d

General filtration equation:

Constant pressure filtration

Constant P filtration - integrate general equation:

to give:

PA

RV

PA

c

V

t m

2d

d

PA

RV

PA

c

V

t m

22

baVV

t

i.e:

Time over filtrate volume

Filtrate volume

b

a


summary:

Need to know:

PA

RV

PA

c

V

t m

22

viscosity, pressure, and filter area

& slurry mass fraction, liquid density (and cake moisture - if poss.)

Time over filtrate volume

Filtrate volume

b

a

Need to calculate:c then

and Rm



Constant pressure:

PA

RV

PA

c

V

t m

22

PA

RV

PA

c

V

t m

2d

d

y = m x + c


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:



specific resistance - possibly as f(pressure),

medium resistance cake concentration - possibly as

f(pressure) or moisture ratio



To obtain values of:



Liquid viscosity filtration

pressure filter area



Also required for scale-up or simulation:

Slurry mass fraction

liquid density solid density - if

cake height is required

Constant pressure filtration p. 41 – vacuum filter leaf

To v a cu u mp u m p

C a lib ra tedf il tra te

rec e iv e r

D ra in

L e af o r

M e ch an ica la g ita tio n

Ve n t

Va lv e - fu lly o p e n in te st

S lu rry tan k

F ilte r in g s id e

B u ch n e r

S tir re r

fu n n e l

Experimental characterisation


Constant rate filtration – p. 36

Constant rate:


PA

RV

PA

c

V

t m

2d

d

t

V

A

RV

t

V

A

cP m

2

V

t

t

V

d

d

Filtration pressure

Filtrate volume

b

a

Variable rate & pressure filtration


Variable pressure and rate equation:

PA

RV

PA

c

V

t m

2d

d

A

RV

A

c

Q

P m

2

plot numerical integration of:V

Q &

1

Q

Vt

d

Industrial equipment – p. 35

Rotary vacuum filter (continuous) Stages

• cake formation in slurry tank (F)

• drying and/or washing (D and W)

• discharge - then back to formation (D & Di)

F

DW

D & Di

Industrial equipment

Constant pressure:

PA

RV

PA

c

V

t m

22

Rearrange for a quadratic:

02

22

tV

PA

RV

PA

c m

Industrial equipment – p. 36

Simulation of Rotary Vacuum Filter:

02

22

tV

PA

RV

PA

c m

i.e. aV2 + bV - t = 0

a

atbbV

2

42

where ‘form’ time t = F/n (submergence/speed)


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/t for output per hour.


Vacuum belt filter (continuous)

Image appears courtesy of Polyfilters UK Limited www.polyfilters.com

http://www.polyfilters.com/


Vacuum belt filter (continuous)

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

http://www.bhs-sonthofen.de/


Vacuum disc filter (continuous)

Image courtesy of FLSmidth, Inc.


Tube pressure filter (batch)

Image courtesy of Mesto Minerals (Sala) AB

Filtration

Types Cake filtration mechanism Modification of Darcy's law Constant pressure filtration Constant rate filtration Variable rate & pressure

filtration Industrial equipment

This resource was created by Loughborough University and released as an open educational resource through the Open Engineering Resources project of the HE Academy Engineering Subject Centre. The Open Engineering Resources project was funded by HEFCE and 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 for more 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 more details.

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. See http://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. See http://www.metso.com/miningandconstruction/MaTobox7.nsf/DocsByID/C44A6B216E52C95142256AF6002D6148/$File/Tube_Press_ES.pdf for more details.

© 2009 Loughborough University

This work is licensed under a Creative Commons Attribution 2.0 License.

The name of Loughborough University, and the Loughborough University logo are the name and registered marks of Loughborough University. To the fullest extent permitted by law Loughborough University reserves all its rights in its name and marks, which may not be used except with its written permission.

The JISC logo is licensed under the terms of the Creative Commons Attribution-Non-Commercial-No Derivative Works 2.0 UK: England & Wales Licence. All reproductions 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 appropriate acknowledgement is given to the Higher Education Academy as the copyright holder and original publisher.

http://www.hydro-international.biz/irl/wastewater/dynasand.php

http://www.polyfilters.com/process.html

http://www.bhs-sonthofen.de/

http://www.flsmidthminerals.com/Products/Filtration/Vacuum+Filtration/Vacuum+Disc+Filters/Agidisc+Vacuum+Filters/Agidisc+Vacuum+Filters.htm

http://www.metso.com/miningandconstruction/MaTobox7.nsf/DocsByID/C44A6B216E52C95142256AF6002D6148/$File/Tube_Press_ES.pdf

http://creativecommons.org/licenses/by/2.0/uk/

http://engsc.ac.uk/

http://www.jisc.ac.uk/

http://engsc.ac.uk/an/oer-project/oer-project.asp

http://creativecommons.org/licenses/by/2.0/uk/