Chapter 8-Filtration (56 P)

8/13/2019 Chapter 8-Filtration (56 P)

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PART III. CASE STUDIES

Chapter 8. Filt ration

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Characteristics

1) Filtration used for removal of suspended and colloidal solids.

Coa-Floc-Sed followed by filtration

Direct filtration

Direct filtration of high solids

2) Porous media captures solids and transports water.

Solid: suspended vs. dissolved?

Capture dissolved solids?

3) Filtration is primary a physical process but chemicals can be added to improve

performance.

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3

10-3um, < colloids < 1 um

1 um < suspended solids < 103um


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Characteristics

4) Two phase process: Solids removal during filtration followed by solids removal

(backwashing).

5) Because it is a two phase process, filtration is typically discontinuous but some

filters are designed to simultaneous filtration and backwashing. Alternatively, you can

design several filtration units in parallel.

- Membrane filtration or separation is excluded in this chapter.

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General Classif ication of f ilters According to the Types of Media

1)Single Medium Filters

-One type of medium

-Typically sand or crushed anthracite coal

2) Dual-media filters

-Two types of media

-Typically crushed anthracite and sand

3) Multimedia filters

-Three types of media

-Typically crushed anthracite, sand, and garnet

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General Classification of Filters According to Filtration Principles

1) Granular medium filtration.

- Rapid sand filters

2) Surface filtration

- Micro-screens- Vacuum filters/Pre-coat filters

- Slow sand filters

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Desired characteristics of the Perfect filter

1)2)

3)

4)

5)

6)

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Definition sketch for length of filtration run.

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Granular Medium Filtration (Rapid Sand Filtration (vs. slow sand fil tration))

Classification

1) Flow direction

- Downflow

- Upflow

- Biflow

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Granular Medium Filtration

Classification

2) Types of Filtering Materials & Filter Configurations.

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Classification

3) Driving Force

-Gravity

-Pressure

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Classification

4) Flow Control

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Classification

5) Backwash/Surface Wash

15Operation of conventional downflow, granular-medium, gravity-flow filter


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18Removal of Suspended Particulate Matter with a Granular Filter

Straining

Sedimentationor inertial impaction

Interception


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Removal of Suspended Particulate Matter with a Granular Filter

Adhesion

Flocculation


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Solids Removal in Depth Filtration

It is important to realize that particles that contact the media surface must attach or

bond to the surface, with the exception of particles removed by straining. The

bonding forces in filtration are the same as those on coagulation and flocculation:

van der Waals forces. It is also possible that particles will be sheared off or detach

from the media, but reattach deeper in the filter.


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== .CoeffUniformityUC

Grain size and distribution

Effective size = D10

However, grain shape is also an important factor in calculating filtration headlosses and

bed expansion during bachwashing.

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D10

If D10and CU are small, ??? (vice

versa)


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grainsandofareasurfaceactual

deqwithspherevolumeequalofareasurfaceDefine sphericity, =

Grain density: affects mostly ??

Grain hardness: affects mostly ??

23

In the absence of determining dequse the mean diameter between sieves as an

approximation of deq.


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==volumebedTotal

volumeVoidPorosityBedFixed

hrmhrm

mton

AreaSurface

FlowmediaofrateFiltration /

)(, 2

3

=

=

24

, head-loss but water quality


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26

day

ftgalFiltrationSand

/180m

7.5m/hr

hr/m7.5m

hrL/m7500

min/3,

3

23

2

2

=

=

=

=

watertonorm

population

personperL

3000,500

000,000,1

500

)176176(5353

2778180

000,500 2

ftftormm

mrequiredareaFiltration

=

==


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Hydraulics of depth fi ltration flow

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Darcys Law Laminar flow

Divided by A

KSX

hKqAQ =

==/

Darcys law can be applied for the hydraulics to estimate how much water can be

transported away from the site

Darcys law: a phenomenologically derived constitutive equation that describes the

flow of a fluid through a porous medium.
http://en.wikipedia.org/wiki/File:Darcy%27s_Law.png


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KSX

hKq =

=

Darcys Law

q = hydraulic flux, or velocity of flow (apparent velocity, Va), m/d

K = permeability coefficient or hydraulic conductivity, m/d

h = head-loss (or pressure drop)

X = distance where the head-loss occurs

S = hydraulic gradient, m/m

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Laminar flow in Circular Pipes (Void Space)

VD

L

gVD

L

hL 22 3232

==

L

hgDV L

32

2

=

weightspecificg==


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KSX

hKq =

=

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Laminar flow in Circular Pipes (Void Space)

VD

L

ghL 232

=

What happens in Circular Pipes (Channel) with

Medium

?????32 2VD

L

ghL

=
http://en.wikipedia.org/wiki/File:Darcy%27s_Law.png


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Apply the equation now to flow through porous media.

Consider media is composed of spheres and voids.

= Porosity

T

V=

V= Void volumeT= Total volume

30

L32

hgDV L

2

a

=

Face velocity = Vapparent= Va

Va=V

V = average velocity through pores

dP,4

dA,

P

AR

2

H =

==

Relating D to the hydraulic radius, RH

For a pipe flowing full D=4RH


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L32

hgDV L

2

a

=

Relating D to the hydraulic radius, RH

For voids & spheres

spheresofareasurface

volumevoid

AR

R

LA

LR

LA

LP

LAR

S

VH =

=

=

=

=

244

244

2

TV =

( )== 1

TVTS

= 1S

T

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S

SH

AR

=

1

SV

=

1


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( )L

hR

gV LHa

24

32

=L

hR

g LH

2

2

=

( )

2

2

3

12

=

S

SLa

ALhgV

( )a

S

SL LV

A

g

h

2

3

212

=

6,

3

2 S

SS

ddA

==

SS

S

dV

ASdefine 6

==

For non-sphereseqd

S

6=

32

S

SH

AR

=

1


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( ) LVd

)'S(1

g

2h a2

S

2

3

2

L

=

S' = 6 for spheres

Finally

This is essentially the Fair- Hatch eq.

In AWWA it is called the Kozeny equation.

33

seqs

s

d

S

dV

AS

'6===


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( )g

V

d

L1fh

2a

3

=

dVNwhere

NVfbut a

a

== ReRe

641

Other equations developed f rom theoretical considerationsCarmen Kozeny based on Darcy-Weisbach

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( )LV

d

)'S(1

g

2h a2

S

2

3

2

L

=

Friction factor


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Headloss Equations Summary


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( ) ( ) 23223

2

Vd

L

e

e1

g

75.1V

d

L

e

e1

g150h

+

=

( ) ( ) ( ) 23223

2

Vdeq

L

e

e1

g

88.274.1V

deq

L

e

e1

g150h

+

=

( )V

d

L

e

e1

g180h

223

2

=

( )V

deq

L

e

e1

g180h

223

2

=

Headloss Equations Summary

Carmen Kozeny M&E

Ergun AWWA

Kozeny AWWA

Fair-Hatch M&E

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BGD FFF =

Backwashing Hydraulics (Recall Chapter 7 for Particle Settling)

When particles are completely fluidize; i.e. no particles are touching (Discrete)

( ) PWSsp

wPD gV

AC = 2

2

Vb = Backwash velocity m/s

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DBGT FFFF =0

eeL ,


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Backwashing Hydraulics

( )2

22

2

22

2

22

1

2 b

spb

wPDb

b

spwPDPWS

sp

wPD V

VVAC

V

VVACg

VAC ===

Vb = Backwash velocity m/s

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eeL ,

(e) = Correction factor to relate backwash velocity to

the discrete particle settling velocity, Vsp

PWSe

b

wPDb

spb

wPD

gVV

ACV

VVAC )()(

22

2

2

22

==

)()( 2 eb

sp

V

V=

B k hi H d li


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Backwashing Hydraulics

( ) ( ) PWSeb

wPD gV

AC = 2

2

( )

=

P

P

WD

WPsp

AC

g2V

Recall V For a sphere (Chapter 7)

39

laminar.,.24

1

Re

Re ei

N

CNfor D

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Chapter 8-Filtration (56 P)