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Water and Wastewater Treatment (CEGE0022) : Sand Filtration - Part 2

This document provides an overview of sand filtration and backwashing processes. It discusses key learning outcomes related to understanding backwashing, fluidized beds, and calculating fluidization velocity and head loss in an expanded filter bed. Equations and videos are presented to explain concepts such as how backwashing fluidizes the sand bed, calculates minimum fluidization velocity, and determines expanded bed depth and head loss. Design considerations and an example calculation are also provided.

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174 views14 pages

Water and Wastewater Treatment (CEGE0022) : Sand Filtration - Part 2

This document provides an overview of sand filtration and backwashing processes. It discusses key learning outcomes related to understanding backwashing, fluidized beds, and calculating fluidization velocity and head loss in an expanded filter bed. Equations and videos are presented to explain concepts such as how backwashing fluidizes the sand bed, calculates minimum fluidization velocity, and determines expanded bed depth and head loss. Design considerations and an example calculation are also provided.

Uploaded by

abdul5721
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© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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DEPARTMENT OF CIVIL, ENVIRONMENTAL and GEOMATIC ENGINEERING

WATER AND WASTEWATER TREATMENT


(CEGE0022)

SAND FILTRATION – Part 2

DR LUIZA C. CAMPOS
Learning Outcomes

•to understand the backwashing process


• to be able to identify a fluidised bed
• to be able to calculate the fluidisation velocity
• to be able to calculate head loss in an expanded filter bed

Watch these videos:

https://www.youtube.com/watch?v=SdN3g85zfzM

https://www.youtube.com/watch?v=31ZUXx6NXDA
2
Backwashing

Rapid gravity, granular media filters need regular


backwashing to remove clogging deposits and maintain
efficient operation.

Backwashing of a gravity filter involves upward flow to


dislodge the deposits that have accumulated during
filtration and flush them away.

3
Filter backwashing

(1) Start with air


(2) Air + water

(3) Air + water (4) Wash water flow time 10 min

Watch this video: https://www.youtube.com/watch?v=whwEBxqa3yU


Backwashing

Backwashing fluidises the bed Area,a

Fluidised bed:
solid particles/grains suspended by
fluidising medium, e.g. gas or liquid
when grains in equilibrium
sand
upward force = downward force

5
Backwashing

Downward force = weight of grains in water

FD  ALe 1   e  s   g (7)

A : X-sectional area
Le : Expanded depth of bed
e : porosity of expanded bed
s : density of grains

Upward force = pressure difference * area


Fup= ρgheA (8)

where he is the head loss


6
Backwashing
Equating the downward (Eq. 7) and upward (Eq. 8) forces gives

 Le 1   e  s   g
A
 ghe (9)

A
Rearranging gives an expression for the head loss gradient in a fluidised bed

1  e s    he (10) (Fair and Hatch, 1933)


 Le

7
The head loss (hydraulic gradient) can also be given by the
Kozeny-Carman equation as
he u  1   e 2 36
5 (11)
Le g   e 3 ds 2

where ds is grain diameter, m is dynamic viscosity of water.


Equating Eq (10) and (11) gives
1  e  s   
5
u  1   e 2 36 (12)
 g  e3 ds2

which can be rearranged to give an expression for the


minimum fluidisation velocity, umf.
g s    e3ds2 (13)
umf 
180  1  e  8
Expanded Depth of Bed
x
u 
Porosity of expanded bed can be related to settling velocity vt
 e    (14)
 vt 
Where x is an experimental value equal to 0.22

The volume of the sand in an unexpanded bed will equal the volume of sand in
an expanded bed

AL0 (1 - ε ) = A Le ( 1 - εe ) (15)

L1  0 
L e  L0
1  0 
(16)
Le 
0.22
(17)

1  e  u
1   
 vt 
Need to calculate terminal settling velocity
9
Design Considerations

• Aim for expanded bed porosity of 0.6 to 0.7 (initial porosity


usually 0.4 for sand)
• Expanded depth 1.2 to 1.55 times original depth
• Ensure no loss of media

Minimum fluidisation velocity


• Calculate fluidisation velocity for each fraction
• Take maximum value
Bed Expansion
• Calculate expanded bed length for each fraction
• Add up values
10
Exercise – bed expansion and fluidisation velocity
Data:
0 0.4
L 0.67 m
 0.85
K 5
ds 0.0004 m
 0.00102 Nms-2
vt 0.39 ms-1
 998.2 kgm-3
s 2650 kgm-3
g 9.81ms-2
e 0.65

Calculate the minimum fluidisation velocity and using Fair-Hatch equation


calculate the expanded depth of bed ?

g s    e3ds2 umf = 0.011 ms-1


umf 
180  1  e  = 39.6 mh-1

௢ ଴
௘ Le=1.14m
௘ 11
Head loss in expanded bed
Consider the simplest case of a single media filter.
Equation 10 gives us the head loss gradient in the fluidised bed as
1   e  s     h e (10)
 Le
If we want to know the backwash head loss, we need to eliminate Le
and e from the equation, as they are not known and not easily
measured.

We know that in the fluidised bed the total volume of solids is unchanged

L e  L0
1  0 
1  e  (16)

So we can substitute Le in Equation 10 using Equation 16 and we get

௦
௘ ଴ (18)
12
For a typical filter sand we know that the voidage, 0 = 0.4 and the
density, s=2650 kg/m3 , so we can put these values into the
equation 18
 = 1000 kgm-3

0.6 x1650 xL
h
1000
 h  Lo

where the head loss is measured in m of water and the bed depth
is also in m.

Note: this is a very useful thing to remember for sand filters. But,
please remember it only applies to sand, as the figures we plugged
into the equation were for sand only
13
Acknowledgement

Part of these lectures was taken from the lectures of Dr R.


Mackie (University of Dundee) and Professor Caroline
Fitzpatrick (UCL).

References
Qasim et al. 2000 Water works engineering – planning, design & operation.

Casey, T.J. 1997 Unit treatment processes in water and wastewater engineering

14

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