10/25/2023

Water Supply and Wastewater

Management

6506CVQR

Week 6

Filtration
By
Dr. Reem F. Digna

Lecture Outline

In this lecture, we will discuss the following points:

 The importance of the filtration process in water treatment

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Learning Outcomes

The learning outcomes of the current lecture are:

 Understand the concepts and importance of the filtration processes.

 Design the slow and rapid sand filters.

Filtration
Filtration
 Although the majority of the colloids are removed from water through the coagulation,
flocculation, and sedimentation processes, further removal of colloidal matters is still
required to ensure high-quality water, which can be achieved by the filtration process.
 Filtration process is the oldest form of water treatment, and it is nature's own water
treatment process. For example, when the water flows through the geological formations,
such as sand and rocks, it will be cleaned and purified from the majority of the suspended
solids.
 However, the natural filtration process is slow. Therefore, advanced method are currently
used to accelerate the filtration process in water treatment plants.

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Filtration
Filtration

 The filtration process used in water treatment depends on flowing water through layers of
granular material, which could be a natural materials such sand, or artificial materials, such
as activated carbon.
 When the water flows through the granular material, the suspended particles are entrapped
in the pores of the material and separated from the water stream.

Filtration
Filtration

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Filtration
Theory of Filtration
The mechanism by which filters separate particles from water are
complex and divided more than one mechanisms. The common Straining
theories are:

• Straining: This theory indicates that large colloidal particles are

trapped in the pores of the filtration material and are removed. This
mechanism explains the direct filtration process, where flocculated
water is trapped directly into the pores of the filter.

Inertial Impaction
• Inertial Impaction: In this mechanism; the large mass particles
strike the filter material and held there because inertia is greater
than the hydrodynamic force. What Are The Mechanisms Of
Filtration (air-quality-eng.com)

Filtration
Theory of Filtration
Interception
• Interception: In some cases, the flow streamlines pass very
close to a media grain. At times, a particle following these
streamlines will touch a media grain and become lodged. These
particles are removed by interception

• Sedimentation: This mechanism takes place when

the particles pass through low – velocity zones within Diffusion
the filter bed.

• Diffusion: This mechanism occurs as result of

random (Brownian) motion of particle causes its contact
What Are The Mechanisms Of Filtration (air-
to filter material. quality-eng.com)

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Filtration
Types of Filters
Filters in water treatment are classified into different types
according to:

A. Filtration rate: Slow sand filters, rapid sand, and high-rate

filters.
B. Driving force: Gravity filters and pressure filters
C. Direction of flow: Downflow or upflow.
Downflow filters are commonly used in water treatment. In this type of system, the flow
through the media bed is downward

Filtration
Types of Filters

Slow sand filters differ from all other types of filters in

that their work includes a complex biological film that
grows naturally on the surface of the sand. This biological
film is known as schmutzdecke and it is made from dirt,
debris, and microorganisms builds up on the top of the
sand. However, slow sand filters have a low productivity.
Thus, rapid sand filters are widely used nowadays.

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Filtration
Types of Filters
Main Components of Slow sand filter:
1. A covered structure to hold the filter media
2. An underdrain system
3. Graded rock that is placed around and above the
underdrain
4. The filter media, consisting of 30 to 55 in. of sand
with a grain size of 0.25 to 0.35 mm
5. Inlet and outlet piping to convey the water to and
from the filter.

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Filtration

Filtration Rate (Loading rate):

𝑄
𝑣 =
𝐴

𝑣𝑎 = Loading rate, m3/m2.day =face velocity = approaching velocity (m/d)

Q = flow rate onto filter surface (m3/day)

As = surface area of filter (m2)

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Filtration
Example
A company installs rapid sand filters after their sedimentation tanks. The design loading rate
is 180 m3/m2.day. Calculate:

A) Surface area that should be provided for the design flow rate of 0.6 m3/sec

B) Number of filter boxes required if the surface area per filter is to be limited to 40 m2.

Limitations:

• The recommended maximum loading rate < 235 m/day.

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Filtration
Solution
𝟎.𝟔 ×(𝟐𝟒×𝟔𝟎×𝟔𝟎 )
𝑣 = 𝐴 = = = 288 m2
𝟏𝟖𝟎
.

Number of filters= = =7.2, use 8 filter boxes (round it to an

integer)
Check the limitations:
The recommended maximum loading rate <235m/day

.𝟔 ×(𝟐𝟒×𝟔𝟎×𝟔𝟎 )
𝑣 = =162m/day  OK (<235m/day)
𝟖×𝟒𝟎

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Filtration
Head Losses in Filters

1. If initial head loss > 0.6 m, the loading rate is too high OR the sand has too large a
proportion of fine grain sizes.

2. Head loss through a granular-media (Head loss before backwash ) is generally 2.4 -3.0 m.

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Filtration
Head Losses in Filters
The Kozeny Equation
This equation is used to determine the head loss in a homogeneous granular-materials bed.
ℎ 𝐽 × 𝑣 × (1 − 𝜀) × 𝑉 × 𝑆
=
𝑙 𝑔×𝜀 ×𝑑 𝜺 = Porosity of the filter bed (dimensionless)
h = head loss(m)
V = superficial velocity of water above the bed (m/sec)
𝓵 = depth of filter (m)
ν = kinematic viscosity (m2/sec)
J = constant (dimensionless)
d = mean grain diameter (m)
S = shape factor (6.0 for spherical grains (e.g., sand), 7.5 for angular grains (e.g., anthracite))

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Filtration
Example

Using the Kozeny equation, determine the initial head loss through a 0.5 m filter made from
sand having a porosity of 0.39 and a grain diameter of 0.4 mm. The used sand particles are
spherical in shape, and the J constant is 6. Water temperature is 10°C, and the filtration rate
(Surface Loading rate) is 2.9x 10-3 m3/sec.m2.

𝒉 𝑱 × 𝒗 × (𝟏 − 𝜺)𝟐 × 𝑽 × 𝑺𝟐
=
𝒍 𝒈 × 𝜺𝟐 × 𝒅𝟐

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Filtration
Solution

ν = 1.31x10-6(m2/sec)

× ×( ) × × . ×( . × )× . ×( . × )× .
=  = =3.279
× × . × . ×( . × )

= 3.279  h=1.64m
.

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Filtration
Exercise
Using the Kozeny equation, determine the depth of a filter that is made from sand having a
porosity of 0.4 and a grain diameter of 0.54 mm. The used sand particles are spherical in
shape, and the J constant is 6. Water temperature is 20°C, the filtration rate (Surface Loading
rate) is 2.6x 10-3m3/sec.m2 , and the initial head loss 1.1m

𝒉 𝑱 × 𝒗 × (𝟏 − 𝜺)𝟐 × 𝑽 × 𝑺𝟐
=
𝒍 𝒈 × 𝜺𝟑 × 𝒅𝟐

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Next Lecture:

Design Practice

Thank you very much

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