Filtration

Mechanisms for particle removal

Transport process, attachment, detachment
Effect of process variables on collection efficiency
Mathematical analysis of flow through porous media
Roughing filters, SSF and RSF
Process selection

CE6301: Theory of Water Treatment Dr. Tanvir Ahmed

Why filtration?

 Sedimentation with or without coagulation will not ordinarily

give clear sparkling and bacteriologically safe water

 Filter media are very efficient in retaining fine and colloidal

particles of clay and silt.

 Aids in removing color, odor, iron and manganese

 Filters are capable of removing a wide range of particulate

materials of both natural and human origin (algae, colloidal
humic substances, viruses, asbestos fibers, colloidal clay
particles) provided that proper design parameters are used.

CE6301: Theory of Water Treatment Dr. Tanvir Ahmed

Types of filters

 Granular materials (sand, anthracite, coal, magnetite) 0.1 –

10 mm
Slow Sand Filter (SSF)
Rapid Sand Filter (RSF)
Roughing filters (RF)
 Diatomaceous earth(7 – 50 μm), a deposit formed form
siliceous fossil remains of diatoms
 Membrane Filtration (0.45 – 0.2 μm), capable of removing
bacteria and in some cases molecular separation

CE6301: Theory of Water Treatment Dr. Tanvir Ahmed

Underdrainage system and filter arrangement

CE6301: Theory of Water Treatment Dr. Tanvir Ahmed

Mechanism for particle removal
In filtraiton process, particulate materials either accumulate on the
surface or collected through the filter bed

(A) Physicochemical process

Mechanical Non-straining
straining mechanism

(Impaction, Interception,
diffusion, electrostatic
attraction etc.)

(B) Biological process

Formation of a thin layer of
microbial film around the sand grains
(‘Schmutzdecke’)

CE6301: Theory of Water Treatment Dr. Tanvir Ahmed

Mechanical straining
Principle mechanism of particle removal in filters where thin media are
used (i.e. screens or membranes).

No unambiguous criteria has

been established yet to
determine when mechanical
straining becomes important.

Undesirable for granular media

filters as head loss will increase
rapidly due to the formation of
surface mats.
www.vokesair.com

CE6301: Theory of Water Treatment Dr. Tanvir Ahmed

Non straining mechanisms (transport and attachment)
Isolated single-sphere model is used to describe the transport mechanisms.

(A) Impaction: due to inertia of

particles.

(B) Hydrodynamic forces: non-

uniform shear distribution
within pore spaces

(C) Interception: particles along

the streamlines which pass
within a distance < radius of
the particle.

(D) Diffusion: Particles influenced by Brownian motion.

CE6301: Theory of Water Treatment Dr. Tanvir Ahmed

Non straining mechanisms (transport and attachment)
(E) Sedimentation: Particles with density > water will tend to deviate
from the fluid streamlines.

(F) Other transport mechanisms:

Van der Waals forces of attraction,
electrostatic attraction
small
sedimentation
basin

Attachement mechanisms:
(A) Coagulation
(B) Adhesion
(C) Adsorption

CE6301: Theory of Water Treatment Dr. Tanvir Ahmed

Quantifying Particulate collection efficiency
Particle collection Successful number of collisions
efficiency (η) = Total no. of possible collisions in cross-sectional area
perpendicular to isolated collector (area =πdm2/4)

Assuming individual transport

efficiencies are additive, all collisions
lead to attachment and particle
destabilization is complete

𝐾𝑇
2/3
3 𝑑𝑝
2
𝜌𝑝 − 𝜌 𝑔𝑑𝑝 2 dm
𝜂 = 0.9 + +
𝜇𝑑𝑝 𝑑𝑚 𝑉0 2 𝑑𝑚 18𝜇𝑉0 2

Diffusion Interception Sedimentation

K = Boltzman constant
= 1.38×10-23 J/°K
T = absolute temp (°K)

CE6301: Theory of Water Treatment Dr. Tanvir Ahmed

Quantifying Particulate Removal Efficiency
Fraction of particle removed (removal efficiency),

𝑁 −𝜓(1 − 𝜀0 ) Ψ = shape factor

= 𝑒𝑥𝑝 𝐿𝜂 ε0 = initial porosity of granular material
𝑁0 𝑑𝑚
L = media depth

removal efficiency can

be increased by
 decreasing media
porosity
 increasing media
depth
 decreasing media
size

CE6301: Theory of Water Treatment Dr. Tanvir Ahmed

Factors affecting collection efficiency
(A) Effect of particle size

(B) Effect of media size and filter velocity: inversely proportional to

collection efficiency

Although it is possible to manipulate media size and filter velocity to

obtain optimum collection efficiency, adequate destabilization is required
for satisfactory filtration.

CE6301: Theory of Water Treatment Dr. Tanvir Ahmed

Factors affecting collection efficiency

𝑁 −𝜓(1 − 𝜀0 )
= 𝑒𝑥𝑝 𝐿𝜂
𝑁0 𝑑𝑚

CE6301: Theory of Water Treatment Dr. Tanvir Ahmed

Flow through porous media: mathematical analysis
Analogous to flow through a system of interconnected pipes formed by
voids in a bed of particles.
𝐿 𝑉2
𝑕𝑓 = 𝑓 [Darcy-Weisbach equation]
4𝑅 2𝑔
hf = head loss, V = velocity of flow, f = friction factor,
R = hydraulic radius, L = length of pipe

𝐿 1 − 𝑒 𝑉𝑆 2
𝑕𝑓 = 𝑓′ [Carman-Kozeny equation]
𝜑𝑆 𝐷𝑃 𝑒 3 𝑔

𝑒 𝑉𝑝
R = volume of voids/wetted surface area = 1−𝑒 𝑆 = 𝜑𝑆 𝐷𝑃 /6
𝑝
V = VS/e, e = porosity, VS = superficial velocity
DP = particle diameter, φS = shape factor f’ = friction factor
including other constants

CE6301: Theory of Water Treatment Dr. Tanvir Ahmed

Flow through porous media: mathematical analysis

The friction factor f’ has been correlated with Reynold’s number:

1−𝑒 𝜑𝑆 𝐷𝑃 𝑉𝑆 𝜌
𝑓′ = 150 + 1.75, 𝑅𝑒 =
𝑅𝑒 𝜇

CE6301: Theory of Water Treatment Dr. Tanvir Ahmed

Flow through porous media: mathematical analysis
The following Rose equation similar to Carman-Kozeny equation has been
developed to compute the head loss in a rapid filter media
𝐿 1 𝑉𝑆 2
𝑕𝑓 = 𝑓′′
𝜑𝑆 𝐷𝑃 𝑒 4 𝑔
The friction factor f’’ has been correlated with Drag coefficient, CD:

′′
𝑏 Re b n
𝑓 = 1.067𝐶𝐷 , 𝐶𝐷 = 𝑛
𝑅𝑒 <1.9 24 11.9
1.9 - 500 18.5 0.65
500 – 200,000 0.44 0
For particles of various sizes:
2 𝑛
𝐿 1 𝑉𝑆 𝑥𝑖
𝑕𝑓 = 1.067 𝐶𝐷,𝑖
𝜑𝑆 𝑒 4 𝑔 𝐷𝑃,𝑖
𝑖=1

xi = weight fraction of particle in the ith layer/fraction of size Dp,i

CD,i = Drag coefficient, n = number of layers
CE6301: Theory of Water Treatment Dr. Tanvir Ahmed
Flow through Expanded particle bed
When particles reach to the point of fluidization, the effective weight of the
particles is just balanced by the force tending to lift the particles
∆𝑃𝐴 = 𝐿𝐴(1 − 𝑒) 𝜌𝑆 − 𝜌

𝑕𝑓 = 𝐿(1 − 𝑒) 𝜌𝑆 − 𝜌

𝐿𝑒 = 𝐿(1 − 𝑒)/ 1 − 𝑒𝐸

ΔP = pressure difference,
A = Area
ρS = density of particle
eE = porosity of expanded bed
Le = length of expanded bed

CE6301: Theory of Water Treatment Dr. Tanvir Ahmed

Flow through Expanded particle bed
For stratified beds:
𝑛
𝑥𝑖
𝐿𝑒 = 𝐿(1 − 𝑒)
1 − 𝑒𝐸 𝑖
𝑖=1

eE can be estimated from VS and Vt

(terminal velocity):

𝑒𝐸 = 𝑉𝑆 /𝑉𝑡 0.22

4 𝑔 𝜌𝑆 −𝜌
Where, 𝑉𝑡 = 𝐷𝑃 1/2
3 𝐶𝐷 𝜌
𝑏
𝐶𝐷 = 𝑛
𝑅𝑒

CE6301: Theory of Water Treatment Dr. Tanvir Ahmed

Problem
A sieve analysis of a fine Ottowa sand yields the information recorded in
the table below. Compute the initial head loss across a stratified bed of the
san, 18 inch deep and with a porosity of 0.41, when water at 45°F is filtered
at a rate of 3 gal/min/ft2. If the sand filter is to be backwashed hydraulically
at a rate just sufficient to fluidize the bed, compute the (a) backwash rate
(b) the head loss at this rate and (c) depth of the expanded bed

Sieve Numbers, Weight Fraction of

US Sieve Series Particles retained, ×103
14 – 20 0.80
20 – 25 4.25
25 – 30 15.02
30 – 35 16.65
35 – 40 18.01
40 – 50 18.25
50 – 60 15.65
60 – 70 9.30
70 - 100 2.07

CE6301: Theory of Water Treatment Dr. Tanvir Ahmed

 Roughing filtration: layout and design

Purpose:
Pretreating
water with
high turbidities
Three types

Decreasing
gravel size

CE6301: Theory of Water Treatment Dr. Tanvir Ahmed

Roughing filtration: cleaning and efficiency
Cleaning:
Either hydraulically (shock drainage) or manually

Up-flow filters Excavation of filter

possess a favorable bed, washing and
layout refilling

Efficiency:
 SS removal upto 95% and turbidity removal of 50-90% have been
reported
 Color removal 20-50% and faecal coliform reduction 0.65 – 2.5 log
units
 50% removal of iron and manganese has also been achieved

CE6301: Theory of Water Treatment Dr. Tanvir Ahmed

Roughing filtration: advantages and disadvantages

Advantages:
 Allows deep penetration of filter materials
 Have large silt storage capacity
 Often used before SSF because of their effectiveness in removing SS
 More effective as a pretreatment than pre-sedimentation for raw
water to the physical standards required by SSF

Disadvantages:
 Limited to average turbidity of 20-150 NTU to prevent frequent
clogging

CE6301: Theory of Water Treatment Dr. Tanvir Ahmed

Slow Sand Filtration (SSF)
Purpose:
 Reduce the number of microorganisms in water
 Retain fine organic and inorganic solid matters
 Oxidize organic compounds dissolved in water

~1m depth, with Fine sand

~0.1m overboard (upgraded), free
from impurities

Suitable for the development of surface water-based water supply

systems in developing countries
CE6301: Theory of Water Treatment Dr. Tanvir Ahmed
Particle Removal Mechanism in SSF

CE6301: Theory of Water Treatment Dr. Tanvir Ahmed

SSF Characteristics
 Very low rate of filtration

Limitations of SSF
 High removal of turbidity (80-85%) and color (95-99.9%)
 No pretreatment generally required for water <30NTU
 Not very effective in removing colloidal matters, treating
water >30NTU or with excessive algal growth
 Low cost operation and maintenance
 2-4 weeks ripening period required after installation, however
it can regain full biological activities (formation of
‘Schmutzdeke’) after a few hours of cleaning thereafter.
 Cleaning done by removing scraping and removal of the top
1.5-2 cm of sand
 Perform best under continuous operation and constant flow
conditions

CE6301: Theory of Water Treatment Dr. Tanvir Ahmed

SSF design criteria

 Filtration rate 0.1 – 0.2 m/hr

 box height 2 m
 Sand gradation: d10 between 0.1 – 0.3 mm, d60/d10 <3.
 Sand quality: clean sand free from clay, silt and organic matter
 Underdrain system should have a gravel layer of 0.3 – 0.5 m
 Number of rectangular filters required for a plant:

3
𝑛 = 0.5 𝐴

A = total surface area in m2 computed on the basis of filtration rate and

design water demand.

CE6301: Theory of Water Treatment Dr. Tanvir Ahmed

Rapid Sand Filtration (RSF)
Higher filtration rate is achievable because of the coarse sand (d10 = 0.4-1.2
mm) and relatively uniform-sized particles that are used as the filter medium

Graded gravel, 0.5 m thick Coarse sand layer, 1 m thick

Can be both gravity type and pressure type

CE6301: Theory of Water Treatment Dr. Tanvir Ahmed

Particle Removal Mechanism in RSF
Surface Adsorption on
coarse media bed

gravel
gravel
gravel gravel

gravel gravel

CE6301: Theory of Water Treatment Dr. Tanvir Ahmed

Characteristics of RSF
 High filtration rates 5-15 m3 per m2 per hour
 High removal of turbidity (80-85%) and color (85-95%)
 Pretreatment such as coagulation, flocculation and sedimentation are
required
 Suitable for all types of turbid and colored water
 Relatively high cost of operation and maintenance.
 Cleaning of filter bed by backwashing

CE6301: Theory of Water Treatment Dr. Tanvir Ahmed

Operational difficulties in RSF

(A) Negative head and air binding (B) Formation of mud balls

CE6301: Theory of Water Treatment Dr. Tanvir Ahmed

Operational difficulties in RSF

(C) Cracking of filter bed (D) Jetting and sand boils

(E) Sand Leakage

CE6301: Theory of Water Treatment Dr. Tanvir Ahmed
Design considerations of RSF
 Economy in construction and operation
 Provision of future consideration
 Soil conditions, foundation and structural stability
 Flexibility in operation
 Compactness, minimization of head losses and operational
 Utilization of topography to minimize earth work and to make proper
use of gravity
 Size of the filter is determined by the required capacity of the plant

𝑁 = 0.04 𝑄

N is the number of units and Q is the plant capacity in m3 per day

CE6301: Theory of Water Treatment Dr. Tanvir Ahmed

General features of SSF and RSF

CE6301: Theory of Water Treatment Dr. Tanvir Ahmed

Characteristic Differences among SSF, RSF and RF

CE6301: Theory of Water Treatment Dr. Tanvir Ahmed

Problem
A rapid sand filter is to be designed for a capacity of 27000 m3/day. What
should be the number and size of the units. Calculate the percentage of
filtered water required to wash the filter bed and the capacity of the
wash water tank.
Assume: Rate of filtration: 5 m3/hr/m2
rate of washing: 35 m3/hr/m2
Length of the filter run: 24 hours including 5 min for filter
washing and 10 min for resettlement of sand bed

CE6301: Theory of Water Treatment Dr. Tanvir Ahmed

Process Selection
1. Characteristics of the media depending on the particular type of
application

CE6301: Theory of Water Treatment Dr. Tanvir Ahmed

Process Selection

2. Different filtering devices/media must be overviewed.

o Screens – 1-100 μm (effective size opening)
o Diatomaceous earth – 7-50 μm
o Granular – 0.1 - 10 mm

3. Comparison with other solid-liquid separation processes

o screening
o sedimentation
o Flotation
o Membrane filtration

Selection process is usually based on experience

CE6301: Theory of Water Treatment Dr. Tanvir Ahmed

Process Selection
4. Physical characteristics of the particulates to be removed
o Initial number and mass concentration
o Average size characterizing the distribution

Process Avg size (μm) SS (mg/L)

Gravity Sedimentation >100 >50
Screening ~30 <50
Filtration using granular media <30 <50
without sedimentation
Coagulation sedimentation <30 >50
prior to filtration

For high algae concentration, microscreens are used before

granular media filtration

CE6301: Theory of Water Treatment Dr. Tanvir Ahmed

Process Selection
4. Physical characteristics of the particulates to be removed
o Initial number and mass concentration
o Average size characterizing the distribution

CE6301: Theory of Water Treatment Dr. Tanvir Ahmed

Process Selection

Example
o When particle size↓, turbidity ↓ ------ use SSF
o When particle size↑, turbidity ↑ ------ use RSF but with prior
sedimentation and coagulation

5. Other considerations for ultimate selection of design criteria

o Analytical models of the process
o Previous experience
o Pilot studies
o Published literature

CE6301: Theory of Water Treatment Dr. Tanvir Ahmed