CE 428 Water and Wastewater Design
Dr. S.K. Ong
Sand Filters
Purpose - used primarily to remove suspended particulate materials from water, example, silt and clay,
microorganisms, colloidal and precipitated humic substances, alum or iron, calcium carbonate and magnesium
hydroxide from lime softening, iron and manganese precipitates.
Types of filters
____________________ - solids are removed within the granular materials, example rapid granular-bed filters
____________________ - solids are removed on the entering face of the granular material or filtering material,
example, slow sand filters, membrane filters
Important Design Data for rapid granular-bed filters
1. Loading rate or filtration rate,
Where Q
As
= flow rate (m3/d)
= surface area of filter (m2)
Loading rates
 Conventional pretreatment using alum and iron salts/sand medium
 High rate with dual or triple media (anthracite coal layer)
__________ gpm/ft2 (______ m/h)
__________ gpm/ft2 (_____ m/h)
(note that rates as high as _______ gpm/ft2 (_____ m/hr) and ______ gpm/ft2 (_____ m/h) have been used)
(in contrast - slow sand filters - ______________ gpd/ft2)
2.
Practical maximum area of an individual gravity bed filter _________________ m2.
3.
Minimum number of individual filter beds - ____________. When one is backwashing or under
maintenance, the other bed must be capable of meeting water demands.
4.
Grain size and the total depth of media affect the filtration operation. Both affect the head loss and build up
of headloss during filter run.
Size distribution of the media is usually determined by sieve analysis (see Table 11-3 page 1046)
Effective size is defined as the ________ percent size based on mass and is designated as d 10.
The uniformity coefficient (UC) is defined as the ratio of the 60 percent size to the 10 percent size
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Typical media sizes and depths for rapid gravity sand filters for water treatment
Effective size
(mm)
A. Common US Practice after coagulation and settling
1. Sand alone
0.45 – 0.55
2. Dual Media
0.9 – 1.1
Anthracite (0.1 to 0.7 of bed) (note fraction)
3. Triple media
0.2 – 0.3
Garnet (0.1 m)
B. US Practice for direct filtration
Practice not well established. With seasonal diatom blooms, use coarser
top size. Dual or deep mono medium, 1.5 mm effective size
C. US Practice for Fe and Mn Filtration
1.Dual media similar to A-2 above
2. Single medium
< 0.8
D. Coarse single medium filters washed with air and water simultaneously
1. For coagulated and settled water
0.9 – 1.0
2. For direct filtration
1.4 – 1.6
3. For Fe and Mn removal
1–2
Total Depth
(m)
0.6 – 0.7
0.6 – 0.9
0.7 – 1.0
0.6 – 0.9
0.9 – 1.2
1–2
1.5 – 3
Rule of thumb
- allow approximately __________________ m above the top of the sand for washwater troughs
- approximately ___________________ m above the sand for water to build up above the filter
5.
Clean Water Head loss calculations through the sand filter (Table 11-5, equation 11-2, page 1051)
Carman-Kozeny equation
 1   vs 2
pi

hL  
L f
 3   g  fi d i
  
where
hL

vs

ffi
pi
di
NR


= head loss, m
= porosity
= superficial filtration velocity (m/s)
= particle shape factor (0.75 for average sand, 0.73 for crushed coal)
= friction factor
1 
 1.75
= 150
NR
= fraction of particles within adjacent sieves with mean geometric diameter of d i
= geometric mean diameter between sieve sizes di and di+1
= Reynolds Number
 d vs 
=

= viscosity Ns/m2
= density kg/m3
Initial head loss through media < ____________ m
Terminal head loss through media between _____________ m
2
The head loss for a clogged filter is difficult to estimate since the porosity of the media changes with the degree of
clogging. Book provides an equation (11-30), page 1061 which relies on several regression analysis curves (Figure
11 - 10) to estimate the headloss.
Total Head loss through the filter:
where
H = total head loss
hL = head loss through the media
hg = head loss through the gravel, if any
hu = head loss through the underdrain
hp = head loss through the pipes, valves and flow controller, if any
Air Binding of Filters (Negative pressure within the filer)
Bernoulli’s equation
v12 p1
  z1 
2g 
Assume the datum as
Then
v2
2
p
 2  z2  H
2g

z2 = 0
P1 = 0
V1= 0
v2
p2
 z1  2  H

2g
Sand depth
Underbed gravel
Underdrain
Water depth over sand
Total z1
= ___________’
= ___________’
= ___________’
= ___________’
= ___________‘
Assume velocity of water in pipe at 2 is ________ ft/s
Then
When clean H = ____________’, pressure at 2 is positive
After running the filter, H increases, if H > __________’, negative pressure develops, dissolved gases come out of
water causing bubbles to form. This action causes release of particles from the filter media which will result in
shorter filter run time and poor water quality.
To prevent this, filters are backwashed when head loss reaches _________‘. Or the elevation of the effluent weir is
located at the same elevation as the top of the media (but this means that the depth of water over the media must be
increased to achieve the same throughput of water).
6. Underdrain System:
Manifold and lateral underdrain system
- first and oldest, not common now
- high head loss
- graded gravel needed
Self supporting underdrain system
- grouted to the filter floor
- vitrified clay block
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False floor underdrain system
- concrete floor or steel plate (usually in small filters or pressure filters)
- located 1 to 2 feet above the bottom of the filter
- nozzles are used to collect the water and the fine openings retain filter medium
- no need for grout
7. Backwash Rate and backwash head
- backwash water needed to clean the filters, water may be provided from the clear well or from a separate
backwash water tank
- different approaches in estimating the backwash rate
- typically _____________________ m/d (___________________ gpm/ft2)
- about ___________ times more than the filter loading rates
- expand bed by ______________%
- wash time is about _____________ minutes, total time backwash filter (including preparation, draining,
etc.) may take about _______________ minutes
- for typical systems, amount of backwash water used should be between __________% of filtered water
produced
- surface wash system – to ensure thorough cleaning and to prevent the formation of mud balls – provided
for by directing jets of water downward on the surface of the filter media or by using rotating arms that
sweep the surface of the filter.
- air wash system – air introduced into the underdrain at a rate of ____________ m/min based on filter area.
The rolling action of the air scours the deposits on the sand – releasing them.
Backwash rate estimation:
Approach 1 - Book’s approach:
This approach is given in the book and also in the "Introduction to Environmental Engineering" book. Equations
used are listed below (in this case a back wash rate is selected which is equal to the settling velocity of the smallest
particle that must be retained):
Le
p
 (1   ) 
L
1 e
v
 e   b
 vs
where




0.22
p = mass fraction of sand with expanded porosity
vb = backwash water velocity
vs = settling velocity
Head loss during bed expansion is given by:
   w 

h  L e (1   e ) s

 w 
where w
= density of water
s
= density of media
For a typical media of different sizes, divide the media into __________ different sizes and compute L e accordingly.
Approach 2
Compute the minimum fluidization velocity for the d 90 particle of the filter medium.
using the following equations
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Re mf  [( 33.7 ) 2  ( 0.0408 )Ga ] 1 / 2  33.7
Re mf 
v mf  d

d  (  s   )g
3
Ga 
where
Remf

s
vmf
d

2
= Reynold’s Number for minimum fluidization
= density of water
= density of particle
= minimum fluidization velocity
= particle diameter
= viscosity
To ensure adequate movement of the grains, a backwash rate equal to ________ vmf is recommended. Procedure is
sufficient for selecting the minimum backwash rate for a single medium filter. For a dual media filter, the minimum
fluidizing velocity for the mixed interfacial region between the two adjacent media may be somewhat lower than the
fluidizing velocity of the coarser grains of the upper layer at the interface.
e=(vb/vi)n
Bed expansion is given by the following equation:
where
e
vb
vi
n
= expanded bed porosity
= superficial backwash velocity
= intercept velocity for e = 1 for a log-log plot of e and vb
= 0.4 to 0.5
This approach needs experimental data to find vi. To overcome this some engineers suggest using vs – settling
velocity of a representative particle.
Once e is found, the bed expansion is computed:
L ei
1 i

Li
1   ei
Approach 3
A more rational approach for the estimation of backwash rate, vb is given by the following equations (See Theory
and Practice of Water and Wastewater Design, Droste, equations 14.29, 14.31 and 14.32b ):
  (  )g( d) 3 
s




2
2
36 
(1   e ) 

Re f  0.2
use   18 .1 Re f

 3e
Re f  0.2
use log( / 6)  0.56543  1.09348 log Re f  0.17979 (log Re f ) 2  0.00392 (log Re f ) 4  1.5(log ) 2
Re f 
 vb d
6(1   e )
L ei
1 i

Li
1   ei
5
where
e

Lei
Li
i
si
=porosity of the expanded bed
= sphericity
= expanded media depth of layer i
= fixed bed depth of layer i
= porosity of fixed bed layer i
= porosity of expanded bed layer i
In this approach, a backwash velocity is initially selected (usually the minimum fluidization velocity in the first
approach) and then by trial and error, find the value of e that satisfies the above equations for a given expansion
Backwash Trough
- see notes and example
- bottom of backwash trough should locate about ________ m above the expanded bed, spacing of troughs
approximately ___________ m.
Types of operation (see Figure 11-24)
Constant rate filters with variable head
- Influent water is distributed using an influent weir box
- as impurities fill the media the water level above the bed rises to maintain a constant filtration
rate
- Head loss is apparent by the depth of the water above the filter bed
- Effluent flow rate controllers are not required
Constant rate filters with fixed head
- Water level is maintained constant throughout the run
- As impurities fill the media the head loss in the filter builds up
- Constant flow rate is maintained by using effluent flow rate controllers,
initial run - low head loss, flow controller is close to close,
at end of filter run - high head loss, flow controller is completely open.
Declining rate filters or Variable Rate Filtration
- influent water is usually below the water level from a common channel supplying a series of
filters
- the depth of the water is all filters are the same at all time
- filtration rate is dependent on the head loss through the bed, and therefore the cleanest filter
accepts the greatest flow and the dirtiest the least. The water level rises in all filters to maintain a
constant water quality and distribution of water. When the water level reaches the maximum
level, the dirtiest filter is backwashed to increase the rate of filtration.
- usually have a flow restricting or flow controller at the effluent
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