Conventional Surface Water
Treatment for Drinking Water
From: Water on Tap, USEPA
pamphlet accessed on 01/04/09 at
http://www.epa.gov/safewater/wot/
pdfs/book_waterontap_full.pdf
(From Opflow,
November 2005)
Filter backwash water flowing into
(above) and out of (right) launders
Photos by Dan Gallagher
From: Virginia Tech Water Treatment Primer, accessed on 01/04/09 at
http://www.cee.vt.edu/ewr/environmental/teach/wtprimer/backwash/backwash.html
Headloss
90
10 gpm/ft2
80
6 gpm/ft2
Headloss (inches of water)
70
8 gpm/ft2
60
4 gpm/ft2
50
40
30
Coagulant = FeCl3 (30 mg/L)
Temperature = 10 oC
20
10
0
0
10
20
30
40
Time (hour)
50
60
70
80
Filter 3 effluent particle counts (1 - 150 µm) (#/mL)
Effluent particle counts
100000
10000
10 gpm/ft2
1000
8 gpm/ft2
6 gpm/ft2
4 gpm/ft2
100
10
Coagulant = FeCl3 (30 mg/L)
Temperature = 10 oC
1
0
10
20
30
40
Time (hour)
50
60
70
80
Filtration Complexity
• Two dependent variables of importance
– Head Loss
– Effluent Quality
• Never at Steady State
• Two different modes of operation (filtration and backwashing)
• Numerous Independent Variables
d  NVL,CV 
dt
 QN  Q  N  dN   VL,CV rp
Assume pseudo-steady state, so
d  NVL,CV 
Q  Av0
0   Av0 dN  VL ,CV rp
Av0 dN  VL ,CV rp
dt
0
Number of
 Rate of Removal of Particles  

VL ,CV rp   
 Collectors in Layer 
by
a
Single
Collector



Number of
 Rate of Approach of   Removal Efficiency of  

 
  a Single Collector  Collectors in Layer 
Particles
to
a
Collector




Ac 
 dc2
4
 Rate of Approach of 
 dc2
 Particles to a Collector   Nv0 4


 Removal Efficiency of 
 a Single Collector   


Total Volume of 
Number of

  Collector Media  AdL 1   
Collectors in Layer    Volume of a    d 3 / 6


c
Single Collector 


Number of
 Rate of Approach of   Removal Efficiency of  

VL,CV rp   
  a Single Collector  Collectors in Layer 
Particles
to
a
Collector





 d c2   AdL 1    
   Nv0

   
3
4

d
/
6

 
c

3 1   

Nv0 AdL
2 dc
“Single Collector
Removal Efficiency”
Av0 dN  VL ,CV rp
3 1   
Av0 dN  
N v0 A dL
2 dc
dN
3 1   

dL   dL
N
2 dc
N out
ln
  L
N in
Nout  Nin exp   L 
“Filter coefficient”
Summary: Mass Balance Analysis of
Particle Removal in a Granular Filter
• Based on relative sizes of particles and
collectors, sieving is unimportant and removal
can be modeled based on interactions with
isolated “collector” grains
• Assuming pseudo-steady state, concentration of
any given type of particle is expected to decline
exponentially with depth
• Each type of particle has a different coefficient
for the exponential loss rate
• If we could predict  for a given type of particle,
we could predict Nout/Nin for that particle
 Br
 k BT 
 0.905 
  d d v 
 c p 0
2/3
Accelerating Filter Ripening by Adding
Coagulant to Filter Influent (Opflow 11/05)
Accelerating Filter Ripening (Opflow 11/05)
Modeling Filter Ripening
s is specific deposit, mass deposited
per unit volume of filter media
Relationship is assumed, not
theoretical; a is the ripening coefficient
Head Loss in Clean Filters
E
h 
L g
E  Energy per unit volume;
h  "head" (units of length)
hL (“head loss”) refers to the loss of total energy
per volume of water between the top of the filter
bed and some other point (usually the bottom)
In a filter, the main contributions to fluid energy or
head are elevation and pressure; the contribution
of velocity is negligible
Head Loss in Clean Filters
For flow through a clean bed, headloss can be related to
flow rate and geometry based on fluid dynamics principles
and the equality of the gravitational force (causing flow) with
the resistance force. The result is known as the CarmanKozeny Eqn.:
hL
 L 1    2
k
So vo
3
L
L g 
2
Carman-Kozeny Eqn:
k is a geometric constant usually assume to equal 5
 is porosity, typically ~0.4
So is surface area per unit volume of media
vo is superficial velocity, Q/A
Components of Head in a Filter:
No Flow Condition
Water Level
Depth
Top of media
htot
hP
1
1
hel
Head
Components of Head in a Filter:
Flow Through a Clean Filter
Water Level
Depth
Top of media
htot
hP
hel
n>1
1
Head
Note: Blue and red arrows
represent hL,p and hL,tot,
respectively. At a given
depth, they must be equal.
Components of Head in a Filter:
Early in Filter Run
Water Level
Depth
Top of media
hP
htot
hel
n
1
Head
Components of Head in a Filter:
Late in Filter Run
Water Level
Depth
Top of media
htot
hP
hel
n
1
Head
Use of Piezometers to Measure Total
Head and Pressure Head in a Filter
Water Level
Top of media
Depth
Port 4
Port 3
hp,2
htot,2
Port 2
Port 1
Head
hp,2 = Pressure head at Port 2, relative to atmospheric
htot,2 = Total head at Port 2, relative to datum at bottom of filter
Typical Headloss Profiles in a Rapid Sand Filter
0.00
0.00
0.25
0.25
t = 0 hr
Depth in Filter (m)
0.50
t = 1 hr
0.75
0.50
0.75
2 hr
1.00
1.00
4 hr
1.25
1.25
8 hr
1.50
1.50
16 hr
12 hr
1.75
2.00
3.00
1.75
3.25
3.50
3.75
4.00
4.25
Pressure Head (m)
4.50
4.75
2.00
5.00
• Head loss is entirely due to changes in hp
• With no flow, head loss is zero everywhere. As a
result, total head loss from top of bed to a given
location equals pressure head loss at that
location compared to no-flow condition
• For constant-flow operation, head loss gradient
through clean media is constant (throughout bed
initially, only at bottom later)
• Total head (elevation plus pressure) must
decrease monotonically in direction of flow
• Pressure head is universally reported based on
gage pressure; it can be negative (vacuum
relative to atmosphere), but such a situation is
undesirable