Filtration Theory
On removing little particles with big
particles
Monroe L. Weber-Shirk
School of Civil and
Environmental Engineering
Filtration Outline
 Filters galore
 Range of applicability
 Particle Capture
theory
 Transport
 Dimensional Analysis
 Model predictions
 Filters
 Rapid
 Slow
 “BioSand”
 Pots
 Roughing
 Multistage Filtration
Filters Galore
Slow Sand
Rapid Sand
Cartridge
Bag
Pot
“Bio” Sand
Diatomaceous earth filter
Candle
Rough
Categorizing Filters
 Straining
 Particles to be removed are larger than the pore size
 Clog rapidly
 Depth Filtration
 Particles to be removed may be much smaller than the
pore size
 Require attachment
 Can handle more solids before developing excessive
head loss
 Filtration model coming…
All filters remove more particles near the filter inlet
The “if it is dirty, filter it” Myth
The common misconception is that if the
water is dirty then you should filter it to
clean it
But filters can’t handle very dirty water
without clogging quickly
Filter range of applicability
1
1
10
NTU
100
1000
SSF
10
100
1k
people
RSF+ DE
10k
100k
Cartridge Bag
Pot Candle
Developing a Filtration Model
Iwasaki (1937) developed relationships
describing the performance of deep bed
filters.
dC
=  0C
dz
dC
=  0 dz
C
C
z
dC
C C =  0 0 dz
0
C 
 ln   =0 z
 C0 
C is the particle concentration [number/L3]
0 is the initial filter coefficient [1/L]  log  C   pC*  1  z
 
0
C
ln
10
z is the media depth [L]
 
 0
The particle’s chances of being caught are the same at
all depths in the filter; pC* is proportional to depth
C
C* 
C0
Graphing Filter Performance
1
p( x)  log( x)
0.8
1
0.6
p ( Remaining)
0.4
0.8
0.2
Removed0.6
0
1
2
0.4
0.2
3
4
t
1
2
3
4
2
t
This graph gives the
impression that you can
reach 100% removal
p ( Remaining)
1
0
1
2
3
4
t
Where is 99.9% removal?
Particle Removal Mechanisms in
Filters
collector
Transport to a surface
Molecular diffusion
Inertia
Gravity
Interception
Attachment
Straining
London van der Waals
Filtration Performance: Dimensional
Analysis
What is the parameter we are interested in
Effluent concentration
measuring? _________________
How could we make performance
C/C0 or pC*
dimensionless? ____________
What are the important forces?
Inertia
Viscous
London van der Waals
Gravitational
Electrostatic
Thermal
Need to create dimensionless force ratios!
Dimensionless Force Ratios
Reynolds Number
Froude Number
r Vl
Re =
m
V
Fr =
gl
V 2 l
V2
fi = r
l
V
fu = m 2
l
fg = r g
s
fs = 2
W
Weber Number
l

r c2
f Ev =
V
Mach Number
l
M
c (Dp + r g Dz )
2Drag
2
D
p
(
)
Cd 
Pressure/Drag Coefficients C p =
V 2 A
rV2
 (dependent parameters that we measure experimentally)
What is the Reynolds number for
filtration flow?
 What are the possible length scales?
 Void size (collector size) max of 0.7 mm in RSF
 Particle size
 Velocities
 V0 varies between 0.1 m/hr (SSF) and 10 m/hr (RSF)
 Take the largest length scale and highest velocity to
find max Re
 m hr 
Re 
Vl

3
10
  0.7 10 m 
hr 3600s 
Re  
2
 6 m 2 
10 s 


 For particle transport the length scale is the particle
size and that is much smaller than the collector size
Choose viscosity!
In Fluid Mechanics inertia is a significant
“force” for most problems
In porous media filtration viscosity is more
Inertia
important that inertia.
We will use viscosity as the repeating
parameter and get a different set of
dimensionless force ratios
Gravitational
Viscous
Thermal
Viscous
Gravity
velocities
vpore
vg =
(  p   w ) gd p2
18
g =
vg
V0
V
fu   2
l
fg = r g
forces
g =
fg
f
 g
g =
V0
 2
dp
Gravity only helps when
the streamline has a
2
2
(



)
gd
(



)
gd
_________
horizontal component.  g = p w p  g = p w p
18V0
Use this definition
V0
Diffusion (Brownian Motion)
vpore
D
vd 
dc
Diffusion velocity is
high when the particle
diameter is ________.
small
kT
D B
3 d p
 L2 
T 
 
kB=1.38 x 10-23 J/°K
T = absolute temperature
 Br
dc is diameter of the collector
k BT

3 d pV0 d c
London van der Waals
The London Group is a measure of the
attractive force
It is only effective at extremely short range
(less than 1 nm) and thus is NOT
responsible for transport to the collector
H is the Hamaker’s constant
 H = 0.75 1020 J
 Lo
4H
=
9 d 2pV0
Van der Waals force
Viscous force
What about Electrostatic
repulsion/attraction?
Modelers have not succeeded in describing
filter performance when electrostatic
repulsion is significant
Models tend to predict no particle removal
if electrostatic repulsion is significant.
Electrostatic repulsion/attraction is only
effective at very short distances and thus is
involved in attachment, not transport
Geometric Parameters
What are the length scales that are related to
particle capture by a filter?
______________
Filter depth (z)
__________________________
Collector diameter (media size) (dc)
______________
Particle diameter (dp)
Porosity (void volume/filter volume) (e)
Create dimensionless groups
(dc)
Choose the repeating length ________
R 
dp
dc
z 
z
Number of collectors!
dc
3 1  e   z 

2ln(10)  d.c
Definition used in model
.z 
Write the functional relationship
pC*  f   R ,  z , e ,  g ,  Br 
doubles
If we double depth of filter what does pC* do? ___________
pC*   z f   R , e ,  g ,  Br 
How do we get more detail on this functional relationship?
Empirical measurements
Numerical models
Numerical Models
Trajectory analysis
A series of modeling attempts with
refinements over the past decades
Began with a “single collector” model that
modeled London and electrostatic forces as
an attachment efficiency term (a)
pC*   z f   R ,  g ,  Br , e  a
Filtration Model
  e    1  e 
A.s e  
1
3
Porosity
5
2 1    e  
2  3  e   3  e   2  e 
5
6
Geometry
d.p
 .R d.p 
d.c
 
 .z 
3  1  e   z 

2 ln( 10)  d.c 
k.b T
 .Br d.p 
3   d.p V.a d.c
 
 
 .g d.p 
2


d.p   .p   .w g
18  V.a
Force ratios
Transport Equations
1
3
 
 
3
 Br dp  As  e   R dp
4
 

 
As  e   R dp
 R dp 
21.5
1
1
6
1.425
 
 
 
 
 
 dp   Br dp   R dp   g dp
Transport is additive
 
Brownian motion
Interception
Gravity
 g dp  0.31  g dp
 
 
 Br dp
2
3
Total is sum of parts
 
pC d.p   .za  d.p
Filtration Technologies
 Slow (Filters→English→Slow sand→“Biosand”)
 First filters used for municipal water treatment
 Were unable to treat the turbid waters of the Ohio and
Mississippi Rivers
 Can be used after Roughing filters
 Rapid (Mechanical→American→Rapid sand)
 Used in Conventional Water Treatment Facilities
 Used after coagulation/flocculation/sedimentation
 High flow rates→clog daily→hydraulic cleaning
 Ceramic
Rapid Sand Filter
(Conventional US Treatment)
Size
(mm)
Anthracite
Influent
Drain
Effluent
Sand
Gravel
Specific Depth
Gravity (cm)
0.70
1.6
30
0.45 - 0.55
2.65
45
5 - 60
2.65
45
Wash water
Filter Design
 Filter media
 silica sand and anthracite coal
smaller particles
 non-uniform media will stratify with _______
at the top
 Flow rates
 60 - 240 m/day
Compare with sedimentation
 Backwash rates
 set to obtain a bed porosity of 0.65 to 0.70
 typically 1200 m/day
Backwash
Anthracite
Influent
Drain
Effluent
Sand
Wash water is
treated water!
WHY?
Only clean water
should ever be on
bottom of filter!
Gravel
Wash water
Rapid Sand predicted performance
kg
Brownian
Interception
Gravity
Total
3
m
m
Va  5
hr
T  293K
z  45cm
dc  0.45mm
Particle removal as pC*
 p  1040
100
10
1
a  1
e  0.4
0.1
0.1
Not very good at removing particles that
haven’t been flocculated
1
10
Particle Diameter (m)
100
Slow Sand Filtration
 First filters to be used on a widespread basis
 Fine sand with an effective size of 0.2 mm
 Low flow rates (2.5-10 m/day) Compare with sedimentation
 Schmutzdecke (_____
____) forms on top of the
filter cake
filter
 causes high head loss
 must be removed periodically
 Used without coagulation/flocculation!
 Turbidity should always be less than 50 NTU with
a much lower average to prevent rapid clogging
Slow Sand Filtration Mechanisms
Protozoan predators (only
effective for bacteria removal,
not virus or protozoan removal)
Aluminum (natural sticky
coatings)
Attachment to previously
removed particles
No evidence of removal by
biofilms
Fraction of influent E. coli
remaining in the effluent
Typical Performance of SSF Fed
Cayuga Lake Water
1
0.1
0.05
0
1
2
3
Time (days)
4
5
(Daily samples)
Filter performance doesn’t improve if the filter
only receives distilled water
Particle Removal by Size
1
Fraction of influent particles
remaining in the effluent
control
3 mM azide
0.1
Effect of
the Chrysophyte
0.01
What is the physicalchemical mechanism?
0.001
0.8
1
Particle diameter (µm)
10
Techniques to Increase Particle
Attachment Efficiency
Make the particles stickier
The technique used in conventional water
treatment plants
Control coagulant dose and other coagulant aids
(cationic polymers)
Make the filter media stickier
Biofilms in slow sand filters?
Mystery sticky agent present in surface waters
that is imported into slow sand filters?
Cayuga Lake Seston Extract
Concentrate particles from Cayuga Lake
Acidify with 1 N HCl
Centrifuge
Centrate contains polymer
Neutralize to form flocs
Seston Extract Analysis
volatile solids
Al
13%
Na
Fe
11%
P
S
Si
17%
Ca
carbon
other metals
16%
other nonvolatile solids
I discovered
aluminum!
56%
How much Aluminum should be added to a filter?
E. coli Removal as a Function of
Time and Al Application Rate
E. coli remaining (pC*)
20 cm deep filter columns
No E. coli detected
7
control
6
4
5
20
4
3
100
2
end azide
1
0
0
2
4
6
time (days)
8
mmol Al
m 2  day
Horizontal bars
indicate when
polymer feed was
10
operational for each
filter.
pC* is proportional to accumulated mass of Aluminum in filter
Slow Sand Filtration Predictions
T  293K
z  100cm
dc  0.2mm
a  1
e  0.4
Brownian
Interception
Gravity
Total
3
m
cm
Va  10
hr
Particle removal as pC*
 p  1040
1000
kg
100
10
0.1
1
10
Particle Diameter (m)
100
How deep must a filter (SSF) be to
remove 99.9999% of bacteria?
 Assume a is 1 and dc is
0.2 mm, V0 = 10 cm/hr
 pC* is ____
6
pC  1m  25.709 for z of 1 m
23 cm for pC* of 6
 z is ________________
 What does this mean?
Suggests that the 20 cm deep experimental filter
was operating at theoretical limit
Typical SSF performance is 95% bacteria removal
Only about 5 cm of the filters are doing anything!
Head Loss Produced by Aluminum
head loss (m)
1
0.8
0.6
0.4
3.9
20
0.2
0
0
100
50
Total Al applied
mmol Al
m2
150
mmol Al
m 2  day
Aluminum feed methods
Alum must be dissolved until it is blended
with the main filter feed above the filter
column
Alum flocs are ineffective at enhancing
filter performance
The diffusion dilemma (alum microflocs
will diffuse efficiently and be removed at
the top of the filter)
Particle removal as pC*
100
 
 
pCg  dp
pC dp
pCPe dp
pCR dp
10
1
0.1
1
dp
m
particle diameter
10
Performance Deterioration after Al
feed stops?
Decays with time
Sites are used up
Washes out of filter
Research results
Not yet clear which
mechanism is
responsible – further
testing required
E. coli remaining (pC*)
Hypotheses
7
control
6
5
4
4
3
100
20
end azide
2
1
0
0
2
4
6
time (days)
8
Horizontal bars
indicate when
10 polymer feed was
operational for each
filter.
Sticky Media vs. Sticky Particles
 Sticky Media
 Potentially treat filter
media at the beginning
of each filter run
 No need to add
coagulants to water for
low turbidity waters
 Filter will capture
particles much more
efficiently
 Sticky Particles
 Easier to add coagulant
to water than to coat
the filter media
The BioSand Filter Craze
 Patented “new idea” of slow sand filtration
without flow control and called it “BioSand”
 Filters are being installed around the world as
Point of Use treatment devices
 Cost is somewhere between $25 and $150 per
household ($13/person based on project near
Copan Ruins, Honduras)
 The per person cost is comparable to the cost to
build centralized treatment using the AguaClara
model
“BioSand” Performance
“BioSand” Performance
Pore volume is 18 Liters
Volume of a bucket is ____________
Highly variable field performance even
after initial ripening period
Field tests on 8 NTU water
in the DR
http://www.iwaponline.com/wst/05403/0001/054030001.pdf
Field Performance of “BioSand”
Table 2 pH, turbidity and E. coli levels in raw and BSF filter waters
in the field
Parameter
raw
filtered
Mean pH (n =47)
7.4
8.0
Mean turbidity (NTU) (n=47)
8.1
1.3
Mean log10 E. coli MPN/100mL (n=55) 1.7
0.6
http://www.iwaponline.com/wst/05403/0001/054030001.pdf
Potters for Peace Pots
 Colloidal silver-enhanced ceramic water purifier
(CWP)
 After firing the filter is coated with colloidal
silver.
 This combination of fine pore size, and the
bactericidal properties of colloidal silver produce
an effective filter
 Filter units are sold for about $10-15 with the
basic plastic receptacle
 Replacement filter elements cost about $4.00
What is the turbidity range that these filters can handle?
How do you wash the filter? What water do you use?
Horizontal Roughing Filters
1m/hr filtration rate (through 5+ m of
media) Equivalent surface loading = 10 m/day
Usage of HRFs for large schemes has been
limited due to high capital cost and
operational problems in cleaning the filters.
Roughing Filters
 Filtration through roughing gravity filters at low filtration
rates (12-48 m/day) produces water with low particulate
concentrations, which allow for further treatment in slow
sand filters without the danger of solids overload.
 In large-scale horizontal-flow filter plants, the large pores
enable particles to be most efficiently transported
downward, although particle transport causes part of the
agglomerated solids to move down towards the filter
bottom. Thus, the pore space at the bottom starts to act as a
sludge storage basin, and the roughing filters need to be
drained periodically. Further development of drainage
methods is needed to improve efficiency in this area.
Roughing Filters
 Roughing filters remove particulate of colloidal size
without addition of flocculants, large solids storage
capacity at low head loss, and a simple technology.
 But there are only 11 articles on the topic listed in
 (see articles per year)
 They have not devised a cleaning method that works
Size comparison to floc/sed systems?
Multistage Filtration
 The “Other” low tech option for
communities using surface waters
 Uses no coagulants
 Gravel roughing filters
 Polished with slow sand filters
 Large capital costs for construction
 No chemical costs
 Labor intensive operation
What is the tank area of a multistage filtration
plant in comparison with an AguaClara plant?
Conclusions…
Many different filtration technologies are
available, especially for POU
Filters are well suited for taking clean water
and making it cleaner. They are not able to
treat very turbid surface waters
Pretreat using flocculation/sedimentation
(AguaClara) or roughing filters (high capital
cost and maintenance problems)
Conclusions
Filters could remove particles more
efficiently if the attachment
_________ efficiency were
increased
SSF remove particles by two mechanisms
____________
Predation
______________________________________
Sticky aluminum polymer that coats the sand
Completely at the mercy of the raw water!
We need to learn what is required to make
ALL of the filter media “sticky” in SSF and
in RSF
References
 Tufenkji, N. and M. Elimelech (2004). "Correlation equation for predicting
single-collector efficiency in physicochemical filtration in saturated porous
media." Environmental-Science-and-Technology 38(2): 529-536.
 Cushing, R. S. and D. F. Lawler (1998). "Depth Filtration: Fundamental
Investigation through Three-Dimensional Trajectory Analysis." Environmental
Science and Technology 32(23): 3793 -3801.
 Tobiason, J. E. and C. R. O'Melia (1988). "Physicochemical Aspects of
Particle Removal in Depth Filtration." Journal American Water Works
Association 80(12): 54-64.
 Yao, K.-M., M. T. Habibian, et al. (1971). "Water and Waste Water Filtration:
Concepts and Applications." Environmental Science and Technology 5(11):
1105.
 M.A. Elliott*, C.E. Stauber, F. Koksal, K.R. Liang, D.K. Huslage, F.A.
DiGiano, M.D. Sobsey. (2006) The operation, flow conditions and microbial
reductions of an intermittently operated, household-scale slow sand filter
Contact Points
Polymer Accumulation in a Pore