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```									                 Filtration Theory

On removing little particles with big
particles

School of Civil and
Monroe L. Weber-Shirk   Environmental Engineering
Filtration Outline

 Filters galore               Filters
 Range of applicability       Rapid
 Particle Capture                Slow
theory                          “BioSand”
 Transport                    Pots
 Dimensional Analysis         Roughing
 Model predictions            Multistage Filtration
Filters Galore

Slow Sand

Rapid Sand               Bag

Cartridge                 Pot
“Bio” Sand
Diatomaceous earth filter
Rough
Candle
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
 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   10   100      1k   10k   100k
people

SSF   RSF+ DE           Cartridge Bag      Pot Candle
1

10

NTU

100

1000
Developing a Filtration Model

Iwasaki (1937) developed relationships
describing the performance of deep bed
filters.
C 
C           z
dC                                  dC
 C =  0  dz
=  0C      dC
=  0 dz                           ln   =0 z
dz              C                C0         0               C0 
C is the particle concentration [number/L3]
0 is the initial filter coefficient [1/L]  log  C   pC*  1  z
 
ln 10 
0
z is the media depth [L]                          C0 

The particle’s chances of being caught are the same at             C
C* 
all depths in the filter; pC* is proportional to depth             C0
Graphing Filter Performance
1

1
0.8       p ( x)  log ( x)
0.6
p ( Remaining)
0.8
0.4

Removed                                        0.2
0.6
0
1        2        3       4
0.4
t

0.2
1   2       3     4
2
t
p ( Remaining)
This graph gives the                               1
impression that you can
reach 100% removal                                 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
measuring? _________________
Effluent concentration

How could we make performance
dimensionless? ____________
C/C0 or pC*

What are the important forces?
Inertia   London van der Waals    Electrostatic
Viscous     Gravitational        Thermal

Need to create dimensionless force ratios!
V2
Dimensionless Force Ratios                            fi = r
l

r Vl             V
Re =            fu = m 2
Reynolds Number                         m               l
V
Fr =             fg = r g
Froude Number                            gl
V 2 l          s
fs = 2
Weber Number                    W
                 l
r c2
f Ev =
Mach Number                     M
V
l
c (Dp + r g Dz )
Pressure/Drag CoefficientsC p =         - 2 (Dp ) C d  2Drag
rV2              V 2 A
 (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 
  0.7 10 m 
3
10
Re  
hr 3600s 
Vl                                         2
Re                           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
important that inertia.                  Inertia

We will use viscosity as the repeating
parameter and get a different set of
dimensionless force ratios
Gravitational   Thermal
Viscous       Viscous
V
fu   2
l
Gravity                         fg = r g

velocities           forces
vpore                                             fg
(  p   w ) gd p
2
g =
vg =                               f
18

 g
vg            g =
g =                       V0
V0                  2
dp
Gravity only helps when
the streamline has a
(  p   w ) gd p
2
(  p   w ) gd p
2
_________ component.  g =
horizontal                                    g =
18V0                  V0

Use this definition
Diffusion (Brownian Motion)

kT             L2 
vpore                        D B             T 
vd 
D             3 d p         
dc

Diffusion velocity is              kB=1.38 x 10-23 J/°K
high when the particle             T = absolute temperature
diameter is ________.
small                dc is diameter of the collector
k BT
 Br   
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
4H        Van der Waals force
 Lo   =
9 d 2V0
p         Viscous force
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)
______________ p)
Particle diameter (d
Porosity (void volume/filter volume) (e)
Create dimensionless groups
Choose the repeating length ________
(dc)
dp              z                                 3 1  e   z 
R             z       Number of collectors!   .z             
2ln(10)  d.c
dc              dc                                             
Definition used in model
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
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
1

  e    1  e 
3
Porosity
2 1    e  
5
A.s e  
2  3  e   3  e   2  e 
5          6
Geometry
d.p
 
 .R d.p 
d.c

3  1  e   z 
 .z                   
2 ln( 10)  d.c 

k.b T
 
 .Br d.p 
3   d.p V.a d.c

Force ratios
2

d.p   .p   .w g  
 
 .g d.p 
18  V.a
Transport Equations
1               1              2

 Br dp  As  e   R dp
                                        
3          3               6              3
 Br dp
4                                                Brownian motion

                          
As  e   R dp
1                      1.425
 R dp                                                   Interception
21.5

 
 g dp  0.31  g dp                                   Gravity

                        
 dp   Br dp   R dp   g dp                        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       Specific Depth
(mm)        Gravity (cm)
0.70         1.6     30
Anthracite
Influent        Sand       0.45 - 0.55    2.65     45

Gravel        5 - 60       2.65     45
Drain
Effluent                   Wash water
Filter Design

 Filter media
 silica sand and anthracite coal
 non-uniform media will stratify with _______ particles
smaller
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

Wash water is
treated water!
Anthracite    WHY?
Only clean water
should ever be on
Influent     Sand
bottom of filter!

Gravel
Drain
Effluent                Wash water
Rapid Sand predicted performance
100
kg                                                 Brownian
 p  1040                                                      Interception
3
m                                                  Gravity

Particle removal as pC*
m                                                        Total
Va  5                                                  10
hr
T  293K

z  45cm
1
dc  0.45mm

a  1
e  0.4                                                0.1
0.1            1              10    100

Particle Diameter m)
(
Not very good at removing particles that
haven’t been flocculated
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 (_____ cake forms on top of the
filter ____)
filter
 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
Typical Performance of SSF Fed
Cayuga Lake Water
1
Fraction of influent E. coli
remaining in the effluent

0.1

0.05
0   1     2     3     4       5
Time (days)       (Daily samples)

Filter performance doesn’t improve if the filter
Particle Removal by Size
1
control
3 mM azide
Fraction of influent particles
remaining in the effluent

0.1

Effect of
the Chrysophyte
0.01

What is the physical-
chemical 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
I discovered
Al                            13%                aluminum!
Na
Fe
P                        11%
S                                          56%
Si
Ca                         17%
carbon
other metals
16%
other nonvolatile solids

How much Aluminum should be added to a filter?
E. coli Removal as a Function of
Time and Al Application Rate
20 cm deep filter columns                                   No E. coli detected
7                                        control
E. coli remaining (pC*)

6
4           mmol Al
5
20          m 2  day
4
3                                        100
2                                        end azide
1                                 Horizontal bars
indicate when
0
polymer feed was
0   2   4        6    8    10
operational for each
time (days)           filter.

pC* is proportional to accumulated mass of Aluminum in filter
Slow Sand Filtration Predictions
1000
kg                                      Brownian
 p  1040                                           Interception
3
m                                        Gravity

Particle removal as pC*
Total
cm
Va  10
hr
100
T  293K

z  100cm
dc  0.2mm
a  1                                        10
0.1            1              10    100

e  0.4                                                    Particle Diameter m)
(
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
 z is ________________
23 cm for pC* of 6
 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!

1
0.8

0.6
0.4
0.2
3.9   mmol Al
20    m 2  day
0
0   50             100   150
Total Al applied
mmol Al
m2
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)                                                  
100

Particle removal as pC*
pCPe dp

pCR dp 
pCg dp     10

pC  dp

1
0.1           1           10
dp
m
particle diameter
Performance Deterioration after Al
feed stops?
Hypotheses
Decays with time
7                                        control

E. coli remaining (pC*)
6                                        4

Sites are used up
5
20
4
3                                        100

Washes out of filter                              2                                        end azide
Horizontal bars
1

Research results                                    0
0   2   4        6    8
indicate when
10 polymer feed was

Not yet clear which                                           time (days)          operational for each
filter.

mechanism is
responsible – further
testing required
Sticky Media vs. Sticky Particles

 Sticky Media                  Sticky Particles
 Potentially treat filter       Easier to add coagulant
media at the beginning          to water than to coat
of each filter run              the filter media
coagulants to water for
low turbidity waters
 Filter will capture
particles much more
efficiently
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
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

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