Monroe L. Weber-Shirk
School of Civil and
Environmental Engineering
Filtration Theory
On removing little particles with big particles
Filtration Outline
Filters galoreRange of applicability
Particle Capture theoryTransportDimensional Analysis Model predictions
FiltersRapidSlow “BioSand”PotsRoughingMultistage Filtration
Filters Galore
“Bio” Sand
Rapid Sand
Cartridge
Bag
Pot
Candle
Diatomaceous earth filter
Slow Sand
Rough
Categorizing Filters
StrainingParticles to be removed are larger than the pore sizeClog rapidly
Depth FiltrationParticles to be removed may be much smaller than the
pore sizeRequire attachmentCan handle more solids before developing excessive
head lossFiltration 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
1000
NTU
1
10
100
SSF
1 10 100 1k 10kpeople
100k1 10 100 1k 10kpeople
100k
Cartridge BagRSF+ Pot CandleDE
Developing a Filtration Model
Iwasaki (1937) developed relationships describing the performance of deep bed filters.
0=dC Cdz
C is the particle concentration [number/L3]0 is the initial filter coefficient [1/L]z is the media depth [L]
The particle’s chances of being caught are the same at all depths in the filter; pC* is proportional to depth
0=dC dzC
0
00
=C z
C
dC dzC
00
ln =C zC
00
1log *ln 10
C pC zC
0
* CCC
Graphing Filter Performance
1 2 3 40.2
0.4
0.6
0.8
1
Removed
t
1 2 3 40
0.2
0.4
0.6
0.8
1
p Remaining( )
t
p x( ) log x( )
This graph gives the impression that you can reach 100% removal 1 2 3 4
0
1
2
p Remaining( )
t
Where is 99.9% removal?
Particle Removal Mechanisms in Filters
Transport to a surface
Attachment
Molecular diffusionInertiaGravityInterception
StrainingLondon van der Waals
collector
Filtration Performance: Dimensional Analysis
What is the parameter we are interested in measuring? _________________
How could we make performance dimensionless? ____________
What are the important forces?
Effluent concentration
C/C0 or pC*
Inertia London van der Waals Electrostatic
Viscous
Need to create dimensionless force ratios!
Gravitational Thermal
Dimensionless Force Ratios
Reynolds Number
Froude Number
Weber Number
Mach Number
Pressure/Drag Coefficients (dependent parameters that we measure experimentally)
Re Vlrm
=
Fr Vgl
=
( )2
2C p
pVr
- D=
lVW
2
cVM
AVd
2
Drag2C
2fuVl
m=
fg gr=
2flss=
2
fvE
clr=
2
fiVl
r=
( )p g zrD + D
What is the Reynolds number for filtration flow?
What are the possible length scales?Void size (collector size) max of 0.7 mm in RSFParticle size
VelocitiesV0 varies between 0.1 m/hr (SSF) and 10 m/hr (RSF)
Take the largest length scale and highest velocity to find max Re
For particle transport the length scale is the particle size and that is much smaller than the collector size
3
26
10 0.7 103600Re 2
10
m hr mhr s
ms
Re Vl
Choose viscosity!
In Fluid Mechanics inertia is a significant “force” for most problems
In porous media filtration viscosity is more important that inertia.
We will use viscosity as the repeating parameter and get a different set of dimensionless force ratios
Inertia
GravitationalViscous
ThermalViscous
Gravity
2
g0
( )=
18p w pgd
V
2
g
( )=
18p w pgd
v
vpore
g0
= gvV
Gravity only helps when the streamline has a _________ component.horizontal
2fuVl
fg gr=
g = gff
g02
=
p
gVd
2
g0
( )= p w pgd
V
velocities forces
Use this definition
Diffusion (Brownian Motion)
kB=1.38 x 10-23 J/°KT = absolute temperature
vpore
Br0
3
B
p c
k Td V d
3B
p
k TDd
2L
T
dc
Dvd
dc is diameter of the collector
Diffusion velocity is high when the particle diameter is ________.small
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 collectorH is the Hamaker’s constant
Lo 2p 0
4H = 9 d V
20 = 0.75 10H J
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?______________________________________________________Porosity (void volume/filter volume) ()
Create dimensionless groupsChoose the repeating length ________
Filter depth (z)Collector diameter (media size) (dc)Particle diameter (dp)
pR
c
dd
zc
zd
(dc)
Number of collectors! .z3 1 2 ln 10( )
zd.c
Definition used in model
Write the functional relationship
,g Br* , , ,R zpC f
Length ratios
Force ratios
,g Br* , ,z RpC f
If we double depth of filter what does pC* do? ___________doubles
How do we get more detail on this functional relationship?Empirical measurements
Numerical models
Numerical Models
Trajectory analysisA series of modeling attempts with
refinements over the past decadesBegan with a “single collector” model that
modeled London and electrostatic forces as an attachment efficiency term ()
, ,g Br* ,z RpC f Interception
Sedimentation
Diffusion
Filtration Model
1 13
A.s 2 1 5
2 3 3 5 2 6
.g d.p d.p
2 .p .w g
18 V.a
.R d.p d.pd.c
.z3 1 2 ln 10( )
zd.c
.Br d.p k.b T
3 d.p V.a d.c
Porosity
Geometry
Force ratios
Transport Equations
Br dp 34
As 13
R dp 16
Br dp
23
R dp 121.5
As R dp 1.425
g dp 0.31 g dp
dp Br dp R dp g dp
pC d.p .z d.p
Brownian motion
Interception
Gravity
Total is sum of partsTransport is additive
Filtration Technologies
Slow (Filters→English→Slow sand→“Biosand”)First filters used for municipal water treatmentWere unable to treat the turbid waters of the Ohio and
Mississippi RiversCan be used after Roughing filters
Rapid (Mechanical→American→Rapid sand)Used in Conventional Water Treatment FacilitiesUsed after coagulation/flocculation/sedimentationHigh flow rates→clog daily→hydraulic cleaning
Ceramic
Rapid Sand Filter (Conventional US Treatment)
Sand
Gravel
Influent
DrainEffluent Wash water
Anthracite
Size(mm)0.70
0.45 - 0.55
5 - 60
SpecificGravity
1.6
2.65
2.65
Depth(cm)30
45
45
Filter Design
Filter media silica sand and anthracite coalnon-uniform media will stratify with _______ particles
at the top Flow rates
60 - 240 m/dayBackwash rates
set to obtain a bed porosity of 0.65 to 0.70 typically 1200 m/day
smaller
Compare with sedimentation
Sand
Gravel
Influent
DrainEffluent Wash water
Anthracite
Backwash
Wash water is treated water!
WHY?Only clean water should ever be on bottom of filter!
0.1 1 10 1000.1
1
10
100BrownianInterceptionGravityTotal
Particle Diameter (m)
Parti
cle
rem
oval
as p
C*
Rapid Sand predicted performance
p 1040kg
m3
Va 5mhr
T 293K
z 45cmdc 0.45mm
1
0.4
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 mmLow flow rates (2.5-10 m/day) Schmutzdecke (_____ ____) forms on top of the
filter causes high head lossmust be removed periodically
Used without coagulation/flocculation!Turbidity should always be less than 50 NTU with
a much lower average to prevent rapid clogging
filter cakeCompare with sedimentation
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
0.05
0.1
1
0 1 2 3 4 5Time (days)
Frac
tion
of in
fluen
t E. c
oli
rem
aini
ng in
the
efflu
ent
Filter performance doesn’t improve if the filter only receives distilled water
(Daily samples)
Particle Removal by Size
0.001
0.01
0.1
1
0.8 1 10Particle diameter (µm)
control
3 mM azide
Frac
tion
of in
fluen
t par
ticle
s re
mai
ning
in th
e ef
fluen
t
Effect of the Chrysophyte
What is the physical-chemical mechanism?
Techniques to Increase Particle Attachment Efficiency
Make the particles stickierThe technique used in conventional water
treatment plantsControl 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 LakeAcidify with 1 N HClCentrifugeCentrate contains polymerNeutralize to form flocs
Seston Extract Analysis
11%
13%
17%
56%
volatile solidsAlNaFePSSiCaother metalsother nonvolatile solids
How much Aluminum should be added to a filter?
carbon16%
I discovered aluminum!
01234567
0 2 4 6 8 10
time (days)
E. c
oli
rem
aini
ng (p
C*)
control
4
20
100
end azideHorizontal bars indicate when polymer feed was operational for each filter.
E. coli Removal as a Function of Time and Al Application Rate
pC* is proportional to accumulated mass of Aluminum in filter
2
mmol Alm day
No E. coli detected20 cm deep filter columns
Slow Sand Filtration Predictions
p 1040kg
m3
Va 10cmhr
T 293K
z 100cmdc 0.2mm
1
0.40.1 1 10 100
10
100
1000BrownianInterceptionGravityTotal
Particle Diameter (m)
Parti
cle
rem
oval
as p
C*
How deep must a filter (SSF) be to remove 99.9999% of bacteria?
Assume is 1 and dc is 0.2 mm, V0 = 10 cm/hr
pC* is ____ z is ________________What does this mean?
23 cm for pC* of 66
Suggests that the 20 cm deep experimental filter was operating at theoretical limit
pC 1m 25.709 for z of 1 m
Typical SSF performance is 95% bacteria removal Only about 5 cm of the filters are doing anything!
Head Loss Produced by Aluminum
0
0.2
0.4
0.6
0.8
1
0 50 100 150
Total Al applied
head
loss
(m)
3.920 2
mmol Alm day
2
mmol Alm
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)
0.1 1 101
10
100
particle diameter
Parti
cle
rem
oval
as
pC*
pCPe dp pCR dp pCg dp pC dp
dpm
Performance Deterioration after Al feed stops?
HypothesesDecays with timeSites are used upWashes out of filter
Research resultsNot yet clear which
mechanism is responsible – further testing required
01234567
0 2 4 6 8 10
time (days)E
. col
i re
mai
ning
(pC
*)
control
4
20
100
end azideHorizontal bars indicate when polymer feed was operational for each filter.
Sticky Media vs. Sticky Particles
Sticky MediaPotentially 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 ParticlesEasier 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
Pore volume is 18 LitersVolume of a bucket is ____________Highly variable field performance even
after initial ripening period
http://www.iwaponline.com/wst/05403/0001/054030001.pdf
Field tests on 8 NTU water in the DR
Field Performance of “BioSand”
Table 2 pH, turbidity and E. coli levels in raw and BSF filter waters in the fieldParameter raw filteredMean pH (n =47) 7.4 8.0Mean turbidity (NTU) (n=47) 8.1 1.3Mean 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)
Usage of HRFs for large schemes has been limited due to high capital cost and operational problems in cleaning the filters.
Equivalent surface loading = 10 m/day
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 coagulantsGravel roughing filters Polished with slow sand filtersLarge capital costs for constructionNo chemical costsLabor 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 _________ efficiency were increased
SSF remove particles by two mechanisms__________________________________________________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
PredationSticky aluminum polymer that coats the sand
attachment
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