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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
     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   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
        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)
       ______________ 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
 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
                                        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
          Transport is additive

           
  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
    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
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
  only receives distilled water
                                  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!
Head Loss Produced by Aluminum

                 1
                0.8
head loss (m)




                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
   No need to add
    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
 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

				
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