Monroe L. Weber-Shirk S chool of Civil and Environmental Engineering Filtration Theory On removing little particles with big particles.

Monroe L. Weber-Shirk

School of Civil and

Environmental Engineering

Filtration TheoryFiltration Theory

On removing little particles with big particles

Filtration OutlineFiltration Outline

Filters galoreRange of applicability

Particle Capture theoryTransportDimensional Analysis Model predictions

FiltersRapidSlow “BioSand”PotsRoughingMultistage Filtration

Filters GaloreFilters Galore

“Bio” Sand

Rapid Sand

Cartridge

Bag

Pot

Candle

Diatomaceous earth filter

Slow Sand

Rough

Categorizing FiltersCategorizing 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” MythThe “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 applicabilityFilter 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 ModelDeveloping 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

0

0

=C z

C

dCdz

C 0

0

ln =C

zC

00

1log *

ln 10

CpC z

C

0

*C

CC

Graphing Filter PerformanceGraphing 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

Particle Removal Mechanisms in Filters

Transport to a surface

Attachment

Molecular diffusionInertiaGravityInterception

StrainingLondon van der Waals

collector

Filtration Performance: Dimensional Analysis

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)

ReVlrm

=

FrV

gl=

( )2

2C p

p

Vr- D

=

lV

W2

cV

M

AVd

2

Drag2C

2fu

Vl

m=

fg gr=

2fls

s=

2

fvE

clr

=

2

fi

Vl

r=

( )p g zrD + D

What is the Reynolds number for filtration flow?

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 103600

Re 2

10

m hrm

hr s

ms

ReVl

Choose viscosity!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

GravityGravity

2

g0

( )=

18p w pgd

V

2

g

( )=

18p w pgd

v

vpore

g0

= gv

V

Gravity only helps when the streamline has a _________ component.horizontal

2fu

V

l

fg gr=

g = gf

f

g02

=

p

gV

d

2

g0

( )= p w pgd

V

velocities forces

Use this definition

Diffusion (Brownian Motion)Diffusion (Brownian Motion)

kB=1.38 x 10-23 J/°KT = absolute temperature

vpore

Br0

3

B

p c

k T

d V d

3B

p

k TD

d

2L

T

dc

Dv

d

dc is diameter of the collector

Diffusion velocity is high when the particle diameter is ________.small

London van der WaalsLondon 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?

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 ParametersGeometric 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

d

d z

c

z

d

(dc)

Number of collectors! .z3 1 2 ln 10( )

z

d.c

Definition used in model

Write the functional relationshipWrite 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 ModelsNumerical 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

Diffusio

n

Filtration ModelFiltration Model

1 1

3

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.p

d.c

.z3 1 2 ln 10( )

z

d.c

.Br d.p k.b T

3 d.p V.a d.c

Porosity

Geometry

Force ratios

Transport EquationsTransport Equations

Br dp 3

4As

1

3 R dp

1

6

Br dp 2

3

R dp 1

21.5As 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 parts

Transport is additive

Filtration TechnologiesFiltration 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 DesignFilter Design

Filter media silica sand and anthracite coalnon-uniform media will stratify with _______ particles

at the top

Flow rates60 - 240 m/day

Backwash 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)

Par

ticle

rem

oval

as

pC*

Rapid Sand predicted performanceRapid Sand predicted performance

p 1040kg

m3

Va 5m

hr

T 293K

z 45cmdc 0.45mm

1

0.4

Not very good at removing particles that haven’t been flocculated

Slow Sand FiltrationSlow 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 MechanismsSlow 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

Typical Performance of SSF Fed Cayuga Lake Water

0.05

0.1

1

0 1 2 3 4 5Time (days)

Frac

tion

of

infl

uent

E. c

oli

rem

aini

ng in

the

effl

uent

Filter performance doesn’t improve if the filter only receives distilled water

(Daily samples)

Particle Removal by SizeParticle Removal by Size

0.001

0.01

0.1

1

0.8 1 10Particle diameter (µm)

control

3 mM azide

Fra

ctio

n of

infl

uent

par

ticl

es

rem

aini

ng in

the

effl

uent

Effect of the Chrysophyte

What is the physical-chemical mechanism?

Techniques to Increase Particle Attachment Efficiency

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 stickierBiofilms in slow sand filters?Mystery sticky agent present in surface waters

that is imported into slow sand filters?

Cayuga Lake Seston ExtractCayuga Lake Seston Extract

Concentrate particles from Cayuga LakeAcidify with 1 N HClCentrifugeCentrate contains polymerNeutralize to form flocs

Seston Extract AnalysisSeston Extract Analysis

11%

13%

17%

56%

volatile solidsAlNaFePSSiCaother metalsother nonvolatile solids

How much Aluminum should be added to a filter?

carbon16%

I discovered aluminum!

0

1

2

3

4

5

6

7

0 2 4 6 8 10

time (days)

E. c

oli

rem

aini

ng (

pC*)

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

E. coli Removal as a Function of Time and Al Application Rate

pC* is proportional to accumulated mass of Aluminum in filter

2

mmol Al

m day

No E. coli detected20 cm deep filter columns

Slow Sand Filtration PredictionsSlow Sand Filtration Predictions

p 1040kg

m3

Va 10cm

hr

T 293K

z 100cmdc 0.2mm

1

0.40.1 1 10 100

10

100

1000BrownianInterceptionGravityTotal

Particle Diameter (m)

Par

ticle

rem

oval

as

pC*

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 AluminumHead Loss Produced by Aluminum

0

0.2

0.4

0.6

0.8

1

0 50 100 150

Total Al applied

head

loss

(m

)

3.9

20 2

mmol Al

m day

2

mmol Al

m

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

Par

ticle

rem

oval

as

pC*

pCPe dp pCR dp pCg dp pC dp

dp

m

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

0

1

2

3

4

5

6

7

0 2 4 6 8 10

time (days)E

. col

i r

emai

ning

(pC

*)

control

4

20

100

end azideHorizontal bars indicate when polymer feed was operational for each filter.

Sticky Media vs. Sticky ParticlesSticky 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 CrazeThe 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

“BioSand” Performance“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” 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 PotsPotters 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 FiltersHorizontal 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 FiltersRoughing 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 FiltersRoughing 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 FiltrationMultistage 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…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)

ConclusionsConclusions

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

ReferencesReferences

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 PointsContact Points

Polymer Accumulation in a PorePolymer Accumulation in a Pore