Monroe L. Weber-Shirk

School of Civil and

Environmental Engineering

Filtration TheoryFiltration Theory

Field Trip To CUWTPField Trip To CUWTP

Monday at 2:20 pm at loading dock

Public Health reportsPublic Health reports

The decline happened over time and not rapidly as if it were associated with a centralized intervention Chlorine was not responsible for the decline Filtration was not responsible for the decline The relatively high dose required for an infection would require gross

contamination of the water supply Therefore typhoid was generally not waterborne

There is some evidence that typhoid was greater in the summer. This suggests multiplication in the environment, most likely in food.

Improved personal hygiene was likely the dominant factor Jakarta and Army evidence that the sources are local: (not centrally distributed like

milk, water, or meat, but food preparation with contaminated hands) Improved hygiene reduced contamination of food Refrigeration would have reduced the summertime typhoid by reducing

multiplication in food. Home refrigeration happened after the decline began, but commercial refrigeration

Filtration OutlineFiltration Outline

Particle Capture theoryTransportShort range forcesGrain contact pointsDimensional Analysis Trajectory Models

FiltersRapidSlow (lots of detail here…)

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.

Overall Filter PerformanceOverall Filter Performance

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

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 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

Thus viscosity is generally much more significant than inertia

331000 10 0.7 10

3600Re 2

0.001

kg m hrm

m hr skg

m s

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

LondonViscous

GravitationalViscous

ThermalViscous

ElectrostaticViscous

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 equation

Diffusion (Brownian Motion)Diffusion (Brownian Motion)

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

vpore

2/32/3-2/3 0

Br0

= 3

c B

p c

V d k TPe

D d V d

3B

p

k TD

d

2L

T

0 cV dPe

D

dc

Dv

d

dc is diameter of the collector

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

The exponent was obtained from an analytical model

London van der WaalsLondon van der Waals

The London Group is a measure of the attractive forceH 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?What about Electrostatic?

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.

So until we get a better model we will neglect this force with the understanding that filter performance is poor if electrostatic repulsion is significant

Geometric ParametersGeometric Parameters

What are the length scales that are related to particle capture by a filter?______________________________________________________

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!

Write the functional relationshipWrite the functional relationship

, ,g Br Lo* , ,R zpC f

Length ratios

Force ratios

, ,g Br Lo* ,z RpC f

If we double depth of filter what does pfz do? ___________doubles

How do we get more detail on this functional relationship?

Empirical measurements

Numerical models

Numerical ModelsNumerical Models

Trajectory analysis (similar to the analysis of flocculation)

A series of modeling attempts with refinements

Began with a “single collector” model that modeled London and electrostatic forces with an attachment efficiency term ()

, ,g Br Lo* ,z RpC f Interception

Sedimentation

Diffusio

n

g Br*ln 10

zRpC

Addition assumption

Array of Spheres Model (AOS)Array of Spheres Model (AOS)

Includes simplified geometry describing the contact between collectors

Used trajectory analysis to determine which particles would be captured

Used the numerical model results to determine the form of the equation based on dimensional analysis

AOS: The Media TrapAOS: The Media Trap

Isolated collectors Array of spheres model

Collector Contacts

Contacts Matter! Two Particle TrapsContacts Matter!

Two Particle Traps

Particles that enter centered above a collector are trapped in the stagnation point.

Particles that enter on a streamline that passes

through a contact point between collectors get

trapped between two collectors

This trajectory analysis ignores Brownian Motion

Collectorcontact straining

0.012 0.023 1.8 0.38* 0.029 0.48ln 10

zLo R g RpC

Array of Spheres Model Results and Critique

Array of Spheres Model Results and Critique

0.012 0.023 1.8 0.38Br* 0.029 0.48 13.6

ln 10z

Lo R g RpC

Brownian wasn’t modeled

The transport to the media surface by either the fluid (interception, R), gravity (g), or diffusion (Br) is followed by an attachment step controlled by van der Waals (Lo)

The transport and attachment steps occur in series and thus removal should be described by the product of these groups

More work to be done!13.6=4.04*As

1/3

AOS model deficienciesAOS model deficiencies

0.012 0.023 1.8 0.38Br* 0.029 0.48 13.6

ln 10z

Lo R g RpC

1.8 0.38Br* 0.029 0.48 13.6

ln 10z

g RpC

=1!

This suggests a third transport mechanisms that is constant and doesn’t require Brownian motion or sedimentation! Could be interception, but interception increases with particle size.

Given this error (and the likelihood that the numerical model contained errors) the model results from the AOS model should probably not be used!

Tufenkji and Elimelech with Analysis by Weber-Shirk

Tufenkji and Elimelech with Analysis by Weber-Shirk

vdW

H = N

kT

Pe0 03

B

c p c

k TDN

V d d V d

2

G0

( )=

18p p wd g

NV

pR

c

dN

d0 D I G

1/3 0.081 0.715 0.0522.4D s R Pe vdWA N N N

5

5 6

2 1

2 3 3 2sA

1/31

vdW

Pe 0

H =

3Lop c

NN

N d V d

1/3 0.081 0.715 0.052 0.0522.4D s R Pe Pe LoA N N N N

1/3 2 /3 0.081 0.0522.4D s Pe R LoA N N N

Lo 2p 0

4H =

9 dN

V

Note that my NPe is the inverse of T&E

InterceptionInterception

1.55 0.125 0.1250.55I S R Pe vdWA N N N

1.55 0.1250.55I S R LoA N N

Pe vdW0

A =

3Lop c

N N Nd V d

GravityGravity

0.24 1.11 0.0530.22G R G vdWN N N Pe vdW

0

H =

3Lop c

N N Nd V d

0.24 1.11 0.053 0.0530.22G R G Lo PeN N N N vdWPe

LoNN

N

Total removalTotal removal

0 D I G

1/3 2 /3 0.081 0.0522.4D s Pe R LoA N N N

1.55 0.1250.55I S R LoA N N

0.24 1.11 0.053 0.0530.22G R G Lo PeN N N N

1/3 2/3 0.081 0.052 1.55 0.125 0.24 1.11 0.053 0.0530 2.4 0.55 0.22s Pe R Lo S R Lo R G Lo PeA N N N A N N N N N N

1/3 2 /3 0.081 1.55 0.072 0.24 1.11 0.053 0.0530 2.4 0.55 0.22s Pe R S R Lo R G Pe LoA N N A N N N N N N

0

ln =C

zC

0

3 1

2 cd

1/3 2 /3 0.081 1.55 0.072 0.24 1.11 0.053 0.0530 2.4 0.55 0.22s Pe R S R Lo R G Pe LoA N N A N N N N N N

*

0

1log

ln 10

CpC z

C

*0

3 1

2ln 10 c

zpC

d

3 1

2ln 10zc

zN

d

*

0zpC N

For particles less than 1 mFor particles less than 1 m

1/3 2/3 0.081 0.0532.4D s Pe R LoA N N N

0.01

0.1

1

0.01 0.1 1 10 100

particle diameter (m)

0nD

nI

ng

ntotal

* 1/3 2 /3 0.081 0.0532.4 s Pe R Lo zpC A N N N N

Brownian MotionBrownian Motion

Brownian motion dominates the transport and collection of particles on the order of 1 m and smaller

Brownian transport (diffusion) leads to nondeterministic behavior and results in trajectories defined by stochastic differential equations

The problem is traditionally decoupled using the assumption that the Brownian and deterministic transport mechanisms are additive

Sedimentation is less important for small particles because the R group is small and the Br group is large

0.012 0.023 1.8 0.38Br* 0.029 0.48 13.6

ln 10z

Lo R g RpC

Filter Performance as function of particle size

Filter Performance as function of particle size

The exact location of the minimum varies, but is generally around 1 m.

For small particles diffusion dominates and we have

Br* 13.6ln 10

zpC

0.012 0.023 1.8 0.38Br* 0.029 0.48 13.6

ln 10z

Lo R g RpC

attachment

Estimate Dimensionless Brownian Transport for a Bacteria Cell

Estimate Dimensionless Brownian Transport for a Bacteria Cell

viscosity 1.00E-03 Ns/m2

dp Particle diameter 1.00E-06 m

kB Boltzman constant 1.38E-23 J/°K

dc Collector diameter 0.2E-03 m

T Absolute temperature 293 °K

V0 Filter approach velocity

0.1 m/hr

Advection is 40x greater than diffusion

2/3

Br0

13.6 = 13.63

B

p c

k T

d V d

2/3

23

Br3 6 3

2

1.38 10 29313.6 = 13.6

N s3 1 10 1 10 0.10 0.2 10

m 3600

JK

Km hr

m mhr s

Br13.6 = 0.025

The Diffusion SurpriseThe Diffusion Surprise

As particle size decreases Brownian motion becomes more effective

Viruses should be removed efficiently by filters (if attachment is effective)

2/3

Br0

13.6 = 13.63

B

p c

k T

d V d

0.001

0.01

0.1

1

10

1.E-09 1.E-08 1.E-07 1.E-06 1.E-05

Particle diameter (m)

Br13.6

viruses

bacter

ia

How deep must a filter (SSF) be for diffusion to remove 99% of bacteria?

Assume is 1 and dc is 0.2 mm

is ____ pfz is ____

z is _____What does this mean?

3.7 cm

1

2

Br* 13.6ln 10

zpC

Br

ln 10 *

13.6zc

pCz

d

Br

ln 10 *

13.6cpC d

z

3ln 10 2 0.2 10

0.025 1

mz

If the attachment efficiency were 1, then we could get great particle capture in a 1 m deep filter!

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 Rivers

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 rates2.5 - 10 m/hr

Backwash rates set to obtain a bed porosity of 0.65 to 0.70 typically 50 m/hr

smaller

Sand

Gravel

Influent

DrainEffluent Wash water

Anthracite

Backwash

Wash water is treated water!

WHY?Only clean water should ever be on bottom of filter!

Slow Sand FiltrationSlow Sand Filtration

First filters to be used on a widespread basisFine sand with an effective size of 0.2 mmLow flow rates (10 - 40 cm/hr)Schmutzdecke (_____ ____) forms on top

of the filtercauses high head lossmust be removed periodically

Used without coagulation/flocculation!

filter cake

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)

How do Slow Sand Filters Remove Particles?

How do slow sand filters remove particles including bacteria, Giardia cysts, and Cryptosporidium oocysts from water?

Why does filter performance improve with time?Why don’t SSF always remove Cryptosporidium

oocysts? Is it a biological or a physical/chemical mechanism?Would it be possible to improve the performance of

slow sand filters if we understood the mechanism?

Slow Sand Filtration Research Apparatus

Sampling tubeLower to collect sample

Manifold/valve blockPeristaltic pumps

Manometer/surge tubeCayuga Lake water(99% or 99.5% of the flow)

Auxiliary feeds(each 0.5% of the flow)

1 liter E. coli feed

1 liter sodium azide

To waste

Filter cell with18 cm of glass beads

Sampling Chamber

Biological and Physical/Chemical Filter Ripening

0.05

Quiescent Cayuga Lake water

0.1

1

0 2 4 6 8 10Time (days)

Control

Sodium azide (3 mM)

Continuously mixed 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

What would happen with a short pulse of poison?

Gradual growth of _______ or ________biofilm predator

Physical/chemical

Biological Poison Biological Poison F

ract

ion

of in

flue

nt E

. col

i re

mai

ning

in th

e ef

flue

nt

predator

predator

Biofilms?Abiotic?

Conclusion? _________ is removing bacteria

0.08

0.1

1

0 1 2 3 4 5 6Time—h

Control

Sodium azide pulse

Sodium chloride pulse

Chrysophyte

long flagellum used for locomotion and to provide feeding current

short flagellum

stalk used to attach to substrate (not actually seen in present study)

1 µm

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?

Recall quiescent vs. mixed?

Role of Natural Particles in SSFRole of Natural Particles in SSF

Could be removal by strainingBut SSF are removing particles 1 m in

diameter!To remove such small particles by straining

the pores would have to be close to 1 m and the head loss would be excessive

Removal must be by attachment to the sticky particles!

Particle Capture EfficiencyParticle Capture Efficiency

Sand filters are inefficient capturers of particles

Particles come into contact with filter media surfaces many times, yet it is common for filters to only remove 90% - 99% of the particles.

Failure to capture more particles is due to ineffective __________

Remember the diffusion surprise?attachment

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 stickier

Potato starch in rapid sand filters?Biofilms in slow sand filters?Mystery sticky agent present in surface waters

that is imported into slow sand filters?

Mystery Sticky AgentMystery Sticky Agent

Serendipity!Head loss through a clogged filter decreases

if you add acidMaybe the sticky agent is acid solubleMaybe the sticky agent will become sticky

again if the acid is neutralizedEureka!

Cayuga Lake Seston ExtractCayuga Lake Seston Extract

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

AMP CharacterizationAMP Characterization

11%

13%

17%

56%

volatile solidsAlNaFePSSiCaother metalsother nonvolatile solids

How much AMP should be added to a filter?

Hypothesis: The organic fraction is most important

carbon16%

Organic Carbon Accumulation in Filters Fed Cayuga Lake Water

Organic Carbon Accumulation in Filters Fed Cayuga Lake Water

0.0000001

0.000001

0.00001

0.0001

0.001

0.0001 0.0010 0.0100 0.1000 1.0000x (m)

G (g

carb

on/g

glas

s be

ads)

day 1

day 3

day 7

day 70

Filters fed Cayuga Lake Water

Organic Carbon Accumulation Rate

Organic Carbon Accumulation Rate

Approximately 100 ppb (g/L) of carbon from Cayuga Lake water is removed in SSF

230 mg TOC /m2/day accumulated in filters fed Cayuga Lake Water

100 mg to 2,500 mg AMP as TOC /m2/day fed to filters (CAMP*V0)

Calculate application rate of AMP when fed Cayuga Lake water

Total organic carbon

0 3 2

100 1000 10 1 24240

100 1000TOC

AMP

mg AMPg L cm m hr mgC V

L m hr cm day g m day

Attachment Mediating Polymer

0

1

2

3

4

5

6

7

0 2 4 6 8 10

time (days)

pC*

control

100

500

2500

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

2

mgTOC

m day

0

1

2

3

4

5

6

7

0 2 4 6 8 10

time (days)

pC*

control

100

500

2500

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

2

mgTOC

m day

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

pC* is proportional to accumulated mass of polymer in filter

Head Loss Produced by AMPHead Loss Produced by AMP

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8 10

time (days)

head

loss

(m)

control

100

500

2500

end azide

2carbonmg

m day

How much AMP does it take to get 1 m of head loss?

2 2

5006 3carbon carbonmg g

daysm day m

What do we know about this Polymer?

What do we know about this Polymer?

Soluble at very low (<1) and at very high (>13) pH

Forms flocs readily at neutral pHContains protein (amino acids)

In acid solution amino acids are protonated and exist as cations

In basic solution amino acids are deprotonated and exist as anions

Could be irrelevant!

Dipolar Structure of Amino Acids

Dipolar Structure of Amino Acids

H—N —CH—C—O—H

H

R O..

In acid solution In base solution

H—N —CH—C—O

H

R O..

H—N —CH—C—O—H

H

R O

H

+

Carboxyl group

Amino group

cation anion

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

Current and Future ResearchCurrent and Future Research

Produce the polymer in the lab with an algae culture Develop methods to quantify the polymer Develop application techniques to optimize filter

performance How can we coat all of the media? Will the media remain sticky through a backwash? Will it be possible to remove particles from the media with a

normal backwash? What are the best ways to use this new coagulant?

Why does the filter performance deteriorate when the AMP feed is discontinued?

Characterize the polymer

ConclusionsConclusions

Filters could remove particles more efficiently if the _________ efficiency increased

SSF remove particles by two mechanisms_________________________________________

pC* is proportional to accumulated mass of AMP in the filter

Predation

Sticky polymer that coats the sand

attachment

, ,g Br Lo* ,z RpC f

Contact PointsContact Points

Polymer Accumulation in a PorePolymer Accumulation in a Pore