Flocculation Models

Overview•Flocculation definition and regulation •Mechanical Design•Hydraulic conventional design•Fractals•Collisions

•Laminar Flow•Turbulent Flow

•Conclusions•Surface coverage

23

89

0

8

9

139 8 6* log 1

8 9P

pC k t

d

23 2

30

3 2 6* log 12 3

p GtC k

What is Flocculation?• A process that transforms a turbid suspension of

tiny particles into a turbid suspension of big particles!

• Requires• Sticky particles (splattered with adhesive nanoclusters)• Successful collisions between particles

• Flocs are fractals (“the same from near as from far”)

• The goal of flocculation is to reduce the number of small particles (that haven’t been flocculated)

• One goal is to understand why some particles are always left behind (turbidity after sedimentation)

• Another goal is to learn how to design a flocculator

The Challenge of Flocculation

•We would like to know•How do particles make contact to

aggregate?•What determines the time required for

two flocs to collide?•How would you design a flocculator for a

target settled water turbidity?•How strong are flocs?•The challenge of the large changes in scale•The Al(OH)3 nanoclusters begin at a

scale of 10 to 100 nanometers•Flocs end at a scale of 100 micrometers•Flocculators are meters long

Ten State Standards• The detention time for floc formation should be at least 30

minutes with consideration to using tapered (i.e., diminishing velocity gradient) flocculation. The flow‑through velocity should be not less than 0.5 nor greater than 1.5 feet per minute.

• Agitators shall be driven by variable speed drives with the peripheral speed of paddles ranging from 0.5 to 3.0 feet per second.  External, non-submerged motors are preferred.

• Flocculation and sedimentation basins shall be as close together as possible.  The velocity of flocculated water through pipes or conduits to settling basins shall be not less than 0.5 nor greater than 1.5 feet per second.  Allowances must be made to minimize turbulence at bends and changes in direction.

• Baffling may be used to provide for flocculation in small plants only after consultation with the reviewing authority.  The design should be such that the velocities and flows noted above will be maintained.

http://10statesstandards.com/waterrev2012.pdf

Hydraulic flocculators allowed only by special permission!

Mechanical Flocculation

•Particle collisions caused by gentle stirring

•Advantage •energy dissipation rate can be

varied independent of flow rate

•Disadvantage •potential short circuiting (some

fluid moves quickly from inlet to outlet)

•moving parts in a wet environment

•Highly nonuniform energy dissipation rate

Recommended G and Gq values:

Turbidity or Color Removal (Mechanical

flocculators)

Type

“Velocity gradient” (G) (1/s)

Energy Dissipation Rate

()+ Gqq*

(minute)Low turbidity, color removal

20-70 0.4 – 4.9 50,000-250,000

11 - 210

High turbidity, solids removal

70-180 4.9 - 32 80,000-190,000

7 - 45

Sincero and Sincero, 1996 Environmental Engineering: A Design Approach

mWkg

* Calculated based on G and Gq guidelines+ average value assuming viscosity is 1 mm2/s

G is the wrong parameter… (Cleasby, 1984)

G

2G

Mechanical Design: mixing with paddles

3 3

2D P paC A a V

GV

“v

elocit

y grad

ient”

Drag co

effici

ent

Project

ed ar

ea of

padd

les

Ratio o

f rela

tive t

o

absol

ute ve

locity

of pa

ddles

Reactor volume1.9DC

extra

Mechanical Flocculators and Energy Dissipation Rate

•Model the mixing unit as a flat plate moving normal to the fluid (infinite fluid)

•The maximum energy dissipation rate is given by

•Closely spaced plates willhave higher

3Plate

MaxPlate

VW

Computational Fluid Dynamics Analysis

•Flat plate normal to the flow•1 m wide•Flow was 2-D•V=1 m/s•Re = 100,000• = 0.04 W/kg

• = 0.34

3Plate

MaxPlate

VW

13

Max PlatePlate

WV

Energy dissipation rate

Streamlines

What is for mechanical flocculators?•The maximum velocity for mixing

units given by 10 State Standards is 3 ft/s

•No minimum plate width is specified•For narrow plates

is comparable to rapidmix!

•If is 10 mW/kg then the ratio of couldexceed 100 http://10statesstandards.com/waterrev2012.pdf

3Plate

MaxPlate

VW

1 10 1000.1

1

10

Plate width (cm)

Max

imum

ene

rgy

diss

ipat

ion

rate

(W/k

g)

Mechanical Flocculators Summary

•Waste (a small amount of) electricity•Require unnecessary mechanical

components•Have a wide distribution of energy

dissipation rates (highest in the wake of the paddles) that may break flocs

•Have a wide distribution of particle residence times (completely mixed flow reactors)

extra

Hydraulic Flocculators

•Horizontal baffle

•Vertical baffle

•Pipe flow

•Gravel bedVery low flows and pilot plants

A bad idea (cleaning would require a lot of work)

Flocculator Geometry

2 Channels

Upper Baffles

Port between channels

Entrance

Lower BafflesExit

extra

Why aren’t hydraulic flocculators used more

often?• Simple construction means that there aren’t any items that private companies (venders) can sell as specialized components

• Consulting firms want to be able to pass the design responsibility off to a vender

• The presumed operation flexibility of mechanical flocculators (variable speed motor driving a slow mixing unit)

• Poor documentation of design approach for hydraulic flocculators (special permission required to use in the US!)

• Using electricity is cool, design innovation is suspect…

• Prior to AguaClara we didn’t have a design algorithm based on the fundamental physics

extra

Schulz and Okun (Hydraulic

flocculators)•Recommend velocity between 0.1 and 0.3 m/s

•Distance between baffles at least 45 cm•Water must be at least 1 m deep•Q must be greater than 10,000 m3/day

(115 L/s)These aren’t universal constants!We need to understand the real constraints so we can scale the designs correctlyWhat length scale could make a dimensionless parameter?

Surface Water Treatment for Communities in Developing Countries, (1984) by Christopher R. Schulz and Daniel A. Okun. Intermediate Technology Publications

AguaClara Flocculator Design Evolution

• 2005 - We used conventional guidelines based on velocity gradient to design the first low flow vertical flocculator

• 2010 - We designed using energy dissipation rate and accounted for the nonuniformity of the energy dissipation rate (q = 15 minutes)

• 2015 – We added obstacles to decrease the distance between expansions to make all of our flocculators have maximum collision efficiency (q = 8 minutes)

• 201x –We increase the efficiency of removal of small particles (q = 3 minutes) ???????

Edge of Knowledge Alert•Why would we ever think that the baffled

flocculators invented over 100 years ago were the optimal design for flocculation? (room to improve!)

•We have better coagulants now. Shouldn’t that influence flocculator design?

•We are only now beginning to understand the physics of fractal flocculation

•We are improving the design of hydraulic flocculators based on our evolving understanding of the physics of flocculation

extra

Fractal Flocculation Theory•Turbulence is caused by the expansion

that results when the water changes direction as it flows around each baffle in the flocculator

•Particles and flocs are transported to collide with each other by turbulent eddies and over short distances by viscous shear and Brownian motion.

•Flocs grow in size with each successful collision

•Collisions between particles of very different sizes are not very succesful.*

Flocculation model and collision potential for reactors with flows characterized by high Peclet numbers Monroe L. Weber-Shirk

, a, and Leonard W. Liona

http://dx.doi.org/10.1016/j.watres.2010.06.026*hypothesis from 2012!

How do the flocs grow?

Exponential growth•How many sequential collisions are

required to make a 1 mm particle starting from 1 mm particles?

•How much larger in volume is the 1 mm diameter particle?

•____________1,000,000,000 !

Doubling Collisions•1 collision 1+1=2•2 collisions 2+2=4•3 collisions 4+4=8•4 collisions 8+8=16•Number of original particles in the

floc = 2n

•What is n to obtain 1,000,000,000 = 2n?

•n=30This assumes volume is conserved!

log(1000000000) log(2)log(1000000000)

log(2)

n

n

Fractal Dimensions

•What happens to the density of a floc as it grows larger?

1

0FractalDd d i

diamete

r of p

rimary

parti

cle

diamete

r of f

loc

Number of primary particles in the floc

Frac

tal di

mensio

n

If volume is conserved, what is DFractal? ____3

3

0FractalDV V i

Floc density approaches the density of water because the floc includes water

Fractal Geometry•Fractal geometry explains the

changes in floc density, floc volume fraction, and, ultimately, sedimentation velocity as a function of floc size

•The fractal dimension of flocs is approximately 2.3 (based on floc measurements)

•Fractal dimension is a function of the size ratio of the colliding flocs

3

0FractalDV V i

Floc Volume Fraction•The fraction of the reactor volume

that is occupied by flocs•For fractal dimensions less than 3 the

floc volume fraction increases as floc size increases

•Use conservation of volume to estimate initial

Floc FlocFloc

Suspension Floc

V CV

0 3( )Floc Clay Al OH

3 3

0 3

ClayAl OH Al OHClay

Floc Clay Al OH

C C CC

Floc

Floc

dominates

Floc Volume Fraction

0.001 0.01 0.1 1 101 10 5

1 10 4

0.001

0.01

0.1

1Fractal dimension = 1Fractal dimension = 2.3Fractal dimension = 3

Floc diameter (mm)

Floc

Vol

ume

Frac

tion

0

3

0

FractalD

Floc Flocdd

Primary particle diameter (clay + coagulant)

“super fluffy” flocs

Dense flocs

Buoyant Density of Flocs

0.001 0.01 0.1 1 100.1

1

10

100

1000

1 104

Fractal dimension = 1Fractal dimension = 2.3Fractal dimension = 3

Floc diameter (mm)

Floc

den

sity

- wat

er d

ensit

y (k

g/m

^3)

2 0 2

30

FractalD

Floc H O Floc H Odd

Will these flocs settle faster than the primary particles?

Fractal Terminal Velocity Equations

2

2 2

2

18

Floc H Ot

H O H O

gdV

2 0 2

30

FractalD

Floc H O Floc H Odd

0 2

2 2

0 2

2 2

0 2

2 2

320

2 3220

0 0

1

0

0

18

18

18

Fractal

Fractal

Fractal

DFloc H O

tH O H O

DFloc H O

tH O H O

DFloc H O

tH O H O

dgdVd

dgd d dVd d d

gd dVd

0.001 0.01 0.1 11 10 4

0.001

0.01

0.1

1

10

Floc diameter (mm)

Term

inal

vel

ocity

(mm

/s)

Floc Terminal Velocity

1 mm

Upflow velocity for floc blankets

Capture velocity for AguaClara plate settlers

Why flocculation is necessary!

The model takes into account the changing density of flocs

0 2

2 2

120

018

FractalDFloc H O

tH O H O

gd dVd

DFractal = 2.3 and d0 = 1 mm

2

2 2

2

18

Floc H Ot

H O H O

gdV

shape factor for drag on flocs

Laminar flow

Collision Model of the Flocculation Process

•The velocity between flocs is a function of whether the separation distance is less or greater than the Kolmogorov scale

•The time required per collision is a function of the relative velocity between flocs, the average separation distance between flocs, and the floc size•In the next slides we will explore how to

characterize collision time for flocs•We will assume that collisions occur between

similar sized flocs. There is some evidence that flocs of very different diameters don’t attach when they collide.

Are the two flocs in different eddies?

How much water is cleared (filtered) from a floc’s

perspective?•Volume cleared is proportional to a collision area defined by a circle with diameter = sum of the floc diameters

•Volume cleared is proportional to time

•Volume cleared is proportional to the relative velocity between flocs

2Cleared Floc rV d v t

2Flocd

t

rv

rv t 2Flocd

How much volume must be cleared before a collision

occurs?•The average volume of

water “occupied” by a particle!

•Need to know number of particles per volume (nP)

•The number of flocs decreases as the flocs grow in size

13

1

Pn

0

0FractalD

P PP

dn nd

3

6P P PP

P P P P P

C CnV V d

13

6P

PP

dC

Use dimensional analysis to get a relative velocity

2

3

LT

,rv f

1

3rv

Viscous range Inertial range , ,rv f

rv

2LT

,rv f Assume linear

Confirmation of the G notation for laminar flow

13 4

KL

Re=1

laminar turbulent

If the flocculator has laminar flow, then this side doesn’t apply

is separation distance

13

1

Pn

The velocity of an eddy scales with the size of the eddy and the energy dissipation rate.

rv G

L dimensions

Collision Rates

tc is average time per collision

viscous inertia

13 4

KL

2Cleared P r cV d v t

3OccupiedV

13

rv

3

2 cP r

td v

3

12 3

c

P

td

rv G

2

2 cP

td G

Relative velocity

Time for one collision

is number of sequential successful collisions. is fractional surface coverage of particles by adhesive nanoclusters.

cc

dN dtt

2

2 Pc

ddN G dt

12 3

2 2 Pc

ddN dt

Collision Rate and Particle

Removal viscous inertia

13 4

KL

2

2 Pc

ddN G dt

12 3

2 2 Pc

ddN dt

136P P

P

d C

236 P

cP

CdN G dt

13

23

23

2

6

6

Pc

PP

PP

CdN dt

dC

13

6P

PP

dC

8 19 3

2

6 Pc

P P

CdN dtd

Pc

P

dC dNkC

236P P

P P

dC C G dtkC

8 19 3

2

6P P

P P P

dC C dtkC d

First order removal of particles with collisions

Track small particle concentration as flocculation progresses with particle concentration as our master variable

What is particle size?

Geometry

Tracking residual turbidity!

Integrateviscous inertia

13 4

KL

236P P

P P

dC C G dtkC

8 19 3

2

6P P

P P P

dC C dtkC d

0

8 117 9 39

20

6 1P

P

C t

P PP PC

C dC k dtd

0

253

3

0

16

P

P

C t

P P PC

C dC k dtG

0

22 23

3 332 6P P PC C k t

G

0

2233

03 2 6log 12 3

P

P

Cp kG tC

0

8 18 8 9 3

9 92

9 6 18 P P

P P

C C k td

0

188399

02

9 8 6log 18 9

P

P P

Cp k tC d

What is the p function?

Particle size and density is assumed constant because the model is tracking the small particle population that won’t be removed during sedimentation.

Remember our Goal?•Introduce pC*•Sloppy parlance… log removal•What is the target effluent turbidity

for a water treatment plant?•What is pC* for a water treatment

plant treating 300 NTU water?•What is required effluent turbidity?•How many orders of magnitude

reduction?

Coiled Tube Flocculation Residual Turbidity Analyzer

Dr. Karen Swetland Dissertation research

Floc Model: PACl

0.1 1 10 1000

0.5

1

1.5

2

θ=1200s, 5 NTUθ=1200s, 15 NTUθ=1200s, 50 NTUθ=1200s, 150 NTUθ=1200s, 500 NTUθ=800s, 5 NTUθ=800s, 15 NTUθ=800s, 50 NTUθ=800s, 150 NTUθ=800s, 500 NTUFitted Model

Γ*G*θ*ϕ^2/3

pC*

23 2

30

3 2 6* log 12 3

p GtC k

Floc Model: Alum

0.1 1 10 1000

0.5

1

1.5

2

θ=1200s, 5 NTUθ=1200s, 15 NTUθ=1200s, 50 NTUθ=1200s, 150 NTUθ=1200s, 500 NTUθ=800s, 5 NTUθ=800s, 15 NTUθ=800s, 50 NTUθ=800s, 150 NTUθ=800s, 500 NTUFitted Model

Γ*G*θ*ϕ^2/3

pC*

23 2

30

3 2 6* log 12 3

p GtC k

Laminar Flow Floc Model

Velocity gradient

Flocculation time

Fractional surface coverage of particle by coagulant

Floc volume fraction

12

23 2

30

3 2 6* log 12 3

p GtC k

First order rate constant (model fitting

parameter)

Proposed Turbulent Flocculation Model

Energy dissipation rate

Flocculation time

Fractional surface coverage of particle by coagulant

Initial floc volume fraction

-log(fraction remaining)

Characteristic particle size

What does the plant operator control? ________What does the engineer control? __________

13t

What changes with the raw water? __________𝜙0

23

89

0

8

9

139 8 6* log 1

8 9P

pC k t

d

Model assumptions and deficiencies

•Assume that small flocs can’t successfully attach to large flocs

•Don’t yet include the effect of the sedimentation tank design (we know performance deteriorates when the capture velocity of the sedimentation tank increases)

•Preliminary work to test turbulent model is underway now

•Viscosity may still be significant in turbulent flocculators

Why might floc collision fail if the flocs are of very different

sizes?•Tangent and rotational velocities cause shear and unzipping of bonds between particles of different sizes•Perhaps the ratio of approach velocity divided

by tangent velocity determines likelihood of attachment

•Tangent velocity is proportional to the diameter of the larger particle

•Flocs reach a terminal size based on a balance of the adhesive force of the bonds and the shear force that tends to tear them apart •Once a floc has reached its terminal size any

further collisions are unsuccessful

Collision of two similar sized flocs

•Tangent velocities of the particles surfaces at collision is similar in magnitude to the normal velocity

Collision of flocs of very different sizes

• Tangent velocities of the approaching particle surfaces increase as size of either particle increases

• Bonds formed on impact are unzipped due to rotation and high tangent velocities

• Ratio of normal to tangent velocities may be correlated with attachment

Floc maximum diameter vs. average

1 10 1000.1

1Gθ = 23000 Gθ = 19000 Gθ = 15000 Gθ = 11000 Gθ = 7500 power fit

ε (mW/kg)

d (m

m)

The average floc size as a function of average in a laminar flow tube flocculator. Floc diameter is independent of the collision potential for large collision potentials. Can these flocs be captured by plate settlers? _________

dmax ( ) 75 mmW

kg

1

3

-Ian Tse Spring 2009Yes!

0.001 0.01 0.1 11 10 4

0.001

0.01

0.1

1

10

Floc diameter (mm)

Term

inal

vel

ocity

(mm

/s)

Turbulent Flocculation Sedimentation Model

Questions•Characteristic size of a particle that won’t settle. We need further work to better define what this characteristic particle size means.

•Function of the characteristic size of the coagulant precipitate, geometry of the particles, and loss of coagulant to reactor walls

23Pd

Fractal Flocculation Conclusions

•It is difficult to flocculate to a low residual turbidity because the time between effective collisions increases as the number of particles and non-settleable flocs decreases

•Particles can’t attach to full size flocs•Perhaps because the surface shear on the big

floc is too high for a particle to attach (surface shear increases with diameter)

•If we could maintain a high energy dissipation rate to limit the size of flocs perhaps we could speed the aggregation process

What is the model missing?The model doesn’t include any particle aggregation that occurs in the sedimentation tank. Residence time in the sed tank is long and energy dissipation rate is low. Flocculation in the sed tank (especially if there is a floc blanket) could be very important.Thus real world performance is likely better than model predictions.

Flocculator Collision Potential

•We hypothesize that the majority of the collisions in a turbulent hydraulic flocculator are in the inertial range and the collision potential is determined by flocculator residence time, q, and energy dissipation rate, .

•The collision potential is given the symbol y and has the dimension of m2/3 and this length scale will be a property of the reactor geometry

•The next set of notes provides guidance for designing the geometry of a flocculator to obtain a target collision potential

Kolmogorov Concentration•The concentration of particles that

has an average separation distance equal to the Kolmogorov length scale

10 100 10001

10

100

1000

20 °C0 °C

Energy Dissipation Rate (mW/kg)

Kol

mog

orov

Con

cent

ratio

n (N

TU)

343

36KP P PC d

Assumes clay particle size is 3 mm.

Review•Why is it that doubling the

residence time in a flocculator doesn’t double pC* for the flocculator?

•Why does increasing floc volume fraction decrease the time between collisions?

•Which terms in the model are determined by the flocculator design?

23

89

0

8

9

139 8 6* log 1

8 9P

pC k t

d

What are the questions?•Are collisions between particles

actually dominated by inertia or does viscosity continue to play a very important role as long as the separations distances are close to the Kolmogorov length scale?

•Are collisions between different sized particles unfavorable as assumed in the model?

•Is the flocculation model derivation correct?

What does Gt mean?

0 0

rv

r

Deformation r

Deformation

duGdy

Gdy du

G vL v t

LGt

Definition of velocity gradient

Find relative velocity between flocs separated by distance

The relative distance traveled due to fluid deformation is proportional to time

A Gt of 1 means that the particles have a relative displacement equal to their separation distance

u x

y

𝛬y

𝐿𝐷𝑒𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛

velocity Displacement in time t𝑣𝑟

32

223

1

Inertial

Pc

d dtdN

Models for Sequential Successful Collisions

•Required collision potential is a function of reactor properties (velocity gradient and time) and is dimensionless.

•Required collision potential has dimensions of

• is efficiency factor due to non uniformity of energy dissipation in real reactors

viscous inertia

Reactor properties (collision potential)

2

2 Viscous

Pcd ddN G t

Suspension properties Coagulant coating

23 Ly

113 3t y y q

ideal real

Relationship between laminar and turbulent

collisionsSet the collision rate (dN/dt) equal to get the relationship

29

1 23 3

1P

G nq

q

1

2 2 3

2 2 2 P Pd dG

1 13 3

y q y q

29P

G nqy

29P

G

n

qy

Collision potential for a real reactor

Need to define a particle number concentration

Estimating the Collision Potential for Hydraulic

FlocculatorsUse the target settled water turbidity as the best guess for a relationship between conventional Gq and y. For a settled water turbidity (ignoring turbidity reduction by floc blanket) of 1 NTU (1 NTU=0.68 mg/L), clay diameter of 3 mm, clay density of 2650 , the number of clay particles is 180,000,000 per liter.

3

6 PP

P P

Cnd

Schulz and Okun suggest 20,000 as a minimum value of Gq.

29P

G

n

qy

Collision potential equivalent to Gq of 20,000 is approximately 100 AguaClara design collision potential is 75 (fall 2015).

Surface coverage () of clay by coagulant precipitate

In our modeling work we didn’t cover how to calculate what fraction of the clay surfaces are coated with coagulant. The following slides are the equation heavy derivation of that coverage. We assume coagulant precipitate has some characteristic diameter when it sticks to the clay and that the clay can be represented as a cylinder. We also assume that the coagulant sticks to everything including reactor walls. The coagulant approaches the clay surface randomly and thus accumulates in a Poisson distribution. The random bombardment means that some coagulant is wasted in double coverage of previously covered clay.

extra

Floc Model Equations for

Clay Total

ClayTotalA A

ClayTotal Wall

SASA SA

Wall Tube TubeSA D L

2

4Clay

ClayTotal Tube Tube ClayClay

SASA D L

V

1

1Clay TotalA A

Wall

ClayTotal

SASA

3

26

6

ClayClay Clay Clay

ClaySphereClay Clay Clay

DSA SA DV D V

6Clay ClaySphere

Clay Clay

SAV D

232

Tube Tube ClaySphereClayTotal Clay

Clay

D LSA

D

Surface area to volume ratio for clay normalized by surface area to volume ratio for a sphere

Surface area of clay divided by total surface area of clay + reactor walls

extra

Ratio of clay surface area to total surface area (including

reactor walls)

2

1

13

2

Clay TotalA ATube Tube

Tube Tube ClaySphereClay

Clay

D LD L

D

12

13

Clay TotalA AClay

Tube ClaySphere Clay

DD

extra

Poisson distribution and coagulant loss to walls combined to get surface

coverage

2

1Coag CoagPerClay

A AClay TotalClay

D NSAe

3

1

6

CoagPerClay Coag Clay Clay

Clay Coag Clay ClayCoag

N C VSA SA CD

1

21

3

Clay TotalA AClay

Tube ClaySphere Clay

DD

6Clay ClaySphere

Clay Clay

SAV D

2

Coag CoagPerClay Coag Clay

Clay Clay Coag ClaySphere

D N DSA D

1A ACoag Clay Clay Total

Clay Coag ClaySphere

DDe

The surface coverage is reduced due to stacking (which is handled by the Poisson distribution) and by the loss of coagulant to the reactor walls.

loss of coagulant to the reactor walls

extra

Clay platelet geometry

ClayPlateletHD

ClayPlatelet

HD

2

4Platelet ClayPlatelet ClayPlateletV D H

3

6Platelet ClayV D

3

4Platelet HD ClayPlateletV D

3 3

4 6Platelet HD ClayPlatelet ClayV D D

132

3ClayPlatelet ClayHD

D D

D.Clay is the diameter of a sphere with equal volume as the clay platelet

Model clay as cylinder with height and diameter

D.ClayPlatelet is the diameter of a cylinder given ratio of height to diameter and equal volume spherical diameter

extra

Clay platelet geometry

2 23 3

2 22 224 3 3ClayPlatelet Clay HD Clay

HD HD

SA D D

2ClayPlatelet

ClaySphereClay

SAD

231 2

2 3ClaySphere HDHD

224ClayPlatelet ClayPlatelet ClayPlatelet ClayPlateletSA D D H

132

3ClayPlatelet ClayHD

D D

ClayPlateletHD

ClayPlatelet

HD

23

21 22 3ClayPlatelet HD Clay

HD

SA D

extra

Surface coverage of clay

1A ACoag Clay Clay Total

Clay Coag ClaySphere

DDe

231 2

2 3ClaySphere HDHD

1 12

31

Coag Clay

ClayClay CoagClaySphere

Tube Clay

DDD

De

12

13

Clay TotalA AClay

Tube ClaySphere Clay

DD

12

3

Clay TotalA A

ClayClaySphereClaySphere

Tube Clay

DD

23

1 1

21 22 3 3

1Coag Clay

Clay CoagClay

HDHD Tube Clay

DD

DD

e

23

1 1

1 22 3

1Coag Clay

Clay Coag

HDHD

DDe

If you neglect wall loses

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Solving for Coagulant Dose

23

1 1

21 22 3 3

1Coag Clay

Clay CoagClay

HDHD Tube Clay

DD

DD

e

23 21 2 ln 1

2 3 3Clay Coag Clay

Coag Coag HDHD Tube Clay Clay

D DC

D D

Coagulant dose is inside coagulant volume fractionSolve for dose…

Given a target residual turbidity, solve for required , then solve for coagulant dose

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ln 1Clay Total

Coag Coag ClaySphereCoag Clay

Clay A A

DC

D

0

188 8 2 39

9 998 6 1

P PP P

dC Ck t

Loss of clay to reactor walls

0.001 0.01 0.1 1 100.001

0.01

0.1

1

5 NTU50 NTU500 NTU5000 NTU

Tube diameter (m)

Frac

tion

of c

oagu

lant

on

clay

Loss of coagulant to reactor walls can dominate for low turbidities and small reactors. For the EStaRS in India treating 5 NTU water and injecting coagulant into 7.5 cm pipes the clay only gets 23% of the applied coagulant!There may be a way to design a larger contact chamber for the coagulant to reduce losses to the walls.

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Effect of stacking and wall loss in a 10 cm diameter flocculator with 20

NTU

0 1 2 3 4 50

0.2

0.4

0.6

0.8

1

No Stacking and No Wall LossNo Wall LossStacking and Wall Losses

Coagulant concentration (mg/L)

Frac

tiona

l cla

y su

rfac

e co

vera

ge

Stacking due to random bombardment of the clay surface with coagulant nanoclusters. Stacking becomes significant for high surface coverage. Wall losses also cause a significant reduction in clay surface coverage.

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