Monroe L. Weber-Shirk S chool of Civil and Environmental Engineering Coagulation and Rapid Mix Basis for a rational design? Aggregation Intermolecular.

Monroe L. Weber-Shirk School of Civil and

Environmental Engineering

Coagulation and Rapid MixBasis for a rational design?

Aggregation

Intermolecular bonding

Mixing

Energy Dissipation

Diffusion

Sustainable Municipal Drinking Water Treatment

Sedimentation of Small Particles?

How could we increase the sedimentation rate of small particles?

2

18

p wt

w

d gV

Increase d (stick particles together)

Increase g (centrifuge)

Decrease viscosity (increase temperature)

Increase density difference(dissolved air flotation)

Definitions

Coagulation: The process of adding a sticky solid phase material (adhesive nanoglobs) that attaches to the colloids so they can attach to each other (the topic of these notes)

Flocculation: The process of producing collisions between particles to create flocs (aggregates) (next set of notes)

Stages of colloid removal

Filtration SedimentationFlocculationCoagulation

Nanoglob deposition

Collisions Gravity!

Floc Blanket

More Collisions

Last chance!

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The Conventional Coagulation Myth*

“The purpose of addition of coagulant chemicals is to neutralize the negative charges on the colloidal particles to prevent those particles from repelling each other.

Coagulants due to their positive charge attract negatively charged particles in the water.”http://www.thewatertreatments.com/wastewater-sewage-treatment/coagulation-flocculation-process/

* This myth has been the dominant “theory” of coagulation for close to 100 years

Sante Mattson J. Phys. Chem., 1928, 32 (10), pp 1532–1552, DOI: 10.1021/j150292a011

Publication Date: January 1927

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Electrostatic hypothesis inconsistencies

The coagulant self aggregates – this is inconsistent with the positive charge that should prevent aggregation

Electrostatic repulsion extends only a few nm from the surface of a colloid – and the coagulant adhesive nanoglobs are many times larger than the reach of the repulsive electrostatic force

The electrostatic hypothesis doesn’t provide any attachment mechanisms. It only provided a mechanism for colloids to get close together. The hypothesis that London van der Waals forces result in attachment neglects to account for the presence of water in the system. Water molecules will also be attracted to surfaces by London van der Waals forces and thus there will be competition between the coagulant and water. Thus eliminating repulsion is NOT sufficient to produce a bond between the colloids.

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The electrostatic hypothesis wrongly predicts…

a stoichiometric relationship between coagulant and colloid concentrations.

that positively charged coagulant precipitates don’t aggregate.

resuspension of colloids at a high dosage of coagulant that causes the surface charge to become positive

Sweep Floc: the mystery mechanism

The majority of water treatment flocculation is not explained by charge neutralization.

Sweep flocculation is used to “explain” the flocculation that occurs where charge neutralization predicts flocculation should not occur.

Sweep floc overcomes the repulsive surface charge by some other unexplained mechanism (sweeping???)

100 years with the wrong hypothesis!

Surface charge and charge neutralization does explain some aggregation and sedimentation processes under very low shear conditions

The water treatment application was always perceived to be so complex that a detailed understanding of the mechanism was assumed to be impossible

Results that didn’t fit the hypothesis such as sweep flocculation were explained as the result of the complex nature of the problem

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Coagulation: The adhesive nanoglob hypothesis

Aluminum coagulants (alum and polyaluminum chloride) produce adhesive nanoglobs of precipitated aluminum hydroxide that attach to surfaces including other nanoglobs

The attractive attachment force must be stronger than the hydrogen bond between water molecules so the nanoglobs can push water out of the wayPredictive performance model for hydraulic flocculator design with polyaluminum chloride and aluminum sulfate coagulants Karen A. Swetland, Monroe L. Weber-Shirk*, Leonard W. Lion

Sticky Nanoglobs?

Effective flocculation only occurs when the coagulant is in the solid phase

Al(OH)3 likes to stick to itself and to other surfaces

Why is the solid phase Al(OH)3 sticky? (We are trying to figure this out…)

The problem of WET

Hydrogen bonding between water molecules and also between a water molecule and electronegative atoms

(oxygen) in the colloidal surfaces provides competitive bonds that normally prevent bonding between colloids (water gets in the way)

Making wet objects stick together is hardWe need a bond between molecules that is

stronger than hydrogen bonds (to push water away)

Strong Intermolecular Bonds:Stronger than hydrogen bonds?*

We know that aluminum and iron work as coagulants. But why?

Both coagulants have an oxidation state of +3 and both precipitate as X(OH)3

AlO

OO

d+++

d--d-

- d--d+ d+

d+

H

HH

OHH d+d+

d--

*Edge of knowledge alert

Stronger than a Hydrogen Bond?

Al is very weakly electronegative and thus it maintains a charge of +3 when combined with 3 oxygen (oxygen keeps all of the electrons)

Hypothesis*: intermolecular bonds between oxygen and aluminum are stronger than intermolecular bonds between oxygen and hydrogen

* Edge of knowledge alert

O - H = 3.5 - 2.1 = 1.4

O - Al = 3.5 – 1.5 = 2

Polarity of water

Polarity of Al(OH)3

Aluminum Sulfate Chemistry Alum [Al2(SO4)3*14.3H2O]

A widely used coagulantTypically 10 mg/L to 100 mg/L alum is

used (0.9 to 9 mg/L as Al)High concentrations (stock solutions) don’t

precipitate because the pH is lowThe alum precipitates when it blends with

the water in the water treatment plantThe primary reaction produces Al(OH)3

Al2(SO4)3 + 6H2O2Al(OH)3 + 6H+ + 3SO4-2

pH = -log[H+]

Acid Neutralizing Capacity (ANC or Alkalinity) Requirement

Al2(SO4)3 + 6H2O2Al(OH)3 + 6H+ + 3SO4-2

ANC is measured as mg/L of CaCO3

How much ANC is consumed by alum?Alum Calcium Carbonate

Molecular Formula Al2(SO4)3*14H20 CaCO3

Molecular mass 600 g/mol 100 g/mol

eq/mol 6 2

Molecular mass/eq 100 g/eq 50 g/eq

Simple guide 1 mg/L Alum consumes 0.5 mg/L Calcium Carbonate ANC

This sets the maximum alum dose that can be used for low alkalinity waters

Polyaluminum Chloride (PACl)

Slowly titrated with a base (in the chemical plant) to produce a meta-stable and soluble polymeric aluminum (partially neutralized)

Consumes less alkalinity (ANC)PACl forms flocs more rapidly than does

alum (plant operator observation)Aluminum mass fraction is higher than in

alum (no 14.3 H2O) so the mass of PACl required is less than for alum (1-15 mg/L)

5 6 7 80.01

0.1

1

10

Theoretical Al solubilityExperimental PACl solubilityMinimum EPA MCLMaximum EPA MCLMin dose Al

pH

Al co

nce

ntr

atio

n (

mg

/L)

Aluminum Solubility

5 6 7 80.01

0.1

1

10

Theoretical Al solubilityExperimental PACl solubilityMinimum EPA MCLMaximum EPA MCLMaximum dose Al

pH

Al concentration (m

g/L

)

1

4Al OH

2Al OH

pH control is critical!

Coagulation fails at low pH and high pH because the coagulant becomes too soluble

Coagulation Geometry

Clay plateletsCoagulant nanoglobs

Surface charge of Particles and Natural Organic Matter (NOM)

NOM significantly increases the required coagulant dose in some waters

Charge density (conventional explanation)Clay: 0.05 to 0.5 meq/mg (1 mg/L clay ≈ 1 NTU)Fulvic acid 5 to 15 meq/mg C

Alternative explanation - NOM has a larger surface area* per unit mass than colloids and thus provide many attachment sites for adhesive nanoglobs

Rapid Mixers

A high-intensity mixing step used before flocculation to disperse the coagulant(s) and to initiate the particle aggregation process*

In the case of hydrolyzing metal salts, the primary purpose is to quickly disperse the salt so that contact between the simpler hydrolysis products and the particles occurs before the metal hydroxide precipitate is formed* (This is probably not true)

“This process is poorly understood…”*

*Water Quality and Treatment 5th edition p 6.57

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On Rapid Mixing…

“In summary, little is known about rapid mix, much less any sensitivity to scale. However, the models and data reviewed suggest the need to be on the lookout for certain effects. From what is presently known, it can be speculated that since coagulant precipitation is sensitive to both micro- and macro-mixing, scale-up must consider not only energy dissipation rate, but also the reaction injection point and the contacting method.”

Mixing in Coagulation and Flocculation 1991 page 292

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Traditional rapid mix units

Backmix mechanical reactors

In-line blendersHydraulic JumpIn-line static

mixers

Traditional Design

Conventional design is based on the use of G (velocity gradient) as a design parameter.

G does not characterize the mixing caused by turbulence (G is valid for laminar flow)

Rapid mix units are fully turbulent In part because of the error in choice of

parameters, conventional design guidelines are not able to characterize the effects of scaling

G

Power, height, and G

“velocity gradient” caused by mixing

Reactor volume

Power required

Power required to lift water

Equivalent potential energy measured as a height used for mixing

P Q g h

Ph

Q g

This is the traditional approach

2Gh

g

2P G Q

V Q

1

2PG

V

Equivalent potential energy as a function of G

2G

Traditional Design Guidelines:Mixing with a Propeller

Residence Time (s)

“velocity gradient” (G) (1/s)

Energy dissipation rate (W/kg)

Equivalent height (m)*

0.5 4000 16 0.8

10 – 20 1500 2.25 2.3 – 4.6

20 – 30 950 0.9 1.8 – 2.8

30 – 40 850 0.72 2.2 – 2.9

40 – 130 750 0.56 2.3 – 7.5

from Environmental Engineering: A Design Approach by Sincero and Sincero. 1996. page 267

No mention of scale effects

* A measure of mechanical energy converted to heat

2Gh

g

Hydraulic Energy Constraint

If we use the same amount of mechanical energy in hydraulic water treatment plants as is used in mechanical water treatment plants we will need between 0.8 and 7.5 m of water height change just to power the rapid mix unit!!!!!

Rapid mix is one of the largest energy consumers in mechanical plants

We need to be more efficient (and hence smarter)

Caveat: It is a short walk to the edge of knowledge

The analysis presented next was designed to achieve adequate mixing so that nanoglobs have a chance to attach to all colloids

Coagulant self aggregation occurs at the same time as mixing

Self aggregation (especially in high alkalinity waters) can have a significant detrimental effect* because it reduces the surface area of the adhesive nanoglobs

There is a significant opportunity for further research that will lead to an improved understanding of the rapid mix process

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Why might RAPID mixing be necessary?

Vague answer is that we need to mix the adhesive nanoglobs with the water

But why RAPID?IF RAPID mixing matters then there must

be something bad that happens if the mix is SLOWSelf aggregation of nanoglobs into microglobsNonuniform distribution of nanoglobs

between colloids

Why might RAPID mixing be necessary?

Self aggregation of nanoglobs will begin when diffusion blends enough raw water with the coagulant to raise the pH so that the nanoglobs become sticky – this diffusion may occur in a few seconds

If the nanoglobs are only dispersed in a fraction of the raw water then some raw water colloids won’t receive any nanoglobsWe will find that we need an energy dissipation rate of

>1 W/kg to distribute nanoglobs between colloids

Rapid Mix: From macro to nano scale (in a few seconds)

Length scale Transport Processm

mm

mm

nm

Large scale eddies

Small scale eddies

Molecular diffusion

Result

Molecular scale

13 4

KL

Kolmogorov scale

Rapid Mix flow dimension

Three steps for mixing

Large scale eddies to mix at the dimension of the reactor (Macro mixing)Generate large eddiesFlow expansion with dimensions similar to the

dimension of the reactor

Small scale eddies to mix down to the Kolmogorov length scale (Micro mixing)Generate energetic tiny eddies so that turbulence can

mix to the length scale of colloid separation

Molecular diffusion to finish the job

Turbulence – Mixing – Energy Dissipation

The turbulent eddies cause stretching and thinning of concentration gradients and “shuffle” packets of fluid

The intensity of the turbulence can be characterized by the rate at which mechanical energy is being lost to thermal energy

W

Kg

J

s Kg

N m

s Kg

2

kg m m

s s Kg

2

3

m

s

How Far Can Turbulence Mix? (Kolmogorov length scale)

Dissipates energy from the mean flow through chaotic eddies and through viscosity where the kinetic energy is converted to heat

Turbulence is a great mixer down to the Kolmogorov scale!

13 4

KL

Kolmogorov length scale

Kolmogorov time scale

1

2

K

,n viscosity, for water is 10-6 m2/s

1 ms

Let e = 1 W/kg30 mm

This is the ______ scale for the flowRe=1

1 10 100 10000

50

100

150

200

Energy dissipation rate (mW/kg)

Kol

mog

orov

Len

gth

scal

e (μ

m)

Viscosity kills inertia (and eddies)!

13

6Separation ColloidColloid

L D

Average distance between colloids

What is the average volume ofwater “occupied” by a colloid?

Need to know colloid diameter (DColloid) and colloid volume fraction (fColloid)

3

6 Colloid

ColloidOccupied

D

V

Floc volumeSuspension volume

3

6 Colloid

OccupiedColloid

DV

Colloid ColloidColloid

Suspension Colloid

V C

V

Hypothesis: Energy Dissipation Rate for Micromixing

If the Kolmogorov length scale is large compared with the distance between colloids, then distribution of nanoglobs between colloids will be non-uniform

Therefore… set energy dissipation rate to make Kolmogorov length scale less than separation distance between colloids

13 4

KL

13

6Colloid

Separation ColloidColloid

L DC

3

43

4

6

MinRM

ColloidColloid

Colloid

DC

1 10 100 10000.1

1

10

100

1000

10000

Turbidity due to clay (NTU)

Ene

rgy

diss

ipat

ion

rate

(m

W/k

g)

Energy dissipation rate for uniform nanoglob application

We need an energy dissipation rate of approximately 3 W/kg to ensure uniform application of nanoglobs to colloids!

Below 10 NTU the mixing in the flocculator should be adequate!

1 10 100 10000

50

100

150

200

Turbidity due to clay (NTU)

Cla

y se

para

tion

dis

tanc

e (μ

m)

13

6Colloid

Separation ColloidColloid

L DC

1 10 100 1000 100000

50

100

150

200

Energy dissipation rate (mW/kg)

Kol

mog

orov

leng

th s

cale

(μ

m)

13 4

KL

3

43

4

6

MinRM

ColloidColloid

Colloid

DC

After turbulence: Let diffusion begin!

100 mm

500 NTU clay suspension

2 mm diameter clay (4 mm cylinder) PDH = 8

Separation distance for clay is 32 mm

Kolmogorov length scale of 100 mm

Adhesive nanoglobs

Adhesive nanoglobs

After turbulence: Let diffusion begin!

32 mm

500 NTU clay suspension

2 mm diameter clay (4 mm cylinder) PDH = 8

Separation distance for clay is 32 mm

Kolmogorov length scale of 32 mm

Adhesive nanoglobs

Adhesive nanoglobs

Turbulent Micromixing followed by molecular diffusion

Large scale eddies move packets of fluid around at the scale of the flow (or the scale of the separation distance of the injection points

…Smaller eddies move packets of fluid over smaller length scales…

Smallest scale eddies create high concentration gradients at Kolmogorov scale (viscosity kills turbulence at this scale)

Molecular diffusion finishes the job

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Velocity gradients increase interfacial area

Turbulence causes chaotic movement of the fluid with spatially and temporally varying velocity gradients (not like this image!)

Net effect is to increase the interfacial area between the fluids being mixed by stretching and deforming the fluids

What will I find if I take 1 mm3 samples and measure the concentration after short exposure to turbulent mixing?

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Turbulent Mixing

Cowen - "An Experimental Investigation of Scale-Dependent Plume Physics"

10 cm

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How Fast can Diffusion Mix?

What are the units of diffusion?Diffusion is the product of a velocity and a path

length – [L2/T]

How long will it take for diffusion to blur the concentration gradient left by turbulent mixing?

Molecular Diffusion DiffusionD V L

DiffusionMolecular Diffusion

Diffusion

LD L

t

2Diffusion

DiffusionMolecular

Lt

D

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Molecular Diffusion Quantified

Einstein relation (by Albert Einstein in 1905)

P P AMW V N

3

6P

P A

dMW N

3B

MP

k TD

d

1

3

3 6B P A

M

k T ND

MW

1

36P

P A

MWd

N

kb 1.38065051023

joule

K

N.A 6.02214151023 mole

1

.AlOH3 2420kg

m3

Avogadro’s constant

Boltzmann’s constant

For Al(OH)3 the molecular diffusion coefficient is 10-9 m2/s

Temperature (K)

Boltzmann’s constant

Density of th

e particle

Avogadro’s constant

Molecular weightFluid dynamic viscosity

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Turbulent Mixing so that Molecular Diffusion can finish the job1

3 4

KL

D M DiffusionL D t

Turbulence will mix to the Kolmogorov length scale

Diffusion will mix this far in this time

K DL L Set the length scales equal

13 4

M DiffusionD t

3

2DiffusionM

tD

10 100 10001

10

Energy dissipation rate (mW/kg)

Dif

fusi

on t

ime

(s)

If we use a 1 W/kg micromix event then diffusion will take 1 s

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This assumes that diffusion rather than shear is the dominant transport mechanism. Need to model collision time between clay particle and nanoglob based on shear transport to determine whether shear or diffusion dominate.

How do we generate intense turbulence?

We need to be converting mechanical energy (kinetic energy) to thermal energy

We want “concentrated” head loss! (this shouldn’t be too hard to achieve!)

Therefore use minor loss (related to a change in flow geometry) rather than major loss (from shear at the solid boundaries)

Almost all minor losses are caused by expansions (We need a flow EXPANSION)

Flow Expansion

The control volume analysis gave us the total energy loss, but it doesn’t give us the energy dissipation rate.

The energy dissipation rate varies with location in the expanding jet

22

12

in ine

out

V Ah

g A

Jet Mixing

3

RoundJet JetMax

Jet

V

D

3 3

4

50

2Jet Jet

Centerline

Jet

D V

x D

3 3

4

50

7 2Jet Jet

Centerline

Jet Jet

D V

D D

Minimum x for which this relationship is valid is 7 JetD

(Baldyga et al., 1994Baldyga, J., Bourne, J. R. and Zimmermann, B., 1994, Investigationof mixing in jet reactors using fast, competitiveconsecutivereactions. Chem. Engn 0 Sci. 49, 1937.

VJet

4

6

8

10

m

s JetMax

896

3084

7401

13530

W

kg

Jet

DJetArticle JetMax 1

3

VJet

0.482

0.485

0.487

0.477

0.4RoundJet

x is distance from the jet origin

The value we will use in our analysis. Further work is require to determine the best value of this parameter for different jet geometries.

3

4

50

5Jet

MaxJet

V

D

50

54

1

3

0.431

0 2 4 6 8 10 12 14 16 18 200

0.2

0.4

0.6

0.8

1

x/D.Jet

ε.M

ax (

W/k

g)

Energy Dissipation RateThree orifices, same velocity

3

RoundJet JetMax

Jet

V

D

Which jet has the highest energy dissipation rate?

A

B

C

Which jet has the highest shear (or velocity gradient)?

Big eddies create smaller eddies

Which jet has the largest eddies?

Which jet will make the smallest eddies first?

Which jet will dissipate energy the fastest?

ReVD

Higher energy dissipation rates give a smaller Kolmogorov scale!

Rapid Mix in a jet?Combined macro and micro mix

Orifice plate

Pin to keep plate in placeAccess pipe for coagulant delivery tube

Coagulant delivery tube

Orifice Diameter to Obtain Target Mixing (Energy Dissipation Rate, Kolmogorov Length Scale)

3

2

4RoundJet

JetMax

Jet

QD

D

Orifice vc JetA A Orifice vc JetD D

3

7

1

3

4 1RoundJetOrifice

vcMax

QD

Substitute for DJet and solve for DOrifice

The orifice must be smaller than this to achieve the target energy dissipation rate

3

RoundJet JetMax

Jet

V

D

Rapid Mix Head Loss

2

2Jet

e

Vh

g

1

3Jet Max

JetRoundJet

DV

2

3

22Jet Max

eRoundJet

Dh

g

3

7

1

3

4 RoundJetJet

Max

QD

22 7

2

4

2

RoundJet Max

eRoundJet

Q

hg

This is one of the scale effects for rapid mix

Why?

3

RoundJet JetMax

Jet

V

D

1 10 100 10000

10

20

30

40

50

Flow rate (L/s)

Rap

id m

ix o

rifi

ce h

ead

loss

(cm

)

What can you do to reduce the required head loss through the rapid mix for large plant flows?

Rapid Mix head lossincreases with Q

How could we maintain a high energy dissipation rate while reducing the velocity and the head loss?

What else is needed?Use a plate with multiple orifices in the

rapid mix pipe and add macro mixing upstream

3

RoundJet JetMax

Jet

V

D

22 7

2

4

2

RoundJet Max

eRoundJet

Q

hg

Hypothesis: Macomixing minor loss coefficient and length scale

The eddy velocities are comparable to the mean velocities for a minor loss coefficient of 1

The minimum distance in the direction of flow (L) for mixing over the dimension perpendicular to the direction of flow (D) would then be equal to D. (L>D)

This length is the pipe minimum length before the micromixing event (unless the two are combined in a single orifice)

Mechanized Rapid Mix vs. Hydraulic Rapid Mix

Vampire loadsA 100 L/s AguaClara plant costs

approximately $600,000After 25 years the electricity cost for

mechanized rapid mix would be $230,000 “Another way to give is to not take…”The total energy cost for a package plant

that uses a total of 400 J/L is 1.5 million USD! 400

J

L

50¤

109J

100L

s25 yr 1577846¤

Reflections

At lower than design flow ratesthe energy dissipation rate will be lower than the target

The hydraulic rapid mix head loss is tiny compared with traditional designs

For flow rates less than 1000 L/s it probably isn’t necessary to mix in two stages (micromix and macromix are combined)

3

RoundJet RoundJetMax

Jet

V

D

Edge of Knowledge Reminder

We need to test the hypothesis that colloid spacing and Kolmogorov length scale influence performance

The energy dissipation rate in a jet is not uniform and we are using the max energy dissipation rate in this analysis

We haven’t addressed loss of coagulant precipitate to reactor walls