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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!
extra
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
extra
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.
extra
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
extra
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
extra
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
extra
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
extra
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
extra
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?
extra
Turbulent Mixing
Cowen - "An Experimental Investigation of Scale-Dependent Plume Physics"
10 cm
extra
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
extra
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
extra
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
extra
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