Chapter 6-2.Chapter 6 2.

Coagulation & Flocculationg

V. Coagulation-Flocculation Process

Stable“primary” particulates

Unstablemicroflocs

Floc aggregates

Steady-statefloc sizedistributionprimary particulates

Destabilization

1 sec

microflocsTransportandAttachment

Floc breakup

Figure 6.7. Subprocesses controlling rate of particulate aggregation.

Coagulation : Process of destabilization of the colloid particles.Flocculation : Collision and aggregation of the destabilized particles into large flocsFlocculation : Collision and aggregation of the destabilized particles into large flocs

(transport step).* Often, Coagulation and flocculation are used interchangeably.

But, among engineersCoagulation : overall process of particle aggregation

(destabilization + transport)

Flocculation : only transport step

V. Coagulation-Flocculation Process

1. Rapid mixing, Dispersion, Reaction(Coagulant + wastewater) with rapid mixing

Coagulation

destabilizing particles.

Fl l ti

2. Rapid mixing, Dispersion and AdsorptionCombining primary particles together to give larger

Flocculationaggregates.

3. Slow mixingFormation of larger flocs of sufficient size to separateout.

V-1. Flocculation model

Transport of colloidal particles- Rate of aggregation depends upon :① Collision rate between particles (particle transport)② Collision effectiveness in permitting attachment between particles

(particle destabilization)

- Inter particle contact mechanisms- Inter particle contact mechanisms.① Contacts by thermal motion (Brownian motion)

Perikinetic flocculation② Contacts resulting from bulk fluid motion, for example,

from transport induced by stirring Ortho kinetic flocculation③ C l i f li if h i l (A idl li i l③ Contacts resulting from settling if the particles (A rapidly settling particle

overtakes and collides with a particle which is settling at a slower rates)Differential movement from particle sedimentationDifferential movement from particle sedimentation

V. Flocculation model

Th d i f h ll id l i l l f h id d

1) Perikinetic (Brownian ) flocculation

- The random motion of the colloidal particles results from the rapid and random bombardment of the colloidal particles by molecules of the fluid(Brownian motion)(Brownian motion).

- The instantaneous rate of change in the total concentration of particles withtime due to Perikinetic flocculation, JPk, becomes,

4 TkdNNT : the total concentration of particles in

i t ti t2)(34

Tt

Pk NTkdt

dNJ ⋅⋅

⋅−==μ

η suspension at a time t: collision efficiency factor (= the fractionof the total no. of collisions which aresuccessful in producing aggregates)

η----- (1)

successful in producing aggregates): Boltzman constant

T : Absolute temp.: Fluid dynamic viscosity

k

μ

* JPk is 2nd order with respect to NTJPk is independent of particle size

: Fluid dynamic viscosityμ

V. Flocculation model

Integration of eq. (1) yields,

1) Perikinetic (Brownian ) flocculation

g q ( ) y ,

tNTkNN

T

TT

⋅⎟⎟⎠

⎞⎜⎜⎝

⎛ ⋅⋅+

=

μη

o

o

341

----- (2) NTo : Initial particle

concentration at t = 0⎟⎠

⎜⎝ μ3

1 N o

At t = t1/2 , NT = ½ NTo

2/1341

21

tNTkNN

T

TT

⋅⎟⎟⎠

⎞⎜⎜⎝

⎛ ⋅⋅+

=∴

μη

o

o

oTNTk

t⋅⋅

=∴η

μ4

32/1

from eq. (2), ⎟⎞

⎜⎛

=1 t

NN TT

o

----- (3)

⎟⎟⎠

⎜⎜⎝

+2/1

1t

1) Perikinetic (Brownian ) flocculation

For water at 25,

t11106.1 ×

=∴ ----- (4)oTN

tη2/1 =∴

(sec) (particles / ml)

(4)

< Example > A water containing only 10,000 viruses / mlt½ = 200 days. if = 1.η

Remark : 1) eq. (1), the rate constantat 25, if = 1

sec/104.534 15 lTk −×=

⋅=

μη

η,∴ compared to most chemical reactions in solution, aggregationof particles by Brownian flocculation is relatively slow process.

η

2) The removal of viruses by coagulation must require the presenceof large numbers of other colloidal particles or enmeshment ina voluminous precipitate of metal hydroxide.

V. Flocculation model

2) Orthokinetic flocculation

- Dominant mechanism of particle contact in the rapid mixingp p g

- If agitation occurs, velocity of fluid varies both spatially (from pointg , y p y ( p

to point) and temporarily (from time to time). The spatial change in

velocity is characterized by a velocity gradient Ğ. Particles whichy y y g

follow the fluid motion will also have different velocities, so that

opportunities exist for interparticle contacts.pp p

2) Orthokinetic flocculation

- From a colloidal suspension of particles having a uniform particle size, therate of change in the total concentration of particles with time due to Orthokinetic flocculation, JOk, becomes,

)(2 23Tt NdGdNJ η

(5) d : diameter of colloidal particles3

tOk dt

J −== ----- (5) p: mean velocity gradientG

μ⋅=

VPG

,2

GVP μ=

P : power input to the basin [ft-lbf /sec]: absolute viscosity [lbf -sec/ft2]μμ , V : mean velocity gradient [1/sec]

V : volume of basin [ft3]G

2) Orthokinetic flocculation

< Example > Velocity gradient ( ) of two fluid particles which are0.05 ft apart nd have a velocity relative to each other at sec/0.2 ft

G

1sec4005.0

sec/0.2 −==ft

ftG

Let Ω = volume fraction of colloidal particles (volume of colloidalparticles per unit volume of suspension)

⎞⎛⎟⎟⎠

⎞⎜⎜⎝

⎛=Ω TNd

6

3π----- (6)

Substitution eq. (6) into (5), TT

Ok NGdt

dNJ Ω−== ηπ4

----- (7)

Integration of eq. (7) for the boundary conditionsNT = NT

o at t = 0 tGNT Ωη4ln ----- (8)tG

NT

⋅⋅Ω⋅−= ηπ

lno

(8)

2) Orthokinetic flocculation

Remark : i ) The rate of Orthokinetic flocculation is 1st order with respect tothe concentration of particles, the velocity gradient, and the flocp , y g ,volume fraction (eq. (7))

Tt

Ok NGdNJ Ω−== η4----- (7)

ii) onflocculati icOrthokinetby occur contactsat which Rate

TOk dtη

π( )

TkdG

eqeq

JJOk

2)1()5.(

onflocculaticPerikinetiby occur contactsat which Rate3μ

===TkeqJ Pk 2)1.(

In water at 25 if d = 0 1 μ J = J when = 10 000 sec-1 (impossible)Gif d = 0.1 μ , JOk = JPk when = 10,000 sec (impossible)if d = 1 μ , JOk = JPk when = 10 sec-1

if d = 10 μ , JOk = JPk when = 0.01 sec-1

GGG

* in water and wastewater treatment, = 0.01 sec -1G

2) Orthokinetic flocculation

iii) Stirring will not enhance the aggregation rate of small particlesiii) Stirring will not enhance the aggregation rate of small particlesuntil they grow to a size of about 1 . Therefore flocculationtankes cannot aggregate viruses (0.1 or smaller in size) untilthey are absorbed on or an enmeshed in large particles.

iv) Once particle size reach 1 , stirring must be provided to promotefurther aggregation, because 1 particles do not settle veryrapidly.

V-2. Evaluation of mixing (Rapid mixing and flocculation)

- The types of devices usually used to furnish the agitation required in bothrapid mixing and flocculation may be generally classified :

1) Mechanical agitators (such as paddles) most common1) Mechanical agitators (such as paddles) most common2) Pneumatic agitators3) Baffle basins

Figure 2.13.Pneumatic Rapid Mixing

Figure 2.14.Baffle Basin Rapid Mixing

V-2. Evaluation of mixing (Rapid mixing and flocculation)

- By T.R.Camp, rapid mixing and flocculation are basically mixingti d tl d b th i i loperations and, consequently, are governed by the same principles

and require similar design parameters.

- Degree of mixing is based on the power imparted to water

P (It is also related to shear forces in the water

μ⋅=

VPG

(∴excessive shear forces prevent the desiredfloc formation)

- The total number of particle collisions proportional to the product ofthe velocity gradient, G, and the detention time T, (GT)the velocity gradient, G, and the detention time T, (GT)

V-2. Evaluation of mixing (Rapid mixing and flocculation)

Figure 2 5 Mixing PowerFigure 2.5. Mixing PowerRequirementsAdapted Iron Water TreatmentPlant Design by permission.Copyright 1969 The AmericanCopyright 1969. The AmericanWater Works Association.

* The relationship between the velocity gradient, the water temperatureand the power imparted to the water per unit volume.

V-3. Rapid Mixing

Although power for rapid mixing may be imparted to the water by1) Mechanical Agitation, 2) Pneumatic Agitation, and 3) Baffle Basins,

the power required for each method must be same, if the mixing is to beat the same intensityat the same intensity.

1) Mechanical Agitation) g- Most common method for rapid mixing since it is reliable, very effective,

and extremely flexible in operation.

- Usually vertical-shaft rotary mixing devices Turbine impellersP ddl i llPaddle impellersPropeller impellers

V-3. Rapid Mixing

V-3. Rapid Mixing

Figure 2.9. Types of Paddle Impellers Figure 2.10. Flow Regime inP ddl i ll T ka Paddle-impeller Tank

V-3. Rapid Mixing

Figure 2.11. Types of Propeller ImpellersAd t d f U it O ti f Ch i l E i i b W LAdapted from Unit Operations of Chemical Engineering by W. L.McCabe and J. C. Smith. Copyright 1976 by McGraw-Hill Book Co.,Inc. Reprinted by permission.

(a) StandardThree Balde

(b) Weedless (c) Guarded

V-3. Rapid Mixing

Figure 2.12. Flow Regime in a Propeller-Impeller TankAdapted from “Mixing-Present Theory and Practice Parts I and II.” bJ. H. Ruahton and J. Y. Oldshue. In Chemical Engineering Progress 46.no. 4 (April 1953); 161; and 49. no. 5 (May 1953); 267.

V-3. Rapid Mixing

- Detention times and velocity gradient for typical rapid mixing basins.

Detention time (sec) G (sec-1)20 1,00030 90030 90040 790

50 or more 70050 or more 700

* 20 ~ 60 sec are generally used.g y

V-3. Rapid Mixing

The power imparted to the liquid by various impellers- The power imparted to the liquid by various impellers.

For turbulent flow (NRe > 10,000), the power imparted by an impeller

in a baffled tank :in a baffled tank :

P = power [ft lb /sec]

iT DnKP γ53

=

P = power, [ft-lbf /sec]KT = impeller constant for turbulent flow.n = rotational speed, [rps]

cgP = p , [ p ]

Di = impeller diameter, [ft]γ = specific weight of fluid, [lbf /ft3]gc = acceleration due to gravity, [32.17 ft /sec2]

V-3. Rapid Mixing

For laminar flow (NRe < 10 to 20), the power imparted by an either( Re ), p p ya baffled or unbaffled tank is :

DK 32

c

iL

gDnKP μ32

= KL = impeller constant for Laminar flowμ = absolute viscosity [lbm / ft-sec]

μγnDN i

2

Re = NRe = Reynolds number for impeller

V-3. Rapid Mixing

Table 2.2. Values of Constants KL and KT in Eqs. (2.12) and (2.13) for BaffledTanks Having Four Baffles at Tank Wall, with Width Equal to 10Percent of the Tank DiameterPercent of the Tank Diameter

V-3. Rapid Mixing

2) Pneumatic mixing

- The detention times and velocity gradients are of the same magnitudeand range as those used for mechanical rapid mixing.

- Variation of G may be obtained by varying the air flow rate- Variation of G may be obtained by varying the air flow rate.

⎟⎞

⎜⎛ +

=34log581 hGP

P = power, [ft-lbf /sec]Ga = Air flow rate at operating temp. and⎟

⎠⎜⎝

⋅=34

log5.81 GP aGa Air flow rate at operating temp. and

pressure, [ft3 /min]h = depth to the diffusers, [ft]

3) Baffle basinsG d d h d li b l- G depends on hydraulic turbulence

- These basins have very little short-circuiting- Baffle basins are not widely usedBaffle basins are not widely used.

V-3. Rapid Mixing

- Interparticle contacts are accomplished by hydraulic mixing withinthe fluid as it flows through the tank.g

- The velocity gradient for baffle basins :γ = specific weight, [lbf /ft3]h h d l d f i i b l

ThG L

⋅⋅

=μγ hL = head loss due to friction, turbulence,

and so on.T = detention timeT detention time

* By Camp (1955) Q : flow rated i ( )

Lc hgQP ⋅⋅⋅= ρρ : mass density (v = ρ gc)hf : head loss in the tankT : detention time

ki ti i ithgQPG Lc

⋅⋅⋅⋅

=⋅

=∴υμ

ρυμ

v : kinematic viscosity

ρμ

=v

Tvhg

Th

Thg LcLLc

⋅⋅

=⋅⋅

=⋅⋅⋅

=μγ

μρ ρ

V- 4. Flocculation

- The power required for the gentle agitation or stirring of the water duringflocculation may be imparted by mechanical and pneumatic agitation.(Mechanical Most common)

- GT : related to the total No. of collisions during aggregation in theflocculation process. (104 ~ 105 : satisfactory performance)

- GCT : More accurate parameter, where c = (floc volume)/(water volume)

- G : too high the shear forces will prevent the formation of a large floc.too low Adequate interparticle collisions will not occur and a propertoo low Adequate interparticle collisions will not occur and a proper

floc will not be formed.

V- 4. Flocculation

Table 2.3. Values for Various Paddle Dimensions

Length-Width Ratio C0

5 1.20

20 1.50∞ 1.90

V- 4. Flocculation

- Peripheral velocity of paddle blades : 0.3 ~ 3.0 fps

- Total paddle-blade area on a horizontal shaft should not exceed 15 to20% of the total basin cross-sectional area, or excessive rotationalflow will resultflow will result.

- The power imparted to the water by paddle wheels may be determinedp p y p yby Newton’s law for the drag force exerted by a submerged objectmoving in a liquid.

V- 4. Flocculation

- Flocculation basins are frequently designed to provide for taperedflocculation (the flow is subjected to decreasing G values as it passesflocculation (the flow is subjected to decreasing G values as it passesthrough the flocculation basin)

G = 80 40 20 sec-1 (example)smalldense

larger, denserapid-settling

flocsp g

floc particles

M h i l i ddl h l- Most mechanical agitators are paddle wheels- Velocity of paddle blade relative to water

= peripheral blade velocity water velocity= peripheral blade velocity-water velocity= ¾ of peripheral blade velocity

V- 4. Flocculation

Properties of water in English units.

English SI

v (specific weight)lbf /ft3 kN/m3

( p g )

62.41 9.789 (20)

ρ (mass density)lbf ·sec2/ft4 kg/m3

1 936 998 21.936 998.2

μ (absolute viscosity)lbf ·sec/ft2 kg/m·s

2 735×10-5 1 002×10-32.735×10 1.002×10

v (kinetic viscosity)ft2/sec m2/s

1.410×10-5 1.003×10-6. .

g (gravity acceleration)ft/sec2 m/sec2

32.17 9.806

V- 4. Flocculation

Figure 2.16. Horizontal-Shaft Paddle-Wheel Flocculator(Cross Flo Pattern)(Cross-Flow Pattern)

V- 4. Flocculation

V- 4. Flocculation