Chapter 8-2.

Coagulation & Flocculation

V. Coagulation-Flocculation Process

Coagulation : Process of destabilization of the colloid particles.Flocculation : 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

Stable“primary” particulates

Destabilization

1 sec

Unstablemicroflocs

TransportandAttachment

Floc aggregates

Steady-statefloc sizedistribution

Floc breakup

Figure 6.7. Subprocesses controlling rate of particulate aggregation.

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

Coagulation

Flocculation

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

aggregates.3. Slow mixing Formation of larger flocs of sufficient size to separate

out.

V. Coagulation-Flocculation Process

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.① Contacts by thermal motion (Brownian motion) Perikinetic flocculation

② Contacts resulting from bulk fluid motion, for example,from transport induced by stirring Ortho kinetic flocculation

③ Contacts resulting from settling if the particles (A rapidly settling particleovertakes and collides with a particle which is settling at a slower rates) Differential movement from particle sedimentation

V-1. Flocculation model

- 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).

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

2)(34

Tt

Pk NTkdt

dNJ

NT : the total concentration of particles in

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

: Boltzman constantT : Absolute temp.

: Fluid dynamic viscosity

k

----- (1)

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

1) Perikinetic (Brownian ) flocculation

V. Flocculation model

Integration of eq. (1) yields,

tNTkNN

T

TT

341

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

concentration at t = 0

At t = t1/2 , NT = ½ NTo

2/1341

21

tNTkNN

T

TT

TNTk

t

4

32/1

from eq. (2),

2/1

1tt

NN TT

----- (3)

1) Perikinetic (Brownian ) flocculation

V. Flocculation model

For water at 25,

TN

t

11

2/1106.1

(sec) (particles / ml)

----- (4)

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

Remark : 1) eq. (1), the rate constantat 25, if = 1∴ compared to most chemical reactions in solution, aggregationof particles by Brownian flocculation is relatively slow process.

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.

sec/104.534 15 lTk

1) Perikinetic (Brownian ) flocculation

2) Orthokinetic flocculation

- Dominant mechanism of particle contact in the rapid mixing

- If agitation occurs, velocity of fluid varies both spatially (from point

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

velocity is characterized by a velocity gradient Ğ. Particles which

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

opportunities exist for interparticle contacts.

V. Flocculation model

- 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,

3)(2 23

TtOk

NdGdt

dNJ ----- (5) d : diameter of colloidal particles

: mean velocity gradientG

VPG

,2

GVP

P : power input to the basin [ft-lbf /sec]: absolute viscosity [lbf -sec/ft2]: 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

1sec4005.0

sec/0.2 ft

ft

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

TNd

6

3----- (6)

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

Ok NGdt

dNJ 4

----- (7)

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

o at t = 0 tG

NN

T

T 4ln

----- (8)

2) Orthokinetic flocculation

sec/0.2 ftG

G

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

ii)

TkdG

eqeq

JJ

Pk

Ok

2)1.()5.(

onflocculati cPerikinetiby occur contactsat which Rateonflocculati icOrthokinetby occur contactsat which Rate

3

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

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

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

GGG

G

2) Orthokinetic flocculation

Tt

Ok NGdt

dNJ 4

----- (7)

iii) 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.

2) Orthokinetic flocculation

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 common2) Pneumatic agitators3) Baffle basins

Figure 2.13.Pneumatic Rapid Mixing

Figure 2.14.Baffle Basin Rapid Mixing

- By T.R.Camp, rapid mixing and flocculation are basically mixingoperations and, consequently, are governed by the same principlesand require similar design parameters.

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

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

VPG

(It is also related to shear forces in the water∴excessive shear forces prevent the desired

floc formation)

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

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

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

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

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 intensity.

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

and extremely flexible in operation.

- Usually vertical-shaft rotary mixing devices Turbine impellersPaddle impellersPropeller impellers

V-3. Rapid Mixing

V-3. Rapid Mixing

Figure 2.9. Types of Paddle Impellers Figure 2.10. Flow Regime ina Paddle-impeller Tank

V-3. Rapid Mixing

Figure 2.11. Types of Propeller ImpellersAdapted 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 90040 790

50 or more 700

* 20 ~ 60 sec are generally used.

V-3. Rapid Mixing

- 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 :

c

iT

gDnKP 53

P = power, [ft-lbf /sec]KT = impeller constant for turbulent flow.n = rotational speed, [rps]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 eithera baffled or unbaffled tank is :

nDN i

2

Re

c

iL

gDnKP 32

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

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 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.

34

34log5.81 hGP a

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

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

3) Baffle basins- G depends on hydraulic turbulence- These basins have very little short-circuiting- Baffle basins are not widely used.

V-3. Rapid Mixing

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

- The velocity gradient for baffle basins :

ThG L

γ = specific weight, [lbf /ft3]hL = head loss due to friction, turbulence,

and so on.T = detention time

* By Camp (1955)

Lc hgQP

Tvhg

Th

Thg

hgQPG

LcLLc

Lc

Q : flow rateρ : mass density (v = ρ gc)hf : head loss in the tankT : detention timev : kinematic viscosity

v

V-3. Rapid Mixing

- 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 proper

floc will not be formed.

V- 4. Flocculation

V- 4. Flocculation

Length-Width Ratio C0

5 1.20

20 1.50∞ 1.90

Table 2.3. Values for Various Paddle Dimensions

- 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 result.

- The power imparted to the water by paddle wheels may be determinedby 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 passesthrough the flocculation basin)

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

larger, denserapid-settlingfloc particles

- Most mechanical agitators are paddle wheels- Velocity of paddle blade relative to water

= 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

62.41 9.789 (20)

ρ (mass density)lbf ·sec2/ft4 kg/m3

1.936 998.2

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

2.735×10-5 1.002×10-3

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-Flow Pattern)

V- 4. Flocculation

V- 4. Flocculation

V- 4. Flocculation