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5. Sedimentation Process Main Topics: 5.1 Introduction 5.2 Discrete particle settling theory 5.3 Discrete particle settling in sedimentation basins 5.4 Flocculent particle settling in sedimentation basins 5.5 Zone settling 5.6 Conventional sedimentation basin design 5.7 Innovations in sedimentation basin design 5.8 Physical factors affecting sedimentation 5.9 Dissolved air flotation systems Reference: 1. Crittenden et al., Water Treatment Principles and Design, Chap 10. 5.1 Introduction Sedimentation is the process of removal of suspended particles that are heavier than water by gravitational settling. Most raw water will contain mineral and organic particles. The density of mineral particles is usually between 2000 to 3000 kg/m3 and can easily settle out by gravity. Organic particles, on the other hand, have densities ranging from 1010 to 1100 kg/m3 and take a long time to settle by gravity. In conventional water treatment, coagulants are used to destabilize particle to form larger and settlable solids. The relevant terms with respect to sedimentation are: (a) Plain Sedimentation: refers to the separation of suspended particles from liquid by

gravitation and natural aggregation of settling particles. Examples are settling of sand in filtration and the settling of grits, and sandy and silty particles in pre-sedimentation treatment. Such particles are usually greater than 10 µm in size.

(b) Coagulation and Flocculation: the addition of chemicals or other substances to induce

or hasten aggregation and settling of finely divided suspended matter, colloidal substances, and large molecules. Examples are the removal of colour and turbidity in water.

(c) Chemical precipitation: the addition of chemicals to remove dissolved impurities such

as hardness, Fe, Mn, etc. out of the solution. The sedimentation process can be used to treat raw water containing suspensions ranging from a very low concentration of nearly discrete particles to a high concentration of flocculent solids. Particles can be classified based on their concentrations and morphology: Type I – discrete particles: the settling of relatively low concentration of discrete particles that will not readily flocculate or grow in size. An example is the settling of granular particles after backwashing in the filtration process; and in pre-sedimentation basins.

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Type II – flocculent particles: the settling of relatively low concentration of flocculent material. An example is the settling of coagulated water. Type III: also known as zone settling, occurs when the settling velocities of particles are affected by the presence of other particles. An example is at the lower regions of the sedimentation basin where the concentration of suspended particles is highest. Also known as hindered settling. The material may be flocculent. Another example is sludge thickening. Type IV: also known as compression settling occurs when particle concentration is higher than Type III settling. The particles are not readily settled; but rather, water flows or drains out of a mat of particles.

Fig. 1 Settling characteristics of solids in water. 5.2 Discrete particle settling theory (Type I settling) A discrete particle is one that does not alter in size, shape or weight while settling. In falling through a quiescent liquid, such a particle accelerates until the gravitational force (FG) is equaled by the sum of particle drag (FD) and buoyancy forces (FB).

FG – FB – FD = dtdv m s (1)

where m is the particle mass (kg). Thereafter, the particle settles at a uniform velocity known as terminal velocity (vs), which is an important hydraulic characteristic of the particle. At

terminal velocity, dtdv m s = 0, and forces acting on the particle are thus: FG – FB = FD

ρs g Vp – ρw g Vp = 12

CD Ac ρw vs2 (2)

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where ρs = density of particle, kg/m3

ρw = density of liquid, kg/m3 (= 1000 kg/m3 for water) Vp = volume of particle, m3 CD = drag coefficient, dimensionless

Ac = cross-sectional area of particle, m2 vs = terminal settling velocity of particle, m/s g = acceleration due to gravity = 9.81 m/s2 The terminal velocity vs of a discrete particle depends on its size, shape, and density, and also the density and viscosity of the liquid. For spherical particles,

Vp = 6d 3π (3) Ac =

4d 2π (4)

The general equation for sedimentation of discrete spherical particles described by Newton’s law is by substituting Eqn. (3) and (4) into (2):

w

ws

Ds

)(Cgd

34v

ρρ−ρ

= (5)

The drag coefficient CD is dependent on the settling velocity and diameter of the particle d, and the density and viscosity of water, which are represented by the dimensionless Reynolds number, Re, with µ being the absolute viscosity of water in kg m/s or Ns/m2, and υ = kinematic viscosity in m2/s.

forces viscousforces inertiadvdvRe ssw ≈

υ=

µρ

= (6)

(a) Laminar flow regime (Re ≤ 1) For Reynolds numbers Re ≤ 1 (for particles that are very small, and with very low settling velocities), CD is related to Re by the linear relationship in Eqn. 7.

Fig. 2 Drag coefficients for varying Reynolds number.

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Re24CD = (7)

Eqn. (5) can be simplified as follows, which is also known as Stokes’ law:

µρ−ρ

= 18

d)(gv2

wss (8)

(b) Transitional flow regime (1<Re ≤10,000) This occurs when Reynolds number is between 1<Re ≤10,000. The relationship between CD and Re is non-linear but can be approximated by:

34.0Re3

Re24CD ++= (9)

In this Re range, Eqn. 5 is used to compute the settling velocity of particles. (c) Turbulent flow regime (Re >10,000) In the turbulent flow regime, Reynolds numbers are high (Re >10,000), and CD is approximately 0.4 (see Fig. 2). The settling velocity relationship becomes:

w

wss

)(gd

310v

ρρ−ρ

= (10)

Example 1 (a) Determine the settling velocity of alum (aluminum hydroxide) flocs of diameter d = 1 µm

and ρs = 1020 kg/m3. Take µ of water = 0.89 x 10-3 Ns/m2 for water at 25oC.

Assume laminar flow condition. Applying Eqn (8): vs = 12247 d2 (d in metres)

For d = 1 µm, vs = 1.22 x 10-8 m/s

Check Reynolds number using Eqn. 6: Re = 10-8 < 1 ok. Laminar flow condition. (b) Determine the settling velocity of alum flocs of diameter d = 1000 µm and ρs = 1020

kg/m3.

Assume laminar flow condition: for d = 1000 µm, vs = 0.01225 m/s

Check Re = 14 > 1 Stokes’ law is not valid: need to use Eqn. (5).

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(c) Determine the settling velocity of sand grains of diameter d = 1 mm and ρs = 2650 kg/m3.

Assume laminar flow condition: for d = 1 mm, vs = 1.01 m/s Check Re = 1135 > 1 Stokes’ law is not valid: need to use Eqn. (5).

Note: solving Part (b) and (c) in the above example using Eqn. (5) require trial and error. Figure 3, which is based on Eqn. (5) can be used to estimate the settling velocity for a given particle diameter and specific gravity.

Fig. 3 Settling velocity of particles (Reynolds & Richards, 1996).

Non-spherical shaped particles For non-spherical shaped particles, CD is higher for a given Re value, which will result in a lower settling velocity vs. This effect is more critical in the turbulent flow region. A correction factor for d – the sphericity factor ψ, is used. It is obtained as a ratio of the surface area of the actual particle to that of an equivalent spherical particle:

ψ = sphericity = ( )( )particlep

spherep

V/A

V/A

particle of area surfacesphere volumeequivalentan of area surface

= (11)

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or d’ = ψ d (12) where d’ = effective spherical diameter to be used in the computations, m d = diameter of actual particle, m ψ = 0.8 for sharp, angular sand; 0.94 for worn sand Fractal particles Flocculated particles have a fractal morphology composing many flocculated small particles. They do not settle as rapidly as a hard-sphere and do not follow the Stokes’ or Newton’s law. Brownian Motion There are many very small colloidal particles in natural waters that do not settle because of Brownian motion – causing them to move and overcome gravitation settling forces. This random motion can be computed by the following equation. When vB > vs (from Stokes’ law), particles will not settle out of solution.

⎟⎟⎠

⎞⎜⎜⎝

⎛πµ∆

=d3Tk2

x1v B

B (13)

where vB = particle velocity in one direction due to Brownian motion, m/s kB = Boltzmann’s constant, 1.38 x 10-23 Nm/K T = absolute temperature, K (273 + oC) ∆x = net distance traveled in x-direction due to Brownian motion, m µ = absolute or dynamic viscosity of water, Ns/m2 d = particle diameter, m Example 2 Calculate the smallest settleable sand particle (sg = 2.65) in water at 25oC (µ = 0.89 x 10-3 Ns/m2). Assume the Brownian velocity that must be overcome for settling to occur is based on a travel distance of 0.01 m.

d1081.9

d3Tk2

x1v

17B

B−×

=⎟⎟⎠

⎞⎜⎜⎝

⎛πµ∆

= m/s

µ

−ρ=

µρ−ρ

=18

d)sgsg(g18

d)(gv2

wp2s

s = 1.01 x 107 d2 = (9.81 x 10-17)/d

d = 2.1 x 10-8 m = 0.02 µm

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5.3 Discrete particle settling in sedimentation basins (a) Rectangular sedimentation basins The study on settling of discrete particles is best described using an ideal sedimentation tank as shown in Fig. 4. There are four distinct zones in the ideal tank: inlet zone, settling zone, sludge zone, and outlet zone.

Fig. 4 Functional regions within a rectangular basin.

The following assumptions are made in developing the tank’s removal efficiency equations: • horizontal flow in the settling zone • uniform horizontal velocity in the settling zone • uniform concentration of all-size particles across a vertical plane at the inlet end of the

settling zone • particles are removed once they reached the bottom of the settling zone • particles settle discretely without interference from other particles at any depth The theoretical design of sedimentation processes is based on the concept of the ideal settling tank. A schematic tank with flow and dimensional parameters is shown in Fig. 5. All particles in the settling zone travel in a straight line path.

Fig. 5 Trajectories of discrete particles in the settling zone of a rectangular basin (Crittenden).

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As shown, there are two components to the particle trajectories in the settling zone: the settling velocity vs, and the horizontal fluid velocity vh. Discrete particle 1 which enters at the top of the basin is not removed in the sludge zone but will be carried into the outlet zone by the flow. A second particle 2 enters at the top of the basin and settles in the sludge zone just before the outlet, is assigned a settling velocity of vo or the critical settling velocity, which can be computed from:

thv o

o = (14)

where vo = critical settling velocity of particle, m/h

ho = depth of sedimentation basin, m t = hydraulic detention time of basin, h

Since t = V/Q and V = A ho,

SORAQ

AhQh

Q/Vh

thv

o

oooo ===== (15)

where SOR = surface overflow rate, m3/m2.h

Q = flow rate of water, m3/h A = area of top of basin (=length L x width W), m2 V = volume of basin, m3

The inlet zone is assumed to be homogenous and particles enter the settling zone at any height hs. Particles with settling velocity vs ≥ vo will be removed, regardless of the height it enters. Particles with a settling velocity less than vo may also be removed, depending on their position at the inlet (e.g. particle 3). The fraction of these particles that can be removed is given by:

v v

tv tv

hhX

o

s

o

s

o

sr === (16)

where Xr = fraction of particles with vs < vo removed in a horizontal flow tank vs = velocity of specified particle size, m/s vo = critical velocity defined as ideal tank surface overflow rate, m/s (b) Circular sedimentation basins The settling of discrete particles in a circular sedimentation basin is shown in Fig. 6. These particles have a parabolic trajectory due to the change in the horizontal water velocity from the basin centre (inlet):

oih h)rr(2

Qv−π

= (17)

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where r = distance measured from centre of basin, m ri = radius of inlet zone, m The trajectory of particle 1 starts at the top of the inlet zone and enters the sludge zone just before the outlet. The settling velocity of particle 1 is thus the critical settling velocity:

SORAQ

)rr(Q

h)rr(Qh

Q/Vh

thv 2

i2oo

2i

2o

oooo ==

−π=

−π=== (18)

where ro = radius of the inlet and settling zones, m

Fig. 6 Trajectories of discrete particles in the settling zone of a circular basin (Crittenden).

Scouring of bed settled material Actual sedimentation in a water treatment plant clarifier operation is more complex than the ideal settling concept. Particle interaction and currents in the settling area are the most significant effects that can alter the particle settling paths and may also scour particles already settled. To avoid bottom scouring, the flow velocity in the tank should be less than the critical scour velocity for discrete particle suspensions:

d)1S(gfk8v sscour −= (19)

where vscour = scour velocity, m/s k = 0.04 for sand and 0.06 for “sticky” material f = Darcy Weisbach friction factor, ranges between 0.02 and 0.03

Ss = w

sρρ

= specific gravity of particle

d = diameter of particle, m

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Example 3 Calculate the scouring velocity for settled particles having the following characteristics: d = 1 mm and 0.1 mm; f = 0.03 k = 0.06 for sticky material; Ss = 1.1 (a) d = 1 mm

3scour 101)11.1(81.9

03.006.08v −××−××

×= = 0.125 m/s or 451 m/hr

(b) d = 0.1 mm

3scour 101.0)11.1(81.9

03.006.08v −××−××

×= = 0.04 m/s or 142.6 m/hr

Settling tanks are normally less than 100 m long, with detention times in the order of a couple of hours. Thus, horizontal flow velocity vh = L/t is less than 100 m/hr and scouring of the above small particles would not happen. Removal rate for a suspension of discrete particles A graphical procedure is often used to determine an approximation of overall removal of discrete particles in a suspension. The results can be obtained by carrying out a settling column test on a suspension of particles and plotted as shown:

Fig. 7 Typical discrete particle settling curve.

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Procedure for determining the overall removal efficiency of a suspension of discrete particles: (1) Prepare a discrete settling curve as shown in Fig. 7 (2) Integrate the area to the left of the curve representing overall removal efficiency: Fraction removed:

Pv

v1)P1(

dP vv

)P1(X

i s

oo

oP

0 o

sor

∆+−=

+−=

∑

∫ (20)

Xr = I

ECC1− (21)

where Po = fraction of particles with vs < vo

(1 – Po) = fraction of particles with vs ≥ vo CE = effluent concentration CI = influent concentration

Pvv1 or dP

vv

i s

o

oP

o o

s ∆∑∫ = fraction of particles with vs < vo but are removed

Fraction remained = I

ECC

= Po Pvv1

i s

o∆− ∑ (22)

Example 4: Removal of a suspension of silica particles ρs = 2650 kg/m3 ρ = 1000 kg/m3 µ = 1x 10-3 Ns/m2 Size interval (µm) 0-10 10-

20 20-30

30-40

40-50

50-60

60-70

70-80

80-100

Weight fraction 0.05 0.2 0.25 0.2 0.15 0.075 0.05 0.02 0.005

Assume laminar flow:µρ−ρ

=18

d)(gv

2s

s = 0.9 x 106 d2 m/s

Check: For largest sand size d = 100 µm, v s = 0.009 m/s, µ

ρ=

dvRe sw = 0.9 < 1 ok

Average size, d (µm) 5 15 25 35 45 55 65 75 90 v s (m/s) x 10-3 0.02 0.2 0.56 1.1 1.8 2.7 3.8 5 7.3 v s (m/hr) 0.08 0.72 2 4 6.5 9.7 13.7 18 26.3 P (wt. fraction < v s) 0.05 0.25 0.5 0.7 0.85 0.925 0.975 0.995 1 Plot graph of settling velocity of particles v s (m/hr) versus the respective weight fraction, P.

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Suppose vo = 4 m/hr. From plot, Po = 0.7.

Mass fraction removed = (1 – 0.7) + Pvv1

i s

o∆∑ ≅ 0.3 + 0.25 = 0.55 or 55%

= I

ECC1−

If CI = 10 mg SS/L, effluent SS concentration CE = 4.5 mg/L. Repeating procedure for different vo, relation between mass fraction removed and surface overflow rate is obtained:

Summary for Type I discrete settling: removal efficiency in an ideal sedimentation basin depends on the basin’s overflow rate only and is independent of depth and hydraulic detention time.

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5.4 Flocculent settling in sedimentation basins (Type II settling) In Type II settling, particles flocculate either by velocity gradients or by differential settling in the sedimentation basin i.e. they tend to coalesce into a bigger particle during settling. Flocculent settling has two advantages over discrete settling: (1) the combination of smaller particles to form larger ones results in a faster settling particle

because of increase in diameter (2) flocculation tends to have a sweeping effect in which large particles settling at a velocity

faster than slow particles tends to sweep some of them from suspension. Tiny particles which otherwise would not settle are removed.

Again, the design of sedimentation tanks in removing flocculent particles can be based on settling column tests. The depth of the column is normally equal to or greater than the depth of the proposed tank. The diameter of the column is about 150 to 300 mm and sampling ports are provided at 500 mm intervals. A suspension is poured into the column and gently mixed with a perforated plunger to obtain a uniform dispersion of particles. At predetermined time intervals, samples are removed from the ports and analyzed for suspended solids concentrations. Experimental data of suspended solids removal are then plotted on a time-depth graph as shown:

Fig. 8 Typical pilot settling test results for flocculent suspension (for Eqn 23).

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The overall percent removal, Xr, can be calculated using:

⎟⎠

⎞⎜⎝

⎛ +∆+⎟

⎠

⎞⎜⎝

⎛ +∆

+⎟⎠

⎞⎜⎝

⎛ +∆+⎟

⎠

⎞⎜⎝

⎛ +∆+⎟

⎠⎞

⎜⎝⎛ +∆

=

2RnR

ZZi

2RR

ZZ

2RR

ZZ

2RR

ZZ

2RR

ZZX

5

6

54

6

4

43

6

332

6

221

6

1r

(23)

where Xr = percent removal of total suspended solids ∆Z = water depth between iso-removal lines, m Z = water depth from surface, m

R = removal percentages (Rn = removal corresponding to design water depth & time) Another method of computing the overall removal and is used in many other textbooks is:

nn1-no

n21

o

21

o

1T R)R-(R

hh....)R-(R

hh)R-(100

hhR ++++= (24)

where: h1, h2, …., hn = vertical distance from the top of the settling column to the mid-point between two consecutive lines of iso-removal at desired detention time ho = desired design side water depth R1, R2,….., Rn-1 = consecutive iso-removal curves in percent removal RT = Total removal, percent (equivalent to Xr in Eqn. 23)

Fig. 9 Settling trajectories for a flocculent suspension (for Eqn. 24).

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The accuracy of estimation can be improved by decreasing the interval between iso-concentration lines and adding more terms to the removal equation. The test results allow the overflow rate and detention time for a sedimentation tank to be determined. Non-ideal conditions in actual sedimentation tanks such as short-circuiting, inlet and outlet turbulence, density, and temperature-induced currents result in reduced removal efficiency compared to that obtained from settling column test. To compensate for the non-ideal conditions, a factor of safety equal to 0.65 to 0.85 for the overflow rate and 1.75 to 2 for the detention time are recommended. (Hence, corrections are to have a smaller SOR and a longer retention time). Since flocculent particles tend to grow in size during settling, the depth of the settling tank and detention time are important design parameters. Deeper tanks improve the possibility of bigger particles to sweep smaller particles from suspension. Deeper tanks therefore perform better in removing flocculent particles. Example 5 The results of a column settling test are given in the following table. Find the overall removal for a settling basin 1.75 m deep with an overflow rate of 105 m/d.

Percent removal of particles at various time Water depth from

surface 5 min 10 min 20 min 30 min 40 min 50 min

0.5 m 14* 17 56 66 74 79 1.0 m 13 16 49 50 71 - 1.5 m 12 17 43 47 70 72

* Percent removal = [(TSSI – TSSF)/TSSI] x 100% where TSSI = initial suspended solids concentration in column, mg/L

TSSF = suspended solids concentration in sample after certain time, mg/L Indicate the numerical percent removals on a plot of time versus water depth as shown in Fig. 9. Draw the iso-removal lines at 15% intervals, by interpolating the numerical values. Surface overflow rate = 105 m/d = ho/t For ho = 1.75 m, the required detention time t = 1.75m/(105 m/d) = 24 min From Fig. 9, 45% of particles are having settling velocities greater than SOR = 105 m/d The overall particles removal can be computed using: Equation (23): ∆Z1 = 0.2m, ∆Z2 = 0.3m, ∆Z3 = 1.25m, Z4 = 1.75m,

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R1 = 100%, R2 = 75%, R3 = 60%, R4 = 45%

⎟⎠⎞

⎜⎝⎛ +

+⎟⎠⎞

⎜⎝⎛ +

+⎟⎠⎞

⎜⎝⎛ +

=2

456075.125.1

26075

75.13.0

275100

75.12.0Xr = 59%

Equation (24): h1 = 0.1m, h2 = 0.35m, h3 = 1.1m, ho = 1.75m, R1 = 100%, R2 = 75%, R3 = 60%, R4 = 45%

45)45-(601.751.1)60-(75

1.750.35)75-(100

1.750.1R T +++= = 58.9%

5.5 Zone settling (Type III settling) In zone settling, the settling velocities of individual particles decrease due to the interaction of particles as they settle. When this occurs, the particle aggregates tend to form a blanket with a distinct interface between the settling particles and the clarified supernatant. Zone settling or Type III settling usually occurs at the lower region of a sedimentation tank where the concentration of suspended solids is highest. In water treatment, zone settling is more of importance to sludge thickening rather than settling tank performance. The concept of zone settling is illustrated in the figure. Initially, a uniform suspension of concentration B is poured into a column and a distinct interface forms at the top separating the supernatant A after some time. The settling of particles at B is considered to be hindered, changing to compaction at C and a layer of dense sludge forms at the bottom D.

Fig. 10 Typical zone settling column test.

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5.6 Conventional sedimentation basin design (a) Pre-sedimentation basins They are used to remove easily settleable sand and silt, especially from river raw water source, prior to pumping to the treatment plant. A minimum of two basins is required so that one can be taken out of service for maintenance. For rectangular basins, the length can be estimated by:

hs

o vvhKL ⎟⎟

⎠

⎞⎜⎜⎝

⎛= (25)

where L = basin length, m K = safety factor (typically 1.5 to 2) ho = effective water depth, m vs = settling velocity of particle to be removed, m/s vh = mean water velocity at maximum day flow rate, m/s

Table 1 Typical pre-sedimentation basin design criteria (Crittenden).

Parameter Value Depth (m) 3.5 – 5 Minimum length to depth ratio 6 : 1 Length to width ratio 4: 1 to 8: 1 Surface overflow rate m3/m2.d 200 – 400 Horizontal mean flow velocity (at maximum daily flow), m/s 0.05 Detention time, min 6 – 15 Minimum size of particle to be removed, mm 0.1 Bottom slope, m/m Minimum 1: 100 (b) Rectangular sedimentation basins The common shapes of conventional sedimentation tanks in water treatment and reclamation are rectangular, circular, or square. In rectangular basins, the influent flow is distributed across the entire cross-section of the basin by an inlet baffle structure, which provides energy dissipation and uniform flow distribution. The outlet structure usually comprises a system of effluent launders located on the opposite side of the tank.

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Fig. 11 Rectangular sedimentation basin (Crittenden).

Table 2 Typical rectangular sedimentation basin design criteria (Crittenden).

Parameter Value Depth (m) 3 – 5 Length to depth ratio, minimum 15 : 1 Length-to-width ratio 4: 1 to 5: 1 Surface overflow rate m3/m2.d 30 – 60 Horizontal mean flow velocity (at maximum daily flow), m/s 0.005 – 0.018 Detention time, h 1.5 – 4 Launder weir loading, m3/m.h 9 – 13 Reynolds number <20,000 Froude number >10-5 Bottom slope, m/m 1: 600 to 1 : 300

Weir overflow rate = Q/total weir length (m3/m.h) (26)

The Reynolds number Re and the Froude number Fr are used as a check on turbulence and backmixing. The recommended values for settling zone design are: Re < 20,000 to avoid high degree of turbulence; and Fr > 10-5 to prevent backmixing (back motion of water).

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υ= hhRvRe (27)

where Re = Reynolds number based on hydraulic radius vh = average horizontal fluid velocity in tank, m/s Rh = hydraulic radius = Ax/Pw, m Ax = cross-sectional area, m2

Pw = wetted perimeter, m υ = kinematic viscosity, m2/s

h

2h

gRvFr = (28)

where Fr = Froude number g = acceleration due to gravity, 9.81 m/s2 (c) Circular sedimentation basins Circular basins are fed from a central inlet or from the peripheral. Effluent structures are normally consisting of a V-notch weir constructed at the outside perimeter of the tank. Diameters of tanks are calculated from the overflow rates. Square basins have the advantage of common-wall construction as in rectangular tanks. Effluent launders are also constructed along the perimeter of the basins.

Fig. 12 Circular sedimentation basins (a) centre feed (b) peripheral feed (Crittenden).

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5.7 Innovations in sedimentation basin design Variations in basic sedimentation basin design have been employed to enhance the performance of the sedimentation process. (a) Laminar-flow devices Sedimentation can be accelerated by increasing particle size or decreasing the distance a particle must fall for removal. This can be achieved by coagulation and flocculation to increase particle size. A shorter fall distance can be achieved by providing parallel plates (commonly called plate settlers) or square-shaped tube (commonly called tube settlers) near the outlet of the basin. The plate spacing or tube sizes and feed rates are set to maintain laminar flow at all times. Alum coagulated sludge can remain deposited in the tubes at an angle as steep as 60o from the horizontal. Launders are usually spaced at 3 to 4 m.

Fig. 13 Rectangular basin with (a) incline plate settlers and (c) tube settlers (Crittenden).

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Table 3 Typical design criteria for horizontal-flow rectangular tanks with plates and tube settlers (Crittenden).

Parameter Value

Depth (m) 3 – 5 Surface overflow rate for alum floc, m/h 2.5 – 6.25 Surface overflow rate for heavy floc, m/h 3.8 – 7.5 Typical hydraulic diameter, mm 50 – 80 Maximum flow velocity, m/min 0.15 Detention time in tube settlers, min 6 – 10 Detention time in plates settlers, min 15 – 25 Fraction of basin covered by plates or tube settlers < 75% Launder weir loading, m3/m.h 3.75 – 15 Plate or tube angle 60o Reynolds number <20,000 Froude number >10-5 Process configuration There are three alternatives for placement of tubes or plates in a sedimentation basin: (a) countercurrent (b) co-current, and (c) cross-flow. Only the countercurrent inclined settling system is covered here.

Fig. 14 Flow patterns for inclined countercurrent settling systems (Crittenden).

The settling time for a particle to move between two parallel plates is given by:

θ=

cosvdt

s (29)

22

where t = settling time of particle, s d = distance between two parallel plates (perpendicular to plates), m vs = particle settling velocity, m/s θ = inclination angle of plates from horizon If flow in the plates is uniform, the particle travel time spent in the plates is:

θ−=

θ sinvvL

tsf

pp (30)

where tp = particle travel time spent in the plates, s Lp = length of plate, m vfθ = fluid velocity in channel, m/s Consider the particle trajectory shown in Fig.14, all of the particles with settling velocity vs will be removed when tp = t. Particles with settling velocities > vs are removed. Hence, for a given d and Lp, the smaller is the vs/vfθ ratio, the better is the removal of particles. Equating tp = t,

θ+θ= θ

sindcosLd vv

p

fs (31)

The fluid velocity may be determined from the number of channels:

w d NQvf =θ (32)

where Q = flow rate, m3/s N = number of channels d = distance between two parallel plates (perpendicular to plates), m w = width of channel, m The fluid velocity is also related to the overflow rate of the basin assuming that the surface area of the basin is comprised of plates:

since wsin

dNAθ

= , θ

=θ sinAQvf (33)

where A = plan area of basin, m2 Example 6 A sedimentation basin is to be retrofitted with 2 m square inclined plates spaced 50 mm apart. The plates are arranged for countercurrent flow. Determine if the angle of inclination of the plates should be 60o or 80o from the horizon.

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Rewriting Eqn. 31, θ+θ

=θ+θ

=θ sin05.0cos2

05.0sindcosL

d v

v

pf

s

For θ = 60o, 048.0 v

v

f

s =θ

For θ = 80 o, 126.0 v

v

f

s =θ

Select θ = 60o since the vs/vfθ ratio is smaller – for a given fluid velocity vfθ, vs will be small, hence more particle can be removed (settled on the plates). (b) Solids-contact clarifiers Such devices employ a sludge blanket at the bottom of the basin to promote flocculation and enmeshment of incoming solids. The same removal efficiency as in conventional sedimentation process can be achieved at higher loading rates. Figure 15 shows a solids-contact clarifier where coagulation and flocculation take place with sedimentation in one tank. The flow, however, does not pass through the sludge blanket. An example of this kind of clarifiers is a centre feed circular tank where coagulation and flocculation occur in a central conically shaped compartment.

Fig. 15 A solids-contact clarifier. For sludge blanket clarifiers (Fig. 16), there is a distinct layer or blanket of suspended solids which acts as a filter, trapping smaller particles which would otherwise following the up-flowing water out of the tank.

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Fig. 16 A sludge blanket clarifier.

(c) Proprietary sedimentation systems A number of proprietary systems that can enhance sedimentation are also available in the market. These systems are mostly modifications of the solids-contact clarifier. One is the Degremont pulsator clarifier (Fig. 17), which is used in Singapore. Water is fed through the bottom laterals. The feed rate is not constant. Instead, a specially designed vacuum chamber produces a pulsating flow.

Fig. 17 The Pulsator clarifier.

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The two-tray system offers a large sedimentation area in a relatively compact space by effectively stacking one basin on top of another. Flocculated water is fed through a perforated wall into a bottom chamber. The water flows horizontally to the end of the basin, then upwards into the upper chamber. The water then flows horizontally to the outlet zone in the end of the upper chamber. A chain-and flight sludge collection system sweeps the sludge along the floor into the lower chamber, where it settles and then raked to the sludge pit to be pumped out of the system.

Fig. 18 The two-tray sedimentation basin.

5.8 Physical factors affecting sedimentation A number of factors not considered in the design of sedimentation basins can affect the basin performance. These are temperature gradients, wind effects, inlet energy dissipation, outlet currents, and equipment movements. Temperature differentials When warm influent water overflows into a sedimentation basin of cold water, it flows over it and reaches the outlet weirs in a much shorter time than the theoretical hydraulic retention time. This leads to the phenomenon of short-circuiting where bigger suspended particles can be carried away without settling due to the higher flow velocity.

Fig. 19 Surface density currents (Crittenden).

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On the other hand, cold water entering a basin of warmer water tends to flow along the tank bottom as they are heavier (e.g. at 4oC, ρw = 1000 kg/m3; at 20oC, ρw = 998 kg/m3) and rise at the outlet end (Fig. 20).

Fig. 20 Bottom density currents (Crittenden).

Solids concentration effects Density currents may also be caused by changes in influent solids concentration as a result of flash flood or strong winds on reservoir surfaces which increase the suspended solids (SS) concentration in water. Increase in solids concentration will increase the density of influent causing it to dive to the bottom of the basin. (e.g. at 100 mg SS/L, density of mixture =1000.06 kg/m3; at 10,000 mg SS/L, density of mixture = 1006 kg/m3) Wind effects Strong wind can cause water to overflow the outlet weir in addition to causing a surface current in the direction of the wind. There will be a return flow of water at the bottom of the tank in the opposite direction. Thus, wind actions can also cause short-circuiting of flow from inlet to outlet as well as scouring of settled particles at the bottom of the basin.

Fig. 21 Wind-induced currents (Crittenden).

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Inlet energy dissipation The design of the inlet of a sedimentation tank can significantly influence its performance. Influent water normally enters the basin via a pipe at a sufficient velocity to keep the flocculated particles in suspension. At the inlet, the flow is distributed across the basin section for the sedimentation process and the flow slows down significantly. This sudden reduction in energy is achieved by using baffles to dissipate the energy. If the baffles are not properly designed, density and eddy currents will be created and may cause short-circuiting of flow. Outlet currents The design and location of the outlet weirs are of equally importance in the basin performance. If the weir length is too short, outlet currents may form and sweep settleable particles into the effluent. V-notch weirs are normally used to allow better lateral distribution of outlet flow when basin level is imperfect. Equipment movement The movement of equipment within the basin can affect its performance. Chain-and-flight scrapers, bridge-mounted scrappers, or hydraulic suction units are often used to remove settled sludge from the basin. Their movements, if excessive, will introduce currents which can stir up the settled particles and upset the sedimentation process.

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5.9 Dissolved air flotation systems Commonly used in waste treatment for sludge thickening, dissolved air flotation (DAF) has also been used in water treatment. It is a unit operation where solids are removed from the liquid by attaching to rising air bubbles. There are three steps in the flotation process: bubble generation, attachment of solids to the bubbles, and solids separation. The figure shows a DAF system where raw water is first coagulated and flocculated prior to entering the DAF basin. The water enters the basin near the bottom beneath a baffle to prevent short-circuiting. At the same entry point, a cloud of air bubbles called white water (typically 10 to 100 µm) is released and adhere to floc particles and causing them to float. The layer of solids formed on the water surface, known as float, is collected at the effluent end of the basin and is removed into a collection trough by a mechanical skimmer. Clarified water is removed through a perforated pipe system near the bottom of the basin.

Fig. 22 Schematic of a DAF system (Crittenden). Generally, DAF is most effective when it involves the removal of: (a) low-density particulate matter such as algae (b) water with dissolved organic matter e.g. natural colour (c) low-density flocs resulting from coagulation and flocculation of low- to moderately-turbidity waters (d) low-temperature waters as particulates are more difficult to settle Important factors affecting DAF process Floc characteristics – small, low-density floc is more suitable for DAF as oppose to large, readily settleable floc for gravity sedimentation. This may be achieved by reducing coagulant

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dosage, reducing flocculation time (e.g. to 5 min), higher flocculation energy (G from 50 to 100 s-1), and not using polymers. Bubble size – micro-bubbles are generated by aerating the recycled stream at an elevated pressure. When the super-saturated air is mixed with water, pressure is released and micro-bubbles are formed. As floc-air bubble attachment is a surface phenomenon, bubbles must be small enough (between 10 – 100 µm) to have a large surface area. Bubbles must not be larger than 130 µm to maintain laminar flow conditions where maximum collision and attachment between floc particle and bubbles occur.

Fig. 23 Bubble size versus rise velocity (Crittenden).

The density of the floc-bubble aggregate can be calculated by:

3bab

3p

3bbab

3pp

pbdNd

d Nd

+

ρ+ρ=ρ (34)

where ρpd = particle-bubble aggregate density, kg/m3

ρp = particle density, kg/m3 ρb = bubble (air) density, kg/m3 dp = particle diameter, m db = mean bubble diameter, m Nab = number of air bubbles attached to floc particle

The equivalent spherical diameter of the floc-bubble aggregate can be determined from:

( ) 3/13bab

3ppd dNdd += (35)

where dpd = equivalent spherical diameter of floc-bubble aggregate, m

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Air loading – the recycle system provides the required air loading to the water to ensure dense bubbles form within the contact zone. Turbidity in the treated effluent declines with increasing air loading until a breakpoint is reached. Beyond which, additional air provides no further increase in turbidity removal.

Fig. 24 Air loading rate versus effluent turbidity (Crittenden).

The mass concentration of air released Cb, bubble volume concentration φb, and bubble number concentration Nb can be calculated from:

rr1CCC flr

b +−

= (36)

air

bb

Cρ

=φ (37)

3b

b12

bd

610Nπ

φ×= (38)

where Cb = mass concentration of air released, mg/L

Cr = mass concentration of air in recycle flow, mg/L Cfl = mass concentration of air in floc tank effluent, mg/L r = recycle ratio φb = bubble volume concentration, L/L ρair = density of air saturated with water vapour, mg/L Nb = bubble number concentration, number/mL 1012 = conversion factor, µm3/mL db = mean bubble diameter, µm

Solubility of air at elevated pressure – the solubility of air in water increases linearly with increasing pressure but reduces at elevated temperatures.

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Fig. 25 Pressure and temperature on dissolved air concentration (Crittenden).

Floc-bubble attachment: The likely mechanisms for floc-bubble attachment are (a) bubbles adhere to preformed floc due to electrostatic or other attraction (b) bubbles become physically entrapped within preformed floc (c) bubbles become entrapped in floc particles as they aggregate, and (d) floc particles act as nuclei for bubble formation.

Fig. 26 Mechanisms for floc-bubble aggregation (Crittenden).

Example 7 A DAF plant is operating at 10% recycle with a saturator pressure of 500 kPa. Flocculated water enters the contact zone with a floc particle concentration of 2000 particles/mL and a floc volume concentration of 2 x 10-6 L/L (2 ppm). Calculate the air mass concentration, bubble zone volume concentration, and bubble number concentration in the contact zone. Compare the concentrations of bubbles to floc particles.

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Assume the following: - water temperature = 20oC - ρair = 1.2 kg/m3 = 1200 mg/L - air concentration in flocculated water = 24 mg/L - mean bubble diameter = 40 µm

From Fig 25, mass of air in recycle water Cr = 130 mg/L for 601 kPa (500 kPa gauge pressure + 101 kPa atmospheric pressure)

Concentration of air released 64.91.01.0124130r

r1CCC flr

b =×+−

=+−

= mg/L

Bubble volume concentration L/L1080331200

64.9C 6

air

bb

−×==ρ

=φ or 8033 ppm

Bubble number concentration:

53

612

3b

b12

b 104.240

108033610d

610N ×=×π

×××=

π

φ×=

−bubbles/mL

Concentration of bubbles to floc particles = 2.4 x 105/2000 = 120 (a high ratio indicates a high chance of particle collision and attachment with the bubbles) Ratio of bubble volume concentration to floc volume concentration = 8033 ppm/2 ppm = 4107 (a high ratio indicates a low floc-bubble density, resulting in a higher rise velocities of the particle-bubble aggregate).

Table 4 Typical design criteria for DAF system (Crittenden).

Parameter Value Basin design Hydraulic loading rate, m/h 10 – 20 Basin length, m < 11 Basin length-to-width ratio <1 Surface area, m2 90 – 110 Maximum hydraulic capacity for single basin, m3/s 0.26 – 0.52 Basin depth, m 1.5 – 3 Detention time in contact zone, s 60 – 240 Recycle system Recycle ratio, % of influent 6 – 10 Recycle system pressure, kPa 448 – 586 Air loading, kg air/m3 raw water 6000 – 10200 Air bubble size, µm 10 – 100 Bubble concentration, bubbles/mL 1 x 105 – 2 x 105 Bubble volume concentration, ppm 3500 – 8000