CE 428 Water and Wastewater Treatment Design
SEDIMENTATION
Sedimentation or gravity sedimentation or settling is a solid-liquid separation utilizing gravitational settling
to remove suspended solids.
In water and wastewater treatment, applications include:
(i)
presedimentation tanks - settling of suspended particles, eg., sand, prior to entering water
treatment plant
(ii)
settling of floc after coagulation
(iii)
settling of solids in municipal wastewater treatment plants (WWTP)
To simply analysis, settling may be classified as:
Type 1 Settling
free settling, discrete settling, settling of nonflocculent particles in dilute
suspensions. Particles settle as separate units and there is no apparent
flocculation or interaction between particles.
Examples: presedimentation and settling of sand in grit chambers of WWTP.
Type II Settling
settling of flocculent particles in dilute suspensions. The particles flocculate
during settling thus they increase in size and settle at a faster velocity.
Examples: settling of coagulated waters, primary settling of municipal
wastewater.
Type III Settling
zone or hindered settling, settling of an intermediate concentration of particles in
which particles are so close together that interparticle forces hinder the settling
of neighboring particles. Particles remain in a fixed position relative to each
other and all settle at a constant velocity. As a result there will be a distinct
solid-liquid interface between the settling particle mass and the clarified liquid.
Examples: settling in the intermediate depths of water treatment clarifiers and
WWTP secondary clarifiers.
Type IV Settling
compression settling, settling of particles of high concentrations that the settling
occur by compression of the compacting mass and interparticle liquid is
squeezed out.
Examples: compression settling in lower depths of thickening clarifier for
activated sludge plants
Sedimentation tanks may be circular, square or rectangular in plan view. Depths of sedimentation tanks
vary from 6 to 18 feet deep. For circular tanks the tanks may be from 15 to 300 feet diameter while
rectangular tanks have widths from 5 to 250 feet and lengths up to 250 feet.
Ideal Settling Tank
Has four zones
- Inlet
- settling
- sludge collection
- outlet
Assumptions
- steady flow
- when particles hit the sludge zone - remain there
- flow through period = detention time (no dead zones)
- settling in discrete particles
- move forward with the same velocity as the water
Particle Settling Theory
Discrete settling velocities can be estimated using the Newton's and Stokes Law (see Equations 5-18, 5-21,
5-22, 5-24)
A particle settling in water is subjected to the following forces:
FG = gravitational force
FB = Buoyancy force
FD = Drag force
When upward and downward forces are equal, particles will settle at a constant velocity called terminal
velocity. Equating forces:
FG - FB = FD
FG = s g VP
FB =  g VP
FD = CD AP  (Vs2/2)
s = density of particle (kg/m3)
g = gravitational acceleration (m/s2)
VP = volume of particle (m3)
 = density of fluid/water (kg/m3)
CD = Drag coefficient
AP = cross sectional area of particle (m2)
Vs = terminal velocity (m/s)
s g Vp -  g Vp = CD Ap  (Vs2/2)
Vs 
  s    VP


   AP
2g
CD
Assume the particle is spherical with a diameter d:
VP = (/6) d3
AP = (/4) d2

d3
VP
2
 6
 d
AP  d 2 3
4
Then
Vs 
2g
CD
 s    2
4gd

 d 
3C D
  3
 s   


  
CD is dependent on the flow regime and is given by:
Laminar flow
Re < 0.5
CD = 24/Re
Transition flow
0.5 < Re < 10,000
CD = 24/Re + 3/Re½ + 0.34
Turbulent flow
Re > 10,000
CD = 0.4
Re = Reynolds number =  d Vs/
where
 = kinetic viscosity (m2/s)
 = shape factor, to describe the nonspherical shape of the particle
For particles falling under laminar conditions,
CD = 24/Re
Therefore
 gd 2 Vs   s   


18 
  
Vs 
Vs 
= 24 / ( d Vs/) = 24  / d Vs
 gd 2   s     gd 2  s  


18    
18
Stoke’s Equation
where  = dynamic viscosity (Pa s-1)
Design parameters
In the design of sedimentation tank, the objective is to design a basin where the terminal velocity of the
particle is not exceeded. This leads to several generalized design parameters that are typically used.
- overflow rate or surface loading rate or clarification rate (m3/s/m2)
- weir overflow rate (m3/d/m)
- solids loading rate (lbs/ft2/d or kg/m2/d) (more important for secondary sedimentation tanks)
Others
- detention time (hr)
- particle settling velocity Vs (m/s)
(1) Overflow Rate/Surface Loading Rate
In a horizontal or vertical flow sedimentation tank, the velocity of the water in the tank is given by:
Vo = flow rate/ surface area of sedimentation tank = Q/As
(note independent of depth)
If Vs > Vo particles will settle
If Vs < Vo, particles will be carried over
(Vo is usually set a < 80% of Vs)
Notes
 there is a distribution of particle sizes therefore will have a range or distribution of V s
 the overflow rate is the average fluid velocity at about the mid section of the sedimentation tank. At the
collection weir at the edge of the clarifier, the fluid velocity may be higher, resulting in a carry over of the
particles. Therefore sufficient length must be provided to ensure that water will not rush over the weir.
This lead to the second design parameter.
(2) Weir overflow rate given by:
= flow rate/length of weir = Q/L
(3) Solids loading rate
= mass of solids/per unit area per unit time
= Q x solids concentration/ surface area
This parameter is important when there is high solids loading such as in the secondary sedimentation tank.
(4) Detention Time - approximately 2 - 8 hours
shorter times for biological solids 2 - 4 hours
chemical solids - water treatment - 4 - 6 hours typical
For some lime softening system - a detention time of 2 hours is used.
(5) Typical Depths - 2 to 6 m.
Laboratory Approach in determining Removal Rates and Detention Time
- use a column with the same depth as the clarifier. At various depths, sampling points are provided to
remove samples to measure the suspended solids concentration
- provide gentle mixing
- start with uniform concentration throughout and at various times collect samples throughout the length of
the column.
- compute the mass fraction removed at each depth and time
% removed P = ( 1 - Cij/Co) x 100
where
Cij = concentration at depth I and time I
Co = initial concentration
- plot depth vs time, the percent removal at each time and depth
- draw iso-removal rate lines
- for a given retention and depth, compute the overall removal rate
R = r o +  ri
where
ri
= (di/D)pi
ro
= fraction of solids removed at the given depth and retention time
pi
= differential removal rates
di
= depth of clarifier for ri (at the mid-point of differential removal rates)
D
= depth of clarifier
Example Problem - Flocculation Analysis - Detention Time and Removal Rates
Column analysis of a flocculating suspension is presented below. The initial average concentration
throughout the column was 250 mg/L. What is the overall removal efficiency of a settling basin which 3 m
deep with a retention time of 1 hour and 45 minutes
Depth (m)
0.5
1.0
1.5
2.0
2.5
3.0
30
133
180
203
213
220
225
60
83
125
150
168
180
188
Time of Sampling (mins)
90
120
50
38
93
65
118
93
135
110
145
123
155
133
150
30
55
75
90
103
113
180
23
43
58
70
80
95
Time of Sampling (mins)
90
120
80
85
63
74
53
63
46
56
42
51
38
47
150
88
78
72
64
59
55
180
91
83
77
72
68
62
Solution
Step 1 - Compute Removal Rates
Depth (m)
0.5
1.0
1.5
2.0
2.5
3.0
30
28
19
15
12
10
60
67
50
40
33
28
25
Step 2 - Plot Iso-removal rate lines
0.0
0.5
47
67
80
85
88
91
1.0
28
50
63
74
78
83
1.5
19
40
53
63
72
77
2.0
15
33
46
56
64
72
2.5
12
28
42
51
59
68
3.0
10
25
38
47
55
62
30
60
90
120
150
180
Detention time = 105 mins, ro = 43%
ri
0.07
0.1
0.1
0.1
0.1
0.1
ri di = ri
0.18
0.18
0.12
0.08
0.045
0.015
di
2.6
1.8
1.2
0.8
0.45
0.15

R = r o +  ri
= 0.43 + 0.61/3.0
= 63%
0.61
Inclined (tube and plate settling)
Principle: efficiency of discrete particle settling in horizontal liquid flow is dependent on the area available
for settling and independent of the depth of the sedimentation tank
V0 = Q/A
 Efficiency can be improved by increasing the area, i.e., by using multiple floors in sedimentation tanks.
 Another alternative is to use uniformly and closely spaced inclined surfaces called tube or plate or lamella
settlers.
 Inclined settling systems are usually made of plastic. Angles of the plates may be as low as 5 o to as high
as 70o. Flow in the channels must be laminar and in practice Reynolds number must be less than 800 in the
channel. System comes in three flow arrangements: countercurrent, co-current and cross-flow. Most
systems are counter current as shown in the diagram below.
For each arrangement, conditions for removal of particles with a settling velocity Ut and greater are
removed if:
Countercurrent
co-current
cross-flow
Ut 
where
Uo
L p cos    sin 
Ut 
Uo
L p cos    sin 
Ut = settling velocity of particle
Lp = length of surface needed
Uo = liquid velocity between the surfaces = Q/Nb
N = number of channels
b = width of channel
 = perpendicular spacing between surfaces
 = angle of surface inclination
Ut 
Uo
L p cos 