Settling

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PAVAN MANDAPAKA
ASST. PROFESSOR
DEPT. OF CI VI L & ENVT. ENGG.
UNI VERSI TY OF PETROLEUM & ENERGY
STUDI ES
DEHRADUN
Sedimentation & Settling in
Water Treatment
• Most wastewaters and waters contain
solids, and in many treatment processes
solids are generated e.g., phosphate
precipitation, coagulation and activated
sludge bioxidation.
• Particles in water and wastewater that will
settle by gravity within a reasonable period
of time can be removed by "sedimentation"
in sedimentation basins (also known as
"clarifiers").
2
PAVAN MANDAPAKA
• “Settleable” doesn’t necessarily mean that
these particles will settle easily by gravity.
• In many cases they must be coaxed out of
suspension or “solution” by the addition of
chemicals or increased gravity (centrifugation
or filtration).
• Because of the high volumetric flow rates
associated with water and wastewater
treatment systems, gravity sedimentation is
the only practical, economical method to
remove these solids. i.e., processes such as
centrifugation are not economical, in most
cases.
3
PAVAN MANDAPAKA
Gravity separation can obviously be applied
only to those particles which have density
greater than water. But this density must be
significantly greater than that of water due to
particle surface effects and turbulence in the
sedimentation tanks.
Goals of gravity sedimentation:
1) Produce a clarified (free of suspended
solids) effluent.
2) Produce a highly concentrated solid
sludge stream.
4
PAVAN MANDAPAKA
Type I (Discrete sedimentation):
• Occurs in dilute suspensions, particles
which have very little interaction with
each other as they settle.
• Particles settle according to Stokes law
• Design parameter is surface overflow rate
(Q/A
s
)
5
PAVAN MANDAPAKA
Type II (flocculent sedimentation)
• Particles flocculate as they settle
• Floc particle velocity increase with
time
• Design parameters:
1. Surface overflow rate
2. Depth of tank or,
3. Hydraulic retention time
6
PAVAN MANDAPAKA
Comparison of Type I and II sedimentation
7
PAVAN MANDAPAKA
Zone Settling &Compression (Type III and IV)
• Zone settling occurs when a flocculent suspensions with
high initial concentration (on the order of 500 mg/L)
settles by gravity.
• Flocculant forces between particles causes settling as a
matrix (particles remain in a fixed position relative to
each other as they settle).
• When matrix sedimentation is constrained from the
bottomthe matrix begins to compress.
• Such a situation occurs when the matrix encounters the
bottom of tank in which it is settling. This is called
compression (Type IV) settling.
8
PAVAN MANDAPAKA
9
PAVAN MANDAPAKA
Type I Settling
Discrete Settling
 Settling of discrete, non-flocculating particles
 Particles settle as individual entities at a constant
velocity
 Minimal interaction between particles
 Applies only to particles in a suspension with a low
solids concentration
10
PAVAN MANDAPAKA
Type I Settling
Discrete Settling
Gravitational Force
F
g
Frictional Drag Force
F
D
Bouyant Force
F
b
11
PAVAN MANDAPAKA

F
G
= (p
p
÷ p
w
)gV
p
(1) Effective Gravitational Force

F
D
=
C
D
· A
p
· p
w
· v
p
2
2
(2) Drag Force

v
s
= v
p(t )
=
4g
3C
D
p
p
÷ p
w
p
w
|
\

|
.
|
d
p
Assumes Spherical
Valid for any N
R
Equating (1) = (2)
(3) Settling Velocity
Type I Settling
Determination of Particle Settling Velocity
12
PAVAN MANDAPAKA

N
R
=
v
P
d
P
p
w
u
Type I Settling
C
D
= f(Reynolds Number, Particle
Shape)
(4)

C
D
=
24
N
R
+
3
N
R
+ 0.34
(5)
For spherical particles:
13
PAVAN MANDAPAKA

C
D
=
24
N
R
Type I Settling
When N
R
< 1 (laminar flow range)
First Term in Eq’n (5) dominates
(6)
Substituting Eq’n (6) in Eq’n (3)
Settling velocity in laminar conditions
Only Valid for N
R
< 1

v
s
= v
p
=
g(p
p
÷ p
w
)d
p
2
18u
(7)
14
PAVAN MANDAPAKA
Type I Settling
Settling in the Transitional to Turbulent Region
 When 1 < Re < 10000
 For spherical particles, the complete form of Eq’n 5 is
used to describe the coefficient of drag
 The settling velocity distribution of the particles can be
solved using an iterative method
 Need to know C
D
to calculate the velocity using Eq’n 3
 The coefficient of drag is dependent on N
R
, which is dependent
on the velocity!
 Need to assume a value for the velocity and then iterate
15
PAVAN MANDAPAKA
Type I Settling
Discrete Settling in an Ideal Settling Tank
16
PAVAN MANDAPAKA
Type I Settling
Discrete Settling
 Where it occurs in WWTP:
 Grit tanks
 Top zone of the primary clarifiers
 In order to design a settling tank, the settling
velocities must be determined
 The physical properties of a particle determine its
settling velocity (size and density)
17
PAVAN MANDAPAKA
Type I Settling
Ideal Settling Basins
18
PAVAN MANDAPAKA
Type I Settling
Inlet Zone - Assumptions
 The suspension is uniformly distributed over the cross-
section of the tank
 Concentration of the suspended particles of each size is the
same across the entire vertical plane
19
PAVAN MANDAPAKA
Type I Settling
Settling Zone - Assumptions
 Direction of the flow is horizontal
 Fluid velocity (u) is constant at all points
20
PAVAN MANDAPAKA
Type I Settling
Sludge Zone - Assumptions
 Solids collect in the sludge zone at the bottom of the tank
 All particles reaching the sludge zone will be permanently
removed from suspension (i.e. no re-suspension)
21
PAVAN MANDAPAKA
Type I Settling
Outlet Zone - Assumptions
 Clarified effluent is distributed uniformly across the
cross-section of the basin
22
PAVAN MANDAPAKA
Type I Settling
Settling Paths of Discrete Particles
- Particles follow a straight line
- Vector is the sum of 2 velocity components
23
PAVAN MANDAPAKA
Type I Settling
Critical Settling Velocity
 v
o
= critical settling velocity
 A particle starting at the top of the inlet zone with a settling
velocity of v
o
will just reach the bottom of the tank at the
beginning of the outlet zone
24
PAVAN MANDAPAKA
Type I Settling
What Happens to the Particles?
 If v
s
≥ v
o
 Particles will be completely removed from the WW
 If v
s
= v
o
 If the particle is starting at the top of the settling zone (H), it
will just barely settle before the end of the tank
25
PAVAN MANDAPAKA
Type I Settling
What Happens to the Particles?
 If v
s
< v
o
 Partial removal
 If the particle enters at or below height “h”:
 100% removal
 If the particle enters above height “h”:
 It will not reach the bottom before the outlet zone
26
PAVAN MANDAPAKA
Type I Settling
Design Strategy for Sedimentation Basins
 Select a particle with a terminal velocity of v
o
and
then design a basin so that all particles that have a
terminal velocity greater than or equal to v
o
will be
removed
27
PAVAN MANDAPAKA


v
o
=
H
t
o

=
Hu
L

=
HuW
LW

=
Q
A

t
o
=
L
u
Type I Settling
Critical Velocity
 t
o
= residence time in the settling zone
28
PAVAN MANDAPAKA
 Q/A is called the OVERFLOW RATE of the settling
tank
 Q = flowrate of water [m
3
/s]
 v
o
= critical settling velocity [m/s]
 A = surface area of basin (L· w) [m
2
]
 In design, the overflow rate is set to ensure complete
removal of the particles of a given size


v
o
=
Q
A
Type I Settling
Overflow Rate
29
PAVAN MANDAPAKA
F
X
= fractional removal of particles with a settling velocity v
s
Type I Settling
Fractional Removal of Particles


F
X
=
h
H

=
v
s
t
o
v
o
t
o

=
v
s
v
o
F
x
< 1
When v
s
< v
o
30
PAVAN MANDAPAKA
Type I Settling
Fractional Removal of Particles
 The fractional removal of the particles is dependent
on:
 Particle settling velocity
 Total flowrate
 Surface area of the settling tank
NOT A FUNCTION OF DEPTH!

F
x
=
v
s
v
o
=
v
s
Q
A
|
\

|
.
|
31
PAVAN MANDAPAKA
Type I Settling
Overall Removal (F)
 Where:

F = (1÷ f
o
) +
1
v
o
v
s
df
o
f
o
í

(1÷ f
o
)
Fraction of particles with v
s
≥ v
o
(all completely removed)

1
v
o
v
s
df
o
f
o
í
Fraction of particles with v
s
< v
o
that are removed; F
x
= v
s
/v
o

f
o
Fraction of particles with v
s
< v
o
32
PAVAN MANDAPAKA
33
PAVAN MANDAPAKA
Types of Settling
Type I: Discrete Settling
Type II: Flocculent Settling
Type III: Hindered or Zone Settling
34
PAVAN MANDAPAKA
Type II Settling
Flocculant Particle Settling
 Settling initially starts as Type I (discrete), but the
particles coalesce (flocculate) during settling
 Flocculation leads to a change in size, shape and
weight as they settle ÷v
s
changes with time
 Paths of the particles are curved (not linear as in
discrete settling)
35
PAVAN MANDAPAKA
Type II Settling
Flocculant Particle Settling
 There is no theoretical model that can predict the rate
of flocculation
 Can perform batch tests to obtain the data required to
size primary sedimentation basins where flocculation
is occurring
 Use a batch settling column with a height equal to the
depth of the clarifier that is to be designed
 IMPERATIVE!
36
PAVAN MANDAPAKA
Type II Settling
Flocculant Particle Settling
 Particles initially settle independently, but coalesce
(flocculate) as they proceed down the tank
 Particles change in size, shape and weight as they
settle
 Larger particles have higher v
s
 Rate of settling (v
s
) changes with time
37
PAVAN MANDAPAKA
Type II Settling
Flocculant Particle Settling
 Particles flocculate as
settling, increasing in
mass and settling at a
faster rate
 Paths of the particles
are curved rather than
straight, as the velocity
changes with time
38
PAVAN MANDAPAKA
Type II Settling
Influencing Factors
 Factors influencing the degree of flocculation
 Collision frequency; f(concentration, velocity, mixing)
 Surface properties
 Charges
 Particle shape and surface area
 Density
 These factors are poorly understood and there is no
theoretical model to predict the rate of flocculation
 Can do simple batch tests that provide the data required for
sizing primary (with flocculation) and secondary clarifiers
39
PAVAN MANDAPAKA
 Q/A is called the OVERFLOW RATE of the settling tank
 Q = flowrate of water [m
3
/s]
 v
o
= critical settling velocity [m/s]
 A = surface area of basin (L· w) [m
2
]
 In design, the overflow rate is set to ensure complete removal
of the particles of a given size


v
o
=
Q
A
Type II Settling
Overflow Rate
40
PAVAN MANDAPAKA
Type II Settling
Clarifier Dimensions
 A = L x W = surface area of the basin (m
2
)
 Default aspect geometry:
 L = 4W
 A = 4W
2
41
PAVAN MANDAPAKA
Type II Settling
Scouring Velocity
 Re-suspension of particles due to large horizontal velocities (u)
 Where:
 u = horizontal velocity (m/s)
 Q = water flowrate (m
3
/s)
 HW = cross-sectional area (entry area) in the direction of flow (m
2
)
To prevent scouring, u < (9 * v
o
)

u =
Q
HW
42
PAVAN MANDAPAKA
Types of Settling
Type I: Discrete Settling
Type II: Flocculent Settling
Type III: Hindered or Zone
Settling
43
PAVAN MANDAPAKA
Type III Settling
Hindered or Zone Settling
 At high solids concentrations (such as those seen in
secondary clarifiers), there are cohesive forces
between the particles/flocs
 The particles settle collectively as a “zone”
 Maintain the same relative position with respect to one
another
 At a given cross-section, all of the settling velocities are equal,
regardless of size
44
PAVAN MANDAPAKA
Type III Settling
Hindered or Zone Settling
 Occurs in solutions with a very high solids
concentration
 Secondary clarifiers following the activated sludge process and
sludge thickeners
 Distinct interface between the settled particles and
the clarified effluent
 A relatively clean layer of water is produced above the settling
particles
 Liquid tends to move between interstices
45
PAVAN MANDAPAKA
PAVAN MANDAPAKA
46
Type I
(Discrete)
PAVAN MANDAPAKA
47
Type II
(Flocculent)
PAVAN MANDAPAKA
48
Type III
(Zone)
Type III Settling
Settling Test
Zones:
A. Clarified liquid
B. Uniform
concentration/settling
velocity
C. Transition
D. Compression
1. Initial phase
2. Zone settling phase
3. Transition phase
4. Compression phase
Time
49
PAVAN MANDAPAKA
Type III Settling
Settling Test
1. Initial Phase
 Slow settling
 No floc adherence
2. Zone Settling Phase
 Constant settling period
 Suspension settles at a uniform velocity characteristic of the
initial solids concentration
3. Transition Phase
 Interface settling velocity begins to decrease
4. Compression Phase
 Solids concentration at the interface increases and settling
velocity increases until equilibrium is reached (settling stops)
50
PAVAN MANDAPAKA
PAVAN MANDAPAKA
51 Figure 5-28, Metcalf & Eddy
Type III Settling
Clarifier Design
 To obtain data for design, settling tests are repeated
for different initial concentrations
 Typical range is X = 1 to 15 kg/m
3
 Plot solids/liquid interface height versus time for each initial X
 Estimate the zone settling velocity for each initial X from the
slope
 v
s
= f(X)
52
PAVAN MANDAPAKA
Type III Settling
Interface Height vs Time
 Find v
s
in region where
there is a constant
settling velocity
 Slope decreases as the
concentration increases
 C1 lowest concentration
 C6 highest concentration
 v
s
decreases as increases X
53
PAVAN MANDAPAKA
Type III Settling
Clarifier Design
 Clarifiers need to be designed for two purposes:
 Clarification: Removal of solids from liquids to produce an
effluent with a low solids concentration.
 Thickening: Concentrating the suspension to produce a
concentrated underflow. The solids must have sufficient time
to travel to the bottom of the tank.
54
PAVAN MANDAPAKA
Type III Settling
Solids Flux and Clarifiers
 Size of clarifier required is dependent on the
concentration and the settling velocity
 If a suspension has a high solids concentration with a high
settling velocity, it is not necessary to have a large clarifier
 If a suspension has a low solids concentration with a low
settling velocity, a large clarifier would be required
55
PAVAN MANDAPAKA
Type III Settling
Solids Flux and Clarifiers
 The solids flux is the product of the settling velocity
by the solids concentration
 Where:
 G
s
= solids flux [M/L
2
•T]
 v
s
= settling velocity [L/T]
 X = concentration [M/L
3
]

G
s
=v
s
X
56
PAVAN MANDAPAKA
Type III Settling
Clarifier Design
 Clarifiers need to be designed for two purposes:
 Clarification: Removal of solids from liquids to produce an
effluent with a low solids concentration.
 Thickening: Concentrating the suspension to produce a
concentrated underflow. The solids must have sufficient time
to travel to the bottom of the tank.
57
PAVAN MANDAPAKA
PAVAN MANDAPAKA
58
Type III Settling
Batch Settling Test
 Use a uniform suspension of known concentration
 In zone settling, the suspension will settle at a uniform
settling velocity
 Measure the position of the solid/liquid interface with time
59
PAVAN MANDAPAKA
Type III Settling
Designing Clarifiers
 Separately calculate areas required for:
1. Clarification - removal of solids from liquid
2. Thickening - concentrating the suspension to provide a
concentrated underflow
 The larger of the two areas determines the design
of the clarifier (i.e. the area needed to achieve the
specified performance)
60
PAVAN MANDAPAKA
PAVAN MANDAPAKA
61 Figure 5-28, Metcalf & Eddy
Type III Settling
Clarification Area
 Clarification area must be large enough so that the
velocity of the overflow liquid (effluent velocity) is
less than the batch settling velocity of the interface
 Allows the solids to settle in the tank
 Reduces the concentration of solids in the overflow (X
e
)
62
PAVAN MANDAPAKA
Type III Settling
Clarification Area
 Perform a batch settling test
 Where:
 v
o
= initial zone settling velocity at the feed concentration (X),
[m/h], (function of X)
 A
c
= surface area for clarification [m
2
]
 Q
e
= overflow rate of clarified liquid [m
3
/h]

v
o
=
Q
e
A
c
63
PAVAN MANDAPAKA
Type III Settling
Thickening Area
 Area required for thickening is determined by mass flux
analysis based on data derived from batch settling tests
Mass flux = mass of material crossing an area per time [kg/(m
2
·h)]
 In the thickening region, both solids and some of the liquid
move toward the underflow
64
PAVAN MANDAPAKA
Type III Settling
Thickening Area
 The underflow contains less water than in the settling
zones above
 The liquid velocity is less than the solids velocity
 The solids settle and the concentration increases with the
depth
 The depth of the thickening portion of the clarifier
must be sufficient to:
 Ensure that un-thickened solids are not recycled
 Temporarily store any excess solids that may be applied
65
PAVAN MANDAPAKA
Type III Settling
Gravity Flux
 In the secondary clarifier operating at steady state, a
constant flux of solids is moving downward due to
gravity settling
 At any depth in the clarifier, the mass flux of solids due
to gravity settling is:
 Where:
 G
g
= gravity flux [M/L
2
•T] (kg/(m
2
•h))
 v
i
= settling velocity at solids concentration X
i
[L/T] (m/h)
 X
i
= local concentration of solids [M/L
3
] (kg/m
3
)

G
g
= v
i
X
i
66
PAVAN MANDAPAKA
Figure 8-35a, Metcalf & Eddy
Type III Settling
Determination of Gravity Flux
Step A
Determination of the Zone Settling Velocity
67
PAVAN MANDAPAKA
Figure 8-35, Metcalf & Eddy
Type III Settling
Determination of Gravity Flux
Step B
Settling Velocity (from Step A)
vs Concentration
Step C
Gravity Flux vs Concentration
68
PAVAN MANDAPAKA
Type III Settling
Determination of Gravity Flux
Figure 8-35, Metcalf & Eddy
At low X, gravity flux is
small because X
i
is small
At high X, gravity flux is
small because v
i
is small
69
PAVAN MANDAPAKA
Type III Settling
Bulk Flux
 There is also a downward flux of solids due to bulk
transport from underflow pumping
 Solids are removed from the clarifier in the recycle and
sludge wastage streams
 Where:
 u
b
= bulk downward velocity of the solids [L/T] (m/h)
 Q
u
= underflow flowrate [L
3
/h] (m
3
/h)
 A = surface area of settling tank [L
2
] (m
2
)

u
b
=
Q
u
A
70
PAVAN MANDAPAKA
Type III Settling
Bulk Flux
 At any depth in the clarifier, the mass flux of solids due
to bulk transport/underflow pumping is:
 Where:
 G
u
= bulk mass flux [M/L
2
•T] (kg/(m
2
•h))
 u
b
= bulk downward velocity of the solids [L/T] (m/h)
 X
i
= local concentration of solids [M/L
3
] (kg/m
3
)

G
u
= u
b
X
i
71
PAVAN MANDAPAKA
Type III Settling
Determination of Bulk Flux
• The bulk flux of solids is a linear function of the solids concentration with a slope
equal to u
b
72
PAVAN MANDAPAKA
Type III Settling
Total Flux
 The total mass flux of solids at a concentration X
i
is:

G = G
g
+ G
u
G = X
i
v
i
+ X
i
u
b
G = X
i
(v
i
+ u
b
)
73
PAVAN MANDAPAKA
Type III Settling
Total Flux
Figure 8-36, Metcalf & Eddy
G
L
is the limiting solid flux
74
PAVAN MANDAPAKA
Type III Settling
Limiting Flux
 The rate at which sludge can fall limits the ability of
the system to remove the solids
 Minimum of the total flux gives gives X
L
and G
L
(Limiting flux)
 This represents the limit where sludge cannot reach
the bottom of the tank - “Thickening failure”
 To ensure that all sludge reaches the bottom, the
applied flux needs to be less than the limiting flux
 The goal is to design the system as close to G
L
as
possible
75
PAVAN MANDAPAKA
 Area = Solids Applied to the Clarifier (kg/h)
Limiting Flux (kg/m2•h)
 Where:
 Q = influent flow rate (m
3
/h)
 G
L
= limiting solid flux (kg/(m
2
h))
 X
o
= influent concentration of solids (kg/m
3
)
Design with a factor of safety of 1.75
Type III Settling
Thickening Area

A =
Q· X
o
G
L
76
PAVAN MANDAPAKA

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