Settling Design

Wastewater Engineering and Design

Wastewater Engineering
and Design

Chapter 2: Physical Treatment Units;
Design of Sedimentation Tanks

1

Outline

n Physical Treatment Unit
n Types of Sedimentation
n Principle of Sedimentation
n Primary Sedimentation Tank
n Settling Thickener

2

By Assist. Prof. Dr. Wipada Sanongraj

1

Wastewater Engineering and Design

Figure 2-1: Physical Unit Treatment (Metcalf and Eddy, 1991)

3

Physical Treatment Unit
Operation
n Flow metering
n Screening
n Flow equalization
n Mixing

n Flocculation

By Assist. Prof. Dr. Wipada Sanongraj

Application
Process control, process monitoring
and discharge reports
Removal of coarse and settleable
solids by interception
Equalization of flow and mass loading
of BOD and suspended solids
Mixing chemicals and gases
with wastewater, and
maintaining solids in suspension
Promotes the aggregation of
small particles into larger particles
to enhance their removal by
4
gravity sedimentation

2

Wastewater Engineering and Design

Physical Treatment Unit
Operation
n Sedimentation
n Flotation

n Filtration

n Microscreening
n Gas transfer
n Volatilization

Application
Removal of settleable solids
and thickening of sludges
Removal of finely divided
suspended solids and particles
biological sludges
Removal of fine resudual
suspended solids remaining
after biological or chemical
treatment
Same as filtration
Addition and removal of gases
Emission of volatile and semivolatile and gas stripping
5
organic compounds from WW

Types of Sedimentation

Bar Screening

By Assist. Prof. Dr. Wipada Sanongraj

6

3

Wastewater Engineering and Design

Types of Sedimentation
Four Types of Settling
Type I: Discrete Settling
1. Particles settle out individually and do not interact
with one another.

2. Suspension of low solids concentration.

7

Type I: Discrete Settling

3. Occur in:
a) Grit chambers
and some primary
clarifiers used in
wastewater treatment
plants.
b) Some
presedimentation
basins in water
treatment.
8

By Assist. Prof. Dr. Wipada Sanongraj

4

Wastewater Engineering and Design

Type II: Flocculants Settling

1. As particles flocculate (due to velocity
differences), they increase in mass and velocity:
a) Mixing due to hydraulic gradients in clarifier
produces particle collisions:

9

Type II: Flocculants Settling

b) Larger particles overtakes smaller ones and
flocculate:

10

By Assist. Prof. Dr. Wipada Sanongraj

5

Wastewater Engineering and Design

Type II: Flocculants Settling
2. Suspension of low solids concentration
3. Occurs in:
a. Most primary and all secondary clarifiers in
wastewater treatment.
b. Most sedimentation basins in water treatment.

11

Type II: Flocculants Settling

12

By Assist. Prof. Dr. Wipada Sanongraj

6

Wastewater Engineering and Design

Type III: Zone Settling or Hindered Settling
1. Formation of dense mat of particles that settle
out as a unit:

Settling of different size particles will
eventually form thick settling blanket that
settles at a constant velocity.

13

Type III: Zone Settling or Hindered Settling
2. Suspension of intermediate concentration.
3. Intraparticle forces are sufficient enough to affect
adjacent particles.
4. Occurs in:
a. Thickeners (sludge disposal)
b. Bottom of clarifiers and sometimes
sedimentation basins.

14

By Assist. Prof. Dr. Wipada Sanongraj

7

Wastewater Engineering and Design

Type IV: Compression Settling
1. Settling occurs by compression where water is
forced out of the interstitial voids between
particles.

In order to settle, water must pass through particles
arranged like porous media. Furthermore, there is a
high head loss due to a large surface to volume
ratio. Therefore, settling occurs slowly.
15

Type IV: Compression Settling
2. Suspension by very high concentration.
3. All particles are influenced by the presence of
other
particles.
4. Occurs in drying beds and some filtration
process.

16

By Assist. Prof. Dr. Wipada Sanongraj

8

Wastewater Engineering and Design

Grit Materials
Sand, gravel, egg shells, coffee grounds, fruit
rinds, seeds, bones (who’s)

17

Principles of Sedimentation

Vp = Volume of particles = 1/6 π Dp3 (cm3)
Ap = Projected surface area of particle = π/4Dp2 (cm2)
Fp = Drag force = friction factor * inertial force (g-cm/s2)
Fb = Bouyant force (g-cm/s2)
Fg = Force due to gravity (g-cm/s2)
Vs = Velocity of particle (cm/s)
mp = Mass of particle (g)
g = Acceleration due to gravity (cm/s2)
rl = Density of water (g/cm3)
18
rp = Density of particle (g/cm3)

By Assist. Prof. Dr. Wipada Sanongraj

9

Wastewater Engineering and Design

Momentum Balance
d (m pVs )

d (m pVs )
dt

dt

= å F = Fg - Fb - Fd

Vs2
= r pV p g - r l V p g - C d r l A p
2

Determination of the Drag Coefficient in water
Cd = f(NR) & Particle Shape
Cd can be determined if the pressure and shear stress
characteristics surrounding an object are known. However,
Cd can also be determined if the total drag is measured by
19
a force dynamometer.

Principles of Sedimentation

20

By Assist. Prof. Dr. Wipada Sanongraj

10

Wastewater Engineering and Design

Principles of Sedimentation
Larminar region: viscous forces control the drag force
Turbulent region: inertial forces of displaced fluid are
controlling the drag force

For laminar flow: (NR < 1)
r l D pV s
NR =
ml

Cd =

24
NR

2 2
Vs2 æç 24m l ö÷æç r lpD pVs ö÷
Fd = Cd r l Ap
=
= 3pm l D pVs
2 çè r l D pVs ÷øçè 4 * 2 ÷ø

21

Principles of Sedimentation
Remembering the general equation:
mp

d (Vs )
= r pV p g - r lV p g - 3pm l D pVs
dt

d (V s ) r pV p g r lV p g 3pm l D pV s
=
dt
mp
mp
mp

Substituting for mp and Vp:
d (V s ) r pV p g r lV p g 3pm l D pV s
=
dt
Vp r p
Vp r p
pD 3p
rp
6
d (Vs ) æç r p - r l ö÷
18m V
=
g- 2l s
ç
÷
dt
Dp r p
è rp ø

By Assist. Prof. Dr. Wipada Sanongraj

22

11

Wastewater Engineering and Design

Principles of Sedimentation
t=

Let

D p2 r p
18m l

d (Vs ) æç
r ö
V
= 1 - l ÷g - s
ç
dt
r p ÷ø
t
è

Using the integration factor method and the initial
conditions: Vs = 0 @ t = 0
æ r ö
Vs = gt ç 1 - l ÷ (1 - e - t / t )
ç r ÷
p ø
è
Where the relative measure of the fractional
approach to SS is:
(1 - e- t / t )

23

Principles of Sedimentation
D p2 r p
t = relaxation
time =
18 m l

When tà∞ then VsàVt
æ r ö
Vt = gt ç 1 - l ÷
ç r ÷
p ø
è
or

Vs = Vt (1 - e - t / t )
24

now (1-e-3) = 0.95 (it takes 3t to attain 0.95Vt)

By Assist. Prof. Dr. Wipada Sanongraj

12

Wastewater Engineering and Design

Example 2-1: Typical grit particle (sand)
Dp = 100 mm = 0.01 cm
rp = 2.65 g/cm3

Since the typical retention time for a particle may be
on the order of hours or more, we are not
concerned about non-steady state.
25

Example 2-1: Typical grit particle (sand)

Therefore, we can assume steady-state:
æ r - rl ö 18m l Vs
d ( Vs )
=0=ç p
g- 2
ç r ÷÷
dt
D prp
p
è
ø

Solve for Vs: (Stoke’s law for settling)
Vs =

g(rp - rl )D p2
18ml

for

NR £ 1

26

By Assist. Prof. Dr. Wipada Sanongraj

13

Wastewater Engineering and Design

Example 2-2: Bio floc particle
ml = 0.01185 g/(cm-s) rp = 1.05 g/cm3 rl = 1.0 g/cm3
Dp = 100 mm T = 25 oC

Check NR

Since NR < 1, laminar flow exists and Stoke’s Law is Valid

27

Example 2-2: Bio floc particle
What about a large particle size (sand)?
rp = 2.65 g/cm3 Dp = 200 mm T = 25 oC

Since the Reynolds number is greater than 1.0,
Stoke’s law is not valid because the drag coefficient of
the particle in water does not vary as 24/NR, but as:
28

By Assist. Prof. Dr. Wipada Sanongraj

14

Wastewater Engineering and Design

Example 2-2: Bio floc particle

Rearrange the original force balance:

d ( m p Vs )
dt

Vs2
= rp Vp g - rl Vp g - Cd rl A p
=0
2

Solving for Vs yield the following equation for Newton’s law
for settling particles:

29

Example 2-2: Bio floc particle
Since we cannot solve explicitly for Vs as in Stokes’s Law expression, we
must now use a trial and error solution as demonstrated below:

Using NR = 5.11 from above:
24
3
Cd =
+
+ 0.34 = 6.36
5.11
5.11

recalculate NR

NR = 4.38

30

By Assist. Prof. Dr. Wipada Sanongraj

15

Wastewater Engineering and Design

The procedure for calculating the settling velocity
of a particle when NR > 1 is:
1. Use Stoke’s Law to obtain the initial guess for
VS.
2. Use this Vs to obtain NR, if NR > 1, then go to
next step.
3. Use the following iteration process:
a) Use NR to get Cd
Cd =

24
3
+
+ 0.34
NR NR

31

b) Use Cd to get new Vs

c) Use Vs to find new NR
d) Repeat until convergence is met.

32

By Assist. Prof. Dr. Wipada Sanongraj

16

Wastewater Engineering and Design

Brownian Motion

In water and WW, colloidal particles are usually
present and are hard to remove by settling. A
colloidal particle may be thought as a giant
“molecule” and its Brownian motion is really a
diffusion process, where diffusion results from the
random thermal motion (due to thermal gradients
within the fluid).

33

Brownian Motion

The above particle motion was first observed for
water molecules by Dr. Robert Brown. In 1905,
Einstein used Stokes’s relationship and developed
the following equation to describe the motion.
34

By Assist. Prof. Dr. Wipada Sanongraj

17

Wastewater Engineering and Design

Brownian Motion
VB =

1 æ 2kT ö
ç
÷
DX çè 3pmD p ÷ø

Where: k = Boltzman constant = 1.38*10-16 (g-cm2)/(s2-K)
T = temperature (K)
DX = net x component distance of travel (cm)
m= kinematic fluid viscosity (g/cm-s)
Dp = mean particle diameter (cm)
VB = particle velocity due to Brownian Motion (cm/s)
When VB > Vs (stokes), particles will not settle out of solution
because the motion of the particle is governed by collision with
35
the water molecules.

The following characteristics are typical for water
and wastewater colloids:
Table 2-1: Characteristics of water and wastewater colloids
(Metcalf & Eddy, 1991)

36

By Assist. Prof. Dr. Wipada Sanongraj

18

Wastewater Engineering and Design

Example 2-3:
Calculate the smallest settleable sand particle in water
at 25 oC.
Solution
Assume DX = 1.0 cm

37

Example 2-3:
Setting VB = Vs

Coagulation and flocculation can be used to bring
particles together to form larger ones that will settle
out of solution by gravitational forces.

38

By Assist. Prof. Dr. Wipada Sanongraj

19

Wastewater Engineering and Design

Characteristics of Colloidal Particles in Water
1) Size-Very Small
1-1000 nm
10-10,000 Angstroms
10-4 – 10-7 cm
2) Surface Area – Very Large
Diameter of Spheres
Surface Area
1 cm
0.0487 in2
-4
10 cm
33.8 ft2
10-8 cm
3.8 yd2
10-6 cm
0.7 acres
10-7 cm
7.0 acres
3) Charge – Colloidal particles are usually NEGATIVELY
charge causing repulsion of similar charge and colloidal
39
stability.

Design of Type I Sedimentation Basins

Assumptions:
1. Plug flow exists in settling zone where fluid
moves across the settling zone with a constant
velocity.
2. Designed to remove discrete particle (settling
zone only considered)
3. Particles uniformly distributed at inlet.
40

By Assist. Prof. Dr. Wipada Sanongraj

20

Wastewater Engineering and Design

Design of Type I Sedimentation Basins
Key Process Variables
1. Hydraulic retention time = t = V/Q = Vol. tank/Flowrate
2. Overflow rate = Vo =Q/Atop
Vs = Flowrate/Top cross sectional area = h0/t
If Vs≥Vo, all particle of that
diameter are removed.
If Vs<Vo, particle removal,
%R = (Vs/Vo)100

Vf = horizontal fluid velocity
L = Length of settling zone

ho = height of settling zone

41

Example 2-4:
Assuming that the particle of various sizes are uniformly
distributed at the inlet, it can be seen from an analysis of
particle trajectory that particles with settling velocities
less than Vo will be removed in the ratio Vs/Vo.

42

By Assist. Prof. Dr. Wipada Sanongraj

21

Wastewater Engineering and Design

Example 2-4:
Say Dp = 200 mm,

Vs = 0.0235 m/s

Will all the particles be removed?

43

Example 2-4:
Say Dp = 100 mm,

Vs = 0.0076 m/s

l

l
44

By Assist. Prof. Dr. Wipada Sanongraj

22

Wastewater Engineering and Design

Removal efficiency is independent of depth (ho) and
retention time (t)

Vs = f(g,ml,rl, rp,Dp)

Vo = f(Q, Atop)

How can we use this information to determine the R.E. of a
sedimentation tank with many sizes of particles?

(Metcalf & Eddy,
1991)

45

Break the problem into two parts.
1. For particles which have Vs ≥ Vo all particles are
removed or (1-Xo) is removed.
2. For Vs ≤ Vo a fraction of the particles with such
velocities are removed.

46

By Assist. Prof. Dr. Wipada Sanongraj

23

Wastewater Engineering and Design

Break down the curve for all particles with settling
velocities Vs<Vo

(Metcalf & Eddy,
1991)

47

Where

(1-Xo)
xo

ò
o

By Assist. Prof. Dr. Wipada Sanongraj

Vs
dx
Vo

Vs ≥ Vo
Vs < Vo

48

24

Wastewater Engineering and Design

How do we obtain the necessary information to
make this calculation?
Two ways:
1. Use Stoke’s equation or Newton’s equation
depending on NR
2. Use a column settling test (most common)
1. Put a suspension in
column.
2. Mix well and
sample to
determine Co.
3. Stop mixing and
begin timing.
4. Take samples from
same depth.

49

Example 2-5:
For the following data and an overflow rate of 2.0
m/hr, what is the R.E.?

Solution
1. Plot x vs. Vs
2. Determine Xo from overflow rate (Vo)
3. Determine R.E. from

By Assist. Prof. Dr. Wipada Sanongraj

50

25

Wastewater Engineering and Design

Example 2-5:
1
R .E . = (1 - X o ) +
Vo

xo

ò V dx
s

o

51

Example 2-5:

Now suppose you’re given R.E. and you need to
calculate Vo.
Solution:

1. Plot x vs. Vs
2. Assume an Xo
3. Go to curve and get Vo
4. Calculate:
52

By Assist. Prof. Dr. Wipada Sanongraj

26

Wastewater Engineering and Design

Example 2-5:

5. Calculate R.E.
6. Plot R.E. vs. Vo
7. Use graph to get overflow for the R.E. of interest.
53

Example 2-6:
For the following data, calculate the overflow rate
for a R.E. of 75%.

1
R.E. = (1 - X o ) +
Vo

By Assist. Prof. Dr. Wipada Sanongraj

xo

ò V dx
s

54

o

27

Wastewater Engineering and Design

Example 2-6:
Solution
1. Assume Xo = 0.207

2. Assume Xo = 0. 417

55

Example 2-6:
3. Assume Xo = 0. 65

56

By Assist. Prof. Dr. Wipada Sanongraj

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Wastewater Engineering and Design

57

Figure 2-1: Two approaches to determining minimum particle size
58
removed in a nonturbulent chamber (Mihelcic, 1999)

By Assist. Prof. Dr. Wipada Sanongraj

29

Wastewater Engineering and Design

Type I Sedimentation for a Circular Clarifier

59

But Vf = Q/SA = Q/2prH = area of a cylinder with height H

All particles with Vs > Vo will be 100% removed. The analysis
is the same for both circular and rectangular tanks
60
employing type I sedimentation.

By Assist. Prof. Dr. Wipada Sanongraj

30

Wastewater Engineering and Design

Figure 2-2: Typical rectangular primary
sedimentation tank (Metcalf & Eddy, 1991)

61

Horizontal Flow Grit Chambers
Advantages

Disadvantages

Flexibility to alter performance is possible
by adjusting outlet control device

Difficulty in maintaining a 0.3 m/s velocity
over a wide range of flows

No unusual construction is required

Excessive wear on submerged chain and
flight equipment and bearings

With effective flow control, removal of grit
not requiring further classification is
possible

Where effective flow control is not
achieved, channels will remove significant
quantities of organic material requiring grit
washing and classifying

Flow control weirs typically require free
discharge and hence a relatively high head
loss (typically 30 – 40% of flow depth)

Proportional weirs may cause higher
velocities at the bottom leading to bottom
62
scour

By Assist. Prof. Dr. Wipada Sanongraj

31

Wastewater Engineering and Design

Aerated Grit Chambers
Advantages

Disadvantages

The same efficiency of grit removal is
possible over wide flow range

Power consumption is higher than other
grit removal processes

Head loss through the grit chamber is
minimal

Additional labor is required for
maintenance and control of the aeration
system

By controlling the rate of aeration, a grit of
relatively low putrescible organic content
can be removed

Some confusion exits about design criteria
necessary to achieve a good spiral roll
pattern removal system

Pre-aeration may alleviate septic conditions
in the incoming wastewater to improve
performance of downstream treatment units

Significant quantities of potentially harmful
volatile organic and odors may be
released from wastewaters containing
these constituents

Flexibility to remove grit can adapt to
varying field conditions
Aerated grit chambers ca also be used for
chemical addition, mixing, pre-aeration, and
flocculation ahead of primary treatment

63

Table 2-2: Horizontal Flow Grit Chambers Typical Design Criteria
(Metcalf& Eddy, 1999)

Item

Range

Comment

Water depth, m

0.6-1.5

Depend on channel area and
flow rate

Length, m

3-25

Function of channel depth and
grit velocity

Allowance for inlet and outlet
turbulence, %

20-50

Based on theoretical length

Detention time at peak flow, s

15-90

Function of velocity and channel
length

Horizontal velocity, m/s

0.15-0.4

Optimum velocity is 3 m/s

Dimension

64

By Assist. Prof. Dr. Wipada Sanongraj

32

Wastewater Engineering and Design

Table 2-3: Aerated Grit Chambers Typical Design Criteria
(Metcalf & Eddy, 1999)

Item

Range

Comment

Dimensions
Depth, m
L: W ratio
W: D ratio

0.2-5
3:1 – 5:1
1.1 – 5.1

Varies widely
4: 1 typical
1.5:1 typical

Minimum detention time (at
peak flow), min

2–5

3 typical

Air supply m3/min-m
Type of diffuser

0.27 – 0.74

0.45 typical

Medium to coarse
bubble
Transverse roll velocity, m/s

0.6 – 0.75

Provide valves and flow
meters to allow proper
adjustment
65

Type II: Primary Sedimentation Tanks
Primary sedimentation tanks are designed to:
1. Reduce solids loading to minimize operational
problems in downstream treatment processes.
2. Lower the oxygen demand.
3. Decrease the rate of energy consumption for
oxidation of particulate matter.
These effects enhance soluble substrate removal during
aeration and reduce the volume of waste activated sludge
that is generated. Also removes floating material, thereby
minimizing operational problems in downstream treatment
processes (scum build-up in secondary treatment
processes. If efficiently designed, removal rates of 50 to
70% of suspended solids and 25 to 40% of BOD5 can be66
realized.

By Assist. Prof. Dr. Wipada Sanongraj

33

Wastewater Engineering and Design

Flocculent Settling

Depends Upon:
1. Overflow Rate
2. Depth of Basin
3. Velocity Gradients in the Basin
4. Concentration of Particles
5. Range of Particle Sizes
6. Settling Column Analysis of
Flocculating Particles.

67

Example 2-7:
A column analysis of flocculating suspension is
performed in the settling column shown below. The
initial solids concentration is 250 mg/L. The data is also
shown below. What will be the overall removal efficiency
of a settling basin that is 3 meters in depth with a
retention time of 1 hour and 45 minutes

68

By Assist. Prof. Dr. Wipada Sanongraj

34

Wastewater Engineering and Design

Solution:
1) Determine the removal rate at each depth and time.

69

2) Plot iso-concentration lines as shown is the accompanying
figure.
3) Construct vertical line at to = 105 min.
4) Calculate the percentage removal using the following
equation:

70

By Assist. Prof. Dr. Wipada Sanongraj

35

Wastewater Engineering and Design

71

This procedure is very cumbersome and time
consuming. Another easier method is to calculate
the removal efficiency from the average
concentration in the column. For a given retention
time, t, the average concentration in the column
can be calculated using the following equation:
72

By Assist. Prof. Dr. Wipada Sanongraj

36

Wastewater Engineering and Design

73

Now add 1 to both side of the last equation in the
previous slide.

74

By Assist. Prof. Dr. Wipada Sanongraj

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Wastewater Engineering and Design

75

76

By Assist. Prof. Dr. Wipada Sanongraj

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Wastewater Engineering and Design

Type III Settling - Thickening

Definition: a process for removing water from
sludge which produces a more concentrated slurry
(i.e. end product is a liquid).
This process is not dewatering which produces end
product with the properties of solid.
Importance of Thickening:
1. Produce a greater volume of product water.
2. Produce a smaller volume of sludge.
3. Reduces the size of a sludge treatment facility,
(e.g. digester).
77

Purposes of Sedimentation Basins:
1. Clarification
2. Thickening
With respect to design of sedimentation basins
(or clarifiers) it is essential to consider both of
these functions.

78

By Assist. Prof. Dr. Wipada Sanongraj

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Wastewater Engineering and Design

(Metcalf & Eddy, 1991)

79

(Metcalf & Eddy, 1991)

80

By Assist. Prof. Dr. Wipada Sanongraj

40

Wastewater Engineering and Design

Batch Settling Test
(Metcalf & Eddy, 1991)

81

Design Considerations for Thickening of Sludge

82

By Assist. Prof. Dr. Wipada Sanongraj

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Wastewater Engineering and Design

In which,
Q
= influent flow rate to the clarifier/thickener, (L3/t)
Co
= influent suspended solids concentration, (M/L3)
Ce
= effluent suspended solids concentration, (M/L3)
Ac
= area available for clarification, (L2)
AT
= area available for thickening, (L2)
Qu
= flow rate leaving bottom of the
clarifier/thickener, (L3/t)
Cu
= suspended solids concentration leaving the
bottom of the clarifier/thickener, (M/L3)
Vi
= settling velocity of the suspended solids, (L/t)
Ci
= suspended solids concentration of the blanket,
(M/L3)
Ub
= velocity of the solids in the underflow due to
83
pumping (L/t)

Assume: Ce << Cu or Co and no biological reactions
taking place in the clarifier.

84

By Assist. Prof. Dr. Wipada Sanongraj

42

Wastewater Engineering and Design

2) Sizing a clarifier for thickening based on solids flux
method.
GT = Totalflux(

masssolids
)
area.time

In which, area is equal to the cross sectional area
of the sludge blanket
GT = Gg + Gb
In which,
GT
= total solids flux in the clarifier (M/L2-t)
Gg
= settling flux in the clarifier due to gravity (M/L2-t)
Gb
= bulk flux due to under flow pumping (M/L2-t)
85

At the bottom of the clarifier, Ci = Cu so the
expression for Gb can be written as:

Gb =

Qu Cu
= U b Cu
AT

Since the product of QuCu is usually unknown, it can
be replaced by QCo from the above mass balance,
QCo = QuCu.
86

By Assist. Prof. Dr. Wipada Sanongraj

43

Wastewater Engineering and Design

In addition, at the bottom of the clarifier, Gg = 0,
therefore, the area for thickening can be rewritten as:

AT =

Q u Cu QCo
QCo
=
=
GL
GL
CL (VL + U b )

87

(Metcalf & Eddy, 1991)

By Assist. Prof. Dr. Wipada Sanongraj

88

44

Wastewater Engineering and Design

(Metcalf & Eddy, 1991)

89

(Metcalf & Eddy, 1991)

90

By Assist. Prof. Dr. Wipada Sanongraj

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Wastewater Engineering and Design

91

(Metcalf & Eddy, 1991)

Alternative definition sketch for the analysis of settling data using
the solids-flux method of analysis (Metcalf & Eddy, 1991). 92

By Assist. Prof. Dr. Wipada Sanongraj

46

Wastewater Engineering and Design

Example 2-8:

Given the treatment scheme, estimate the maximum
concentration of the aerator mixed-liquor biological suspended
solids concentration that can be maintained if the
sedimentation tank application rate is fixed at 600 gal/ft2-d and
the sludge recycle rate, Qr, is 40% of Q. The following settling
93
data was obtained from operation of a pilot plant.

94

By Assist. Prof. Dr. Wipada Sanongraj

47

Wastewater Engineering and Design

Solution
1. Develop the
gravity solidsflux curve from
the given data.

95

2. Determine the underflow bulk velocity and plot
the curve on the same graph as the gravity solids
flux curve.

é
æ
öù
ê
ç
÷ú
æ 0.4Q ö
gal
1
ft
ê
ç
÷ ú = 0.95
Ub = ç
600
÷
2
gal öæ h ö ÷ ú
ft - d ç æ
h
è Q + 0.4Q ø ê
7.48
24 ÷ ÷ ú
ç
3 ֍
ç
ê
ft øè d ø ø û
èè
ë

Ub is the slope of the curve for the underflow solids
flux. The underflow flux curve can be plotted using the
following equation:
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By Assist. Prof. Dr. Wipada Sanongraj

48

Wastewater Engineering and Design

G b = kCi U b
In which,

97

3. Develop the total flux curve for the system by
summing the gravity flux curve with the underflow
flux curve, and determine the value of the limiting
flux and the maximum underflow concentration.

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By Assist. Prof. Dr. Wipada Sanongraj

49

Wastewater Engineering and Design

CR = Cu = 21,800 mg / L

99

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By Assist. Prof. Dr. Wipada Sanongraj

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Wastewater Engineering and Design

Example 2-9:

101

Given the settling data in the following table
derived from an activated sludge pilot plant,
determine the limiting solids flux values when the
concentration of the recycled solids concentration
is 10,500 and 15,000 mg/L, respectively.
Determine the recycle rate to the sedimentation
tank required for thickening in conjunction with the
aeration tank, if the MLSS in the aeration tank is to
be maintained at 5,000 mg/L and the underflow
concentration from the sedimentation tank is
12,000 mg/L. Neglect the effect of biological
growth in the sedimentation tank and assume the
flow is equal to 1.0 MGD.
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By Assist. Prof. Dr. Wipada Sanongraj

51

Wastewater Engineering and Design

103

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By Assist. Prof. Dr. Wipada Sanongraj

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Wastewater Engineering and Design

105

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By Assist. Prof. Dr. Wipada Sanongraj

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Wastewater Engineering and Design

10,500

107

For an underflow concentration of 12,000 mg/L the limiting solid
108
flux, SFL, = 1.8 lb/ft2-h

By Assist. Prof. Dr. Wipada Sanongraj

54

Wastewater Engineering and Design

109

A=

lb
mg
)
L ´ 8.34 MG = 1, 650 ft 2
2
mg
(1.8lb / ft - hr )(24 hr / d )
L

(1 + 0.71)(1.0 MGD)(5, 000

The corresponding surface hydraulic loading rate is 606 gal/ft2-d.
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By Assist. Prof. Dr. Wipada Sanongraj

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Wastewater Engineering and Design

Table 2-4: Typical Design Information for Secondary Clarifiers
(Metcalf & Eddy, 1999)

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By Assist. Prof. Dr. Wipada Sanongraj

56