DEVELOPMENT AND UTILIZATION OF GRAVITY SETTLING
SOLIDS FLUX CURVE FOR THE DESIGN AND
OPERATION OF A SECONDARY CLARIFIER
- BATCH SETTLING FLUX APPROACH BACKGROUND
The batch settling flux approach has been employed for years as one method of designing
secondary clarifiers. Although this is certainly an important application of this technique,
another equally important use of batch settling flux curves can be found in the generation of
secondary clarifier operation and control data. In this text, an activated sludge system is
comprised of an activated sludge basin (also referred to as the aeration basin) and a secondary
classifier. This is the most logical way of thinking of the activated sludge process, since both
individual unit operations (the aeration basin and the final clarifier) are in a cooperative
relationship.
Please refer to Figure 1 for a review of the activated sludge system and definition of terms.
Qi = Influent treatment plant flow rate
Qu = Clarifier underflow flow rate
QR = Recycle flow rate
Co = Clarifier influent TSS concentration (often referred to as mixed liquor suspended
solids (MLSS) and is the concentration in the aeration basin)
Cu = Clarifier underflow TSS concentration
Qw = Clarifier waste sludge flow rate
Qi + QR
Qi - QW
Qi
Aeration Basin
Co
(MLSS)
Final
Clarifier
Cu , Qu
QR
Cu
QW
Figure 1. Schematic of an activated sludge system
1
SETTLING FLUX DEFINED
Activated sludge entering the secondary clarifier from the activated sludge basin settles toward
the bottom of the clarifier by two velocity components;
(i)
A velocity component that results from gravitational forces (Vs) and
(ii)
A velocity component resulting from the removal of sludge from the bottom of the
clarifier (Vb = Qu/A), where A is the clarifier surface area.
The solids flux that results from gravitational settling velocity is termed settling flux (Gs) while
that flux resulting from underflow flow rate is termed bulk flux (Gb). The total flux is the sum of
the settling and bulk flux components and has units of mass per unit clarifier area per time
(lb/ft2_day). The components comprising total flux are mathematically defined in equation 1 and
2.
G s = Vs C
(1)
Gb = Vb C
(2)
where C is the concentration of solids passing through a given unit area of clarifier.
DEVELOPMENT OF A FLUX CURVE
Settling flux data are collected by performing column settling tests. These tests are conducted in
a series (6 to 8) of glass columns (3” ID x 24”) in which a range of concentrations of activated
sludge is added. The interface (the zone between the clear water and the top of the sludge
blanket) height is recorded as a function of time and a plot generated from the height-time data
pairs for each sludge concentration (Figure 2).
A velocity is determined using the linear portion of each curve (Figure 2). The resulting
velocity-concentration data pairs are then plotted as velocity vs. concentration and the data fit
with a nonlinear line of best fit (exponential works well). An example of such a curve is
represented in Figure 3. The line of best fit is then used to obtain V-C data pairs that are used to
calculate Gs (recall Gs=VsC). Each value of Gs represents the gravity settling flux per unit area
of clarifier that would be expected to occur at the corresponding activated sludge concentration
(MLSS).
Values of Gs, resulting from the use of Figure 3, are used to develop a batch settling flux curve as
shown in Figure 4.
2
Time (min)
0
10
20
30
40
50
0
1
2
Increasing
Concentration
Ht (in)
3
4
5
6
V2
7
V3
V1
8
9
10
Figure 2. Interface height - time profiles as a function of solids concentration.
160
140
V1, C1
120
V2, C2
V (ft/day)
100
V3, C3
80
V4, C4
60
40
20
0
0
2
4
6
8
C (g/L)
10
12
14
16
Figure 3. Interface settling velocity at different activated sludge concentrations and the associated
line of best fit. An example of obtaining four Vi, Ci data pairs is shown in the figure.
3
18.0
16.0
14.0
G (lbs/ft2-day)
12.0
10.0
8.0
6.0
4.0
2.0
0.0
0
2
4
6
C (g/L)
8
10
12
Figure 4. Batch settling flux data developed using the line of best fit in Figure 3 to collect Vi, Ci
data pairs.
FLUX CURVE UTILIZATION FOR CLARIFIER DESIGN
Use of a flux curve for design (clarifier surface area determination) is a relatively straight
forward process. A desired clarifier underflow concentration (Cu) is first selected (8000 - 12000
mg/L represents a common range with 10,000 mg/L often selected as a “typical” value for an
initial design exercise as it is reasonably representative of a final clarifier underflow TSS
concentration). A line is then drawn from this value, tangent to the flux curve, intersecting the yaxis. This line is the underflow operating line and has a slope equal to Qu/A, the bulk underflow
velocity Vb. The y-intercept is termed the limiting flux (GL). For example, if a Cu of 9500 mg/L
was selected as a clarifier design value, the underflow operating line depicted in Figure 5would
be constructed. When the underflow operating line is tangent to the flux curve, the clarifier is
said to be critically loaded. We will give further consideration to this term when we discuss
clarifier operation.
4
18
16
14
G (lbs/ft2-day)
12
Critically Loaded
Underflow Line
GL
10
8
6
4
Cu
2
0
0
1
2
3
4
5
6
C (g/L)
7
8
9
10
11
12
Figure 5. Underflow operating line in a critically loaded condition.
Next, an over flow operating line is drawn from the origin through a point on the underflow
operating line defined by the clarifier activated sludge feed concentration (MLSS = Co). This
line, depicted in Figure 6, has a slope of Qi/A (surface overflow rate) and is termed the overflow
operating line. The intersection of the overflow and underflow operating line is defined as the
operating state point. The y coordinate of the state point is Go and is often used to calculate the
clarifier surface area using Equation 3.
A=
Qi C o
Go
(3)
5
18
16
14
State Point
G (lbs/ft2-day)
12
Qi/A = SOR
GL
10
8
6
GO
4
Cu
2
0
0
1
2
3
4
5
6
C (g/L)
7
8
9
10
11
12
Figure 6. Underflow and overflow operating lines and location of state point.
FLUX CURVE UTILIZATION FOR CLARIFIER OPERATION
Essentially all WWTPs experience short term (diurnal), intermediate term (seasonal), and long
term (design period) changes in influent flow. It is instructive to consider how these changes
affect the operational state of the plant and how a plant operator should respond to the flow
changes that are imposed. First, let’s introduce and define two terms. In Figure 7, three
underflow operating lines are represented. The line below the critically loaded condition
represents an underloaded condition. There is no particular problem operating in this condition.
It can be seen, however, that Cu is less in an underloaded condition. Underloading could impact
downstream sludge handling systems since Qw would need to be increased to maintain a solids
balance in the activated sludge basin, if the underloaded condition was significant and
maintained for an extended period.
When the underflow operating line lies above the lower portion of the flux curve, the system is
termed overloaded. This means that a greater mass of solids is entering the clarifier than can be
transported to the bottom by Vb and Vs. In other words, the limiting flux (GL) is being exceeded,
resulting in an increase in sludge blanket height in the clarifier. This may lead to clarifier failure
if the sludge blanket rises too high, resulting in solids being carried over the weir.
The settling flux curve can be used to quantify a response action by the operator to prevent
clarifier failure. For example, consider a system that is operating in a critically loaded condition,
6
as shown in Figure 8. A flow increase is represented graphically by determining the new
overflow operating line with slope (Qi’/A = SOR’) and placing this line on the flux plot as shown
in Figure 8. The state point rises to the intersection of SOR’ at Co and the underflow operating
line (shown as dotted line) is brought up to the new state point and placed parallel to the original
underflow operating line. It can be seen that the new underflow line (dotted line) is above the
flux curve at concentrations above approximately 5 g/L, indicating that the system is overloaded.
The system can be brought back to a critically loaded condition by increasing the slope of the
underflow operating line until it is tangent to the flux curve. This yields a new underflow
concentration and limiting flux (Cu’ and GL’, respectively). Operator action can be determined
by taking the slope of the new underflow operating line and applying the relationship u = Qu/A.
Where u is the underflow velocity imposed by the underflow flow rate, Qu.
18
16
14
G (lbs/ft2-day)
12
GL
10
Overloaded
8
6
4
Underloaded
2
Cu
0
0
1
2
3
4
5
6
C (g/L)
7
8
9
10
11
12
Figure 7. Underflow operating lines for underloaded, overloaded, and critically loaded conditions.
7
18.0
G (lbs/ft2-day)
16.0
SOR'
GL'
14.0
SOR
12.0
10.0
GL
8.0
6.0
4.0
2.0
0.0
0
2
4
Co
6
C (g/L)
8
10
Cu'
12
Cu
Figure 8. Result of WWTP flow increase on state point location and operator response to avoid
clarifier failure.
The previous example represented a case of active operator control. If the operator takes no
action in response to a hydraulic increase, then the clarifier’s thickening capacity would be
overloaded as previously mentioned. The system would respond by transferring solids from the
aeration basin to the clarifier thereby diluting the solids in the aeration basin resulting in a
decrease in MLSS. The solids blanket would rise in the clarifier resulting from the solids
transfer.
The shift in operational states is shown in Figure 9. From the overloaded state (state point b) the
state point would shift down along the overflow rate operating line until it reached the location of
state point c, which corresponds to a stable operational state for the aerator/clarifier system for
which the recycle rate was not changed. Thereafter, no further change in the operating state of
the system would be observed; i.e., no additional bio-solids would be transferred from the aerator
to the clarifier.
8
18.0
SOR'
G (lbs/ft2-day)
16.0
14.0
SOR
12.0
b
10.0
GL
8.0
c
6.0
4.0
2.0
0.0
0
2
Co'
4
Co
6
8
10
12
C (g/L)
Figure 9. Self correcting response of a clarifier from a WWTP flow increase.
REFERENCES
1.
Metcalf and Eddy, Inc., (1991), Wastewater Engineering: Treatment, Disposal, Reuse,
Third Edition, Irwin/McGraw-Hill, pub.
2.
Reynolds and Richards, (1996), Unit Operations and Processes in Environmental
Engineering, Second Edition, PWS, Pub.
3.
Keinath, T.M., Operational Dynamics and Control of Secondary Clarifiers, Journ. WPCF,
59, 770 (1985).
9
APPENDIX A
Design Example
10
DESIGN EXAMPLE
An activated sludge interface height settling test resulted in the flux curve presented in Figure 10.
Design (determine surface area and diameter) a secondary clarifier for a municipal WWTP flow
of 5 MGD with a desired underflow concentration of 9500 mg/L and MLSS (Co) of 2500 mg/L.
Following clarifier design, determine what operator action would return the clarifier to a
critically loaded condition following a 20% plant flow (Qi) increase. Also determine the clarifier
response to the flow increase with no operator action. Assume an activated sludge basin volume
of 1.3 MG.
Solution
Determine Clarifier Area and Diameter
The flux plot is used to:
1. draw an underflow operating line,
2. find the “x” coordinate of MLSS on the underflow operating line,
3. draw the overflow operating line from the origin through this coordinate, and
4. determine Go.
The actions are depicted in Figure 11.
18.0
16.0
14.0
G (lbs/ft2-day)
12.0
10.0
8.0
6.0
4.0
2.0
0.0
0
1
2
3
4
5
6
C (g/L)
7
8
9
10
11
12
Figure 10. Design example solids flux plot.
11
18
16
14
SOR = Qi/A
G (lbs/ft2-day)
12
GL
10
8
6
Go
4
Qu/A
2
Co
0
0
1
2
3
4
5
6
7
C (g/L)
8
9
Cu
10
11
12
Figure 11. Construction of underflow and overflow operating line and location of state point.
Equation 3 can then be applied to determine surface area.
A=
Qi C o
Go
A=
5 MGD(2500 mg/L)8.34
= 1.45 x10 4 ft 2
2
7.2 lb/ft day
A = 1.45 x10 4 ft 2
D = 136 ft
Operator Action
First, a new surface overflow line is constructed as shown in Figure 12 by calculating the x-y
coordinates resulting from the 20% flow increase. One method of doing this is to determine the
new Go (Go’) as shown below. The MLSS concentration (Co) is assumed to stay the same for
some time following the flow increase. Therefore, the x-coordinate would be 2.5 g/L and the ycoordinate would be 8.6 lb/ft2-day and represents the new state point.
12
Go'−Go Go'−7.2
=
= 0 .2
Go
7 .2
Go' = 8.6 lb/ft 2 - day
3) draw the SOR’ line from the origin through the new sate point.
The new value of underflow flow rate (Qu’) that is required to prevent an overloaded condition is
then determined by drawing an underflow operating line through the new state point, tangent to
the flux curve (Figure 12). The slope of this line is calculated and Qu’ determined from
G 'L 12 lb/ft 2 day 
mg/L  Q 'u
Slope = u' = ' =
16017
=
9000 mg/L 
lb/ft 3  A
Cu
Q 'u
= 21.4 ft/day
A
Q 'u = A(21.4 ft / day )
u' =
G (lbs/ft2-day)
Qu' = 1.45 x10 4 (21.4 ft / day ) = 3.1x10 5 ft 3 / day = 2.32 MGD
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
SOR' = Qi'/A
GL'
SOR = Qi/A
Go'
u' = Qu'/A
Go
u = Qu/A
Co
0
1
2
3
4
5
6
C (g/L)
7
8
9
Cu'
Cu
10
11
12
Figure 12. Construction of SOR’ line, determination of Cu’, and u’.
13
System Response Without Qu Modification
If the operator elects to leave the system alone (i.e., no adjustment made to Qu), we can
determine what the natural response of the system would be.
As before, the state point rises to intersect the SOR’ overflow operating line (Figure 13). The
new underflow line shows an overloaded condition. With no operator response, a net transfer of
biosolids from the activated sludge basin to the clarifier occurs, diluting the MLSS concentration
in the basin. This is evidenced by the state point coming down the SOR’ line until it intersects
the original underflow operating line. It can be seen that the new value of MLSS (Co’) is
approximately 2200 mg/L. The mass of solids transferred to the clarifier can be calculated by
taking the difference between the MLSS concentrations and multiplying this difference by the
activated sludge basin volume as shown below
(
)
M t = C O − C O' V
where
M t = mass of solids transfered
C O = original MLSS concentration
C O' = MLSS concentration following net solids transfer to the clarifier at the new flow (Qi' )
V = activated sludge basin volume = 1.3MG = 4.92 x10 6 L
M t = (2500mg / L − 2200mg / L )4.92 x10 6 L = 1.476 x10 9 mg = 3254lb
Now we can estimate the sludge blanket rise by knowing the mass of biosolids transferred. The
concentration of the upper portion of the solids blanket in a clarifier is given by the “x”
coordinate of the tangent point of the underflow operating line on the flux curve. For this
problem, we have a value (CL) of approximately 7500 mg/L (0.47 lb/ft3). This concentration can
be used to determine the storage of solids per foot of clarifier depth.
S f = CL A
where
S f = sludge storage per foot of clarifier depth
A = clarifier surface area
S f = 0.47lb / ft 3 (1.45 x10 4 ft 2 ) = 6815lb / ft
We can now calculate the rise in blanket height using the solids transferred:
14
h=
Mt
3254lb
=
= 0.48 ft
Sf
6815lb / ft
where
h = blanket height rise
G (lbs/ft2-day)
Clarifiers under normal operating conditions can have up to 6 feet of solids storage. It can be
seen that clarifiers can have considerable capacitance for diurnal fluctuations in plant flow.
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
SOR' = Qi'/A
SOR = Qi/A
u = Qu/A
Co
Co'
0
1
2
3
CL
4
5
6
7
8
C (g/L)
9
Cu
10
11
12
Figure 13. Response of system without operator control.
15