WATER POLLUTION CONTROL, RESEARCH SERIES
17090 FJW 02/72
A Mathematical Model
of a Final Clarifier
U.S. ENVIRONMENTAL PROTECTION AGENCY
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WATER POLLUTION CONTROL RESEARCH SERIES
The Water Pollution Control Research Series describes the results
and progress in the control and abatement of pollution in our
Nation's waters. They provide a central source of information
on the research, development, and demonstration activities in
the water research program of the Environmental Protection Agency,
through inhouse research and grants and contracts with Federal,
State, and local agencies, research institutions, and industrial
organizations.
Inquiries pertaining to Water Pollution Control Research Reports
should be directed to the Chief, Publications Branch (Water),
Research Information Division, R&M, Environmental Protection
Agency, Washington, D.C. 2O46O.
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A MATHEMATICAL MODEL OF A FINAL CLARIFIER
by
Rex Chainbelt, Inc.
Milwaukee, Wisconsin 532O1
for
Office of Research and Monitoring
ENVIRONMENTAL PROTECTION AGENCY
Project #17090 FJW
Contract #14-12-194
February 1972
For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 - Price $1.00
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EPA Review Notice
This report has been reviewed by the Environmental
Protection Agency and approved for publication.
Approval does not signify that the contents necessarily
reflect the views and policies of the Environmental
Protection Agency, nor does mention of trade names or
commercial products constitute endorsement or recommenda-
tion for use.
11
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ABSTRACT
The final clarifier in the activated sludge process performs a vital
role in secondary waste treatment systems. The final clarifier must
perform the dual function of providing an effluent low in suspended
solids and must be capable of providing an underflow of sufficient
concentration to permit the maintenance of a suitable population of
active microbial mass in the aeration tank. The purpose of this project
was to develop a mathematical model to predict the solids concentration
of both the underflow and overflow of a final clarifier as a function of
the mixed liquor characteristics. This model was to utilize, as much as
possible, those parameters which are normally available to engineers
involved in the design of final clarifiers.
An experimental testing program was carried out on final clarifiers at
three treatment plants in order to provide a set of data for the formula-
tion and testing of the model. The techniques of multiple regression
analysis were used to develop the following equations for estimating the
return sludge and effluent suspended solids concentrations.
Maximum Return Sludge _ 106
Concentration (mg/1) 54Q x A*.397 x gO.213
where: A = fraction of volatile suspended solids
B = BOD loading Ibs BOD/day/#MLVSS
,,
Effluent Suspended _
Solids (mg/1) MLSS'35 x Detention Time1'03
The effluent solids equation had a multiple correlation coefficient of
0.63. The magnitude of the correlation coefficient for the effluent solids
equation was lower than anticipated because of changes in sludge quality,
both interplant and intraplant which were not accounted for by the parameters
considered in this study.
Based on the results of this work it can be concluded that neither the
effluent suspended solids nor the return sludge concentration can be
estimated with good accuracy from those parameters which are normally
available to the design engineer.
Recommendations for future work which would enable a more realistic approach
to the preliminary design of final clarifiers are made. For example,
techniques for estimating the sludge subsidence characteristics in terms
of the operational parameters of the activated sludge system need to be
developed because generally only the operational parameters are available
for preliminary design and simulation studies.
This report was submitted in fulfillment of Project Number 17090FJW,
Contract 14-12-194, under the sponsorship of the Environmental Protection
Agency.
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CONTENTS
Conclusions 1
Recommendations for Future Research 3
Introduction 5
Literature Search 7
Theoretical Development 41
Experimental Procedures 45
Results 59
Discussion of Results 79
Summary 85
Acknowledgments 87
Bibliography 89
Appendices
1. Example of Output from Computer Regression
Analysis 95
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LIST OF FIGURES
Figure
1 Settling Zones for Class III Suspensions 3
2 Parameter Response to Organic Loading,
Domestic Waste. . '
3 Parameter Response to Organic Loading,
Petrochemical Waste « 8
4 Parameter Response to Organic Loading,
Brewery Waste '
5 Settling Characteristics of an Activated Sludge .
• •
12
6 The Influence of Initial Solids Concentration and
Mixing on the Settling Rate of Class III Solids .... 13
7 Effect of Settling Column Diameter on Batch
Settling Rate ..................... 16
8 Effect of Sludge Volume Index and Temperature on
the Effluent Solids Concentration ..... . ..... 19
9 Functional Zones of a Final Settling Tank ....... 23
10 Center Feed Basin ................... 25
11 Peripheral Feed Basin ....... . ......... 26
12 Density Currents in a Final Clarifier ......... 28
13 Typical Dispersion Curves for Peripheral and
Center Feed Tanks ...... ...... ..... • •
14 Flow Diagram - Racine, Wisconsin Water
Pollution Control Plant ................ 39A
15 Return Sludge Piping Arrangement - Racine,
Wisconsin Water Pollution Control Plant ........ ^2
16 Flow Diagram - Brookfield, Wisconsin Water
Pollution Control Plant
17 Flow Diagram - Fort Atkinson, Wisconsin
Water Pollution Control Plant
vi
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LIST OF FIGURES (Cont'd)
Figure Page
18 Typical Settling Curve 49
19 General Flow Sheet and Nomenclature for
Final Clarifier 53
20 Effect of Return Rate on Compaction Ratio 56
21 Solids Deposition Pattern in Final Clarifier 62
22 Solids Deposition Pattern in Final Clarifier 63
23 Percent Solids Concentration at Various Times
after the Passage of the Sludge Collector . 64
24 Observed and Calculated Values of Effluent
Suspended Solids 68
vii
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CONCLUSIONS
1. The maximum return sludge concentration from a final clarifier can
be estimated from the relationship:
TSS6
540 x AA'397 x B°-213
where: A = fraction of volatile suspended solids
B - BOD loading - Ibs BOD/day/lb MLVSS
2. The effluent suspended solids from a final clarifier can be estimated
from the relationship:
„ = 382 x Overflow Rate0'12 x BOD Loading0'27
3S 1 03
MLSS"" x Detention Time1* J
3. The relationship for effluent suspended solids needs to be improved.
Based on information collected in this study a new parameter, sludge
quality, is proposed which would account for the various classifica-
tions of solids comprising activated sludge (active cells, inert
cells, digested fines, etc.) and the ability of these solids to
flocculate.
4. Future studies of activated sludge systems should include an evalua-
tion of the sludge subsidence characteristics and sludge quality as
a function of the operational parameters of the activated sludge
system.
5. The most pressing need in the development of sedimentation models is
a formula relating the settling rate of activated sludges to the
operational characteristics of the aeration tank.
6. Commonly accepted parameters of settling rate and overflow rate are
gross measurements which are not sensitive enough to adequately
predict final clarifier performance. They are, however, useful as
design and operational parameters.
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RECOMMENDATIONS FOR FUTURE RESEARCH
There is a great necessity for a mathematical model to predict the
performance of final clarifiers. Reliable estimates of solids output
from final clarifiers are needed to design tertiary treatment system^
as input to river basin treatment optimation studies and for in-plant
optimization studies. In order to improve the reliability of the
equations presented in this report and to permit preliminary design, the
following items need further investigation.
1. A more reliable laboratory procedure that will closely
approximate the settling rate in full-sized clarifiers
needs to be developed. Particular emphasis should be
given to cylinder diameter, cylinder depth and mixing.
2. A method to permit the prediction of the settling rate
of the activated sludge as a function of the solids
characteristics and the operational parameters of the
activated sludge system needs to be developed. This
procedure would then permit the preliminary design of
final clarifiers based on a knowledge of the sludge to
be separated.
3. The sludge quality parameter as defined in this report
needs to be evaluated to determine the effect of the
various classifications of solids comprising the sludge
on the effluent quality from the clarifier.
4. Side by side tests of various types of final settlers need
to be made to evaluate the effect of geometric configura-
tion on final effluent quality. It is only when two
clarifiers are evaluated while handling the same sludge
that meaningful conclusions can be drawn concerning the
effect of tank geometry and inlet and outlet configurations.
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INTRODUCTION
The increased demands for the abatement of water pollution in the
United States has resulted in an increased interest in mathematical
modeling of the unit processes in the waste treatment field. Mathematical
models are useful both as an aid in the understanding of process behavior
and in optimizing a system composed of a number of unit processes.
The purpose of this project has been to develop a mathematical model to
predict the performance and design requirements of a final clarifier in
the activated sludge process. An attempt has been made to use parameters
in the model which are routinely available to consulting engineers. It
is felt that this approach is necessary in order to make the model of
practical use and not just a theoretical study.
Since the effluent of the final clarifier represents the quality of treat-
ment achieved at most treatment plants prior to its discharge into the
receiving waters, the final clarifier might be considered the most import-
ant unit process in a secondary waste treatment plant.
The final clarifier in the activated sludge process has two major functions.
It must discharge an effluent (overflow) which is low in suspended solids.
At the same time, it must be capable of removing settled activated sludge
(underflow) at a sufficiently high concentration to maintain a satisfactory
inventory of viable solids in the aeration tanks. In addition to the very
important considerations of the activated sludge settling rate, the
general hydraulic parameters, and the clarifier design, the sludge reten-
tion time and distribution within the clarifier are of utmost importance.
It must be realized that an activated sludge system is an integral treat-
ment process consisting of both an aeration and a sedimentation step.
This interrelation must always be considered when either step is under
study. For example, under certain conditions of deficient aeration, a
"bulking" activated sludge may be produced. This sludge, which exhibits
very poor settling characteristics, may prevent the final clarifier from
producing an effluent which is low in suspended solids. Under normal
operation, with sufficient aeration, the sludge produced in the aeration
tanks may readily be settled out in the associated final clarifiers.
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LITERATURE SEARCH
The sedimentation process has been the subject of much research and
design effort. A literature search has been made in an attempt to
assemble the currently accepted theories of the final clarification
of activated sludge in order to elucidate the methods and procedures
to be followed in fabricating a mathematical model to predict the
performance of a final clarifier. The literature search has been
narrowed to include the topic of sedimentation only as it applies to
activated sludge.
The first section of this review deals with the sludge solids and their
relationship to the overall process. The second section discusses the
design requirements and the operational characteristics of final
clarifiers.
Characteristics of the Solids
Katz et al(l) have divided suspensions into three general classifica-
tions :
Class I - Discrete particles, which will not readily flocculate
and which predominate in relatively low concentrations.
An example of this type of suspension is encountered in
grit chamber design and in clarification of certain
industrial wastes such as sand and gravel washings, etc.
Class II - Relatively low solids concentrations of flocculent
material. An example of this type of material is
found in primary settling tank influents, water which
has been subjected to flocculation and numerous indus-
trial wastes.
Class III - Encompasses materials of relatively high concentrations.
The material may be flocculent, but not necessarily so.
Hindered settling is the term generally used to describe
separation of this type of solids. Examples of this
type of separation are found in activated sludge settling
and industrial wastes, such as paper and pulp.
Class I and II suspensions are not normally encountered in final clarifiers
and hence will not be further considered here.
The settling process of Class III suspensions has been described by
Eckenfelder and 0'Connor(2) and is shown in Figure 1. During the initial
settling period (A) the sludge floe settles at a uniform velocity under
conditions of zone settling. The magnitude of this velocity is dependent
on the initial solids concentration. The concentration of solids during
this period remains constant until the settling interface approaches an
interface of critical concentration. With an increase in depth of the
settled sludge, the floe begins to press on the layers below and the
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HINDERED SETTLING
CONSTANT COMPOSITION
VELOCITY « F (CONCENTRATION)
TRANSITION ZONE
VARIABLE COMPOSITION
COMPRESSION
ZONE
TIME
FIGURE I
SETTLING ZONES FOR CLASS III SUSPENSIONS
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transition zone occurs. The settling velocity decreases in the transi-
tion zone due to the increasing density and viscosity of the suspension
surrounding the particles. A compression zone (C) occurs when the floe
concentration becomes so great as to be mechanically supported by the
layers of the floe below. The solids concentration in the compression
zone is related to the depth of the sludge and the detention time of the
solids in this zone.
Activated Sludge Modifications
The activated sludge process can be and is operated over a broad spectrum
of growth phases ranging from high rate - dispersed growth to extended
aeration systems. The growth phase or physiological state of the micro-
organisms has been implicated as an important factor in the separation of
the activated sludge solids from water (3)(4). An idealized growth curve
for the various activated sludge modifications has been presented by
Lespcrance(S).
High rate activated sludge systems operate in the log growth-declining
growth phases and the solids tend to be difficult to separate in gravity
separation systems. Their primary use is found in areas where a high
quality effluent is nor required for discharge to the receiving waters.
Conventional activated sludge is probably the most commonly used method
of treatment. The systems are operated in the declining and endogenous
growth phases with BOD loadings up to about 0.5 Ib.BOD/day/lb.MLSS. Most
of the difficulties reported in the literature concerning activated sludge
treatment have occurred in the conventional systems.
The step aeration process was developed in an effort to overcome some of
the problems associated with the conventional activated sludge process.
In this method, the raw waste is introduced at a number of points along
the length of the aeration tank. The process tends to stabilize the
growth phase within a narrow range as compared to wide fluctuations in
the conventional process. In addition, it allows a savings in aeration
tank volumes(6). The gross BOD loading would be of the same order of
magnitude as the conventional system.
A more recent development, complete-mixing activated sludge, has been
advocated by a number of people(7)(8). In this modification, the raw
waste is intimately mixed with the activated sludge solids to maintain
a uniform BOD and mixed liquor solids loading in the entire tank. Pro-
ponents of the process feel that steady state organic loading and bio-
logical growth characteristics can best be maintained in this type of
system.
Numerous other activated sludge modifications exist, each having merit
under certain conditions. These modifications have arisen primarily as
a result of plant operators' efforts to solve a particular problem. For
example, the Kraus modification was developed in an attempt to overcome
a bulking sludge which was very difficult to separate.
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Extended aeration is the extreme process modification on the low organic
loading scale. Aeration detention times of 24 hours are normally main-
tained at BOD loadings of 0.1 to 0.2 Ib.BOD/day/lb.MLSS. Final clarifi-
cation of the mixed liquor from these systems often results in poor
quality effluent resulting from denitrification or pinpoint floe result-
ing from overaeration.
A summary of the design and operational parameters for the various
activated sludge modifications is shown in Table 1. Although there is
little or no data in the literature relating the solids subsidence
characteristics of activated sludges to the various process modifica-
tions there can be little doubt that some relationship does exist.
Ford and Eckenfelder(A) reported on the results of literature studies
in which three industrial wastes were studied over a range of organic
loadings. These results are shown in Figures 2, 3, and 4. It can be
seen that increases in organic loadings tend to decrease the subsidence
and compaction characteristics of the sludges. For these wastes, the
optimum loading from a solids separation standpoint was about 0.3 to
0.4 Ib.BOD/day/lb.MLSS.
Based on the data available in the literature, it would appear that
additional investigation of the effect of organic loadings on the subsi-
dence characteristics of sludges would be fruitful.
Biological Factors
The development of an activated sludge depends on a number of parameters
including the waste characteristics, growth rate of the micro-organisms
and the availability of the essential nutrients. Depending on these
variables, the sludge may range from predominantly bacteria to filamentous
bacteria to fungi. Since the overall performance of secondary waste treat-
ment is primarily a function of the solids separation which occurs in the
final settler, the predomination of various types of micro-organisms
becomes an important consideration.
An activated sludge developed from a nutritionally balanced waste is
generally predominantly bacterial in composition with some protozoa and
higher forms of life. Bacterial sludges generally have good subsidence
characteristics.
Wastes high in carbohydrates, or low in nitrogen have been shown to
produce filamentous type sludges. Data shown in Figures 2, 3, and 4
indicate that organic loadings in excess of 0.5 Ib.BOD/day/lb.MLSS also
tend to promote filamentous type sludges. Filamentous sludges tend to
be difficult to settle because of their large surface area to volume
ratio and their low density.
10
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TABLE 1
A Comparison of the Biological Characteristics of
Various Activated Sludge Processes (61)
Characteristics
Primary
Sedimentation
Aeration Period
(hours)
Secondary
Sedimentation
Return Sludge Flow
(% of Raw Flow)
BOD Loading
(lb/day/100 Ib MLSS)
Sludge Age (days)
BOD Removal (%)
Conventional
Usually
Provided
5-10
Yes
25-50
25-50
3-6
85-90
High Rate
or Modified
Optional
2-3.5
Yes
10
200-400
1/4-1/2
60-75
Contact
Stabilization
Optional
0.33-0.67
(contact)
Yes
30-50
15-35
3-7
90
Extended
Aeration
Generally
None
24
Yes
up to 100
about 15
>10
98
Complete
Mixing
Optional
2
Yes
up to 100
about 60
1-2
85-90
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85
8O
i75
UJ
o
LL
ii TO
65
U
60
55
250 r-
2OO
150
tu
2
o
100
o
tn
50
PARAMETER RESPONSE TO ORGANIC LOADING, DOMESTIC WftSTE
FIGURE 2
20
18
ZONE SETTLING VELOCITY
»/o BOD 5 REMOVAL
% COD REMOVAL
Lf
LOADING FACTOR
(Ibs COD/ day/ Ib solids)
100
90
UJ
o
u.
U.
UJ
80
UJ
a:
o
o
m
70
6O
.5
(Ibs BOD5/day/lb solids)
1.0
-------
IOO
9O
80
u.
u.
UJ
I
70
50 L
500
PARAMETER RESPONSE TO ORGANIC LOADING, PETROCHEMICAL WASTE
FIGURE 3
400
UJ
o
t
UJ
300
UJ
0200
CO
60 - IOO -
0 L.
25
20
§15
UJ
svi
% BOD- REMOVAL
5
ZONE SETTLING VELOCITY
100
90
u
80 g
o
u.
u.
UJ
70 o
S
UJ
a:
o
§
60
50
1.0
2.0
3.0
4.0
5.0
LOADING FACTOR
(Ibs COD/day/ Ib solids)
I
I
.40
.80
1.20
1.60
2.0
(Ibs BOD e /day/ Ib solids)
5
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IOO T- §OO ,-
PARAMETER RESPONSE TO ORGANIC LOADING, BREWERY WASTE
FIGURE 4
95
90
o
UJ
o
65
UJ
60
75
o
8
70
65
400
x
u
o
^300
UJ
UJ
o
§200
IOO
ZONE SETTLING
VELOCITY
.6 .8 1.0
LOADING FACTOR
(Ibs COD/ day/ Ib solids)
I I I f I
I
0
1.0
(Ibs BOD5 /day / Ib solids)
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The environmental conditions in the aeration tank are important to the
development of a sludge with good subsidence characteristics. The
environmental conditions affecting sludge characteristics include dis-
solved oxygen concentration, pH, sludge age, and intensity of aeration.
Pipes(9) has discussed various types of activated sludges and attempted
to classify sludges according to whether they bulked or not. The basic
classifications presented by Pipes together with their apparent causes
are shown in Table 2. This classification clearly indicates the intimate
relationship between the environmental conditions in the aeration tank and
the design and performance of the final clarifier.
The various types of sludges and their related causes will not be discussed
in detail because the majority of the causes have not been proven. As
Pipes pointed out in his discussion, much work needs to be done to improve
the understanding of the causes of solids separation problems in activated
sludges.
Settling Characteristics of Solids
The settling rate of mixed liquor solids is normally obtained by observing
the position of the water-solids interface as the solids settle in a one
liter graduate. The settling rate is then determined as the slope of the
line in the free settling zone expressed in units of feet per minute or
feet per hour.
When sludge samples are available prior to the design of a sedimentation
tank, this settling rate is used in the design procedure. The settling
rate can be converted to an upflow velocity expressed in gallons per day
per square foot. This upflow velocity must always be greater than the
design overflow rate.
The concentration of mixed liquor solids is known to affect the settling
rate of the solids (1)(10) . This relationship is shown in Figures 5 and 6.
In Figure 5 the initial settling velocity is plotted versus initial depth
for various MLSS concentrations. The settling velocity decreases linearly
with increases in MLSS. Figure 6 is a plot of settling rate versus initial
solids concentration. The decrease in settling rate with increased MLSS
is similar to that shown in Figure 5.
The effect of gentle mixing on the settling rate can also be seen. The
effect of mixing becomes more beneficial at high MLSS concentrations.
Dick and Ewing(lO) also observed the benefits derived from gentle mixing
which can influence the zone settling velocities .arid increase the solids
transmitting capacity of activated sludge.
A number of mathematical expressions have been presented in the literature
which relate mixed liquor suspended solids concentrations to the settling
velocity of activated sludges. These equations are in most cases entirely
15
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TABLE 2
Classification of Various Difficult-to-Separate Activated Sludges
Classification
Probable Cause
I. Bulking Sludge
a) Non-Filamentous
Bulking
b) Filamentous
Bulking
11. Rising Sludge
111. Septic Sludge
IV. Overaerated Sludge
V. Floating Sludge
VI. Pinpoint Floe
VII. Billowing Sludge
Presence of large quantities of extracellular materials with a
high degree of hydration producing a sludge with excessive
amounts of bound water.
The predomination of fungi; as a result of certain environmental
factors, i.e., low pH, low dissolved oxygen.
Denitrification in the sludge blanket.
Excessive sludge detention times in the final clarifier resulting
from poor elarifier design.
Excessive aeration causes bubbles to be carried into the final
clarifier end causes the sludge to be buoyed to the surface by
the rising bubbles.
Presence of sludge particles whose density is less than water.
Excessive turbulence in the aeration tank.
Hydraulic surges, density currents, stirring by sludge scrapers.
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X
K-'
LL
O
3
UJ
K-
UJ
3l75mg/L
4415 mg/L
5440 mg/L
59IO mg/L
6435 mg/L
6635 mg/L
4567
DEPTH (FT.)
FIGURE 5
SETTLING CHARACTERISTICS OF AN
ACTIVATED SLUDGE
8
10
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10 -
THE INFLUENCE OF INITIAL SOLIDS
CONCENTRATION AND MIXING ON THE
SETTLING RATE OF CLASS 3 SOLIDS
FIGURE 6
1 \ 1 1 T
A- 1000ml GRADUATE WITH GENTLE MIXING
B- 1000 ml GRADUATE WITHOUT MIXING
8
id
I-
UJ
1000
2000 300O 4OOO 50OO
INITIAL SOLIDS CONCENTRATION Cppm)
18
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empirical and may result in serious error when used for sludges other
than those for which they were developed. These equations are presented
in Table 3 to give an estimate of the general form of the equations.
In addition to concentration, settling column diameter and initial sludge
depth have been shown to affect the subsidence rate of activated sludges
(10)(11). Vesilind(ll) presented a particularly interesting curve (Figure
7) which relates the diameter of the test cylinder to the relative settling
velocity for various mixed liquor suspended solids concentrations. These
curves, although specific f>r the sludges tested, clearly indicate the
effect of Qolumn diameter on batch settling rates . For suspended solids
concentrations less than about 5000 mg/1, small diameter settling columns
yield settling rates greater than might be expected in a final clarifier.
Vesilind attributed this increased velocity to wall effects. For suspended
solids concentrations greater than about 5000 mg/1, settling rates less
than what might be expected in full scale units were found to occur. This
effect is thought to be caused by bridging of the sludge in the small
diameter cylinders. Dick and Ewing(12) confirmed this observation and
suggested that settling properties of activated sludges be investigated in
columns as large as practically possible. Mancini(13) reported that
cylinder diameters up to 12 inches had no effect on the initial sludge
settling rate for the sludges he tested.
Based on the curves presented by Dick and Ewing(lO), it would appear that
the variation in sludge settling velocity with depth is important at small
initial depths such as occur in laboratory tests (Figure 5). For initial
sludge depths greater than about six feet, very little change in settling
rate was observed with increased depths.
The effect of temoerature on the settling rate of activated sludge and
sewage has been discussed by Rudolfs and Lacey(lA) and Ridenour(15). The
rate of settling of sewage solids has been shown to increase with an
increase in temperature up to about 30°C(15). For settling periods longer
than 30 minutes, this difference in settling rate had no significant effect
on the settling efficiency. The settling rate of activated sludge was
found to decrease for decreases in temperature(14). The difference in
settling rates at low temperatures may be partially explained by the slower
rate of sludge oxidation and flocculation which may occur at low temperatures,
The difference might also be accounted for by an increase in the density
of the liquid medium at lower temperature, thus lowering the driving force
for sedimentation. Pflanz(16) presented data which indicated that the
effluent suspended solids of a final clarifier increased from 1.5 to 2 times
at similar surface loading rates (Kg/m^hr) as the temperature decreased from
approximately 14°C to 20°C.
Sedimentation tanks may also be affected by thermal gradients resulting
from differences in temperature between the sedimentation tank contents and
the influent mixed liquor flow. Hall(17) has attributed short-circuiting
in sedimentation tanks to temperature gradients.
19
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TABLE 3
Mathematical Expressions for Settling Rate as
a Function of Solids Concentration
Equation Presented By
Krone(62)
Equation
Definitions of Variables
NS
O
Duncan and Kawata(63)
Vesilind(ll)
V - V0(l - KC)4'65
V -
V - Group settling velocity
Vo " Settling velocity of individual
aggregates
C - Initial concentration of suspended
solids
K • Volume of aggregate/gram of solids
V - Initial settling rate
c - Initial solids content
b - Empirical constant
a - Sludge constant
V - Initial settling rate
Vo - Experimentally determined settling
rate at cencentration c
c - Sludge concentration
k - Sludge constant
-------
NJ
o:
LU
O
ro
o
or
LU
LU
o
LJ
UJ
LJ
II
^
1.3
1.2
I.I
LO
T 1 1 1 T
i I
IO.OOO mg/L
8,OOOmg/L
.9
.8
.7-
4.OOP mg/L
2,000 mg/L
JL
J.
J.
6
FIGURE 7
) 12 15 18 21 24 27 30 33 36
CYLINDER DIAMETER (INCHES)
EFFECT OF SETTLING COLUMN DIAMETER
ON BATCH SETTLING RATE
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Flocculation of bacteria is essential to the operation of the activated
sludge process. Without flocculation, the bacteria remain dispersed
and are difficult to separate from the liquid. Camp(18) has proposed
that flocculation in a sedimentation basin is due to 1) differences in
settling velocities of particles wherein "fast" particles overtake
"slow" particles and 2) velocity gradients in the liquid which cause
particles in a region of higher velocity to overtake those in adjacent
lower stream paths. Although they are not often discussed in the
literature, such factors as the physical and chemical properties of the
bacterial surfaces and the biological properties of the activated sludge
have a significant effect on the flocculation of the bacteria.
McKinney(3) has stated that the average size of a bacteria is 0.5 to 3.0
microns which is slightly larger than colloidal particles (.001 to 1
micron) . Riddick(19) states that particles of a size from 1 to 10 microns
behave in a manner similar to colloids. Because of the presence of
electric charges on their surface, colloidal particles possess a certain
stability or resistance to flocculation. This stability has been
attributed to the magnitude of the zeta potential (O which is defined
by the equation:
C » 4ir6q/D
In which q is the charge on the particle (or the charge difference between
the particle and that of the solution), 6 is the thickness of the layer
round the particle through which the charge difference is effective and
D is the dielectric constant of the medium (20).
Zeta potential is used in some water treatment plants (19) to control the
chemical dosages for the coagulation of water. Schroepfer(21) felt that
under normal conditions, electrical charges on particles of suspended
matter in sewage do not influence their rate of sedimentation to any
great extent. No mention is found in the literature of zeta potential
measurements on activated sludge.
The close relationship between the operation of the aeration tanks and
the performance of the final clarifiers cannot be overemphasized. The
operational parameters of BOD loading, sludge age, and dissolved oxygen
concentration all contribute to the quality of the mixed liquor solids.
These parameters together with the raw waste characteristics determine
the biological predomination and hence provide a significant contribu-
tion to the subsidence characteristic of the sludge.
Garrison and Nagel(22) have shown that low sludge volume indexes result
in powdery, pinpoint floe which is carried out in the effluent. High
SVI's have poor settling characteristics and require the handling of
large quantities of return sludge. They reported that the SVI could be
controlled by the quantity of air supplied, reaeration of the return
sludge and by control of the organic loading. High organic loadings are
generally associated with high SVI's. Similar conclusions can be drawn
from the work reported by Dye(23).
22
-------
Keefer(2A) reported an improvement in the quality of the effluent from
final clarifiers with the presence of a bulking sludge. Superimposed
on this phenomenon is the requirement of adequate capacity in the final
sedimentation tanks and return sludge pumps. Figure 8 shows this
relationship for various temperatures and overflow rates. Increases in
SVI above that shown in Figure 8 tended to increase the effluent
suspended solids. It would appear thus that there exists an optimum
overflow rate and SVI level for maximum suspended solids removal.
Factors Affecting Sludge Thickening
The design of final clarifiers must also consider the concentration of
suspended solids in the underflow. Economic waste treatment design
would dictate that the underflow solids be concentrated as much as
possible, consistent with good clarification and economic tank design.
Most of the modern thickening procedures are based on the work of Coe
and Clevenger(25). They proposed that each concentration of a suspension
has a certain capacity to discharge its solids. This capacity is given
by:
C = V[(l/Ci) - (1/Cu)]
In which C - capacity of the suspension at concentration Cj., to transmit
solids if the suspension is being thickened to a concentration Cu. The
settling velocity is represented by V.
The authors pointed out that if a layer in a suspension has a lower
solids-handling capacity than an overlying layer, it will not be able
to discharge solids as fast as they are being received and the solids
layer will build up. Similarly, if a layer is able to transmit solids
at a faster rate than they are received from the overlying area, its
thickness will remain infinitesimal. Design should then be based on an
area sufficiently large to assure that solids are applied at a rate less
than the solids handling capacity of the limiting layer. The limiting
layer can be determined from a series of batch settling tests at various
concentrations.
Kynch(26) proposed a theory for thickener operation based on the assump-
tion that at any point in a dispersion, the settling velocity of particles
is determined by the local particle density only. While Kynch's analysis
created much interest(27)(28) among those involved in thickener research
and design, it has been found inapplicable to flocculent materials such
as activated sludge(lO)(29). Fitch(29), one of the authors originally
applying the Kynch analysis for design purposes has recently stated that
"modern theory has not answered the unsolved problems left by Coe and
Clevenger and in this respect we have not advanced much during the past
half century". Based on this statement by Fitch, it would appear that
most thickener design is based on Coe and Clevenger's basic theory with
some modifications to facilitate collection and handling of experimental
data.
23
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BLACK RIVER WASTEWATER
TREATMENT PLANT
BALTIMORE, MARYLAND
en
o
bJ
u_
u.
LU
30
25
20
tn 15
Q
ILJ
O
10
• 800 GPD/ft2 12-14° C
© 8OO GPD/ ft2 22-24°C
A 52O GPD/ft2 9-l7°C
520 GPD/ ft2 I8-25°C
50 100 150 200 250
SVI (ml/gm)
FIGURE 8
EFFECT OF SLUDGE VOLUME INDEX AND
TEMPERATURE ON THE EFFLUENT SUSPENDED
SOLIDS CONCENTRATION
24
300
-------
Dick(lO) found that the rate of subsidence of activated sludge was
dependent on the concentration, the sludge depth and the mixing of
underlying areas. He also felt that the area required to accomplish
thickening in a settling tank is not fixed by the observed settling
velocity of the rate-limiting concentration of sludge. It should be
possible to reduce the required thickener area by adequate control
of sludge depth and manipulation of the sludge to minimize the effect
of interparticle forces.
Design and Operation of Final Tanks
The current basic requirements to be met in the design of final
clarifiers are outlined in the Ten States Standards(30), and the
Sewage Treatment Plant Design Manual of the Water Pollution Control
Federation(31).
The design requirements of the Ten States Standards are summarized in
Table 4. The design requirements take into account the extreme varia-
bility in flows to small plants by providing extra capacity in an
attempt to level out the hydraulic surges. Allowance is also made for
the various activated sludge modifications although data to substantiate
this allowance is not available in the literature. No allowance is
made for the various tank configurations and inlet and outlet devices
that are commercially available.
The design recommendations of the Sewage Treatment Plant Design Manual
are in most cases very similar if not identical to those of Ten States
S tandards. In addition to the usual parameters of detention time and
overflow rate, the variable "solids loading" is introduced. They report
that successful operation had been achieved at loads of 12 to 18 lb./
sq.ft./day with sludge volume indexes under 100. As a general guideline,
for mixed liquor concentration of 3000 mg/1 or less with a sludge index
of 100 or less and with the tank underflow at not more than 1.0% solids,
the area determined by the overflow rate is adequate for the solids.
When these conditions are exceeded the design area becomes a function
for mass loading rather than the overflow rate.
Area and Volume Requirements
Although most regulatory agencies have defined criteria for area and
volume requirements of final clarifiers, the ultimate purposes of the
final clarifier must be met. That is to say, that a final sedimentation
tank must provide a clarified supernatant low in suspended solids and
also must concentrate the return solids to a level acceptable to return
to the aeration tank.
At Sioux Falls, South Dakota, side-by-side tests were conducted in two
circular tanks, 80 feet in diameter, one a center-feed and one a peripheral-
feed. Effluent suspended solids concentrations of 30 mg/1 were attained
25
-------
TABLE 4
Design Requirements for Final Settling Tanks
Type of Process
Conventional, Modified, or
"High Rate" and Step Aeration
Contact Stabilization
Extended Aeration
Average Design
(Flow-MGD)
to 0.5
0.5 to 1.5
1.5 and up
to 0.5
0.5 to 1.5
1.5 and up
to 0.05
0.05 to .15
.15 and up
Detention
(Time-Hours)
3.0
2.5
2.0
3.6
3.0
2.5
4.0
3.6
3.0
Surface Settling Rates
(gal/day/sq ft)
600
700
800
500
600
700
300
300
600
General: The inlets, sludge collection and sludge withdrawal facilities shall be so designed as to
minimize density currents and assure rapid return of sludge to the aeration tanks.
Multiple units capable of independent operation are desirable and shall be provided in
all plants where design flows exceed 0.1 MGD unless other provision is made to assure
continuity of treatment.
The detention time, surface settling rate and weir overflow rate should be adjusted for
the various processes to minimize the problems with sludge loadings, density currents,
inlet hydraulic turbulence and occasional poor sludge settleability.
-------
2
at a hydraulic loading of 1200 gpd/ft for the peripheral-feed basin
and 250 gpd/ft2 for the center feed basin(l). Obviously, design
loading criteria should be a function of tank geometry and inlet and
outlet conditions.
In Germany, secondary basins are usually dimensioned on the basis of
detention time. Detention times of from 2 to 3 hours are normally
used. Pflanz(16) in reviewing the German literature reported that
Schmidt-Bregas had proved, based on numerous tests, that the success
of sedimentation requires hydraulic efficiency, that is, the maximum
conformity of the actual with the computed detention time.
In the United States, the design of final tanks had been based on the
concept of overflow rate as developed and presented by Hazen(32) and
Camp(18). Recently, this concept has been questioned by Fitch(33).
Fitch felt that particularly with flocculent suspensions, detention
time plays a significant role and should not be discarded as a design
factor. He presented data which showed that removals of some materials
in an ideal basin, would be governed more by detention time than by
overflow rate.
As the understanding of final clarification and the variables affecting
it increase, it becomes more and more important that the design require-
ments be modified to reflect the differences in tank geometry, types of
sludges and hydraulic regimes. It is only through modernization of the
design requirements that economies in costs and improvements in perform-
ance become possible.
General Arrangements
Sedimentation basins normally are composed of four zones, an inlet zone,
an outlet zone, an effective settling zone, and a solids removal zone.
The location of these zones are shown schematically in Figure 9(2).
The suspension to be separated is introduced into the sedimentation tank
through an inlet device of some type. The zone of turbulence extends
for a distance beyond the inlet device thus rendering this zone ineffective
for settling except possibly as a flocculation zone.
The area and volume of the inlet zone is a function of the inlet device.
The effective settling zone is a quiescent zone in which the solids-liquid
separation takes place. The clarified liquid is removed through some
outlet device, generally an overflow weir. A certain area of turbulence
surrounds this outlet device and is known as the outlet zone. Additional
volume in the tank must be provided for the solids removal zone. The
volume of this zone is a function of the suspension being clarified and
the solids removal mechanism.
Katz, et al(l) report that the design of clarifiers is generally controlled
by one or more of the following factors:
27
-------
N3
oo
f
m
N
o
m
— fc.
_.^ erirircPTiv/cr ....•
^ c.rrtA/1 Ivt. •
SETTLING
ZONE
•i _ ^_ ^
* ^^
i i i i i
SLUDGE REMOVAL ZONE
0
m
H
O
3
FIGURE 9 FUNCTIONAL ZONES OF A
FINAL SETTLING TANK
-------
1. Conditions such as short-circuiting, turbulence, density
currents, and inlet and outlet conditions will affect all
of the following factors.
2. The method of sludge withdrawal must be considered in light
of the specific application.
3. The area required for clarification is related to the
volumetric overflow rate. The vertical liquid rise rate
at any level must be less than the solids subsidence rate.
The area and volume required to produce the desired under-
flow solids concentration may be an important design
criterion. The allowable solids detention time in the
basin is dependent on its biological properties.
Each of the previous criteria will be discussed according to how it
affects sedimentation tank design and operation.
HYDRAULIC FACTORS
Inlet Zone
The purpose of an inlet device is to uniformly distribute the flow across
the cross-sectional area of flow of the tank. Ingersoll(34) has stated
that his results, which substantiate the claims for most other investigators,
confirm that inlet conditions are far more important than those at the out-
let.
A basin inlet much accomplish both horizontal and vertical distribution
of the flow over the entire cross-sectional area of the tank in order to
effectively utilize the entire tank volume for sedimentation. Hydraulic
equality is obtained by either subjecting the dividing flow to equal
frictional resistances or by inserting at each point
-------
PERIPHERAL
EFFLUENT
INFLUENT
FIGURE 10
CENTER FEED BASIN
-------
r
CLARIFICATION
ZONE
n r
FIGURE II
PERIPHERAL FEED BASIN
-------
A peripheral feed tank is shown in Figure 11. Flow is introduced around
the periphery of the tank and below a skirt baffle. A peripheral inlet
device such as this is advantageous because it permits a large distribu-
tion area, thus minimizing the velocity gradients at the point of introduc-
tion to the clarification zone. A comparative study of the hydraulic
characteristics of center and peripheral feed basins has shown the
peripheral feed basin to be more effective than the center feed basin
particularly at high overflow rates(37).
Outlet Zone
Outlet devices are designed to collect the effluent uniformly at the outlet
with minimal take-off velocities required to prevent carryover of sludge
solids to the effluent channel.
The commonly used method of effluent collection is the overflow weir. The
procedures for designing effluent weirs are contained in most sanitary
engineering textbooks. Allowable weir rates vary with the configuration
of the sedimentation tank and with different regulatory agencies. Anderson
(38) gave a maximum of 20,000 gallons per day per foot of weir for weirs
located away from the upturn of the density current. For weirs located
within the upturn zone, the rate should not exceed 15,000 gallons per day
per foot. These values were determined for circular tanks with center-
feed. Pflanz(16) reported on three secondary sedimentation tanks in
Germany with weir overflow rates ranging from 10,700 to 46,600 gals'per day
per foot of weir.
Settling Zone
Since clarification or separation of the suspended solids takes place in
this zone, quiescent conditions should exist.
Particular emphasis should be placed on the design of the cross-sectional
area so that the horizontal velocity in this zone will not be large enough
to scour solids which have already been deposited. Ingersoil, McKee, and
Brooks(39) recommend that the ratio of the critical tank displacement
velocity to the settling velocity of the critical size particle should be
less than 9 to 15 to prevent scour.
Anderson(38) reported density currents in final clarifiers treating
activated sludge. He attributed these currents to the difference in
density between the mixed liquor suspended solids and the clarified
liquid in the tank. This difference in density caused the mixed liquor
to plunge to the bottom of the tank and flow along the bottom until some
obstruction was encountered. The encounter with an obstacle, usually
the side of the tank, induces a counter-current in the upper levels of the
tank. These currents are shown schematically in Figure 12. No density
currents were observed in primary settling tanks. Gould(40) reported
similar density currents at the New York City Sewage Treatment plants.
32
-------
INFLUENT
EFFLUENT WEIRS
A
/ \
OJ
OJ
SLUDGE WITHDRAWAL
FIGURE 12 DENSITY CURRENTS IN A FINAL CLARIFIER
-------
He found that when sludge withdrawal was at the outlet end of the tank,
the velocity of the current decreased with the increasing sludge
density. Thus, the sludge blanket was successful in diminishing the
velocity of the density current.
Fitch and Lutz(41) have presented a method for calculating the velocity
of density currents and have discussed a number of methods for minimizing
the effects of these currents based on both hydraulic and hydrostatic
stabilization techniques.
SHORT CIRCUITING
The subject of short-circuiting has been much discussed in the sedimenta-
tion literature. Efficient sedimentation procedure dictates that maximum
use be made of the entire tank volume. Dye studies to determine the
effects of short circuiting have been made by a number of investigators
(37) (38)(42)(43)(44)(45).
Early tracer studies were performed using a sodium chloride technique(46).
This method has been shown to cause density currents and is no longer a
generally accepted procedure(34). Modern tracers include Fluorescein Dye
and Rubidium86(43) and radioactive potassium1*2(44). Katz and Geinopolos
(47) used a water insoluble oil Red T.A.X. to study the retention charac-
teristics of activated sludge particles in a final clarifier.
The general procedure for hydraulic studies involves introducing the
tracer material into the basin and then collecting effluent samples for
a period of time and analyzing for dye concentration. Figure 13 shows the
results of a typical dye study on the hydraulic characteristics of two
circular basins(37).
The dispersion curve was then analyzed to determine Ti, the time at which
the initial appearance of dye occurred; Tmax, the time at which the
maximum concentration of dye was observed; Tf, the most probable flow-
through time; and T90/T10, the dispersion index. These parameters were
then used to characterize the hydraulic behavior of the tank.
Fair and Geyer(20) report that short-circuiting may be used by:
1. Eddy currents that are set up by the inertia of the
incoming flow.
2. Wind induced currents when the basins are not covered.
3. Convection currents that are thermal in origin.
4. Density currents that cause cold or heavy water to under-
run a basin and warm or light water to flow across its
surface.
Any or all of these factors can cause the departure of a basin from ideal.
34
-------
OO
Ul
ro
g
x
o
u
X
o>
Z
h-
LU
O
I
LU
TYPICAL DISPERSION CURVE FOR THE
PERIPHERAL- FEED TANK
FIGURE 13
OVERFLOW RATE* 2.0 (gal)/(sq ftMmin)
TYPICAL DISPERSION CURVE FOR
THE CENTER-FEED TANK
-------
It would be difficult to accurately quantify the effect of short-circuit-
ing but the importance of this parameter can be judged by the efforts of
design engineers to minimize it.
Caop(48), while stressing the concept of overflow rate as the controlling
factor in sedimentation tank design, also pointed out that short-circuiting
can seriously affect the performance. Eliassen(49) questioned whether
short-circuiting really would deteriorate the performance since short-
circuiting could occur without changes in surface overflow rate. Camp
pointed out that the overflow rate could also be defined as depth divided
by detention time which shows that a decrease in detention time by short-
circuiting would increase the overflow rate.
SLUDGE WITHDRAWAL
The rapid removal of settled sludge from the bottom of final clarifiers
is very important to the overall sewage treatment process. Shapiro,
et al(50) have shown that phosphates removed from solution during aeration
would be released back to solution under conditions of low redox potential.
They proposed rapid removal of solids from the settling basin as a method
of preventing this phosphate release. With the present emphasis in the
pollution control field on phosphate removal, rapid removal of settled
sludge becomes even more important.
A number of authors(51)(52)(53), have commented on the problem of rising
sludge in final clarifiers. This problem has been attributed to denitri-
fication with the subsequent release of nitrogen gas. The rising gas
bubbles cause quantities of sludge to be buoyed to the surface with a
decrease in effluent quality. Sawyer and Bradney(Sl) found the best
solution to this problem was the rapid removal of sludge from the tank.
Although prolonged anaerobisis(24 hours) has little effect on the assimi-
lative capacity of an activated sludge and, in fact, has an inhibitory
effect on filamentous organisms(4), it would appear that the benefits to
be gained from rapid sludge removal from the final clarifier dictate that
solids should be removed as rapidly as is feasible from the final clarifier.
There are essentially two methods for removing solids from final clarifiers,
mechanical and hydraulic collectors.
Mechanical collectors move the sludge to a centrally located collection
point by means of plows, rakes, or flights. A controversy exists as to
the exact mechanism of sludge movement(38)(54).
Regardless of the exact mechanism of movement, it has been shown that the
efficiency of sludge removal is a function of the differential velocity
between the flight speed and the mean basin flowthrough velocity(l).
Additionally, when the sludge movement is in the same direction as the
flow through the basin, the sludge carrying capacity of the flights was
significantly approved.
36
-------
Hydraulic sludge collectors remove sludge from the point of deposit
rather than conveying them to a central collection point as for
mechanical collectors. Hydraulic sludge collectors are well adapted
to activated sludge because of their ability to rapidly remove sludge
from the point of deposition.
DEPOSITION PATTERNS
The deposition pattern of solids in final clarifiers treating activated
sludge have been reported by Anderson(38), Pflanz(16), and Albrecht
et al(55).
Anderson(38) studied a center-feed peripheral-drawoff circular basin
with a 126 foot diameter. He made soundings on a radius of the tank
and found suspended solids distributions ranging from 1 ppm at the
surface to 18,900 ppm in the sludge drawoff hopper. The solids profiles
were slightly raised near the effluent weirs indicating the effect of
velocity currents near the overflow weir. Velocity measurements are
also shown and indicate the beneficial effect of the sludge blanket in
reducing the sludge density currents. Although the suspended solids
concentration in the sludge blanket immediately above the sludge hopper
was 10,000 ppm, its depth was only about two feet. High sludge drawoff
rates could draw quantities of water with significantly less solids
concentration. These low solids levels are less than the MLSS concentra-
tion and over a period of time would materially reduce the activated
solids in the aeration tank.
Pflanz(16) presented an excellent set of data showing the change in
solids profile for corresponding changes in influent flow rate. As the
flow rate increased from 15m3/hr to SOm^/hr, the suspended solids
concentration at the effluent weir rose from 3 to 40 mg/1. Meanwhile,
the return sludge concentration increased from 8.4 gms/1 to 21.6 gins/I.
This increase in return sludge concentration shows the benefit of main-
taining a deep sludge blanket over the sludge drawoff hopper. However,
the benefits gained by increased concentration of return sludge were
partially offset by the deterioration in effluent quality.
For the basin studied by Pflanz, it is interesting to note the solids
concentration at the floor in the outer portions of the lightly loaded
basin. Since there are very few solids in the outer one-half of the
basin, a hydraulic sludge collector would be drawing nearly clear water
from these portions of the basin. At the higher loading rate, the entire
basin, except for the outermost portion, contained a sludge blanket of
some depth.
Albrecht et al(55) found that the solids deposition pattern in the
immediate vicinity of the inlet is a function of the inlet well design.
They also compared two activated sludges, one a healthy aerobic sludge,
the other sludge being deficient in oxygen. The aerobic sludge exhibited
a sharp sludge blanket interface while the oxygen deficient sludge
exhibited a relatively constant sludge concentration in the top portion
of the tank. In this case the environmental conditions in the aeration
37
-------
tank appeared to be the controlling factor in the settling tank.
SUMMARY
This literature search has attempted to report the commonly accepted
procedures for the design and operation of final clarifiers. Current
design requirements were summarized by the Ten States Standards(30)
and the WPCF Sewage Treatment Design Manual(31). Based on the results
of this survey of the literature, it may be concluded that the design
requirements are general guidelines obtained through years of practical
experience. They do not include considerations for final clarifier
geometry or hydraulic effectiveness.
The variables discussed in the literature review which were indicated
as being important to either the clarification or thickening functions
of a final clarifier are summarized in Table 5. The main effects and
interacting effects of these variables were analyzed in an attempt to
arrive at a dimensionally balanced equation. This equation will be
presented in the Results Section.
The techniques of multiple regression will also be used in the formula-
tion of the mathematical model.
38
-------
TABLE 5
Variables Affecting the Clarification and Thickening of
Activated Sludge
Clarification
A. Tank Characteristics
1. Surface area
2. Depth
3. Weir length and position
4. Inlet device
5. Hydraulic efficiency
B. Sludge Characteristics
1. Settling rate
2. Compaction characteristics (SVI)
3. MLSS
C. Operational Characteristics
1. Overflow rate
2. Detention time
3. Weir overflow rate
4. Mass loading
5. Mixed liquor flow
D. Biological Characteristics
1. Activated sludge mode
2. BOD loading
Thickening
A. Tank Characteristics
1. Surface area
2. Tank depth
3. Type of sludge removal mechanism
B. Sludge Characteristics
1. Settling rate
2. Compaction characteristics (SVI)
3. MLSS
C. Operational Characteristics
1. Mass loading
2. Return rate
3. Sludge blanket depth
4. Mixed liquor flow
39
-------
THEORETICAL DEVELOPMENT
The performance of a final clarlfier is measured by the quality of
the effluent in terms of suspended solids and by the concentration of
the return sludge. The tank must provide a high degree of clarifica-
tion and at the same time, it must be capable of providing a return
sludge of reasonable concentration. An economic design must incorporate
both the clarification and the thickening functions of a final clarifier.
The most commonly recommended procedures for clarifier and thickener
designs involve the selection of a unit area for each of the functions
and then selecting the larger of the two unit areas as the area controll-
ing variable.
Area for Sedimentation
The procedure for determining the unit area required for sedimentation
involves the measurement of the settling rate of the sludge in question,
using the laboratory settling rate procedure outlined in the Experimental
Procedure Section. The settling rate expressed in feet per hour can be
converted to an overflow rate by means of the following equation:
OR
(SR ft/hr) x 7.45 gal/ft3 x 24 hr/day (1>
*\
where, OR - overflow rate (gallons/day/ft )
SR - settling rate (ft/hr)
This overflow rate based on the laboratory settling rate thus determines
the maximum overflow rate which can be expected to produce a reasonably
clarified effluent. Hydraulic considerations and short-circuiting introduce
inefficiencies in the final clarifier which should be accounted for in the
design. An adjusted overflow rate can be calculated which will make allow-
ances for the above mentioned inefficiencies. This relationship is given
by Equation 2.
ORD - KI x OR <2>
where, ORD » design overflow rate (gpd/ft2)
t\
OR » laboratory overflow rate (gpd/ft )
KI » a dimensionless correction factor
The magnitude of the constant KI is a function of the tank configuration,
the inlet and outlet design, and the hydraulic efficiency of the clarifiers.
Although exact measurements of KI are not available, the magnitude of this
factor ranges from about 0.5 to 0.8 for the various final settlers which
are commercially available. Determination of these KI values is an area
requiring future research.
41
-------
It should be pointed out that the determination of the laboratory over-
flow rate, OR, should be made at various mixed liquor suspended solids
concentrations. The range of concentrations should include the maximum
mixed liquor suspended solids concentration that might be expected since
this will impose the most severe solids separation condition on the final
clarifier. The laboratory overflow rate is very definitely a function of
mixed liquor suspended solids concentration. However, this function has
not been found to be consistent for activated sludges from different
plants(10). The development of an equation relating mixed liquor suspended
solids to the laboratory overflow rate would provide a significant addition
to the theory and practice of sedimentation since it would allow the
estimation of the settling rates of various sludges without performing
laboratory testing. This would be particularly useful in simulation
models where laboratory data are unavailable but the subsidence rate of
the sludge is desirable.
Area for Thickening
The area required for thickening is often not considered in the design of
final clarifiers.
This factor is, however, very important particularly when the clarifier
is expected to handle high (>5,000 mg/1) mixed liquor suspended solids
concentrations or when sludges with poor subsidence characteristics are
encountered.
Dick(56) has proposed that in a continuous thickener, solids are trans-
mitted downward by two mechanisms:
1. By subsidence under the influence of gravity. This
sedimentation occurs at a velocity Vi which in turn is
primarily a function of the initial solids concentra-
tion Ci.
2. By bulk transport as a result of sludge removal. This
occurs at a velocity y which depends on the rate at
which solids are removed from the bottom of the basin.
The total possible flux, S, of solids through a layer with solids concen-
tration GI is given by:
S - Ci Vi + GI ' y (3)
Subsidence Sludge Withdrawal
Associated with the settling velocity - concentration relationship there
exists a limiting solids handling capacity SL which determines the area
required for thickening.
42
-------
By utilizing a curve relating the settling velocity YI to the mixed
liquor suspended solids concentration Co and the relationship given
in Equation (3), a plot can be made of the return sludge concentration
versus the solid flux. This curve will then indicate the limiting
solids flux rate SL and will enable the calculation of the area
required for thickening.
A - Qo ' Qo ' 8-3A (4)
SL
Where:
A » area required for thickening (ft2)
Qo = mixed liquor flow rate (mgd)
C0 - mixed liquor solids concentration (mg/1)
This approach, although easy to use, is not functional in a simulation
model since no a priori knowledge of the MLSS settling rate relation-
ship is available. As with the calculation for area requirements for
sedimentation, the lack of knowledge of a consistent relationship to
describe the settling rate of a sludge as a function of its concentra-
tion makes a theoretical analysis of thickening unavailable for use in a
simulation model.
43
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EXPERIMENTAL PROCEDURES
Experimental Approach
The original work scope for this project required the development of a
mathematical model to predict the performance of a single final clarifier.
This was later expanded in an attempt to develop a more generally applica-
ble series of equations which could be used to predict the performance of
final settlers in general.
As a part of the original work scope, a detailed experimental program was
conducted at the Racine, Wisconsin Water Pollution Control Plant. This
program involved the testing of two peripheral feed final clarifiers under
a variety of hydraulic and operational conditions.
An experimental program was designed using the concepts of Box-Wilson(57).
This technique allows the simultaneous variation of the parameters under
consideration. The technique is well suited to this type of study since
the formulation of empirical equations with multiple regression techniques
requires a balanced spread of the variables under consideration.
The experimental design involved testing of three variables, mixed liquor
suspended solids, sludge blanket depth and overflow rate at five different
levels with replicates at the central point. Analysis of the data at the
conclusion of this design showed that the dependent variable, effluent
suspended solids, varied over only a small range despite wide changes in
the independent variables. Additional data were collected and combined
with those collected in the experimental design to broaden the results of
the study.
In order to expand the usefulness of the model, data were also collected
at Brookfield and Fort Atkinson, Wisconsin Sewage Treatment Plants on
rectangular final clarifiers. At these plants, close control of the flows
was not possible. However, the data collected at these plants did incor-
porate into the model the variability in sludges which can be found at
various plants.
Additional data were also obtained from operating records at various plants
throughout the country. Of particular use was the data from the Hyperion,
California plant supplied by Mr. Robert Smith, Chief, Operations Research
Section of FWPCA.
Description of Plants Studied
During the course of this project, studies were made at three sewage treat-
ment plants in the southern Wisconsin area in order to obtain data under
controlled experimental conditions for use in the construction and testing
of the mathematical model.
A description of the three plants at which data were collected as well as
the design data from those plants from which operating data were used follows,
45
-------
Racine, Wisconsin Sewage Treatment Plant
The majority of the test work for this project was performed at the Racine,
Wisconsin, Water Pollution Control Plant. This plant accepts the domestic
and industrial wastes of the City of Racine as well as the towns of Mount
Pleasant and Caledonia, and the villages 6f North Bay, Lakeside, and
Colonial Heights.
The plant is designed to handle 23 million gallons per day (mgd) of raw
waste for primary treatment and 12 mgd for secondary treatment. A flow
diagram for the plant is shown in Figure 14. The basic plant design
criteria are presented in Tables 6 and 7.
During the period of the test program, the plant was operating utilizing
two different activated sludge modifications. Prior to April 15th, 1969,
the plant was operated as Contact Stabilization and thereafter as the
Kraus Process.
The waste at the Racine Plant is a mixture of both industrial and domestic
sewages and is low strength based both on BOD and suspended solids. For
the period of this study, the average raw waste BOD and suspended solids
were 102 and 142 mg/1 respectively. The per capita contribution of flow
was 227 gallons per day.
Because of an overloaded primary sedimentation system, the average
removal of suspended solids and BOD in the primary settling tanks was
approximately 20 and 10% respectively. The primary system does, however,
perform the useful function of removing grease and other floatable
materials.
The activated sludge tanks are of a conventional design, being 15 feet deep
by 30 feet wide by 168 feet long. The flow pattern is of the down, around,
and back type giving an effective length of 336 feet for the Contact
Stabilization and Kraus Processes. Aeration is provided by a Kraus dual
aeration system with air being introduced at high and low levels on opposite
sides of the tank. Periodic checks of dissolved oxygen at different points
along the aeration tank indicated that dissolved oxygen levels greater than
2.0 mg/1 existed in all cases.
Final clarification of the activated sludge is accomplished in two peri-
pheral-feed, center-takeoff clarifiers equipped with hydraulic sludge
collectors. These final clarifiers are 85 feet in diameter with a side
wall depth of 12.0 feet. The Tow-Bro®is equipped with two headers and the
time for one revolution is 21 minutes. This means that each position in
the tank is being swept once every 10.5 minutes.
The return sludge pumps were a combination of both fixed and variable
speed and were valved in such a manner that nearly any return sludge flow
was possible.
A schematic diagram of the return sludge piping arrangement is shown in
Figure 15. Return sludge sampling valves were installed in each pump head
and return sludge samples were withdrawn at that point.
46
-------
OUTFALL
MAIN EQUIPMENT
BUILDING
CHLORINE CONTACT
TANKS
PLANT INFLUENT
FLOW DIAGRAM —RACINE, WISCONSIN
WATER POLLUTION CONTROL PLANT
-------
TABLE 6
Basic Design Criteria
Racine, Wisconsin Water Pollution Control Plant
Description:
Design Flows:
Design Wastewater
Characteristics:
Expected Overall
Removals:
Design Population:
Modified activated sludge with separate sludge
digestion, sludge filtering, and chlorination
of effluent.
23.0 MGD for Year 1974
Primary Treatment
Secondary Effluent
Suspended Solids
BOD5
Design Flow
Suspended Solids
BODs
Connected 1974
23.0 MGD
12.0 MGD
200 mg/1
200 mg/1
81.0 percent
67.5 percent
125,000
48
-------
TABLE 7
Design Criteria for Various Process Units
Racine, Wisconsin Water Pollution Control Plant
Process Units:
Primary Settling Tank - Detention Time 1.56
Aeration Tanks
Contact Stabilization Process
Aeration Detention Time
Sludge Reaeration Detention Time
Kraus Process
Aeration Detention Time
Nitrification Detention Time
Conventional Process
Detention Time - Raw Waste Basis
Detention Time - Mixed Liquor Basis
(50% return)
Final Settling Tanks Detention Time -
@12.0 MGD
Return Sludge Pumping Capacity
Chlorine Contract Detention Time -
15.0 minutes (§70.0 MGD
Digester Volume per Capita
Sludge Vacuum Filter Capacity
hours @23 MGD
12.0 MGD
1.57 hours
5.2 hours
1.58 hours
23.9 hours
6.0 hours
4.0 hours
2.04 hours
12.0 MGD
2.35 cubic feet
3000 pounds dry
solids per hour
49
-------
FROM
NORTH TANK
FROM
SOUTH TANK
Ul
o
X
X
X
WASTE SLUDGE
TO PRIMARY
\
RETURN SLUDGE
TO AERATION TANK
PUMP
I
2
3
4
CAPACITY
2800 GPM
2800 GPM
1130 GPM
700 GPM
FUNCTION
RETURN
RETURN
RETURN
WASTE
FIGURE 15
PIPING DIAGRAM FOR RETURN SLUDGE GALLERY
-------
Return sludge flows were metered by means of Fischer and Porter magnetic
flow meters installed in the return sludge lines.
The effluent flows from the final clarifiers were measured in two Parshall
flumes and transmitted to two readout boxes and a strip chart recorder.
Brookfield Sewage Treatment Plant
The Brookfield Sewage Treatment Plant serves the City of Brookfield,
Wisconsin, with a population of approximately 11,000 people. The plant
was originally designed as Conventional Activated Sludge with a capacity
of 1 mgd.
The average BOD and suspended solids of the raw sewage are 100 and 150
mg/1 respectively. The average daily flow through the plant is approxi-
mately 1.5 mgd.
A flow diagram together with sizes for the treatment units important to
this study is shown in Figure 16,
Average BOD and suspended solids reductions through the primary settling
tanks are 35 and 60%, respectively. This results in a light loading on
the activated sludge system.
As a result of problems with high SVI's the operator has recently changed
to a modified Kraus activated sludge system with a resultant improvement
in sludge settleability.
The final clarifiers consist of two rectangular final settling tanks 60
by 14 by 10.2 feet deep. Both tanks are equipped with mechanical sludge
scrapers with sludge being scraped to the inlet end. There are 56 linear
feet of effluent weir in each tank located approximately 2.5 feet from
the end of the tank. The average mixed liquor detention time in the final
clarifier is 1.5 hours.
Fort Atkinson Sewage Treatment Plant
The treatment plant serving the City of Fort Atkinson was constructed in
1934 as a conventional activated sludge plant, with a capacity of 0.5
mgd. In 1960, extensive additions, including a trickling filter, enlarged
aeration and final clarifier tanks, and the additional digesters increased
the plant capacity to 1.5 mgd.
A flow diagram together with sizes for the treatment units are shown in
Figure 17.
The activated sludge system is used to treat the effluent from the rough-
ing filter. The effluent BOD of the roughing filter ranged from 18 to 60
mg/1. The filter effluent also contained the sloughed bacterial slimes
from the filter. Incorporation of this slime into the activated sludge
mixed liquors resulted in a sludge with excellent subsidence characteristics,
51
-------
BARMINUTOR
RAW SEWAGE
+ BY PASS
FACILITY
BAR
SCREEN,,
O
o
Ul
ISJ
WET
WELL
PUMPING
STN.
SLUDGE
DRYING
BEDS
DIGESTERS
4
60'
1 7'DEEP
PRIMARY
SEDIMENTATION
TANKS
•IOO'-
20'
AERATION TANK
12' DEEP
EFFLUENT
CHLORINATION
NITRIFICATION TANKS
RETURN ^ SLUDGE
METER
60'-
14'
10.2' DEEP
FINAL CLARIFIERS
I SLUDGE
(PUMPING
I FACILITIES
FIGURE 16
FLOW DIAGRAM- BROOKFIELD SEWAGE TREATMENT PLANT
-------
FINAL CLARIFIERS
SUJDGE
DRYfNG
BEDS
RAW
SEWAGE
PRIMARY
SEDIMENTATION
TANKS
COMMINUTOR
BAR SCREEN
FIGURE 17
FORT ATKINSON
*•- DISCHARGE
-------
The final clarifiers of the plant consist of three rectangular tanks
each 14 feet wide, 34.3 feet long and 7.75 feet deep. The weir length
per tank is 47 feet. All three tanks are equipped with mechanical
sludge scrapers. Sludge is scraped to the inlet end. Return sludge
flow is adjusted with telescopic valves and a constant speed pump. The
average mixed liquor detention time in the final clarifier is .75 hours.
ANALYTICAL PROCEDURES AND EXPERIMENTAL ERROR
Suspended Solids
Suspended solids were determined by the membrane filter technique as
described by Engelbrecht and McKinney(58). Gelman Instrument Company
glass fiber filters, Type A, 47 mm diameter were used. Gelman reports
a 99.7% retention efficiency using the DOP test (0.3n). A detailed
description of the preparation and handling of the filters follows.
Preparation of Filters
The filters were washed with 100 ml of distilled water prior to use. This
procedure was followed in order to purge from the filters any fines which
might be washed from the filter during filtration of the sample. After
washing, the filters were placed in aluminum pans and dried at 103°C for
a minimum of four hours. The aluminum pan and filter were then cooled
for one hour in a dessicator and weighed. The tared aluminum pans and
filters were stored in aluminum cake pans for transportation to the test
site.
The suspended solids filtrations were performed at the field test site
using a standard Millipore Filter apparatus and a vacuum pump. Aliquot
size was variable depending on the suspended solids concentration but in
general aliquots were as large as possible. Typical aliquot sizes are
shown in Table 8.
TABLE 8
Typical Aliquot Size for Suspended Solids Analysis
Aliquot Size
Sample Stream (milliliters)
Return Sludge 2- 3
Mixed Liquor 10- 15
Final Clarifier Effluent 75-250
After filtration, the filters and aluminum pans were returned to the
Milwaukee lab and dried overnight at 103°C. The following morning, the
filters and pans were cooled in a dessicator for one hour and weighed.
The one hour cooling time was considered quite critical and was adhered
to as closely as possible.
54
-------
All analyses were performed in duplicate and the arithmetic average of
the duplicates was used in reporting the data.
It is difficult to establish measurement of variability in suspended
solids analysis due to a lack of a standard for analysis. Volk(57),
however, presented a technique for establishing confidence limits on
a pair of measurements based on the expected mean difference between
a pair of measurements. The 95% confidence range for the X~ of a pair
of measurements is 1C ± 1.23tT where H is the mean difference between a
pair of measurements.
Based on the results of 100 duplicate analyses the mean difference ~5 was
found to be 0.94. Thus, the 95% confidence limit for the mean of two
samples was found to be:
X ± 1.22 x 0.94
X ± 1.2 mg/1 for the effluent suspended solids
Sludge Blanket Depth
The depth of the sludge blanket in the final clarifiers was measured with
a small hand-held bilge pump. A 14 foot, calibrated section of tygon
tubing was attached to the suction side of the pump. Sludge blanket depth
was then estimated by visual observation of the sludge pumped from various
depths. It is estimated that the accuracy of this technique is about
± 0.5 feet.
Solids Sensor Tests
A more detailed analysis of the sludge deposition patterns and blanket
depths was made using the Rex Chainbelt solids sensor.
The major coponents of the solids sensor are: (A) a solids sensing probe,
(B) electrical converter, (c) recorder, (D) extendible boom, (E) drive
motor, and (F) boom support.
The solids sensing probe consists of a waterproof electrical junction box,
a coil assembly, a vibratory paddle, and a paddle guard cage.
The paddle is connected to the two coils located in the coil assembly by
two rods. One of the coils is operated at a closely controlled frequency
of 120.1 CPS. This vibrational energy is transmitted through one of the
rods to the paddle. The amplitude through which the paddle will vibrate
is dependent on the specific gravity of the media in which it is immersed.
The other rod transmits this amplitude modulated vibration into the field
of a permanent magnet located in the center of the other (pickup) coil.
A voltage is generated, measured, and recorded which is related to the
amplitude of this vibration. The sensor probe has been designed to
operate over the specific gravity range of approximately 1.0000 to 1.2500.
55
-------
The procedures for calibration and operation of the solids sensor were
similar to those outlined by Albrecht et al(55).and will not be detailed
in this report. This apparatus was used during the latter stages of the
report to investigate some of the basic assumptions regarding solids
deposition patterns and buildup.
Settling Rate and SVI
Settling velocities and the sludge volume index were determined using an
unstirred 1 liter graduate. The position of the solids-liquid interface
was observed at various time periods to establish the settling curve. A
typical curve is shown in Figure 18. Prior to the onset of sedimentation,
the solids in the graduate were uniformly dispersed by means of a 2 inch
diameter circular disc attached to the end of a stirring rod.
The settling rate was established by determining the slope of the linear
portion of settling curve (Figure IS). The sludge volume index was
determined by dividing the settled volume of sludge at 30 minutes by the
mixed liquor suspended solids concentration.
Additional studies were also performed with 4 inch and 4.75 inch diameter
settling columns to determine the effect of cylinder diameter on the
settling rate. The diameter of the cylindrical mixing disc was determined
from the following relationship:
Di2/Ai - D22/A2
where:
DI » diameter of cylindrical disc in 1 liter graduate
AI » surface area of 1 liter graduate
D£ » diameter of cylinder
A2 •• surface area of cylinder
Dissolved Oxygen
Dissolved oxygen measurements were periodically made at various points in
the aeration and reaeration tanks to assure that oxygen limiting conditions
did not exist. These tests were made using a silver-lead galvanic cell
with a KOH electrolyte contained by a polyethylene member. The probe was
fabricated by Rex Chainbelt Inc. research personnel. The depolarizing
effect of dissolved oxygen on the cell causes changes in probe output.
The output was measured on a 0 to 25 microampere DC microammeter. The
probe was calibrated in oxygen saturated secondary effluent.
Flow Adjustments and Sampling Procedures
A general procedure was developed for testing of the final clarifiers and
was followed throughout this study unless specifically mentioned. The
56
-------
1000
900
TYPICAL SETTLING CURVE
MLSS = 2000 mg/L
TIME
(MINUTES)
57
-------
flows to be investigated were controlled by diverting the required
portion of the total mixed liquor flow to the tank being studied. The
return flow was then set at the proper rate using the techniques of
Bloodgood(60). In the case where deep sludge blankets were to be
studied, the return flow was turned off for a period of time to permit
the blanket to build up. After all the conditions under investigation
were set, a one hour stabilization time was observed before the collec-
tion of samples was instigated.
Samples were generally collected over a 3.5 hour period at one-half hour
intervals. All flows from the basin were noted and recorded whenever a
sample was collected. Effluent and mixed liquor samples were generally
collected and analyzed for each sampling period. Return sludge samples
were taken at the start, midpoint, and end of the 3.5 hour sampling period.
Settling rates, SVI, and other miscellaneous parameters were measured as
often as physically practical.
58
-------
RESULTS
The purpose of this project was to develop a mathematical model of a
final clarifier for the activated sludge process. This model is to
be incorporated into the FWPCA Preliminary Design and Simulation of
Wastewater Renovation Systems Digital Computer Model. For this reason
the model had to be formulated using only those parameters which would
be available during preliminary design of simulation studies.
These parameters include the mixed liquor solids concentration, the raw
waste flow and the BOD loading on the aeration tank. In order to use
any additional parameters to evaluate final tank performance it is
necessary to provide them to the model as input. An example of informa-
tion which needs to be entered as input to the model would be the surface
area and depth of the final settler. A minimum amount of input is
desirable.
The selection of variables to be evaluated for possible inclusion in the
model was based on the results of the literature review. A summary of
these variables was given in Table 5.
Experiments were conducted at the three plants described in the Experimental
Procedures Section in order to evaluate the performance of the final clari-
fiers. The data collected in these experiments are on file at the Robert A.
Taft Sanitary Engineering Center, Cincinnati, Ohio. These experiments
were based on a Box-Wilson experimental design procedure and were aimed
at gathering data over a wide range of operating conditions.
Although seven half-hour interval sampling periods were monitored for each
day of testing, only the daily average was included in the final data
analysis. It was felt that this procedure would best reflect an average
tank performance for a steady state analysis.
Analysis of Data
The data collected in this study were analyzed using statistical analysis
packages available from the Service Bureau Corporation Call/360 Time Shar-
ing Service and the General Electric Time Sharing Service.
These packages make available a large number of statistical techniques
including scatter diagrams, elementary statistical analysis, multiple
regression and step-wise multiple regression.
A general procedure of analysis included a scatter diagram to establish
trends in the data, elementary statistical analysis to evaluate the mean,
standard deviation and range of the data under investigation. This was
followed by a step-wise multiple regression analysis.
Step-wise regression was used to select independent variables in the order
in which they account for the variation in the dependent variable. Their
accounting for variation is based on the reduction of sum of squares: the
59
-------
independent variable which reduces the largest sum of squares in a given
step is entered next into the regression(64). A detailed description of
the statistical analysis techniques is available from the time sharing
manuals(64)(65). An example of the output from the computer regression
analysis is given in Appendix 1.
Development of the Models
The models developed for predicting the return sludge and effluent solids
concentrations from a final settler will be presented in the following
discussion. For purposes of clarity they will be presented separately
although in reality the two functions cannot be separated.
Return Solids Concentration
A final clarifier in the activated sludge process is a solids separation
and concentration device for which a mass balance must exist. For a
clarifier which is designed and operated properly 95 to 100% of the
solids entering the clarifier should be removed in the underflow. The
remainder will escape in the effluent. Using the nomenclature expressed
in Figure 19 this mass balance can be written as:
Lbs of Solids - Lbs of + Lbs of Waste + Lbs of ± Storage or
into Final Return Sludge Sludge Solids Eff. Solids Depletion
Clarifier Solids
Q4 x 8.34 x MLSS -
Q6 x 8.34 x TSSe + Q? x 8.34 x TSSy + Q5 x 8.34 x TSSs ± Storage or (5)
Depletion
This equation is exact since it establishes the conditions necessary for
a mass balance on a final settler. An equation can be written for the
storage or depletion as follows:
S or D • ± A x ADg x pg
where:
S » Storage (pounds)
D - Depletion (pounds)
A - Floor area of final settler (square feet)
ffls - Incremental change in blanket depth (feet)
pg - Density of sludge in increment of depth
change (pounds/cubic feet)
Sludge storage in a final settler necessitates a rising sludge blanket.
Sludge blanket depth must be controlled within certain limits to prevent
the excessive discharge of solids in the effluent. For this reason,
sludge storage in the final clarifier must be a short term operation.
As such it is not seen as an important factor in the mass balance term
except under severe nonsteady state conditions.
60
-------
RETURN SLUDGE (Q6,TSS6)
PRIMARY
1
EFFLUENT
(Q2)
AERATION
TANK
MIXED LIQUOR
(Q4 , MLSS)
FINAL
CLARIFIER
A« SURFACE AREA OF FINAL CLARIFIER ( ft*)
V= VOLUME OF FINAL CLARIFIER (MILLION GALLONS)
Q4 = MIXED LIQUOR FLOW (mgd)
Q5 = EFFLUENT FLOW (mgd)
Q= WASTE FLOW (mgd)
Q6 = RETURN FLOW
MLSS = MIXED LIQUOR SUSPENDED SOLIDS (mg/ L)
TSS5= EFFLUENT SUSPENDED SOLIDS (mg/L)
TSS6= RETURN SLUDGE SUSPENDED SOLIDS (mg/L)
TSS7 = WASTE SLUDGE SUSPENDED SOLIDS (mg/L)
(WASTE ACTIVATED SLUDGE
(Q7,TSS7)
EFFLUENT
FLOW
(Q5,TSS5)
FIGURE 19
GENERAL FLOW SHEET FOR FINAL CLARIFIER
-------
It is conceded that increased sludge blanket depths can be beneficial
in providing a more concentrated return sludge. This benefit is,
however, often overriden by deleterious effects on the performance of
the activated sludge system (denitrification, phosphate leaching etc.).
The maintenance of deep sludge blankets is most often reserved to
gravity thickness.
At steady state and for most applications, the storage or depletion would
be equal to zero. In addition, the solids lost in the effluent are small
in proportion to the solids in the other streams. Setting the storage or
depletion and the effluent solids equal to zero yields.
Q4 x MLSS - Q6 x TSS$ + Qy x TSS? (6)
but TSS6 « TSSy
QA x MLSS
Therefore TSS6 - * (7)
Inspection of this equation indicates that the return sludge concentration
is directly proportional to the mixed liquor flow and solids content and
inversely proportional to the underflow rate.
Although this equation is theoretically sound, it does not take into account
the thickening requirements of the clarifier. Biological sludges do not
concentrate to an infinite concentration. An underflow rate must be
selected which will insure that a sufficient mass of solids is removed in
the underflow to prevent the buildup of solids in the final settler. It
thus becomes apparent that the return sludge concentration is a function
of the mixed liquor input as well as the operation of the final clarifier.
In actual plant operation, the return rate can be controlled by a number
of different methods. Bubbler tubes can be used to visually observe the
sludge blanket depth and the rate can be set to maintain the blanket at a
particular depth. Various methods of controlling sludge return rate by
means of photoelectric cells have also been used.
Bloodgood(60) proposed a method of selecting the minimum return rate based
on the sludge volume index. Although this procedure has recently been
criticized(66) it is felt to be the only currently available procedure
which can be used in a simulation model. For sludges which settle well
such as at the Racine plant the procedure has been found to offer reason-
able results.
Using Bloodgood's procedure, the percent return can be estimated from the
following relationship:
p . SVI x MLSS
106
where:
P - (Qe + Q7)/Q4
SVI is the Sludge Volume Index, and
MLSS is the Mixed Liquor Suspended Solids in mg/1.
62
-------
The use of this equation in a simulation or preliminary design model
requires an estimate of the Sludge Volume Index. Quantitative relation-
ships defining the SVI as a function of the activated sludge operational
parameters are nonexistent. Historically, activated sludge mathematical
models have either neglected the sludge subsidence and compaction charac-
teristics or assumed a value with no concern for the consequences.
Data from the Hyperion, California plant were analyzed in an attempt to
relate the SVI to various operational parameters of the activated sludge
process. The data resulted from a special FWPCA - Hyperion study, the
purpose of which was to evaluate various key parameters for the FWPCA
activated sludge mathematical model. Since the data were obtained under
different organic loading rates, detention times and cell residence times
it presented the opportunity to attempt to relate SVI to the operational
characteristics of the activated sludge system.
Data were available for nine different modes or conditions of operation
from the Hyperion study. Those parameters which were thought to possibly
influence SVI included, Ibs BOD/day/lb MLSS, Ibs BOD/day///MLVSS, Mixed
Liquor Aeration Time, Cell Residence Time, Temperature, and volatile
solids concentration. The average value for each parameter was calculated
for each mode of operation. These values were then subjected to a multiple
regression analysis. The following empirical relationship is a result of
this analysis:
SVI = 540 x A4'397 x fiO-213 (9)
where:
A * Fraction of volatile suspended solids in the mixed liquor (% VSS/100)
B - BOD loading (Ibs BOD/day/#MLVSS)
This equation had a multiple correlation coefficient of 0.914. Utilizing
the mean values from each of the Hyperion modes of operation resulted in
9 values upon which this analysis is based. Each of the 9 values repre-
sents an average of from 5 to 12 individual observations. A brief statis-
tical analysis of the raw data is shown in Table 9.
TABLE 9
Variable Mean Std. Deviation Maximum Minimum Range
SVI
Percent VSS
Ibs BOD/day/lb MLSS
123.6
73.0
0.513
58.96
5.78
0.302
232
81.97
1.00
61.5
64.7
0.207
170.5
17.3
0.79
The actual and calculated SVI's for the data used in the regression analysis
are shown in Figure 20.
63
-------
250
200
1
s
M
w 150
01
u
a
T-l
o
3 100
50
1 T~ I ' i
O
_
G
- ~"
0°
O O
G
0
, i i i I
50
100 150 200
Actual SVI (ml/gm)
250
FIGURE 20 ACTUAL VS CALCULATED SVl's
FOR HYPERION DATA
64
-------
Equations 7, 8, and 9 can be combined to provide an estimate of the
maximum possible return sludge concentration.
(10)
Return sludge concentrations less than this maximum result from return
sludge flow rates in excess of the theoretical rate given by equation 8.
The return sludge concentration at flows greater than theoretical is
proportional to the ratio of the return sludge rates. In practice, the
return sludge rate should be operated as close to the theoretical rate as
possible in order to minimize sludge pumping costs. In addition, the
effective raw waste detention time in the aerator can be increased when
the minimum sludge return rate is used.
The use of equations 8, 9, and 10 can best be illustrated by the follow-
ing example. It is desired to calculate the return sludge concentration
from a final clarifier. The input mixed liquor concentration is 2000 mg/1,
percent volatile solids is 75%, and the BOD loading is 0.4 Ibs BOD/day/lb
MLVSS.
The SVI is estimated from equation 9.
SVI - 540 x 0. 75^-397 x 0.4°'213 - 125
The percent return is given by equation &
P. 125x2000 =0>25
106
The mixed liquor flow can be determined from the following relationship:
Q4 * Q5 + Q6 + 0.7
Since Q? is very small in proportion to the total flow (1-2%) it can be
neglected and:
Q5 - Q2
Q6 + Q?
b '
Als«
n
Q4
.-. Q4 - Q2 + (PQ4)
and
65
-------
QA = 1«P _ = 1.33 MGD
*
Q6
(1 - .25)
Q6 - Q4 - Q2
= 1.33 - 1.0 -
10 6
0.33
TSS6 = - 7-^97 - 5-013 - 7974
540 x .75*
-------
TABLE 10
Empirical Equations for Predicting Return Sludge Concentration
Plant Name
Hyperion
Racine
Brookfield
Fort Atkinson
Combination of
4 Plants
Equation
27.8 (MLSS)-428 x (ML)'432
CR " p. 896
6.18 (MLSS)'656 x (ML)'263
CK p. 94
_ 5.31 (MLSS)-889
k i 07 $•*•}
P-1'" x ML'DJJ
.618 (MLSS)1-16 x ML-038
CR ' p. 649
2.57 (MLSS)-84 x (ML)'12
CR = P. 88
Proportion of Total
Sum of Squares
Equation Multiple Corr. Reduced by
Number Coefficient Each Variable
11 .977 MLSS - .926
ML - .001
P - .028
12 .979 MLSS - .193
ML - .012
P - .752
13 .949 MLSS - .051
ML - .815
P - .032
14 .948 MLSS - .128
ML - .019
P - .754
15 .971 MLSS - .149
ML - .722
P - .073
Where: MLSS = Mixed liquor suspended solids mg/1
ML = Mass loading Ibs. MLSS/day/ft2
P * Percent return
-------
TABLE 11
Return Cone.
Actual rng/1
6000
5800
5900
5600
6500
7300
7700
7200
8100
8100
8100
8000
8100
7400
7200
6800
7500
7500
7500
5700
5700
6100
6500
5900
5800
5900
6100
4700
5300
3460
3820
3100
4060
3760
3540
3120
2500
2700
2900
2300
3800
2800
2200
3200
2800
3300
9346
7367
7633
3045
10235
5848
14265
6750
Lculated Values
Return Cone.
Cal. mg/1
5432
4533
5041
5693
5296
7589
7121
7347
6843
7562
7980
7773
7776
6984
6843
6909
7290
7050
7062
5607
5465
5808
5796
5487
5379
5716
5660
4583
5170
3050
3559
2852
3180
3180
3097
2952
2509
2753
2569
2560
3076
2523
3001
3001
2864
2864
8879
6856
6959
3844
9124
6167
10646
6339
for Return Slut
Return Cone.
Actual mg/1
8792
5172
12023
16221
18292
6920
9416
9966
11876
5274
20175
6280
5280
5278
6595
5507
9740
10400
26962
8113
19565
14763
25163
8250
16263
8075
21500
5575
19450
20625
5768
17250
4642
32600
7040
7180
7350
6450
6380
5430
5335
5670
6430
6060
6190
6180
5320
5540
6430
6060
6190
6180
5130
5320
Return Cone.
Cal. mg/1
9886
5317
10842
17916
19128
6299
8071
8388
12468
5779
14376
5878
4786
4801
6346
5428
12042
8397
28486
7571
18353
13524
21003
8335
14781
9392
19187
6462
18871
19054
6493
15211
5382
25515
8000
7650
7972
6684
7129
5990
5555
6166
7528
6912
6734
7529
6426
6378
7526
6910
6734
7061
5770
6447
68
-------
It can be seen from Table 10 that different variables make the most
significant contribution at the different plants. For example, MLSS
reduces the total sum of squares by 92.6% for the Hyperion data but
only 19.3 for Racine and 5.1% for Brookfield. Similarly, the mass
loading reduces the total sum of squares by 0.1% for Hyperion but 1.2%
for Racine and 81.5% for Brookfield. The reason for this is thought to
be the design and operation of the final clarifiers. For example, at
the Racine and Fort Atkinson plants, the sludge settled very rapidly so
it might be expected that the percent return would be controlling
variable. However, at the Brookfield plant the sludge did not settle
well and the area required for thickening may have been the limiting
factor.
The regression analysis on the combined data from the four plants is a
general equation derived from four different sludges, rectangular and
circular basins and a hydraulic and mechanical sludge collector. It is
thought to give the best estimate of return sludge concentration of all
the possible empirical formulations investigated. This empirical formula-
tion can, however, be mathematically rearranged to yield essentially a
mass balance type of equation similar to equation 7. It is, therefore,
probably more meaningful to use the procedure outlined earlier in this
section to calculate return sludge concentration.
Solids Sensor
The Rex solids sensor was used in an attempt to investigate the deposition
pattern of sludges in a final clarifier and the solids profiles at various
positions in the tank. Of particular interest was the maximum sludge
concentration which could be achieved at the bottom of the clarifier.
An analysis of the solids inventory in a final clarifier is a very compli-
cated task because of the large area to be analyzed. In order to facilitate
this analysis only one-half of the tank was studied.
Figures 21 and 22 show the solids inventory expressed in pounds of dry
solids/day/foot2 at various positions in the tank. All values were deter-
mined at a 2 to 3.5 minute interval after the passage of the sludge collector.
As a general pattern it can be seen that the highest solids inventory was
located closest to the tank inlet. In the absence of dye studies it is
impossible to determine whether this is due to an uneven distribution of
flows or the result of the heavier solids settling out in the inlet channel.
It should be pointed out that the activated sludge at the time of this study
was approximately 50% volatile with an SVI of 32. This sludge is not
typical of most activated sludges.
In Figure 23 the solids concentration at various times after the passage of
the sludge collector is plotted. The sludge concentration increased from a
minimum immediately after the sludge collector had passed to a maximum just
before the passage of the next collector arm.
69
-------
MIXED LIQUOR INLET
14 APRIL 1969
FIGURE 21
SOLIDS DEPOSITIONS PATTERNS IN Ibs DRY SOLIDS PER SQ. FOOT,
MEASURED APPROX. 2 MIN. AFTER TOWBRO PASSAGE
70
-------
MIXED LIQUOR INLET
10 APRIL 1969
FIGURE 22
SOLIDS DEPOSITION PATTERNS IN Ibs, DRY SOLIDS PER SO. FOOT
MEASURED APPROX. 3.5 MIN. AFTER TOWBRO PASSAGE
71
-------
FIGURE 23
RACINE
PERCENT SOLIDS CONCENTRATION
VERSUS
TIME AFTER PASSAGE OF THE SLUDGE COLLECTOR
4.0 —
3.5
3.0
v>
a
25
2.0
1.0
II' LEVEL
468
TIME (MINJ AFTER TOWBRO PASSING
10
-------
The solids concentrations at the various tank depths indicate the
solids profile and clearly show the thickening process in the clarifier.
A comparison of the maximum sludge concentration at the 11 foot depth,
the approximate depth of sludge withdrawal, and the theoretical concen-
tration derived from the laboratory settling test can be made. The
theoretical concentration derived from the laboratory settling test was
28.7 grams/liter. The actual concentration at this withdrawal point in
the tank was about 35.5 grams/liter. The actual return concentration
was about 30.0 grams/liter. Whether this discrepancy is true for the
whole tank or only at the single point tested cannot be proved because
point analysis could not be conducted in the inner 20 feet of the tank
radius due to the complicated underwater structural members. It is
reasonable to assume that with this fast settling sludge, a differential
deposition pattern exists. This would mean that the inner section of the
hydraulic sludge collector would be drawing a slightly more dilute sludge
than the outer sections.
Since the information available from the use of the solids sensor was not
of great use in the formulation of the model, only a limited amount of
tests were made with the sensor. It is felt that the greatest potential
use of this apparatus would be in the analysis of gravity thickeners and
final clarifiers with deep sludge blankets.
Effluent Suspended Solids
The primary function of a final clarifier is to provide an effluent which
is low in suspended solids. Since the effluent stream, in most cases,
represents the final step in secondary waste treatment, the performance of
the final settler is of primary importance in the overall treatment scheme.
An attempt has been made to develop a mathematical relationship which will
predict the effluent suspended solids given the mixed liquor flows, solids
concentration and the operational parameters of the aeration tank.
Based on the results of the literature survey and an understanding of the
sedimentation process, it would appear that the effluent solids from a
final clarifier are a function of the hydraulics of the tank and of the
sludge quality. This relationship is expressed in the following equation:
Effluent Suspended
Solids - f overflow rate, detention time, sludge
return rate, weir loading, mass load-
ing
+ subsidence characteristics, flocculation
characteristics, active bacterial mass,
shear imparted in aeration, inert solids
in the activated sludge, particle size
distribution
73
-------
Analysis of this equation indicates that for a fixed sludge quality, the
effluent suspended solids are a function only of the hydraulics of the
basin. Basin hydraulics factors are commonly measured and are defined
below.
The overflow rate of the final clarifier is defined as:
ORA = (16)
A
Where ORA is the actual tank overflow rate ( gal Ions/ day /f t2) , 0.5 is the
effluent flow gallons/day and A is the surface area of the final settler.
The detention time is based on the mixed liquor flow and is defined by:
T = 1- x 24 (17)
Q4
Where T is the tank detention time in hours, V = tank volume in million
gallons and Q4 is the mixed liquor flow in MGD.
The mass loading is defined as the pounds of mixed liquor solids per square
foot of tank area per day.
Q4 x 8.34 x MLSS
ML = — - - - (18)
A
Where:
ML = mass loading (pounds mixed liquor solids /day/foot^)
Qml * mixed liquor flow (MGD)
Cjni = mixed liquor suspended solids (mg/1)
A « tank surface area (sq ft)
The weir loading is given by equation 20.
WL - ^ (19)
Li
Where: ($5 is the effluent flow (gallons/day) and L is the length of weir
(feet) .
These parameters can be used to characterize the hydraulic flows within a
basin.
74
-------
Multiple regression analysis was performed on the data collected at
each of the plants in an attempt to find a relationship to predict the
effluent suspended solids from a final clarifier. Scatter diagrams
were used to indicate the form of the equations. In most cases no
definite trends were obvious.
Throughout the course of this study it has been found that when data
collected over a short period of time are analyzed a relatively good
fit to the data can be made with a multiple regression analysis. An
example of this was seen at the Racine plant. When the data from the
period of April 10, 1969 to May 21, 1969 were subjected to a regression
analysis, an equation of the form:
Eff . SS = 18.2 + .0136 x ORA - .0033 x MLSS (20)
This equation had a multiple correlation coefficient of 0.91 based on
47 observations.
However, when data collected over a longer period of time were analyzed
the fit of the equation decreased significantly. It is felt that the
reason for this decrease in fit is a basic change in the composition of
the sludge which is unaccounted for by a gross parameter such as mixed
liquor solids concentration.
Various attempts to provide a measurement of sludge characteristics using
parameters such as aeration time, sludge age and BOD loading have not
proven exceptionally fruitful.
A multiple regression analysis of the data from the Racine and Hyperion
plants has shown some promise for the predication of effluent suspended
solids. The equation is shown below:
„« oo _ 382 x OR-12 x (#BOD/dav///MLSS)-27
Err. bb - - -57 i To
This equation has a multiple correlation coefficient of 0.63. The results
of a statistical analysis on the input data are shown in Table 12. A plot
of the actual and calculated values is shown in Figure 24.
TABLE 12
Statistics for Input Variables for Regression Analysis
Std.
Variable Mean Deviation Max. Min. Range
Eff SS 19.84 11.95 66 3 63
0 R* 734 364 1990 115 1875
fBOD/day/#MLSS .423 .313 1.49 .044 1.45
MLSS 2128 1026 4437 500 3937
D T 2.84 1.075 4.37 .91 3.46
75
-------
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14.3 27.8 41.2 54.7 68.
OBSERVED EFFLUENT SUSPENDED SOLIDS (mg/L)
FIGURE 24
OBSERVED AND CALCULATED EFFLUENT SUSPENDED SOLIDS
76
-------
This equation is felt to offer the best results over a broad range of
input variables of any of the equations tested in this study. The
equation is proposed, therefore, as a preliminary model to predict
effluent suspended solids under steady state conditions.
Additional work is required to improve the ability of this equation to
predict effluent suspended solids. The following discussion will include
suggestions for future work.
The results of attempts to develop an equation to predict the effluent
suspended solids have shown the need for further research. It is felt
that a more complex relationship describing the sludge quality is necessary
to adequately characterize the sludge. Sludge quality will be discussed
in a later section.
Two factors which are felt to influence the effluent suspended solids over
which no control was exerted were the scum and colloidal materials.
The amount of scum materials on a final clarifier is a function of the
efficiency of the primary sedimentation facilities and the operational
characteristics of the treatment plant. Scum materials do not flow from
a final clarifier as a function of flow rate. Moreover, their separation
paths deviate from that of the activated sludge solids, and their magnitude
may be of the same order as the effluent suspended solids. They tend to
accumulate on the leeward side of the tank and are generally carried from
the tank immediately following a shift in the wind. Thus, depending on
the time that the sample is collected, the suspended solids due to scum
materials may or may not influence the results. The problem of floating
materials on final clarifiers has become more serious in recent years.
For example, with the advent of biodegradable LAS, an increase in floatable
materials is being encountered in the final clarifier. It is felt that the
influence of scum materials is responsible for part of the difficulties
encountered in obtaining a good correlation.
Colloidal materials are present in raw sewage and are generated during the
biological treatment process. Colloids are by definition particulate
matter smaller than 0.2 - 0.5 microns. Since this is in the range of the
pore size openings, it is not unreasonable to expect that some colloidal
materials will be captured on the filter during the suspended solids
analysis. This additional weight contributed by colloidal materials which
are not by definition suspended solids can account fcr some of the unexplained
variance in the regression model. Colloidal materials should be defined
by the sludge quality parameter.
This equation neglects the hydraulic effectiveness of the various basins
studied. Although hydraulic effectiveness is felt to play an important
role in the performance of the final clarifier, it is impossible to
investigate except under side by side testing with different tanks and
the same sludge. Hydraulic effectiveness needs further investigation and
should eventually be incorporated into the model.
77
-------
DISCUSSION OF RESULTS
The formulation of a series of equations to predict the performance of
a final clarifier has been presented. As the result of the extensive
effort to develop these equations, a certain amount of qualitative
information and observations which cannot be expressed in mathematical
terms have evolved. This information will be presented in this section
together with recommendations for the improvement of the model.
Mathematical models of the activated sludge process are abundant and a
tremendous amount of research effort has been expended in order to
develop the biochemical theories and to measure the reaction rates for
the various process modifications and waste characteristics. The majority
of this work has ignored the effect of the sedimentation function of the
process and has concentrated only on the biochemical response. As a result
there exists almost no information on solids separation characteristics of
various activated sludges.
It should always be remembered that the activated sludge process consists
of two interrelated functions, aeration and sedimentation. There is no
way to separate these functions as what happens in sedimentation and vice-
versa. For example, an activated sludge model can predict the effluent
soluble BOD from an aerator under given loading conditions but the return
sludge rate might have to be 100% of the raw flow to attain the desired
biological solids concentration. This high return rate will then decrease
the detention time in the aerator to one-half the raw waste detention time
and undoubtedly will influence the biochemical results.
Thus, mathematical models of the activated sludge process should be con-
cerned with the subsidence characteristics of the sludge as well as the
biochemical reaction rates. In order for an activated sludge model to be
truly useful it should give some estimates of the subsidence properties of
the sludge based on the operational parameters of the activated sludge
system.
The harmonious operation of the clarification and thickening functions of a
final settler requires a knowledge of the sludge characteristics. It has
been shown that with relatively constant sludge characteristics the effluent
solids from a final clarifier can be described by the overflow rate and
mixed liquor solids concentration (equation 20).
As a result of observations made during this study, a new parameter, sludge
quality, will be defined. Sludge quality is an expression defining those
properties of an activated sludge which determine its settleability and
effluent clarity.
Activated sludge is made up of active microbial solids, the biodegradable
volatile solids in the primary effluent, the nonbiodegradable volatile
suspended solids in the primary effluent, the nonbiodegradable suspended
solids resulting from endogenous respiration, and the inert nonvolatile
solids in the primary effluent resulting from chemical precipitation in
the aeration tank. Although classification of these solids is a formidable
job, some of the latest activated sludge models(67) have made an attempt to
perform this function.
79
-------
An example for this type of approach was seen during the Racine testing
program when the activated sludge system was switched from contact
stabilization to the Kraus process. The introduction of the anaerobic
digester supernatant into the activated sludge system resulted in a
sludge which settled very rapidly. However, a fration of very fine
digested solids which did not settle well began to appear in the effluent
from the final settler. A solids classification system would account for
these solids and would hopefully improve the prediction of effluent
suspended solids.
The data presented by Keefer(24), Figure 8, appears to confirm this
observation. Sludges which settle poorly and consequently have a high
sludge volume index generally have a large area to volume ratio. If the
tank overflow rate is low enough to prevent the gross carryover of solids,
a very high effluent quality is generally observed. Gross measurements
such as MLSS do not account for this quality of tie sludge and make the
prediction of effluent suspended solids difficult, if not impossible.
It is recognized that biological predomination plays an important role in
the settleability of a particular sludge. However, this can generally be
controlled by assuring optimum environmental conditions in the aeration
tank.
Observation of the laboratory settling rate of a number of different
sludges casts some light on the necessity for a sludge quality parameter.
The supernatant clarity after the sludge interface has passed a particular
position in the graduate is markedly different for various sludges.
Although the laboratory settling rate describes the removal of the bulk
of the sludge solids, it is those solids which remain in the supernatant
after the passage of the interface which become effluent solids in a final
clarifier.
It appears that these supernatant solids are fine particles which have
escaped both flocculation and/or entrapment with the bulk of the sludge.
Since it is reasonable to expect that the different classes of materials
comprising an activated sludge will have different flocculation and
settling properties, it is felt that the dassification of activated sludges
according to their various components will allow a more accurate prediction
of the effluent solids from a final clarifier.
One additional parameter which might be useful in the definition of the
sludge quality is the zeta potential. During the early phases of this
project some zeta potential measurements were made to determine its
influence on effluent suspended solids from a final clarifier. These
efforts were abandoned, however, since the amount of work required to
develop this variable into a useful parameter to use in the math model
for a final clarifier far exceeded the work scope of the project. In
addition, it would be necessary to correlate zeta potential to the opera-
tional parameters of the aeration tank in order for this parameter to have
any use In simulation or design models.
80
-------
Samples of mixed liquor supernatant from the Milwaukee Sewage Treatment
Plant were analyzed for zeta potential. Samples were taken at the start
and end of the aeration tank. Thfcse data are summarized in Table 13.
TABLE 13
Zeta Potential Before and After Aeration Milwaukee Sewage
Median Zeta Potential Specific Conductance
Date Before Aer. After Aer. Before Aer. After Aer.
11-11-68 -14.9 -14.8 1150 835
11-14-68 -17.0 -13.6 1210 950
11-15-68 -10.7 -12.1 830 720
11-18-68 -14.4 -12.6 1150 835
11-19-68 -12.7 -12.3 1100 960
11-20-68 -11.5 -10.3 1200 935
In all cases except one, there was a reduction in zeta potential as a
result of aeration. It should be pointed out that this analysis was made
on grab samples with no allowance for the lag time in the aeration tank.
Based on the few analyses which were made, it is felt that zeta potential
does play a role in the clarification of activated sludge. However, a
study of a very basic nature needs to be performed to evaluate zeta
potential measurements. In order to be useful in a mathematical model,
zeta potential would need to be correlated to some parameter such as BOD
loading, sludge age, etc. Zeta potential is a parameter which should be
investigated in a laboratory study where close controls can be exerted.
If correlation between zeta potential and the flocculation of activated
sludges, particularly the fine particulate matter left in suspension can
be demonstrated, then this parameter would be extremely useful in predict-
ing the effluent solids from a final clarifier.
The definition of the sludge quality as a function of the operational
parameters of the activated sludge system is seen as a very important
requirement to the improvement of the effluent solids prediction equation.
Preliminary Design
One of the original objectives of this project was to formulate a basis for
the preliminary design of final clarifiers. As work progressed on the
project it became increasingly obvious that this objective was impossible
to meet utilizing the available information.
Clarifiers are normally designed with some knowledge of the subsidence
characteristics of the sludge. The techniques for determining the limiting
area were outlined in the experimental development section. The largest
area required for either thickening or clarification is selected as the
design area. This procedure is felt to be the best design procedure
currently available.
81
-------
However, this procedure is absolutely useless for the purposes of prelim-
ary design since no knowledge of the subsidence characteristics of the
sludge are available. The only remaining possibility is the use of design
guidelines outlined in the Ten States Standards(30) or the Water Pollution
Control Federation's, "Sewage Treatment Design Manual"(31).
In order to utilize a rational design approach, it is necessary to develop
a mathematical relationship which relates the subsidence characteristics
of activated sludges, such as settling rate, to the solids concentration,
sludge quality and other operational characteristics of the aerator.
A suggested approach to this relationship would be to evaluate the subsi-
dence characteristics of activated sludges under various conditions of BOD
loading, sludge quality, and activated sludge modification. The only
possibility for a realistic approach to the preliminary design of final
clarifiers lies in the development of this relationship.
Settling Rate of the Solids
Settling rate has been shown tote an important variable affecting the
performance and design of final clarifiers. For example, if the effluent
flow upward (overflow rate) is greater than the solids settling rate,
effluent quality will be adversely affected. Discussion regarding the
effect of initial depth and cylinder diameter on the determination of the
laboratory settling rate was presented in the literature search. Because
this variable is thought to play such an important role in the performance
of final clarifiers, the effect of cylinder diameter was investigated.
Side-by-side tests of a one liter graduate and a 4.75" diameter, 1 foot
deep cylinder were run on sludges from three different plants.
Representative settling curves were selected and tie settling rates are
presented in Table 1A. For dense sludges such as at Racine, and for dilute
sludges from the Milwaukee plant, no consistent trend was noted when compar-
ing the two settling rates. For the Brookfield sludge which did not settle
well, 3 of the A settling tests indicated a higher rate in the larger diameter
cylinder than in the liter graduate.
Based on these studies it can be concluded that cylinder diameter does
have an effect on the settling rate of the solids. Future work is required
to develop a standard laboratory settling test which represents as closely
as possible the settling rate of the solids in a full size final clarifier.
Only with a realistic estimate of the settling rate can a final clarifier
be properly designed.
82
-------
oo
TABLE 14
Effect of Test Cylinder Diameter on Settling
Brookfield Sludge
f\aV.J-LLC U J-Vl-apjVi
Settling Rate
(ft /hour)
1 Liter
36.9
_
31.9
18.5
-
21.95
4.75" Dia.
35.3
26.1
-
17.1
16. 45
MLSS
(mg/1)
2130
1920
3200
4620
4570
3400
Settling Rate MLSS
(ft/hour* (mg/1)
1 Liter 4.75" Dia.
1.34 - 2920
6.9 2870
18.95 - 1490
17.15 1450
27.5 - 890
28.6 885
Settling Rate
(ft/hour)
1 Liter 4.75" Dia.
4.1 7.70
_
8.06 9.38
7.3 6.60
-
4.42 9.52
MLSS
(mg/1)
1600
-
1575
1545
-
1585
26.0 - 535
35.3 495
-------
SUMMARY
The purpose of this project has been to develop a series of equations
to predict the performance and preliminary design requirements of a
final clarifier in the activated sludge process. Equations to predict
the overflow and underflow solids concentrations have been developed.
The limitations of these equations have been discussed, together with
suggestions for future research efforts to improve the equations.
The currently accepted design procedures for final clarifiers requires
a knowledge of the settling rate of the sludge. Since no method is
currently available for estimating the settling rate from the solids
characteristics and the operational parameters of the activated sludge
system, it is felt that the only alternative is to use the Ten States
Standards(30) for preliminary design purposes in the model.
85
-------
ACKNOWLEDGMENT
The author, Dr. Robert W. Agnew, gratefully acknowledges the assistance
and cooperation of Mr. Gary Coates, Engineer-Manager, and Mr. Stan Budry,
Superintendent, City of Racine Water Pollution Control Plant; as well as
Mr. Jack Budde, Superintendent, City of Brookfield Water Pollution Control
Plant and Mr. Karl Kutz, Superintendent, City of Fort Atkinson Sewage
Treatment Plant. The many hours of assistance rendered by these men is
truly appreciated. The support of Mr. Robert Smith, Project Officer for
the Environmental Protection Agency, formerly the Federal Water Pollution
Control Administration, is also gratefully acknowledged.
87
-------
BIBLIOGRAPHY
1. Katz, W. J., Geinopolos, A., and Mancini, J. L., "Concepts of
Sedimentation Applied to Design", Water and Sewage Works, 109,
162, 169, 257 (1962).
2. Eckenfelder, W. W., and O'Connor, D. J., "Biological Waste Treat-
ment" Pergamon Press (1961) .
3. McKinney, Ross E., "Fundamental Approach to the Activated Sludge
Process - II. A Proposed Theory of Floe Formation", Sewage and
Industrial Wastes, 24_, No. 3, 280 (1952).
A. Ford, Davis L., and Eckenfelder, W. W., Jr., "Effect of Process
Variables on Sludge Floe Formation and Settling Characteristics",
JOURNAL Water Pollution Control Federation, 39, No. 11 (Nov. 1967).
5. Lesperance, Theodore W., "A Generalized Approach to Activated
Sludge Part II Developing the Process", Water Works and Wastes
Engineering, (May 1965).
6. Sawyer, C. N., "Milestones in the Development of the Activated
Sludge Process", JOURNAL Water Pollution Control Federation, 37,
No. 2 (Feb. 1965).
7. McKinney, Ross E., "Mathematics of Complete-Mixing Activated Sludge
Systems", JOURNAL Sanitary Eng. Div., ASCE, Vol. JJ8» SA3 (May 1962).
8. Keshavan, K., Behn, V. C., and Ames, W. F., "Kinetics of Aerobic
Removal of Organic Wastes", JOURNAL Sanitary Eng. Div., Amer. Soc.
Civil Eng., 90_, No. SA1, Proc. Paper 3808, 99 (1964).
9. Pipes, Wesley 0., "Types of Activated Sludge which Separate Poorly",
JOURNAL Water Pollution Control Federation, 41, No. 5, Part 1,
715, (May 1969).
10. Dick, Richard I., and Ewing, Benjamin B., "Evaluation of Activated
Sludge Thickening Theories", JOURNAL Sanitary Eng. Div. ASCE, SA4,
9, (1967).
11. Vesilind, D. Aarne, Discussion of "Evaluation of Sludge Thickening
Theories", JOURNAL Sanitary Eng. Div. ASCE 94, No. SA1, 185,
(Feb. 1968).
12. Dick, Richard I., and Ewing, Benjamin B., Closure "Evaluation of
Activated Sludge Thickening Theories", JOURNAL Sanitary Eng. Div.,
ASCE 95 No. SA2, 333 (April 1969).
89
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13. Mancini, John L., "Gravity Clarifier and Thickener Design", Proceed-
ings Purdue Industrial Waste Conference (May, 1962).
14. Rudolfs, Willem, Lacey, I. 0., "Settling and Compacting of Activated
Sludge", Sewage Works JOURNAL, 16, No. 4, 647 (1934).
15. Ridenour, G. M., "Effect of Temperature on Rate of Settling of Sewage
Solids", Sewage Works JOURNAL. 2^ No. 2, 245 (1930).
16. Pflanz, Peter, "The Sedimentation of Activated Sludge in Final
Settling Tanks", Water Research, The Journal of the International
Association on Water Pollution Research, 2,, 1, 80 (1968).
17. Hall, E. J., Formal Discussion Paper 11-16, "Hydraulic and Removal
Efficiencies in Sedimentation Basins", presented 3rd International
Conference on Water Pollution Research, Munich, Germany, 1966.
18. Camp, Thomas R., "Studies of Sedimentation Basin Design, Sewage
and Industrial Wastes. 25, 1, 1 (1953).
19. Riddick, T. M., "Control of Colloid Stability Through Zeta Potential",
Volume 1, Livingston Publishing Company, Pennsylvania (1968).
20. Fair, Gordon M., and Geyer, John Charles, "Water Supply and Waste-
Water Disposal", John Wiley & Sons, Inc., New York (1959).
21. Schroepfer, G. J., "Factors Affecting the Efficiency of Sewage
Sedimentation", Sewage Works JOURNAL, 5., No. 2, 209 (1933).
22. Garrison, Walter E., and Nagel, Carl A., "Operation of the Whittier
Narrows Activated Sludge Plant", Water and Sewage Works, Reference
No. R-189 (Nov. 1965).
23. Dye, E. 0., "Solids Control Problems in Activated Sludge", Sewage and
Industrial Wastes, 30^, 11, 1350 (1958).
24. Keefer, C. E., "Relationship of Sludge Density Index to the Activated
Sludge Process", JOURNAL Water Pollution Control Federation, j)5, 9,
1166 (1963).
25. Coe, H. S., and Clevenger, G. H., "Methods for Determining the
Capacities of Slime Settling Tanks" Transactions, American Institute
of Mining Engineers, Vol. 55, 356, (1916).
26. Kynch, G. L., "A Theory of Sedimentation", Transactions. Faraday
Soc. 48, 166, (1952).
27. Talmadge, W. P., and Fitch, E. B., "Determining Thickener Unit Areas",
Industrial and Engineering Chemistry, 47, 38, (Jan., 1955).
28. Behn, Vaughn, C., and Liebman, Jon C., "Analysis of Thickener Opera-
tion", JOURNAL Sanitary Eng. Div.. ASCE 47, 38, (Jan., 1955).
90
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29. Fitch, E. B., "Current Theory and Thickener Design", Ind. & Eng.
Chem.. 5.8, 18, (1966).
30. "Recommended Standards for Sewage Works", Great Lakes - Upper
Mississippi River Board of Sanitary Engineers, 1968 Edition.
31. "Sewage Treatment Plant Design", Water Pollution Control Federa-
tion, MANUAL OF PRACTICE NO. 8, (1959).
32. Hazen, Allen, "On Sedimentation", Transactions, American Society
of Civil Engineers, Vol. 53, 63, (1904).
33. Fitch, E. B., "The Significance of Detention in Sedimentation",
Sewage and Industrial Wastes, 29, 10, 1123 (1957).
34. Ingersoll, Alfred C., "The Fundamentals and Performance of Gravity
Separation - A Literature Review", Paper presented at American
Petroleum Institute's Division of Refining, Tulsa, Oklahoma (1951).
35. Giles, J., Henry, L., "Inlet and Outlet Design for Sedimentation
Tanks", Sewage Works Journal, 15, No. 4, 609 (1943).
36. Rohlich, G. A., "Investigation of the Behavior of Oil-Water Mixtures
in Separators", University of Wisconsin (1951).
37. Katz, William J., and Geinopolos, Anthony, "A Comparative Study of
the Hydraulic Characteristics of Two Types of Circular Solids
Separation Basins", Paper presented at the Manhattan College Water
Treatment Conference (1957).
38. Anderson, Norval E., "Design of Final Settling Tanks for Activated
Sludge", Sewage Works Journal, 17., No. 1, 50, (1945).
39. Ingersoll, A. C., McKee, J. E., and Brooks, N. H., "Fundamental
Concepts of Rectangular Settling Tanks", Proc. Amer. Soc. Civil
Eng., 81, No. 590 (Jan. 1955).
40. Gould, R. H., Discussion "Design of Final Settling Tanks for Activated
Sludge", Sewage Works Journal, 17, 1, 63 (1945).
41. Fitch, E. B., and Lutz, W. A., "Feedwells for Density Stabilization",
JOURNAL Water Pollution Control Federation, 32, 2, 147 (1960).
42. Rebhun, M., and Argaman, Y., "Evaluation of Hydraulic Efficiency of
Sedimentation Basins", JOURNAL Sanitary Eng. Div., ASCE, 91, SA5
(1965).
43. Ambrose, Homer, Jr., Baumann, E. Robert, and Fowler, Eric B., "Three^
Tracer Methods for Determining Detention Times in Primary Clarifiers ,
Sewage and Industrial Wastes. 29, 1, 24 (1957).
91
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44. Seamen, William, "Settling Basin Detention Time by Radiotracer",
Sewage and Industrial Wastes, 28, 3, 296 (1956).
45. Muszkalay, L. and Vagas, "Modification of the Tracer Measuring
Method in Settling Basins", Sewage and Industrial Wastes, 30, 9,
1101 (1958).
46. Schroepfer, G. J., Discussion of "Sedimentation in Quiescent and
Turbulent Basins", by J. J. Slade Jr., Trans. Am. Soc. Civil Engrs.,
102, 317 (1937).
47. Katz, W. J., and Geinopolos, A., Discussion of "Flow Patterns in a
Rectangular Sewage Sedimentation Tank", Advances in Water Pollution
Research, Proceedings 1st International Conference, London,
Pergamon Press, Oxford (1964).
48. Camp, T. R., "Sedimentation and the Design of Settling Tanks",
Discussion, Trans. Am. Soc. Civil Engineers, 111, 895 (1946).
49. Eliassen, R., "Sedimentation and the Design of Settling Tanks",
Discussion, Trans. Am. Soc. Civil Engineers, 111, 952 (1946).
50. Shapiro, J., Levin, G., Zea, U., "Anoxically Induced Release of
Phosphate in Wastewater Treatment", JOURNAL Water Pollution Control
Federation. 39_, 11, 1810 (1967).
51. Sawyer, C., and Bradney, L., "Rising of Activated Sludge in Final
Settling Tanks", Sewage Works Journal, 17, No. 6, 1191 (1945).
52. Brandon, T. W., and Grindley, J., "Effect of Nitrates on the Rising
of Sludge in Sedimentation Tanks", (Abstract) Sewage Works Journal.
_17, No. 3, 652 (1945).
53. Lockett, Wm. T., "The Phenomenon of Rising Sludge in Relation to
the Activated Sludge Process", (Abstract) Sewage Works Journal, 17,
No. 3, 654 (1945).
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Treatment of Sewage and Industrial Wastes, Reinhold Publishing Corp-
oration, New York (1957).
55. Albrecht, A. E., Wullschleger, R. E., and Katz, W. J., "In Situ
Measurement of Solids in Final Clarifiers", JOURNAL Sanitary
Engineering Division, ASCE, Vol. 92, SA1, Proc. Paper 4686, 183
(February 1966).
56. Dick, Richard I., "Gravity Thickening", Summer Institute in Water
Pollution Control - Biological Treatment, Manhattan College, New
York (1969).
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York (1963).
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58. Englebrecht and McKinney, "Membrane Filter Applied to Activated
Sludge Suspended Solids Determinations", Sewage and industrial
Wastes, 28, 1321 (Nov. 1956).
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(1958) .
60. Bloodgood, D. E., "Application of Sludge Index Test to Plant
Operation", Water and Sewage Works. 91, No. 6, 222 (June 1944).
61. Schmidt, 0. J., "Developments in Activated Sludge Practice",
Public Works, 109 (1963).
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Theories, JOURNAL Sanitary Eng. Dig... ASCE, 94_, No. SA3, 554
(June 1968).
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Sludge Thickening Theories", JOURNAL Sanitary Eng. Div., ASCE 94_,
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What Is It?", JOURNAL Water Pollution Control Federation. 41., 7,
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JOURNAL Sanitary Engineering Division, ASCE, 95, No. SA1, Proc.
Paper 6426, 117 (February 1969).
93
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APPENDIX L
Example of Output from Computer Regression Analysis
94
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Load ***Statpack
Ready
Infile Refile
Ready
Run
Statpack 11:07 08/09/68 Friday SJ
Note: No outfile - data cannot be saved
Are you a statpack expert
?* No
Do you wish to list names of available analyses
?* No
What analysis do you wish to perform
?* Stepwise regression
Do you wish to enter data from your input file now
?* Yes
30 rows, 6 columns (infile)
Last data item read from input file
Do you wish to print the data just read in
?* No, this is the same data used in the regression section
Do you wish to change some values
?* No
Specify the dependent variable
?* 6
Do you wish to delete any variables
?* No
Step 1
Variable selected 2
Sum of squares reduced in this step 10.300
Proportion of variance of Y reduced 0.178
F for this variable (D.F.-l, 28) 6.063
Cumulative sum of squares reduced 10.300
Cumulative proportion reduced 0.178 of 57.867
Multiple correlation coefficient 0.422 (Adjusted R - 0.422)
F for analysis of Vari. (D.F.- 1, 28) 6.063
Standard error of estimate 1.303 (Adjusted SE- 1.303)
95
-------
Variable Reg.Coef. Std.Error-Coef. Computed T Beta Coef.
2 0.00521 0.00212 2.462 0.42189
Step 2
Variable selected...... 5
Sum of squares reduced in this step..... 13.324
Proportion of variance of Y reduced 0.230
F for this variable (D.F.-l, 27) 10.506
Do you wish to enter this variable in the regression
?* SOS, are there any suggestions
In a given step, the variable that reduces the largest amount of sum of
squares is selected. If the reduction indicated by the above 3 lines
is significant, enter this variable in the regression. Otherwise,
selection of variables will be terminated.
Do you wish to enter this variable in the regression
?* Yes
Cumulative sum of squares reduced...... 23.624
Cumulative proportion reduced 0.408 of 57.867
Multiple correlation coefficient 0.639 (Adjusted R - 0.622)
F for analysis of vari.(D.F.- 2, 27)... 9.314
Standard error of estimate 1.126 (Adjusted SE - 1.146)
Variable Reg.Coef. Std.Error-Coef. Computed T Beta Coef.
2 0.00632 0.00186 3.397 0.51162
5 0.04316 0.01332 3.241 0.48817
Step 3
Variable selected 3
Sum of squares reduced in this step..... 7.572
Proportion of variance of Y reduced 0.131
F for this variable (D.F.-l, 26) 7.382
Do you wish to enter this variable in the regression
?* Yes
Cumulative sum of squares reduced 31.196
Cumulative proportion reduced 0.539 of 57.867
Multiple correlation coefficient 0.734 (adjusted R - 0.711)
F for analysis of vari.(D.F.« 3, 26).... 10.137
Standard error of estimate 1.013 (adjusted SE - 1.050)
Variable Reg.Coef. Std.Error-Coef. Computed T Beta Coef.
2 0.00744 0.00172 4.318 0.60233
5 0.05363 0.01258 4.263 O.I0648
3 0.01497 0.00551 2.717 0.38618
Intercept -5.53531
96
-------
Step 4
Variable selected 1
Sum of squares reduced in this step.... 0.127
Proportion of variance of Y reduced.... 0.002
F for this variable (D.F.- 1, 25) 0.120
Do you wish to enter this variable in the regression
?* No
Do you wish to print the table of residuals
?* Yes
Case No
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Y Observed
1.000
2.000
2.000
0.0
2.000
2.000
3.000
2.000
3.000
0.0
4.000
1.000
1.000
1.000
3.000
2.000
3.000
4.000
4.000
3.000
4.000
4.000
1.000
0.0
4.000
1.000
3.000
4.000
4.000
0.0
Y Estimated
0.599
1.884
2.266
0.907
1.998
1.584
3.499
2.233
3.859
0.989
2.513
1.959
2.050
1.107
2.920
1.765
2.541
3.366
3.680
2.654
3.700
1.846
2.069
1.956
1.340
1.798
2.245
4.413
3.926
0.333
Residual
0.401
0.116
-0.266
-0.907
0.002
0.416
-0.499
-0.233
-0.859
-0.989
1.487
-0.959
-1.050
-0.107
0.080
0.235
0.459
0.634
0.320
0.346
0.300
2.154
-1.069
-1.956
2.660
-0.798
0.755
-0.413
0.074
-0.333
Std.Resid
0.396
0.115
-0.263
-0.896
0.002
0.411
-0.492
-0.231
-0.848
-0.977
1.469
-0.947
-1.037
-0.106
0.079
0.232
0.454
0.626
0.316
0.341
0.296
2.126
-1.055
-1.932
2.626
-0.788
0.745
-0.407
0.073
-0.329
Test of extreme residuals
Ratio of ranges for the smallest residual 0.263
Ratio of ranges for the largest residual 0.316
Critical value of the ratio at alpha • .10 0.332
Do you wish to plot Y observed and Y estimated
?* No
D o you wish to compute more regression
?* No
97
-------
What analysis do you wish to perform
?* Finish
End of run
Time 0 min. 1 sees.
98
-------
SELECTED WATER i. Report No.
RESOURCES ABSTRACTS
INPUT TRANSACTION FORM
2. 3. Accession No.
w
A MATHEMATICAL MODEL OF A FINAL 5- ReP°rtD*te
CLARIFIER 6-
_____ 8. Performing Organization
7. Author(s) Report If o.
Robert W. Agnew
9. Organization
Rex Chainbelt Inc.
10. Project No.
1T090 FJW
11. Contract/Grunt No.
14-12-194
13. Type of Report and
Period Covered
12. Sponsoring Organization
15. Supplementary Notes
16. A bstract
An experimental testing program was carried out on final clarifiers
at three treatment plants in order to provide a set of data for formu-
lation and testing of a mathematical model for sludge compaction and
solids separation performance. Multiple regression was used to evaluate
the empirical coefficients in power functions for expressing the compaction
and solids separation performance. The concentration of solids in the
final effluent was related to overflow rate, BOD loading, mixed liquor
suspended solids, and detention time. Maximum return sludge concentration
was related to volatile fraction of mixed liquor suspended solids and
BOD loading.
17a. Descriptors
*Settling Basins, ^Mathematical Models, *Activated Sludge, Mathematics,
Regression Analysis, Waste Water Treatment.
17b. Identifiers
17c. COWRR Field & Group
18. Availability 19. Security Class.
(Report)
20. Security Class.
(Page)
21. No. of Send To:
Pages
22 Price WATER RESOURCES SCIENTIFIC INFORMATION CENTER
U.S. DEPARTMENT OF THE INTERIOR
WASHINGTON, D. C. 20240
Abstractor Robert Smith I institution EPA
WRSIC 102 (REV. JUNE 1971) GPO 913.261
eU.S. GOVERNMENT PRINTING OFFICE:1972 484-483/113 1-3
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