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

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  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

-------
                                                             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

-------
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    LU
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       or
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                   1.3
                   1.2
             I.I
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                                            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

-------
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

-------
              BLACK RIVER  WASTEWATER

                 TREATMENT  PLANT

                BALTIMORE, MARYLAND
en
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  30
  25
   20
tn  15


Q
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   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

-------
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	 _.^ erirircPTiv/cr ....•
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SETTLING
ZONE
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SLUDGE REMOVAL ZONE



0
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                         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

-------
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   x
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  X
   o>
  Z
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LU
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                              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

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                           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

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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

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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

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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

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                                                                                     OUTFALL
            MAIN EQUIPMENT
              BUILDING
                                                                                  CHLORINE CONTACT
                                                                                      TANKS
PLANT  INFLUENT
                                 FLOW DIAGRAM —RACINE, WISCONSIN
                              WATER  POLLUTION  CONTROL  PLANT

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                                 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

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                                 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

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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

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                  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

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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

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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

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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

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1000
 900
                            TYPICAL SETTLING  CURVE

                               MLSS = 2000 mg/L
                                 TIME
(MINUTES)
57

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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

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                                  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

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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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                     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

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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

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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

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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

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                           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

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                                BIBLIOGRAPHY
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2.  Eckenfelder, W. W., and O'Connor, D. J., "Biological Waste Treat-
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3.  McKinney, Ross E., "Fundamental Approach to the Activated Sludge
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6.  Sawyer,  C.  N.,  "Milestones in  the Development of the Activated
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7.  McKinney,  Ross  E., "Mathematics of  Complete-Mixing Activated Sludge
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9.  Pipes,  Wesley 0., "Types  of Activated  Sludge  which Separate Poorly",
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10.  Dick,  Richard I., and Ewing, Benjamin B.,  "Evaluation  of  Activated
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11.   Vesilind, D.  Aarne, Discussion of "Evaluation of Sludge Thickening
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12.   Dick,  Richard I., and Ewing, Benjamin B.,  Closure "Evaluation  of
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     ASCE 95 No. SA2,  333 (April 1969).
                                       89

-------
13.  Mancini, John L., "Gravity Clarifier and Thickener Design", Proceed-
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14.  Rudolfs, Willem, Lacey, I. 0., "Settling and Compacting of Activated
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15.  Ridenour, G. M., "Effect of Temperature on Rate of Settling of Sewage
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16.  Pflanz, Peter, "The Sedimentation of Activated Sludge in Final
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17.  Hall, E. J., Formal Discussion Paper 11-16, "Hydraulic and Removal
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18.  Camp, Thomas R., "Studies of Sedimentation  Basin Design, Sewage
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19.  Riddick, T. M.,  "Control  of Colloid Stability Through Zeta Potential",
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20.  Fair, Gordon M., and  Geyer, John Charles,  "Water  Supply and Waste-
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21.  Schroepfer, G.  J.,  "Factors Affecting  the Efficiency of Sewage
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22.  Garrison, Walter E.,  and  Nagel,  Carl A.,  "Operation  of  the Whittier
     Narrows Activated Sludge  Plant", Water and  Sewage  Works, Reference
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23.  Dye, E. 0., "Solids Control Problems in Activated  Sludge",  Sewage and
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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

-------
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

-------
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).

54.  Sawyer, C. N., "Final Clarifiers and Clarifier Mechanisms",  Biological
     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).

57.  Perry, J., "Chemical Engineers Handbook", McGraw-Hill,  Inc.,  New
     York (1963).
                                      92

-------
58.  Englebrecht and McKinney,  "Membrane Filter Applied to Activated
     Sludge Suspended Solids Determinations",  Sewage and industrial
     Wastes, 28, 1321 (Nov.  1956).

59.  Volk, W., "Applied Statistics  for Engineers",  McGraw-Hill Inc.
     (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).

62.  Krone, Ray B., Discussion of "Evaluation of Sludge Thickening
     Theories,  JOURNAL Sanitary Eng. Dig... ASCE, 94_, No. SA3, 554
     (June 1968).

63.  Duncan,  J. W. K., and Kawata, K., Discussion of "Evaluation of
     Sludge Thickening Theories", JOURNAL Sanitary Eng. Div., ASCE 94_,
     No.  SA2,  431 (April  1968).

64.  Call/360:   Statpack  Statistical Package,  Service Bureau Corporation
     (1969).

65.  Regression Analysis, General Electric  Time-Sharing Service, Program
     Library  Users Guide  (1968).

66.  Dick, Richard I.,  and  Vesilind, P.  A.,  "The Sludge Volume Index -
     What Is  It?", JOURNAL  Water Pollution  Control Federation. 41.,  7,
     1285 (July 1969).

67.  Smith, Robert,  "Preliminary Design of  Wastewater Treatment  Systems",
     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

-------
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

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What analysis do you wish to perform
?* Finish
End of run

Time    0 min.    1 sees.
                                        98

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   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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