Environmental Protection Technology Series
Environmental Research Laboratory
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U.S. Environmental
Protection Agency, have been grouped into nine series. These nine broad cate-
gories were established to facilitate further development and application of en-
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The nine series are:
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EPA-600/2-77-120
July 1977
PROCEDURES FOR ESTIMATING DRY WEATHER
POLLUTANT DEPOSITION IN SEWERAGE SYSTEMS
by
William C. Pisano
Celso S. Queiroz
Energy & Environmental Analysis, Inc.
Boston, Massachusetts 02116
Grant No. R804579
Project Officer
Richard Field
Storm and Combined Sewer Section
Wastewater Research Division
Municipal Environmental Research Laboratory (Cincinnati)
Edison, New Jersey 08817
MUNICIPAL ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
CINCINNATI, OHIO 45268
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DISCLAIMER
This report has been reviewed by .the Municipal
Research Laboratory, U.S. Environmental Protection Agency, and
approved for publication. Approval does not signify that the
contents necessarily reflect the views- and policies of the U.S.
Environmental Protection Agency, nor does mention of trade
names or commercial products constitute endorsement or recommen-
dation for use.
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FOREWORD
The Environmental Protection Agency was created because of
increasing public and government concern about the dangers of
pollution to the health and welfare of the American people
Noxious air, foul water, and spoiled land are tragic testimony to
the deterioration of our natural environment. The complexity of
that environment and the interplay between its components require
a concentrated and integrated attack on the problem.
Reseraeh and development is that necessary first step in
problem solution and it involves defining the problem, measuring
its impact, and searching for solutions. The Municipal
EnVirotimental Research Laboratory developes new and improved
technology and Systems for the prevention, treatment, and manage-
ment of wastewater and solid and hazardous waste pollutant dis-
charges from municipal and community sources, for the preserva-
tion and treatment for public drinking water supplies and to
minimize the adverse economic, social, health, and aesthetic
effects of pollution. This publication is one of the products
r£«StiuS*fltSc5(, a m0£St vital. communications link between the
researcher and the user community.
The deleterious effects of storm sewer discharges and com-
bined sewer overflows upon the nation's waterways have become of
increasing concern in recent times. Efforts to alleviate the
problem depend in part upon the development of improved flow
attenuation and treatment devices.
This report presents a series of generalized predictive
approaches for estimating the amount of sewage solids and other
pollutants that deposit in sewerage systems during dry weather
conditions. These procedures are intended to provide estimates
Of overall pollutant deposition for entire sewer collection
Systems«
Francis T. Mayo
Director
Municipal Environmenta.1 Research Laboratory
111
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ABSTRACT
A set of generalized procedures for estimating pollutant
loadings associated with dry weather sewage solids deposition in
combined sewer systems has been prepared to provide planners,
engineers and municipal managers with technical information so
that they can make intelligent informed decisions on potential
sewer flushing programs in combination with other combined
sewer management controls.
The predictive equations relate the total daily mass of
pollutant deposition accumulations within a collection system to
physical characteristics of collection systems such as per
capita waste rate, service area, total pipe length, average pipe
slope, average diameter and other more complicated parameters
that derive from analysis of pipe slope characteristics.
Several alternative predictive models are presented reflecting
anticipated differences in the availability of data and user
resources. Pollutant parameters include suspended solids,
volative suspended solids, biochemical oxygen demand, chemical
oxygen demand, total organic nitrogen and total phosphorous.
Sewer system age and degree of maintenance was also considered.
Factors are presented for estimating the increase in collection
system deposition resulting from improper maintenance. A user s
guide has been presented to establish the necessary data input
to utilize the predictive procedures.
This report was submitted in partial fulfillment of
Grant No. R804579 by Northeastern University and Energy &
Environmental Analysis, Inc., under the sponsorship of the U.S.
Environmental Protection Agency. This report covers the period
of August 1, 1976 to December 30, 1976. Work was completed
as of April, 1975.
IV
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CONTENTS
Disclaimer
Foreword
Abstract . . . . . . . . iv
Figures .viii
Tables . . ix
Abbreviations and Symbols x
Acknowledgement xii
1. Introduction ........... 1
1.1 Purpose of Study 2
1.2 Report Format -f 2
1.3 Data and Information Sources , 2
2. Conclusions 3
3. Recommendations
4. Development of Generalized Predictive Models
4.1 Overviews 6
4.1.1 Objectives 6
4.1.2 Executive Overview of Methodology . 6
4.2 General Methodology-Detailed Overview . 7
4.2.1 Discussion of Model Variables . . 9
4.3 Design of Experiment . . . . . . . 12
4.3.1 Description of Three Sewer Systems . 12
4.3.2 Range of Flows ... .... 14
4.3.3 Age and Maintenance Conditions... 15
4.4 Data Preparation for the Regressive
Model .17
4.4.1 Deposition Model Results .... 17
4.4.1.1 Brief Description of the
Deposition Models ... . . 17
4.4.1.2 Input Data Required by the
Deposition Model lg
4.4.1.3 Deposition Input Data
Preparation . 19
4.4.1.4 Deposition Model Runs and
Results. ........ 20
4.4.2 Areas and Total Pipe Lengths. . . 20
4.4.3 Distribution of Pipe Slopes. . . 20
4.4.4 Average Pipe Diameter. 32
4.4.5 Distribution of Solids Deposited
by Pipe Length 35
4.4.6 Pipe Lengths Corresponding to 80%
of the Loads Deposited-Lpo. . . .39
4.4.7 Slope Corresponding to PLD (Sp^) . . 39
4.4.8 Slope Corresponding to PLD/4-
(sPD/4) 39
v
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CONTENTS (continued)
4.4.9 Summary of Results »
4.5 Regression Analysis. .
4.5.1 Regression Procedures. .... -
4.5.2- Regression Results
4.5.3 Alternative Model Selections . . .
4.5.3.1 The Elaborate Model. . .
4.5.3.2 An Intermediate Model . ...
4.5.3.3 The Simplest Model. . ...
4.5.3.4 Final Comments on the Selection
of the Model .
4.5.4 Effects of Age and Maintenance
4.5.5 Predictions of other Parameters .
5. Model Utilization
5.1 Introduction, . . . .
5.2 Summary of Formulas for the Estimation
of TS
5.2.1 Formulas for Estimation of Total
Loads Deposited - TS
5.2.1.1 The Elaborate Model
5.2.1.2 The Intermediate Model
5.2.1.3 The Simplest Model
5.2.2 Estimation of Total Pipe Length .
5.2.3 Estimation of Mean Pipe Slope S .
5.2.3.1 Pipe Slope Data Available
5.2.3.2 Pipe Slope Data Not Available
5.2.4 Distribution of Total Solids
Deposited by Pipe Segment - Determi-
nation of PLD
5.2.5 Determination of Slopes SPp and SPD/4
5.2.5.1 Pipe Slope Data is Available .
5.2.5.2 Pipe Slope Information Not
Available .
5.2.6 Formulas for the Average Pipe
Diameter
5.3 General Description of User's Steps .
5.3.1 Determination of the Total Solids
Deposited ...-
5.3.2 Application of Procedures .
5.3.2.1 Data Requirements
5.3.2.2 Estimation of Loads
5.3.3 Determination of Deposition Extent
Collection Systems
in
40
40
40
41
48
48
49
50
50
50
54
56
56
'56
56
56
57
57
57
58
58
58
58
59
59
59
59
60
60
62
62
65
68
VI
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CONTENTS (continued)
Appendices
A. Brief Review of R&D Sewer Flushing Project
B. Discussion of Simplified Sewer System
Deposition Model. . .
C. Preliminary Deposition Model Calibration.
Results . . . ..."
71
82
90
vi r
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FIGURES
Number,
Page
1 General Methodology of the Study ...... 8
2 Collection System Pipe Slope Variables . . .. . 11
3 Representation of Sediment Beds and Pipe Slope
For Two Age and Maintenance Conditions 18
4 Distribution of Pipe Slopes . . ..... 23
5 Distribution of Pipe Slopes . . ..... 24
6 Complementcy Distribution of Pipe Slopes
Basin 29 - WRNDB 25
7 Complementary Distribution of Pipe Slopes
Basin 49 - Dorchester .26
8 Complementary Distribution of Pipe Slopes
Basin 61 - Dorchester ... . ..... 27
9 Complementary Distribution of Pipe Slopes
Basin 71 - Dorchester . . . . . . . .28
10 Complementary Distribution of Pipe Slopes
Basin 73 - Fitchburg 29
11 Histograms of Collection System Pipe Slopes. . . 30
12 Distribution of Solids Deposited by Pipe
Lengths- WRNDB System . .36
13 Distribution of Solids Deposited by Pipe
Lengths - Dorchester System. . . ... .37
14 Cumulative Distribution of Solids Deposited vs
Pipe Length. . . . . .. .. . . .38
15 User Steps to Determine Total Solids Deposited-
TS . ... .... . .....61
16 Determination of the Cut-Off Slope for a
Percentage of Mass Deposited "69
A-l Schematic Overview of Program . . . ... .73
B-l Schematic of Collection System 87
viii
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Number
1
2
3
5
6
7
8
9
10
11
12
13
14
15
16
17
A-l
A-2
A-3
B-l
C-l
TABLES
Sewer Density
Population Density. . . . . .
Per Capita Waste Rates for Various Population
Densities and Infiltration Rates
Per Capita Values Relative to the Density of
45 Persons/Acre. .......
Total Pipe Lengths and Areas of the Basins.
Slopes Corresponding to the Intervals Shown on
Figure 11.
Formulas for Equivalent Circular'Diameters' Used
in Computing the Basin Average Diameter, ,
Summary Data on Derived Lengths, Slopes and
Pipe Diameters . . . . . .
Linear Regression Results.
Coefficients of the Linear Regression Results.
Log Regression Results ......
* *»
Coefficients of the Natural Log Regression
Equations .
Ranges, Means, and Standard Deviations of the
Independent Variables Used in the Regression
Average Values of the Ratios of Computed Loads
in Deposited Pipes Over Clean Pipes. ...
Regression of Different Pollutants on TS . ,
Distribution of Pipe Slopes for Basin 70 .
Comparison of Estimated Daily Solids Deposited
For Basin 70 Using Different Procedures
Total Mass of Pollutant Removed by Flush .
,
Statistics of Pollutant Mass Removals (kg)
Raw Data . ........
Statistics of Pollutant Mass Removals (kg/
antecedent day) Data .
Deposition Analysis of Idealized System
Preliminary Overall Comparison of Measured and
Predicted Results of Solids Deposition
Test Segments ... . . .
16
16
21
31
33
34
42
43
44
45
46
51
53
55
64
.6.7
76
80
81
91
IX
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LIST OF ABBREVIATIONS AND SYMBOLS
ABBREVIATIONS
CDF - cumulative distribution function
ft - foot
gpcd - gallons per capit per day
kg - kilogram
Ib/day- pounds/day
log - logarithm
mi - mile
WRNDB - sewerage system within the area covering portions of West
Roxbury, Dedham, Newton and Brookline in metropolitan
Boston.
SYMBOLS
A - Area of collection system
(acres)
AV - Indicates a variable in
the regression analysis
which is available to
enter the regression
equation
BOD - Biochemical Oxygen
Demand (5 day)
COD - Chemical Oxygen Demand
D - Mean pipe diameter of a
collection system, (in)
Dj[ - Pipe diameter of sewer
segment i, (in)
DP - Indicates the dependent
variable in the regres-
sion analysis
e - Base of the natural
logarithms;
FI - Indicates a variable in
the regression analysis
to be forced in the re-
gression equation
FO - Indicates a variable in
the regression analysis
to be kept out of the
regression equation.
FS - Indicates the cumula-
tive probability of
a value s of the pipe
slopes
GS - Indicates comple-
mentary cumulative
probability distri-
bution
L - Total length of the
collection system
(ft)
li .- Length of sewer seg-
ment i
LPD - Length of pipe over
which 80% of the
total loads deposit
in the collection
system
LPM - Estimated length of
pipe over which the
percentage PM of the
total loads deposit
in the collection
system
n - The total number of
pipe segments in a
collection system
NH3 - Ammonia
p - Particle size (mm)
P - Total Phosphorous
P(a) - Indicates the proba-
bility of a
x
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PL
PLD
PLD/4
PM
PP
q
QAV
QMAX
r
R
R2
ss
Si
SG
SPD
Percentage of pipe
length corresponding
to a percentage of
PM of the loads
depositing in the
collection system
Percentage of pipe
length corresponding
to 80% of the loads
depositing in the
collection system
One fourth of PLD
Any given percentage
of the solids deposited
in a collection
system
population in service
area
Discharge per capita, in-
cluding infiltration,
(gpcd)
Average daily dry "
weather flow, (cfs)
Peak daily dry
weather flow (cfs)
hydraulic radius
(ft)
Multiple regression
coefficient in the
regression analysis
Portion of the total
variation about the
mean (predicted by
the regression equa-
tion) which is ex-
plained by the re-
regression
Mean pipe slope of the
collection system
A particular value of
pipe slope
Energy slope
Slope of sewer segment i
Mean ground slope
Slope corresponding to
PLD in the CDF of the
pipe slopes
SpD/4
TKN
TS
TSa-b
TS
VSS
X
Y
Z±
TC
Average of pipe_ slopes
below SPD in the
CDF
One fourth of SPD
Slope corresponding
to PL in the CDF of
the pipe slopes
Total Kjeldhal
Nitrogen
Indicates the total
mass of solids that
deposit in the sys-
tem (Ib/day)
Indicates the total
mass of solids that
deposit in the col-
lection system,
assuming pipe bottom
sediment varying from
a to b (inches)
Total Suspended Solids
Volatile Suspended
Solids
Major dimension of non-
circular pipe
Minor dimensions of non-
circular pipe
Percentage daily
solids deposition
rate in pipe seg-
ment i
Amount of daily dry
weather sewage solids
input along pipe seg-
ment i
specific weight of
water
- Fluid shear stress
- Critical shear stress
XI
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ACKNOWLE DGEMENTS
The successful completion of this report was dependent on
the cooperation and assistance of a number of individuals and
organizations. We are indebted particularly to Richard Field,
Chief of the Storm and Combined Sewer Section, Muncipal
Environmental Research LaboratoryCincinnati, EPA, Edison,
New Jersey and Richard Traver, staff engineer of the Storm and
Combines Sewer Section, for their guidance and review of the work.
The analytical results of the field flushing program was
performed by Northeastern University, Boston, Massachusetts.
Dr. Fredric C. Blanc and Dr. James O'Shaughnessy are the pro-
ject officers for Northeastern University,
This work was conducted under the supervision and direction
of Dr. William C. Pisano, Project Director and Celso S, Queiroz,
Environmental Systems Analyst, Energy & Environmental Analysis,
Inc. Gerald L. Aronson and Paul G. Soper of EEA were responsible
for the field engineering phase of the sewer flushing
experiments.
Xll
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SECTION 1
INTRODUCTION
Control of combined and storm sewer runoff is a problem of
increasing importance in the field of water quality management.
The control of combined sewer pverflows employing structural
measures such as sewer separation, storage and treatment have
been used for a number of major cities in the United States.
Nationwide application of these techniques for the control of com-
bined sewer overflows would require expenditures critically tax-
ing present and forseeable future resource allocations. New
strategies are needed to reduce these costs to tolerable limits.
Non-structural controls such as sewer system upgrading and active
maintenance, improved catchbasin operation, street sweeping and
sewer flushing are upstream collection system management.practices
that collectively can reduce total combined sewer pollutant load-
ings and accordingly the costs of downstream structural controls.
The concept of depositing solids control in sewer lines,
although widely used around,the turn of the century as a mainte-
nance practice, is still in its infancy in regard to being viewed
as a viable pollution control alternative for combined sewer
systems. Much theoretical but little applied research has been
performed to develop and quantify uniform criteria for estimating
deposition loadings, and for flushing sewers.
The deposition of sewage solids during dry weather in com-
bined sewer systems has long been recognized as a major contri-
butor to "first-flush" phenomena occurring during wet weather run-
off periods. The magnitude of these loadings during runoff
periods has been estimated to range up to 30 percent of the total
daily dry weather sewage loadings. Estimation of these loadings
for a given sewer system is an extremely difficult task. Measure-
ment for extended periods is possible but extremely expensive.
Some literature information is available from experiments on
build-up of sanitary sewage solids in a pilot sewer study
conducted by the FMC Corporation (1). No predictive procedures
are available for estimating deposition build-up as a function of
collection system characteristics. These predictive procedures
are necessary as a first step in the development of sewer
flushing programs as a non-structural management practice.
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1.1 Purpose of Study
The purpose of this study is to provide municipal managers
and planners with technical information on the amount and location
of pollutant deposition within sewerage collection systems so
that they can make intelligent, informed decisions on the potential
for sewer flushing systems in their community,
1.2 Report Format
The detailed findings derived from this study are presented
in the two sections that follow which deal with development of the
theoretical predictive model (Section 4); and the user's guidance
procedures (Section 5). Section 4 is subdivided into five .sub-
sections: section 4.1 - the general methodology; section 4.2 -^
the conceptual model; section 4.3 - the design of the experiment;
section 4.4 - the data preparation; and section 4*5 - the re-
gression results.
1.3 Data and Information Sources
The data and information for this study were derived
principally from four data sources: (1) the preliminary first
phase field flushing results from Research Grant no. R804579
conducted by Northeastern University and Energy & Environmental
Analysis, Inc., sponsored by U.S. EPA Storm and Combined Sewej?
Section; (2) sewer atlas physical data for portions of West
Roxbury, Dedham, Newton and Brookline, Massachusetts for an
infiltration/inflow study conducted by Energy & Environmental
Analysis, Inc., for the Metropolitan District Commission? (3)
sewer atlas physical data for portions of the City of Fitchburg,
Massachusetts for a section of 208 combined sewer management
study conducted by Energy & Environmental Analysis, Inc. for the
Montachusetts Regional Planning Commission; and (4) sewer atlas
physical data for portions of Dorchester and South Boston for a
combined sewer management study sponsored by the Metropolitan
District Commission.
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SECTION 2
2.
3.
CONCLUSIONS
Conclusions derived from this investigation are as follows:
This present study develops a methodology for providing
first-cut assessemnts of: a) the total amounts of solids
and other pollution indicators, (Ib/day), that deposit in a
sewerage collection system; and b) the extent of the collec-
tion system over which the deposition takes place. A
complex distributed-parameter dry weather sewage depostion
model was first applied to 75 separate and combined sewer
collection systems in eastern Massachusetts to generate
estimates of solids deposited in the systems (Ib/day). These
estimated loads were then regressed with selected variables
representing the physical characteristics of the collection
system resulting in four predictive single term power func-
tions with at most four independent variables. The regres-
sion analysis revealed a remarkable degree of fit of the non-
linear functions to the data set, with the R2 values ranging
from 0.85 to 0.95.
A comparative error analysis of predicted daily dry weather
solids deposition for a test case collection system using
the procedures generated in this study and the complex dis-
tributed-parameter model indicated a relative error ranging
from 8 to 18 percent. The analysis also showed that the
simplest of these procedures requiring comparatively little
input data may be more cost effective than the more complex
of these procedures for providing reliable "first-cut" esti-
mates. ,
The complex-:distributed parameter model was tentatively cali-.
brated using actual field flush;-information lending credulence
to the adoption of the simplified procedures generated in this
study.
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The field analytical results of a sewer flushing project
currently in progress were used to regress other pollutants
such as BOD, COD, TKN, Total Phosphorous, NH3 and VSS with
suspended solids, all with high values of R2, extending
therefore the use of the predictive equations for total
solids deposited to the estimation of other pollutants.
The effects of sewer system age and maintenance on solids
deposition was simulated by considering prior sediment depo-
sits to develop multiplicative coefficients to the four pre-
dictive equations for total solids deposited.
Extensive statistical analyses of sewerage system pipe slopes
revealed that collection system pipe slopes can be repre-
sented by an exponential probability model. Analysis of the
distribution of loads deposited versus cumulative pipe length
lead to the development of generalized curves as a function
of collection system mean slope for estimating the total
fraction of collection system pipe footage over which a given
percentage of the total loads deposit. These findings can be
combined to locate segments associated with the required
fractions.
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SECTION 3
RECOMMENDATIONS
1. The major improvements to the methodology developed in this
study involve extending the range of the regression model's
applicability by expanding the observed ranges of the
independent predictive variables used in the analysis. The
reliability of the model's estimates will be improved.
These improvements can be accomplished by augmenting the
existing data base with new data from other sewer collection
systems having different physical characteristics, in terms
of average slopes, system configurations and extent, pipe
sizes and shapes, etc., from those used in this study.
Inclusion of systems with flatter and steeper average pipe
slopes would broaden substantially the range of application
of the regression equations derived in this study.
2. Another area meriting further study is the analysis of the
cumulative distribution function of pipe slopes, especially
for applications where only a limited amount of information
on the collection system is available.
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SECTION 4
DEVELOPMENT OF GENERALIZED PREDICTIVE MODELS
4.1 Overview
4.1.1 Objectives
The severity of combined sewer overflows is often associated
with problems of dry weather solids deposition. Deposition
build-up reduces conveyance capactiy and contributes to the pollu-
tants that discharge into receiving waters. The analysis of
remedial solutions to mitigate these problems involves estimating
the amounts of solids deposited and their distribution throughout
the system, so that control costs can be assessed.
The techniques presently available to estimate dry weather
deposition in sewerage systems involve the use of computerized
mathematical models, that are both complex and expensive arid re-
quiring more effort than appropriate for preliminary "first-6ut",
assessments. The objectives of this study is to develop
predictive tools capable of defining on a preliminary basis:
a) the total amounts of solids and other pollutants that
deposit in the sewerage system; and
b) the extent of the collection system over which the
deposition takes place;
It is therefore possible with these two estimates to crudely
evaluate the costs associated with sewer flushing andOther means
of reducing and/or eliminating these pollutants.
4.1.2 Executive Overview of Methodology
An empirical model relating pollutant deposition loadings to
collection system characteristics is the goal of this study.. The
approach is to use least squares to fit parameters of a. postulated
model. The data base used in the fitting process consists, in
part, of a number of collection system parameters developed from an
extensive data analysis of the physical details of several major
sewerage collection systems in eastern Massachusetts. These
-------
characteristics are some of the independent variables used in the
analysis. The data for the dependent variables are the total
daily sewage solids deposited in these collection systems for a
wide variety of different operating conditions, These quantities
are estimated using an existing exogenous model that uses extreme-
ly detailed information to compute deposition loadings throughout
an entire collection system network. An analysis of the detailed
outputs of this model together with some of the physical data of
the collection systems provided the remaining independent vari-
ables in the data base. Simply stated, the dependent variable
data was generated from an exogenous predictive analysis while
the independent variable data was obtained from primary collection
system data and from a secondary analysis-of the exogenous simula-
tion outputs with selected collection system data.
The results of the first phase field flushing program
are described in Appendix A along with a brief overview of the
entire project. The methodological details of the existing
exogenous deposition model that predicts solids deposition in all
segments of an entire sewerage collection system are presented
in Appendix B. Preliminary calibration efforts using the data in
Appendix A and the model in Appendix B are presented in Appendix
C, These results are given to justify the application of that
model to produce simulated data for the purposes of this study,
4,2 General Methodology-Detailed Overview
The general methodo.logy used in the study is outlined in
Figure l. The first step is to define the general characteristics
and parameters of the conceptual model. This discussion is pre-
sented in Section 4.2,1. Next, a series of experiments is
designed to generate deposition loadings using the model described
in Appendix B for a wide range of conditions likely to be
encountered in practice. The regression equations would be valid
for use over these ranges of conditions. The design of the
experiments,, described in Section 4.3, consists of defining the
study areas to be used in the experiments and the hydraulic condi-
tions under which the numerical experiments would be performed.
The suspended solids per capita waste rate is discussed in the
design of the experiments.
The next step involved the collection of all pertinent
physical data associated with the selected collection systems,
such as system configuration, pipe lengths, shapes and sizes, in-
vert elevations, so that the deposition model referred to in
Appendix B could be used. This physical data, together with the
deposition model and the total loads deposited simulated for each
Of the collection systems. This work is described in Section
4,4.1
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rH
id
,4J
>iJ3 id
en p< c
-Define study area
-Define surrogate
per capita waste
contributions to
cover a wide range
of the flow condi-
tions
-Define per capita
solid waste contri-
bution
/\
CO
w
H
PL,
-------
The analysis of the collection system service areas and total
pipe lengths, distributions of pipe slopes and average collection
system pipe diameters are presented in. Section 4.4.2 and 4.4.4.
The deposition model results included the total Ib/day
deposited in each pipe segment of each basin and the total loads
accumulated throughout each system. The information on loads by
pipe segment, is then used to generate curves for each bas,in,
showing the accumulated percentages of the loads deposited against
the accumulated percentage of pipe lengths where deposition took
place. This part of the work is described in Section 4.4.5.
The physical data of the system together with the distribution
of loads by pipe length are then used to define the derived
variables Lpp, SpQ and Spp/4 described in Section 4.4.6 tq 4.4.8
The total loads by basin generated by the deposition model
together with primary variables (pipe length, area, average slope,
average diameter) and the derived variables (Lpp, Spo, Spo/4) are
then used as input for the regression analysis described in
Section 4.5.
Finally, the results of the regression analysis were examined
and considered satisfactory and the process was complete.
4.2.1 Discussion of Model Variables
A discussion of the independent variables considered in the
model and a few descriptive details of the preliminary analyses
preceding the selection of the complete list of variables is given
in this section.
The obvious and simplest of variables that can be used to
characterize a collection system are the total service area,
total pipe length, average slope and the average pipe diameter.
It was believed from the onset of this study that these variables
alone would not be adequate to explain the variability of the
estimated loads from the deposition model. Clearly, a better
characterization of the collection systems was necessary.
An exploratory analysis applying the deposition model on a
number of sample collection systems revealed an interesting in-
sight. Plots of the cumulative percentages of total loads
deposited in each basin versus cumulative pipe lengths were pre-
pared. A number of these curves can be inspected from Figures 12
and 13 on pages 36 and 37. The curves spread around the range of
70% to 90% of the total mass deposited suggested the use of the
pipe length corresponding to 80% of the total mass, deposited as a
potential variable to include in the regression analysis.
-------
Anpther set of plots of the cumulative distribution of pipe
slopes for a few basins also suggested that the mean pipe slope
alone would not be adequate to explain the effects of the pipe
slopes on the variations of the deposition loads. A better
characterization of the collection system pipe slopes could be
obtained by defining various parameters at the flatter pipe slope
range. Three other pipe slope parameters besides "the mean pipe
slope were initially selected for inclusion into the regression
model. These parameters are as follows:
the pipe slope corresponding* to the percentage of the
pipe length where 80% of the total load of the collec-
tion system deposits
a)
b) the average of the slopes in the basin below SPD
c) the slope corresponding to some fraction of SPD/ arbitra-
ily taken as the slope corresponding to 1/4 the percent-
age of pipe lengths below which 80% of the total mass
deposits (SpD/4) -
These slope parameters can be seen in Figure 2.
Further analyses revealed that SPD and SPD were very strongly
correlated, so that retaining both in the regression analysis was
not necessary. This finding was fortunate since the variable
is much more difficult to determine than Spo- The variable
was excluded from the analysis.
Finally, it is clear that the deposition process is also
strongly affected by the sewage flows in the system. Variations
in population density and the degree of, infiltration affects the
dry weather flow rates. These effects were incorporated into the
per capita waste rates used in the deposition model simulations
and in the regression analysis. The summary list of variables
considered in the regression analysis is the following:
1. Total collection system pipe length (L) - ft?
2. Service area of collection system (A) - acres;
3. Average collection system pipe slope (S) - ft/ft;
4. Average collection system pipe diameter (D) - inches;
5. Length of pipe corresponding to 80% of the solids
deposited in the system (LPD) - ft;
* Note that the correspondence indicated in Figure 2 does not
necessarily imply that the pipe length over which 80% of the
load deposits has slope smaller than or equal to SPD at all
segments. See section 5.3.2
10
-------
fM
D
O
H
11
-------
6.
7.
8.
Slope corresponding to
- ft/ft;
Slope corresponding to 1/4 of the percentage of pipe
length (PLD) below which 80% of the solids deposit
(SPD/4) - ft/ft; and
Flow rate per capita, including allowance for infiltrar
tion (q) - gpcd.
With respect to the mathematical forms' of the regression
model both linear and alternative non-linear models were initially
postulated. Non-linear fitting techniques were not needed in the
analysis since the linear models, that is, the strictly additive
form and the logarithmic multiplicative form converted in the log
domain, resulted in excellent fitting results with the R2
approaching 95%.
4.3 Design of Experiment
In this section an overview will be presented of how collec-
tion system data from three major sewerage sytems was used to
design the data base for the multivariate regression experiment.
A description of the three sewer systems whose data were assumed
to represent an adequate sample from the universe of all collec-
tion system is presented in section 4.3.1. A discussion of the
per capita waste rates used in the experiment is presented in
section 4.3.2. These surrogate waste rates reflect wide variations
in population density and infiltration conditions encountered in
practice. This parameter can be considered as a decision variable
from a planning standpoint. Various sewer system age and mainte-
nance considerations are discussed in section 4.3.3,
4.3.1 Description of Three Sewer Systems
The physical characteristics of the three major collection
systems used in this analysis derive from three prior studies.
The first area, covering portions of West Roxbury in Boston,
Dedham, Newton and Brookline is strictly separated. The second
area covering major portions of Dorchester and South Boston, two
neighborhoods of the Boston metropolitan area is a mixed combined
and separate area while the third basin covering a portion of the
City of Fitchburg is served by a combined sewer system. The
total pipe length, service area and pipe density for each basin
are given in Table 1. The total pipe footage for all three areas
entails 196 miles of separate and combined sewer systems
encompassing a total area of 8.9 square miles.
12
-------
TABLE 1. SEWER DENSITY (mi/acre)
Overall
System
Pipe
Length (mi)
Area
(acres)
Pipe #
Density (mi/acre)
WRNDB**
35 basins
Dorchester
(37 basins)
Fitchburg
(3 basins)
64.87
119.85
11.17
2464.
2753
485.
0.026
0.044
0.023
Weighted averages: by pipe length: 0.036, by area: 0.034
Sewerage system with area covering portions of West Roxbury,
Dedham, Newton and Brookline in Boston metropolitan area.
13
-------
The land use in the first area in West Roxbury and neighboring
communities is mostly moderate to high density single and two
family dwellings with a population density ranging from 10 to 15
people/acre. The topography is mild with several hilly portions in
the area. This area was investigated in a recent infiltration/
inflow study and was subdivided into 35 distinct sewer collection
subsystems.
The land use in Dorchester and South Boston is mostly high
density multi-family dwellings with population density ranging
from 30 to 60 people/acre. The topography in Dorchester is moder-
ate with a number of hilly sections while portions of South
Boston are fairly flat. There are a total of 37 distinct sewer
collection systems in this study area.
The land use in the third area in Fitchburg is mixed commercial
and high density multi-family dwellings with a small portion of
single family homes. The population density is similar to
Dorchester. The study area is subdivided into three collection
systems.
A total of 75 different sewer collection systems form the data
basis for the analysis. It is assumed that these basins collect-
ively represent a wide variety of different pipe slope conditions,
pipe sizes and shapes and network system configurations. Some
basins serve narrow strips of land while others are broad fanned-
shape with a high hierarchial network order. A central assump-
tion is that the collection system characteristics represented by
the sample of 75 sewer sheds is an adequate representation of the
total universe of collection systems. This assumption is not
completely valid since, for example, extremely flat collection
systems were not part of the sample set. Future work should
broaden this data base. This' sample however is deemed reasonably
complete for the purposes of this analysis.
A complete sewer atlas of manhole to manhole descriptive
physical data including pipe length, slope, shape, size and net-
work ordering designations was available for each of these systems.
Much of this data had been previously processed for computer
application although a considerable portion of the data had to be
placed in EDP format for purpose of this study. Roughly 6000
manhole to manhole segments incorporating all of the aforementioned
parameters were necessary to represent the hydraulic character-
ization of the 75 sewer collection systems.
4.3.2 Range of Flows
The degree of deposition in a sewer pipe is strongly dependent
on the discharge. As flow increases through a pipe the depth,
velocity/ hydraulic radius all change resulting in higher shear
stress with less deposition. Discharge therefore is' an extremely
14
-------
imporant parameter in the analysis. The dry weather discharge in
a sewer system is dependent upon the local population density, ,the
domestic per capita contribution, the degree of infiltration and
any industrial waste contributions.
It was envisioned that a single per capital surrogate waste .
rate would be generated incorporating a wide range of population
density and infiltration conditions encountered in practice.*
This variable would embed all these variations and be used in
both the deposition model to predict daily dry weather solids
deposition and in the regression model as an independent variable.
Population densities ranging from 15 people/acre up to 90
people/acre were considered. Using a factor of 0.035 miles of
sewer per acre the corresponding number of people per 100 feet
of sewer pipe was computed. These factors are shown in Table 2
and are used in the deposition model which requires as input the
number of people per 100 feet of sewer.
The dry weather per capita contribution of 85 gpcd was con-
sidered fixed in this analysis. Four different infiltration
estimates of 500, 1000, 2000 and 4000 gallons per acre per
day were used to cover the range of normally encountered infiltra-
tion conditions. The adjusted per capita waste rates incorpora-
ting the various rates of infiltration for the range of popula-
tion densites considered in the analysis are shown in Table 3.
These per capita values are again adjusted to the mid-range of
population density of 45 people/acre and are given in Table 4.
This last conversion permits considering one single range of
surrogate per capita flow rates using 45 people/acre as the norm.
Four different flow rates are considered in the analysis and
cover the full range of per capita waste rates for different
population densities and infiltration conditions. The per capita
waste rate used in the analysis are: 40 gpcd,. 110 gpcd, 190 gpcd
and 260 gpcd.
The per capita solids waste rate of 0.5 Ib/capita/day was
used in all computations. This parameter was established from
field measurements in the sewer flushing project described in
Appendix C. All regression results presented in Section 4,5 can
be linearly scaled for any other desired per capita solids waste
rate.
4.3.3 Age and Maintenance Conditions
The presence of long-term accumulations of organic matter,
sand, gravel, grit and debris in the form of sediment beds,
* Industrial waste contributions were not explicitly considered.
The user can readjust the per capita waste rates used in this
analysis to reflect industrial contributions.
15
-------
TABLE 2. POPULATION DENSITY (PERSONS/100 FT OF PIPE)
Density (person/acre) Persons/100 ft of pipe*
15 8.15
30'
45
60
90
16.30
24.46
32.61
48.91
* Assumes 0.035 mi/acre or 184.8 ft of pipe/acre
TABLE 3. PER CAPITA WASTE RATES FOR VARIOUS POPULATION
DENSITIES AND INFILTRATION RATES*
Density
(person/acre)
15
30
45
60
90
Infiltration Rate
500
118.3
101.7
96.1
93.3
90.6
1000
151.7
118.3
107.2
101.7
96.1
(goad)**
2000
218.3
151.7
129.4
118.3
107.2
4000
351.6
218.3
173.9
151.7
129.4
* Assumes a dry weather contribution of 85 gpcd
** gallons per acre per day
TABLE 4. PER CAPITA VALUES RELATIVE TO
THE DENSITY OF 45 PERSONS/ACRE
Density
(person/acre)
15
30
45
60
90
Infiltration Rate (gpad)
500
39.09*
67.28
96.10
124.39
179.69
1000
50.14
78.20
107.20
135,59
190.60
2000
72.14
100.27
129.40
157.72
212.62
4000
116.20
144.2!)
173.90
202.25
256.25**
* minimum value
** maximum value
16
-------
shoals, or bars can significantly alter the hydraulic character-
istics and accordingly the degree of deposition, particularly '
for lateral pipes with little dry weather discharge. These
accumulations can easily result in new well-constructed sewer
systems with sound joints and few hydraulic obstructions such as
protruding house connections,etc. Similar deposits can occur in
systems that are rodded and frequently cleaned but either are old
and/or have poor joints and many hydraulic obstructions. Per-
forated manhole lids provide the perfect opportunity for child-
ren to jam sticks into manholes that can result in massive
blockages of accumulated rags and toilet paper. The above con-
ditions are but a few of the possible age and maintenance prob-
lems encountered in practice.
Three different categories of sewer system age and mainte-
nance were considered in this analysis. The first category of
clean pipe conditions represents good maintenance practices and
well-constructed sewer systems. No sediment beds were considered
in this case.
Two cases simulating different degrees of maintenance other
than perfect clean pipe conditions were also considered. In the
first case or the intermediate maintenance category, sediment
beds ranging from 1 to 3 inches in depth were assumed for all
pipes with slopes less than 0.0075. Figure 3 shows the assumed
ranges of beds between pipe slopes of 0.0005 and 0.0075. In the
third category, the aero maintenance care, the sediment beds
range from 3 to 6 inches for the same range of pipe slopes.
This range was. established using judgment and also based on
visual inspection of numerous combined sewer pipes in eastern
Massachusetts combined sewer systems.
These three conditions were used in the deposition model
analysis to compute daily collection system deposition loadings.
4.4. Data Preparation for the Regression Model
4.4.1 Deposition Model Results
4.4.1.1 Brief Description of the Deposition Model
The deposition model used in this study to generate estimates
of solids deposition in the sewerage systems selected in Section
4.3 is described in detail in Appendix B. The model considers
peak daily dry weather flow and uses a shear stress critera to
determine the.limiting diameter of the solid particles that
deposit at each segment. Then, with this limiting particle size
and assuming a given distribution for the particle sizes present
in the dry weather sanitary flow, the model determines the
percentage of the suspended solids that deposit at each pipe seg-
ment. The model also has mechanisms to account for the fact that
particles of diameters up to a given size that deposit in a given
pipe segment are not available for deposition in downstream seg-
ments . 3
17
-------
Case 2 - Intermediate Maintenance (A=3 inch, B= 1 inch)
Case 3 - Poor Maintenance <&-6 inch,, B= 3 inch)
B1
.0005 .0075
Collection System Pipe Slope
FIGURE 3. REPRESENTATION OF SEDIMENT BEDS AND PIPE SLOPE FOR TWO
AGE AND MAINTENANCE CONDITIONS
18
-------
Some of the results given by the model are: (1) the flow
conditions at each pipe segment, including discharge, average
velocity, water depth and shear stress; (2) the loads (Ib/day)
deposited at each pipe segment and (3) the accumulated value of
the loads deposited in all upstream segments. A verification
of the results given by the deposition model is presented in
Appendix C.
4.4.1.2 Input Data Required by the Deposition Model ,
The input data required by the deposition model consists
of:
Segment identification (by a segment number);
Segment upstream-and downstream pipe inverts;
Segment length;
- Pipe shape (10 shapes possible);
- Pipe sizes (diameter or height and width);
Segment type (zero, one or two tributary segments);
- Network location designation (defined by the segment type
in conjunction with the next downstream segment number);
Sediment depth in the segment;
- Population per 100 feet of pipe;
Average daily waste flow contribution in gpcd;
- Peak daily to average flow peaking'coefficients (see
page B-3);
- Manning's resistance coefficient, n, and its variability
with flow depth; and ',
Total solids contribution in Ib/capita/day.
4.4.1.3 Deposition Input Data Preparation
In Section 4.3, the description of the three different
sewerage systems considered in this study was presented. A total
of 75 subsystems were used in this analysis including 35 separate
collection systems from the WRNDB sewer system, 37 collection
systems from the Dorchester and South Boston combined sewer
systems; and 3 collection systems from the Fitchburg combined
sewer system .
All the necessary physical data in the form of computer
cards were available for the Dorchester and Fitchburg system
from previous studies. For the WRNDB system all the pipe eleva-
tions, lengths, shapes and sizes were also available from a pre-
vious study, but all the segment numbering and the additional
information required to establish the system configuration had
to be generated in this study.
Other information on waste flow rates and solid matter
contribution to the systems, necessary to run the model, were
given in section 4.3.
19
-------
4.4.1.4 Deposition Model Runs and Results
Three sets of runs were performed for all 75 basins. The
first set of runs were performed assuming no previous sediment
deposits present in the pipes, that is clean pipe conditions.
The second set of runs were performed in which sediment depths
ranging from 1 to 3 inches were assumed to represent moderate
maintenance conditions. The third set of runs were performed
assuming sediment depths from 3 to 6 inches intended to simulate
poor maintenance.
Selected information from these runs were punched, out on
cards for use in future phases of the study. The values of the
loads (Ib/day) deposited by pipe segment were used to define for
each basin the accumulated percentages of the total load versus
the accumulated percentages of total pipe lengths where deposition
occurs. An overall curve for all 75 basins was also prepared.
These curves were useful in deriving several variables used in
the regression analysis. The total loads per basin were used as
the observed values ofthe dependent variable in the regression
analysis.
4.4.2 Areas and Total Pipe Lengths
The total service area and total pipe lengths were known
from prior studies for all 75 basins. These values were necessary
for the regression analysis described in Section 4.5, and are
presented in Table 5. The first 35 basins cover portions of the
WRNDB sewerage system. Basins 36 through 72 cover the* Dorchester
and South Boston sewerage system while the last three basins
cover portions of the City of Fitchburg sewerage system. The
data on Table 5 was also used for a simple regression of total
pipe length on total area and is described in Section 5.2.2.
This regression may be useful in extreme cases where the total
pipe length is not known or cannot be immediately determined.
4.4.3 Distribution of Pipe Slopes
The regression model proposed in Section 4.2.1 included
several collection system pipe slope parameters, SPD and SpD/4,
that required computation of the cumulative pipe slope distri-
butions. A computer program was prepared to compute these
distributions from data on the pipe segments upstream and down-
stream invert elevations and segment lengths. The program com- ,
puted the slope distribution weighing the segment slopes by their
lengths. The mean, standard deviation, coefficient of variation,
coefficient of skewness and coefficient of kurtosis of pipe
slopes per collection system were also computed. The program
computed the distribution and the aforementioned statistics for
each system (WRNDB, Dorchester and Fitchburg) and finally an
20
-------
TABLE 5. - TOTAL, PIPE LENGTHS AND AREAS OF THE BASINS
6AS1N NO
PIPE LENGTH
.
96.
100.
45.
ITS.
4'.
3'.
29.
19.
17.
26.
16.
25.
25.
57.
44.
24.
4'.
245.
5.
36.
7.7.
51.
28.
15.
34.
91.
9.
120.
65.
728.
78.
26.
54.
177.
47.
30.
57.
24.
233.
315.
360.
264.
78.
143.
21
-------
overall distribution and the first four moments of all data
lumped into one data set.
Plots of the slope distributions for a few basins are
shown in Figures 4 and 5. The concave shapes of those cumula-
tive distributions (CDF) without a point of inflexion, suggest
an exponential distribution for the pipe slopes. Several of
the cumulative distributions were plotted on normal, log normal
and Gumbel's probability paper. All plotted curves resulted in
very non-linear shapes, indicating that the pipe slopes do not
follow any of those distributions. Plots of the complementary
CDF of the pipe slopes on semi-logarithmic paper, nontheless,
resulted in remarkably linear shapes shown in the illustrative
cases in Figures 6 through 10. Although no formal numerical
test of goodness-6f-fit was performed, this fact indicates that,
at least for the sample data used in this study, the distribution
of the pipe slopes is exponential.
The solid lines drawn on Figures 6 through 10 were plotted
using the expression of the exponential cumulative distribution
function given by:
FS = 1 - e
-s/S
(1)
where FS = P (s <= S) (cumulative pipe slope distribution) ;
s = any given slope;
S = the mean slope computed for the basin, as indicated
above; and
e = the base of the natural logarithms.
Figure 11 presents the histograms for the WRNDB, Dorchester
and Fitchburg sewerage systems and the overall histograms con-
sidering all data. The slope values corresponding to the inter-
vals in Figure 11 are given in Table 6.
Two observations can be noted from these histograms:
a) the shapes of the histograms for all 13 systems are
similar with minor differences between them (the same
is true for the global histogram compared to any of the
other three); and
b) they all indicate an exponentially decaying shape,
characteristics of the exponential distribution with the
CDF given by equation CD
22
-------
23
-------
24
-------
1.0-
.9-
a-
7-
.6-
.5-
Basin 29 - WRNDB
.2-
in
f
tn
0
o.
u-i
o
.1-
.09-
.07-
.06-
.05-
J04-
O3-
.02-
0.0
FIGURE
0*505 .06)104 J077I87 5
Collection System Pipe Slope, s
COMPIEMENTARY DISTRIBUTION OF PIPE SLOPES: GS = 1-FS
25
-------
1.0-
.9-
.8-
.7-
JB-
m
CM
III
I
g, -09
ft -
g X)7
C6
JOZ
Basin 49 - Dorchester
3b~
09
.012943 .028996 JM5O5 .061104 .077157
Collection System Pipe Slope, s
FIGURE 7 . COMPIEMENTARY DISTRIBUTION OF PIPE SLOPES: Gs = 1-FS
26
-------
1.0-
.9
a
7-
.6
Basin 61 - Dorchester
u
f
II
10
tt)
8-
fl)
81
0.
O
01
10
4J
.1-
.09'
.08-
.07-
.06-
.05
.04
.03-
.02-
.OH
OJO JOI294 .OZ8996 .045O5 .06IIO4 .077157
Collection System Pipe Slope, s
FIGURE 8 COMPIEMENTARY DISTRIBUTION OF PIPE SLOPES: G
.09
27
-------
I.O"
.»
.8-
.7-
£
(I)
f
u
u
I
r-l
U)
8
s
.p
c
3-
,2-
x»
.02-
Basin 71 - Dorchester
JOHi r-
JCMZS43
B28996 .04505 .061104 .077157
Collection System Pipe Slope, s
.09
FIGURE 9. COMPLEMENTARY DISTRIBUTION OF PIPE SLOPES: GS = 1-FE
28
-------
1.0-
.9-
.8-
.7-
.6-
.5-
01
Cu
I
in
u
m
a.
0
4J
C,
(U
.2-
.09-
.08-
.07-
.06-
.05-
.04-
.03-
.OE-
.oi-1-
Basin 73 - Pitchburg
OJO .001384 .00299 .045O5 J06II04 J077I57 OO
Collection System Pipe Slope, s
FIGURE 10. COMPLEMENTARY DISTRIBUTION OF PIPE SLOPES: Gs = 1-FS
29
-------
CO
w
CO
w
ft
H
PM
- 8
CO
H
EH
O
W
O
CO
EH
CO
H
fa
H
30
-------
TABLE 6. SLOPES CORRESPONDING TO THE INTERVALS
SHOWN ON FIGURE 11
Interval
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
Slope Limit
of Range
0,000100
0,003311
0.006521
0.009732
0.012943
0.016154
0.019364
0.022575
0.025786
0.028996
0.032207
0.035418
0.038629
0.041839
0.045050
0.048261
0,051471
0.054682
0.057893
0,061104
0.064314
0.067525
0,070736
0.073946
0,077157
0.080368
0.083578
0.086789
0.090000
> 0.090000
31
-------
A final justification for the assumption that the pipe
slopes are exponentially distributed is the following. The
mean and standard deviation of the coefficients of variation of
the slope for all 75 basins are 0.87 and 0.25, respectively.
The mean value of 0.87 for the coefficients of variation very
closely approximates the theoretical value of 1.0, character-
istic of the exponential distribution.
This finding has significant importance in the practical
application of the regression model developed in this study.
This is especially true for cases where detailed statistical
analysis of pipe slopes information is not available and only
the mean value of the pipe slope is required to completely
define with reasonable accuracy the pipe slope distribution.
The special slope parameters SPD and Spo/4 can then be
estimated through this pipe approximation. Definition of the
pipe slopes distribution using the exponential model is also
important in delineating the extent and geographic location of
the deposition loads in the system. This topic will be further
discussed in Section 5.3.2*.
4.4.4 Average Pipe Diameter
The average pipe diameter of all segments within each
collection system was computed by weighing circular diameters of
each segments by its corresponding lenghts. An equivalent
circular pipe diameter was first determined for non-circular
sections before the weighted average was computed. The fraction
of non-circular pipes was a small percentage of the total pipe
length. All pipes are circular in the WRNDB system. The num-
ber of non-circular pipes represent about 5% of the total for
the Dorchester system, whereas in Fitchburg they represent less
than 1% of the total pipe lengths.
The formulas used for the equivalent circular diameter for
the non-linear sections are presented in Table 7 and have been
derived to yield roughly the same hydraulic radius at low depths
of flow. For rectangular and U-shaped pipes a simple equiva-
lence of total areas are indicated in Table 7. These forms are
non-existent in the data for this study. The average pipe
diameters determined for all 75 basins are presented in Table 8.
It should be stressed here that in the generation of the slope
data for the regression analysis described in Section 4,5 the
assumption that the pipe slopes are exponentially distributed
was not used. The probability distributions of slopes for all
basins were determined from their respective slope data.
32
-------
TABLE 7. FORMULAS FOR EQUIVALENT CIRCULAR DIAMETERS
USED IN COMPUTING THE BASIN AVERAGE DIAMETER
Pipe
Shape
Dimensions
Equivalent
Circular D
Circular
Rectangular
Ellipse
Egg
Horseshoe
Oval
Ovoid
Modified Circle
Arch
U
D
X.,Y
X,Y
X,Y
X,Y
X,Y
X,Y
X,Y
X,Y
X,Y
(1.273 X Y)
(X Y)1/2
1/2
5.51X5-38AX+Y:)4'39
(X+Y) /2.0
0.67 X
5. SIX5'38/ (X+Y,)4-39
(X Y)
1/2
(1.273 X Y)
,1/2
33
-------
TABLE 8.-SUMMARY DATA ON DERIVED LENGTHS, SLOPES AND PIPE DIAMETERS
BASIN NO. 80t DEPOS.
LENOTH(PT|
1 15050.
2 2080.
> 434.
4 450.
5 1502.
6 180.
7 741.
P 1019.
5.
If 715.
17 74879.
1C 19B3.
19 5938.
?0 B*.
71 171.
77 648.
?3 1839.
'4 9228.
25 4517.
>* 1370.
'7 5914.
?b 48O.
».* 929.
3H 6005.
31 576.
32 7967.
>» 6903.
34 3956.
35 10954.
^fc 2591.
>7 1461.
33 936.
3<~ 1100.
4" 1913.
41 1445.
4' 7P6.
4" 7540.
44 1695.
45 4Rt9.
46 5279.
47 2893.
4fl 7647.
40 5293.
51 571.
51 1040.
5? 7795.
5-» 1545,
54 2530.
55 929.
56 1972.
57 1461.
5P 1373.
50 4847.
60 2613.
61 4934.
62 6016.
63 642.
64 3408.
6« 1815.
66 3434.
67 2726.
6A 6498.
69 2106.
70 13312.
71 26905.
72 18773.
73 13588.
74 1306.
75
:HAGP
I(IN)
)
10.5
10.0
10. o
10. 0
10.7
10. 0
10.8
10.0
10.0
10.0
10.0
10.0
10.9
10.8
in.o
10. 0
12.1
9.5
R.6
o.n
8.0
8.0
n.o
a. 6
1.7
11.1
11.0
12.0
10.2
12.7
10.8
a. 7
10.0
11.6
12.6
17.3
10.3
11. T
17.0
12-3
9.3
12.0
12.7
12.0
12.0
14.1
19.9
12.4
12.2
11. 7
11.4
11. B
14.6
13.9
10.6
11.2
14.1
13.1
14.3
12.7
12.7
12.6
12.1
12.5
12.9
13.1
14.3
12.7
12.0
15.6
13.3
12.4
12.4
10.7
13.6
AVERAGE
SLOOP S
0.027901
0.036746
0.046065
0.009118
0.021963
0.008611
0.016157
0.015280
0.006409
0.017163
0.012293
0.013985
0.013979
0.019666
0.030103
0.004528
0.014539
0.009127
0.017344
0.017852
0.026175
0.019257
0.021631
0.027730
0.019560
0.016939
0.016298
0.00*485
0.025510
0.013617
O. 016448
0.016991
0.015655
0.017855
0.01820'
0.014155
0.034669
0.005660
0.030361
0.005365
0.027941
0.037994
0.002575
0.029394
0.006341
0.024465
0.011737
0.025934
0.022566
0.038857
0.035336
0.012463
0.015749
0.011539
0.005995
0.041951
0.015366
0.010369
0.017349
0.024400
0.025037
0.055506
0.022864
0.077835
0.029568
0.034241
0.079921
0.011681
0.018102
0.019405
0.015667
0.026287
0.002375
0.033799
0.029285
SLOPF
SPO
0.009965
0.027575
0.058940
0.008010
0.017470
0.009732
0.005849
0.014440
0.006118
0.019364
0.004222
0.009737
0.005996
0.007681
0.021642
0.005510
0.006521
0.005119
0.005765
0.017050
0.037207
0.014923
0.012943
0.009732
0.004989
0. 00973?
0.009732
0.005012
0.003311
0.005064
0.006521
0.006344
0.006870
0.008449
0.006143
0.002892
0.004*63
0.005396
0.011499
0.004528
0.025786
0.013749
O.OO2547
0.019364
0.004945
0.007763
0.003065
0.016154
0.001077
0.047799
0.007467
0.011354
0.002514
0.007625
0.005086
0.012943
0.002852
0.004675
0.009732
0.006521
0.005449
0.002802
0.002143
0.009732
0.003311
0.012943
O.OOR435
0.008106
0.011068
0.006521
0.002787
0.008287
0.009732
0.006521
0.016154
SLOP"
SPD/4
0.003870
0,007320
0,024900
0,004290
0,, 006 230
0.1009030
0., 001900
0., 005050
0,, 002 2 00
0,, 004 5 60
0,003480
0.004290
0,, 002040
0.. 003660
0,, 01 0600
0.000089
0.001830
0.001230
0.003430
0,006270
0.010400
0.004780
0.004460
0.003660
0,, 001 8 50
0.003810
0,001840
0.002130
0.001060
0.001910
0.003280
0,004070
0.002180
0,002240
0.003460
0.000798
0,001100
0,003380
0.004090
0.001230
0,007380
0,004240
0.007100
0.004800
0.003330
0.004180
0.000841
0.006410
0.000344
0.002560
0.002350
0.007200
0.000704
0.004020
0.002170
0.000788
0.001370
0.001780
0.003930
0.003930
0.002820
0.000776
0.000611
0.003800
0.001180
0.004610
0.001790
0.003280
0.004420
0.003020
0.000772
0.000310
0.004270
0.004020
0.005560
34
-------
4.4.5 Distribution of Solids Deposited by Pipe Length
The cumulative distribution of solids deposited in the col-
lection system versus the cumulative length of sewer pipe where
the deposition occurs is the only exogenous information that
the user will have to accept in applying this methodology. In
other words, this distribution is the only information that
cannot be derived from local data and can only be modified in a
minor way by input from local conditions. These modifications
will be covered later.
Some simplifications had to be made in deriving these dis- '
tributions especially considering the great number of pipe seg-
ments (around 6000) that were numerically considered. The pro-
cedure established for each basin, as a function of the maximum
and minimuiti estimated loads, a series of 200 intervals where
loads of approximately equal values were accumulated, together
with their corresponding pipe lengths. Whenever the basin had
less then 200 pipe segments the number of intervals would be
made equal to the number of pipe segments of the basin. The
cumulative values of loads versus lengths were then computed
for each of these intervals.
Plots of several cumulative probability functions for a few
basins are presented in Figures 12 and 13. An overall curve
computed from all 75 basins is also presented.in Figure 13.
A total of 5000 intervals were used, in computing the overall
curve, yielding a smooth curve as can be seen from Figure 13.
Plots in semi-log paper of the complementary values of the load
probabilities, (l.-Fioad) (in the log axis) versus the cumula-
tive probability of pipe lengths, resulted in nearly straight
lines, indicating that this distribution is also exponential.
It was observed by associating the curves in Figures 12 and
13 with their respective mean slopes that the average basin slope
increases moving, from the lower to the upper curves. This ex-
plains comparatively higher percentages of loads depositing in
lower percentages of pipe lengths. Based on this observation,
Figure 14 was prepared. In its preparation a smooth curve was
drawn at approximately the middle of the range of curves from
Figures 12 and 13 with mean slopes corresponding approximately to
the range limits in the legend of Figure 14. With the mean pipe
slope known for a given basin, Figure 14 can be used to estimate
the percentages of pipe lengths corresponding to given percent-
ages of total solids deposited. Further discussion on the
applications of Figure 14 will presented in Section 5.3.3.
35
-------
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EH
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P
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fcl
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38
-------
The choice of the pipe length corresponding to 80% of the
loads deposited as an independent variable in the regression
analysis discussed in section 4.2.1, resulted solely from the
observation of higher separation of the curves around the value
of 80%. Other percentages of mass deposited could have given the
same results. It should be noted that the loads estimated by the
regression equations presented in Section 4.5 correspond to
100% of the loads deposited. The length Lpo corresponding to 80%
of the loads is only one regressor devised to explain the varia-
tion in the total loads.
4.4.6 Pipe Lengths Corresponding to 80% of the Loads
Deposited - Lpp '
The cumulative distribution of loads deposited versus the
cumulative lengths of pipe for all basins were prepared. The
values of LPD to be used in the regression,analysis were determ-
ined in the following manner. The computer printouts of the
distributions were scanned for the percentages of pipe length
(PLD) corresponding to 80% of the total loads deposited and
either read directly or more often they were interpolated. Those
percentages were then applied to the total pipe lengths in the
basins resulting in the LPD values for all basins presented in
Table 8.
4.4.7 Slope Corresponding to PLp(Spp)
The determination of SPD/ the slope corresponding to the
percentage of pipe (PLD) where 80% of- the total loads deposits
is illustrated in Figure 2. The value of PLD in the cumulative
distribution of pipe slopes for a given basin is established and
the corresponding slope value SPD is determined. This was per-
formed for all basins by reading directly or interpolating
values in the tables of the cumulative distributions of the
pipe slopes of these basins. ' The values of SPD for all the 75
basins considered are given in Table 8.
There is no theoretical justification for the choice of
as a regressor. As ..a matter of fact the average of the slopes
(SPD) below SPD had originally been thought -of as a better re-
gressor than SPD itself, and was the first to be included_in the
regression analysis. A high correlation between SPD and SPD was
observed and SPD was included in the regression since its re-
duction of the sum of squares was slightly better than SPD. The
variable SPD was dropped from further consideration since its
determination required far more effort than that for SPD.
4.4.8 Slope Corresponding to PLD/4 - (Spo/4)
The determination of Spo/4 is illustrated in Figure 2,
First of all, multiply by 1/4 the percentage , PLo/ corresponding
39
-------
to 80% of the loads deposited. Next enter that value in the
cumulative distribution of pipe slopes for a given basin and
determine the corresponding value, SPD/4. This step was done by
reading directly or interpolating values in the tables of the
cumulative distributions of the pipe slopes for the basins. The
values of SpD/4 for all 75 basins are presented in Table 8.
The choice of Spo/4 as an independent variable in the .
analysis regression did not involve any theoretical consideration.
It's choice resulted from an
"a priori"
belief that representing
the lower ranges of the pipe slope distribution would be signi*
ficant in the regression analysis. It is shown in Section 4.5
that this assertion is true.
4.4.9 Summary of Results
Descriptions of how the data for the regression analysis was
generated was presented in Sections 4.4.1 through 4.4.8 and of
how the valuesof the dependent variable, TS, were generated by
the use of a deposition model. The independent variables of the
regression were described in Sections 4.4.2 through 4.4,8. The
only remaining independent variable not described in those
sections is the waste flow rate contribution in gpcd. This
variable, as described in Section 4.3 and mentioned again in
Section 4.3.2, was fixed at the values of 40., 110., 190., and
260. gpcd, covering, therefore, a wide range of flows.
To summarize, the values obtained for the independent
variables are given in Tables 6 and 8. The tabular values of L
and A are given in Table 6 and the values of LPD, D, S, and
Spo and Spo/4 determined for all 75 basins are given in Table 8.
The results from the deposition model are lengthy and are not
presented in this report.
4.5 Regression Analysis
4.5.1 Regression Procedures
The linear regression program used to empirically establish
the relationships of the total daily suspended solids (TS)
deposition within a sewerage collection system with the indepen-
dent variables described in previous sections, is one that operates
in a step forward manner. At each step in the analysis the parti-
cular variable entered into the regression equation accounts for
the greatest amount of variance between it and the dependent
variable, i.e., the variable with the highest partial correlation
with the dependent variable. The program is flexible to allow any
independent variable to be: (1) left free to enter the regression
equation by a criteria of the sum of squares reduction; (2) forced
into the regression equation; or (3) be kept definitely out of the
regression equation in one given selection. The procedure permits
examination of several alternative considerations of the indepen-
dent variables by optional selections of variables to be forced
40
-------
in and out of the regression equation or to be simply left free to
enter the equation using variance reduction criteria. The relative
importance of each variable in the regression equation can be
ascertained using this procedure.
4.5.2 Regression Results
In this analysis various predictive models are analyzed
relating total suspended solids deposition within a collection
system with the aforementioned independent variables under the
assumption of clean pipe conditions. These relationships are
therefore applicable for situations in which the sewer piping
system is properly maintained. The effects of age and improper
maintenance on collection deposition loadings were examined and
the results are presented in section 4.5.4. The degree of
increased daily deposition resulting from improperly maintained
systems was crudely simulated using several assumed depths of
bottom sediments.
In this analysis both linear additive and multiplicative
models were investigated. The untransformed observed values of
the dependent and independent variables were initially used,
leading to a strictly linear regression equation. In the second
case the observed values of both the dependent and independent
variables were transformed by taking their natural logarithms,
leading to a linear equation in the logarithmic domain which can
then be put into a non-linear multiplicative form.
The results of the regression analysis are presented in
Tables 9 through 12 noting only those selections considered more
significant. Tables 9 and 10 refer to the linear model regression
results and Tables 11 and 12 refer to the multiplicative model
logarithmic regression results. The sequence of independent
variable inclusions for several selections using the linear form
are given in Table 9. The symbols in the table are explained as
follows. The letters DP under the variable TS indicates that TS
is the dependent variable. The other letters under the indepen-
dent variables for any selection indicate:
AV - the variable, is available to enter the regression equa-
tion subject to the threshold variance reduction limit
fixed at 0.0001 for all selections and all runs, imply-
ing that a variable will enter the regresson if it can
further reduce the total sum of squares be at least
0,01%.
FI - the variable is to be forced in the regression although
it is also subject to the 0.0001 limit noted above. PI
implies priority over the AV variables in entering the
regression.
41
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FO - means that the variable is to be kept out of the
regression equation.
In selection number 1 shown in Table. 9 all variables were
free to enter the regression equation. The numbers above the
selection symbols, AV, FO, and FI indicate the order in which
the variables stepped into the equation. They reflect, there-
fore, the relative marginal importance of each variable present
in the final equation of a given selection. Variables available
to enter the regression shown without this ordering number are
the ones that did not meet the 0.0001 variance reduction require-
ment .
The first number below the AV, FO and FI symbols is the
multiple regression coefficient (.adjusted for the degrees of
freedom) achieved with the entrance in the regression of the
present variable. The square of that number is the R2 value at
that step. For example, referring to selection 1 in Table 9,
the first variable to enter the regression is the total pipe
length in the basin L. At the first step the regression co-
efficient, R, is 0.776 implying R2 = 0.602. When the second
variable, LPD, enters the regression the multiple regression co-
efficient improves to 0.892, explaining therefore 79.57% of the
total sum of squares (R2 = 0.7957). The successive reductions
in the total sum of squares and the marginal contribution of each
addition variable can be assessed by following through the order
of the variables entering the regression. The second number be-
low the AV, FI and FO symbols represent the standard error of
the estimate, adjusted for the degrees of freedom. The square of
that number is the variance of the estimate. The reduction in
the uncertainty of the estimate can be noted by following that
number throughout the sequence of variables introduced to the
regression. An increase of the standard error at a given step
indicates that the additional information realized by introducing
the variable is off-set by the loss in degrees of freedom, imply-
ing that the regression equation is better off without that
particular variable.
Other selections shown in Table 9 were designed to: (1)
compare regression equations based on primary variables only, such
as total length of pipe, L, total area, A,average pipe slope , S,
etc. and equations containing more refined variables , derived from
primary data, such as LPD, SPD, SPD/4; or (2) to assess the impor-
tance of a .given variable or variables given that others were
forced into the regression. Although several selections may have;
the same final equation, the order in which the variables entered
the regression is useful to assess the importance of the indivi-
dual variables. The last column in Table 9 indicates the maximum
multiple correlation coefficient for a given selection. The
linear regression is very good for all selections, with correla-
tion coefficients ranging from 0.814 to 0.906 (R2 from 0.663 to
47
-------
0.821, respectively). The coefficients of the variables selected
in Table 9 which entered the regression equation are given in
Table 10. For each of the selections shown on Table 9 these co-
efficients define the corresponding regression equations using
the general equation presented at the bottom of Table 10. A
blank in Table 10 indicates that the corresponding variable does
not belong to the regression equation of the given selection.
Similar results for the logarithmic regression are contained
within Tables 11 and 12. The last column in Table 11 shows ex-
cellent results for the logarithmic regression in all selections,
with a minimum multiple regression coefficient of 0,923 and a
maximum of 0.974. This implies values of R2 ranging from 0.852
to 0.949. The multiplicative model is superior to the linear
forms explaining roughly 95 percent of the total variability of
the dependent variable.
4.5.3 Alternative Model Selections
In this section several of the regression models described
in Section 4.5.2 with all the relevant information presented in
Tables 9 through 12 will be recommended for user application.
Alternative forms reflecting the availability of data and/or
user resources will be presented. The simplest forms require
little data and have the least predictive reliability whereas the
more complicated models, requiring greater user resources and
data availability, provide estimates with extremely high relia-
bility.
Comparison of the multiple correlation coefficients for the
linear and the logarithmic regressions in Tables 9 and 11,
respectively, indicates that the logarithmic multiplicative models
are superior. Therefore, all the models selected below will
derive from the logarithmic regression results.
4.5.3.1 The Elaborate Model
The highest multiple correlation coefficient, 0,974 (R2 =
0.949) was obtained in selection 1 in Table 11. Inspection of
that table indicates that this maximum correlation value had al-
ready been attained at the fourth regression step (under SpD/4) «
The addition of a fifth variable, A, in the regression does not
improve the multiple correlation coefficient nor the standard
error of the estimate. Beyond the fifth variable the standard
error increases. Therefore, .only the first four variables should
be retained in the regression equation yielding;
0.0038 L
°-8142
SPD/4-0'1078 q"0'5098
-------
where TS is deposited solids loading in Ibs/day, L is total length
of sewer_system in feet, SPD and SPD/4 are slope parameters
defined in Section 4.4 and q is the per capita waste rate in gpcd.
The above coefficients are slightly different from those shown
on Table 12, which are for the full equation, that is, for all
seven variables entered into the equation.
Utilization of equation (2) requires knowledge of total
pipe length, the per capita contribution and the two pipe slope
parameters, Spo and Spc/4. These slope parameters in turn are
a function of the percentage of pipe where 80% of the total mass
(TS) deposits (?LD) and the probability distribution of the pipe
slopes. The value PLD is assumed given for the regression
analysis, derived from the"extensive computer analyses performed
during this study and reported in Section 4.4.5. The probabil-
ity distribution of the pipe slopes can either be derived from
histograms computed from local pipe slope data or it can be
defined with reasonable approximation from the mean pipe slope
(S) only, as described in Section 5.2.5.2. If the pipe slopes
are not available a regression of mean ground slope and mean
pipe slope, as also described in Section 5.2.3.2, could be
performed.
4.5.3.2 An Intermediate Model
A simpler model than that given by equation (2), including
only the primary variables, can be derived from selection 2 in
Table 11 and is given by:
TS = 0.001303 L1'18 A"0'178 (sT0'418 (D)0'604 q0'51 (R2=.852) (_3)
where S is average pipe slope, and D is the average equivalent
diameter in inches; and A is service area (acres).
In this case the coefficients above are the same as shown in
Table 12, since all variables that entered the regression were
retained. All five independent variables present in equation (3)
can be defined with good precision in any practical application.
Neither the distribution of deposited loads versus pipe length
nor the probability distribution of the pipe slopes are required.
The mean pipe slope S, again, can be correlated to the mean
ground slope as described in Section 5.2.3.2, if no information on
pipe slopes is available. A fitted equation for L as a function of
A was derived from the data used in this study and is presented in
Section 5.2.2
If the mean pipe diameter, 5, is eliminated from this
regression the loss in precision of the estimate is not significant,
resulting in the expression:
TS = 0.00389 L1'2195 A"0'1866' (S)'0-4343 q"0-51 (R2=0.848) (3)
49
-------
4.5.3.3 The Simplest Model
The highest R2 value that can be obtained with the least
number of independent variables is also derived from selection 2
in Table 11. That is given by the regression equation:
TS = 0.0076 L1'063 (S)-°-4375 q-°-51 (R2=0.845)
4.5.3.4 Final Comments on the Selection of the Model
(5)
The selection of the regression equations was meant to
summarize the 16 possibilities presented in Tables 9 through 12.
Other choices can be made from other selections presented, that
may be more compatible with particular applications, although at
lower values of R2. It should be noted that the coefficients
presented in Tables 10 and 12 apply only to the complete regres-
sion equations, and if one variable is deleted from the equation
those coefficients do not remain the same.
The user should note that the parameters of the regression
equation estimated by the least squares procedure are a function
of the data used in their estimation. These parameters are not
known with certainty and represent only estimates of the true
parameters of the model. The estimation of the parameter is
improved as the number of data points increase and as the spread
or variance of the independent variables also increases.
It is known from regression theory that the procedure pro-
vides the best estimates (least variance) around the means of the
independent variables used in computing the parameters of the
regression equation. As the values of the independent variables
depart from the mean the uncertainty of the estimation given by
the equation increases and can become large outside the range of
values used as data in the regression. in other words, the un-
certainty of the estimate given by the regression equation may be
large when the model is used for conditions requiring extrapola-
tion beyond the range of data used to develop the model,
The values of the independent variables used in the regres-
sion analysis for all 75 basins were presented in Tables 6 and
8. The range, mean and standard deviations of the independent
variables were computed from the data given in Tables 6 and 8 and
are presented in Table 13. A total of 300 observations were
used in the regression analysis since the deposition loadings for
each of the 75 basins were computed for four per capita waste
generation rates.
4.5.4 Effects of Age and Maintenance
The regression equations presented in Section 4.5,3 were
derived from deposition data computed under the assumption of
50
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clean pipes, with no bottom sediments. In this section the
impact of poorly maintained systems was crudely simulated by
arbitrarily assuming various levels of prior sediment accumula-
tion in the pipes. These sediment levels would change the
bottom cross-sectional shape of the pipe channel and hence the
depth of flow, the hydraulic radius and the shear stress
characteristics.
Two cases simulating different degrees of maintenance other
than perfect clean pipe conditions were considered. In the
first case, or the intermediate maintenance category, sediment
beds ranging from 1 to 3 inches in depth were assumed for all
pipes with slopes less than 0.0075. A sediment bed of 3 inches
was assumed for all pipes with slopes less than 0.0005. The
bed depths then ranged linearly starting at 3 inches for a pipe
slope of 0.0005 up to one inch for a pipe slope of 0,0075. This
range was established using judgment and also based on visual
inspection of numerous combined sewer laterals in eastern
Massachusetts sewerage systems. In the second category of
maintenance, the zero maintenance case, sediment beds ranging
from 3 to 6 inches for the same range of slopes was considered.
Considering the two age and maintenance criteria mentioned
here, the deposition model was used to estimate total deposition
loadings for each of the 75 sewer systems for each of the four
per capita waste generation rates of 40, 110, 190 and 260 gpcd.
Before similar regression computations were performed on the
deposition results obtained for pipes with bottom deposits, a
comparison was made of the total deposited loads computed under
the assumptions of clean and sedimented pipes.
For each basin the ratios of TS computed for sedimented pipes
with sediment beds of 1-3 inches and 3-6 inches and the TS values
for clean pipes were calculated for all four per capita waste
rates considered, i.e., 40, 110, 190 and 260 gpcd. The resulting
ratios were very stable for a given per capita waste rate for
both cases of sediment deposits. The mean and coefficient of
variation of these ratios are presented in Table 14 for both con-
ditions of bottom deposits.
The results shown on Table 14 suggest that the prediction
of TS in sedimented pipes could be accomplished by a simple
functional multiplicative correction of the results given by any
of the regression equations for clean pipes. An equation was
fitted using the data of Table 14 for each of the bed deposit
conditions.
These equations are:
- For a system with deposits ranging from 1 to. 3 inches;
TSi-3 inches = 1-68 g'0'076 TS (clean) (R2=0.988) (_6)
52
-------
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where g = flow per capita, and TS(clean) = load of total
solids computed from any of the regression equations presented in
Section 4.5.2
- For a system with deposits ranging from 3 to 6 inches:
TS3-6 arches = 1-79 q"°'°84 *B (clean) (R2=0.999) 07)
The R2 values indicated above refer to the regression of
the ratios of TS on the values of flow per capita .The small
difference found between the two conditions of bottom dJP°f^
may well be the result of an inappropriate accounting of these
factors by the deposition model. On the other hand it may smp-
Iv have resulted from the particular combination of pipe
diameters and sediment depths used as data, which may have led
to actually small differences in flow depths above the sediment
levels, and therefore small differences in shear stress between
the cases.
4.5.5 Predictions of Other Parameters
In Appendix A some of the results from the first phase of
the sewer flushing experiments are presented. In Table A~l of
the appendix the results of 83 flushing experiments performed
at 4 different sites in the Boston area are presented indicating
the mass removals per flush of various pollutants including BOD,
COD, TKN, NH3, P, TS and VSS. The values represent estimates of
the various pollutant masses removed by flushing as well as the
total mass of depositing pollutants. Those results can serve as
a basis for the estimation of other parameters associated with
the total solids that deposit in the system.
A regression was performed between TS and each one of the
other 6 indicators presented in Table A-l. The resulting
regression equations are presented in Table 15, with their
associated correlation coefficients.
Estimates of the total daily BOD, COD, TKN, NH3, P and VSS
depositing loads within a given collection system can be made
using the regression equations in Table 15 with the predicted TS
loadings calculated from any of the regression equations pre-
sented for clean pipe conditions in Section 4.5.3 and the bias
correction factors for pipes with sediment beds given in
Section 4.5.4.
54
-------
TABLE 15. REGRESSION OF DIFFERENT POLLUTANTS ON TS
Regression Equation*
Correlation Coefficient
BOD = 0.344TS
1.308
COD = 0.875TS
1.04
TKN = 0.0.39TS1*135
NH3 =-0.0336 + .017TS
P =-0.006 + .00768TS
VSS = 0.689TS1'033
* Units are Ib/day
0.80
0.77
0.67
0.44
0.67
0.97
55
-------
SECTION 5
MODEL UTILIZATION
5.1 Introduction
This section summarizes the steps required by the user to
achieve the objectives set forth in Section 4.1.1, which are to
define on a preliminary basis: a) the total amounts of solids
and other pollutants that deposit in the sewerage system; and
b) the extent of the collection system over which the deposition
takes place.
The nature of the available data and/or the degree of
resources the user can commit will define different work pro-
grams which in turn will lead to different levels of confidence
in the results. In order to avoid references to past sections,
all necessary formulas will be summarized in Sections 5.2.1 to
5.2.6.
5.2 Summary of Formulas for the Estimation of TS
This section summarizes all necessary formulas for the
estimation of TS, separating formulas already presented in
Section 4 and introducing a few new formulas. Only variable
symbols introduced here will be defined in the following sections,
5.2.1 Formulas for Estimation of Total Loads Deposited - TS*
5.2.1.1 The Elaborate Model
The elaborate model derived in Section 4 * 5.3.1 for clean
pipe conditions is given by:
0.0038
(*=0.949)
(.8)
* These equations are for predicting deposited solids for clean
pipe conditions. The user is referred to Sections 4.5.3 and
4.5.4 for age and maintenance considerations and for the pre-
diction of other pollutants.
56
-------
5.2.1.2 Intermediate Model
The intermediate models in Sections 4.5.3.2 for clean pipe
conditions are given by:
TS=0. 001303
~°~178 0*
(R=0.852)
TS=0.00389 L1'2195 A'0'1866 (sT0'4343 g ~0-51 (R2=0.848)
(9)
(10)
The difference between the_two models is that the second neglects
the average pipe diameter D, with a small loss in precision.
5.2.1.3 The Simplest Model
The simplest model defined in Section 4.5.3.3.for clean pipe
conditions is given by:
TS=0.0076 Ll-063(§)-0.4375 g-0.51 (R2=Q>845) (n)
5.2.2 Estimation of Total Pipe Length
The total pipe length of the system, L, and its correspond-
ing collection area, A, are generally assumed to be known. In
cases where this information is not known and where crude
estimates will'.suffice, the total pipe length can be estimated
from the total basin area using the expressions:
0 Q 98 9
L = 168.95 A * (Rz= 0.821)-low population density (10-20
people/acre)
L = 239.41
fl
"-
(R = 0 . 821) -moderate-high population density
(30-60 people/acre)
These expressions were derived from the data for the 75 basins
used in this study, yielding a correlation coefficient of 0.906.
Since detailed population density estimates for each collection
system in the data set were not available, the following approach
was used to account for the effect of population density on
length of sewer. The data for the 75 basins were separated into
two distinct data sets representing low population densities
(the 35 basins from the West Roxbury-Newton-Dedham-Brookline
sewerage system) and moderate to high population densities (the
latter 40 basins from the Dorchester and Fitchburg sewerage
systems). A dummy variable approach was used in the regression
analysis to obtain the two expressions given in equation (12) . A
more explicit treatment of population density would be possible
if detailed population density estimates per collection system
were available.
57
-------
5.2.3 Estimation of Mean Pipe Slope S
5.2.3.1 Pipe Slope Data is Available
In this case:
n
Sili
S =
sir
(13)
where: S = slope of segment i
1 = length of segment i
n = total number of pipe segments
5.2.3.2 Pipe Slope Data Not Available
If data on pipe slope is not available the user will determ-
ine a mean value for the ground slope using any procedure, such
as the techniques of uniform grid sampling or random sampling.
With the mean ground slope value, determine the mean pipe slope
by:
S - 0.348 (&G)°-818(R2=0.96) (14)
where: SG = mean ground slope (ft/ft)
The expression above resulted from a regression of mean ground
versus mean pipe slope for all 75 basins of this study. The
resulting correlation coefficient was 0.98.
This relation was derived in the following manner. Topo-
graphic mylar overlays with ground contour at ten feet intervals
were developed for the WENDB and the Fitchburg sewer system service
areas. Similar maps existed for the Dorchester and South Boston
sewer systems. Using the topographic maps the collection system
areas were subdivided into smaller fractions considered to have
uniform slopes. The ground slopes were computed for each of the
subareas. Those ground slopes were then associated with the per-
centages of the ;collection system area they covered. The basin
average ground slope was then computed by weighing the individual
slopes by their associate subarea percentages. Ground slopes in
the smaller basins were determined by using one or two subareas
whereas the ground slopes in the large basins were determined
using 10 to 21 subareas.
5.2.4 Distribution of Total Solids Deposited by Pipe Segment -
Determination of PLp
The distribution of total solids deposited by pipe length is
presented in Figure 14. The user can determine PLD corresponding
58
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to 80% of the solids deposited by entering the graph with "% of
mean deposited" equal to 80% and, from the curve that best
appropriate the average pipe slope S, read in the horizontal axis,
"% pipe length", the value of PLj^. This value will be required
to determine SPD and SpD/4 in Section 5.2.5.2
5.2.5 Determination of Slopes SPD and SpD/4
5.2.5.1 Pipe Slope Data is Available
The collection system pipe slopes can be directly used to
define the cumulative pipe slope distribution. In this study
the pipe lengths (as integer values) associated with the observed
slopes were taken as their frequencies. The user should adopt
the same approach for compatability with the equations for TS
derived in this study. Simplified methods may also be used, with
less accurate results. If, for example, the slopes are not
weighted by,their lengths, this is equivalent to assuming that
all pipe segments have the same length, which in some cases may
be a reasonable assumption.
5.2.5.2 Pipe Slope Information Not Available
The average slope S can be computed using either equation
(13) or equation (14) to define the pipe slope cumulative
density function (CDF) as follows:
FS = 1-e
-s/S
(.15)
If the probability FS is known, with a fixed S the corresponding
slopes can be computed, and vice-versa. For the basins used in
this study, equation (15) was verified with excellent results.
To determine the slope SPD/ use the value of PLo determined
in Section 5.2.4, and make:
FS=l-e~s/§=PLD
and determine s.
Then:
SPD=S
To determine the slope Spo/4/ make:
s/S
Fs=l=e ' =1/4PLD and determine s. Then:
SPD/4=s.
5.2.6 Formula for the Average Pipe Diameter
If the system contains non-circular shapes, first compute
their equivalent circular diameters using the equations for
59
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equivalent pipe diameters presented in Table 7, Then, compute
the average diameter by:
n
Dl
D =
Eli
(16)
where: Di = diameter of segment i
li = length of segment i
n = total number of pipe segments.
5.3 General Description of User's Steps
5.3.1 Determination of the Total Solids Deposited
The generalized procedure for obtaining total solids
deposited estimates is presented in Figure 15 and should be
referred to in the ensuing discussion.
The first question to be answered at the onset is whether
pipe slope data are available. If the answer is positive the
user should use equation (13) to determine the average pipe slope
S; otherwise/ a mean ground slope should be determined as des<-
cribed in Section 5.2.3.2 and then equation (14) should be used
to determine S.
The next question that arises is whether the total pipe
length of the collection system is known. In the negative case
the total area of the collection system is assumed known and the
total pipe length is estimated by equation (12). The per
capita waste rate including infiltration is then established.
The selection of the equation for the estimation of the
solids deposited, TS, follows. If the simplest model is desired
the user has at this point all the elements required by equation
(11) to compute TS. If the intermediate model is chosen and the
pipe diameter information is available the mean pipe diameter is
computed by equation (16). All information is computed to
estimate TS from equation (9). If pipe diameters are not avail-
able then use equation (10). If the elaborate model is chosen,
the value of PLc must be determined using Figure 14 as described
in Section 5.2.4. The next variables to be determined are SPD
and SPD/4.
If no pipe slope information is available the user has no
alternative but to use the exponential approximation for the
pipe slope cumulative distribution. If the pipe data are
available but the user considers the exponential approximation _
satisfactory he may use equation (15), associated with PLo and S
60
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to determine SPD and SpD/4 as described in Section 5.2.5.2.
Finally, the user can define the pipe slope CDF from the pipe
slope data and derive from it, the values of Spo and SpD/4 as
described in Section 5.2.5.2. Finally, the user can define the
pipe slope CDF from the pipe slope data and derive from it, the
values of SPD and Spo/4 corresponding"to the percentages PLD
and 1/4PLD, respectively. At this point, all the elements are
prepared to estimate TS from equation (8) which provides the most
reliable estimate of TS.
The resulting estimate of -TS is the total daily solids depo-
sition in the collection system of interest. If the user wishes
to modify this estimate for'pipes with existing sediment beds the
multiplicative equations in Section 4.5.4 should be used. If
estimates of other pollutants are desired, the deposited solids
results, TS, should then be used as predictors to compute other
pollutant estimates using the equations given in Section 4.5.5.
5.3.2 Application of Procedures
In this section an example problem illustrating the methodol-
ogies developed in this report is presented. The test case is
one of the collection systems in the Dorchester sewerage system.
Estimates of total daily solids deposition in this collection
system will be given for different assumptions of data availa-
bility using the simplified procedures. These estimates will also
be compared with the results computed for this system using the
much more detailed procedure described in Appendix B.
The test case used is basin number 70 of the Dorchester
combined sewer system. There are 190 manhole segments in this
collection system. The topography of this combined sewer collec-
tion system is fairly hilly. ' The -land use 'in the area is exclus-
ively high density multi-family dwellings with a population den-
sity of 30 people/acre. The areal extent and total collection
system pipe footgate is about one standard deviation above the
mean of all the systems used in the regression analysis. The
values of all the independent variables for basin 70 are given
in Tables 5 and 8.
5.3.2.1 Data Requirements
The total pipe length, L, for the basin is .35,033 feet and
the total service area, A, is 233 acres. The total pipe length
can also be computed using equation (12) for high population
density yielding 37,740 feet, representing an overestimation error
of 7.7 percent.
There are three possible ways to compute the values of the pipe
slope variables required as input for the various regression equa-
tions. The first method involves computing these parameters from
62
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the distribution derived from actual pipe slope data. The second
procedure requires knowledge of only the mean collection system
pipe slope, S, and assuming that the pipe slopes can be represented
by an exponential distribution. The third alternative approach
assumes that only ground slope information is available and that
the exponential distribution is applicable to represent collection
system pipe slopes.
The collection system pipe slope histogram representing the
distribution of 190 pipe segments in basin 70 of the Dorchester
sewerage system is given in Table 16. This table was prepared
using the invert elevations for each of the 190 segments. The pipe
slope histogram is divided into 30 intervals with the upper pipe
slope limit of each interval given. The elements under the column
labeled "frequency" are the actual pipe footages associated with
each pipe slope interval. The last two columns give the interval
probability computed using the pipe footage per interval relative
to total pipe footage and the cumulative probability. The mean
and standard deviation are also given in Table 16. The average
equivalent circular diameter, D, is 15.6 inches and was computed
using the formulas given in Table ?/ page 33 and equation (16) .
The average pipe slope, S, is 0.0194. The slope parameter
SPD can be estimated in the following manner. Three curves are
available in Figure 14, page 38, for relating the cumulative
distribution of solids deposited to cumulative distribution of
collection system pipe length. Curve 2 is applicable in this
case since the average pipe slope is 0.0194. The percentage of
pipe associated with 80 percent of the total daily load deposited
is 38%.* The value of the variable, SPD, can then be determined
by entering 0.38 in the last columun of Table 16 and interpolating
the corresponding value of slope in column two. The interpolated
value of SPD is 0.00629. The value of SPD/4 is obtained by enter-
ing the same table with 0.38/4 = 0.095, yielding Spo/4 = 0.00302.
In the second procedure the mean pipe slope can be used in-the
exponential cumulative distribution function given by equation (1),
page 22,to compute the values of SPD and SPD/4. The value of
SPD is 0.00928 results from using FS = 0.38, s = SPD and
S = 0.0194 in equation (1). The value of Spo/4 is 0.00194 results
from setting FS = 0.38/4 = .095 in equation (1).
* The distribution of loads by pipe length derived for basin 70
yields exactly 38% at 80% of the total load. The error involved
in using Figure 14 is zero in this example.
63
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The only information required for the third procedure is the
average ground slope, §G. The average ground slope for basin 70
was determined by graphical procedures to be 0.0359. An estimate
of the mean pipe slope, S, can be obtained using the mean ground
slope in equation (14). The estimated value of mean pipe slope,
S, using the mean ground slope, SG, is 0.02287 differing from the
actual^mean pipe slope by 17%. Values of SPD and SPD/4 can now
be estimated using the exponential relationship in equation (1),
yielding SPD = 0.00985 and Spo/4 = 0.00228.
5.3.2-2 Estimation of Loads
The detailed manhole to manhole dry weather deposition model
described in Appendix B was used to estimate total solids deposited
for the entire collection system network in basin number 70. The
estimated load is 169.11 Ibs/day using an average per capita waste
rate of 190 gpcd. This model requires detailed specification of
the hydraulic parameters for each segment in the system and the
use of a computer. Similar estimates will be computed from using
the simplified power functions generated in this study for the three
different estimates of the pipe slope variables.
The elaborate model given in equation (8) requires specifica-
tion of L, SPD, SPD/4 and the per capita flow rate, q. This
equation was solved for the three different estimates of SPD
and SPD/4 with q = 190 gpcd. The deposited load, TS, is 155.73
Ibs/day using the values of SPD and Spo/4 derived from the analysis
of detailed collection system pipe slope information. The
estimated load is 118.72 Ibs/day using values of SPD and Spo/4
computed from the mean pipe slope and the exponential cumulative
function. The estimated load is 111.11 Ibs/day using values of
SPD and SpD/4 for the third situation where the mean ground slope
is used to compute mean pipe slope for input into the exponential
function.
_ The intermediate model given by equation (10) requires that L,
A, S, and q be specified. Three variations are computed using
this formulation. The first estimate is_determined using the
measured pipe length, L and pipe slope, S, derived from data; the
second case uses the measured pipe length and an estimate of mean
pipe slope from ground slope estimate; and the third result is
computed using the estimated pipe slope, S, and an estimate of
pipe length derived from equation (12). These three estimates
are 186.89, 174.02 and 190.55 Ibs/day, respectively.
The simplest model given by equation (11) requires specifica-
tion of L, S and q. The estimated loads are 198.82 Ibs/day using
exact estimates of L and S, 195.02 Ibs/day using exact estimates
of pipe length and an estimate of pipe slope ground ground slope,
ami, 200.26 Ibs/day using estimated values of both pipe length
and mean pipe slope.
65
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A comparison of all computed loadings for the different pre-
dictive models under different assumptions of data availability is
given in Table 17- The percentage error relative to the estimate
provided by the procedure in Appendix B is also provided. These
results show that the estimated values given by all three regression
equations are reasonably close to the value derived from the
detailed model described in Appendix B. The elaborate model con-
sistently gave over estimates.
It is an invalid conclusion to infer from this comparison
that the simpler approach might be superior to the more elaborate
one. It should be noted that this comparative result is only for
one basin and that on the average, the elaborate model_will pro-
vide consistently superior results because the coefficient of
determination R2, is higher for the elaborate model. The under
estimates given by the elaborate model using approximations for
the pipe slopes are explained by the fact that, for this parti-
cular basin, the exponential approximation over estimated by
about 50% the slope, SPD- Nevertheless, one of the simpler models
would be more appropriate in cases where little data is available
requiring many assumptions and approximations. Moreover, the
utilization of the simpler models for planning "first-cut" purposes
may be more cost effective from the standpoint of collecting,
analyzing and preparing the required data inputs.
In sum the simplified procedures given by equations (8), (10)
and (11) provide estimates of daily solids deposition using exact
data for basin 70 with a relative error of 8 to 18 percent in
comparison to the estimate given by the complicated procedure des-
cribed in Appendix B. It is shown in Appendix C of this report
that the complicated procedure given in Appendix B was tentatively
calibrated using actual field flush information lending credulence
to the adoption of the simplified procedures generated in this
report.
66
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TABLE 17. COMPARISON OF ESTIMATED DAILY SOLIDS DEPOSITED FOR
BASIN 70 USING DIFFERENT PROCEDURES
Procedure
Solids
Deposited
(Ibs/day)
Percentage Error
Relative to Appendix
B Results
Deposition Model (Appen. B) 169.11
Elaborate Model (Eg. (8))
Exact Data 155.73
Exponential Data 118.72
SG and Exponential Approx. 111.11
Intermediate Model (Eg. (10))
Exact Data 186.89
Estimated Slope S 174.02
Estimated L and S 190.55
Simplest Model (Eg. (11))
Exact Data 178.82
Estimated S 185.03
Estimated L and S 200.26
-7.9%
-30.0%
-34.0%
+10.5%
+3.0%
+12.7%
+17.6%
+ 9.4%
+18.4%
67
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5.3. 3 Determination of Deposition Extent in Collection Systems
Estimates of total pipe footage for given percentages of the
total solids deposition can be made using Figure 14. These
estimates are computed irrespective of their actual location in
the collection system. The appropriate curve in Figure 14 can be
chosen. Using the average pipe slope S as a guide, several
values of "% pipe length" can be read directly from the figure
as a function of values of "% mass deposited".' Multiplication of
the total basin pipe length by those percentages yields estimates
of pipe footage corresponding to the various percentages of total
solids deposited. Those estimates can be used in preliminary
assessments of costs associated with pipe cleaning by mechanical
or flushing techniques to achieve different levels of total
deposited mass removals.
It should be noted that the estimates of total pipe footage
corresponding to given levels of deposition do not define where
in the system those pipes lie. With one simple assumption, the
locations in the system of the deposited pipes can be tentatively
established. This assumption can be understood considering Figure
16. In part a of Figure 16, an estimate of the percentage of the
total pipe length PL over which a percentage of the total mass of
solids, PM, deposits is shown. The percentage of total pipe
length in the basin with pipe slope smaller than or equal to
is shown in part b of Figure 16. Combining the two parts in
Figure 16, does not necessarily mean that the pipes over which PM
deposits all have slopes flatter than or equal to SPL. This may be
a reasonable working assumption and, if it is made, locations of
depositing segments can be determined. This step can be accomp-
lished by noting on a sewerage system map all pipe segments with
slopes equal to or smaller than SPL. This procedure will quanti-
fy the sewer segments associated with the percentage PM of the to-
tal load. A check of the approach can be made be measuring those
pipe lengths and comparing their sum with the estimate given by
LPM = PLxL
where: LPM = estimated length over which the percentage PM of
the total mass deposits;
PL = the corresponding percentage of pipe length (from
Figure 1.4) ; and
L = total length of pipe in the basin.
68
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REFERENCES
1. FMC Corp., "A Flushing System for Combined Sewer Cleansing,"
U.S. EPA Report 11020 DNo, March, 1972.
2. Process Research, Inc., "A Study of Pollution Control
Alternatives for Dorchester Bay," Metropolitan District
Commission, December, 1976.
3. "Design and Construction of Sanitary and Storm Sewers".
Prepared by a joint committee of the American Society
of Civil Engineers and the Water Pollution Control
Federation (1969).
4. Yao, K.M., "Sewer Line Design on Critical Shear Stress,"
Journal Environmental Engineering Div., (ASCE) 100: E22,
April, 1974.
5. Camp, T.R., "Design of Sewers to Facilitate Flow," Sewage
Works Journal, 18:3 (Jan. 1946).
6. "Minimum Velocities for Sewers", Final Report of Committee
to Study Limiting Velocities of Flow in Sewers,
Boston Society of Civil Engineers, 29:4 (October, 1942).
7. Raths, C.H., McCauley, R.F., "Deposition in a Sanitary
Sewer", W&SW, No. 1962, pp 238-243.
8. Metcalf & Eddy, Inc., "University of Florida, Water
Resources Engineers, Inc., "Storm Water Management Model",
EPA (July, 1971).
9. Fair, G.M., Geyer, J.C., Okun, D.A., Water and Wastewater
Engineering, Vol. 1: WAter Supply and Wastewater Removal
(1966) ....
10. Hughmark, G.A., "Aqueous Transport of Settling Slurries ,
Industrial and Engineering Chemistry, Vol. 53 (Mciy 1961).
11. FMC Corp., "Relationship of Sewage Characteristics to
Carrying Velocity for Pressure Sewer", August, 1969,
American Society of Civil Engineering, No. R-2598.
70
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APPENDIX A
BRIEF REVIEW OF R&D SEWER FLUSHING PROJECT
A brief review of the R&D sewer flushing program objectives
and project scope will be presented in this appendix. Next a
summary review of the pollutant removals resulting from manual
flushing of four test segments during the first phase of the pro-
gram will then be provided.
Conceptual Views of Program
The solids control demonstration/research program has been
developed to address many of the issues relating to the feasibil-
ity, cost-effectiveness, and ease of application of upstream
solids control program as an integral part of overall combined
sewer management. Basically, there are five fundamental issues
that must be answered before widespread acceptance of upstream
solids control may be considered. The issues include: 1) what
are the best flushing methods to use for a given situation; 2)
what is the expected pollutant removal efficiency associated
with the various methods; 3) what are the costs associated with
such programs; 4) how do you screen large systems to identify
problem pipes with respect to deposition and; 5) what are the
effects of stormwater runoff on such a strategy as applied to com-
bined sewer systems.
Program Objectives
1. Test the feasibility of applying various solids control
techniques as a method of deposition control in combined
and sanitary sewer lines on test segments in the Boston
sewer system.
2. Carefully monitor deposition rates on a number of test
segments.
3. Monitor pollutant removals including solids, organics
and nutrients associated with the various solids con-
trol techniques.
4. Assess pollution oriented characteristics of both the
flushed and remaining materials versus maintenance pro-
Jblems of grit, sand and.gravel accumulations.
71
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5. Recommend most favorable solids control techniques for
operational testing by both automated and manual means.
6. Develop, test and evaluate automated control systems in
a field operational testing program.
7. Develop, test and evaluate manual sewer flushing tech-
niques utilizing specially equipped water tankers in a
field operational testing program.
8. Assess the operational feasibility and performance of
flushing both long and short upstream collection segments
and/or networks.
9. Assess the effects of stormwater washoff on the
characterization of combined sewer solids.
10. Refine existing deposition model and flushing criteria;
11. Compare solids control vs selected structural options
as a combined sewer abatement technique.
12. Develop user guideline for solids control program as an
integral part of sewer management schemes.
Figure A-l is an overview schematic of the program. The
program is broken into three distinct phases: 1) a field
feasibility analysis of various solids control (flushing) tech-
niques to test the feasibility of applying various techniques to
actual sewer lines; 2) an operational testing program to assess
the operational feasibility of applying optimum strategies to
sewer systems; and 3) a detailed data analysis and costing phase
to develop a reasonable deposition model and flushing criteria,
and analyze the concept of upstream solids control as an integral-
part of combined sewer abatement schemes.
The feasibility analysis is aimed at answering the question
of what are typical deposition rates in sewerage collection
systems, what are the best flushing techniques to use, and what
pollutant reductions can be reasonably expected as well as
supplying a wealth of data for the refinement of the existing
deposition model and flushing criteria. The operational testing
program will take the optimum strategies developed in the feasi-
bility analysis and put them into an actual 10 week program aimed
at continuing data development as well as testing the operational
feasibility of such a program by both manual and automated means.
From the large data base developed during the two field
programs, a refined practical deposition model and flushing cri-
teria will be generated. These refined formalisms will allow for
scanning of large-scale sewer systems to identify problem pipes
with respect to deposition. The refined tools will allow for
72
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-------
comparative analysis of upstream solids control vs selected
structural options to compare program efficiencies. The tools will
also allow for rough assessment of first flush phenomena as
related to combined sewer systems to better clarify the questions
over the use of upstreams "first-flush" collection devices.
Finally, the program will develop data to generate a set of en-
gineering user guidelines to apply the deposition analysis to large-
scale systems.
Results of First-Phase Feasibility Flushing Programs
After a careful review and inspection program, four streets
were selected for the flushing experiments. These streets are
all in Dorchester characterized by high density, 3-story multi-
family dwellings. Two of the test segments located on Port
Norfolk and Walnut Street are served by flat combined sewer
laterals of 12" and 15" circular pipe, respectively. The total
tributary population down to and including the test segments are
94 and 71 people, respectively. The other two test segments on
Shepton and Templeton Streets, are serviced by separate sewer
laterals of 12" and 15" circular pipe, respectively. There are
downspouts on both streets connected to the sanitary sewer.
The total tributary population for these two streets are 224 and
221, respectively. The pipe slopes of the test segments range
from 0.003 to 0.004. The flushing program in this phase is con-
cerned only with the effects of flushing a single manhole to man-
hole segment. Three different methods of manual flushing were
performed. The first method consisted of backing up the upper end
of the flushing manhole with an inflatible rubber stopper with
quick release. The other two methods were gravity and pressurized
dump discharge into the flush manhole with the upper end of the
flush manhole blocked off. These flushes were performed using a
specially designed water tanker with two 1000 gallon tanks mounted
on a steel I-beam skid. The< tanker was equipped with a pneumatic
system to pressuirze the tanks to 30 psi. The operation under
gravity conditions provided a controlled flush release of 35 to
50 cubic feet at a rate of 0.25 to 0.50 cfs. Under pressurized
conditions the same volumetric range of flush was accomplished at
a rate of 0.5 to 1.25 cfs* Sixteen to eighteen grab samples of
flush wave were taken at 10 second intervals for the first 80 sec-
onds after the flush wave reached the downstream manhole and then
at 20 second intervals. Wave heights were taken at each interval
of time which were later used to determine the instantaneous flow
rate for computing mass pollutants removed by the flushing experi-
ment.
The total pollutant mass removals in kilograms, for each of
the four test segments are given in Table A-l. This data is
preliminary and is subject to change pending further field
refinment of stage/discharge rating procedures used to convert
flush wave heights to discharge quantities. The mean and standard
74
-------
deviation of the pollutant mass removals in kilograms for each of
the four test segments is given in Table A-2. The mean and
standard deviation of the pollutant mass removals normalized for
the number of antecedent days between flushing experiments is
provided in Table A-3. These statistics are computed for all
experiments including those impacted by rainfall events occurring
between the flushing experiments. Statistics for subsets of this
data excluding the rainfall impacted experiments are presented in
Appendix C. The data used in the regression analysis presented in
Table 15 of Section 4.5.4 was prepared by normalizing the raw
results given in Table A-l and then converting the results into
Ibs/day.*
* It is assumed in the regression analysis cited in Section 4.5.4
that the normalized pollutant loads removed by flushing equals
the daily deposition rate. Preliminary results of the second
phase of field flushing indicates flushing removal effectiveness
ranging from 75 to 90 percent. These results will be used dur-
ing a later phase in this project to reexamine the results
given in Section 4.5.4
75
-------
TABLE A-l. TOTAL MASS OF POLLUTANT REMOVED BY FLUSH
Location: Port Norfolk Street
TOTAL MASS (kg)
DATE
8/30/76
9/2
9/1
9/16
9/21
9/24
10/1
10/4
iO/8
10/12
10/15
10/18
10/25
10/22
10/29
11/1
11/5
11/8
11/12
COD
1.54
5.49
4.60
9.37
7.49
4.51
5.68
3.71
3.36
BOD
0.81
2.92
0.78
3.40
2.90
1.61
2.00
1.17
1.42
3.30
TKN
0.04
0.25
0.22
0.33
0.28
0.16
0.16
0.12
0.10
NH3
0.01
0.05
0.04
0.04
0.06
0.02
0.03
0.03
0.03
P
0.02
0.05
0.06
0.04
0.06
0.04
0.001
0.02
0.03
TSS
3.94
12.37
16.04
2.90
6.50,
5.74
11.36
7 . 10
2.97
5.81
2.73
4.90
1.52
2.36
3.04
2.94
2.23
3.32
4.79
VSS
1.24
7.58
11.02
1.96
3.14
3.67
9.35
5.42
1.92
4.27
2.16
4.03
1.11
1.79
2.49
2.30
2.04
2.57
4.47
continued
76
-------
TABLE A-l (continued)
Location: Templeton Street
TOTAL MASS (kg)
COD
8/30
9/2
9/7
9/10
9/13 2.54
9/16
9/21
9/24
10/1
10/4
10/8
10/12
10/15
10/18
10/22
10/25
10/29
11/1
11/5
11/8
11/12
BOD TKN
2.96
3.66
0.45 0.07
0.08
1.50
0.96
3.92
4.41
5.25
3.80
NH3 p TSS '
10.84
7.68
1.19
8.51
0.01 0.01 2.26
0.23
1.88
0.32
5.13
2.70
6.89
13.06
4.97
13.95
5.06
4.40
10.04
4.70
12.74
5.38
_
vss
4.01
4.93
1.01
6.52
1.70
0.16
1.10
0.27
3.60
2.19
5.95
10.49
3.45
11.09
3.32
3.58
7.44
3.23
10.52
3.96
continued
77
-------
TABLE A-l (continued)
Location: Shepton Street
TOTAL MASS (kg)
COD
8/23 5.63
8/30
9/2
9/7
9/10
9/13
9/16
9/21
9/24
10/1
10/4
10/8
10/12
10/15
10/18
10/22
10/25 8.00
10/29
11/1
11/5
11/8
11/12
BOD TKN
1.21 0.09
1.75
1.58
1.89
0.65
2.31
2.64
1.38
2.09 0.20
0.99
2.35
NH3 P TSS
0.03 0.03 3.91
2.84
5.70
14.11
5.71
2.42
5.67
4.27
2.57
3.34
5.76
6.09
4.32
4.82
6.54
2.93
0.04 0.05 4.53
3.51
3.60
5.49
5.51
1.03
VSS
2.81
1.71
4.17
11.04
4.58
1.93
4.46
2.83
1.87
2.31
4.71
4.84
3.12
3.87
5.24
2,31
3.83
2.86
2.93
4.55
4.37
0.89
continued
78
-------
TABLE A-l (continued)
Location: Walnut. Street
COO
8/23 3.5
8/26
8/30 12.44
9/2
9/7 0.66
9/10
9/13 3.06
9/16
9/21 1.36
10/1 3.37
10/4 1.15
10/12 13.70
10/15
10/18 1.21
10/22
10/25 2.12
10/29
11/1 1.67
11/5
11/8 4,25
11/12
TOTAL MASS (kg)
B°D TKN NH3 P TSS
0-83 0.07 0.04 0.03 2.74
i-18 0.52
1-29 0.35 0.1 0.07 14.94
1.76
0-22 0.03 0.02 0.01 0.63
0.98
0.61 0.08 0.07 0.02 14.23
0.46
0.24 0.03 0.01 0.02 2.75
1 ^<> 0. 10 0.02 0.04 2.83
0.45 0.05 0.01 0.01 1.21
3-61 0.25 0.05 0.04, 14.32
0..57
0.57 0.07 0.03 0.0005 1.08
. 4.24
O'SZ 0.07 0.03 0.02 1.53
1.34
0.70 0.06 0.02 0.01 1.01
3.33
1.67 0.11 0.06 0.02 3.34
0.48
vss
1.17
0.22
7.72
0.90
0.27
0.87
8.25
0.37
0.78
1.91
0.84
8.13
0.30
0.82
4.17
0.87
1.00
0.74
2.39
2.18
0.48
79
-------
TABLE A-2. STATISTICS OF POLLUTANT MASS REMOVALS (kg) RAW DATA
STREET STATISTICS
COD BOD TKN NH3
TSS
Port Mean 5.08 2.03 0.18 0.03 0.04 5.39 3.82
Norfolk St. Deviation 2.31 1.02 0.09 0.02 0.02 3.90 2.76
Shepton Mean 6.82 1.71 0.145 0.035 0.04 4.76 3.69
St. Deviation 1.68 0.62 0.078 0.007 0.01 2.53 2.03
OempletonMean 2.54 2.70 0.07 0.01 0.01 6.10 4.43
St. Deviation - 1.81 - - - 4.27 3.33
Walnut
Walnut
4.04 1.01 0.11 0.04 0.024 3.54 2.11
4,37 0.90 0.10 0.03 0.019 4.71 2.64
_ Too few data points to compute standard'deviation,
80
-------
Templeton
TABLE A-3. STATISTICS OF POLLUTANT MASS
REMOVALS (kg/ANTECEDENT DAY) DATA
NORMALIZED FOR ANTECEDENT DAYS
STREET
Port
Norfolk
S hep ton
STATISTICS
Mean
St. Deviation
Mean
St. Deviation
COD
1.
0.
1.
1.
41
53
89
09
BOD
0.55
0.25
0.50
0.21
TKN
0
0
0
0
.05
.02
.05
.04
NH3
0.01
0.04
0.01
*
P
0.
0.
0.
0.
01
005
02
01
TSS
1.49
1.04
1.36
0.63
VSS
1.03
0.64
1.06
0.52
Mean 0.85 0.81 0.02 0.002 0.003 1.66 1.25
St. Deviation - 0.54 - - - 1.17 0.92
Walnut
Mean 0-95 0.25 0.027 0,010 0.006 0.90 0 54
St. Deviation 0.83 0.15 0.021 0.008 0.004 1.19 0.67
- Too few data points to compute standard deviation
* Smaller than 0.0001
81
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APPENDIX B
DISCUSSION OP SIMPLIFIED SEWER SYSTEM DEPOSITION MODEL
The details of a procedure for obtaining quick and inexpen-
sive estimates of the amount of daily dry weather deposition load-
ings within each manhole to manhole segment of a sewer collection
system are provided in this appendix. A number of crude approxi-
mations and simplifications are used in this procedure and there-
fore, the results are not purported to be a substitute for those
provided by more rigorous approaches.
One distinct advantage of this model is that it. is devised
to consider each element of an entire collection system network.
It is intended to provide estimates for only dry weather condi-
tions and has no provisions for considering transient wet weather
phenomena. No distinction is made between bedload, suspended
load and washload deposition and resuspension characteristics.
The major simplifying assumption of the model is that the amount
of deposition remaining in any segment over the course of a day
is computed as the residual loadings not washed or moved down-
stream during peak dry weather flow conditions. No detailed
accounting is made of the temporal pattern of diurnal deposition,
resuspension and transport phenomena. The basic structure of the
model was developed during a prior combined sewer management
study (2). In a latter phase of this R&D sewer flushing^prpject
the data obtained from the field flushing program will be used to
further refine formalisms presented in this appendix.
General Concepts
A well designed sewerage system should not only convey flows
but should also minimize the deposition of sewage solids during
dry weather conditions. There are in use an ample number of
suitable empirical and theoretical equations for flow design but
no uniform criteria have been established to prevent solids
depostion.
The approach commonly used to prevent deposition is the
method of minimum permissible velocity (3). However, the use of
average velocity consideration is not necessarily the most robust
criterion to use for a wide range of typical operating conditions,
82
-------
A more fundamental approach is the method of critical shear stress,
T, given by equation (1) .
T = prss (1)
where p = specific weight of water
r = hydraulic radius, and
ss = energy slope
Yao (4) reviewed experimental results dealing with fluid
shear stress measurements and concluded that the average boundary
shear stress computed by equation (1) will approximate the actual
local boundary shear stress within the possible region of deposi-
tion, provided that the flow depth is equal to or greater than one-
third of the sewer diameter.*
Yao also included that a shear stress of .02 or .04 psf is
adequate for self-cleaning sanitary sewers, while a shear stress
of .06 to .08 psf is necessary to dislodge heavy sand and gravel,
and is required for self-cleaning of combined systems. In
addition, this work showed that the present practice of using a
constant minimum velocity for all sewer sizes tends to under-
design larger sewers and over design smaller sewers.
Deposition Mechanisms
Shield's classic results are commonly used to predict solids
deposition in sewerage systems. Shield's results, however,
relate to bedload movement and specifically to uniform particles
moving on the surface of the bed. In simple terms, there are two
primary mechanisms involved in the transport of sewage particles;
bedload transport and suspension.
The first to used bedload transport considerations to predict
deposition was Camp (5,6,) and others have since used this tech-
nique (7,8,9). Shield's relationship** for bedload transport
is given by:
TC = .020 p
where p = particle diameter, (mm) and
TC = critical wall shear (psf)
(2)
* The actual or local boundary shear stress varies considerably,
with the maximum occurring around the center line of the
channel and the minimum near the water surface.
** Shield's constant equals 0.06 in this formulation.
83
-------
The second transport mechanism is suspension. Hughmark (10)
correlated 14 sets of data on slurry transport and Raths (7) con-
ducted experiments on sand sediment in sewers. In order to pre-
vent deposition of sand particles (specific gravity = 2.7), a
critical wall shear must be maintained or exceeded. The results of
their experiments can be summarized by the following relationship:
TC = .021 pV3
(3)
The smaller particles (less than .05 mm) of Hughmcirk's data
closely agree with the above functional form. A reasonable
first order approximation is to assume that both mechanisms trans-
port heterogenous materials through sewer systems. The geometric
average of equations (2) and (3) can be used to predict transport
requirements. The equation relating the critical wall stress, TC,
necessary to move (and conversely to settle)* a particle of
given diameter, p, is the following:
TC = .02 p2/3 (4)
Single Segment Deposition Model
Equation (4) and sewage particle size distributions can be
used to predict the quantity of suspended solids deposited from
dry-weather flow over a single length of pipe. The results computed
from equation (4) with two particle distributions (11, 8) and the
experimental results from the FMC study (1) were fitted by a simple
single term power function given by equations (5) and (.6) :
-1.2
40 (-
004
for T > .004 psf
Z = 40
for
.004 psf
(5)
(6)
where -Z is the percentage of the suspended solids in the dry weath-
er sanitary flow that is deposited if the wall shear is less than
T.
The shear stress, T, would be computed for maximum daily dry
weather flow conditions. Maximum daily flow, QMAX» can be computed
from average dry weather flow, QAV, using equation (7).
QMAX
QAV
a PPb
(7)
* Recent findings have shown that this assumption is erroneous,
that is, a greater shear stress is required to move a particle
of a given diameter than to permit settling. In a later phase
of this project this assumption will be examined.
84
-------
where PP is the contributing population in 1000's and a and b are
determined from analysis of flow measurements. Typical values of
the constant "a" rariqe from 1.25 to 1.5 and a value of 1.47 was
used in the computations described in Section 4. A value of 0.08
was used for the exponent "b". Both values were established from
analysis of flow measurements.
Multi-Segment Models
In considering a series of sewer pipes having low values of
fluid tractive shear, that is, characterized by low slopes or
low flows (or both), the condition can arise where solids from an
upstream reach can successively deposit in downstream pipes. The
relative amounts deposited in any section would depend on the
shear stress during peak flow in that link and also on the amounts
deposited upstream. A general procedure is desired to predict the
total cumulative load in any section from all upstream sources.
The procedure used is the following:
"m"
1. Segment the collection system into a network of
links where each link may be a section of pipe between
manholes or several sections combined into a single sec-
tion (similar hydraulic characteristics);
2. Establish, for all links, a list of all downstream sec-
tions that convey waste from the given link;
3. Compute cumulative upstream length of pipe at each
link;
4. Compute average daily dry weather flow for each link
using the cumulative length from step 3 and an average
per capita waste rate;
5. Compute maximum daily dry-weather flow for each link
using equation (7);
6. Compute shear stress for each link associated with the
maximum daily flow, using equation (1) for the appropri-
ate pipe shape;
7. Compute the dry-weather suspended solids deposition rates,
Zi(i = l,...,m) from the shear stresses calculated in
Step 6, using equations (5) and (6);
8. Compute the suspended solids load ZLi(i = l,.,.m) devel-
oped along each link using length of link, population per
unit length and daily solids generated per capita;
85
-------
9. Starting at the uppermost link, i, compute the amount of
input material that will deposit, that is Zi ZLi;
10. Search the list of downstream links for the deposition
rate, Zj, greater than the rate at the link where the
load is initially generated, and compute the amoiint
deposited as the jth link from the ith component input
load using (Zj - Zi) ZLi;
11. Continue searching the list of downstream links for a
deposition rate Zk greater than Zj and compute the
deposition at the kth link from the ith component using
(Zk - Zj) ZLi;
12. Set Zk = Zj and repeat Steps 10 and 11 until the complete
list of downstream links is completed;
13. Start with the next uppermost link in the system and
repeat Steps 9 through 12 while maintaining a running
sum of all the deposited loads in each link from pre-
vious iterations; and
14. Sequentially proceed downstream until all components
are completed.
In other words, a fraction of the load generated in an up-
stream section may deposit in that section (if the shear stress
is sufficiently low) and more of that load may deposit in down-
stream sections only if the shear stress falls below levels
experienced upstream.
The present model is coded to assume any collection system
geometry with the one rule that only three segments can be
considered at a given manhole. The model is coded to compute
shear stress for circular, egg, ovoid, rectangular, horseshoe
shaped cross-sections with and/or without pre-set sediment beds.
An idealized example using the schematic in Figure B-l
illustrates this procedure. Assume that the shear stress developed
during peak dry-weather flow in links 1, 4, 5, 8 and 11 results
in deposition rates of 10, 5, 5, 15 and 20 percent, respectively.
Assume that the shear in all other links, i.e., 2, 3, 6, 7, 9 and
10, is sufficiently high to preclude any localized deposition.
The dry weather load developed along each of the 11 links is,
say, 100 units of dwf solids.
86
-------
o
o
12"
12"
O-
© 12"
O
15'
o
15'
12"
o-
L7) 12"
18'
O-
00) 15'
©
30"
12"
TRUNK SEWER
FIGURE B-l. SCHEMATIC OF COLLECTION SYSTEM
87
-------
TABLE B-l. DEPOSITION ANALYSIS OF IDEALIZED SYSTEM
Link Numbers
12345678910
1 10.
2-0.
3 - 0. 0.
| 4 0. 5. 5. 5.
1 5 0. 0. 0. 0. 5.
Jj 6 ----- 0.
7 - - - - 0. 0.
8 5. 10. 10. 10. 10. 15. 15. 15.
9____----0.
10 _ _ _ - - _ - o. o.
11 5. 5. 5. 5. 5. 5. 5. 5. 20. 20.
Total amount
Deposited, in
11 Each Link
10
0.
0.
15.
5.
0.
0.
90.
0.
0.
20. 100.
The ijth in the table represents the amount deposited in link i
that originated in link j. Thus element (8,1) = 5 represents the
amount deposited in link 8 that originated in link 1.
88
-------
Table B-l shows contributions from all upstream links on each
downstream link and the total deposition in section 4 consists of
loads from sections 2, 3, 4 but not from section 1 because the
deposition rate, Zj. is greater than Z4. At link 5, the only
amount deposited is from the load developed along that link
(Zi is greater than Zs: no deposits, Z2 and Z3 less than Zs but
Z4 equals Z5: no deposits; Z4 less than Z5: deposits). The
overall deposition rate for entire system is 20 percent (220 units
deposited/1100 units total load) with nearly equal loadings in
links 8 and 11.
89
-------
APPENDIX C
PRELIMINARY DEPOSITION MODEL CALIBRATION RESULTS
In this appendix a preliminary verification is presented of
the deposition model described in Appendix B using field, flushing
results derived from the data presented in Appendix A. The
results presented here reflect no change in the model's internal
relationships. It is envisioned that modifications will be made
in a later phase of the study.
A comparison of field flushing results for four test segments
with predicted deposition rates is presented in Table C--1. The
contents of this table are described as follows:' .column (1) -
test segment location; column (2) - average mass of suspended
solids removed per flush normalized by the number of antecedent
days between each of the flushes for all experimental data;
column (3) - average mass of suspended solids removed per flush
normalized by antecedent days for selected subset of the experiment-
al results including only good experimental points free of rain-
fall events occurring between the flush periods; column (4) -
predicted daily deposition rates over test segment for two per
capita waste rates of 125 and 250 gallons per capita per day;
column (5) - pipe size of test segment; column (6) - length of
test segment; column (7) - plan slope of pipe segment; and column
(8) - depth of sand and gravel sediment bed. A suspended solids
waste rate of 0.5 Ib/capita/day was used in the analysis. This
rate was determined from an analysis of background samples taken
during the flushing program. Additional sewage background sampling
is presently being conducted in the study and these results will
later be used to sharpen the preliminary results presented here.
The background sewage flow per capita determined from field measure-
ments conducted during the flushing program ranged from 125
gpcd up to 275 gpcd. The peaking factors relating maximum daily
flow to average flow were determined from field data.
Inspection of the measured results shown in column (3) with
the predicted values given in column (4) indicates the deposition
model estimates compare reasonably well with field results,
In general, the model under-estimates deposition loadings and will
be modified to reflect this bias in future phases of work.
90
-------
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-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-600/2-77-120
2.
3. RECIPIENT'S ACCESSION'NO.
4. TITLE AND SUBTITLE
PROCEDURES FOR ESTIMATING DRY WEATHER
POLLUTANT DEPOSITION IN SEWERAGE SYSTEMS
5. REPORT DATE
July 1977 (Issuing Date)
6. PERFORMING ORGANIZATION CODE
7, AUTHOR(S)
William C. Pisano and Celso Queiroz
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Energy & Environmental Analysis, Inc.
264 Beacon Street
Boston, Massachusetts 02116
10. PROGRAM ELEMENT NO.
1BC611
11.
R- 804579
NO.
12. SPONSORING AGENCY NAME AND ADDRESS _. .,
Municipal Environment Research Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Cincinnati, Ohio 45268
13. TYPE OF REPORT AND PERIOD COVERED
Interim Final Planning Doc.
14. SPONSORING AGENCY CODE
EPA/600/14
15, SUPPLEMENTARY NOTES
Project Officer - Richard Field
201/321-6674(8-340-6674)
10. ABSTRACT
A set of generalized procedures for estimating pollutant loadings associated with
dry weather sewage solids deposition in combined sewer systems has been prepared to
provide planners, engineers and municipal managers with technical information so that
they can make intelligent informed decisions on potential sewer flushing programs
in combination with other combined sewer management controls.
The predictive equations relate the total daily mass of pollutant deposition accum-
ulations within a collection system to physical characteristics of collection systems
such as per capita waste rate, service area, total pipe length, average pipe slope,
average diameter and other more complicated parameters that derive from analysis of
pipe slope characteristics. Several alternative predictive models axe presented re-
flecting anticipated differences in the availability of data and user resources.
Pollutant parameters include suspended solids, volative suspended solids, biochemical
oxygen demand, chemical oxygen demand, total organic nitrogen and total phosphorous.
Sewer system age and degree of maintenance was also considered. Factors are presented
for estimating the increase in collection system deposition resulting from, improper
maintenance. A user's guide has been presented to establish the necessary data input
to utilize the predictive procedures.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS
c. COS AT I Field/Group
*Combined Sewers, *Flushing,
*Water Pollution, *Water Quality,
Economics, Mathemati&al Models,
Methodology, *Maintenance
Field Measurements,
Pollution Abatement
Regression Analysis,
Sewer Flushing
13B
18. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
19..SECURITY CLASS (ThisReport)
UNCLASSIFIED
21. NO. OF PAGES
104
20. SECURITY CLASS (Thispage)
UNCLASSIFIED
22. PRICE
EPA Form 222Q-1 (9-73)
92
fr U. S. GOVERNMENT PRINTING OFFICE: !977-757-056/56'l2 Region No. 5-11
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