EPA-600/2-77-212
November 1977
Environmental Protection Technology Series
ABATEMENT OF DEPOSITION AND
SCOUR IN SEWERS
Municipal Environmental Research Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Cincinnati, Ohio 45268
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EPA-600/2-77-212
November 1977
ABATEMENT OF DEPOSITION AND SCOUR IN SEWERS
by
Michael B. Sonnen
Water Resources Engineers, Inc.
Walnut Creek, California 94596
Contract No. 68-03-2205
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 Environmental 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 recommendation 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.
Research 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 Environmental Research Laboratory develops new and
improved technology and systems for the prevention, treatment, and management
of wastewater and solid and hazardous waste pollutant discharges from
municipal and community sources, for the preservation and treatment of public
drinking water supplies, and to minimize the adverse economic, social, health,
and aesthetic effects of pollution. This publication is one of the products
of that research; a most vital communications link between the researcher and
the user community.
This report describes new methodology for analyzing the design of storm
and combined sewer systems. Particularly the work addresses the abatement
of pollution caused by the flushing of accumulated solids from sewers during
storm periods.
Francis T. Mayo
Director
Municipal Environmental Research
Laboratory
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ABSTRACT
The research reported here had two major objectives: a) a review of
feasible methods for reducing the first-flush of solids in overflows from
storm and combined sewers, and b) the development of a mathematical model
that could be used to evaluate the behavior and cost of first-flush
mitigating alternatives.
Feasible methods of controlling first-flush pollution in new designs
include increasing conduit slopes, providing cunette sections or other pipe
shapes that maintain high velocity during low flow periods, providing
upstream capture of solids during high flows, and providing increased amounts
and degrees of treatment downstream. Flushing of sewers already in place
appears to be the most feasible method of reducing first-flush pollution in
existing systems. All these alternatives are directed toward minimizing
accumulation of solids in pipelines and toward providing the maximum amount
of treatment that proves cost effective.
A model was developed, adapted from the existing EPA Storm Water
Management Model, which simulates the behavior of solids in pipelines as
bedload, suspended load, or washload. Example problems are described which
demonstrate both the workings of the model and the improvements in first-
flush mitigation that the model can identify.
This report was submitted in fulfillment of Contract No. 68-03-2205 by
Water Resources Engineers, Inc. under the sponsorship of the U.S. Environ-
mental Protection Agency. This report covers work performed during the
period June 1, 1975 to October 31, 1976, and work was completed as of
November 30, 1976.
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TABLE OF CONTENTS
FOREWORD
ABSTRACT
FIGURES
TABLES
SECTION I.
SECTION II.
SECTION III.
CONCLUSIONS
RECOMMENDATIONS
SCOPE, OBJECTIVES, AND SUMMARY OF FINDINGS
Phase I
Phase II
SECTION IV. ADAPTATION OF SEDIMENT TRANSPORT THEORY
Definitions
Bedload Transport Relationships
Suspended Load Transport Relationships
Washload Transport Relationships
SECTION V. THE NEW MODEL
The "Old" Model
New Routines
Other Changes to the Transport Block
SECTION VI. RESULTS FOR EXAMPLE PROBLEM
The Hypothetical Problem
Example Cases
Demonstration of First Flush
Other Results
Use of the Model in Other Applications
REFERENCES
ADDITIONAL BIBLIOGRAPHY
APPENDIX -- LISTS OF NEW MODEL SUBROUTINES
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FIGURES
Number Page
1 Critical Shear Stress as a Function of Particle Diameter 13
2 Kalinske's Bedload Function 14
3 Advective Transport Concept in the Quality Model 26
4 Transport Concept for Solids in Subroutine SCRDEP 33
5 Example Output by Particle Size 35
6 Example Output by Pipe 36
7 Example Output by Treatment Plant 37
8 Example Output for Entire System 38
9 Example Output of Treatment Costs 39
10 Three Conduit Shapes Added to WRE-SWMM Model 45
11 Example Pipes and Watersheds for Model Demonstration 47
12 Particle Size Distributions Used in Example Cases 48
13 Storm Inputs at Junctions 1, 2, and 3 for All Example Cases 55
14 Dry Weather Inputs for All Example Cases 56
15 Flows and Velocities in Combined Sewer System During
Delayed Storm Case 58
16 Depths and Widths in Combined Sewer System During
Delayed Storm Case 59
17 Disposition of Solids in Combined Sewer System During
Delayed Storm Case 60
18 Concentrations of Solids Throughout Combined Sewer System
During Delayed Storm Case 62
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FIGURES (Continued)
Number Page
19 Flows and Velocities in Pipe 2 of Combined Sewer
Systems with Different Slopes 70
20 Downstream Solids Concentrations in Combined Sewer
Systems as Functions of Pipe Slopes 71
21 Upstream Accumulation of Solids in Combined Sewer
System as a Function of Pipe Slope 72
22 Flows and Velocities in Combined Sewers of Different Shapes 73
23 Disposition of Solids in Combined Sewer Systems
Having Different Pipe Shapes 75
24 Solids Discharge Rate from Combined Sewer System
Having Different Pipe Shapes 76
25 Concentration of Solids in Combined Sewer Outfalls for
Systems Having Different Pipe Shapes 77
26 Effects of Treatment Type and Size on Effluent
Solids Concentration 78
27 Effects of Upstream Stormwater Treatment in Combined
Sewer System on Accumulation of Solids 79
28 Effects of Treatment Type on Effluent Solids Concentrations
from Sanitary Sewer System 81
29 Velocities and Flows in Upstream Storm, Sanitary, and
Combined Sewers as Simulated 82
30 Velocities and Flows in Outfalls from Storm, Sanitary,
and Combined Sewer Systems as Simulated 84
31 Effect of Sewer System Type on Upstream Accumulation of Solids 85
32 Effect of Treatment Type on Effluent Solids Concentration
from Sanitary Sewer System 86
33 Effect of Upstream Treatment for Solids Removal in Storm
Sewer System as Modeled 88
34 Treatment Costs and Solids Removal Percentages for
Example Cases 91
35 Total Sewer System and Treatment Cost vs. Overall Removal
Percentages for Example Cases 92
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TABLES
Number Page
1 New Transport Block Capabilities and Limitations 28
2 Treatment Cost Coefficients and Exponents 41
3 Particle Size Distributions 49
4 Description of Example Cases 51
5 Conduit Sizes in Example Cases 52
6 Junction Invert Elevations for Example Cases 53
7 Treatment Sizes and Types in Example Cases 54
8 Solids Behavior in Combined Sewer--Pipe 1 63
9 Solids Behavior in Combined Sewer--Pipe 2 64
10 Solids Behavior in Combined Sewei—Pipe 3 65
11 Solids Behavior in Combined Sewer--Pipe 4 66
12 Comparison of Results for Combined and Separate Sewer Systems 89
13 Solids Removal and Cost Results for Example Cases 90
VI 1 1
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SECTION I
CONCLUSIONS
Deposition and scour of solid materials in sewer systems have been
studied to evaluate alternative methods for alleviating these problems, and
to demonstrate how deposition and scour and their abatement can be evaluated
through mathematical modeling.
Phase I of the study listed available methods for alleviating the
flushing of deposited solids into receiving waters during high-flow, storm-
runoff periods when treatment plants designed for smaller flows are not able
to treat the entire storm volume. Moreover, Phase I determined the feasi-
bility of mathematically simulating the improvements afforded by these
alternatives. Phase II, which is the major topic of this final report,
included modeling of the deposition, scour and transport processes and
estimating the costs of the simulated facilities. From both phases of the
work, but especially from Phase II, the following conclusions have been
reached.
1) Sewer design based on a velocity criterion only for self-
cleansing does not consider all the relevant variables
that affect deposition and scour, and hence such design
can lead to situations in which deposition may still occur
and "first-flush" pollution will not be prevented. Where
velocity becomes the controlling factor, however, 2 feet
per second appears to be adequate to initiate scour of
deposited materials. This conclusion is based only on
the analyses used here which assume noncohesive deposits
are involved.
2) Sediment transport theory derived over the years for
natural streams, steady-state conditions, and beds having
inexhaustible supplies of particles can be modified and
used adequately to evaluate solids transport problems in
man-made pipe systems operating under transient conditions
and having finite amounts of deposited materials.
3) A combined sewer system configuration can be found that
will have about equal cost and solids capture efficiency
as a comparably designed separate storm and sanitary system.
4) Analyses of example cases presented later in this report
led to some encouraging but unexpected results. For example,
one case included swirl concentrators at upstream points in
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a combined sewer system and secondary treatment at the down-
stream end of the system. Another case included the same
basic features but larger capacities of the swirl concentrators
and secondary treatment and the addition of sand filtration
to the secondary plant. Additionally, the second case had
pipes one foot smaller in diameter than in the first case and
laid at a somewhat higher slope. The savings in the second
example in pipe costs and excavation costs (topographic control
was at the downstream end) more than offset the increased
treatment costs; while the solids capture efficiency increased
from about 50 to over 80 percent. In this case the "better"
system was the cheaper one. In other cases, solids capture
efficiencies were more than doubled by adding pipe and/or
treatment facilities costing only 5 to 10 percent more.
Admittedly, these precise findings are related only to the
physical dimensions of the example problems analyzed here.
But the findings are significant because they are not likely
to be predicted. The general conclusion to be drawn is that
design of systems of connected pipes, storage facilities,
and treatment devices can and should include analyses of a
wide variety of options, each of which will have its peculiar
physical and economic consequences. The design of the total
system should be the objective, not the individual design of
its parts; and fortunately a model now exists to assist that
process.
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SECTION II
RECOMMENDATIONS
It is recommended that the new updated sewer analysis model reported here
be applied in a variety of field applications, both to test its relationships
and inherent assumptions, and to allow sewer cleansing evaluations and designs
to be performed with regard given to a number of the contributing variables
in addition to velocity in the pipes.
Considerably more research should be undertaken in the area of sediment
transport in pipelines. While the model developed here works, in the sense
that it functions and yields helpful answers, it is by no means perfect or
perfectly general. Particularly important topics for research are the
definitions of and separations among bedload, suspended load, and washload;
extension of the relationships now available to account for stickiness and
armoring of deposited materials; and the linkages between "suspended solids"
and other constituents such as organic matter, heavy metals, and nutrients
often reputed to be associated with solids.
The claimed superiority for pollution control of separate storm and
sanitary sewers over combined sewers should be reevaluated as a concept in
light of the preliminary findings here that combined sewer systems can be
comparable in cost but superior in solids capture efficiency to separate
systems.
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SECTION III
SCOPE, OBJECTIVES, AND SUMMARY OF FINDINGS
PHASE I
The initial phase of this project investigated a) the available alter-
native methods for reducing first-flush pollution, and b) the feasibility of
simulating these methods for its reduction. During this phase the following
tasks were performed:
1) First-flush control alternatives were identified.
2) Cost-size relationships for the identified alternatives
were found in existing literature.
3) Solids removal efficiencies of the alternative methods were
obtained from literature reviews.
4) The feasibilities of a) using these alternatives in the field
and b) simulating their behavior and estimating their costs
in a mathematical model were determined.
The findings at the end of Phase I were somewhat paradoxical. Some of
the alternative control measures appearing most feasible for field application,
particularly in existing sewer systems, were going to be the most difficult to
simulate. The converse was also true: the things that could be changed most
easily in a model, such as pipe diameter or slope, were the least feasible in
the field, especially in existing sewer systems.
Nonetheless, it was concluded that a number of feasible modeling alter-
ations to include first-flush mitigation measures could and should be made to
an existing sewer analysis model, namely the Storm Water Management ffodel
(SWMM), which EPA had developed and promulgated over a number of years. Thus
Phase II was then directed to making these changes.
Specific and more detailed findings from Phase I are summarized below.
1) Three major categories of first-flush control alternatives
for sewer systems have been tried in field applications, at
least as demonstration projects. These include a) pipe
configuration changes of size, slope, and shape; b) modifi-
cations at sewer inlets such as inflatable dams to store some
dry weather flow in an upstream pipe, later to be released as
a flushing wave into downstream sewers; and c) upstream and
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downstream storage and treatment alternatives, including
detention basins, swirl concentrators, and conventional
waste treatment with primary and secondary plants.
2) Alteration of pipe configurations to control or lessen first-
flush pollution in existing sewer systems can be very
difficult or even impossible. For example, if it were found
that a pipe in the middle of a sewer network could be kept
clean during dry weather by tripling its slope, such an alter-
ation could prove to be hydraulically infeasible and certainly
not cost effective. In the design of new systems, however,
consideration of self-cleansing properties of sewers has been
a standard and fairly simple practice. One attempts to find
a pipe diameter and slope combination that yields a minimum
velocity at half-full or full flow of 2 feet per second, and
a condition of at least half-full flow once a day. Where
slope and other conditions prevail against a combination of
these two variables that is cost effective, a change in pipe
shape to egg-shaped or cunette cross-section is considered,
whereby low flows will move with velocities and hence scour
potentials rivaling those at half-full or full flow.
A happenstance that occurs, regardless of design considerations,
is that excessive deposition does occur in some pipes of
existing sewer systems. When deposition becomes excessive,
sometimes to the extent that it causes loss of hydraulic
capacity, the alternatives other than changing the pipe
configuration are to flush the sewer or to clean it by hand.
In San Francisco there was a case, though, where deposition
was so rapid and so excessive and the deposits became so
encrusted that continuous cleaning by hand or flushing at
upstream manholes were not as feasible as changing the pipe.
The old sewer section was removed and replaced with one having
a precast cunette section in the bottom, which allowed the
solids to be continually moved toward a downstream treatment
plant. While this action was taken to prevent upstream flooding
caused by the clogging of the sewer, and not for the control of
first-flush pollution; the exception to the rule of infeasibility
of changing existing pipes to solve deposition problems is of
interest.
With respect to the feasibility of simulation of these alter-
natives, changing size and slope in a model like SWMM is
absolutely trivial. One simply has to retype one number on
one card and make a new simulation. Changes in conduit shape
are a bit more difficult to treat, although the SWMM version
ultimately adapted in this project already treated egg-shaped,
baskethandle, horseshoe, rectangular, and trapezoidal sewer
sections, in addition to circular sewers. Cunette sections
were not originally included, and this required some repro-
gramming in Phase II.
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3) Modifications at sewer inlets, including flushing with
piped-in freshwater or with temporarily stored upstream dry
weather flows, capture of solids in catchbasins or offline
storage manholes, or capture of solids from street runoff in
filter bags hung below grate inlets have all been tried. A
variety of operating problems have been reported. Of these,
flushing with freshwater introduced for this purpose appears
to be the most feasible, and research is going forward
currently to determine operating methods and efficiencies
(Pisano, 1976).
From a simulation point of view, it was decided that flushing
alone was the only one of these methods currently feasible
and sufficiently proved in practice to warrant introduction
to the model. Since flushing is practiced by sending a wave
of water through the sewer, having precisely the same charac-
teristics as a storm hydrograph which the model already handled,
no modifications to the model were necessary to evaluate flushing
4) Storage and treatment alternatives have obvious and compelling
logic as first-flush control methods: to stop polluting
overflows, store the excess water for later treatment. The
stormwater detention cases studied from the literature, however,
all were plagued with the difficulty or merely lack of consid-
eration of removing the solids after the storm had passed from
the basin, lagoon, rubber bag, or whatever the storage device
may have been. Because that fairly essential part of the
process had not been addressed and characterized in the liter-
ature, it was decided not to attempt addition of storage and
solids capture capability to the model.
On the other hand, treatment devices such as swirl concen-
trators for upstream solids capture during storm flows and
the conventional downstream methods of waste treatment have
proved so effective in removal of solids that it was deemed
essential to add capability to the model for simulating their
quality improvements. Because the physics and chemistry of
behavior of these devices is still not well understood, actual
representation of their behavior was not attempted in the model.
But fixed removal percentages were estimated for each kind*of
treatment device, and their costs were estimated as well.
PHASE II
The following tasks were undertaken during Phase II.
1) Add simulation capability to an existing sewer transport
model. Modifications were to include simulation of the
deposition and scour phenomena, as well as the influence
of feasible first-flush control alternatives.
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2) Add cost estimation capability to the model. The decision
was made during the project to add this capability to the
existing model, rather than to develop a new, separate program.
3) Demonstrate the added model capabilities. At least five
simulations were to be made. Both behavioral differences
in the physics of solids transport and differences in cost
were to be demonstrated for alternative pipe and plant
configurations.
The Model to Be Adapted
The remainder of this report deals with the changes that were made to
the existing model of sewer behavior. It is appropriate to introduce that
model at the outset. It is described in greater detail later in this report.
The EPA SWMM model was developed in 1971 by Metcalf & Eddy, Inc., the
University of Florida, and Water Resources Engineers, Inc. (Metcalf & Eddy,
et_ aj_., 1971). It was comprised of three parts or Blocks: a) the Runoff
Block, which converted rainfall on urban watersheds to runoff and computed
hydrographs and pollutant mass loadings at sewer inlets; b) the Transport
Block which routed the hydrographs and pollutant masses through the sewer
system; and c) the Receiving Water Block, which simulated the effects on
rivers and estuaries of the storm and sanitary inflows provided by the
Transport Block.
Since that time, a different version of the Transport Block has been
provided to EPA for inclusion in the SWMM package (Shubinski and Roesner,
1973). This option is known as the WRE-SWMM Transport Block. It was this
set of programs that was adapted to include deposition and scour and new cost
estimation capability during this project.
The WRE-SWMM Transport Block consists of two computer programs. One is
the Hydraulics Model, which estimates dry weather flow and quality inputs,
accepts hydrograph inputs at specified junctions in the sewer network, and
routes the water downstream. The second program is the Quality Model which
accepts as inputs the computed pipe flows, junction heads and dry weather
mass inputs from the Hydraulics Model, accepts either from cards or from a
Runoff Block output tape the mass inputs from storm inflows at junctions,
and computes the mass balance of BOD, coliforms, and "suspended solids"
throughout the pipe system for the period of simulation. Suspended solids,
like the other constituents, are represented as a conservative constituent.
In this project, minor changes were made to the Hydraulics Model, but
some substantial additions were made to the Quality Model, all of which are
described in detail later in this report.
Chronology and Results of Phase II
In the sequence reported below, the various model modifications were
made and the two new programs were tested with example problems devised for
this purpose.
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1) The literature was studied at great length to glean
equations for representing the phenomena of deposition,
scour, and solids transport.
2) A deposition and solids transport subroutine was written
and incorporated in the Quality Model. This subroutine
calculates the movement of solids from one junction to
another and the accumulation of solids on pipe bottoms,
as appropriate for the hydraulic conditions simulated in
each time step.
3) A special subroutine was written and added to the Quality
Model to compute the settling velocity of any solid particle
of a given diameter and specific weight. The subroutine
is used as necessary to compute quiescent water settling
velocities for up to 10 different particle size ranges,
which are routed through the sewer system.
4) Two other subroutines were developed and added to the
Quality Model. The first of these summarizes and prints
the results of the sediment transport computations for each
pipe at specified time intervals. The second subroutine
summarizes for each treatment plant in the simulated system
the amount of solids removed during the entire simulation
period and prints information about the plant's size and
type.
5) Alterations were made in several subroutines of the existing
Hydraulics and Quality Models to incorporate conduits with
cunette sections. In addition to the six conduit shapes
listed previously, both models can now treat conduits with
the following shapes: circular with semicircular cunette,
circular with rectangular cunette, and rectangular with
rectangular cunette.
6) Cost equations for construction and operation of pipe systems
and treatment plants were derived from available literature.
Pipe costs are now computed and reported by the Hydraulics
Model. Treatment costs are computed and reported by the
Quality Model.
7) An example combined sewer system was devised consisting of
five junctions and four pipes, with a treatment device of any
size and type specified at the end of any pipe. An example
separate sewer system was also devised, consisting of four
pipes and five junctions in both a separate storm sewer system
and a separate sanitary system, again with treatment being
specified as desired at the end of any pipe section.
8) Approximately 25 simulations were made to show the workings
of the new model features and to show the behavior of solid
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materials in pipe systems under different conditions of
flow and pipe and plant configuration.
The remaining chapters of this report describe the development, testing,
and results of these new model features.
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SECTION IV
ADAPTATION OF SEDIMENT TRANSPORT THEORY
The literature on sedimentation, sediment transport, channel erosion, and
similar or equivalent phenomena is staggering by its sheer volume. Some 25 to
50 books and articles have been reviewed in this project, most of which were
written after 1971, and virtually all of which address sediment motion in
natural streams rather than pipe systems. All of them will not be referenced
here, primarily because in the end all the relationships used in this work
were reported in two or three volumes that summarized the state of the art as
well. Nonetheless, following the references given at the end of the report,
there is a bibliography that includes the other works reviewed. Most of what
follows was taken from the book by Graf (1971) on sediment transport and the
book by an ASCE Task Committee (1975) on sedimentation engineering.
DEFINITIONS
Three basic loads of solid materials transported by water in a stream or
conduit have been defined. These are bedload, suspended load, and washload.
Graf (1971) has introduced other terms as well; for example, bed material load
is represented by the sum of bedload and suspended load. Moreover, he pointed
out that the bed material load is often called the total load, which is
misleading, since more than 50 percent of the total material moving in the
channel may be washload.
Bedload consists of particles rolling, sliding, sometimes jumping along
close to the channel bottom. Some of the qualifiers or subdefinitions one
reads are confusing because this material is considered, even by a single
author, to have "deposited", to not remain stationary, or to be derived from
material some of which deposits and remains at rest while some of it jjever
does deposit. The most often appearing definition is that bedload is
material in motion near the bed. Suspended load is comprised of particles
that have been swept upward into the flow from the bed. Apparently, they
have gone through the experience of being in motion as bedload, at least for
an instant; so it can be said that they are derived solely from bedload, and
not possibly from the stationary bed directly. The distinction between
bedload and suspended load is one of hydrodynamic forces imparted by the
flowing water, by gravity, and by the particles' own characteristics.
Bedload is simply too large or too heavy to be completely suspended in the
water in constant, continuous motion. Washload, on the other hand, is
material so small or so light that it is carried along with the flowing water
virtually as a conservative substance. It may never have been part of the
bed, the bedload, or the suspended load. Graf (1971) has concluded in a
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general way that more than 50 percent of the total material in motion in a
natural stream can be in the form of washload, and Rendon-Herrero (1974) has
indicated that it can be as much as 95 percent. Graf (1971) also says that
washload tends to be derived from materials swept in from the watershed and
hence can be quite different from materials in a (natural) streambed. A
simplification he reports for estimating the characteristics of washload is
that washload can be considered to be materials having diameters less than
those in the smallest 10 percent of the bedload, regardless of their source.
ASCE (1975) has given similar, but more definitions for the various
components of the total material in motion. For purposes of this report,
which deals with quite unnatural channels and very transient conditions, the
following definitions will be used.
Bedload is comprised of solid materials that move near the pipe bottom
in the direction of flow according to the relationships for such motion given
below. Particles of any size may be included in bedload in a given time step.
Hence, they may be derived originally from any source, j_.e_. 5 the watershed,
sanitary flow inputs, or the deposits on the pipe bed from the previous time
period. However, before being moved as bedload they will have previously
deposited to the pipe bottom during a period of sufficiently quiescent flow
to permit this, which may be during the same time period in which they are
also moved.
Suspended load is comprised of materials that have at one time been
deposited and have subsequently been swept from the bedload into the overlying
flow with a distribution throughout the depth as described by relationships
given below.
Hashioad is comprised of particles that have just entered the pipe at
the upstream junction and have been determined to be unable to settle or
deposit (be removed by sedimentation) within the pipe length during the
current time period, given the flow conditions then existing. Washload,
therefore, is not limited to certain sizes or defined by its original source.
BEDLOAD TRANSPORT RELATIONSHIPS
Of many relationships given by Graf (1971) and ASCE (1975) for bedload
transport, the one chosen for use here is that attributed to Kalinske (1947).
Of those relationships reviewed, Kalinske's appears to be as reliable as any
others, it has been corroborated with data, and it requires values for
variables that are knowable from other computations in the Hydraulics and
Quality Models used here. It states:
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in which
qs = volume rate of solids movement per unit width, ft3/sec-ft;
u* = shear velocity, A /p ; ft/sec;
d = median diameter of particles, ft;
IQ = shear stress = j r^ s, lb/ft2;
(n0) = a critical shear stress, obtaining at the moment of
ar incipient motion, lb/ft2;
p - density of water, 62.4 lb/ft3 ± 32.2 ft/sec2 =
1.94 Ib-sec2/ft>,
Y - specific weight of water, 62.4 lb/ft3;
r, = hydraulic radius of flow, ft; and
s = the energy slope, ft/ft.
In the model adapted to solve this problem, all these quantities except
two are known or can be calculated in each time step for each pipe. The
quantity, qs, is being sought; and a separate expression for (i0) is still
needed. " cr
The value of the critical shear stress, (IO)CT, can be obtained from the
relationships of shear stress to particle diameter (in millimeters) shown in
Figure 1. This figure was taken from Graf (1971) (Figure 6.6, page 95). The
dotted lines indicate the range of data from various investigators as
summarized by Graf. The curve for average values fitted for use in this study
consists of two lines represented by the equations:
(i0)or = 0.01484 d1'^0 d >6 mm [2]
and
fi0;er = 0.067 d0-2238 d <6mm . [3]
The units are millimeters for particle diameter and pounds per square foot for
critical shear stress. It might be noted that a similar figure in ASCE's book
(1975) (Figure 2.44, page 99) shows other data considerably below Graf's range
of shear stresses at small diameters. ASCE notes this as well, and is at a
loss to explain it, while Graf (1971) states that his curve "summarizes much
of the important work done and, hence, should prove very helpful for the
hydraulic engineer engaged in channel design." Consequently, Graf's inter-
pretation was accepted for this study.
To solve the relationship in equation 1 for qs, one more curve is needed.
This is given in Figure 2, which is Kalinske's (1947) bedload function.
12
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LU
It
I-
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2.8
2.4
2.0
1.6
1.2
0.8
0.4
0.0
0.001
«^—i APPROXIMATION
IN THIS STUDV
INDICATED FIT OF
KALINSKE'S DATA
BY GRAF (1971)
0.01
O.I
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Again, straight-line approximations have been taken in this study to facil-
itate the modeling aspects, and indeed to more nearly fit the data in the
higher range of qs/u*d. The relationships are:
-^ = 2 x 10 ° or ° 0.3 < (ia)/r0 < 2.0 [4]
~ = 434.1 x 10 CTO; Ao > 2.0 [5]
and
a
, = 27 x ^ c ^o->crA0 < 0.3 [6]
The procedure used is as follows:
1) Determine do^or fr°™ Figure 1 (or equation 2 or 3).
2) Calculate i0 from y r, s.
3) With the ratio of T'S, determine qs/u^d from Figure 2
(equation 4, 5, or 6).
4) Compute qs from i^d /[('T0^cr/T0J.
5) Compute the mass in motion per unit width, gs, as YS 3s
where YS 1S the specific weight of the solid particles.
6) Compute the mass in motion, Gs, as gs b, where b is the
width of the flowing water, estimated as the flow of water,
Q, divided by the velocity, V, and the depth, D, all of
which are known.
The units of Gs are pounds per second, which multiplied by the length of
the time step in seconds, DELTR, yields the weight in pounds of bedload of
diameter d that could move from one junction to the next through the
connecting pipe being considered. Because in a sewer the bed is not without
limit as in a natural stream, the amount of material transferred from one
junction to the next in the model is actually Gs x DELTR or the amount
available in the bottom deposits that time step, whichever is smaller.
SUSPENDED LOAD TRANSPORT RELATIONSHIPS
As with bedload theory, a plethora of suspended load relationships now
exists. Indeed, suspended load transport appears to have received more
attention than bedload dynamics. But ASCE (1975) has said explicitly that
"it is still not possible to predict the sediment discharge of an alluvial
15
-------
stream with a degree of certainty that is satisfactory for most engineering
purposes." However, heeding that caution, we attempted to glean something of
value for the pipe problem at hand from the many investigations reported both
by ASCE (1975) and by Graf (1971).
Relationships Adopted
The basis for the treatment of suspended load in this study and virtually
all others has been the equation attributed to Rouse (Graf, 1971) for the
distribution of suspended sediment throughout the flow depth, namely:
C = C (j^-) [7]
y ay D-a L J
in which
Cy = the concentration of suspended particles at depth, y
in a flow of total depth, D, lb/ft3;
Ca = a reference concentration near the bed, lb/ft3;
a = the reference depth where Ca occurs, taken here
as 2d60, ft;
d = diameter of particles of which 60 percent are finer, ft;
= settling velocity of particles in quiescent water, ft/sec;
- von Karman "constant"; and
u^ = again, shear velocity Vgr^s, ft/sec.
The intent is to compute a mass rate of movement, gss, for suspended load,
analogous to the bedload mass rate, gs, from above:
D
9SS = / cy uy dy [8]
a
In this expression, gss is the mass of suspended load per unit width moving
in a unit time, Cy is the concentration computed from equation 7, Uy is the
velocity at depth y, and dy is a small interval of depth of which y is the
midpoint.
To solve equation 7, values of Ca and z must be found. Much of the work
reported by Graf (1971) and ASCE (1975) on suspended load transport has been
devoted to evaluation of these two parameters and k, which turns out to be
variable and not "constant" at all, although that complication was ignored in
this work after some deliberation.
16
-------
The value of Cq was estimated for each particle size from a relationship
given by Graf (1971):
\.6 u,
in which
u^' = shear velocity computed with a hydraulic radius with
respect to the grains of solids, v'g r^ ' s, ft/sec; and
a' = a reference depth, ft, essentially equal to a above.
The value of gs in this expression is the amount of bedload transport per unit
width for each particle size, computed earlier in step 5 of the bedload pro-
cedure.
To evaluate u*', it was necessary to estimate r^' , the portion of the
total hydraulic radius attributable to the grains. This was done with an
expression from Graf (1971) for velocity distribution which he attributes to
Einstein (1950):
Y* ' 3?
— = 5.75 log (12.27 — - ; [10]
u* Ks
in which V is the average velocity in the pipe, x is a correction factor for
wall effects, ranging from about 0.7 to 1.6 and equal to 1.0 for rough wall
conditions; and ks is the Nikuradse sand roughness height, approximately equal
to ^55. In this study, the value of x was taken as 1.0, and ks was taken as
d60 from before. Therefore, the expression used was:
T '
~ = 5.75 log (12.27 -^-) [11]
* 60
This equation and V - V can be solved iteratively for ^', since V is defined
by equation 11 and is also known from the Hydraulic Model solution, in which
the average velocity computed in each pipe is V. Note also that u*' was used
in equation 11 in place of u* in equation 10. In summary, r^' 1S found in the
new model by changing trial values of r^' until the following function becomes
very nearly equal to zero:
_ r '
F = V - 5.75 Jg r, ' s log (12.27 -~ ) [12]
60
in which V is the value of average velocity in the pipe computed in the
Hydraulic Model .
With this information, equation 9 can be solved directly for ca, which is
needed in equation 7. The value of z in equation 7 was computed from vs/k u.,.;
where vs was the settling velocity in still water for each particle size; u*
17
-------
was computed with the total hydraulic radius, Th\ and k was assumed to be
"constant" indeed and equal to 0.385 (Graf, 1971).
Values of Cy were computed at the midpoints of five equal intervals of
depth, from 0 to D. Values of uu were computed at each interval from velocity
distribution equations given by ASCE (1975):
uy = u, [5.5 + 5.75 log ^-]; RIQ = -*—$°-< 20 [13]
or
u = u, [5.5 + 5.75 log -^-]; R = * 6° > 10 [14]
y a6Q iu v
in which v is the kinematic viscosity of water (1.0877 x 10~5 ft2/sec at 20°C),
It was then possible to solve equation 8 numerically as:
g = Z (C u |j [15]
^ ss y y 5 L J
summing over the five depth intervals. As before, the total mass rate of
movement was then found by multiplying by width, Gss = gss * b, and the total
mass moved through the pipe in one time step was computed as Gss x DELTR.
Summary of Current Procedure
Lest the reader has become confused, the stepwise procedure used here for
computing suspended load is outlined below.
1) Compute u* = Jg T-, s
a = a' = 2 d
60
R n = u^ d /v (a Reynolds number)
k = 0.385
2} Compute r^ ' from
r n r /H ~f~ 7^->^ /"7O O7
h
F = V - 5.75 v'g r^' s log (12.27 ^—) = 0
60
3) Enter particle size loop and compute z = vs/k u*.
4) Compute Ca = g /(11.6 ^g *>h' s a')
5) Enter depth loop and compute
u* y -,
uy = Ujf [5.5 + 5.75 log —^- ] for
or
[5.5 + 5.75 log -^— ] for R > 10
ago iu
18
-------
6) Compute C from equation 7
\J
c = c (D-y a
y
7) Update g and end depth loop or return to step 5.
o o
8) Compute Gss = gss b
and weight of solids moved in the current time step as
suspended load in the current size fraction = Gss x DELTR.
9) Go forward to perform mass balance for total suspended
load moving in the pipe from one junction to the next or
return to step 3 for the new particle size and repeat.
WASHLOAD TRANSPORT RELATIONSHIPS
The only work known to the writer on the subject of transient washload
estimation is that by Rendon-Herrero (1974) in which the sediment discharge
rate is predicted hourly for rural watersheds. It is true that the Universal
Soil Loss Equation has been programmed into several models of watershed runoff
and used in a transient way, even calibrated in that mode. But that equation
was derived to predict average annual loads from a watershed, and its use in
dynamic runoff models has not been shown to be valid.
Moreover, the work of Rendon-Herrero (1974), which bears serious
consideration for use in a rural watershed runoff model, nonetheless is not
applicable in urban areas as it stands; and it only applies to conditions
occurring between the watershed boundary and the stream bank. It does not
treat transport in the stream itself (much less in pipes).
On the other hand, considerable work has been done on the water-carried
transport of bulk materials, such as coal, through pipelines. Graf (1971)
devotes an entire section of his book to these investigation. But while the
thrust of that work has been toward movement of solids without deposit,
precisely our definition of washload in pipes, its purpose has been to define
the head loss and related characteristics of the flow that must exist to get
the transportation problem solved. It has not been toward predicting a) when
material would become washload, or b) how much would move as washload,
suspended load, or bedload.
We did adopt one expression from that work, however. Graf (1971) reports
a relationship attributable to Durand (1953) for a critical velocity, V0,
separating deposit-free flow from the deposit regime:
= Fr, D6]
S2gD(Ss-l)
19
-------
in which
v = the critical velocity.
o
S = the specific gravity of the solids, taken as y /Y-
S 3
FT = a parameter ranging from 0.8 to 1.1 for particles
larger than 0.5 mm and for concentrations between
2 and 15 percent by weight.
~ L
In this study, a value of Fi equal to 0.9 was adopted, which is proper for
higher concentrations than normally would be encountered in sewers. A value
of 0.8 or even 0.7 would perhaps have been more appropriate. On the other
hand, in warning against use of this relationship too rigorously to separate
two regimes whose separation is gradual, Graf (1971) suggests using a conserv-
atively high "working" limit velocity, which is exactly what the value of
FL = 0.9 will produce. Hence that value is not inappropriate after all.
In any event, this expression can be solved for Vc, the "critical veloc-
ity," at which particles will not deposit. That is, their effective settling
velocity in the flow can be taken to be zero. At that flow velocity, all
particles entering the pipe with a specific gravity of 5? or less will
translate down the pipe with the water. At flow velocities less than VCi a
portion of the particles may be able to deposit. When the velocity of the
water approaches zero, the pipe will approach an ideal settling tank, and the
particles will be removed according to their settling velocity in quiescent
water and the detention time in the "tank." For flow velocities between
essentially zero and vc, it can be deduced that the effective settling or
deposit velocity of particles will be reduced from its theoretical, quiescent-
water value to zero. This information can be used as follows.
The proportion of particles that are removed in a horizontal -flow
sedimentation tank is (Fair & Geyer, 1963):
PART = L- M7]
where vs is the settling velocity in an ideal, quiescent tank, Q is the flow
through the tank, and As is the surface area of the tank. In this study the
surface area has been computed as b, the width of the flowing water, £imes the
length of the pipe. The flow, Q, is known from the solution in the Hydraulics
Model. If the average velocity down the pipe is very small, the effective
settling velocity is equal to vs; and a fraction of solids entering the pipe
in the current time period equal to PART times the total mass entering is
placed in the bed and is then available to be moved as bedload or suspended
load, or it may remain at rest. The fraction equal to l - PART is washload,
and this mass is moved from one end of the pipe to the other (from the upstream
junction to the downstream junction).
If the velocity of flow, v, is equal to or greater than vc, the effective
settling velocity is zero, and all the incoming solids in the particle size
under consideration are moved as washload to the next junction.
20
-------
For velocities, 7, between 0.01 ft/sec and vc, an effective settling
velocity is interpolated linearly between 0 and vs with the expression:
V - V
~— v [18]
Then the value of w is used for vs in equation 17, and the proportion of
solids removed is computed. Therefore, washload is computed as:
where WL^ is the washload in pounds in particle size group i moved through the
pipe in the time period, and TRANS-i represents the total solids in pounds in
particle size group i that enter the pipe from the upstream (up-gradient)
junction in the current time period. Deposition occurs in the model at this
point by placing the remainder of TRANSi in the bed. This is done prior to
computing either bedload or suspended load movement, and it is possible that
all the particles temporarily placed in the bed by virtue of their being
nonwashload are then moved in the same time period as suspended load and/or
bedload. These deposited materials cannot become part of the washload in the
same time period.
The washload procedure, therefore, follows the following steps:
1) Compute vs for each particle size.
2) Determine TRANSi from input runoff pollutographs and
dry weather sanitary inputs at the upstream junction.
3) Compute Vc from equation 16.
4) Compute w from equation 18.
5) Compute WL^ from equation 19 and return to step 1 for
next particle size or go forward to perform mass balance
for total washload moved in the pipe.
21
-------
SECTION V
THE NEW MODEL
The mathematical model used in this study is an adaptation and expansion
of WRE's version of the EPA Storm Water Management Model, known quite widely
as SWMM (pronounced "swim"). The original SWMM model (Metcalf & Eddy, et al.,
1971) has been applied, updated, and tested extensively (Huber, et al., March
1975; Heaney, et al., May 1975; DiGiano and Mangarella, 1975; Brandstetter,
1976). WRE has developed sewer transport quantity and quality portions of its
own for use in the SWMM package (which simulates watershed runoff and
receiving water behavior as well) or to be used separately. The WRE
version(s) of SWMM have been used in Seattle, San Francisco, and Hamburg, West
Germany. This set of models has been reported in several places as well
(Kibler, et al., 1973; Kibler, Monser, and Roesner, 1975; Water Resources
Engineers, July 1974; Shubinski and Roesner, 1973). The model is available
from EPA and WRE's other clients, all of whom are public agencies. Therefore,
a full documentation of the model will not be repeated here. Nonetheless, a
general, overall description of the WRE Transport Block of the SWMM model is
given below.
THE "OLD" MODEL
Overview
The WRE Transport Block is comprised of a quantity section, called the
Hydraulics Model, and a quality section or Quality Model. These are separate
programs. The Hydraulics Model simulates behavior of flows and heads
throughout a pipe network over time and stores the resulting values on tape.
These same tapes are then read, along with other card input data, by the
Quality Model, which adds and transports or routes masses of various constit-
uents along with the quantities of water and in response to the head differ-
ential computed in the Hydraulics Model.
The Hydraulics Model
The Hydraulics Model uses a link-node description of a sewer system.
Flows are computed in links, which are the pipes; and heads are computed at
nodes, which are the major pipe junctions. Actually nodal volumes are taken
as the volumes of all the half-pipe lengths connected to a node.
Links transmit flow from node to node. Properties associated with links
are roughness, depth, length, cross-sectional area, hydraulic radius and
surface width. The last three properties are functions of the instantaneous
22
-------
depth of flow. The primary dependent variable in the links is the discharge,
Q, which is time dependent. Velocity and cross-sectional area of flow, or
depth, are also variable with time. Thus the flow condition in a link over
a period of many time steps can be both nonuniform and unsteady.
Nodes or junctions are the storage elements of the model and correspond
somewhat to manholes or pipe junctions in the physical system. The properties
associated with a node are volume, head, and surface area. The primary
dependent variable is the head, H, which is assumed to be changing in time
but constant throughout a single computational time step. Inflows, such as
inlet hydrographs, and outflows such as weir diversions, take place at the
nodes of the idealized sewer system. The change in nodal volume during a
given time step, At, forms the basis of the head and discharge computations.
The equation for describing unsteady flow in a link can be written as:
3Q ,a , OT/ ZA T_2 94 . 9ff r9(V]
3t = - gASf + 2V U + V 9L - gA 9L [20]
The continuity equation for a node is:
9t = T~s
The essence of the Hydraulics Model is to solve these two equations
simultaneously, wherein the terms are:
Q = discharge through a conduit or link, ft3/sec;
V = velocity in the link, ft/sec;
A = cross-sectional area of the link flow, ft2;
L = length of a link or pipe section, ft;
Sf - the friction slope, ft/ft;
H = hydraulic head, ft;
g = acceleration due to gravity, ft/sec2;
As = water surface area associated with a node, ft2; and
ZQ = algebraic sum of the conduit flows entering or leaving a node,
ft /sec.
The friction slope is defined by the Manning equation, i.e.,
s = k Q\V\
23
-------
where k is an empirical coefficient equal to gn2 in the S.I. system, n_being
the Manning roughness coefficient. In the U.S. Customary system of units:
an
*2-
- — - - rr-
(1.486)*
32.2
-
2.208
Yl
2
=
-, *
= 14
-
which is the system used in the current model. The value of Q in the friction
slope equation is the value at the end of the time step,
The finite difference forms of equations 20 and 21 used in the model
become equations 22 and 23:
A?-A Hp-H
+ 2V M. + V2 T At - gA T
Li L
At
[22]
The values of v, r^, and 4 in equation 22 are the weighted average values at
the two ends of the conduit at time, t. The subscript 1 refers to the
upstream junction, and the subscript 2 refers to the downstream junction.
The second equation is:
[23]
Solutions of equations 22 and 23 are performed by a Modified Euler Method to
yield discharges in the links and heads at the junctions at time, t-fAt.
In addition, the Hydraulics Model detects and accounts for numerous
special flow conditions (dry pipes, critical depth occurrences, etc.),
surcharge and flooding, and the presence of certain flow control devices such
as weirs, orifices, and pump stations, and outfall devices such as tide gates.
The Quality Model
The Quality Model is an advective model which transports individual
constituents by advective movement in each conduit. Input masses to be
transported are added at junctions. Masses of constituents in runoff from
the watershed may be read from a tape generated by a runoff model or cdfnputed
from hydrograph flow and concentration values read from cards. The dry
weather masses of constituents are read from a tape generated in the
Hydraulics Model.
The differential equation describing advective transport of quality
constituents in a sewer system can be given in either of two forms:
1) Mass rate of change:
at
[24]
24
-------
whe re
M = mass, Ib;
C = concentration, lb/ft3;
Q = flow rate, ft3/sec; and
t = time, sec.
or
2) Concentration rate of change:
c
VOL
in which FOL is the volume of the node or junction in ft3.
These equations are interchangeable, and some aspects of both are used in the
numerical solution.
The conceptual representation of advective transport in the version of
the model_adapted here is shown in Figure 3. Link or conduit N with a mean
velocity V connects nodes 1 and 2, which have constituent concentrations c|
and c|, respectively at time t. During time interval At, the concentration
gradient moves at velocity V, so that it is in the position shown by the
dashed line at time t+ht. The value C, which was a distance W\t away from
node 2, becomes the new concentration at node 2, £<; * . This process is
repeated for all links and nodes at time t+ht, and the sequence is repeated
for all time steps in the simulated period. (When the concentration gradient
is positive in the direction of flow, the upstream value of C*| is used as the
new concentration downgradient, C~^+^.} The version of the model adapted in
this study simulated BOD, coliforms, and suspended solids in this way. The
major alteration made in this study was to route solids somewhat differently,
as described later in this chapter.
NEW ROUTINES
As indicated earlier, no new subroutines were added to the Hydraulics
Model, although certain changes had to be made to some of the existing
routines. These are discussed later in this chapter under "other changes."
The four new separate routines added to the entire package were all added to
the Quality Model. Their addition gives the new version of the WRE Transport
Block a new kind of capability and generally a new thrust, which is discussed
immediately below. Following that, each of the new routines is described in
some detail .
25
-------
NODE 1
NODE 2
Figure 3
Advective Transport Concept in the Quality Model
-------
The New Overall Capability
Previously, the WRE Transport Block was a simulation tool for analyzing
the hydraulic and quality changes in completely mixed flows in sewer systems.
A subroutine from the EPA SWMM package had been incorporated to determine when
a deposit regime existed and when a scour regime existed. This routine
removed solids from the flow during the deposit regime and added solids to the
flow during the scour regime; but the resulting masses in suspension were
moved conservatively with the water as described earlier, and no net accumu-
lation of material on the pipe bottom was computed.
With the additions made in this project, the model now simulates solids
behavior more precisely, it can be used to evaluate the costs of alternative
systems of pipes and treatment plants, and it gives detailed reports of the
status of the pipe-plant system with respect to solids throughout the simu-
lated period. The model can now be used to analyze such questions as:
1) What are the effects of alternative physical configurations
of conduits and treatment on the solids entering and leaving
a sewer system, separate or combined, and what are the costs
of the alternative systems?
2) In a given situation of new construction, what are the cost
and solids removal consequences of using storm and sanitary
sewers vs. a combined system?
3) What are the effects of conduit shapes, sizes, and slopes on
solids build-up and eventual scour?
4) What are the effects on construction and operation costs
resulting from use of various combinations of pipe slope,
pipe shape, treatment type, treatment distribution, and
treatment capacity? What will be the alternative removal
percentages of solids, both through treatment alone and in
the overall sense including net deposition during the
simulated design period?
Table 1 summarizes the overall capabilities and limitations of the WRE
Transport Block.
The model now simulates the transport, deposition, and scour of solids
in up to ten different particle size ranges, whose representative diameters
are read as input. Particles in each size group are assigned a fixed
percentage of the size distribution for sanitary inflows. These separate
distributions, percentage wise, are not changed with time. However, composite
size distribution is recomputed in each time step, and a weighted specific
weight of the solids in each size group is then determined for that time. The
specific gravities of each sized particle in dry weather flow must be given,
and the specific gravity of each particle size in inflow hydrographs must be
given. The Quality Model then routes the composite masses in all ten particle
sizes either as washload, bedload, or suspended load, and keeps track of net
deposition to or scour from the bottom deposits in each pipe. The other two
27
-------
TABLE 1. NEW TRANSPORT BLOCK CAPABILITIES AND LIMITATIONS
PIPES OR CHANNELS
Number
Flow Characteristics
Shapes
Costs
JUNCTIONS
Number
Storm Inflows
Sanitary Inflows
Controls
TREATMENT PLANTS
Number
Sizes
Types
Costs
OPERATIONAL CHARACTERISTICS
Time Step
Computer Storage
Maximum of 100, including up to 60 weirs, 60
orifices, 25 free outfalls, or 20 multi-stage
pumps
Branched or looped systems, tidal and nontidal
backwater, normal flow
Circular, basket-handle, egg-shaped, horseshoe,
rectangular, trapezoidal, cunette sections (3)
Construction, operation, and total annual costs
computed in Hydraulics Model
-- Maximum of 100
-- Read from runoff model tape or from cards
-- Computed in Hydraulics Model as functions of
land use
-- On-line or off-line storage, tide gates,
location of surcharged nodes
Maximum of 20
Any size, specified as design flow in ft3/sec.
(Flow through plant computed each time period;
never exceeds design capacity—excess is
overflow.)
Sedimentation basins, swirl concentrators, sand
filtration, primary treatment, secondary
treatment
Construction, operation, and total annual costs
computed in Quality Model
Hydraulics: usually less than one minute--
should be about 15 to 30 seconds
Quality: an even multiple of hydraulic time
steps—usually the average L/V
64,000 words
LIMITATIONS
With the exception of pump facilities, the Hydraulics Model is gravity
controlled. Pressurized flow in conduits is not simulated. Also,
hydraulic jumps within the system are not simulated.
BOD and coliforms are simulated as conservative, nondecaying constit-
uents. Also, no linkage is made between BOD and solids concentrations;
and the treatment simulated removes only solids, not BOD or coliforms.
28
-------
constituents in the Quality Model, BOD and coliforms, are still routed as
described earlier and depicted in Figure 3.
The new version of the Transport Block has been limited in one respect
over the older version, in that only 100 pipes and 100 junctions can be
included in a single simulation. Previously, up to 230 junctions and 320
pipes were permissible. It was necessary to reduce these dimensions
throughout to accommodate new scour and deposition variables that require
storage locations, although 100 may not be the true upper limit.
The four new subroutines of the Quality Model are listed in Appendix A
of this report. They are described immediately below. Complete lists and
card image tapes of both models have been supplied to EPA's Storm and
Combined Sewer Section, Edison, New Jersey; and they are available from that
source.
A Subroutine for Settling Velocities
In the main program of the Quality Model, in the major loop of time steps
and just following the input of new masses at system junctions, the subroutine
SETVEL (for "settling velocities") is called to compute the theoretical values
of settling velocity in quiescent water.
The methods used in the subroutine and reported here have all been taken
from Fair & Geyer (1963).
The subroutine is entered with the diameter of each particle size in
feet, d, the weighted specific weight of the solids in that size group, js,
the specific weight of water, y(62.4 lb/ft3), the kinematic viscosity, v, and
the acceleration of gravity, g. The purpose of the subroutine is to determine
the settling velocity vs, given that the Reynolds number may be in either the
turbulent, transitional, or laminar (Stokes) range—which must be determined.
The subroutine first solves the general expression for settling velocity
given by Fair & Geyer (1963):
v = J4 gd rys-YT [26]
3 2 CD y
using a value of the drag coefficient, CD, equal to about 0.4, which applies
if the motion is in the turbulent range of Reynolds numbers (i.e., greater
than 3000). So the first calculation is for Reynolds number R, to see if it
is greater than 3000:
v d
R = -V [27]
and if it is, the value of vs must be correct and control returns to the main
program.
29
-------
If the calculated R is less than 3000, the turbulent condition does not
exist, and the trial values of CD and vs must therefore be corrected. Conse-
quently, it is assumed next that the settling condition would be in the
transitional range of Reynolds numbers (taken as 0.1 to 3000), wherein the
drag coefficient can be computed from:
CD = — + - + 0.34 [28]
This leads to an iterative solution for vs, since equation 26 requires CD
and equation 28 requires R, which requires ug.
So the subroutine attempts first to find a reasonable first trial value
of CD (is it near 1.0, 10, 200?), and having done so it begins an iterative
solution via Newton's method to balance the expression:
v - r
F ~ °D ~
24v
(
(
v
vsd
0 . 5
) - 0.34 =
By this method, the correction to CD to be made each time period is:
CD =
-F
dF/dCD
[29]
[30]
The value of dF/dCD from equation 29, to be used in equation 30, equals unity,
so the correction each time is -F. In each iteration, a new trial value of
vs is computed with equation 26 and the latest value of CD- When closure of
the function in equation 29 is within .5 percent of the latest value of CD,
the latest trial value of vs is deemed acceptably accurate, and control
returns to the main program.
The remaining possibility is that the settling motion of a particle of
this size with this specific weight would be in the laminar range of Reynolds
numbers (taken as less than or equal to 0.1). In this case, the subroutine
uses equation 26 to compute vs with the value of Cp taken as 24/R, where R is
the last trial value in the transition range, whicn by this time must be equal
to or less than 0.1. Having completed this task, the subroutine returns
control to the main program, which either returns again with a new particle or
goes forward to other matters.
The Subroutine for Scour, Deposition, and Solids Transport
The most significant changes made in this project to the Quality Model
are embodied in the subroutine called SCRDEP (for "scour and deposition"),
which performs the solids routing. This subroutine is called from the main
program just following the advective transport of the other constituents,
BOD and coliforms.
The subroutine listing in the Appendix should be fairly simple to follow
since the names of variables are either the same as the variable names given
in Section IV or they are fairly obvious mnemonics, and since the procedure
30
-------
followed is comprised of a small number of separable steps. Those steps
follow this sequence:
1) Update the mass of total solids of size, ISZ, in potential
motion at each junction, J", in the current time period.
This quantity is SED(J3ISZ) . It is equal to the amount
present at the junction in the last time period plus the
mass added from hydrographs and sanitary inputs in this
time period:
SED(J}ISZ) = SED(J,ISZ) + MASSIN(J,2) *SPER(J,ISZ) [31]
in which SED(J,ISZ) on the right-hand side is the value at
the end of the last time period, MASSIN(J.,2) is the mass
of all solids added to the junction in the current time
period from external source (the 2 is the constituent
counter signifying solids), and SPER(J,ISZ) is the fraction
of the total mass entering the junction with size, ISZ.
2} Enter pipe loop and compute various "constants" for the
time period, such as width b, hydraulic slope s, shear
stress T , and shear velocity u^.
3) Determine if treatment is to be applied at the downstream
end of the current pipe. If it is, compute the fraction
of washload, bedload, and suspended load to be removed
there as a function of the treatment process, the capacity
of the plant, and the average flow in the pipe during the
current time step.
4) Compute the hydraulic radius due to the grains, r^' (called
RG in the subroutine), as described in Section IV.
5) Enter particle size loop and compute mass of solids in size
ISZ that moves into pipe N from junction j in the current
time period. This quantity is:
TRANS(ISZ) = SED(J,ISZ) , \QAVE(N)\DELTR [32]
VOL (J)
in which QAVE(N) is the flow in pipe N, away from junction
J. Also compute the mass then in pipe N available for
movement, AVAIL(ISZ), which is equal to TRANS(ISZ) plus
the amount in the bed, BED(N^ISZ), from the last time step.
Next compute the effective settling velocity W, from
Durand's expression for critical nondeposit velocity and
the quiescent water value as described in Section IV.
6) Compute washload mass translated down the pipe WL. Place
the remainder of TRANS(ISZ) in the bed (BED = BED + OTHER),
and remove that amount from the particles in motion at the
upstream junction (SED(J,ISZ) = SED(J,ISZ) - OTHER). Add
31
-------
the translated washload, less any removed by treatment, to
the downstream junction, k:
SED(K,ISZ) = SED(K3ISZ) + WL(ISZ). * (1-R1) [33]
where Rl is the fraction of material removed by treatment
at the end of pipe N.
7) Compute the bedload transport rate per unit width, GS, as
described in Section IV.
8) Compute the suspended load transport rate per unit width,
GSS, as described in Section IV.
9) Conduct the sediment balance in mass terms for bedload
and suspended load, limiting the amount that can be moved
to AVAIL(ISZ) , regardless of the sizes of GS*B*DELTR and
GSS*B*DELTR.
10) End pipe loop and compute the concentrations at the
junctions at the end of the time step as:
10
C(J,2) = I SED(J.ISZ) /VOL(J) [34]
ISZ=1
11) Return to main program and prepare for printing output.
Figure 4 depicts the basic routing process being used in the model. It
might be noted that the bedload is computed prior to suspended load, primarily
because GS is needed to compute GSS; but also that both suspended load and
bedload are subtracted from the stationary bed. Suspended load is not
subtracted merely from bedload, which is in motion. This may appear to be
contrary to what we defined suspended load to be in Section IV, namely
particles derived solely from bedload.
This ambivalence occurs because if material leaving bedload to become
suspended load is immediately replaced by more material from the bed moved
into the bedload., then the distinction is academic. No difference in result
occurs. If material moved from bedload into suspended load is not replaced in
the same time period by material from the bed, then the potential for bedload
transport, GS, must be effectively reduced. This seems contrary to the
theoretical arguments, since the factors that determine GS, namely u^, d,
i0, (i0)Cr> and YS remain constant throughout the time period. Bluntly
stated, then, this issue, if it is one, needs more consideration by other
scientists; and the dichotomous approach taken here appeals for that.
A Subroutine for Reporting Intermediate Solids Behavior
A relatively short subroutine called SCROUT (for "scour output") has been
added to print information on the state of the system with respect to solids
during the simulation. Currently this subroutine is called at the first time
32
-------
CO
CO
SED/TAl =
SEDf-PART* TRANS
(/- PART; x TRANS
GS x DELTR = BL
GSS x DELTR = SL
SED
+ WL
SED.
8L
Figure 4
Transport Concept for Solids in Subroutine SCRDEP
-------
period, every hour thereafter, and at the last simulated time period. The
information printed includes the following for each time period:
1) The "suspended solids" concentration in mg/1 at each
junction by size group, SED(J,ISZ)/VOL(J), and for all
size groups, C(J,2). (The value 0.00006242 in SCROUT
converts pounds per cubic foot of water to mg/1.)
2) The pounds of solids remaining on each pipe bottom by
size group.
3) The total pounds added to each pipe ("this" time).
4) The total pounds leaving each pipe.
5) The total pounds removed by treatment from each pipe.
6) The total pounds remaining on each pipe bottom.
7) The total pounds deposited on each pipe bottom ("this" time).
8) The total pounds scoured, including bedload and suspended
load, in each pipe ("this" time).
Example output reports from this subroutine are shown in Figures 5 and 6,
A Subroutine for Summarizing Treatment Behavior and Cost
The subroutine TREAT (for "treatment") is called after all time steps
have been completed. It has four functions:
1) Prints a summary by treatment plant of the capacity,
removal percentages (fractions really) of washload,
suspended load, and bedload, and the amounts of each
removed over the entire period simulated.
2) Prints an overall summary of the system with respect
to pounds of solids entering and leaving the system,
and those remaining on the bottom of conduits.
3) Computes the construction and operating costs of
each treatment plant.
4) Prints a summary of costs for each treatment plant.
Samples of the three kinds of output are given in Figures 7, 8, and 9.
The only computations of new information made in this routine are those
for treatment plant costs. (Pipe costs are computed in the Hydraulics Model
and are discussed later in this chapter under "other changes".)
34
-------
TIME = 36000.
SUSPENDED SOLIDS CONOS. AT EACH JUNCTION BY SIZE GROUP (ISZ)—MG/L
JUNC
1
2
3
4
5
ISZ=1
20.9
15.6
14.3
.0
.0
ISZ=2
20.9
16.7
14.4
.0
.0
SOLIDS DEPOSITED ON
PIPE
1
2
3
4
5
ISZ=1
.00
.00
.00
.00
.00
ISZ=2
.00
.00
.00
.00
.00
ISZ=3
20.9
15.9
15.3
.2
.1
PIPE BOTTOM
ISZ=3
51.70
.00
9.01
.00
.00
ISZ=4
20.9
15.1
14.9
.2
.1
AT END
ISZ=4
65.59
54.81
113.97
.00
.00
ISZ=5
20.9
14.9
14.9
.2
.1
OF TIME
ISZ=5
68.36
59.34
118.53
.00
.00
ISZ=6
20.9
14.7
14.9
.2
.1
STEP BY
ISZ=6
70.73
63.78
121.35
.00
.00
ISZ=7
20.9
14.7
14.8
.2
.1
SIZE (ISZ)
ISZ=7
72.51
66.91
124.33
.00
.00
ISZ=8
20.9
14.6
14.8
.2
.1
---POUNDS
ISZ=8
73.52
69.91
127.08
.00
.00
ISZ=9
20.9
14.6
14.8
.2
.1
ISZ=9
74.13
72.50
129.26
.00
.00
ISZ=10
20.9
14.6
14.6
.2
.1
ISZ=10
74.67
77.21
132.20
.00
.00
TOTAL
209.2
151.4
147.7
1.5
.9
Figure 5
Example Output by Particle Size
-------
TIME = 36000.
PIPE NO. = 1 IBS ADDED TO PIPE THIS TIME = 12.4
IBS LEAVING PIPE THIS TIME = .8
LBS REMOVED BY TREATMENT, IF ANY = 5.8
IBS REMAINING IN PIPE ON BOTTOM = 551.2
LBS DEPOSITED THIS TIME, IF ANY = 12.4
LBS SCOURED THIS TIME, IF ANY = 6.5
NET LBS SCOURED(-) OR DEPOSITED(+)
--NOT INCLUDING WASHLOAD
PIPE NO. = 2 LBS ADDED TO PIPE THIS TIME = 19.4
LBS LEAVING PIPE THIS TIME = 3.9
LBS REMOVED BY TREATMENT, IF ANY = 24.8
LBS REMAINING IN PIPE ON BOTTOM = 464.5
LBS DEPOSITED THIS TIME, IF ANY = 19.4
LBS SCOURED THIS TIME, IF ANY = 28.7
NET LBS SCOURED(-) OR DEPOSITED(+)
--NOT INCLUDING WASHLOAD = -9.2
" PIPE NO. = 3 LBS ADDED TO PIPE THIS TIME = 40.9
LBS LEAVING PIPE THIS TIME = .5
LBS REMOVED BY TREATMENT, IF ANY = 66.2
LBS REMAINING IN PIPE ON BOTTOM = 875.7
LBS DEPOSITED THIS TIME, IF ANY = 39.6
LBS SCOURED THIS TIME, IF ANY = 65.4
NET LBS SCOURED(-) OR DEPOSITED(+)
—NOT INCLUDING WASHLOAD = -25.8
PIPE NO. = 4 LBS ADDED TO PIPE THIS TIME = .4
LBS LEAVING PIPE THIS TIME = .4
LBS REMOVED BY TREATMENT, IF ANY = .0
LBS REMAINING IN PIPE ON BOTTOM = .0
LBS DEPOSITED THIS TIME, IF ANY = .0
LBS SCOURED THIS TIME, IF ANY = .0
NET LBS SCOURED(-) OR DEPOSITED(+)
—NOT INCLUDING WASHLOAD = .0
Figure 6
Example Output by Pipe
-------
PLANT NUMBER 1 AT END OF PIPE 1
DESIGN FLOW = 100.0 FT3/SEC
WASHLOAD REMOVAL PERCENTAGE = 1.0
SUSPENDED LOAD REMOVAL PERCENTAGE = .9
BEDLOAD REMOVAL PERCENTAGE = .9
WASHLOAD REMOVED DURING EVENT = 43.LBS
SUSPENDED LOAD REMOVED DURING EVENT = 1000. LBS
BEDLOAD REMOVED DURING EVENT = 31 76. LBS
TOTAL LOAD REMOVED DURING EVENT = 4220. LBS
PLANT NUMBER 2 AT END OF PIPE 2
DESIGN FLOW = 150.0 FT3/SEC
WASHLOAD REMOVAL PERCENTAGE = 1.0
SUSPENDED LOAD REMOVAL PERCENTAGE = .9
BEDLOAD REMOVAL PERCENTAGE = .9
WASHLOAD REMOVED DURING EVENT = 53. LBS
SUSPENDED LOAD REMOVED DURING EVENT = 1673. LBS
BEDLOAD REMOVED DURING EVENT = 5485. LBS
TOTAL LOAD REMOVED DURING EVENT = 7210. LBS
PLANT NUMBER 3 AT END OF PIPE 3
DESIGN FLOW = 32.0 FT3/SEC
WASHLOAD REMOVAL PERCENTAGE = 1.0
SUSPENDED LOAD REMOVAL PERCENTAGE = 1.0
BEDLOAD REMOVAL PERCENTAGE = 1.0
WASHLOAD REMOVED DURING EVENT = 472. LBS
SUSPENDED LOAD REMOVED DURING EVENT = 2662. LBS
BEDLOAD REMOVED DURING EVENT = 71 62. LBS
TOTAL LOAD REMOVED DURING EVENT = 10296. LBS
Figure 7
Example Output by Treatment Plant
-------
CO
CO
* * * OVERALL SYSTEM SUMMARY * * *
POUNDS OF SOLIDS ON BOTTOM AT BEGINNING OF EVENT
POUNDS OF SOLIDS ON BOTTOM AT END OF EVENT
POUNDS ENTERING THE SYSTEM DURING THE EVENT
POUNDS DISCHARGED FROM SYSTEM DURING EVENT
(CHECK VALUE)
POUNDS REMOVED BY TREATMENT DURING THE EVENT
NET POUNDS SCOURED(-) OR DEPOSITED(+) IN EVENT
NET POUNDS REMOVED (DEPOSITION + TREATMENT)
OVERALL PERCENTAGE REMOVAL
0.
2147.
27605.
3731.
3732.)
21725.
2148.
23873.
86.5
Figure 8
Example Output for Entire System
-------
SUMMARY OF TREATMENT COSTS
(PIPE COSTS FROM TRANSPORT MODEL MUST BE ADDED)
TREATMENT TREATMENT CONSTRUCTION ANN. CONS. ANN OPER. TOTAL ANN.
PLANT NO. TYPE COST, DOLLARS COST, $/YR COST, $/YR COST, $/YR
1 3 234551. 16419. 3262. 19680.
2 3 292554. 20479. 3691. 24170.
3 4 726223. 50836. 12327. 63162.
TOTALS 1253328. 87733. 19280. 107013.
Figure 9
Example Output of Treatment Costs
-------
The cost equations used in subroutine TREAT have been derived from two
sources (Gulp, Wesner, and Gulp, 1976; Montgomery-WRE, 1974), and these
sources gave general relationships for cost versus plant capacity. Conse-
quently, the cost relationships reported here are worthwhile for preliminary
planning purposes only. However, the equations used have been generalized
such that only the coefficients, which are read as data, might have to be
altered from application to application.
In any event, the cost equations used are as follows
equation is:
DOL
m
= ACC-, X QDES
The capital cost
[35]
where
DOL
'm
ACCk
QDES,
m
BCCk
the construction cost of plant number, m;
a coefficient for plants of type, k;
design capacity of plant m, ft3/sec; and
an exponent for plants of type, k.
The annual operation and maintenance cost is computed with a similar
equation that uses the average amount of water treated rather than the design
capacity.
DOLY
m
[36]
in which
DOLY,
m
OM21<} etc.
OB2kj etc.
QTRT
m
annual operating cost for plant m, $/yr,
coefficients for plants of type, k;
exponents for plants of type, k; and
average annual flow through the plant,
ft3/sec., taken here as the minimum of
QDESm and the largest QAVE(N) attained
in the pipe upstream of the plant at any
time during the simulated period.
Values of the coefficients and exponents for the various kinds of
treatment considered are shown in Table 2.
OTHER CHANGES TO THE TRANSPORT BLOCK
The two major changes made in this project other than the new subroutines
in the Quality Model were the addition of conduit cost calculations in the
40
-------
TABLE 2. TREATMENT COST COEFFICIENTS AND EXPONENTS
Treatment
Type
None
Sedimentation
Swirl Cone.
Filtration
Primary
Secondary1*
1OM32
2OM13
3OM3A
k
1
2
3
4
5
6
ACC BCC OM1
( N 0
111,749 0.8725 1,202
19,065 0.545 --2
76,919 0.6478 656.5
345,000 0.85 29,600
322,570 0.8184 36,570
Values for
5
712
349
2,940
OBI
DATA
0.222
0.273
0.2275
0.690
0.5258
Various
10
1,160
788
5,310
OM2
R E Q U
1.65
0
8.43
0
0
Overflows
20
2,100
1,369
9,150
OB2 OM3 OB3
I R E D )
0.933 --1 0.778
0 00
0.903 — 3 0.100
0 00
0 00
per Years
30
3,220
1,944
15,430
OM4
0
1,760
0
0
0
^Construction and operations costs for secondary treatment must be added to costs
computed for primary treatment.
-------
Hydraulics Model and the addition of capability throughout both models to have
cunette sections in conduits.
Conduit Cost Equations
Pipeline costs are computed and printed in the INDATA (for "input data")
subroutine of the Hydraulics Model. The cost equations used were derived
from those reported in the Seattle RIBCO study (Water Resources Engineers,
December 1974).
The cost equations taken from the Corps of Engineers study in Seattle
(Water Resources Engineers, December 1974) were for the cost per foot of
circular "Class V concrete" pipe, and an ENR index of 1450. In this study
the equations have been altered to account for different shapes and for an
ENR index of 2000 (which may now be generally too low).
The old equations for cost in dollars per foot of circular pipe were:
$/ft = 0.586 DIAM2'25 z°'118 Z < 12' [37]
and 7 7^ n 4^
$/ft = 0.246 DIAM1-1* Z Z > 12' [38]
in which
DIAM = diameter of circular pipe in inches, and
Z = feet of required excavation.
The equations as used in the model were updated for an ENR index of 2000, then
increased by 25 percent to include cost items explicitly not included in the
old equations, and given a coefficient to account for higher costs associated
with constructing conduits of irregular shapes. The equations for cost in
dollars are now:
DOL = ACOF, X DIAM1'25 z°'228 LEN Z < 12'
k n
and
DOL = 0.42 ACOFk X DIAM1'25 Z°'45 LENn Z > 12'
in which
ACOFfc = a coefficient to increase cost for noncircular pipes,
LENn = the length of conduit n in feet, and
DIAM = the diameter in inches of equivalent circular pipe
(computed from the cross-sectional area of the full
conduit).
The values of the coefficient ACOFk used in the model are as follows:
1) Circular pipe--!.0
2) Rectangular pipe--2.0
42
-------
3) Horseshoe pipe--!.5
4) Eggshaped pipe--1.5
5) Baskethandle pipe--!.5
6) Trapezoids--2.0
7) Circle with semi-circular cunette--!.25
8) Circle with rectangular cunette--!.25
9) Rectangle with rectangular cunette--2.0
These values were our own estimates, although construction cost information
for only one noncircular shape (type 7) were available for corroboration.
The operation and maintenance costs were estimated as 0.5 percent per
year of the construction cost (Montgomery-WRE, 1974). The cunette section
operating costs were reduced by 50 percent from that estimated simply because
they are supposed to be more self-cleansing by definition, and hence require
less maintenance (cleaning).
The Hydraulics of Cunette Sections
Throughout both the Hydraulics Model and the Quality Model some
additional computations were programmed to account for the three new cunette-
shaped cross-sections.
In the former programs the values of hydraulic radius, surface width, and
cross-sectional area were computed from ratios of these properties at 25 depth
intervals to those same properties at full flow. The values of the ratios
were built into the programs. The precise values were found by interpolation
between the two values in the table bracketing the computed depth.
Now, in the updated programs, these tabulated ratios are still used when
the flow is in the cunette of a cunette-shaped conduit. The computations at
these depths are equally as precise as before.
When the flow is above the cunette, that is in the large barrel, the
cross-section is changed to a regular circle or rectangle having a full
cross-sectional area equal to the full cunette-large-barrel section, and the
built-in tables are used as before to find the hydraulic radius, surface
width, and cross-sectional area at the less than full depths. This approxi-
mation can result in inaccurate computations of velocity when the flow is
just barely above the top of the cunette in the large barrel. When flow is
considerably above the cunette, this approximation works fairly accurately.
In the example cases reported subsequently, no problems arose as a result of
this simplification.
To avoid this inaccuracy, the programs could be altered to compute the
geometric properties of the cunette sections exactly. The alternatives are
43
-------
a) to recompute the properties from geometric relationships in each time
period, which we felt would require too much computer time; b) compute and
save a tabulated set of depth-to-property ratios in each simulation for each
cunette section in the system being studied, which we predicted could require
excessive storage; or c) build a single table of ratios of depth to other
geometric properties, assuming all cunettes and large barrels would have
relative dimensions that were constant, which we simply did not want to do.
The three shapes and the variables that define their dimensions are
shown in Figure 10. The value of STEETA is dimension!ess and is the ratio of
the cunette-to-large-barrel depth. This value should probably be equal to or
less than 0.25. The value of SPHI is given in feet, and must simply be
smaller than WIDE. These values are read in the Hydraulics Mode! on a card
that defines the length, Manning's n, and other properties of each conduit.
44
-------
TYPE 7 CONDUIT
DEEP = WIDE
STHETA X DEEP
TYPE 8 CONDUIT
SPHI
DEEP = WIDE
STHETA X DEEP
TYPE 9 CONDUIT
SPHI
WIDE
DEEP
STHETA X DEEP
Figure 10
Three Conduit Shapes Added to WRE-SWMM Model
45
-------
SECTION VI
RESULTS FOR EXAMPLE PROBLEM
It should be stressed at the outset that although the former Transport
Block has been used numerous times to simulate real pipe networks, the new
scour and deposition features have only been executed with the hypothetical
examples that follow. The new versions of the programs have not been verified
with field data.
Nonetheless, a number of simulations have been made to check the execu-
tability of the new programs, and some predictable or explainable results have
ensued. These simulations are reported below.
THE HYPOTHETICAL PROBLEM
The setting for the example cases analyzed in this study is shown in
Figure 11. There are assumed to be three subareas in series having the
characteristics noted in the Figure. (These data are used in computing the
dry-weather quantities and qualities in the Hydraulics Model.) The question
is: What type and size of sewers would make the most sense, considering
factors such as cost, quantities of stormwater and sewage to be handled,
treatment options available, and physical conditions such as slope and land
area?
Example simulations were made to show the results achieved with
different slopes, sizes, and shapes of conduits, storm and sanitary sewers,
a single combined sewer, and various levels of treatment installed at various
locations.
The particle sizes of solids and their fractional portions in storm
runoff and dry-weather sanitary flows were held constant for all the "cases
examined. The particle size distributions used are given in Table 3 and are
plotted in Figure 12. The specific gravity of all particles in storm runoff
was given as 2.65. All particles in sanitary flows were given a specific
gravity of 1.20. It might be noted, however, that each size in each of the
two sources can be assigned a different specific gravity. The particle size
distribution and the specific gravities used here were those used by Sullivan
and his coworkers (Sullivan, et al.} 1974) in their study of swirl concen-
trators.
46
-------
SINGLE- FAMILY RESIDENTIAL
$50K HOMES; SSOK/YR INCOMES SUBARtA I
1280 ACRES; 4 PEOPLE /ACRE
1350 D.U. ; 3.8 PEOPLE /D.U.
D.U. = DWELLING UNIT
SINGLE -FAM. RES.
§ 50 K; §25K/YR
1280 AC. ; 4 PEOPLE/AC.
2021 D.U. ; 3.8 PEO./D.U.
|
MULT) -FAM. RES.
$35 K ; $20K/YR
1280 AC. ; 12 PEG. /AC.
4042 D.U. ;3.8PEO./D.U.
1
, ,_
10
/or \
r i
20
L/or \J
r i
30
SUBAREA H
1
r
SUBAREA ZLI
2
A/>
r
^X DWF
o
/•<> RUN
/^\ STO
RUNOFF INFLOWS
STORM OR COMBINED
SEWER JUNCTION
SANITARY SEWER
JUNCTION
1,10 CONDUIT NUMBERS
NORMAL CONDUITS
OUTFALLS
TREATMENT LOCATIONS
(ends of conduits )
Figure 11
Example Pipes and Watersheds for Model Demonstration
47
-------
100
o
UJ
OQ
(t
UJ
UJ
O
cc
LU
Q.
80
60
40
20
0
RUNOFF PARTICLES^
-SEWAGE PARTICLES
I
I I
O.I 0.2 0.4 0.6 I 2 4
PART/CLE DIAMETER, mm
10
Figure 12
Particle Size Distributions Used in Example Cases
48
-------
TABLE 3. PARTICLE SIZE DISTRIBUTIONS
Particle Size Groups (ISZ)
Variable
45 6 7 8 9 10
Representative Diameter, mm-DSOL(ISZ) 0.12 0.32 0.63 1.05 1.50 2.1 2.5 3.2 3.7 4.4
Stormwater
Fraction of total input solids
in each size group
0.22 0.30 0.21 .185 .085
Sanitary Inflows
Fraction of total input solids
in each size group
0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
-------
EXAMPLE CASES
The 16 basic example cases are described briefly in Table 4. The pipe
and junction numbers are those given in Figure 11 previously.
The sizes of the conduits used in the various example simulations are
given in Table 5. The elevations of the junction inverts are given in
Table 6. The Hydraulics Model used these data to compute pipe slopes. The
intent was to have the outfalls drop 10 feet in 5,000 feet, and the remainder
of the pipes were to drop between roughly 4 and 6 feet in 5,000 feet. Hence,
the slopes of the pipes, other than outfalls, ranged from 0.0008 to 0.00125
foot per foot (0.08 to 0.125 percent). Very low slopes were desirable in
these examples to permit deposition to occur at low flows, depths, and
velocities. All pipes were 5,000 feet long.
The treatment sizes and types were varied as shown in Table 7- Since
treatment sizing was not a critical part of the exercise, the treatment
devices were assigned capacities computed from crude rules of thumb. The dry,
weather hydraulic capacity was computed as 4 times the average daily flow
(4 cfs x 4 = 16 cfs), or about twice the normal peak hour flow. The value of
25 cfs for the combined system was chosen as a conveniently larger number to
allow for some downstream treatment capacity for stormwater. The swirl
concentrator capacities were selected between 50 and 150 cfs to show the
effects of bypassing much of the flow in some cases and treating most of the
flow in others; since the assumed input hydrographs rose from zero to a peak
of 100 cfs, and there were several of these hydrographs added at upstream
storm and combined sewer junctions (numbers 1, 2, and 3 in Figure 11).
The assumed input hydrographs and solids concentrations for all cases
are shown in Figure 13. The flow peaked at the first hour after runoff began.
For all but one case, the runoff was started at all three upstream junctions
at 1:00 a.m., one hour after the beginning of the simulation. The dry
weather inputs computed in the Hydraulics Model are given in Figure 14.
From the data presented, one can discern that the points of the
examples were these:
1) Cases I-III and VII-IX were to evaluate the effect of slope
changes in combined and separate systems, respectively.
2) Cases IV and X were to evaluate the effects of upstream
treatment of stormwater.
3) Cases V and XI were to evaluate increases in degree of
treatment for dry-weather or sanitary flows.
4) Cases VI and XII were to evaluate the effect of enlarging
and upgrading treatment generally.
5) The cunette cases were to evaluate the effects of the
shape changes to conduits.
50
-------
TABLE 4. DESCRIPTION OF EXAMPLE CASES
Example Case
Description
en
I
II
III
IV
V
VI
Cunettes-combined
Cunettes-combined-rect.
VII
VIII
IX
X
XI
XII
Cunettes-sep.
Cunettes-sep.-enl.
Circ. pipes—combined sys.--25 cfs pri. treat. @ end of pipe 3--slope = S
Same as I—except slope = 1.5 S
Same as I—except slope = 1.25 S
Same as II—with swirls at pipes 1 and 2
Same as I I—except treatment = secondary
Slope = 1.5 S--circ. pipes, 1 foot smaller; larger swirls at 1 & 2;
filtration plant at 3—cost added to secondary of Case V.
Circ. pipes w/semi-circ. cunettes. Lg. barrels same as pipes in I-V--
STHETA = 0.1667—slope = 1.25 S
Rect. pipes w/rect. cunettes--STHETA = 0.4--SPHI = 2 ft. and 2.8 ft.—
slope = 1.25 S
Circ. pipes--sep. system--16 cfs pri. treat. @ end of pipe 30--slope = S
Same as VII—except slope = 1.5 S
Same as VII—except slope = 1.25 S
Same as VIII—except swirls at pipes 1 and 2
Same as VIII—except treatment - secondary
Slope = 1.5 S, all pipes smaller, larger swirls at 1 & 2--16 cfs. filtration
plant at pipe 30
Same as Cunettes-combined, except san. sys. added
Large barrels enlarged to avoid surcharge of some nodes
-------
TABLE 5. CONDUIT SIZES IN EXAMPLE CASES
Example
Case
I
II
III
IV
V
VI
Cunettes-comb. 1
Cunettes-rect.2
VII
VIII
IX
X
XI
XII
Cunettes-sep. 3
Cunettes-eni . "*
Sizes of Following Conduits, feet
1
6
6
6
6
6
5
6
5
5
5
5
5
5
4.5
5
6
2
7
7
7
7
7
6
7
7
6
6
6
6
6
5.5
6
7
3
8
8
8
8
8
7
8
7
7
7
7
7
7
6.5
7
8
4 10 20 30 40
8
8
8
8
8
7
8
7
7 1.667 2.5 3 3
7 1.667 2.5 3 3
7 1.667 2.5 3 3
7 1.667 2.5 3 3
7 1.667 2.5 3 3
6.5 1.5 2 2.5 2.5
7 1.667 2.5 3 3
7 1.667 2.5 3 3
1 Large barrel sizes given for all cunette sections—STHETA = 0.1667,
2STHETA = 0.4; SPHI - 2, 2.8, 2.8, 2.8, respectively
3STHETA = 0.1667
^STHETA = 0.25 (alI pipes)
52
-------
TABLE 6. JUNCTION INVERT ELEVATIONS FOR EXAMPLE CASES
Example
Case
I
II
III
IV
V
VI
Cunettes-comb.
Cunettes-rect.
VII
VIII
IX
X
XI
XII
Cunettes-sep.
Cunettes-enl .
Invert Elevations at Following
1
23.
30.
26.
30.
30.
31.
25.
25.
24.
31.
27.
31.
31.
31.
26.
26.
5
25
875
25
25
25
54
54
5
25
875
25
25
75
708
708
2
18.5
22.75
20.625
22.75
22.75
23.75
19.29
19.29
19.5
23.75
21.625
23.75
23.75
24.25
20.458
20.458
3
14
16
15
16
16
17
13.67
13.67
15
17
16
17
17
17.5
14.833
14.833
4
10
10
10
10
10
11
8.67
8.67
11
11
n
n
n
12.5
9.833
9.833
5
0
0
0
0
0
0
-1.33
-1.33
1
1
1
1
1
1
-0.167
-0.167
10
28.5
35.25
31.875
35.25
35.25
35.42
31.375
31.375
Junctions
20
23.5
27.75
25.625
27.75
27.75
28.25
25.125
25.125
30
19
21
20
21
21
21.5
19.50
19.50
40
15
15
15
15
15
15.5
14.50
14.50
50
5
5
5
5
5
5
4.50
4.50
-------
TABLE 7. TREATMENT SIZES AND TYPES IN EXAMPLE CASES
Example
Case
I
II
III
IV
V
VI
Cunettes-comb.
Cunettes-rect.
Treatment Design Capacities, cfs, (and Types*) at
Ends of Following Pipes
1 2 3 4 10 20 30 40
25(5)
25(5)
25(5)
50(3) 100(3) 25(5)
25(6)
100(3) 150(3) 50(4)
25(5)
16(5)
VII
VIII
IX
X 50(3) 100(3)
XI
XII 100(3) 150(3)
Cunettes-sep.
Cunettes-enl .
16(5)
16(5)
16(5)
16(5)
16(6)
16(4)
16(5)
16(5)
*3 = swirl concentrator; 4 = filtration, added to secondary;
5 = primary; 6 = secondary
54
-------
100
INFLOWS
5 10 15 20
TIME, hours after rainfall began
25
SOLIDS
J L
5 10 15 20
TIME, hours after rainfall began
25
Figure 13
Storm Inputs at Junctions 1, 2, and 3 for All Example Cases
55
-------
10
to
«*-
o
Is
-J
U.
0
INFLOWS
i i i
0
JUNCTION 3
5 10 15 20
TIME , hours after midnight
25
__ 1500
\
o>
E
O
K-
1000
o
^
o
o
Q
-J
O
500
0
SOLIDS
-JUNCTION f
JUNCTIONS 2&3
JL_L
I I I I i i I I i I J I
0
5 10 15 20
TIME , hours after midnight
25
Figure 14
Dry Weather Inputs for All Example Cases
56
-------
DEMONSTRATION OF FIRST FLUSH
In the cases just itemized the input hydrographs were timed to begin one
hour after the beginning of the simulation. The result was that little
deposition had occurred prior to the storm, which washed the small deposits
away rather quickly. Moreover, as shown in Figure 14, the solids concen-
trations in the dry-weather flow were highest just after this period anyway;
so the differences between what was caused by the storm and what was caused
by the dry weather conditions were not easily discernible.
Consequently, a separate simulation was made for the Case III circular
combined sewer network with moderate slopes, but with the hydrographs delayed
until the 10th hour of the simulated day. This allowed deposition to occur
during the low-flow, high-concentration period, and made the flushing by the
high flows more dramatically discernible. Since the simulation of first
flush was a major point of the model development exercise, those results are
presented here in some detail.
First, the flows and velocities in the 4 pipes are shown in Figure 15.
There was roughly a 10-20 fold increase in flow and a 3-4 fold increase in
velocity from hour 10 to hour 11. The peak flow and velocity occurred in
pipe 1 at 11:00 o'clock, in pipes 2 and 3 at 11:15, and in pipe 4 at 11:30.
In Figure 16 are shown the depths of water at the five junctions and the
computed width's, b, which affect many of the computations in the model. The
values of b shown were computed with the depths in the pipes taken as the
averages of the depths at the two junctions on either end of the pipe. During
the periods of larger values of b, the computed potentials for bedload and
suspended load transport were also larger, since Gs = gsb and Gss = gssb.
Figure 17 shows the modeled deposition that occurred in the three
upstream pipes and the solids discharged through the outfall. (The treatment
rate for the primary treatment plant assumed at the end of pipe 3 was set at
16 cfs in this simulation, not 25 cfs as used in Case III.) The Figure shows
that there was accumulation in all three upstream pipes but not in the outfall
(pipe 4), which had the highest velocity during almost the entire period.
It is interesting to note that pipe 3, with the largest values of flow,
velocity, depth, and width of the upstream pipes, also experienced the
greatest amount and rate of deposition. This resulted because, as we will
see in more detail below, there were more pounds of solids added to this pipe
than to either of the two upstream, and also because the particles assumed in
this exercise were all large enough and heavy enough to be removed in the
5,000 feet of pipe length. This occurred even though the early velocities in
pipe 3 sometimes exceeded 2 feet per second and were 1.8 feet per second or
above virtually throughout the period.
As soon as the hydrograph appeared, however, all three pipes were
immediately scoured completely. The 3,000 pounds of accumulated solids in
pipe 3 and all those in pipes 1 and 2 were gone within 1 hour (the period of
reporting used in the model). Three hours later (hour 14) accumulation began
again in pipe 1; the velocity had dropped in the 13th hour from 2.3 to 1.7
57
-------
en
CO
300 i—
250 —
200 —
I 150
100 —
50 —
0
0
PIPE f
PIPE 2
PIPE 3
PIPE 4
10 15 20
TIME, hours after midnight
PIPE t
PIPE 2
PIPE 3
PIPE 4
L .1 .1 ._!._! I I I I I 1 1 I I I I I 1 1 J. I I
TIME, hours offer midnight
Figure 15
Flows and Velocities in Combined Sewer System During Delayed Storm Case
-------
C71
l-D
JUNCTION I
JUNCTION 2
JUNCTION 3
JUNCTION 4
JUNCTION 5
5 10 15 20
TIME, hours after midnight
25
_ 6
.0
cc"
UJ
1
o
-J
u_
u_
o
Q
UJ
K
3 9
o. 2
s
o
u
0
P/PE / (6'J
PIPE 2 (7')
PIPE 3 (8')
PIPE 4 (8')
I I I I I
\
0
10 15 20
TIME, hours after midnight
25
Figure 16
Depths and Widths in Combined Sewer System During Delayed Storm Case
-------
in
•O
c
3
O
Q.
§
O
h~
K
O
m
UJ
Q.
o!
CO
Q
-J
O
CO
c
'E
3000
2000
2
cc
UJ
i
UJ
CO
Q
UJ
5
O
O
I
e>
Q
UJ
h-
CC
O
O.
CO
co
Q
r>
o
CL
1000
PIPE I
PIPE 2
PIPE 5
(NONE) PIPE 4
I I i I I I I 1 I i i
o
1000 i—
10 15 20
TIME, hours afler midnight
25
800
600
400
200
0
FLOW>/6cfs (TREATMENT
OVERWHELMED)
POUNDS ADDED &
LEAVING
POUNDS DEPOSITED
& IMMEDIATELY SCOURED
AS BEDLOAD OR
SUSPENDED LOAD
POUNDS DISCHARGED AS
WASHLOAD
PIPE No. 4
0
10 15
TIME, hours afier midnight
20
25
Figure 17
Disposition of Solids in Combined Sewer System During Delayed Storm Case
60
-------
feet per second. In pipe 2 accumulation began at hour 16; velocity dropped
in the_15th hour from 2.0 to 1.9 feet per second. But accumulation began
again in pipe 3 at the 17th hour when velocity was still 2.9 feet per second;
and accumulation continued at the highest rate of the three for the remainder
of the period, while velocity never dropped below 2.5 feet per second.
The lower portion of Figure 17 shows what happened to these solids. Most
of them left the sewer-treatment system through the outfall (pipe 4). The
peak rate of solids transport was almost 800 pounds per 5 minutes (the time
step used in the model) or 160 pounds per minute or 9,600 pounds per hour,
which was reported at hour 11. The rate may have been higher earlier,
between hour 10 and 11, though that could not be discerned since these
results were printed at hourly intervals. Recall that the peak flow occurred
in pipe 4 at 11:30, so the results do indicate that the peak load in the
flush occurred prior to the peak flow—one of the characteristics of first
flush.
The concentrations at the four junctions of interest are shown in Figure
18. Concentrations were reported every 15 minutes, so we can see that the
peak concentrations occurred (were reported) at 10:15, just 15 minutes after
runoff began. The concentrations were much lower at junction 4 both before
and after the flush because the 16 cfs treatment plant was just upstream of
that point. However, it cannot be missed that the concentration in the
effluent, at junction 4, was the highest (790 mg/1) of the four during the
storm, and 1 hour and 15 minutes before the peak flow.
Further details about the modeled solids behavior are given in a pipe-
by-pipe, hour-by-hour account in Tables 8, 9, 10, and 11. Each table is for
a single pipe. Table 8 shows the results for pipe 1. For most of the
simulated period the dry-weather, sanitary inputs were 11.5-13 pounds every
5 minutes. In most hours all this was deposited but immediately scoured and
moved along as bedload or suspended load. During the storm runoff period a
small portion was transported as washload. It is worth noting that in the 10th
hour more solids were scoured from the pipe bottom than were deposited. Also
it is noteworthy that well after the storm there continued to be greater scour
in this pipe than before the storm. This resulted because the flow and the
velocity were higher in the later hours of the day due to the dry-weather
inputs alone, which were shown in Figure 14. The velocities, shown in
Figure 16, were about equivalent to what they were just before the storm and
were about one-half a foot per second faster than they had been at the
slowest flow in the morning. Moreover, from 2:00 p.m. forward, while scour
was not equal to deposition, it was higher than it had been in the morning,
and the velocity during this period was dropping from 1.7 to 1.4 feet per
second.
Table 9 shows very similar results for pipe 2. More dry-weather inputs
were being added to the upstream end of this pipe, in addition to the flow
leaving pipe 1. Also during the storm another hydrograph was being added to
junction 2 at its upstream end. Hence there were more pounds of solids and
more flow added to this pipe. Also it was a foot larger in diameter than
pipe 1. Still, behavior was very similar. There was net deposition before
the storm; the solids that were scoured left the pipe, since there was no
61
-------
1200 r—
1000
6
2
O
800
oo
9
o 600
00
u_
o
o
I-
UJ
o
2
O
o
400
200
0
JUNCTION
___ JUNCTION 2
JUNCTION 3
JUNCTION 4
0
5 10 15
TIME, hours after midnight
20
25
Figure 18
Concentrations of Solids Throughout Combined Sewer System
During Delayed Storm Case
62
-------
TABLE 8. SOLIDS BEHAVIOR IN COMBINED SEWER—PIPE 1
Pounds/5 minutes
Time, hrs.
5 min
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
Added Washed
4.5 4.5
11.6
11.8
11.7
11.5
11.8
11.8
12.2
12.5
13.0
12.5
127.5 0.7
64.8 0.2
17.9
11.7
12.0
12.1
12.0
12.0
12.0
12.0
12.0
11.9
11.9
Deposited
11.6
11.8
11.7
11.5
11.8
11.8
12.2
12.5
13.0
12.5
126.8
64.6
17.9
11.7
12.0
12.1
12.0
12.0
12.0
12.0
12.0
11.9
11.9
Scoured Treated
0.9
1.3
0.6
0.1
0.1
0.1
0.1
0.1
2.5
13.4
126.8
64.6
17.9
9.1
6.2
5.6
4.9
4.3
3.7
3.2
2.9
2.7
2.5
Remaining
73.9
199.9
330.8
464.9
603.2
743.2
888.0
1,034.9
1,177.8
1,219.9
0
0
0
5.5
64.3
138.0
219.9
309.2
404.8
507.8
615.4
725.9
837.9
Leaving
4.5
0.9
1.3
0.6
0.1
0.1
0.1
0.1
0.1
2.5
13.4
127.5
64.8
17.9
9.1
6.2
5.6
4.9
4.3
3.7
3.2
2.9
2.7
2.5
63
-------
TABLE 9. SOLIDS BEHAVIOR IN COMBINED SEWER—PIPE 2
Pounds/5 minutes
Time, hrs.
5 min
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
Added Washed
4.7 4.7
15.2
18.9
17.9
16.7
16.7
16.8
17.5
18.0
20.5
28.8
300.0 3.1
146.2 1.8
48.7 0.3
26.7
23.2
23.1
22.5
21.8
21.1
20.6
20.2
20.0
19.8
Deposited
15.2
18.9
17.9
16.7
16.7
16.8
17.5
18.0
20.5
28.8
296.9
144.4
48.4
26.7
23.2
23.1
22.5
21.8
21.1
20.6
20.2
20.0
19.8
Scoured Treated
2.7
5.3
4.4
2.3
1.9
1.3
2.1
2.2
8.4
21.3
296.9
144.4
48.4
26.7
23.0
22.0
20.7
18.4
16.0
14.1
12.2
10.7
9.4
Remaining
79.1
233.1
395.2
564.1
739.7
920.8
1,107.1
1,292.8
1,466.8
1,516.3
0
0
0
0
0.2
7.0
24.0
57.5
110.6
181.0
269.6
374.6
492.8
Leaving
4.7
2.7
5.3
4.4
2.3
1.9
1.3
2.1
2.2
8.4
21.3
300.0
146.2
48.7
26.7
23.0
22.2
20.7
18.4
16.0
14.1
12.2
10.7
9.4
64
-------
TABLE 10. SOLIDS BEHAVIOR IN COMBINED SEWER—PIPE 3
Pounds/5 minutes
Time, hrs.
5 min
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
Added Washed
3.9 3.9
27.2 21.6
43.6
39.6
35.9
35.1
34.9
36.0
37.6
43.4
59.7
590.6 17.2
246.6 5.6
97.9 4.4
58.1 1.1
55.2
56.2
55.3
53.0
50.7
48.9
47.0
45.3
43.9
Deposited
5.6
43.6
39.6
35.9
35.1
34.9
36.0
37.6
43.4
59.7
573.4
241.0
93.5
57.0
55.2
56.2
55.3
53.0
50.7
48.9
47.0
45.3
43.9
Scoured
0.1
14.8
12.4
7.6
5.9
3.7
4.2
6.8
15.8
66.8
573.4
241.0
93.5
57.0
55.2
56.0
54.3
48.0
40.8
35.9
31.2
27.1
23.5
Treated
0.6
18.4
8.9
7.6
4.8
3.7
2.4
2.7
4.3
9.4
36.7
18.2
7.0
7.5
15.9
24.1
24.6
24.0
21.8
19.1
17.3
15.4
13.8
12.4
Remaining
5.5
359.2
689.2
1,026.9
1,371.6
1,736.7
2,114.4
2,492.6
2,813.6
2,953.2
0
0
0
0
0
0.6
9.3
47.4
144.3
285.2
462.0
668.9
903.9
Leaving
3.3
3.3
5.9
4.8
2.8
2.2
1.3
1.5
2.5
6.4
30.1
572.4
239.6
90.4
42.2
31.1
31.4
30.3
26.2
21.7
18.6
15.8
13.3
11.1
65
-------
TABLE 11. SOLIDS BEHAVIOR IN COMBINED SEWER—PIPE 4
Time, hrs.
5 min
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
Added
0
0.8
4.9
5.4
3.4
2.4
1.7
1.5
2.0
5.2
21.7
797.9
258.5
100.3
42.9
31.1
30.8
30.4
27.3
22.8
19.5
16.5
14.0
11.7
Pounds/5 minutes
Washed Deposited Scoured Treated
0.8 0.1
4.9
5.4
3.4
2.4
1.7
1.5
2.0
5.2
21.7
320.1 477.8 477.8
31.8 226.7 226.7
25.8 74.5 74.5
42.9
31.1
30.8
30.4
27.3
22.8
19.5
16.5
14.0
11.7
Remaining Leaving
0
1.6 0.1
4.9
5.4
3.4
2.4
1.7
1.5
2.0
5.2
21.7
797.9
258.5
100.3
42.9
31.1
30.8
30.4
27.3
22.8
19.5
16.5
14.0
11.7
66
-------
treatment; scour was greater after the storm than before; and washload
transport occurred only in the high-flow, high-velocity conditions during the
peak runoff period.
Table 0 shows the results for pipe 3. More sanitary waste inputs and
another hydrograph were added at the upstream end of this pipe (junction 3).
So there were more pounds being added to this pipe than to the two upstream.
While flow and velocity were higher in this pipe than in the previous two,
there was still net deposition occurring; although in the 10th hour there
was a net scouring. Also for this pipe there was some removal by treatment.
Still, many of the characteristics were the same as for the previous two
pipes—most of the solids entering the pipe were able to deposit, partially
removed immediately as bedload or suspended load transport; washload occurred
only at the highest and fastest flows; and deposition with net accumulation
began again after the storm had passed.
Unfortunately, the model was not directed to print the amounts of
material moving in each period as washload, suspended load, and bedload
individually. (The washload numbers in the Tables were computed by
difference.) But the model did print the amounts of material removed by the
treatment plant in these three categories for the entire simulated period.
These were: washload, 369 pounds; suspended load, 2,071 pounds; and bedload,
2,269 pounds. Since the removal percentages specified were 85, 65, and 35
percent, respectively; the total amounts in motion in these three species in
pipe 3 can be computed. These were: washload, 434 pounds; suspended load,
3,186 pounds; and bedload, 6,483 pounds. So most of the material in motion
during the entire 23.5 hour period moved as bedload, at least in this
pipe.
Table "'"• gives the results for pipe 4, the outfall from the system. This
pipe was steeper than the others, and velocities here were above 2.5 feet per
second virtually all the time. Moreover, the depths were lower; and there was
slight chance for accumulation. Hence most of the time the material moved
through the pipe was washload and no accumulation occurred. Curiously,
though, there was apparent deposition with immediate scour during the period
of greatest flow and velocity. How could that be?
The answer lies in the definition of critical velocity for deposit-free
flow, Va (see [16], p. 19). During the early part of the simulated period,
the critical velocity was roughly:
V» = 0.9 [2 x 32.2 x 0.5 x (1.2 - 1)]1/2 = 2.3 ft/sec
o
while the velocity in the pipe was 2.4 to 3.0 feet per second. So no
deposition could occur.
In the storm runoff period the critical velocity was higher because the
depth was greater and the weighted specific gravity of the particles was
greater:
V0 = 0.9 [2 x 32.2 x 4.5 x (1.4 - I)]1/2 = 9.69 ft/sec
67
-------
However, the maximum velocity attained in this pipe was 8.8 feet per second,
so some deposition was possible. It is also possible, of course, that the
critical velocity definition, particularly the coefficient of 0.9, is not
correct. This was discussed earlier. But the coefficient would have to be
below 0.2 for the critical velocity to be 2.0 feet per second, and the
coefficient would have to be below 0.3 to yield a critical velocity of 3.0
feet per second, with this depth and specific gravity. The lowest value
reported for the coefficient is 0.7. So the implication is fairly clear:
Deposition can occur under conditions where the velocity is substantially
above 2.0 feet per second, the long-established rule-of-thumb criterion for
self-cleansing. It is interesting to note from all these results, however,
that when velocities increased past 2.0 feet per second there was net scour
of deposited material. So perhaps the old criterion is not bad for a rule-
of-thumb scour criterion (for noncohesive materials); but this should not be
confused with a no-deposit criterion. In summary, even if the model is not
correct in every detail, it gives strong evidence that particles may be
deposited and immediately moved along as bedload or suspended load in the
same time period and that a velocity sufficient to move particles can be much
smaller than the velocity necessary to keep them fully suspended. This is
consistent with other findings (Graf, 1971; ASCE, 1975).
To complete the discussion of critical velocity in pipe 4, it can also
be noted that after the runoff period the depth lowered to about 1.0 foot and
below and the specific gravity of the particles lowered again to 1.2. So the
critical velocity was then not greater than:
V0 = 0.9 [2 x 32.2 x 1 x (1.2 - I)]1/2 = 3.2 ft/sec
The velocity in pipe 4 ranged from 4.8 down to 3.3 feet per second after the
hydrograph passed, so again no deposit occurred and all the load was
transported as washload.
This simulation alone, analyzed in some detail, indicated that the model
was functioning or executing as had been intended and it produced answers
that could be explained both in terms of behavior noted generally in the past
and in terms of the expressions programmed into it. It cannot be judged that
the expressions used, such as that for the critical velocity or even Kalinske's
expression for bedload transport are absolute descriptions of truth, but the
results indicate that the model with these expressions in it can simulate or
approximate prototype behavior adequately. The results from other"simulation
cases for the example problem are summarized below.
OTHER RESULTS
The Effect of Conduit Slope
Attention is now turned to the other example cases wherein the hydro-
graphs were added to the upstream junctions just after the simulation began
(at midnight). The first three cases were for the combined sewer system
with a 25 cfs primary treatment plant at the downstream end of pipe 3. The
differences among the three cases were in pipe slope only. The slopes in
68
-------
Case I varied from 0.0008 foot per foot in pipe 3 to 0.002 foot per foot in
pipe 4. (See the junction elevations in Table 6.) Case II gave each pipe
a 50 percent greater slope; and Case III was the intermediate condition,
wherein slopes were increased only 25 percent over the Case I conditions.
The flows and velocities in pipe 23 upstream of the treatment plant, are
shown for Cases I and II in Figure 19. The values for Case III, the inter-
mediate slope case fall in between those shown and are omitted from the figure
for clarity. It can be seen that the more steeply sloped pipes gave rise to
very slightly higher flows and somewhat higher velocities, as would be
expected.
The resulting concentrations of solids in motion ("suspended" solids)
are shown in Figure 20. The results shown are for junctions 3 and 4.
Junction 3 was at the downstream end of pipe 3 just following the treatment
plant. The results show that the steeper slopes led to higher concentrations,
both before and following treatment. Figure 21 shows rather dramatically why
that occurred. Here are shown the pounds of accumulated solids in pipe 2.
The lower slope case led to substantial accumulation in the upstream pipes;
while in the highest slope case, the dry-weather flows were able to rescour
the pipes in the afternoon and early evening hours. Therefore, the concen-
trations were lower downstream in the low slope case because so few solids
were reaching the downstream junctions. In another situation where slope is
always kept sufficiently steep to keep solids in motion toward a plant,
solids concentrations downstream would be minimized by increasing slope until
the treatment capacity of the plant was just attained by the resulting
increase in flow rate in the sewers. In other words, increasing pipe slope
will not always lead to increased solids concentrations and indeed may lead
to decreased concentrations. The determinant is the degree to which solids
accumulation can occur upstream.
For the cases analyzed, the increased slopes did allow more solids to
reach the treatment plant so they could be removed. In Case I the treatment
plant removed 4,180 pounds of solids during the event. In Case II, the
steepest slope case, the removal was 7,068 pounds. In the intermediate slope
example, Case III, the plant removed 5,551 pounds. So while the plant
removed 25.6 percent of the solids entering the system during the event in
the steep slope case, 63.3 percent of the entering solids were discharged,
while 11.1 percent accumulated on the pipe bottoms. The flattest slope pipes
led to only 15.1 percent removal by the plant, and to only 49.8 percent of
the solids being discharged, but 35.1 percent of the entering solids remained
behind on the pipe bottoms.
The Effect of Conduit Shape
The simulation of cunette-shaped cross-sections produced some erratic
results. But they are worth reviewing. The flows and velocities in a
rectangular combined sewer system with cunettes are compared with those for
a circular combined sewer system in Figure 22. The conditions being analyzed
are similar to the Case III conditions before--the mildly sloped, combined
sewer with a treatment plant at the end of pipe 3. In both these examples,
however9 the treatment capacity of the primary plant was 16 cfs.
69
-------
200 i—
CASE I SLOPE - S
CASE H SLOPE = f.5S
(IN BETWEEN) CASE HI SLOPE = I.25S
i I i i
1 l l i I i i i -1
10 15 20
TfME, hours offer midnight
25
CASE I SLOPE = S
—— CASE JI SLOPE - J.5S
(IN BETWEEN) CASE HI SLOPE = t.25S
i i i I l i l i I i i i i I l i i i
10 15 20
TIME, hours offer midnight
25
Figure 19
Flows and Velocities in Pipe 2 of Combined
Sewer Systems with Different Slopes
70
-------
2500
§2000
)> 25cfs
(TREATMENT OVERWHELMED)
CASE I SLOPE = S
CASE H SLOPE = J.5S
(IN BETWEEN) CASE HI SLOPE = 1.25S
CASE I
CASE H
JUNCTION 3
JUNCTION 4
1000
500
10 15
TIME, hours after midnight
20
25
Figure 20
Downstream Solids Concentrations in Combined Sewer Systems
as Functions of Pipe Slopes
71
-------
3000
2500
V)
T3
C
3
O
Q.
uj
a.
2000
1500
1000
00
9
~j
o
CO
500
0
CASE I SLOPE = S
CASE H SLOPE = 1.5 S
CASE m SLOPE = 1.255
I I II I.I IN I
0
5 10 15 20
TIME, hours offer midnight
25
Figure 21
Upstream Accumulation of Solids in Combined Sewer
System as a Function of Pipe Slope
72
-------
300
250
200
O 150
100
50
PIPE 3
i I I i i i
0 5 10 15 20
TIME, hours offer midnight
25
10 i—
(17.3)
PIPE 3
I. .. 11
5 10 15 20
TIME, hours offer midnight
25
Figure 22
Flows and Velocities in Combined Sewers of Different Shapes
73
-------
The flows shown in the figure for the two cases were almost identical
throughout the simulated period, although two incongruities occurred in the
hydrograph. One was a momentary drop in flow rate at time 4:15, and the other
was a momentary drop in flow rate at 10:45. Two other incongruities appear
in the velocity data shown at the bottom of Figure 22, one at 1:45 and the
other at 4:00. All of these occurred at times when the depth of water at one
end of the pipe was in the cunette and at the other end the water was deep
enough to be out of the cunette. This caused the model to have widely
different areas and widths to average for conditions at the center of the
pipe and this led to the discontinuities. Nonetheless, the model was able
to recover from these conditions in one time step and to go forward to
represent the majority of the period with results comparable to those for
the circular pipe.
In Figure 23, it can be seen that the Quality Model results were quite
similar for the two cases, despite the momentary upsets in the hydraulics
results for the cunettes. The figure shows the treatment rate for solids
removal at the end of pipe 3 and the accumulation of solids in all the
conduits. It is interesting, if quite unexpected, that the circular pipe
system afforded more removal by treatment and less accumulation than did the
cunette system. This was a function of the sizes chosen for the examples and
is not a general impugnation of cunette's reputed self-cleansing properties.
We simply made the cunettes too large. The dimensions given to pipe 3 were
a 7-by-7 foot box with a 2.8-by-2.8 foot cunette in the bottom. The cunette
contained all the flow after the 4th hour; and at these generally flat slopes,
the potential for deposition with immediate scour was not as great in this
flat-bottomed box as it was in the rounded pipe.
Because there was more accumulation in the cunette system, though, there
was also marginally less discharge of solids from this system. Figure 24
shows the rate of solids discharge through the outfall, pipe 4. The disconti-
nuities in the results for the rectangular conduit occurred as a result of the
flow and velocity discontinuities upstream.
Figure 25 shows the concentrations of solids as discharged into the
outfall from the two pipe systems. The behavior was almost identical,
although the rectangular-cunette shaped sewer produced a very slightly lower
and earlier peak concentration.
The Effect of Treatment Types and Sizes
Figure 26 shows the suspended solids concentrations at the outfall
resulting from adding different types and sizes of treatment to the combined
sewer system. All these cases were analyzed with the highest slopes and
for circular pipes. The only differences were the treatment types, sizes,
and locations. Several things are of interest here. First, the swirl concen-
trators upstream were of little assistance in this case in reducing downstream
concentrations at the outfall, although they did provide some improvement over
primary treatment alone downstream. But in Figure 27 we can see that much
less accumulation occurred in the pipes when the swirl concentrators were in
place. After hour ^3 virtually all the accumulation in the case with the
swirl concentrators occurred in pipe 1, which was upstream of the first
74
-------
10 50
END OF PIPE 3
5297 POUNDS
If REMOVED
DURING EVENT
5701 POUNDS
REMOVED
DURING EVENT
0 i i i i i I i i i i I i i i i I i i i i I i i i i I
0 5 10 15 20 25
TIME, hours after midnight
6000
o
|S
2K 4000
CO 9:
o
a.
2000
0
ALL PIPES
5 10 15 20
TIME, hours offer midnight
25
Figure 23
Disposition of Solids in Combined Sewer Systems
Having Different Pipe Shapes
75
-------
1000
e
'i
ID
\
eo
- 800
2
£
£
LU
CO
Q
LaJ
o
o
co
Q
c!
CO
600
400
200
Q> I6cfs J (TREATMENT OVERWHELMED)
^ \
17,261 POUNDS REMOVED
DURING EVENT
PIPE 4
16,874 POUNDS REMOVED
DURING EVENT
5 10 15 20
TIME, hours after midnight
Figure 24
Solids Discharge Rate from Combined Sewer System
Having Different Pipe Shapes
76
-------
1000
o>
6
9 800
~j
o
V}
Q
LU
Q
Uj 600
Q.
(O
§400
ft
2
UJ
o 200
o
o
0
JUNCTION 4
I i i i
0
i i i i
5 10 15
TIME, hours after midnight
20
25
Figure 25
Concentration of Solids in Combined Sewer Outfalls
for Systems Having Different Pipe Shapes
77
-------
800
700
- 600
O
h-
2
h-
O
500
400
UJ
o
O
o
to 300
200
Q>32
Q>25
Q>I6
100 —
25cfs PR/MARY
IScfs PR/MARY
I6cfs PRIMARY +
50cfs SWIRL® PIPE 1
(OOcfs SWIRL @ PIPE
25cfs SECONDARY
32 cfs SECONDARY +
FILTRATION +
100 cfs SWIRL @ PIPE 1 +
150 cfs SWIRL ft P/PE 2
5 10 15 20
TIME, hours after midnight
Figure 26
Effects of Treatment Type and Size on Effluent
Solids Concentration
78
-------
7000
3
O
cx
co~
O
I-
K
O
OQ
Q.
CL
6000
5000
4000
Q
Ul
I-
«3
U
3
O
O
CO
Q
O
CO
3000
2000
1000
ALL PIPES
25 cfs PRIMARY
0
25 cfs PRIMARY +
50 cfs SWIRL @ PIPE I +
100 cfs SWIRL @ PIPE 2
I I i I I I i i I I i i I i I i i i i
5 10 15 20 25
TIME, hours after midnight
Figure 27
Effects of Upstream Stormwater Treatment in
Combined Sewer System on Accumulation of Solids
79
-------
device. In the case with only the primary plant at pipe 3, most of the
accumulation occurred in pipes 2 and 3, still ahead of the first treatment
device. So in terms of mass removed, the swirl concentrators did help
substantially and the model was able to indicate their contribution.
Secondly, providing secondary treatment rather than primary treatment
downstream produced a significant improvement in effluent concentration.
Finally the most improvement resulted by providing both upstream and down-
stream treatment with rather complete treatment including filtration down-
stream. These results are quite case specific, of course; and again the
results are reflective of the accumulation and later scour that occurred in
these fairly flat sewers. In another sewer system the results of comparing
treatment types and sizes could be quite different.
Figure 28 shows the effects of various treatment types on the sanitary
part of the separate system. The concentrations shown are for junction 40
which follows pipe 30 where the dry-weather treatment plants were located.
The expected result of improved removal with increased degree of treatment
ensued. Notice there is no early peak of solids related to the storm hydro-
graphs , since the stormwater was all in the other storm sewer. Also, no
infiltration flow was assumed. So the pattern of concentrations is very much
the same as that of the dry-weather inputs.
These results show that the model is able to simulate treatment to obtain
expectable results, but also it is able to show that accumulation of solids
upstream and later resuspension of those particles may rather substantially
reduce the effectiveness of treatment for reducing final effluent concen-
trations. It certainly shows that the sewer system must be designed to keep
solids moving toward downstream treatment devices or the treatment can be
largely wasted.
The Effect of Combined vs. Separate Sewers
In establishing the conduit sizes for all the example problems, we
decided to make the storm sewers 1 foot smaller in diameter than the combined
sewer sections, which were analyzed first. As it turned out, almost all the
total flow during the storm period was comprised of the runoff, so the storm
sewers needed to be virtually as large as the combined sewers had been. In
other words9 surcharge of the upstream storm sewers occurred, because they
were a little too small.
But, even though the model treats surcharge somewhat capriciously (it
sets the flow equal to full-pipe flow and the depth equal to diameter; and
it does not compute a pressurized flow rate); nonetheless, the results are
presented here because they are instructive. They will show what the model
does in this situation and they show, if perhaps a bit inaccurately, what
happens in a sewer under these conditions.
Figure 29 compares the combined sewer flows and velocities of Case III
with the storm and sanitary sewer flows of Case IX, which is the counterpart
to Case III in that the slopes were intermediate and all pipes were circular.
Figure shows the results for the second pipe from the upstream end of
-------
300 i—
250
16 cfs PRIMARY
/6 cfs SECONDARY
/6 cfs SECONDARY +
FILTRATION
{3200
O 150
cc
UJ
o
Z
O
O
O
CO
100
50
0
0
5 10 15 20
TIME, hours after midnight
25
Figure 28
Effects of Treatment Type on Effluent Solids
Concentrations from Sanitary Sewer System
81
-------
STORM SEWER (PIPE 2)
—- SANITARY SEWER (PIPE 20)
COMBINED SEWER (PIPE 2)
5 10 15 20
TIME, hours after midnight
25
200
;50
100
o
_J
u_
50
0
0
__,„_ STORM SEWER (PIPE 2)
SANITARY SEWER (PIPE 20)
— COMBINED SEWER (PIPE 2)
I I I
10 15 20
"/ME , hours after midnight
20
Figure 29
Velocities and Flows in Upstream Storm, Sanitary, and
Combined Sewers as Simulated
82
-------
all three pipe networks—pipe 2 of the combined system, pipe 2 of the storm
sewer, and pipe 20 of the sanitary sewer. The curves show that the surcharge
of the upstream storm sewer kept both flows and velocities high for a longer
period than occurred in the combined sewer. They also show that while the
sanitary flows in pipe 20 were fairly small by comparison to the storm flows,
the velocities remained more uniform than in either of the storm-carrying
pipes.
Figure 30 presents the flows and velocities in the downstream outfalls--
pipe 4 in the combined system, pipe 4 in the storm sewer, and pipe 40 in the
sanitary sewer. While the storm sewer flows and velocities remained high for
an extended period, pipe 40 was not itself under surcharge, j_.e_., this pipe
was never full. But its flow pattern and hence its velocity were controlled
by the flows from upstream. Hence the flows and velocities in the storm
sewer outfall appear quite different from those in the combined sewer outfall.
The flows and velocities in the sanitary sewer outfall were again relatively
uniform throughout the day.
Figure 31 shows the solids accumulation consequences in the various sewer
types upstream. The top curve, j^.e_., the most accumulation occurred for the
sanitary sewer. Accumulation during the first nine hours was fairly uniform,
this being the same period when the velocity in the sanitary sewer was less
than 2.0 feet per second. From hour 10 to hour 17, while velocity was greater
than 2.0 feet per second, there was a net scouring of accumulated solids.
Following that, as velocity dropped to 2.0 feet per second and below, there
was a net accumulation again. It is interesting that when velocity was
exactly 2.0 feet per second, the amount of scour and the amount of accumu-
lation were virtually zero. It is worth reiterating that the model does not
use the 2.0 feet per second criterion for self-cleansing in any explicit way.
Nonetheless, values very near this velocity often resulted when the net accu-
mulation rate was zero. Note for example that the net accumulation rate was
zero for the combined sewer at hour 9, when the velocity there was 1.9 feet
per second. While the velocity was at 2.0 feet per second, between hours 10
and 13, net scouring occurred in that sewer. When velocity fell to 1.8 feet
per second and below, accumulation began again in the combined sewer too.
Results are given in the Figure for both the combined sewer having the swirl
concentrator at pipe 1 and for the combined sewer without one. It can be seen
that the concentrator had little effect on the accumulation in pipe 2 of the
combined sewer. This results in part because many of the solids in pipe 1
were accumulating there also and not reaching the concentrator for removal.
Accumulation in the storm sewer does not show in the Figure at all, even
though after hour 6 the velocity was substantially below 2.0 feet per second.
This results because the stormwater contained very few solids after the
initial runoff period, which was sufficient in velocity in the beginning to
keep the pipe scoured clean. After hour 6 there was in fact a minute amount
of deposition in the storm sewer; but this amounted to only 1.7 pounds after
23.5 hours, which cannot even be plotted on the graph at the scale used in
Figure 31.
Figure 32 shows the final result of using the sanitary sewer system with
various levels of treatment. These are the results for the entrance to the
83
-------
10
o
Q>
-------
2500
T3
C
3
O
Q.
co"
P2000 —
h-
o
GO
LU
O.
1500 —
2
O
1000 —
o
o
2 500 —
O
co
SANITARY SEWER (PIPE 20)
COMBINED SEWER (PIPE 2)
?) +
SWIRL
STORM SEWER (PIPE 2)
0
10 15 20
TIME, hours offer midnight
Figure 31
Effect of Sewer System Type on Upstream Accumulation of Solids
85
-------
250
200
o
t-
UJ
o
2
O
o
CO
Q
O
CO
50
100
50
/6 cfs PR/MARY
16 cfs SECONDARY
16 cfs SECONDARY
FILTRATION
JUNCTION 40
5 10 15
TIME, hours after midnight
Figure 32
Effect of Treatment Type on Effluent
Solids Concentration from Sanitary Sewer System
86
-------
sanitary sewer outfall, junction 40. These concentrations may be compared to
those for the combined systems in Figure 26- A comparison will show that the
sanitary system produced comparable, if slightly higher peak solids concen-
tration in the effluent generally but produced no inordinately high peak
during the storm, which of course was not involved in this sewer at all.
Figure 33 shows what are unfortunately not very informative concentration
results for the storm sewer outfalls, both with swirl concentrators upstream
and without. The results are not very helpful in that they show an enormously
high concentration during the runoff event and virtually no concentration
thereafter. While this may be partially reflective of reality, it is also
true that the enormous peak values occurred in part because the storm sewer
outfall was completely dry at the beginning of the storm, and the first drop
of water that got to it contained a large amount of added mass from the storm
hydrographs which were given their highest solids concentrations at the
earliest part of the storm. In other words, the model was a bit overwhelmed
in the first time step or two to try to put some mass into very little water,
and by the time it had enough water to operate with comfortably, the storm-
water concentrations were already becoming very small. Comparison of the
combined sewer results in Figure 26, the sanitary sewer results in Figure 32,
and the storm sewer results in Figure 33 will show that, at least in our
examples, the sanitary sewage had the predominant effect on overall effluent
quality. That is not always the case, and more realistic runoff solids
concentrations would very likely have produced quite different results.
Finally a comparison of cases similar in slope, shape, and treatment
type from the combined sewer set and the separate sewer set is presented in
Table 12. The cases, IIIA, IVA, and VIA, were the same as Cases III, IV,
and VI in the combined sewer set, except that the treatment plant at pipe 3
was reduced to 16 cfs from 25 cfs or to 32 cfs from 50 cfs to make these
cases more nearly comparable to their counterparts in the separate sewer
array. The results of the comparison are that the combined sewer systems
were always comparable in overall removal capability with the separate sewer
systems, and usually they gave rise to a higher degree of removal by treatment
and a lower degree of accumulation in the pipes. This cannot be judged to be
a general finding, but it is the overwhelming indication for the size, shape,
and slope combinations analyzed here.
The Effect on Cost
The costs of all the alternatives analyzed in this project are given in
Table 13. Two of the cases in the table, numbers XIII and XIV, are cases in
which the surcharged storm sewers in Cases VIII and IX were resized to larger
pipes to contain the flow, and the outfalls were made a foot smaller to try
to realize some economy. So the pipe sizes in Case XIII were 6, 7, 8, and 7
feet for the four storm sewers, from upstream to down, and the slopes and
other characteristics were the same as in Case VIII. The sanitary sewers
were unchanged. In Case XIV the storm sewers were also 6, 7, 8, and 7 feet
in diameter, and the remainder of the features were the same as in Case IX.
The data in Table 13 are plotted in Figures 34 and 35. Figure 34 is a
plot of all the annual treatment costs and the removal percentages attained
87
-------
600 i—
STORM SEWER-NO SWIRLS
UPSTREAM
STORM SEWER - SWIRL
CONCENTRATORS UPSTREAM
10 15
TIME, hours offer midnight
20
25
Figure 33
Effect of Upstream Treatment
for Solids Removal in Storm Sewer System as Modeled
-------
TABLE 12. COMPARISON OF RESULTS FOR COMBINED
AND SEPARATE SEWER SYSTEMS
Case I
Case VII
Case II
Case VIII
Case V
Case XI
Case VI
Case XII
Case VIA
Case IIIA
Case IX
Case IVA
Case X
(25 cfs)**
(16 cfs)
(25 cfs)
(16 cfs)
(25 cfs)
(16 cfs)
(50 cfs)
(16 cfs)
(32 cfs)
(16 cfs)
(16 cfs)
(16 cfs)
(16 cfs)
Removed by
Treatment
15.1*
11.8
25.6*
22.0
50.5*
42.1
80.7*
59.6
78.7
20.6
21.8*
53.8*
40.2
Percentage of
Remaining in
Pipes
35.1*
42.7
11.1*
17.7
11.1*
17.7
7.8*
25.7
7.8*
16.9*
17.8
8.6*
17.7
Solids
Discharged
49.8
45.5*
63.3
60.3*
38.4*
40.2
11.5*
14.7
13.5
62.5
60.4*
37.6*
42.1
Removed
Overall
50.2
54.5*
36.7
39.7*
61.6*
59.8
88.5*
I
85.3
86.5
37.5
39.6*
62.4*
57.9
* Indicates better finding of the two compared.
**Numbers in parentheses are the treatment capacities of the
main dry-weather plants.
89
-------
TABLE 13. SOLIDS REMOVAL AND COST RESULTS
FOR EXAMPLE CASES
Example
Case
I (25)*
II (25)
III (25)
IV (25)
V (25)
VI (50)
IIIA (16)
IV (16)
VIA (32)
Cunettes-comb. (25)
Cunettes-rect. (16)
VII (16)
VIII (16)
IX (16)
X (16)
XI (16)
XII (32)
XIII (16)
XIV (16)
Cunettes-sep. (16)
Cunettes-eni . (16)
01
h
Overal 1
Removal
50.2
36.7
44.2
63.1
61.6
88.4
37.5
62.4
86.5
45.9
39.0
54.5
39.6
47.7
57.9
59.8
85.3
39.6
47.8
51.1
51.0
%
Removed by
Treatment
15.1
25.6
20.1
54.6
50.6
80.7
20.6
53.8
78.7
20.4
19.6
11.8
22.0
16.7
40.2
42.1
59.5
21 .8
16.4
14.3
14.4
Annual
Pipe
Cost,
$1,000
324.5
312.6
319.4
312.6
312.6
264.5
319.4
312.6
264.5
412.6
697.7
370.7
356.6
365.0
356.6
356.6
314.8
388.5
398.5
471.2
527.1
Annual
Treatment
Cost,
$1,000
494.4
494.1
494.1
528.7
794.5
918.6
382.5
411.1
707.0
496.3
382.6
376.3
375.9
376.1
408.1
580.2
666.4
375.9
376.1
377.2
377.4
Total
Cost
$l,000/yr.
818.9
806.7
813.5
841.3
1,107.1
1,183.1
701.9
723.7
971.5
908.9
1,080.3
747.0
732.5
741.1
764.7
936.8
981.2
764.4
774.6
848.4
904.5
*Numbers in parentheses are the capacities of the main
dry-wether treatment plants in cfs.
90
-------
1000
800
w
x
o
o
o
*! 600
CO
o
o
LU
LU
o:
400
200
0
O COMBINED SEWER VALUES
X SEPARATE SEWER VALUES
I
0
20 40 60 80
PERCENT REMOVAL BY TREATMENT
100
Figure 34
Treatment Costs and Solids Removal Percentages
for Example Cases
91
-------
1200 r-
1000
CO
o
o
5
600
e
400
200
0
O COMBINED SEWER VALUES
X SEPARATE SEWER VALUES
I
0
20 40 60 80
PERCENT OVERALL REMOVAL
100
Figure 35
Total Sewer System and Treatment Cost vs.
Overall Removal Percentages for Example Cases
92
-------
by treatment in the various cases. As might be expected, greater removal
percentages resulted from providing more treatment capacity and higher
degrees of treatment. At the low end of the removal scale, the separate
system with 16 cfs of primary treatment resulted in the minimum cost. For
higher solids removal levels, the minimum cost was provided via the combined
sewer system with larger and more complete treatment.
Figure 35 shows that the minimum total cost to achieve overall removal
was attained throughout the range of removals by the combined sewer system.
These results, like others reported here, are not general findings but
are related to the scale and other characteristics of the example problem.
In this exercise the combined sewer was the more cost effective because most
of the solids were in the sanitary wastes, not in the stormwater. Therefore,
it could have been expected that one pipe system to deal with the large
majority of the solids would be more cost effective than two pipe systems to
deal with all of them. For collection and treatment of more heavily laden
storm flows, a separate system of storm and sanitary sewers may prove to be
more cost effective. The model developed in this project and described
herein can be used as demonstrated to evaluate such a situation as well.
Indeed the purpose of the model is to analyze wastewater and stormwater
collection and treatment alternatives for a wide variety of conditions.
USE OF THE MODEL IN OTHER APPLICATIONS
Hopefully the example problems discussed here at some length have shown
that there is no simple recipe or cookbook approach to complex sewer system
analysis. There are many variables to consider and they interact to provide
some kinds of benefits while generating opposing kinds of costs. The analysis
of a total waste handling system remains an exercise of selective searching.
But the examples do suggest some guidelines for sewer analysis that may be
helpful. These are itemized below.
1) Sewers that accumulate little or no solids will permit
downstream treatment to be most effective, until the
treatment capacity is attained. Increasing slope by 50
percent or more in new sewer design can improve treatment
by as much as 100 percent, sometimes with a reduction in
cost for the pipe system. Therefore, a first thing to
try in laying out a new sewer network might be:
Increase slopes of pipes to the point that accumulation
does not occur during the design event as modeled.
2) Although the cunette sections analyzed here were not cost
effective, it is possible that the increased cost of
installing these special conduits may be offset by
improvements in dry-weather treatment efficiency and lower
accumulation rates. The second guideline might be:
93
-------
Analyze sewer cross-section shapes to determine the most
cost effective one with a fixed amount and degree of
treatment in place.
3) Upstream treatment of stormwater in the example cases was
a cost effective addition. Solids removal by treatment
increased from 25.6 percent to 54.6 percent for a 4.3
percent increase in cost to provide swirl concentrators
in the combined system. A similar benefit was realized
with adding swirl concentrators to the storm sewer of the
separate system. So the third guideline might be:
Assign dry-weather treatment to handle the peak dry-weather
flow and provide upstream treatment to accommodate all or
part of the storm flow. Analyze alternatives to this
mixture.
4) Increased treatment capacities and degrees of removal cost
money roughly in proportion to the improvement in solids
removal attained, until high degrees of removal are achieved.
After this point there is a decreasing return in removal for
increased treatment efficiency. This must be balanced by
trial and error. The fourth guideline, then, would be:
Analyze alternatives with higher and higher degrees of
removal capability until decreasing marginal gains are
achieved in solids reduction per treatment dollar spent.
These guidelines have been suggested by the examples analyzed in this
project. Quite different situations may well suggest another sequence to
follow. But it seems clear that the model described is capable of analyzing
the solids behavior and capture in pipe systems of various sizes, shapes,
and types. The general finding of greatest significance is probably that
accumulation of solids in the pipe system may occur at several points
throughout a day and the accumulated solids are likely to be swept past a
dry-weather treatment device at precisely the worst moment—when it is
already hydraulically overloaded. Design of the collection system is a
critical part of design for the treatment plant. Indeed these designs should
be conducted simultaneously, and the model developed here permits this.
94
-------
REFERENCES
ASCE Task Committee for the Preparation of the Manual on Sedimentation,
Sedimentation Engineering. Vito A. Vanoni (ed.), American Society of Civil
Engineers, New York. 1975. 745 p.
Brandstetter, A., Assessment of Mathematical Models for Storm and Combined
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(NTIS No. PB 258 644). August 1976. 530 p.
Benjes, H.H. Jr., Cost Estimating Manual--Combined Sewer Overflow Storage
Treatment. U.S. Environmental Protection Agency Report No. EPA-600/2-76-286
(NTIS No. PB 266 359). December 1976. 123 p.
DiGiano, Francis A. and Peter A. Mangarella, Short Course Proceedings:
Applications of Stormwater Management Models. U.S. Environmental Protection
Agency Report No. EPA-670/2-75-065 (NTIS No. PB 247 163). June 1975. 427 p.
Durand, R., "Basic Relationship of the Transportation of Solids in Pipes--
Experimental Research," Proceedings, Minnesota International Hydraulics
Conference, Minneapolis. September 1953. pp. 89-103.
Einstein, H.A., The Bed-Load Function for Sediment Transportation in Open
Channel Flow. U.S. Department of Agriculture, Technical Bulletin No. 1026.
1950.
Fair, Gordon Maskew and John Charles Geyer, Water Supply and Wastewater
Disposal. John Wiley & Sons, Inc., New York. 1954, revised 1963. 973 p.
Graf, Walter Hans, Hydraulics of Sediment Transport. McGraw-Hill Book
Company, New York. 1971. 513 p.
Heaney, J.P., et_ aj_., Urban Stormwater Management Modeling and Decision
Making. U.S. Environmental Protection Agency Report No. EPA-670/2-022
(NTIS No. PB 242 290). May 1975. 186 p.
Huber, W.C., et_ a_L , Stormwater Management Model User's Manual-Version II.
U.S. Environmental Protection Agency Report No. EPA-670/2-75-017. March 1975
350 p.
Kalinske, A.A., "Movement of Sediment as Bed-Load in Rivers," Transactions of
the AGU, Vol. 28, No. 4. 1947.
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Kibler, D.F., e^ aj_., "Berechnung von stadtischen kanalisationsnetzen,"
Report presented at Conf. on Sewer System Calculation Techniques, Dortmund
University, Dortmund, Germany. F.H. Kocks K.G. and Water Resources Engineers.
December 1973.
Kibler, D.F., J.R. Monser and L.A. Roesner, San Francisco Stormwater Model
User's Manual and Documentation. Prepared for the City and County of San
Francisco, Water Resources Engineers, Walnut Creek. 1975.
Metcalf & Eddy, Inc., University of Florida, Water Resources Engineers, Inc.,
Stormwater Management Model, Volume I, Final Report. U.S. Environmental
Protection Agency Report No. 11024DOC07/71 (NTIS No. PB 203 289). July 1971.
364 p.
Metcalf & Eddy, Inc., University of Florida, Water Resources Engineers, Inc.,
Storm Water Management Model Volume 11-Verification and Testing. U.S.
Environmental Protection Agency Report No. 11024DOC08/71 (NTIS No. PB 203 290).
August 1971. 83 p.
Metcalf & Eddy, Inc., University of Florida, Water Resources Engineers, Inc.,
Storm Water Management Model Volume Ill-User's Manual. U.S. Environmental
Protection Agency Report No. 11024DOC09/71 (NTIS No. PB 203 291). September
1971. 373 p.
Metcalf & Eddy, Inc., University of Florida, Water Resources Engineers, Inc.,
Storm Water Management Model Volume IV-Program Listing. U.S. Environmental
Protection Agency Report No. 11024DOC10/71 (NTIS No. PB 203 292). October
1971. 255 p.
Montgomery-Water Resources Engineers, A Joint Venture, Water, Wastewater and
Flood Control Facilities Planning Model, Summary Report. Submitted to the
Comprehensive Planning Organization-San Diego Region. January 1974. 189 p.
Paintal, A.S., "Interceptor Sewer Cost Analysis," Water and Sewage Works,
Vol. 122, No. 11. November 1975. p. 44.
Rendon-Herrero, Oswald, "Estimation of Washload Produced on Certain Small
Watersheds," Journal of the Hydraulics Division, ASCE, Vol. 100, No. HY7.
July 1974. pp. 835-848.
Shubinski, R.P. and L.A. Roesner, "Linked Process Routing Models,"*Paper
presented at Amer. Geophys. Union Annual Spring Meeting, Washington, D.C.
1973.
Sullivan, R.H., et_ aj_., Relationship Between Diameter and Height for Design of
a Swirl Concentrator as a Combined Sewer Overflow Regulator. U.S. Environ-
mental Protection Agency Report No. EPA-670/2-74-039 (NTIS No. PB 234 646).
July 1974. 44 p.
96
-------
Water Resources Engineers, Program Documentation and User's Guide for the
Urban Storm Drainage Simulation Models Including the Urban Storm Drainage
Cost Determination Program. Draft Report submitted to U.S. Army Corps of
Engineers, Seattle. July 1974. With Kramer, Chin & Mayo and Yoder, Trotter,
Orlob & Associates.
97
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ADDITIONAL BIBLIOGRAPHY
American Public Works Association, Combined Sewer Regulator Overflow
Facilities. U.S. Environmental Protection Agency Report No. 11022 DMU 07/70
July 1970. 139 p.
Bremner, Raymond M., "Plastic Relining of Small-Diameter Pipes," Journal of
the Sanitary Engineering Division, ASCE, Vol. 96, No'. SA2. April 1970.
pp. 297-317.
Carstens, Marion R. and Hilmi D. Altinbilek, "Bed-Material Transport and Bed
Forms," Journal of the Hydraulics Division, ASCE, Vol. 98, No. HY5. May 1972.
pp. 787-794.
Central Engineering Laboratories, FMC Corporation, A Flushing System for
Combined Sewer Cleansing. U.S. Environmental Protection Agency Report
No. 11020 DNO 03/72 (NTIS No. PB 210 858). March 1972. 235 p.
Field, Richard and John A. Lager, Countermeasures for Pollution From Overflows.
the State of the Art. U.S. Environmental Protection Agency Report No. EPA-670/
2-74-090 (NTIS No. PB 240 498). December 1974. 30 p.
Fields, David E., CHNSED: Simulation of Sediment and Trace Contaminant
Transport with Sediment/Contaminant Interaction, ORNL/NSF/EATC-19, Oak Ridge
National Laboratory, Oak Ridge, Tennessee. March 1976. 204 p.
Fisher, J.M., G.M. Karadi and W.W. McVinnie, "Design of Sewer Systems,"
Water Resources Bulletin. AWRA, Vol. 7, No. 2. April 1971. pp. 294-302.
Hjelmfelt, Allen T. and Charles W. Tenau, "Nonequilibrium Transport of
Suspended Sediment," Journal of the Hydraulics Division, ASCE, Vol. 96,
No. HY7. July 1970. pp. 1567-1586.
*
Hydro Research & Development A/S Ltd., The Hydro-Brake* System: A New
Approach to Urban Runoff, Oslo, Norway, circa 1975, 21 p.
Jewell, Thomas K. and Peter A. Mangarella, "Workshop Study Guide," in
Applications of Stormwater Management Models--1975. Short Course Sponsored
by the U.S. Environmental Protection Agency, University of Massachusetts.
July 28-August 1, 1975. 83 p.
Joint Committee, ASCE and WPCF, Design and Construction of Sanitary and Storm
Sewers, ASCE Manual No. 37, WPCF Manual No. 9, American Society of Civil
Engineers and the Water Pollution Control Federation. New York and
Washington, D.C. 1969. 332 p.
98
-------
Lager, John A. and William G. Smith, Urban Stormwater Management and Technol-
ogy: An Assessment. U.S. Environmental Protection Agency Report No. EPA-670/
2-74-040 (NTIS No.~PB 240 687). December J974. 446 p.
LeFeuvre, A.R., H.D. Altinbilek and M.R. Carstens, "Sediment Pickup Function,"
Journal of the Hydraulics Division, ASCE, Vol. 96, No. HY10. October 1970.
pp. 2051-2063.
Leiser, Curtis P., Computer Management of a Combined Sewer System. U.S.
Environmental Protection Agency Report No. EPA-670/2-74-022 (NTIS No. PB 235
717). July 1974. 475 p.
Lysne, Dagfinn K., "Hydraulic Design of Self-Cleaning Sewage Tunnels," Journal
of the Sanitary Engineering Division, ASCE, Vol. 95, No. SA1. February 1969.
pp. 17-36.
Merritt, LaVere B. and Richard H. Bogan, "Computer-Based Optimal Design of
Sewer Systems," Journal of the Environmental Engineering Division, ASCE,
Vol. 99, No. EE1. February 1973. pp. 35-53.
Neale, Lawrence C. and Robert E. Price, "Flow Characteristics of PVC Sewer
Pipe," Journal of the Sanitary Engineering Division, ASCE, Vol. 90, No. SA3.
June 1964. pp. 109-129.
Ordonez, J.I., "Modeling Sediment Deposition in a Tidal River," Volume II:
Symposium on Modeling Techniques, San Francisco, September 3-5, 1975, ASCE.
New York. pp. 1347-1368.
Pomeroy, Richard D., "Flow Velocities in Small Sewers," Journal of the Water
Pollution Control Federation, Vol. 39, No. 9. September 1967. pp. 1525-1548.
Pomeroy, Richard D., "Flow Velocities in Small Sewers," Presented to the
Atlantic City Conference of the Water Pollution Control Federation.
October 13, 1965. 18 p.
Robinson, Millard P., Jr. and Walter H. Graf, "Pipelining of Low-Concentration
Sand-Water Mixtures," Journal of the Hydraulics Division, ASCE, Vol. 98,
No. HY7. July 1972. pp. 1221-1241.
Sartor, J.D. and G.B. Boyd, Water Pollution Aspects of Street Surface
Contaminants. U.S. Environmental Protection Agency Report No. EPA-R2-72-081
(NTIS No. PB 214 408). November 1972. 236 p.
Sullivan, Richard H., et. aj_., The Swirl Concentrator as a Grit Separator
Device. U.S. Environmental Protection Agency Report No. EPA-670/2-74-026
(NTIS No. PB 233 964). June 1974. 92 p.
Takamatsu, Takeichiro, Masaaki Naito, Sadataka Shiba, and Yasuyo Ueda,
"Effects of Deposit Resuspension on Settling Basin," Journal of the Environ-
mental Engineering Division, ASCE, Vol. 100, No. EE4. August 1974.
pp. 883-903.
99
-------
Task Committee for Preparation of Sediment Manual (ASCE), "Sediment Transpor-
tation Mechanics: H. Sediment Discharge Formulas," Journal of the Hydraulics
Division. ASCE, Vol. 97, No. HY4. April 1971. pp. 523-567.
Task Committee for Preparation of the Sedimentation Manual (ASCE), "Sediment
Transportation Mechanics: J. Transportation of Sediment in Pipes," Journal
of the Hydraulics Division, ASCE, Vol. 97, No. HY7. July 1970. pp. 1503-1538
U.S. Army Corps of Engineers, Seattle District, Urban Storm Drainage Simu-
lation Models, Appendix B of Part II, Urban Drainage of Environmental
Management for the Metropolitan Area: Cedar-Green River Basins, Washington.
December 1974. 417 p. (With Kramer, Chin & Mayo; Water Resources Engineers;
Yoder, Trotter, Orlob & Associates).
100
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Appendix
LISTS OF NEW MODEL SUBROUTINES
101
-------
S C tf 0 E P
1 . SU3ROUTIME SCROE=
2. CO^ON/SETTLE/G4*S( 10)»GAM,PNU,f.HAV
3. CO^ON /SEOMT/ S-OUOOf 10) ,REP(100, 10) . AVAILMO) , *L( 10) ,SL( 10) ,
a. 1 BLflO) , TRANS(IO)
5. CO^ON/SOIIOS/S = E'*(100,10),GA'HJI(100,10)
fa. CO*MDN/SCOWR/BLCOM(100) , SLCONUOO),«LCON(100),BOT(100),DSOL(10),
7. 1 TAUC(10),DELT3,NDEPS,AOEP,SD()0),VSSUO),R10,SDl"inO),SG.»aiO).
H. 2 SODUO) ,SGD( 10)
9. COMMON /JUMCT/ MJ,JUN(tOO),NCHAN(100,8),MASSlMf100,3),C(100.3),
10. 1 Y(100,2) , YAVEf 1 00) ,VUL( 100) ,VOL3(100) , JSKIPf 100)
11. CnvlwQN/CDMD/ NC,MTC,NCUNO(100),NKLASSMOO),DEFPUOQ),«IDE(100),
12. 1 4FULL(100),:?FJLL(100),LFN(100),MJUMC(10n,?),Q(100,2),04VF(100),
13. ? VC100) ,HY3A3( 100) ,ZP(100,2)
1«. CO^MON/TREET/ REvIOV(10»3),NJTRT,NPLAC(20),NTRCLS(20),TOTRE>'li,
15. 1 QTRTC20) ,QOES(20) ,NLOC( 100) , W4STOT, AMREMV,OEPO
Ib. 2 .ITREAT, IBEO
17. Cn«MON/T:TSnL/OE3DS(100),WLT(aO),SLT(?n),RLTC?0),4w4SM(lOO),
18. 1 SC?SOL( 1 00) ,DEPnST(100) ,80L4ST(100) ,BOFWST( 100)
19. ? ,«ASH( 100) ,TOTI«SHf SCRTOT,SCPTIM(100)
20. RE4L
21. RE4L
22. C
?3. C**** INITI4LIZE V43I43LES
2u. C
25. DEos = M5EPS
2fe. VK = 0.385
27. C**** U"DATE P3UNOS DF SEDIMtMT IN POTENTI4L ^nTTHN 4T JUNCTIONS
2". 00 25 J = 1,MJ
30. N = NCHAM(J,2)
31. MflSTDT = viASTO
32. DO 25 ISZ = 1, 10
33. 4LIWK s SEDCJ,ISZ)
3U. SEO(J,ISZ) = SED(J,ISZ) * MASSIN( J. 2) *SPtP ( J, ISZ)
35. IF(N.GT.MC) SEDCJ.IS7) = SEDtJ.ISZ) -
3fe. IF(SED(J,ISZ) .LT.0.0) StO(J,ISZ) = 0.0
37. 25
38. C
uo . C
Ul. C ilAJOR D(J LOOP flN PIPES
a?. c
uj. C ****»**»*************. *****
a« . c
U5. DO aOOO NJ = 1 , NC
Ub. SCRSOL(N) = 0.0
U7. 3DL4ST(N) 2 0.0
a«. AWASH(N)=0.0
UQ. DEPOS(M) = 0.0
50. AaSH(N')=0.0
51 . SCBTIM(IM) - 0.0
52. C
53. c**** COMPUTE »IPE C3M?T4-MTS
5a. c
55. IF CIENCM) .LE.0.0) GO TO JOOO
58. IF(VCN). LT.0.0. AMP. ArtSlVCNn.LT.O.OOOnvC*1) = -0.0001
S7. IF(A8S(V(M)).LT.0.0001)V(M) s 0.0001
102
-------
S C R D E P
58. J1 = NJUNCCN, 1 )
59. J2 = NJUMCCN,?)
60. IF (QAVE(N)) 100,200,200
61. 1 HO J = J?
62. < = Jl
63. HI = YAVE(J) + ZP(N,2)
b«. H2 = YAV£(K) t Z'CN, 1 )
65. GH TO 300
6b. 200 J = Jl
67. « z J2
b8. HI s YAVE(J) + ZP(N,1)
69. H2 = YAVE(K) + ZP(N,2)
70. 300 CONTINUE
71. OEP = (YAVECJl ) tYAVEfJ2) )/?.
72. IFfDEP.LE. 0.0) GO TO 4000
73. B = QAVE(^) /(V(M)*DEP)
7U. S = (H1-H2)/LEN(VI
75. IF(S.LT.O.OOOOOnS = 0.000001
76. TAU = GAM*HY540(M)*S
77. IF(TAU.LT.O.000001)TAU=0.000001
7fl. USTAR = SQWT(TAU*GRAv/GAM5
79. C
80. ISIZ - 0
9i. no uoo isz = 1,10
82. IFCGAMJI(Jl,ISZ).5T.62.^1.AND.V(N).GE.0.0) ISIZ = ISIZ * 1
93. IFCGAMJKJ2,ISZ).GT.62.^1.AMD.V(N).LT.0.0) ISIZ = TSTZ + 1
8U. *VL(ISZ) = 0.0
«5. SL(ISZ) = 0.0
H6. BL(ISZ) = 0.0
H7. aOO CONTINUE
98. « = ISIZ/2 * 1
«9. 910 = USTAR*DSDLC*)/PNU
90. ADEP = 2.0*0501(^5
91. IF(AOEP.GE.HEP) 40EP = 0.98*OFP
92. C *** DETERMINE If- THE3E IS TREATMENT AT ODVNSTREAM END OF PIPE
93. *T = MLOC(N)
on.
-------
S C R D E P
115. 1300 F = V(N) - 5. 75*SQRT(S*RG*GRAV)*ALOG10(1 2 . 27*RG/OSOL(M))
lib. FF = ARS(F)
117. IF (FF.LT.FMT.M) S3 TO 13bO
1 IS.
-------
S C P 0 E P
171. SED(K,ISZ1 = StD(*,IS7> + l*L (I SZ) * C 1 . -R 11
172. AMRfviv = AMRE^V 4- .iLdSZl * HI
173. Ati'ASH(N) = AdASH(M) + rtL(ISZ)
17U. yMASH(N) = wASH(N) + WL(ISZ)*( 1 ,-Rt )
175. TOTASH r TOTdSH + /vL(ISZ)
176. IF(^T.GT.O)WLTMT)=rtLTCMT)+wL(ISZ)*Rl
177. SED(J.ISZ) = SEDfJ.ISZ) - OTHER
178. BEDCN,ISZ) = 3ED(M,ISZ) + OTHER
179. DEPO = DEPO + 3THER
1«0. OEPOSCNl s DEPDS(N) «• OTHER
181. OEPOSTCN) = OE°3ST(M) + OTHER
182. GO TO 1200
18U. DEPQ = DEPO + TR4MSCISZ)
IBS. DEPOS(M) = DEPDSfM) t TRANS(ISZ)
166. DEPOST(N) = OEPOST(N) + TR4MSCISZ)
1S7. SEO(JrlSZ) = SE'3(J,ISZJ - TR4NSCISZ5
188. «LCISZ5 = 0.0
189. C
IPO. c**** BED L040 COMPUTATIONS
191 . C
192. 1?00 FTCDT ^ T 4UC ( I SZ ) /TAU
193. IF(FTCOT.GT.3.0) -TCOT=3.0
19a. 90UO = 2./10.**FTCOT
195. IF(FTCOT.GT.2.)Q3JD=«3i*.31/10.**(2.18838*FTCnT)
19fc. IF(FTCOT.LE.0.3)30UD=27./10.**CU.771?l*FTCOn
197. Q3 = UST4R*DSOL(ISZ)*QOUO
198. GS = QS*GAMJK Ji, ISZ)
199. IFCV(N) ,LT.O.O)GS = QS*G4MJI ( J2.ISZ)
200. C * * 'GS' IS IN UNITS OF 'LBS/SEC-FT'
201 . C
202. C**** SUSPENDED LOAD CIMPUTATIOMS
?05. C
20«. Z= VSSCISZ)/CV<*JSTAR)
205. IFCZ.GT.3.0) Z = 3.0
206. GSS = 0.0
?o7. DELY = DEP/DEPS
208. YY :-0.5*DELY
209. C
210. C COMPUTE 5EFFREVCE SUSPENDED SEDIMENT CONCENTRATION CCA1
211.
212. CA = GS/( 1 1 .6*SQ3T(S*WG*GRAV)*AP£P)
213.
?ia. C COMPUTE SUSPENDED SEDI^tNT LOAD THROUGHOUT DEPTH
215.
216. DO 1500 IY sl.MDEPS
217. YY s YY + DELY
21«. UY = IJST4R* (5.5+5. 75*4LOG10 ( USTAR* YY/PNU) )
219. IF(R10.GT.10.)JY=USTAR*(8.5+5.75*AL3G10(YY/OSnL(y)))
220. COMY = CA*f ( (DEP-YY) /YY)*(AOEP/(OEP-ADFP) ) 1**Z
?21. GSS = GSS + :OMY»JY*OELY
222. 1500 CONTINUE
223. C * * 'GSS1 IS IN UMITS OF 'LBS/SEC-FT'
22U. C
225. C**** CDMDUCT SEDI^EMT ^ALANCt AND TRANSPORT
226. C
227. GS = GS * R *
105
-------
S C R 0 E P
223.
22°.
230.
?51 .
232.
231.
23U.
235.
236.
237.
238.
239.
2UO.
2SL(TSZ)*R2
BED(N,ISZ) = BED(M,ISZ) - SLCISZ)
GO TO 1900
1650 SEOCK,ISZ) = SEDCK,ISZ)*BEDCN,ISZ)*(1.-R2)
AM^E^V = AMR£Mv +• BED (N, ISZ) *R2
IF(«T.GT.O)SLTCUT) = SLT(MT)+BEDCN,ISZ)*R2
SLC ISZ) = HEDCM,ISZ)
BLC ISZ) = 0.0
9EDCN, ISZ) = 0.0
GO TO 2900
1900 CONTINUE
IFCRLCISZ),GT.3ED(M,ISZ))GO TO 2600
SEDCK,ISZ) = SED«,ISZ) + RL ( I SZ ) * C 1 .-«3 )
AMRE^V = AMRE^V *• 8L(ISZ)*R3
IFC^T.GT.O)fllT(vlT)=BLT(MM+RL(ISZ)*R3
BED(NJ,ISZ) = 3ED(^,ISZ) - RUISZ)
GO TO 2900
2600 SED(K,ISZ) - SED«,ISZ) * RED ( N , I S Z ) * C 1 .-W.3 )
4M«E^V = AMRE^V * BEDCN,ISZ)*R3
IF(«T.GT.O)BLTC"SL(ISZ)*C1.-R2) * HLCTSZ ) *C1 .-R^)
SCRTIMCN) = SC3TI«(M t SLCISZ) + BLCISZ)
SCHTOT = SCRTOT t SLCISZ) + BL(ISZ)
BOLAST(N) = SDL^STCM) + BEDCN.ISZ)
C EMD OF SEDIMENT SIZE UO LOOP
C
3000 CGMTINUE
C
IFt^T.LT.1) 50 T3 3001
C 'WICON1 , 'SLCON1 , AND 'BLCON' ARE THE LPS IF SOLIDS OF
C REMOVED 3Y TRE4T^ENT PLANT 'MT' IN THE CUBPFMT
TYPES
PERIOD
SLCON(MT) = SLT(«T) - SLCON(«T)
9LC3N(«T) -
3001 CONTINUE
EMD OF ?IPF.
C 0 M T I M U E.
U30P
106
-------
S C R D E P
285. C
2flb. C**** COMPUTE CONCENTRATION (L8S/CU8IC FOOT) OF SFDTMENT I M
2«7. C
2S3. 00 5020 J=1,MJ
239. C(J,2) = 0.0
DO 5000 IS?=1 , 10
C(J,2) = C(J,2) + SEO(J.ISZ)
5000 CONTINUE
CCJ,2) * C(J,2)/V3L(J)
29U. IMVOK J3 .LT.0.01 ) C(J.2) = 0.0
295. S020 CONTINUE
296. RETURN
297. END
107
-------
S C R 0 J T
1. SUBROUTINE SCR3UT
2. COMMON /JUNCT/ NJ, JUNC100) ,NCHAN( 100,B) ,MASSIN( 1 00, 3) ,C( 100,3) ,
3, i YC 100,2) ,YA\/E(ioo) ,voiuoo) .voiac too) ,jsKiP(ioo)
q. CO^ON /CDND/ NC,NTC,NCOND( 100) ,NKLASSf 100) ,nEEP(100) ,wIOF( 100) ,
5. 1 AFULK100),RFJLL(100),LEN(100),NJUNC(100,2),QC100,2),QAVF(100),
6. 2 VUOO) ,HYRAO( 1 00) ,ZPUOO,2)
7. CO^ON/SCOWR/qLC3N( 100).SLCON(100),^LCr>N(100),8dT(100),OSOL(10),
B. 1 TAUC(10),DELT°,NDEPS,ADFP,SD(10),VSSUO),Rin,SDW(10),SGAi(10),
9. 2 300(10) ,SGD(10)
10. COMMQN/TREET/ SE'OVt 10,3) ,NJTRT,NPLAC(20) .NTRCLSC20) .TOTREM,
11. 1 QTRT(20J,QDES(20) ,NLOC(10>. T F « . E T . 1 ri ) 3. ITT
57.
110
-------
S F T V E I
58. C * * "OMCDNVE^GEMCE EW3QW MESSAGE - - PRDG^ivi j F- RW T MA r Tf.M
59.
60. "13 NBITE(b,9130)K,« ,F,Fn,CQNl , A.O,H
hi. 0130 *0»«AT ( MO, 1 0*, ' MDMCPNVtfiGfc'NCfc" ES""1« «E SSAGf: ',//,' K1,
b2. 1 ' F ' , ' Fn ' , ' C3M1 ' , ' StT
M. ?' DIAM. ',' REY. NlJW ,//,?T5,?Fl n.h^FlS.^.Fis.'ij
85. ST3P
bb.
67. C * * STORES WAN3E fS.LT.O.l)
bB. °1U M = (GRAtf/18. )*( (GftTRY-GAM)/GAM)* (D**?./PMI)
6«. "315
70. "ETURN
71.
111
-------
TREAT
1. SURROUTIME TREAT
3. 1 TAUC(10),OELTR,MOEPS,AOEP,SD(10),VSS(10),R10,SDWUO),SGAi(10),
4. 2 S00(10),SGO( 10)
5. CO^ON/TREF.T/ REW3VC 1 0, 3) ,NJTPT,NPLAC(20) ,MTRCLSC20) ,TOTRFM,
7! 2 ,ITREAT,IRED
8. CO«viQNj /JUNCT/ M J, JUN ( 1 00 ) ,NCHAN( 1 00, 8) , VASSINC 1 00, 3) , C ( 1 00, 3) ,
9. 1 Y ( 100,2) , YAVEC 1 00) , VOLUOO) , VOL3C 100) , JSKTPM 00)
11. 1 AFULL(tOO),RFJLL(100),LEN(100),NJUNC(100,2),QMOO,2),QAVEttOO),
12. 2 VC 100) ,HY3A9(100),ZP(100,2)
14. 1 SC^SOLC100),DEPOST(100),HOIASTCl00),RDFRST(100)
15. 2 , AUSHC 100) » TOTWSH,SCBTOT,SCf
-------
TREAT
5*.
59. 10 FORMATU/, 5x,' PLANT NUMBER" ,13,' AT END OF piPE',13)
60. 11 FORMATM OX, "OESI3N FLOW =',F5.1," FT3/SEC')
6i. i? FORMAT (iox ,• AIAS-ILOAD REMOVAL PERCENTAGE',i2x,' = ',Fin. ij
62. 15 FORMAT(IOX,'SUSPENDED LOAD REMOVAL PERCENT AGE',6X,' = ',F 1 0 . 1)
63. 1U FORMAT(10X,'9EDL3AD REMOVAL PERCENTAGE', 15X, ' = ',F10 . 1)
6u. 15 FORMATC/,iox,"rtASHLOAD REMOVED DURING EVENT",iox,'=',FIo.o,'LBS')
65. 16 FORMAT(1 OX,'SUSPENDED LOAD REMOVED DURING FVENT ' , 4X, ' = ',F10.0, ' L3S
66. 1 ' )
67- 17 FORMATf10X,MEDL3AD REMOVED DURING EVENT', 11X, " = ",F I 0 . 0 , 'L*S',/)
63. 18 FORMAT( IOX , 'TOTAL LOAD REMOVED DURING EVEMT' , 8X , ' = ' , F 1 0 . 0 , ' LflS ' , / )
69. 20 FORMAT(1H1,15X, ' * * * OVERALL SYSTEM SUMMARY * * *',/)
70. 21 FORMAT(iox,'POUNDS OF SOLIDS ON BOTTOM AT BEGINNING OF FVFNT =',
71. 1 FIO.O)
72. 22 FORMAT!/, IOX, 'POUNDS OF SOLIDS ON BOTTO" AT FND OF EVENT ' ,9X , ' = ' .
73. 1 FIO.O)
7U. 23 FORMAT(/I OX, 'POUMDS ENTERING THE SYSTEM DURING THE FVENT' ,7X, ' = ' ,
75. 1 FIO.O)
76. 2U FOS'"AT(/, 1 OX, ' OQJNDS DISCHARGED FROM SYSTEM DURING EVENT ' ,8X, ' = ' ,
77. 1 FIO.O,/,39X, ' (CHECK VALUE ' , 9X, ' = ' , F 1 0 . 0 , ' ) ' )
78. 25 FORMAT(/, 1 OX, 'POJNDS REMOVED 8Y TREATMENT DURING THE EVENT',6X,'='
79, 1 , FIO.O)
80. 26 FORMATCX.IOX, ' NET POUNDS SCOURED(-) OR OEPOS I TED( + ) IN EVENT", UX,
HI. 1 • -' , FIO.O)
«2. 27 FORMAT (/, IOX,'NET POUNDS REMOVED (DEPOSITION + TREAT«ENT) ' , 7* , ' = ' ,
93. 1 FIO.O)
9U. 29 FORMAT (/,25X ,'OVERALL PERCENTAGE R£yOVAL',°X, ' = ' ,F 1 0 . 1 )
95. IF(ICOST.LT.1) 33 TO 500
97. ICC - 0.0
99. TD3LY = 0.0
99. TCCA = 0.0
90. TOCDST = 0.0
91. DO 300 M : 1,NJT?T
92. < = NTRCLS(M)
95. D^IL = ACC (K) *QDES(M)**6CC (K )
9a. IF(K.EQ.6)DOL = 33LtACC(5)*QDES(M)**RCC(5)
95. TCC - TCC * 30L
97. 1
QR. TDDLY - TDOLY » 50LY
99. CCA = DOL * CRF
100. TCCA = TCCA + CC4
101. TA\JC = CCA + D3LY
102. TOCOST = TOCDST + TANC
103.
10a. ARITE(6,200)vi,K,DOL,CCA,DOLY,TANC
105. 200 FORMATfIi, II 1 , 5X,F16.0,f li.O,F12.0,Fl5.0)
106. 300 CONTINUE
107.
10«. A/RITE(6,UOO)TCC,TCCA,TOOLV,TOCOST
109. yOO FO"yAT(/, 17X, ' TOTALS' .F13.0,PI 3.0,F12.0.F15.0)
no. 101 FORMAT(m,//,?o»,'SUMMARY OF TREATMENT COSTS',/,
111. i 13X.'(PIPE COSTS FROM TRANSPORT MQDEL MUST *E AnOEQ)1,//,
IIP. ?1 X, " TREATMENT TREATMENT CONSTRUCTION AN;KJ. CONS. ANN.
113. 3 TOTAL AN\I. ',/, IX, 'PLANT NO. TYPE COST, POLL ARS COST,
11U. ut/YR COST, ^/YR CUST, T/YR',//)
113
-------
R F A T
115. SOOCIMTINUE
life. RETURN
117. END
114
-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1.REPORTNO. " p;
EPA-600/2-77-212
4. TITLE AND SUBTITLE
ABATEMENT OF DEPOSITION AND SCOUR IN SEWEF
7. AUTHOR(S)
Michael B. Sonnen
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Water Resources Engineers, Inc.
710 South Broadway
Walnut Creek, California 94596
12. SPONSORING AGENCY NAME AND ADDRESS
Municipal Environmental Research Laborator
Office of Research and Development
U.S. Environmental Protection Agency
Cincinnati, Ohio 45268
3. RECIf
5. REPO
<, Nove
6. PERF
8. PERF
10. PRO
1
11. CON
6
13. TYP
v— Cin.,OH F
14. SPOT
E
CENT'S ACCESSIOONO.
RT DATE
mber 1977 (Issuing Date)
ORMING ORGANIZATION CODE
ORMING ORGANIZATION REPORT NO.
12760
GRAM ELEMENT NO.
BC611
TRACT/GRANT NO.
8-03-2205
= OF REPORT AND PERIOD COVERED
inal
vISORING AGENCY CODE
PA/600/14
15. SUPPLEMENTARY NOTES
P.O. Richard Field (201) 321-6674 (FTS 340-6674)
16. ABSTRACT
Feasible methods are identified for reducing first-flush pollution in new
and existing storm and combined sewer systems. A mathematical model is described
which was developed to simulate the behavior of solids in pipelines and to evaluate
the costs of first-flush abatement alternatives.
17. KEY WORDS AND DOCUMENT ANALYSIS
a. DESCRIPTORS
Overflows, Combined sewers, Water pollutioi
Mathematical models, Cost effectiveness,
Cost comparison, Deposition, Flushing
RELEASE TO PUBLIC
b. IDENTIFIERS/OPEN ENDE
i, First-flush miti
Scour, Bed loads
Suspended loads
UNCLASSIFIED
20. SECURITY CLASS (This p
UNCLASSIFIED
EPA Form 2220-1 (9-73) 1 1 C
D TERMS c. COSATI Field/Group
gation,
13B
Report) 21. NO. OF PAGES
123
age) 22. PRICE
. 1
s GOVERNMENT PRINTING OFFICE, 1977- 757-140/661
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