WATER POLLUTION CONTROL RESEARCH SERIES 11024DOC07/71
Storm Water Management Model
Volume I—Final Report
ENVIRONMENTAL PROTECTION AGENCY • WATER QUALITY OFFICE
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WATER POLLUTION CONTROL RESEARCH SERIES
The Water Pollution Control Research Reports describe the results and progress
in the control and abatement of pollution of our Nation's waters. They provide
a central source of information on the research, development and demonstration
activities of the Water Quality Office of the Environmental Protection Agency,
through in-house research and grants and contracts with the Federal, State
and local agencies, research institutions, and industrial organizations.
Previously issued reports on the. Storm and Combined Sewer Pollution Control
Program:
11023 FDB 09/70
11024 FKJ 10/70
11024 EJC 10/70
11023 12/70
11023 DZF 06/70
11024 EJC 01/71
11020 FAQ 03/71
11022 EFF 12/70
11022 EFF 01/71
11022 DPP 10/70
11024 EQG 03/71
11020 FAL 03/71
11024 FJE 04/71
Chemical Treatment of Combined Sewer Overflows
In-Sewer Fixed Screening of Combined Sewer Overflows
Selected Urban Storm Water Abstracts, First Quarterly
Issue
Urban Storm Runoff and Combined Sewer Overflow Pollution
Ultrasonic Filtration of Combined Sewer Overflows
Selected Urban Runoff Abstracts, Second Quarterly Issue
Dispatching System for Control of Combined Sewer Losses
Prevention and Correction of Excessive Infiltration and
Inflow into Sewer Systems - A Manual of Practice
Control of Infiltration and Inflow into Sewer Systems
Combined Sewer Temporary Underwater Storage Facility
Storm Water Problems and Control in Sanitary Sewers -
Oakland and Berkeley, California
Evaluation of Storm Standby Tanks - Columbus, Ohio
Selected Urban Storm Water Runoff Abstracts, Third
Quarterly Issue
To be continued on inside back cover...
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STORM WATER MANAGEMENT MODEL
Volume I - Final Report
by
Metcalf & Eddy, Inc., Palo Alto, California
University of Florida, Gainesville, Florida
Water Resources Engineers, Inc., Walnut Creek, California
for the
ENVIRONMENTAL PROTECTION AGENCY
Contract No. 14-12-501
Contract No. 14-12-502
Contract No. 14-12-503
Project No. 11024EBI
Project No. 11024DOC
Project No. 11024EBJ
July 1971
For sate by the Superintendent of Documents, U.S. Government Printing Office, Washington, B.C. 20402 - Price $2.75
Stock Number 5501-0100
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EPA Review Notice
This report has been reviewed by the Water Quality Office,
EPA, and approved for publication. Approval does not signi-
fy that the contents necessarily reflect the views and poli-
cies of the Environmental Protection Agency, nor does mention
of trade names or commercial products constitute endorsement
or recommendation for use.
ii
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ABSTRACT
A comprehensive mathematical model, capable of representing urban
storm water runoff, has been developed to assist administrators and en-
gineers in the planning, evaluation, and management of overflow abate-
ment alternatives.
Hydrographs and pollutographs (time varying quality concentrations
or mass values) were generated for real storm events and systems from
points of origin in real time sequence to points of disposal (including
travel in receiving waters) with user options for intermediate storage
and/or treatment facilities. Both combined and separate sewerage systems
may be evaluated. Internal cost routines and receiving water quality out-
put assisted in direct cost-benefit analysis of alternate programs of
water quality enhancement.
Demonstration and verification runs on selected catchments, varying
in size from 180 to 5,400 acres, in four U.S. cities (approximately 20
storm events, total) were used to test and debug the model. The amount
of pollutants released varied significantly with the real time occurrence,
runoff intensity duration, pre-storm history, land use, and maintenance.
Storage-treatment combinations offered best cost-effectiveness ratios.
A user's manual and complete program listing were prepared.
THi's report was submitted in fulfillment of Projects 11024 EBI, DOC,
and EBJ under Contracts 14-12-501, 502, and 503 under the sponsorship of
the Environmental Protection Agency.
The titles and identifying numbers of the final report volumes are:
Title EPA Report No.
STORM WATER MANAGEMENT MODEL 11024 DOC 07/71
Volume I - Final Report
STORM WATER MANAGEMENT MODEL 11024 DOC 08/71
Volume II - Verification and Testing
STORM WATER MANAGEMENT MODEL 11024 DOC 09/71
Volume III - User's Manual
STORM WATER MANAGEMENT MODEL 11024 DOC 10/71
Volume IV - Program Listing
ill
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CONTENTS
Section Page
1 Conclusions and Recommendations 1
2 Introduction 11
PART 1 - COMPREHENSIVE MODEL
3 Model Overview 21
4 Programming Considerations 39
PART 2 - QUANTITY (HYDROLOGIC) SUBROUTINES
5 Surface Runoff Quantity Model 51
6 Dry Weather Flow Quantity Model 77
7 Infiltration Model 95
8 Transport Model 111
9 Storage Model 139
10 Receiving Water Quantity Model 157
PART 3 - QUALITY SUBROUTINES
11 Surface Runoff Quality Model 173
12 Dry Weather Flow Quality Model 201
13 Decay Model 213
14 Receiving Water Quality Model 231
15 Treatment Model 245
PART 4 - ECONOMIC DATA
16 Cost-Effectiveness Model 289
PART 5 - ACKNOWLEDGMENTS, REFERENCES, PUBLICATIONS,
GLOSSARY AND ABBREVIATIONS, AND APPENDICES
17 Acknowledgments 307
18 References 311
19 Publications 323
20 Glossary and Abbreviations 329
21 Appendices 333
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FIGURES
3-3 Overview of Model Structure
INTRODUCTION
2-1 Activity Chart
MODEL OVERVIEW
3-1 Schematic System Drawing Rainfall through 25
Overflow
3-2 Typical Storage-Treatment Applications to 26
Limit Untreated Overflows
30
3-4 Bloody Run Drainage Basin, Cincinnati Dry 33
Weather Flow Results
3-5 Cincinnati Combined Sewer Overflow Results - 34
Storm of April 1, 1970, Sampling Point 3
PROGRAMMING CONSIDERATIONS
4-1 Master Programming Routine 43
SURFACE RUNOFF QUANTITY MODEL
5-1 Definition of a Drainage System 58
5-2 Flow Chart, Hydrographic Computation 60
5-3 Typical Chicago 10-Acre Tract Drainage Basin 64
5-4 Rainfall Hyetograph and Calculated Runoff 66
Hydrographs, Chicago 10-Acre Tract
5-5 Calculated and Observed Runoff Hydrographs, 68
Oakdale (Chicago)
5-6 Northwood (Baltimore) Drainage Basin Plan 70
5-7 Calculated and Observed Runoff Hydrographs, 72
Northwood (Baltimore)
VI
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FIGURES (continued)
Page
5-8 Effect of Coarsening Subcatchment System, 74
Northwood (Baltimore)
DRY WEATHER FLOW QUANTITY MODEL
6-1 Determination of Subcatchment and Identification 82
Data to Estimate Sewage at 8 Points
6-2 Test Results, Bradenton (Florida) Gaging Area 89
6-3 Test Results, Valley Wood, Alvy, and Falcon 90
(California) Gaging Areas
6-4 Test Results, Nutwood (Maryland) Gaging Area 91
6-5 Test Results, Pine Valley (Maryland) Gaging Area 92
6-6 Test Results, Springfield (Missouri) Gaging Area 93
INFILTRATION MODEL
7-1 Typical Drainage Basin in which Infiltration 98
is to be Estimated
7-2 Components of Infiltration 102
7-3 Prescribed Melting Period 105
7-4 Rate of Melting 106
7-5 Test Results, Pine Valley (Maryland) 108
TRANSPORT MODEL
8-1 Sewer Schematic for the Kingman Lake 120
(Washington, D.C.) Study Area
8-2 Finite Difference Definition Sketch for Element M, 122
Routing through All Elements at Each Time-Step
8-3 Normalized Flow-Area Relationship for Uniform Flow 125
8-4 Typical Implementation of a Backwater Element 131
8-5 Comparison of Transport Model and Exact Solutions 134
for Pipeline Consisting of 8 Conduit Lengths
vii
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FIGURES (continued)
Page
8-6 Comparison of Transport Model and Exact Solutions 135
for Pipeline Consisting of 15 Conduit Lengths
8-7 Hypothetical Input for Routing Comparisons 136
8-8 Comparison of Transport Model with Exact Solution 137
of Ackers and Harrison
STORAGE MODEL
9-1 Outfall Storage, Selby Street, San Francisco 150
9-2 Hydrograph Modifications Produced by Outfall 153
Storage, Selby Street, San Francisco
9-3 Modifications to BOD Concentration Produced by 154
Outfall Storage, Selby Street, San Francisco
9-4 Modifications to Suspended Solids Concentration 155
Produced by Outfall Storage, Selby Street, San
Francisco
RECEIVING WATER QUANTITY MODEL
10-1 Geometric Representation of a Receiving Water 164
10-2 Test System Flows Showing Hydrograph Effects 172
SURFACE RUNOFF QUALITY MODEL
11-1 BOD and SS Test Results for Combined Sewers, 197
Laguna Street, San Francisco
11-2 Total Coliform Test Results for Combined Sewers 198
DECAY MODEL
13-1 Schematic Drawing of Test Areas, Combined Sewer 222
(Numbered), Selby Street, San Francisco
13-2 Results of Sensitivity Runs for Rate Constant 223
for Decay (Dl), Storms of November 6 and 14
13-3 Bed Load in Conduit 72, Storm of November 6, 225
DWDAY = 1
Vlll
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FIGURES (continued)
Page
13-4 Bed Load in Conduit 72, Storm of November 6, 226
DWDAY =47
13-5 Bed Load in Conduit 72, Storm of November 14, 227
DWDAY = 1.0
RECEIVING WATER QUALITY MODEL
14-1 Advective Transport Phenomena 236
14-2 Input to Node 14 of Test System 241
14-3 Receiving Water Quality Model Results for Node 14 243
of Test System
TREATMENT MODEL
15-1 Treatment Model 250
15-2 Treatment of Overflows by Sedimentation Tanks 257
15-3 Microstrainer at Callowhill (Philadelphia), 269
Mark 0 Screen Cloth
15-4 Microstrainer Capacity, Mark 0 Screen Cloth 271
15-5 Microstrainer Capacity at 30-Inch Head Loss, 273
Mark 0 Screen Cloth
APPENDIX A, INFILTRATION MODEL
A-l Comparison of Predicted and Measured.Flows, M&E 341
Study, Glen Street (Berkeley, California) Subarea
APPENDIX B, DECAY MODEL
B-l Sieve Analysis Plot for Sewer Sediment 349
B-2 Circular Channel Section 351
B-3 Rectangular Channel Section 352
IX
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TABLES
Page
INTRODUCTION
2-1 Component Task Categories and Assignments 15
MODEL OVERVIEW
3-1 General Data Requirements, Storm Water Management 36
Model
PROGRAMMING CONSIDERATIONS
4-1 Representative Values of Core Capacities Used in 47
the Demonstration Runs
4-2 Sample Compile and Execution Times on Demonstration 49
Runs
DRY WEATHER FLOW QUANTITY MODEL
6-1 Allowable Number of Sewer Connections by City Size 83
and Geographic Location
6-2 Actual and Estimated Daily Average Residential 88
Sanitary Sewer Flows to Test Validity of
Subroutine FILTH
STORAGE MODEL
9-1 Storage Model Input Data, Sewer Storage Basin, 151
Selby Street, San Francisco
SURFACE RUNOFF QUALITY MODEL
11-1 Estimated Annual Runoff of Pollutants from 180
Cincinnati Area
11-2 Daily Dust and Dirt Accumulation in Chicago Area 181
11-3 Efficiency of Street Sweeping in Chicago Area 184
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TABLES (continued)
DRY WEATHER FLOW QUALITY MODEL
12-1 Comparison of Quality Constituents of Ground 206
Garbage with Sewage
12-2 Comparison of Quality Constituents with Family 206
Income
12-3 Estimated Typical Wastewater Flow and Characteristics 207
DECAY MODEL
13-1 Test Results Using FMC Project Data, Bed Load 228
Analysis for 18-Inch Sewer with a Length of
795 Feet
COST-EFFECTIVENESS MODEL
16-1 Treatment Processes 293
16-2 Treatment Cost Summary 297
16-3 Irreducible Maintenance Costs 301
16-4 Storm Event Costs 302
16-5 Default Values for Cost Subroutines 303
16-6 Sample Test Runs 305
xi
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SECTION 1
CONCLUSIONS AND RECOMMENDATIONS
CONCLUSIONS 3
Capabilities of the Model 3
Applications of the Model 5
Limitations of the Model 6
Results of Demonstration-Verification Studies 7
RECOMMENDATIONS 8
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SECTION 1
CONCLUSIONS AND RECOMMENDATIONS
CONCLUSIONS
Under the sponsorship of the Environmental Protection Agency a
consortium of contractors—Metcalf & Eddy, Inc., the University of
Florida, and Water Resources Engineers, inc.—has developed a com-
prehensive mathematical model capable of representing urban storm water
runoff and combined sewer overflow phenomena. Correctional devices in
the form of user selected options for storage and/or treatment are
provided with associated estimates of cost. Effectiveness is portrayed
by computed treatment efficiencies and modeled changes in receiving
water quality.
Capabilities of the Model
1. The Storm Water Management Model accepts any rainfall hyetograph or
multiple hyetographs (where several local rain gages are recording the
same storm event) and produces a runoff hydrograph for each modeled
watershed.
2. Continuous runoff quality graphs, called pollutographs, are computed
on the basis of the volume of storm runoff and on antecedent conditions
which include rainfall history, street sweeping data, land use, and
related data.
3. Hydrographs and pollutographs are computed for dry weather flows (in
the case of combined systems) with daily and hourly variations and for
infiltration.
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4. Peal time flow routing is accomplished through a simulation of the
physical collection system allowing for variations in size, length,
slope, and cross-section configuration in the case of conduits and
locations and design parameters for non-conduits.
5. User options for storage facilities may be internal (in-system) or
external (located at the overflow point). Options for storage are:
a. Surface storage
b. Intrasystem storage
c. Flow rerouting
d. Underground storage
e. Underwater storage.
6. User options for treatment may be called in conjunction with or
independent of external storage. The following treatment options and
acceptable combinations of these options are provided:
a. Mechanically cleaned bar racks
b. Fine screens
c. Sedimentation
d. Dissolved air flotation
e. Microstrainers
f. High rate filters
g. Effluent screens
h. Chlorination.
7. Receiving water effects in both flow and quality are computed for
simulated lakes, rivers, or estuaries as applicable.
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8. Capital costs and operation and maintenance costs are computed for
the options selected to permit the development of approximate cost-
effectiveness curves which can be used for decision making.
Applications of the Model
1. The Storm Water Management Model is written in FORTRAN programming
language with a minimum of machine-dependent features. To date the
program has been tested on four independent computer hardware systems.
2. The computer hardware system should be the equivalent of the
IBM 360/65 with peripheral storage devices and a usable core capacity
of not less than 350K bytes.
3. The Model is developed on a general basis so it may be applied to
any municipality by changing only the input data. The approximate size
range of drainage basins over which the Model is applicable is from
10 acres to 5,000 acres.
4. A "User's Manual," Volume III, is furnished describing the main
computer program, all subroutines, data input and output, and complete
instructions on applications to individual systems.
5. The user should be knowledgeable in FORTRAN programming, operating
systems interfacing, and the engineering aspects of the real systems.
6. Data requirements are common to engineering design and analysis and
are mainly descriptive of•the real systems.
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Limitations of the Model
1. Data analyses and interpretation are essential.
2. in its present form only one drainage basin is studied during a compu-
tational run. Thus, the combined effects of multiple coincident discharges
into a single receiving water body are not directly evaluated. However,
the multiple discharge effect can be simulated by executing a series of
runs (one per basin up to a maximum of 20), creating an output master
file of the discharge solutions, and then applying this master file as
input to the Receiving Water Model.
3. Quality and perhaps quantity variations due to geographical or seasonal
differences are inadequately documented due to the sparsity of equivalent
real system data.
4. Costs and treatment data in many instances are based on advanced
processes which have not been in operation beyond the pilot plant or
limited demonstration plant stage. The cost-effectiveness of the treat-
ment alternatives should then be viewed in the light of this limitation.
5. The program, being completely new and of considerable size, will
require much use and continuous modification to fulfill most effectively
its objective of providing a decision-making tool.
6. The Model, as structured, does not optimize to a specific solution,
but rather provides a comprehensive analysis of user selected alternatives.
7. The present Model simulates individual storm events which may or may
not represent the random occurrence and probabilistic nature of the real
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hydrologic phenomena. However, subject to fund limitations, any number
of independent storms may be run separately to support such analyses.
Results of Demonstration-Verification Studies
1. The real time occurrence of the storm event (hour of the day) signi-
ficantly affects the quality of combined sewer overflows.
2. The intensity-duration relationships of the runoff (i.e., the shape
of the hydrograph), as well as the total runoff amount, must be considered
in evaluating combined sewer overflow abatement alternatives.
3. Idealized "design storms" (i.e., the traditional 2-year, 5-year, and
10-year storm) may give a poor representation of the quality character-
istics of overflows by failing to represent the time of occurrence and
shape of the hydrograph.
4. The use of real storm data "design event(s)," together with surface
and system simulation in the EPA Storm Water Management Model, offer a
means of significantly improved characterization of particular drainage
basins.
5. The first flush effect is a function of the antecedent dry weather
flow, the transport system geometry, and the design event. The dry
weather flow provides the source, the transport system determines
location and rate of solids accumulation, and the design event determines
the rate of uptake and travel time to the overflow point.
6. Quality concentrations alone are not adequate indicators of the pol-
lution potential of combined sewer overflows and storm water discnarges
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because of the high variation in flow rates during design events. Mass
(flow times concentration) discharge rates are generally more significant
for the long term effects, and concentrations are perhaps more significant
for the short term shock effects.
7. The areal distribution of rainfall can significantly influence runoff
quality.
8. For the demonstration situations modeled, the combination of storage
followed by high rate treatment offered the best cost-effectiveness ratios.
Since generally only single storms were modeled, the study was not pursued
to determine the most favorable ratios between storage and treatment
capacities.
9. The dynamic modeling of the receiving waters permits the evaluation
of the transient load problem as well as the pollutant effects averaged
out to steady state conditions.
RE COMMEN DATIONS
1. It is recommended, above all else, that the Storm Water Management
Model be put to work on real systems with real problems. The use,
evaluation, and continuous updating of the Model are essential to its
credibility and effectiveness.
2. It is recommended that the Model be used in the research and develop-
ment of representative storm events based upon years of rainfall record
to provide an economical base for evaluating alternate courses of correc-
tive action.
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3. It is recommended that the Model be further developed to encompass
the effects of multiple coincident discharges to common receiving waters.
Storm and combined sewer, treatment plant, tributary stream, and other
significant discharges should be considered. For economy, a correlation
of overflows from non-modeled watersheds with a limited number of modeled
representative areas should be established as a basis for extrapolation.
Such development would be directed toward a truer measure of water quality
improvement accompanying specific steps of corrective action.
4. It is recommended that data gathering efforts be continued to improve
the definition of waste sources and the removals induced by urban storm
water runoff, including the extension to additional quality constituents.
5. It is recommended that the Model be used in conjunction with Demon-
stration Projects for advanced combined sewer overflow waste treatment
processes to assist in the evaluation and optimization of their design
and operation.
6. Finally, it is recommended that the Storm Water Management Model be
used as a control guide in setting up procedures for the retention,
redistribution, treatment, and release of excess flows resulting from
storm events at the time of occurrence.
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SECTION 2
INTRODUCTION
Page
PROJECT CONCEPTION 13
STATEMENT OF WORK 14
Objective A, Intent 14
Objective A, Tasks and Assignments 14
Objective B, Intent 16
Objective B, Assignments 16
METHOD OF APPROACH 17
PRESENTATION FORMAT 17
11
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SECTION 2
INTRODUCTION
An expenditure of billions of dollars is expected in the next decade in
the United States to combat the degradation of streams and other bodies
of water by pollutants discharged through combined sewer overflows or
separate storm sewer discharges. The Environmental Protection Agency
(EPA) is therefore directing or assisting in multiple research and
development programs and investigations to identify, control, and correct
known problems relating to these storm occurrences.
One of these research programs, the development and testing of a compre-
hensive simulation model to represent completely storm event phenomena
in urban areas, is the subject of this report.
PROJECT CONCEPTION
In April 1967, Metcalf & Eddy, Inc., (MSB) submitted a proposal envision-
ing the use of systems engineering techniques to identify storm and sani-
tary flows and characteristics, conveyance systems, and the pollutional
effects of storm water upon the environment. This and earlier proposals,
related in subject matter, by the University of Florida (UP) and Water
Resources Engineers, Inc., (WRE), upon review and evaluation by the EPA's
Storm and Comoined Sewer Pollution Control Branch, led to the concept of
the comprehensive mathematical model. As evolved this model would represent
"...urban storm water runoff phenomena, both quantity
and quality, from the onset of precipitation on the basin,
through collection, conveyance, storage, and treatment
systems, to points downstream from outfalls which are
significantly affected by storm discharges."
13
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The goal was to provide a fundamental tool for administrators and
designers to assist them in the management and allocation of resources
towards optimal storm water quality control. Because the model was to
be universal in its application and all-encompassing in its detail, and
because the duration of the project was restricted to 18 months, a
cooperative effort drawing upon the talents and resources of all three
contractors and the EPA was decided upon. A demonstration-verification
phase was incorporated into the work to insure the validity of the
results and the utility of its application.
STATEMENT OF WORK
Objective A, Intent
The first objective, model development, involved several component tasks.
The goal of each task involving simulation (mathematical modeling) was
to provide a computer program subroutine which could be directly applied
to the comprehensive model. All subroutines were designed to be
dynamic, reflecting time and space variations. All previous data in
each task area were examined, evaluated, and used if suitable. No
sampling was performed. All subroutines were developed on a general
basis so they could be applied to any municipality by changing only the
input data. A sub-basin, multi-level branched system concept was used.
The model was designed to be applicable over drainage basins from 10 to
5,000 acres, and to be operational on the Department of the Interior
computation facilities.
Objective A, Tasks and Assignments
Table 2--1 summarizes the component task categories and assignments.
14
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Table 2-1. COMPONENT TASK CATEGORIES AND ASSIGNMENTS
Tasks Assignment
MANAGEMENT
1. Be responsible for overall coordination and management M&E
2. Be responsible for final development of the compre-
hensive model M&E
3. Participate in coordination meetings and provide
consultation and guidance UP - WRE
QUANTITY (HYDROLOGIC) SUBROUTINES
1. Develop urban runoff model WRE
2. Develop simulation model for dry weather sewage flows UF
3. Develop infiltration model UF
4. Develop transport model, simulating the branched
collection system and main sewer UF
5. Develop storage simulation model M&E
6. Develop receiving water flow model for creek, river,
estuary or lake WRE
QUALITY SUBROUTINES to be integrated with associated quantity
(hydrologic) subroutines
1. Develop runoff quality model MSB
2. Develop dry weather flow quality model MfiE
3. Develop decay model quality routing in transport model UF
4. Develop receiving water quality model WRE
5. Develop treatment simulation model M&E
ECONOMIC DATA
1. Develop cost model for approximating cost-effectiveness
curves M&E
15
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Under Objective A, M&E provided overall direction and coordination
of the project and developed subroutines representing the quality aspects
of storm water runoff and DWF; all storage and treatment options; and
a cost model representing these options. UF developed subroutines
representing DWF quantity and infiltration; the transport simulation,
both quantity and quality; and the decay of constituents in transport.
WRE developed subroutines representing urban storm water runoff quantity
phenomena; and all receiving waters, both quantity and quality. EPA
furnished available process and cost data on the storage and treatment
options.
Objective B, Intent
The second objective, demonstration-verification, was to test the validity
of the Model by applying it to several storm and combined sewer drain-
age basins. Possible solutions to existing problems were proposed by
manipulating flow control and treatment alternatives in the Model.
The apparent best solutions based upon cost-effectiveness were indicated,
disregarding sociopolitical factors.
Objective B, Assignments
M&E continued coordination of the overall project, conducted all computer
runs of the comprehensive Model and associated data reduction to proper
card/tape input form, and was responsible for demonstrating the operation
of the program on the EPA computer. WRE and UF provided necessary
analysis of computer output and refined and debugged their respective
programs. EPA made the initial contacts with the study municipalities
and provided the majority of the raw data.
16
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METHOD OF APPROACH
The activity chart used for project management and control is shown in
Figure 2-1. An initial meeting and five subsequent quarterly meetings,
each of two days' duration, were jointly attended by all contractors
and the EPA to ensure coordination and direct transfer and critique of
information.
The computer language, FORTRAN IV, and primary hardware, IBM 360/65, were
selected as most compatible with Environmental Protection Agency require-
ments and universal acceptance. To ensure high flexibility in the ultimate
program usage, some programs were developed and all were tested on a
UNIVAC 1108 as well as on the primary system.
The "triumvirate" approach enabled simultaneous starts in three prime
program areas—runoff, quality, and transport—and working routines
were well in hand by the six-month target date, permitting the first
comprehensive Model run at that time.
Use of real systems data was sought and integrated into each subroutine's
development, although in many instances the available data were far too
sparse and/or lacking in detail to be of maximum benefit. Contacts with
demonstration municipalities in the third and fourth quarters enabled a
prompt start on verification activities upon completion of the first year
of work and final completion at the end of 18 months.
PRESENTATION FORMAT
The project report is divided into four volumes. This volume, the "Final
Report," contains the background, justifications, judgments, and assumptions
17
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I INITIAL COORDINATION
MEETT!fG START OF
MODELING PHASE
EPA, ME, WH, UF
PROJECT M AN AC. KM EN T. AMD COOHDWAT1OK ->
f PREPARE t DBSEHINATE GUIDIlJhES FOR
DEFINE MANAGEMENT \ DOCUMJEXTATK» 1 DATA MANAGEMENT - f
OBJECTIVES * I ' ——— -
MQUIMMNTS ME Lj
MONITOR! IMPLEMENTATION -
:VEU>P RECEIVING WATKR QUALITY *
REPINE fc TEST - WR
rART l!P^
r-»*i
DEVELOP REd£rv&iC'''ATK:R QUANTITY MOO Ft -»
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i, STORMWATER i \ -X1UAUTY - HE
MODEL DWF QUALITY - HE
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i ' REPORT * MANUAL - "Jfy-y, ^ANUAl^rCmMATS
IOTCKTO PROCEED]
t O»GAhI2ATK». Mi
EVELOPCENERAUZED MODE!) CONCEPTS - MRS ,
V CC*n RECESSIVE ItOOEt ME. V.R. UF
...... ^^ ---- __ — ___j_, — ___. ------
' I
, I
1 MOPE; j UF. ^\.f REFINE t 1 ESI M RAMSfORT WODEi. • VT
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F MODEL - t'F REFINE i TEST \J>. ¥ MCCEI UF
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ta MODELS ME
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PREPARE 1 DtSSEMB-A
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START Utf
! EPA
COLLECT i DEVELOP HEQIJIRED BASIN DATA IN U&A0LE FORM -
''4 5
PROGRAM MONTHS
Figure 2-1. ACTIVITY CHART
18
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c QUARTERLY COOItKNATION
,. MEETING. rrA»T!OFDEIIOK8THATK»i i
' PHAS8 EPA. MEjWB, UF I
PTHAL MSKTTMG, PREOEHTA'
Of RESULTS - EPA. HE, WB,
DRAFT WATERSHED ft RECEIVIKC WATER ASPECTS OF PROGRAM - WH
IAFT tJUAUTY, STORAGE, TREATMENT (i COST-EFTliCTIVKHESS
~~~ ASPECTS OF'PROGRAM - ME
DRAFTTRW3PORT, DECAY, OTJ'F t giTII-TRATlOM AapECTS O
APPLY MOOEL TO SXL&CTKD
COMBINED SEWER BASINS
- MS. WR, UF
DIVE LOij USER
\ TSCHNMVES -Jn. WR. UF
"~ " " --1—
, i DOCUMENT BEST
, PROPOSE & TEST P^SSlBLt SOLOTtONS^ | SOHmoli8- »g
j "~~"~ - ME, wntuF ^ 5
> ! ''
DEMONSTRATE MANAGEMENT BENEFITS FROM
APPL.KAT1OTI TO REAL, SYSTEM -ffS, WH, UF
|/ • 1 PMPARirOWL t
•f IMPROVE KODEL uftLfTV - ME. WS, UrZ FWALIZE MODBL IbutPORT 4 MAXUAl, T^
APPLY MODEL T(|l SELECTED STOHM
SEWER BASINS - UZ, WS. UF . PROPOSE & TEST
LIAISON WITH JBASB* AOI
ENVIRONMENTAL PPQTBCTIQN AGENCY
CONTRACT 14 - 13 - W>
inrORMWATER POLLUTIOM CO»*TBOL MANACESI
ACTIVITY CHART
REV, NO. 1 MAR IT. 19>S
X?
PROGRAM MON
PTffturfti try: METCALF & EDDY
Due: Man-h L. 1989
For: DiWrllxaion M inlliaJ meeting
FIGURE 2-1. ACTIVITY CHART (continued)
19
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used in Model development. It further includes descriptions of unsuccess-
ful modeling techniques that were attempted and recommendations for
forms of user teams to implement systems analysis techniques most
efficiently.
Volume II, "Verification and Testing," describes the methods and results
of Model application in four urban catchment areas:
Size,
Location acres
Baker Street, San Francisco 187
Bloody Run, Cincinnati 2,600
Kingman Lake, Washington, D.C. 4,200
Wingohocking, Philadelphia 5,400
All are existing combined sewer areas which were tested with real time
storm events. Primary Model verification was based on sampling and
investigations on the Bloody Run sewer carried out by the University of
Cincinnati in close association with this project.
Volume III, the "User's Manual," contains program descriptions, flow
charts, instructions on data preparation and program usage, and test
examples.
Volume IV, "Program Listing," lists the main program, all subroutines,
and Job Control Language (JCL) as used in the demonstration runs.
20
-------
PART I
COMPREHENSIVE MODEL
-------
SECTION 3
MODEL OVERVIEW
Page
THE PROBLEM 23
Dry Weather Flow 2^
Storm Water Runoff 24
Combined Sewer Overflows 27
Corrective Action ^7
THE COMPREHENSIVE MODEL 28
MODEL APPLICATIONS 31
Users 32
Data Requirements 35
Programming Costs 37
21
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SECTION 3
MODEL OVERVIEW
The comprehensive Storm Water Management Model is intended to provide a
fundamental tool for modeling and evaluating existing phenomena associ-
ated with storm water runoff and combined sewer overflows from urban
areas and, through simulation, to indicate system responses to selected
means of corrective action.
THE PROBLEM
Precipitation falling on urban areas becomes contaminated as it enters
and passes through or within the human environment (Ref. 1). The first
degradation comes from contact with pollutants in the air; the next,
through contacts as it passes over ground and building surfaces; and
finally, through contacts with residues (depositions from early storms
or usage) and/or wastewaters (DWF in combined systems) in the conveyance
system and appurtenances. This storm runoff with or without sanitary
sewage picked up in transit, will eventually discharge to some receiving
body of water where the contaminants will be held for decomposition
(nonconservative constituents) or accumulation (conservative constituents),
or will be passed on downstream using the receiving waters as a carrier.
How serious is this contamination? Where does it come from? How does
it vary from one location to the next, or from one storm event to the
next? How do the related phenomena interplay? How can this contamination
be controlled? How can alternate schemes of corrective action be
compared? How much will they cost? What will be their effects on the
23
-------
receiving waters? These are the basic questions that guided the develop-
ment of the comprehensive Storm Water Management Model.
Figure 3-1 shows in pictorial form the origins and movements of flows
in typical combined sewerage systems. Figure 3-2 shows some of the
storage and treatment systems now under study to attack the problem to
protect and/or improve the quality of the receiving waters.
Dry Weather Flow
DWF is basically the wastewater discharge of a community diluted by such
infiltration, groundwater leakage into the conveyance system, as may
occur. In volume it is comparatively small, averaging about 100 gal./
capita/day, but its pollutant concentrations are high, and if untreated,
a menace to the public health or environment. DWF may be conveyed in
pipe systems which exclude storm waters (called separate systems) or in
systems which handle both DWF and storm water runoff (called combined
systems).
Storm Water Runoff
Storm water runoff is the precipitation, striking a surface during a
storm event, which exceeds the infiltration capacity (absorption into
the ground) or holding capacity (ponding) of that surface. This excess
flow is conveyed through systems of gutters and pipes which may be
separate or combined as described above. In volume it may be very large,
frequently exceeding the rate of DWF discharge from the same area by
100 times or more, but its pollutant concentrations are generally less
concentrated than DWF, although in total mass units they are generally
greater if limited to the period of the storm event.
24
-------
TREATMENT FACILITY
Note: DWF sources actually overlay tne subcatchments. They are
separated in the figure only to simplify the representation.
Figure 3-1. SCHEMATIC SYSTEM DRAWING RAINFALL THROUGH OVERFLOW
-------
EXCESS FLOW
TREATMENT-
FLOW INFILTRATION
DIVERTER
INTERNAL
IN-SYSTEM
STORAGE-?
^C
-TREATED
EXCESS FLOW
DISCHARGE
Figure 3-2.
TYPICAL STORAGEr-TREATJMENT APPLICATIONS
TO LIMIT UNTREATED OVERFLOWS
26
-------
Combined Sewer Overflows
It is an almost universal practice in the United States to treat DWF
prior to its release to receiving waters regardless of the method of
conveyance. In combined sewer systems this is accomplished by means of
a regulatory device, such as a weir, which in theory, diverts all flows
during non-storm periods. During storm events, however, the flows
arriving at the regulator may be far in excess of the treatment capacity,
and this excess is bypassed directly to the receiving water without
treatment. This excess flow constitutes the combined sewage overflow
and consists of a mixture of storm runoff, DWF, and such residue as may
have been picked up in the conveyance system.
Corrective Action
The state of the art seeking solutions to combat pollution resulting
from storm water runoff and combined sewage overflows centers on
(1) improved maintenance practices and housekeeping, (2) storage
facilities, and (3) treatment facilities.
Improved maintenance practices tend to clear source material off the
streets and out of the conveyance system before the storm event occurs,
thereby reducing the contaminants in the storm water flow. They also
provide the necessary inspection and maintenance of regulatory and
Appurtenant devices to insure their proper functioning (Ref. 2).
Storage facilities are used for contaminant and/or flow rate reduction
the storm influenced flow to permit larger quantities to be
27
-------
treated at existing DWF facilities or new excess flow treatment facilities.
They may also be used to provide relief for over-extended systems to
control or reduce flooding.
Treatment facilities for excess flows may be either on-line or off-line.
On-line facilities are exposed to the complete variations of the
excess flow, both in flow rate and quality, whereas the off-line facilities
may be fed at a controlled rate, the excess being bypassed or temporarily
diverted into storage.
Further descriptions and applications of these storage-treatment schemes
are discussed later in this volume and in Volume II.
An introduction to the modeling techniques developed to represent the
problem phenomena and corrective actions follow.
THE COMPREHENSIVE MODEL
The comprehensive Storm Water Management Model uses a high speed digital
computer to simulate real storm events on the basis of rainfall (hyeto-
graph) inputs and system (catchment, conveyance, storage/treatment, and
receiving water) characterization to predict outcomes in the form of
quantity and quality values.
The simulation technique—that is, the representation of the physical
systems identifiable within the Model—was selected because it permits
relatively easy interpretation and because it permits the location of
remedial devices (such as a storage tank or relief lines) and/or denotes
localized problems (such as flooding) at a great number of points in the
physical system.
28
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Since the program objectives are particularly directed toward complete
time and spatial effects, as opposed to simple maxima (such as the
rational formula approach) or only gross effects (such as total pounds
of pollutant discharged in a given storm), it is considered essential to
work with continuous curves (magnitude versus time), referred to as
hydrographs and "pollutographs." The units selected for quality
representation, pounds per minute, identify the mass releases as these
portray both the volume and the concentration of the release in a
single term. Concentrations are also printed out within the program
for comparisons with measured data.
An overview of the Model structure is shown in Figure 3-3. The actual
programming structure is discussed in Section 4. In simplest terms
the program is built up as follows:
1. The input sources:
RUNOFF generates surface runoff based on an arbitrary rainfall
hyetograph, antecedent conditions, land use, and topography.
FILTH generates dry weather sanitary flow based on land use,
population density, and other factors.
INFIL generates infiltration into the sewer system based on
available groundwater and sewer condition.
2. The central core:
TRANS carries and combines the inputs through the sewer
system in accordance with Manning's equations and continuity;
it assumes complete mixing at various inlet points.
DECAY routes pollutants through transport and models quality
changes -due to sedimentation or scour.
29
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RUNOFF
(RUNOFF)
INFILTRATION
(INFIL)
DECAY
(QUAD
DRY WEATHER
FLOW
(FILTH)
TRANSPORT
(TRANS)
INTERNAL
STORAGE
(TSTRDT)
EXTERNAL
STORAGE
(STORAG)
TREATMENT
(TREAT)
RECEIVING WATER
(RECEIV)
Note: Subroutine names are shown in parentheses.
Figure 3-3. OVERVIEW OF MODEL STRUCTURE
30
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3. The correctional devices:
TSTRDT, TSTCST, STORAG, TREAT, and TRCOST modify hydrographs and
pollutographs at selected points in the sewer system,
accounting for retention time, treatment efficiency, and other
parameters; associated costs are computed also.
4. The receiving waters:
RECEIV routes hydrographs and pollutographs through the
receiving waters, which may consist of a stream, stream bed,
lake, or estuary.
The quality constituents considered for simulation are the 5-day BOD,
total suspended solids, total coliforms (represented as a conservative
pollutant), and DO. These constituents were selected on the basis of
available supporting data and importance in treatment effectiveness
evaluation. Notable omissions, such as floatables, nutrients, and
temperature, fell outside the scope of this initial work. Other
parameters such as COD, volatile suspended solids, settleable solids,
and fecal coliforms can be developed by paralleling the structures of
their modeled counterparts.
MODEL APPLICATIONS
The program is intended for use by municipalities, government agencies,
and consultants as a tool for evaluating the pollution potential of
existing systems, present and future, and for comparing alternate courses
of remedial action. Although cost-effectiveness techniques are fully
utilized in the Model analysis, the preponderance of human decisions
inherent in this field of work precludes the achievement of an optimal
31
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solution. For example, the removal of one pollution unit from a receiv-
ing water will have different values to different people at different
times.
Further, the present limitations in the state of the art in defining
the performance and costs of real corrective facilities must be realized
when interpreting the results. The criteria used in the Model are based
largely on concurrent EPA-sponsored Demonstration Grant activities and
comparisons with conventional sewage (DWF) treatment facilities. Because
of these restrictions the development emphasis has been placed on the
basic structuring of the system phenomena with general credibility,
rather than on the exact reproduction of numerical values in the few
instances where such data are available.
Demonstration test data comparing modeled with measured results for a
2,600-acre combined sewered area in Cincinnati are shown in Figures
3-4 and 3-5 for DWF and combined sewage overflow respectively. Complete
demonstration test data are presented in Volume II.
Programming considerations are discussed in Section 4.
Users
A knowledge of FORTRAN programming and operating systems interfacing is
essential for the initial setup for comprehensive runs on any new test
area. Subsequent runs involving only input data changes, such as the
input rainfall hyetographs or area characteristics, may be readily
accomplished by engineers having only a brief familiarization with
32
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^^APPROXIMATE LIMIT
/ | OF DRAINAGE BASIN
/
i
SAMPLING POINT \—\
SYSTEM MAP WITH SAMPLING LOCATIONS
DRY WEATHER FLOW RESULTS
Sampling
Location
1
2
}
4
S
6
Flow,
Reported*
0.93
0.54
1.45
15.50
0.50
13.94
cfs
Computed
0.90
0.50
2.12
12.58
0.80
13.61
BOD , mg/L
Reported Computed
360. 403.
350.
1,160.
618. 529.
292.
412. 517.
SS, mg/L
Reported Computed
224. 206.
230.
236.
265. 226.
181.
252. 224.
Coli,
MPN/100 ml
Computed
9.5 x. 10
7.0 x 10
7.6 x 10
;
1
7
•Reported values are averages of approximately 10 grab samples each over a
two week period.
Figure 3-4. BLOODY RUN DRAINAGE BASIN, CINCINNATI
DRY WEATHER FLOW RESULTS
33
-------
MEASURED RUNOFF
COMPUTED RUNOFF
ia-oo
TIME. HOURS OF DAY
UCASUREO BOO,
COWKITED UOO. Ibi/mta
E o
o
ICOO I7>OO 17'JO
TIME, HOURS OF DAY
MEASURED SS, mg/l
COMPUTED SS, mfl/t
TIME, HOURS OF DAY
Figure 3-5. CINCINNATI COMBINED SEWER OVERFLOW RESULTS - STORM OF
APRIL 1, 1970, SAMPLING POINT 3
34
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computer programming, by following the step-by-step instructions furnished
in the "User's Manual."
The ideal user team would consist of representatives of the city, for
their knowledge of existing facilities and problems and probably respon-
sibility for implementation; the consultant, for programming and develop-
ment, expertise; and the regulatory agency, for setting standards and
basin-wide considerations.
Data Requirements
A brief summary of generalized data requirements to support an application
of the Storm Water Management Model is shown in Table 3-1. The measured
hydrographs and characteristics referred to in Items 6 and 7 are used
only for correlation-verification analyses. These measurements may be
discontinued or omitted where satisfactory correlation has been estab-
lished.
The data have been set up so that after the initial run only the storm
(rainfall hyetographs), conditions of occurrence (clock time and antecedent
history), and conditions of corrective action (storage/treatment) need to
be revised.
For a 4,200-acre combined sewer area in the District of Columbia the
total data requirement was described on approximately 500-600 punched
cards, and only 10-20 percent of these required modification to handle
multiple storm events and alterations in the system. By comparison there
are over 10,000 card operations in the complete Model routine.
35
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Table 3-1. GENERAL DATA REQUIREMENTS,
STORM WATER MANAGEMENT MODEL
Item 1. Define the Study Area
Land use, topography, population distribution, census tract
data, aerial photos, area boundaries.
Item 2. Define the System
Furnish plans of the collection system to define branching,
sizes, and slopes. Types and general locations of inlet
structures.
Item 3. Define System Specialties
Flow diversions, regulators, storage basins.
Item 4. Define System Maintenance
Street sweeping (description anbl frequency). Catchbasin
cleaning. Trouble spots (flooding).
Item 5. Define the Receiving Waters
General description (estuary, river, or lake). Measured
data (flow, tides, topography, water quality).
Item 6. Define the Base Flow (DWF)
Measured directly or through sewerage facility operating data.
Hourly variation and weekday vs. weekend. DWF characteristics
(composited BOD and SS results). Industrial flows (locations,
average quantities, quality).
Item 7. Define the Storm Flow
Daily rainfall totals over an extended period (6 months or
longer) encompassing the study events. Continuous rainfall
hyetographs, continuous runoff hydrographs, and combined flow
quality measurements (BOD and SS) for the study events.
Discrete or composited samples as available (describe fully
when and how taken).
36
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Programming Costs
Based on experience gained through the demonstration test series, it is
anticipated that costs associated with the use of the Model for compre-
hensive studies will vary from ten thousand to several hundred thousand
dollars per city, depending on the size, complexity, and depth of inves-
tigations. These costs may appear large unless compared with the
millions and perhaps billions of dollars required to be spent to achieve
proposed levels of water quality improvement.
37
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SECTION 4
PROGRAMMING CONSIDERATIONS
Page
PROGRAMMING LANGUAGE 41
PROGRAM BLOCKS 42
Executive Block 44
Runoff Block 44
Transport Block 44
Storage Block 44
Receiving Water Block 4.5
MACHINE REQUIREMENTS AND COMPATIBILITY 45
STORAGE AND DATA FILES 46
Program Input 47
Program Compile and Execution 48
Program Output 49
39
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SECTION 4
PROGRAMMING CONSIDERATIONS
PROGRAMMING LANGUAGE
This version of the EPA Storm Water Model consists of over 10,000 FORTRAN
statements in the form of a main program and a large number of subprograms.
FORTRAN was selected as the programming language because it is possible
to run the program on machines from various manufacturers without changing
the program. In order to meet this objective, certain restrictions were
placed on the programming to ensure that machine-dependent features did
not appear. Thus, the contractors agreed to use only ASA FORTRAN unless
there was assurance that an extension of the language was available on
a reasonable number of machines. As an example of such an extension,
it was agreed that in format statements, single quote marks could be
used to delimit Hollerith information, in addition to the standard nH
format.
it was further agreed that the programming should be carried through in
such a way that it would be comprehensible to each of the contractors
and to qualified personnel from EPA or other interested agencies. Pri-
marily this objective was met by the thorough documentation submitted
in Volumes III and IV of this series. Additionally, certain programming
practices were followed that were believed to be generally helpful,
although not actually required by the rules of FORTRAN IV. Some of
these were as follows:
1. Variable names should in general have mnemonic value.
41
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2. Variable names used in various subroutines should be uniform
for the most part throughout the Model.
3. Typing of FORTRAN variables should follow the standard default
rule that those beginning with I, J, K, L, M and N are of type
INTEGER.
4. High execution speed is desirable, but generally should be
secondary to ease of understanding.
5. Numerical data and results in the printout should be suffi-
ciently labeled so that reference to the FORTRAN program for
identification is unnecessary.
6. Extensive commenting should be provided throughout the FORTRAN
program.
PROGRAM BLOCKS
At the outset of the project it was expected that, machine storage per-
mitting, the whole program would be run at once, corresponding to every
physical event from a rainstorm falling on a watershed down to computing
details of events in the receiving water. If machine storage proved
insufficient, the expectation was that overlay techniques could be used-
As the programming effort went forward, however, it became clear that
there were distinct advantages in keeping the major parts of the program
as separate entities, which are hereafter referred to as "blocks."
The adopted arrangement, as shown in Figure 4-1, consisted of a main
control and service block, the Executive Block, and four computational
blocks: (1) Runoff Block, (2) Transport Block, (3) Storage Block, and
(4) Receiving Water Block.
42
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DATA
CONTROL
AND
SERVICE
BLOCK
DATA CARD
INPUT (TYPICAL)
EXECUTIVE BLOCK
COMPUTATIONAL
BLOCKS
REQUIRES
NO
OUTPUT FILE
RUNOFF
BLOCK
REQUIRES
RUNOFF
OUTPUT FILE
TRANSPORT
BLOCK
[DATA \)
-OUTPUT FILE A
CREATED,
TYPICAL
-o
T
REQUIRES
TRANSPORT
OUTPUT FILE
STORAGE
BLOCK
f DATA )
REQUIRE? "
STORAGE OR
TRANSPORT
OUTPUT FILE
RECEIVING WATER
BLOCK
f DATA )
/ /\
\ DATA /
Figure 4-1. MASTER PROGRAMMING ROUTINE
-------
Executive Block
The Executive Block assigns logical units (disk/tape/drum), determines
the block or sequence of blocks to be executed, and, on call, produces
graphs of selected results on the line printer. Thus, this Block does
no computation as such, while each of the other four blocks are set up
to carry through a major step in the quantity and quality computations.
All access to the computational blocks and transfers between them must
pass through subroutine MAIN of the Executive Block. Transfers are ac-
complished on off-line devices (disk/tape/drum) which may be saved for
multiple trials or permanent record.
Runoff Block
The Runoff Block computes the storm water runoff and its characteristics
for a given storm for each subcatchment and stores the results in the
form of hydrographs and pollutographs at inlets to the main sewer system.
Transport Block
The Transport Block sets up pre-storm conditions by computing DWF and
infiltration and distributing them throughout the conveyance system.
The Block then performs its primary function of flow and quality
routing, picking up the runoff results, and producing combined flow
hydrographs and pollutographs for the total drainage basin and at sel-
ected intermediate points.
Storage Block
The Storage Block uses the output of the Transport Block and modifies
the flow and characteristics at a given point or points according to
44
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the predefined storage and treatment facilities provided. Costs asso-
ciated with the construction and operation of the storage/treatment
facilities are computed.
Receiving Water Block
The Receiving Water Block accepts the output of the Transport Block
directly, or the modified output of the Storage Block, and computes
the dispersion and effects of the discharge in the receiving river, lake,
or bay.
In principle, the capability exists to run all blocks together in a
given computer execution, although from a practical and sometimes
necessary (due to computer core limitations) viewpoint, typical runs
involve one or two computational blocks together with the Executive
Block. Using this approach avoids overlay and, moreover, allows for
examination of intermediate results before continuing the computations.
Further, it permits the use of intermediate results as start-up data in
subsequent execution runs, thereby avoiding the waste of repeating the
computations already performed.
MACHINE REQUIREMENTS AND COMPATIBILITY
All parts of the program have been run on at least two machines. During
development of the program MSB used an IBM 360/67 at the Stanford
University Computation Center; WRE used a UNIVAC 1108 located in Oakland
and accessed by their terminal in Walnut Creek; and UP initially used an
IBM 360/50 until it was replaced at the University of Florida Computation
Center by an IBM 360/65.
45
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In addition to using these various machines with their standard compilers,
M&E tested all parts of the program using the FORTRAN compiler developed
by the University of Waterloo (WATFOR). This compiler uncovered a number
of "bugs" that the IBM FORTRAN IV compilers were willing to tolerate.
Corrections were made accordingly to avoid possible difficulties if the
program were to run in the future on a different type of machine. The
most common bug uncovered by WATFOR was failure to set initial values
for all variables.
STORAGE AND DATA FILES
As it stands, the program can be run on a machine having core storage
capacity of at least 350K bytes (or equivalent). In addition, the program
uses peripheral storage devices which may consist of disk, tape, or drum
units, depending on the machine configuration. The UNIVAC 1108 used
by WRE typically has tape and drum, while the IBM 360 systems used by
M&E, UF, and EPA have disk capabilities that make it possible to avoid
tape usage. One IBM 2314 Disk Storage Device can provide ample room
for all files created by the program, or alternatively, the files can
be placed on several devices, depending on the system configuration.
The disk units are used both for transfer of information between blocks,
in which case data files are created, and for scratch files used only
temporarily in execution of a given block.
A sample of core capacities used by separate program blocks on repre-
sentative demonstration runs is shown in Table 4-1.
46
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Table 4-1. REPRESENTATIVE VALUES OF CORE
CAPACITIES REQUIRED IN DEMONSTRATION RUNS
Machine Core Storage Required,
Program Block (s) bytes
Executive* 225K
Executive and Runoff* 264K
Executive and Transport*
Without internal storage 310K
With internal storage 334K
Storage and Treatment 183K
Executive and Receiving Water* 327K
*0f the storage required, 170K bytes are required in the common
blocks.
The data files correspond to a given storm on a given site, and in many
cases they can be used repeatedly to test alternatives without going
through the entire computation each time. Although the original inten-
tion was to use formatting on these files, it has proven preferable to
use unformatted input/output which greatly speeds up read/write operations.
Program Input
In addition to the files described above, the various blocks of the
program use data card input as described in the "User's Manual," Vol-
ume III of this series. Thus, the user must prepare the data cards
needed for a given block and also supply JCL cards corresponding to the
appropriate file devices.
47
-------
It is also possible with some systems to hold the data card images on a
file. If, in addition, the FORTRAN (or its object module) is held on a
file, the program can be run with no card input. This method has been
used in conjunction with terminal access on the IBM 360/67 at Stanford
University. With so large a program the elimination of card reading is
very convenient.
Program Compile and Execution
A sample of the compile and execution times used by separate program
blocks on representative demonstration runs, IBM 360/67, is shown in
Table 4-2. This table further illustrates the savings which were made
by storing compiled blocks of the program in a permanent job library
(Load Modules).
No general attempt was made for overall optimization of the program with
regard to storage or timing. It is very likely that significant improve-
ments can be made, although the present requirements are not considered
excessive in view of the amount of information generated. Some initial
versions of the Model were restructured to improve timing by eliminating
the need for SORT and MERGE operations on peripheral devices. Also, the
input and output operations onto data files are unformatted to speed up
the read/write operations. Again, it was agreed to avoid the adjust-
able dimensioning feature of FORTRAN IV since it is known to be time-
consuming.
48
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Table 4-2. SAMPLE COMPILE AND EXECUTION
TIMES ON DEMONSTRATION RUNS
Program Block (s)
Executive
Executive and Runoff
Machine
Uncpmpiled*
Execution
CPU*** Time****
1.39 2.22
time, min
Load Module**
Execution
CPU*** Time****
0.18 0.28
1.15 1.97
Executive and Transport
(without internal storage) 2.77
Executive and Transport
(with internal storage) 3.06
Storage and Treatment 0.36
Receiving Water 2.60
4.38
4.71
0.52
3.57
0.72
0.85
1.16
1.30
*Time includes compile/ link-edit, and execute.
**Time required for link-edit and execute only.
***Actual computational time in computer core not including the time
needed to execute the read and write (I/O) statements or to run the
peripheral devices.
****Time required in the computer including I/O statements.
Program Output
Output from the program consists of the usual line printer tabulations,
which, if desired, can be supplemented by selected plotted hydrographs
and pollutographs also produced on the line printer at execution time.
These plots are available through subroutine GRAPH of the Executive Block,
using the output files of any of the computational blocks.
There has been discussion from time to time of incorporating improved
offline plotter capability in the program, but it was unfeasible to do
49
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so within the scope of the current project. In any event, such plotting
would use output files of the kind now generated, and could be added as
a set of subroutines to be called by the Executive Block.
50
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PART 2
QUANTITY (HYDRQLOGIC) SUBROUTINES
-------
SECTION 5
SURFACE RUNOFF QUANTITY MODEL
OBJECTIVES 53
RELATION TO STORM WATER PROGRAM 54
THE MODEL SUBROUTINES 54
THEORETICAL DEVELOPMENT 56
Model Geometry 56
Solution Procedure 57
TEST APPLICATIONS 63
Chicago 10-Acre Tract 63
Oakdale (Chicago) 67
Northwood (Baltimore) 67
Additional Testing 71
CONCLUSION 75
51
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SECTION 5
SURFACE RUNOFF QUANTITY MODEL
OBJECTIVES
The Surface Runoff Quantity model (subroutine RUNOFF) simulates the
runoff phenomena of a drainage basin for any given rainfall pattern.
The objective of the model is to provide a basis for subsequent compu-
tation of pollutographs, a time-history of runoff quality, that are
necessary for planning, design, and operation of the Storm Water Manage-
ment Model.
The EPA has contemplated the use of the Model throughout the United
States. Probably the only information that can reasonably be expected
to be available in any locality is climatological data and the physical
watershed characteristics, such as size, ground slope, and types of
ground cover.
To meet this specific objective, RUNOFF represents the drainage basin by
an aggregate of idealized subcatchments and gutters that are common de-
nominators of the drainage plan and are readily quantifiable. Flexi-
bility of the program to be adopted to any prototype conditions was of
great concern and was considered in the model formulation and develop-
ment.
The model accepts the input of any rainfall hyetograph, a time-history of
rainfall intensity, as given. The rainfall hyetograph for a location is
more readily available from the Weather Bureau and is subjected to less
53
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influence by engineering works. Its prediction by stochastic process is
not part of the Surface Runoff Quantity model.
RELATION TO STORM WATER PROGRAM
RUNOFF is the first computational subroutine of the Storm Water Management
Model. It calculates the hydrographs by a step-by-step accounting of
rainfall, infiltration, detention/ overland flow, and gutter flow. In so
doing, it provides information about the overland flow and gutter flow at
various parts of the drainage system for use by the Surface Runoff Quality
model. It also generates hydrographs for the designated entry points to
the major sewer line. These hydrographs are then accepted by the Transport
Model which routes the quantity and quality of wastewater throughout the
sewerage system, to the treatment plant, and to the receiving water body.
The most important function of RUNOFF is therefore to furnish hydraulic
information at the right time and right place to serve the need of other
models. While the Model can get started by itself, its answers must be
quite accurate and compatible with those of other models.
THE MODEL SUBROUTINES
The computer program developed to perform the Surface Runoff Quantity
model computation consists of six subroutines, i.e., RUNOFF, HYDRO,
RHYDRO, WSHED, GUTTER, and HCURVE. Detailed documentations of each sub-
routine are provided in the "User's Manual," Only a brief description
of their functional relationships is discussed herein.
Subroutine RUNOFF provides the necessary liaison with the master program
of the overall Storm Water Management Model. RUNOFF, in turn, calls
54
-------
HYDRO to coordinate the computation of the hydrograph with the assistance
of three core subroutines, RHYDRO, WSHED, and GUTTER.
Subroutine RHYDRO is called by HYDRO to read all input data related to
the drainage basin and to perform initial preparatory work such as unit
conversion and error detection. Default options are available for the
typical values of physical coefficients describing the roughness factor,
detention requirement, and infiltration characteristics. A normal exe-
cution of RHYDRO provides all the necessary information for the calcu-
lation of a runoff hydrograph.
Subroutine WSHED computes the depth and flow rate of water overland. It
interpolates the rainfall hyetograph to obtain the rainfall intensity for
the period of computation and accounts for infiltration and surface
storage. Upon completion, it returns with a set of water depth and flow
for the subcatchments.
The function of subroutine GUTTER is similar to that of WSHED. It cal-
culates a complete set of water depth and flow for the gutters and pipes
in the system. It accounts for surcharge in full conduits, assuming
temporary storage at the upstream junction until surcharge is no longer
necessary.
The hydrograph solutions are printed in tabulated form. In addition,
HCUKVE will prepare X-Y coordinates of the hydrograph at selected points
of the drainage system for printer plot routines which plot the curves
directly in the computer output.
55
-------
There is a call to subroutine GRAPH (0) from subroutine RUNOFF. GRAPH is
described in Section 4. The Surface Runoff Quality model, subroutine
SFQUAL in RUNOFF, is described in Section 11.
THEORETICAL DEVELOPMENT
Existing methods of runoff estimate were evaluated as background and for
potential use in the contemplated model. Methods evaluated include the
rational method- "rational-rational" method (Ref. 1); British Road Re-
search Laboratory Method (Ref. 2); dimensionless hydrograph method of
Izzard (Refs. 3,4); Chicago Method (Ref. 5); and the Stanford Watershed
Model (Ref. 6).
Empiricism at various degrees was found in all the methods that used
factors not easily determined by any ready rule. However, previous studies
have advanced much of the theoretical ground work related to the funda-
mental process of runoff phenomena, i.e., rainfall, infiltration, deten-
tion, overland flow, and gutter flow. For the development of a compre-
hensive surface runoff quantity model, each of these processes must be
simulated individually and operated simultaneously by a computer program.
Model Geometry
Model geometry is a discretization procedure for the mathematical abstrac-
tion of the physical drainage system. For the computation of the hydro-
graph, the drainage basin may be conceptually represented by a network of
hydraulic elements, i.e., subcatchments, gutters, and pipes. Hydraulic
properties of each element are then characterized by various parameters,
such as size, slope, and roughness coefficient.
56
-------
As was originally envisioned, a subcatchment is rectangular in shape with
reasonably uniform watershed characteristics, such as surface cover and
ground slope. The geometry of a subcatchment is defined by the area,
width, and ground slope. The type of ground cover determines the deten-
tion depth requirements, the roughness factor (such as Manning's coeffi-
cient) , and the coefficients describing the infiltration loss by Horton's
exponential function (Ref. 5).
The subcatchments need not be the same size and the irregular shape can
be approximated by an equivalent rectangle by computing the mean width.
In principle, a series of subcatchments can be designed to cover the
entire drainage basin.
The subcatchments form an aggregated system by gutters and pipes speci-
fying the connectivity of flow. Hydraulically, gutters and pipes are
described by the Manning's coefficient, length, invert slope, and geo-
metric description of the shape. The latter may include the bottom width
and side slopes for rectangles, trapezoids, and triangles and the diameter
for circular pipes.
Figure 5-1 presents a typical but idealized drainage system. As shown,
subcatchment 2 drains into gutter 1. Both gutter 1 and subcatchment 1
discharge into gutter 2. Several subcatchments and gutters can be con-
nected to a given gutter, depending on the topographic condition.
Solution Procedure
Once the properties of each hydraulic element are given, the computer
can be instructed to make a step-by-step accounting of how much water
57
-------
INPUT
TIME
GUTTER-?
•SUBCATCHMENT
SYSTEM
MLET
ggg^ 3
_
U_
O
tr
'!
, ,
!i
jM
TIME
OUTPUT
Figure 5-1. DEFINITION OF A DRAINAGE SYSTEM
58
-------
comes in, how much is lost to infiltration, and what will be the outflow
and the remaining water depth in each increment of time. This accounting
procedure can best be described by the flow chart shown in Figure 5-2.
First, the computer reads and edits data pertaining to the rainfall
hyetograph, subcatchment, and gutter characteristics and their inter-
connections. Unit conversion is made for all parameters to conform in
the pound-foot-second system.
Stepwise computation proceeds as follows (Figure 5-2):
1. Rainfall is added to the subcatchment according to the specified
hyetograph,
D = D + R At (D
where D = Water depth after rainfall
Dfc = Water depth of the subcatchment at time, t
Rfc = Intensity of rainfall in time interval, At
2. Infiltration is computed by Horton's exponential function and is
subtracted from water depth existing on the subcatchment,
fo
and
D2 = Di ~ ItAt (3)
where fQ, f^, and a are coefficients in Horton's equation
D2 is inte*roediate water depth after accounting for infiltration.
59
-------
f
READ
IEDIT DATA
CONSTRUCT
CONNECTIVITY
MATRIX
T
I
M
E
P;
E
R
I
0
D
OVERLAND FLOW
I. RAINFALL
2. INFILTRATION
3. DETENTION
4 FLOW (MANNING'S)
5. DEPTH (CONTINUITY)
SUBCATCHMENTS
TRAPEZOIDN
HYDRAULIC
RADIUS
GUTTER FLOW
I. OVERLAND INPUT
2. GUTTER INPUT
3. FLOW (MANNING'S)
4. DEPTH (CONTINUITY)
PIPE
HYDRAULIC
RADIUS
COMPUTE
HYDROGRAPH
COORDINATE
GUTTERS/ PIPES
PLOT
HYDROGRAPH
( STOP \
Figure 5-2. PLOW CHART, HYDROGRAPHIC COMPUTATION
60
-------
3. If the resulting water depth of the subcatchment, D , is larger
than the specified detention requirement, D,, an outflow rate is
computed using Manning's equation,
v . ±i« (D D ) 2/3 sl/2 (4)
n 2 d
and
Qw = V W (D2 - Dd) <5)
where V = Velocity
n = Manning's coefficient
s = Ground slope
W = Width
Q = Outflow rate
4. The continuity equation is solved to determine the water depth of
the subcatchments, resulting from the rainfall, infiltration, and
outflow,
Dt+At = D2 " (VA)At
(6)
where A is the surface area of the subcatchment.
5. Steps 1 to 4 are repeated until computations for all subcatchments
are completed.
6. The inflow (Q. ) to a gutter is computed as a summation of outflow
from tributary subcatchments (Q .) and flow rate of immediate
upstream gutters (Q .).
Q. = £0 . + ZQ . (7)
xin *w,i g,i
61
-------
7. The inflow is added to raise the existing water depth of the
gutter according to its geometry,
Y = Y + (Q. / A ) At (8)
1 t *in s
where Y and Y = Water depth of the gutter
A = Mean water surface area between Y, and Y.
s It
8. The outflow is calculated for the gutter using Manning's equation,
, 1/2 /QI
n i
and
Q = V A (10)
g c
where R = Hydraulic radius
S^ = Invert slope
A = Cross-sectional area at Y,
1
9. The continuity equation is solved to determine the water depth
of the gutter, resulting from the inflow and outflow.
= Y. + (Q. - 0 ) At / A (ID
10. Steps 6 to 9 are repeated until all the gutters are finished.
11. The flows, reaching the point of concern, are added to produce a
hydrograph coordinate along the time axis.
62
-------
12. The processes from Steps 1 to 11 are repeated for succeeding
time periods until the complete hydrograph is computed.
The step-by-step description of the solution procedure gives a physical
picture of the processes being modeled. The integration of variables in
each time increment was originally performed by the modified Euler's two-
step method. This is now accomplished by the Newton-Raphson method
(Ref. 7), which produces a smoother hydrograph and more stable solution.
As was noted, Manning's equation was used for computation during each
time interval of integration. The "state" of the system, however, is
being updated continuously. Thus, the dynamic behavior of the runoff
phenomena was simulated by a stepwise and successive quasi-steady state
approximation.
TEST APPLICATIONS
Chicago 10-Acre Tract
The Surface Runoff Quantity model as developed was utilized to calculate
a hydrograph for a typical 10-acre tract in Chicago. Land use, geometry,
and direction of flow of the drainage basin are shown in Figure 5-3,
taken directly from the American Society of Civil Engineers (ASCE) Manual
No. 37 (Ref. 8). As shown, the area is 54 percent pervious. For the pur-
pose of simulation, the land was represented by 80 subcatchroents, 40
gutters, and 4 pipes. Size of the subcatchments ranges from 0.04 to 0.48
acre. Necessary information concerning the size, width, slope, retention
depth, and rate of infiltration was obtained from the manual.
63
-------
j _ ; ^ p « , __
« si..*!™' ; i,
'WM'-.'"11" "VlVVr,'ir,Tp'Y1'T! ' - """ri* i "^ 'V'VVr' .". * ",•"V"V-9"V v r
1 I I II11 ' I I ' '
— — UM'
ranageafea an<5 directtwi of flcm
Sources American Society of Civil Engineers, Manual of Engineering Practice No 37
1960 (Ref. 8}. '
Figure 5-3. TYPICAL CHICAGO 10-ACRE TRACT DRAINAGE BASIN
-------
A 181-minute design storm was applied to the drainage basin. The rainfall
hyetograph and the calculated runoff hydrograph were plotted in Figure 5-4.
For the purpose of comparison, the calculated hydrograph by the Chicago
Method is also shown in the figure. Results indicate that these hydro-
graphs have a comparable rising limb. Both of them peak at about the same
time, i.e., 75 minutes from the start of rainfall. However, the Chicago
Method calculates a lower peak value (18 cfs against 22 cfs) and also a
lower recession.
Since both curves are for the hypothetical case, the question of accuracy
is not an issue. However, the Chicago Method is seen to produce a smaller
total runoff. This can only be accounted for by a larger infiltration
loss which might seem anomalous, because both methods use the same
Horton's equation for calculating infiltration loss. The explanation is
that the Chicago Method computed the mass curve for infiltration loss.
Thus, the method tends to satisfy the infiltration rate at any given time
even though there is not sufficient rainfall at that moment. The present
method allows for the infiltration rate as calculated only when there is
sufficient water on the ground at that given instant.
The infiltration, loss of the present method was 28 percent of the total
rainfall. The mass continuity has been maintained within 0.1 percent of
the rainfall. No such information was available on the Chicago Method
for comparison.
65
-------
DESIGN STORM
0.0 40.0 80.0 120.0 160.0 200.0
TIME (MIN)
25.0 T
DESIGN
HYDROGRAPHS
STORM WATER MANAGEMENT
MODEL
CHICAGO METHOD
.0
0.0 40.0 80.0 120.0 160.0 200.0
TIME (MIN)
Figure 5-4. RAINFALL HYETOGRAPH AND CALCULATED
RUNOFF HYDROGRAPHS, CHICAGO 10-ACRE TRACT
66
-------
Oakdale (Chicago)
Some rainfall and runoff data have been gathered at Oakdale (Chicago) for
a drainage basin of 12.9 acres (Ref. 9). The land use is similar to the
typical 10-acre tract described previously in Figure 5-3.
A detailed description of this particular drainage basin is not available.
It was suggested that the Oakdale rainfall hyetograph could be applied on
the typical 10-acre tract. The resulting runoff hydrograph could be
multiplied by 1.29 to account for the difference in areas. This cal-
culated runoff hydrograph could then be compared to the measured Oakdale
hydrograph.
The calculated and measured runoff hydrographs are compared in Figure 5-5.
The measured peak was found to be 2 to 3 cfs higher than the calculated
one. The timing for the first and the second peaks was also noted to be
offset by 5 and 10 minutes respectively. The overall comparison, however,
is reasonably close.
Northwood (Baltimore)
The Johns Hopkins University has conducted an intensive data gathering
program for rainfall-runoff relationships at Northwood (Baltimore). The
data for the verification of the model were taken from an ASCE Urban
Water Resources Research Program publication (Ref. 10).
Briefly, the drainage basin area is 47.4 acres with approximately 60
percent as residential area and 40 percent as a shopping center, including
a large parking lot. Average ground slope is 3 percent and the
67
-------
25 L
_ 201
u_
k- 15 i
U_ I0
10-
OAKDALE (CHICAGO)
STORM OF JULY 2,1960
AREA = 12.9 ACRES
CALCULATED (USING
CHICAGO 10-ACRE TRACT,
SCALED UP BY 1.29)
140 150 160
TIME (WIN)
170
180
190
200
Figure 5-5. CALCULATED AND OBSERVED RUNOFF HYDROGRAPHS,
OAKDALE (CHICAGO)
-------
imperviousness is 68 percent. Other pertinent information concerning
the drainage basin is given in the publication.
It was found that detailed information for the subdivision of the drainage
basin was not available in the Northwood area as it was in the Chicago
case. Moreover, the effort required for such a data acquisition program
was considered too prohibitive. The feasibility of utilizing a coarser
subdivision of the drainage basin was therefore investigated.
The Johns Hopkins University subdivided the Northwood drainage basin into
32 subcatchments (Ref. 10). These subcatchments were combined into 12
basic subcatchments in this simulation study, as shown in Figure 5-6.
In summary, the 47.4-acre drainage basin was represented by 12 composite
subcatchments and 13 pipes in the simulation. The areas of the composite
subcatchments range from 2 to 9 acres. These, as compared to the Chicago
case of 80 subcatchments and 44 gutters (pipes) for a 10-acre tract, are
very coarse.
Because of the aggregation of subcatchments, each composite subcatchment
was not representing any unique properties of ground cover as in the
Chicago case. Some scheme had to be devised to compute the average
physical properties, such as detention depth, infiltration rate, and
Manning's coefficient, for the composite subcatchment. In this study, all
the physical parameters, except Manning's coefficient, were calculated
by a weighted average based on the percent perviousness of the area. For
example, the detention depth is 1/16-inch for an impervious area and 1/4-
inch for a pervious area (Ref. 5). The detention of a composite
69
-------
Rain Gage #2
b
DRAINAGE AREA
3
SUBCATCHMENT BOUNDARY
SUBCATCHMENT NUMBER
Source: L. S. Tucker, "Northwood Gaging Installation,
Baltimore-Instrumentation and Data" (Ref. 10).
Figure 5-6. NORTHWOOD (BALTIMORE) DRAINAGE BASIN PLAN
70
-------
subcatchment with x fraction impervious was calculated by:
x (l~x)
Average detention = — + —r— (12)
In the case of Manning's coefficient n , a harmonic mean was taken
1 = x (1-x) (13)
n 0.014 0.35
where 0.014 and 0.35 are the Manning's coefficients for impervious and
pervious areas respectively (Ref. 6).
The results of a simulation for the Northwood storm of August 1, 1965,
are shown in Figure 5-7. For the purpose of comparison, the measured
runoff is also plotted in the same figure. Again, the simulation is quite
good, with accurate prediction of the peaks. The problem of slow reces-
sion is seen in the figure and is perhaps due to high values of Manning's
coefficient being used for pervious areas.
It must be pointed out that all the necessary coefficients used in the
simulation were estimated from Chicago data. The largest pipe diameter
of the system is 4 feet.
Additional Testing
While the discretization of the drainage basin into finer subcatchments
is theoretically more correct, the coarsening of the system is desirable
from the practical standpoint. However, thare are problems associated
with the gross approximation of the system by large subcatchments.
In the case of the Selby Street drainage basin in San Francisco, the
average detention depth requirement for a gross subcatchment was found
71
-------
80.0 T
NORTHWOOD (BALTIMORE)
STORM OF AUG. I, 1965
AREA = 47.4 ACRES
CO
C
2
Z>
o:
6O.O--
40.0 • •
20.0-•
0.0
0.0
OBSERVED
STORM WATER MANAGEMENT
MODEL
I I I 1 1 > >""v 1 1 H
10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 SO.O 100.0
TIME (WIN)
Figure 5-7. CALCULATED AND OBSERVED RUNOFF HYDROGRAPHS,
NORTHWOOD (BALTIMORE)
-------
to store the early low intensity rainfall. The rising limb of the hydro-
graph is therefore retarded greatly.
This problem was resolved by splitting each subcatchment into a pervious
area and an impervious area according to the percent imperviousness of
the ground cover. Since the impervious area requires small detention
depth, it produces early runoff for the hydrograph. The use of "equiva-
lent" detention depths and friction coefficients is avoided entirely.
The capability to split the area was incorporated into the computer pro-
gram and tested with the data of Northwood (Baltimore). Figure 5-8
presents the result of the simulation for the 12-subcatchment system. The
curve is noted to fit the observed data slightly better than the one
shown in Figure 5-7. The reason it did not make more difference was that
the early part of the rainfall intensity in this case was relatively
high. This fact tends to reduce the importance of the detention depth.
Further analysis led to splitting each subcatchment into three parts:
1. Pervious
2. Impervious, with surface detention
3. Impervious, without surface detention.
This causes "instant" runoff from part of the system and is more in
keeping with observed results. Use of this final version is described in
the verification tests on Baker Street, San Francisco, in Volume II of
this report.
73
-------
-
60
50
40
.-
u.
(J
u.
:
30
20
10
NORTHWOOD (BALTIMORE)
STORM OF AUGUST I, 1965 AM
AREA • 47.4 ACRES
12- SUBCATCHMENT SYSTEM
\ 5- SUBCATCHMENT SYSTEM
t
\ '"V /'
y
OBSERVED
10 20 30 40 50 60 70 80 SO
TIME (M!N)
Figure 5-8. EFFECT OF COARSENING SUBCATCHMENT SYSTEM,
NORTHWOOD (BALTIMORE)
-------
Further coarsening of the subcatchment system was tested with the North-
wood data. The 12-subcatchment system shown in Figure 5-6 was combined
into a 5-subcatchment system. The result of the simulation is presented
in Figure 5-8. As expected, the coarsening of the system reduces the
accuracy of prediction. More experience with the model will be needed
to ascertain the level of detail necessary for the accuracy desired in
any specific application.
CONCLUSION
The method described is only a near theoretical approximation of physical
phenomena occurring in the prototype. The propagation of waves and the
problem of varied flow overland and in the gutters are not treated rigor-
ously in the method. However, the quasi-steady state approximation by
Manning's equation is believed adequate for practical purposes in view
of the fact that prototype conditions are not amenable to a theoretically
more thorough analysis.
Aside from theoretical soundness, the validity of the method can best be
demonstrated by its ability to reproduce the field data. Simulation
results indicate that the verification is reasonably good. Moreover, all
the parameters and coefficients utilized in the simulation were taken
directly from published literature. No optimization procedure was used to
adjust the coefficients for a better fit between the calculated and ob-
served hydrograph.
The use of a discretized system to represent a drainage area increases
the flexibility and latitude for the model to be adopted to other
75
-------
prototype conditions. The capability of the Surface Runoff Model to
treat the pipe problem also enables more subcatchments to be aggregated
into a larger tributary area. Subcatchments interconnected by pipes that
lead to a common confluent point can be combined into an inlet drainage
basin. The aggregation of subcatchments, however, should only be made
to the extent where the inherent assumptions still hold. For example,
the pipe routine uses the invert slope to calculate flow; therefore, the
Surface Runoff Model should not be expanded to cover the larger size
pipes where the backwater effect becomes important. It is believed that
the Surface Runoff Model would be applicable for lateral sewers with pipe
diameters up to 30 inches in most cases. Beyond that, the problem
should be handled by the Transport Model which is described in Section 8
of this report.
76
-------
SECTION 6
DRY WEATHER FLOW QUANTITY MODEL
Page
OBJECTIVES 80
THE MODEL SUBROUTINE 80
THEORETICAL DEVELOPMENT 81
Input Data 31
Methodology 34
TEST APPLICATIONS 37
CONCLUSION 94
77
-------
SECTION 6
DRY WEATHER FLOW QUANTITY MODEL
In the context of the Storm Water Management Model, the quantity and
quality of dry weather flow are important as they occur both prior to and
during periods of storm runoff in combined sewers. At the onset of storm
runoff, the initial volume in the sewer and the amount of settled and
flowing pollutants establish initial conditions for flow and pollutant
routing. This factor is especially important in assessing initial
flushing of sewers by runoff. During runoff, DWF, although having lost
its hydraulic significance, is important because of its relatively large
pollutant concentration. Consequently, DWF serves as a significant
weighting factor in mass balance relationships affecting pollutant
concentrations.
In this study, separate modeling was undertaken for wastewater flow,
wastewater quality, and groundwater infiltration. DWF quality, although
estimated concurrently with quantity in the subroutine FILTH, is thus
discussed separately in Section 12 of this volume. In addition, DWF
quantity, as estimated in subroutine FILTH and defined in the following
discussion, consists of only wastewater flow and excludes any estimate
of infiltration. Although DWF in sewers actually consists of dry weather
infiltration mixed with domestic, commercial, and industrial sewage,
infiltration is modeled separately by subroutine INFIL and, as a result,
is discussed separately in Section 7 of this volume. The following dis-
cussion therefore describes the development and testing of subroutine
79
-------
FILTH as a predictive model for average wastewater flows from residential,
commercial, and industrial urban areas.
OBJECTIVES
Objectives in the development of subroutine FILTH were to predict accurate-
ly average wastewater flows and total pollutant loads. DWF's significance
to the Storm Water Management Model was originally thought to be in
establishing initial conditions for flow routing. However, comparisons
of outfall hydrographs routed both with and without initialized DWF
showed identical results after the first few minutes of overflow. Sub-
sequent development has shown that DWF's primary significance lies in
establishing initial quality conditions. Initial sediment load on sewer
inverts and initial flow concentrations represent a relatively high per-
centage of initial pollutant overflow. Subsequent analyses showed also
that hourly variation in average flow was required to describe DWF quality
adequately.
THE MODEL SUBROUTINE
The computer program developed to perform the DWF quantity computation
is subroutine FILTH. This subroutine also computes the DWF quality.
Subroutine FILTH is called from subroutine TRANS.
Daily and hourly flow variation for the study area are input along with
flow quantities from process flows, if they are known. Information
regarding total population, population density, land use, residential
income, and home valuation, among other factors, are also required.
The DWF quantity is then computed and passed back to subroutine TRANS.
30
-------
THEORETICAL DEVELOPMENT
Input Data
A key consideration in model development was the availability of input
data for estimating purposes. To minimize this constraint, FILTH was pro-
grammed to accept readily census tract and block statistical data. These
data serve as the most complete and accessible information on population
and housing in large urban areas. Other acceptable inputs are sewage
flow and metered water use data gathered for the drainage basin being
modeled.
Using a variety of flow and drainage basin data, the model has been
designed to estimate wastewater inputs at discrete locations along the
trunk sewer of the drainage basin being modeled. These estimates are
calculated from data describing drainage basin subsections (subcatchments)
through which the trunk sewer passes. As shown in Figure 6-1, an input
manhole near the center of each subcatchment is assumed to accept all
sewage flow from that subcatchment. Sewage inputs from all subcatchments
are then added to infiltration estimates from all pipe sections, and in
the case of combined sewers, to runoff estimates from all inlet subcatch-
ments. Noting the locations and timing of all inputs, the Transport
Model (subroutine TRANS) then produces hydrographs at any specified
location along the sewer.
Possible sources of DWF, other than for household wastewater, are listed
in Table 6-1 (Ref. 1). Because of its highly unpredictable nature, dis-
charge from swimming pools has been excluded as a source of DWF both
81
-------
— K\ ^ MANHOLE
SEWER ELEMENT NUMBERS
SUBCATCHMENT OR SUBAREA
NUMBER
INPUT MANHOLES
CONDUITS
SUBAREA BOUNDARIES
SUBCATCHMENT BOUNDARIES
Sewer and Subcatchnent Data
1. Manhole 32 is the most downstream point.
2. Subcatchments 1,2,3, and 4 are single-family residential
areas, each 100 acres in size and each with water retering.
3. Subcatchments 5 and 7 are 220-acre industrial areas.
4. Subarea 6 is a 250-acre park.
5. Subarea 3 is a 50-acre commercial area.
Subareas 6 and 8 constitute a subcatchment draining to
input manhole number 21.
Resulting Data
8 sewage estimates
KTNUM, total Subcatchments and subareas in drainage basin = 8.
TOTA, total acres in drainage basin = 1,140.
KNUM,
subcatchment
or subarea
1
,
1
'
1
-
;!
INPUT,
KLAND,
input manhole land use
number
3
! 1
•
2<
:•:
24
2]
category
1
.
.
1
:
5
-!
1
ASUB,
acres in
subcatchment
or subarea
100
100
100
100
220
250
220
50
Figure 6-1. DETERMINATION OF SUBCATCHMENT AND
IDENTIFICATION DATA TO ESTIMATE SEWAGE
AT 8 POINTS
82
-------
Table 6-1. ALLOWABLE NUMBER OF SEWER CONNECTIONS
BY CITY SIZE AND GEOGRAPHIC LOCATION
oo
u>
Connections
Swimming
Pools
Combined Sewers
City size
0-10,000
10,001-25,000
25,001-100,000
100,001-1,000,000
Over 1,000,000
Geographic location
East
South
Midwest
Southwest
West
Total
Storm Sewers
City size
0-10,000
10,001-25,000
25,001-100,000
100,001-1,000,000
Over 1,000,000
Yes
—
8
9
13
—
15
1
7
1
5
29
—
14
27
21
1
No
—
4
3
2
—
5
—
4
—
—
9
—
5-
6
5
—
Foundation
Drains
Yes
9
10
12
15
2
9
1
4
31
19
32
23
1
No
3
2
3
5
—
2
—
1
8
2
2
3
—
Are Allowed for the discharge of
Roof
Leaders
Yes
8
5
12
14
1
5
1
4
25
18
35
25
1
No
4
7
3
6
1
6
—
1
14
2
1
2
— —
Sump
Yes
10
11
14
17
2
10
1
5
35
15
26
23
1
Pump
No
2
1
1
3
—
1
—
—
4
5
4
5
1
Treated
Cooling Industrial
Water Process Water
Yes No
8 3
9 2
15
15 3
2
10 1
1
4 1
32 5
16 2
27 6
28 1
1
Yes
—
6
8
12
—
13
2
7
1
3
26
—
6
15
16
— —
No
—
4
1
1
—
2
—
2
—
2
6
—
7
13
7
1
Untreated
Industrial
Process Water
Yes
—
5
7
9
—
10
1
6
1
3
21
—
5
4
8
•——
No
—
4
2
3
—
5
1
2
—
1
9
—
6
19
15
~ —
Source: APWA, "Water Pollution Aspects of Urban Runoff," January 1969, WP-20-15 (Ref. 1)
-------
prior to and during runoff. Roof leaders, foundation drains, and sump
pump connections were not considered in the realm of DWf to the extent
that they provide alternate paths for surface runoff and, therefore,
affect the travel time of runoff to storm and combined sewers. Industrial
flows are input to the Transport Model via FILTH.
Methodology
Model development relied heavily on major research programs conducted at
the Johns Hopkins University (Ref. 2). These efforts were concerned with
quantitative formulations of residential and commercial water usage
patterns based on extensive programs of meter installation and data
review. The residential work clearly exceeded the scope, magnitude, and
depth of consideration of any work preceding it. It was national in
scope and utilized advanced statistical techniques for data evaluation.
The commercial usage study, on the other hand, was centered about
Baltimore, Maryland. Because of its well organized approach and thorough-
ness, the commercial water use study has validity for use on a national
scale, as well. Additional estimates of water use were obtained from a
computerized water use study by Hittman and Associates from Columbia,
Maryland (Ref. 3), and a summary of water use in manufacturing from the
U. S. Census Bureau (Ref. 4).
Based upon the previously mentioned objectives and constraints, the
structure and logic of FILTH was developed to read and edit input data,
make necessary flow estimates, and coordinate flow estimates as inputs to
the Transport Model (subroutine TRANS). FILTH was structured to
give priority to sewage flow and metered water use data as predictors of
84
-------
wastewater flow. If estimates were necessary for commercial and indus-
trial subareas, water use coefficients provided in the "User's Manual"
(subroutine FILTH) provided the necessary input (Refs. 2,3,5). Flow
estimates for residential areas are made within the computer program
using water use estimating equations developed in the Johns Hopkins
Residential Water Use Study.
Estimating equations for residential water use were taken from the work
done by Linaweaver. From analysis of water use throughout the country,
Linaweaver stated that the principal factor influencing total annual
water use in any residential area is the total number of homes. Three
other major factors are: economic level of the consumer, climate, and
whether consumers are metered or on a flat rate basis.
Income level of the consumer influences domestic water for two primary
reasons. According to Linaweaver"s investigations, consumers in a high-
valued area have more water-using appliances. As a result, domestic use
is likely to increase because the average time between uses decreases
while the average duration per use increases. To verify this assumption,
Linaweaver analyzed water use data from 29 areas and developed the
following regression equation:
Q,. = 178 + 3.28v (1)
Q/cl
where Q, , = Average domestic use per dwelling unit (gpd)
cl/a
v = Average assessed valuation of property (thousands of
dollars)
85
-------
Subsequent analysis of residential water demand by Howe and Linaweaver
(Ref. 6) resulted in the following equation:
qa,d = f(v'a'V k' V (2)
where q = Average annual quantity demanded for domestic purposes
cl f Q.
(gpd per dwelling unit)
v = Market value of the dwelling unit (thousands of dollars)
a = Age of the dwelling unit (yr)
d — Number of persons per dwelling unit
k = Average water pressure (psi)
p = Sum of water and sewage charges that vary with water
Vr
use, evaluated at the block rate applicable to the
average domestic use in each drainage basin
After extensive analysis of water use data from 21 eastern and western
drainage basins, variabilities in average water use due to the existence
of public sewers, flat rate pricing, and apartments were statistically
blocked out. Regression of average daily water use on the remaining
variables yielded the following linear equations for the type of resi-
dential areas specified.
Metered with public sewer:
q = 206 + 3.47v - 1.30 p (3)
a,d *w
Flat rate and apartments with public sewer:
q , = 28.9 + 4.39v + 33.6d (4)
a,d p
86
-------
Metered with septic tanks:
q , = 30.2 + 39.5d (5)
^a,d p
TEST APPLICATIONS
Preliminary testing of FILTH was accomplished through the use of data
from the Johns Hopkins University Residential Sewerage Research Project.
A summary of the results of this testing is given in Table 6-2 and
Figures 6-2 to 6-6. For subcatchments less than 130 acres in size, it
can be seen that deviations may be as high as 108 percent and average
nearly 40 percent of recorded flow. However, application to one 3,400-
acre drainage basin in San Francisco resulted in underestimation of
sewage flow by only 12 percent. Similar accuracy was noted in the veri-
fication applications of the Storm Water Management Model as described
in Volume II of this report. The significance of the seemingly large
variability of estimates in small upstream subcatchments lies in the
establishment of initial flow in the sewers prior to the occurrence of
runoff. Extreme upstream branches of the sewer may have dry weather flows
that are somewhat above or below actual conditions. These discrepancies
are soon dampened, however, as flows accumulate downstream and have been
shown to be less than 12 percent at the outfall.
During testing of FILTH, it was noted that recorded dry weather sewage
flows and quality exhibited definite variation depending on the time of
the day and day of the week. These variations were accounted for in
FILTH by correcting estimated flow by hourly and daily flow correction
factors. These factors can be determined from historical flow records as
described in the "User's Manual."
87
-------
Table 6-2. ACTUAL AND ESTIMATED DAILY AVERAGE RESIDENTIAL
SANITARY SEWER FLOWS TO TEST VALIDITY OF SUBROUTINE FILTH
00
CD
1
Measured*
Area, Sewage Flow,
Gaging Area acres gpm
Bradenton ^^
(Florida)
IS1?°^ • x 34 24-50
(California)
Nutwood . , _ __ r_.
112 87 . 50
(Maryland)
Valley Wood
,_,.., . . bJ li.bb
(California)
Springfield gg 3? 5g
(Missouri)
.„,.,_ . . 12 11.18
(California)
Pine Valley 4? 45 2Q
(Maryland)
(corrected)
2 3
Estimated Deviation Measured Deviation
Water Use, 2-1 Water Use, 3-1
gpm gpm percent gpm gpm percent
57.50 +11.18 24.1% 38.20 - 8.12 17.5%
22.40 - 2.10 8.6 24.70 + 0.20 8,8
85.92 - 1.58 1.8 95.54 + 8.04 9.1
24.34 +12.68 108.7 19.59 + 7.93 68.0
49.10 +11.51 30.6 28.10 - 9.49 25.2
19.64 + 8.46 75.7 10.86 - 0.32 2.8
25.18 -20.02 44.3 31.58 -13.62 30.1
*Except for Pine Valley (corrected), flow includes groundwater infiltration and storm water penetration.
-------
CO
BRADENTON GAGING AREA
1961
-i . i l i i l i i i i i i i i i l l i t i I I I I I I II I I I II I I I I I LJ
I 19 I* I It 26 8 II It I I* It t l» *• » II II I II II
HPT. OCT. HOY
LIHAWIAVIR'l , ,7 .,
RE..I11 0.
AVCRAtC (««.!)
_ _ WINTER
• ATIR U$l
10
BRAOENTON GAGING AREA
1962
-n n i ill ll i l l l l l i l i i i i i i i i i l i i I i i i i i I l il I I I I I I I I 1 I II 1 I I I I I I I I I
a is » i i* it t it it t it » t it it t i> i* t it n t II t» l II tl I it it I it » i
JAN. H*. MAR. APR, MAY JUNE JULY All*. MPT. OCT. NOV.
Source: F. P. Linaweaver/ "Final and Summary Report on the
Residential Water Use Research Project," July 1966
(Ref. 2).
Figure 6-2. TEST RESULTS, BRADENTON (FLORIDA) GAGING AREA
-------
.
VALLEY WOOD GAGING AREA
1962
LINAWEAVEII'S ,
JA«. FES.
\7
I I I I
— WINTEN ,,« „
1 1 WATCH USE
AVCRASE (117)
>6 *» « II 21 9 15 26 0 TT26 5 Ts25 S IS 2S S It 26 I IS 25
MAY JUNE JULr AUO. SEPT. OCT. HOY. DEC
ALVY GAGING AREA
I 962
I I i
i i i i Y i I I I I I i i i i i i i t i i i i i i i i i i i i I I i I i i I ................ i ..... l i I I
'* *..." " * '*. " * " " * " " •'•»•• l» «• • '5 25 6 II 25 I 15 25 > 15 21 5
'•• MAN. APR. MAT JUNE JULY AU6. SEPT. OCT NOV
LINAWE AVEH'S , ,
REGRESSION
* V E B » 6 t ( 11.2)
WINTCN . lft .
• ATEd USE ' ">••!
JATE.'UIC (14'T1
AVEH A8C ( 24.8)
L ih A WE AVEN'S
• t;»ni ON (11.4)
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 I I I I I I I I I I I I I I I I I I 1 I I I I I I I I I I I I I I I
S IS IS I II 21 5 IS 11 I IS IS S IS 25 5 IS 2S S IS IS S IS 25 S 16 25 I IS 25 S IS II S
J*". '". BAB. APR. MAY JUNE JULY AU«. SEPT. OCT. MOV.
Source: F. P. Linaweaver, "Final and Summary Report on the Residential Water
Use Research Project," July 1966 (Ref. 2).
Figure 6-3. TEST RESULTS, VALLEY WOOD, ALVY, AND FALCON (CALIFORNIA) GAGING AREAS
-------
NUTWOOD GAGING AREA
1961
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 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
.
NUTWOOD GAGING AREA
1962
W-
i I! »« I II
JAM. fit.
HAH. APR. MAY
I ID Z» 5 It 25 S
OCT. HOV.
Source: F. F. Linaweaver, "Final and Summary Report on the
Residential Water Use Research Project," July 1966
(Ref. 2).
Figure 6-4. TEST RESULTS, NUTWOOD (MARYLAND) GAGING AREA
-------
•
PINE VALLEY GAGING AREA
1961
AWCAVC M S
NOV. DEC.
PINE VALLEY GAGING AREA
1962
I 1 I I I I I I I I I I I 1 I I III I I I I I IM I I I 111 I I I I I I I I I I I
OCT. NOV. DCC.
Source: F. P. Linaweaver, "Final and Summary Report on the Residential
Water Use Research Project," July 1966 (Ref. 2)
Figure 6-5. TEST RESULTS, PINE VALLEY (MARYLAND) GAGING AREA
-------
SPRINGFIELD GAGING AREA
1962
~/u. Iv \ r
.
(411)
AVI »» C E ( >7.<)
SPRINGFIELD GAGING AREA
1961
nl 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 I I I I I I I I I I I I I I I I I I I I
18 21 t If 21 f Ift 2» I II 21 t li tl • IB 2f f 19 21 ft 15 25 8 IB 21 5 It IS
UAH. AFN. HAT JUNK JULY AU0. (KPT. OCT. NOV. DIG.
Source: F. P. Linaweaver, "Final and Summary Report on the
Residential Water Use Research Project," July 1966
(Ref. 2)
Figure 6-6. TEST RESULTS, SPRINGFIELD (MISSOURI) GAGING AREA
-------
CONCLUSION
The Dry Weather Flow model was developed to represent DWF quantity and
quality for periods prior to and during storm runoff in the physical
sewer system being studied. Using a regression analysis concept similar
to the research accomplished by Linaweaver, the model is dependent on
the availability of input data for a predictive comparison with the real
world. The Johns Hopkins University Residential Research Project was
used for testing the model. The percent error between model results and
recorded flows at the outfall averaged to a reasonable amount when
validating the model. Thus, the methodology presented herein proved to
be satisfactory during its demonstration.
94
-------
SECTION 7
INFILTRATION MODEL
Page
OBJECTIVES 97
THE MODEL SUBROUTINE 98
THEORETICAL DEVELOPMENT 98
Input Data 99
Methodology 100
High Groundwater Table (GINFIL) 101
Estimation of Antecedent Precipitation (RINFIL) 103
Estimation of Residual Melting Ice and Frost
Infiltration (SINFIL) 103
Apportionment of Infiltration 104
TEST APPLICATION 107
CONCLUSION 107
95
-------
SECTION 7
INFILTRATION MODEL
In order to arrive at a model to determine the relative contribution of
infiltration to flow and quality in combined sewers, two primary assump-
tions were made. It was assumed that a model could be developed to re-
flect the availability, movement, and entry of moisture into a subsurface
conduit. The effect of infiltration upon quality was assumed negligible
except for some dilution.
The present state of the art was such that actual flow measurements of
infiltration for comparison to predictions were unavailable. This con-
straint was overcome by using minimum and average daily sewage flow data
recorded on the Johns Hopkins University Residential Sewerage Research
Project (Ref. 1). An analysis of the Infiltration model is presented in
the remainder of this section.
OBJECTIVES
The incorporation of the Infiltration modal, subroutine INFIL, into the
overall Storm Water Management Model and its adaptability to local
variations and characteristics were of prime concern. Thus, in the
development of INFIL, the objectives were:
1. To predict accurately infiltration into a given sewer system on
the basis of existing local information about the sewer, its
surrounding soil and groundwater, precipitation, and other
climatological data.
97
-------
2. To apportion the predicted infiltration at discrete locations
along the given trunk sewers prior to flow routing.
THE MODEL SUBROUTINE
The computer program developed to perform the infiltration computation is
subroutine INFIL.
Subroutine INFIL is called from TRANS to compute the infiltration from
groundwater, antecedent precipitation, and ice and frost melting.
The infiltration is then combined with the DWF quantity computed in
FILTH to yield the base flow in the sewer.
THEORETICAL DEVELOPMENT
A typical urban drainage basin in which infiltration might be estimated
for use by the Storm Water Management Model is shown in Figure 7-1.
LATERAL SEWERS
CONDUITS TO WHICH TOTAL
INFILTRATION IS APPORTIONED
DRAINAGE BASIN BOUNDARY
NON-CONDUIT ELEMENT
Figure 7-1. TYPICAL DRAINAGE BASIN IN WHICH
INFILTRATION IS TO BE ESTIMATED
-------
In the preliminary stages of model development consideration was given
to the use of existing mathematical relationships representing flow
through porous media. The complexity and inflexibility of these relation-
ships (Ref. 2), together with the stochastic nature of the real problem,
led to the selection of empirical methods.
Initial attempts were made to develop a general predictive equation of
nationwide applicability for infiltration, as presented in Appendix A.
The equation incorporated an antecedent precipitation index, pipe diameter,
pipe length, and factors denoting soil type and joint material. However,
it failed to account for abrupt flow changes and exhibited trends that only
approximated local conditions and measurements. This lack of sensitivity
to local conditions was further accentuated upon comparison with infiltra-
tion measurements taken by M&E in a study for the EPA on storm water
problems and control in sanitary sewers in a six-city area along the
east shore of San Francisco Bay (Ref. 3). The results of this comparison,
however, led to the development of the present model.
Input Data
The availability of input data, therefore, was the key factor in devel-
oping the model. An analysis of variance on time-dependent variables and
minimum flows was conducted on each of seven study areas from the Johns
Hopkins study after obtaining supplementary climatological and geological
information (Ref. 4). Data manipulation went as follows:
1. Determination of the existence of regression using the following
recorded data:
a. Precipitation
99
-------
b. Temperature
c. Relative humidity
d. Study area sewer descriptive parameters.
2. Elimination of variables accounting for the least amount of
variance.
3. Transformation of remaining variables to obtain better correla-
tion and regression as follows:
a. Use of time delays from one to six days on rainfall
b. Use of precipitation index to indicate soil moisture con-
ditions.
From the above data manipulations, only precipitation significantly
accounted for minimum flow variation in each study area. However,
groundwater level was considered in the model when it occurred above the
sewer invert, in which case the sewer was submerged and all infiltration
was assumed due to this condition (Ref. 5). Data describing pipe size
and the number of joints were retained to reflect entry of infiltration
into conduits (Ref. 6). Infiltration into manholes was considered neg-
ligible, therefore elminating any need for manhole infiltration data.
Methodology
For analytical purposes, infiltration includes (1) moisture from miscel-
laneous sources causing a base dry weather inflow, (2) frozen residual
moisture, (3) antecedent precipitation, and (4) high groundwater. Based
upon this assumption, infiltration was defined as:
\DINFIL + RINFIL + SINFIL
QINF = < or (1)
(GINFIL for high groundwater table
100
-------
where QINF = Total infiltration
DINFIL = Dry weather infiltration
RINFIL = Wet weather infiltration - DINFIL
SINFIL = Melting residual ice and snow infiltration
GINFIL = Groundwater infiltration
The cumulative effect of the first three sources can be seen in Figure
7-2 which shows total infiltration as the sum of dry weather infiltration,
wet weather infiltration, and melting residual ice and frost infiltration.
However, in cases where the groundwater table occurs above the sewer in-
vert, it was assumed that groundwater alone would be the dominant source
of infiltration.
High Groundwater Table (GINFIL). For locations and times of the year
that cause the groundwater table to be above the sewer invert, ground-
water infiltration, GINFIL, supersedes any notation of DINFIL, RINFIL,
and SINFIL, as shown in Eq. 1. GINFIL is then determined from historical
sewer flow data, by inspection or regression analysis. Regression analy-
sis involves the determination of the coefficients in the following
equation:
n
GINFIL = Z (BETA(i)) (GWHD)ai (2)
i=l
where GINFIL = Groundwater infiltration
GWHD = Groundwater table elevation above sewer invert (ft)
BETA(i) = Coefficient for ith term in equation
ai = Power to which GWHD is raised in ith term, e.g.,
0, 1, 2, 1/2 for term i = 0, 1, 2, and 3, respectively
101
-------
TIME
QINF = Total infiltration
DINFIL = Dry weather infiltration
RINFIL = Wet weather infiltration
SINFIL = Melting residual ice and snow infiltration
RSMAX = Residual moisture peak contribution
SMMDWF = Accounted for sewage flow
Figure 7-2. COMPONENTS OF INFILTRATION
102
-------
Estimation of Antecedent Precipitation (RINFIL) . Using available precip-
itation and average sewer flow data not affected by melting (Ref . 1) ,
RINFIL was estimated vising the following linear relationship:
RINFIL - ALF + (ALFQ) (RNQ) + (ALF^ (RN^ + . . .+ (ALFg) (RNg) (3)
where RINFIL = SWFLOW - DINFIL - SMMDWF
ALFN = Coefficient to rainfall for N days prior to estimate,
N = 0, 1, ..., 9
DINFIL = Average dry weather flow minus the accountable sanitary
flow
RNN = Precipitation on N days prior to estimate (in.),
N = 0, 1, ..., 9
SWFLOW = Daily average sewer flow excluding surface runoff (gpm)
SMMDWF = Accounted for sewage flow (gpm)
In establishing this relationship for RINFIL, the characteristics of the
local soil conditions are being taken into consideration indirectly.
The uniqueness of this estimate and the nep* for establishing localized
relationships is thus indicated.
Estimation of Residual Melting Ice and Frost Infiltration (SINFIL) . The
length of the melting period as well as the rate of melting was calculated
by using published data (Ref. 7) in the form of degree-days as an index.
Degree-day (NDD) is a unit based upon temperature difference and time.
Based on observed relationships between the degree-days and melting
periods in various geographical locations, the value of 750 degree-days
was selected as the indicator of the point in time at which residual ice
103
-------
and snow would start accumulating and also as an indicator of the onset
of the melting period.
As shown in Figure 7-3, the portion of the curve falling above 750 degree-
days corresponds to the period of accumulation. The beginning of
melting, MLTBE, is taken as the day on which NDD drops below 750. This
melting period is assumed to end at that point in time (MLTEN) in which
the area representing accumulated precipitation, A , equals the area A
during the melting period. Therefore, residual melting ice and frost
infiltration (SINFIL) is determined by the following equation:
SINFIL
RSMAX
JSin 180 |(NDYUD - MLTBE)\ I
I I I(MLTEN - MLTBE)|J J
0.0 if the day under study is not
in the melting period or if NDD
never exceeds 750 (4)
where SINFIL = Melting residual ice and snow infiltration
MLTBE = Day on which melting period begins
MLTEN = Day on which melting period ends
NDYUD » Day on which infiltration estimate is desired
RSMAX = Residual moisture peak contribution
In the absence of evidence to the contrary, the rate of melting is assumed
to be sinusoidal. This is shown in Figure 7-4 where RSMAX represents the
maximum contribution from residual moisture and is determined from pre-
vious gaging of the study area or from local estimates.
Apportionment of Infiltration. Once an estimate of local infiltration,
QINFIL, has been obtained, this flow must be apportioned throughout the
designated study area. The criterion chosen for apportionment is an
104
-------
JUNE
DATE
MLTBE = Day on which melting period begins
MLTEN = Day on which melting period ends
Figure 7-3. PRESCRIBED MELTING PERIOD
105
-------
RSMAX
•MLTBE
MLTEN-
RSMAX = Residual moisture peak contribution
MLTBE = Day on which melting period begins
MLTEN = Day on which melting period ends
Figure 7-4. RATE OF MELTING
106
-------
opportunity factor, OPINF, which represents the relative number and
length of openings susceptible to infiltration. Pipe joints constitute
the primary avenue for entry of infiltration. OPINF for an entire study
area is determined by summing over all conduits the product of the peri-
meter of the conduit and the number of joints in each conduit, that is:
(conduit \
perimeter!
/
number of \
joints in I
each conduit/
(5)
TEST APPLICATION
Preliminary testing of INFIL was accomplished through the use of minimum
daily sewage flow data recorded in the Pine Valley (Maryland) area on the
Johns Hopkins University Residential Sewerage Research Project. Figure
7-5 presents the results of a comparison of measured and predicted sewer
flow.
CONCLUSION
The INFIL model, was developed to estimate infiltration into a given
sewer system based upon existing information about the sewer, its sur-
rounding soil and groundwater, precipitation, and clirnatological data.
Using these data, INFIL estimates average daily infiltration at discrete
locations along the trunk sewers of a given sewer system. Minimum flow
data supplied by the Johns Hopkins University Residential Sewerage Research
Project were used to overcome the constraint imposed by a lack of actual
flow measurements on infiltration, and in this preliminary demonstration,
the model proved to be satisfactory.
107
-------
100 -I
-•
~
.
10-
Measured Sewer Flow
RINFIL
OCT.
RINFIL = Wet weather infiltration
DINFIL = Dry weather infiltration
ADWF = Average daily dry weather flow
SMMDWF = Accounted for sewage flow
Figure 7-5. TEST RESULTS, PINE VALLEY (MARYLAND)
-------
The INFIL model is not intended to represent direct or illegal connec-
tions to a combined or separate sewer system. The short response time
of such connections is better represented through adjustments in the
impurviousness ratio of the Runoff Model.
109
-------
SECTION 8
TRANSPORT MODEL
Page
OBJECTIVES U3
Sewer Routing 113
Component Tasks 115
THE MODEL SUBROUTINE 116
THEORETICAL DEVELOPMENT 117
Overall Model 117
Input Data 117
Element Sequencing 119
inflows 121
Flow Routing by the Transport Model 121
The Transport Model Routing Technique 121
Stability of the Finite Difference Scheme 127
Surcharging and Flow Routing in Manholes 128
Flow Routing at Lift Stations 128
Use of Flow Dividers 128
Flow Routing at Internal Storage Units 129
Modeling of Bakcwater Conditions 129
TEST APPLICATION (Conduit Routing Method) 132
111
-------
SECTION 8
TRANSPORT MODEL
OBJECTIVES
Simulation of urban rainfall-runoff-quality processes necessarily in-
volves consideration of flow in storm and/or combined sewers. Adequate
representation of the response of urban catchments to precipitation inputs
thus requires a proper representation of unsteady, non-uniform, free-
surface flow Which is predominant throughout sewers. In addition, pre-
diction of flow quantities at various points within sewer systems,
rather than only at the outfall, is desirable in order to study the
effect of possible surcharging, overflow and diversion structures,
proposed system modifications, and, in general, the overall capacity of
sewer systems to handle storm runoff. Such a routing model may then
serve also as a prerequisite to studies of quality parameter behavior
in sewer systems.
Sewer Routing
An accurate representation of velocity and deoth of flow (or flow rate
and flow area) along a sewer system can be found from the solution, of
the "shallow water" or "St. Venant" equations ,that are the general
governing equations for gradually varied, unsteady flow (Ref. 1).:.
* !£' V.'«
+ r -»
-------
where y = Depth
v = Velocity
k = Longitudinal distance
t = Time
g = Gravitational acceleration
S = Invert slope
o
S = Friction slope
Q = Flow rate
A = Flow area
Eq. 1 is the dynamic equation and Eq. 2 is the continuity equation, with
the assumption of no lateral inflows. In the absence of abrupt transi-
tions (e.g., hydraulic jumps, bores), it is commonly accepted that
solutions to the St. Venant equations offer a good description of the
actual flow phenomena (Refs. 1,2). Unfortunately, solutions must be
obtained numerically, and are usually arrived at using the method of
characteristics (Refs. 1,2,3). This technique has been applied to
sewer systems (Ref. 4) and has been found to be too consumptive of
computer time for general applications. Thus, approximate techniques
must be used in order to obtain a satisfactory flow routing method at a
reasonable expenditure of computation time.
Traditional computations of flows and depths in sewer systems involve
the assumption of uniform flow and normal depth in the computation of
extremes and means and do not attempt to follow the progress of individ-
ual storm hydrographs in the system (Ref. 5). Eagleson (Ref. 6) has
shown the applicability of the unit hydrograph concept to the prediction
114
-------
of hydrographs at the outfall of sewered areas. Owing to the nature of
unit hydrograph techniques, such a method produces predicted hydrographs
only at points in the system where prior flow measurements have been
made and only for storms of specified duration. The technique also does
not separate flow routing in sewer systems from flow routing of rainfall
to sewer inlets. Unit hydrograph techniques thus lack the desired
generality for application to all quantity and quality processes in
sewer systems.
A recent approach to routing of urban runoff has been developed by
Britain's Road Research Laboratory (Ref. 7). The RRL model, as it is
called, has been applied to the prediction of outfall hydrographs with
encouraging results (Ref. 8). However, it lacks the versatility required
to model all components of a large system. In addition, tests conducted
in the present research have shown it to lack accuracy when applied to
long lengths of conduits with no intermediate inflows.
Component Tasks
A routing method has thus been developed to compute hydrographs accurately
at all points in a given sewer system while avoiding the necessity for
solving the St. Venant equations. Evaluation of the model was subsequently
done to judge its ability to reproduce measured hydrographs in real
systems under a wide variety of situations with minimal time and expense
to the user.
Component tasks performed by the Transport Model are to:
1. Coordinate user input data
115
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2. Prepare routing sequence through trunk sewers
3. Coordinate surface runoff, infiltration, and wastewater quality
and quantity inputs
4. Route flows through various conduit cross-sections and sewer
appurtenances
5. Represent in-system storage, surcharging, and backwater
condi tions
6. Coordinate output to other programs and the user.
THE MODEL SUBROUTINE
The computer program developed to perform the computations for flow routing
in the sewers consists of the following 12 major subroutines: TRANS,
TSTRDT, SLOP, FIRST, INFIL, FILTH, DWLOAD, INITAL, ROUTE, QUAL, PRINT,
and TSTCST.
Subroutine TRANS provides the necessary liaison with the master Storm
Water Water Management Model. TRANS also performs certain functions
in relation to quantity routing which is described in the "User's Manual."
Subroutine TSTRDT, when used, reads in data to identify internal storage
basins (those occurring at locations other than at the outlet of the
system) .
SLOP is called by TRANS to sequence the sewer element data for the later
computations.
FIRST is called by TRANS to perform the initial computations of constants
and flow parameters for each sewer element.
116
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INFIL is called by TRANS to estimate and allocate sewer infiltration.
INFIL is discussed in Section 7 of this report.
FILTH is called by TRANS to compute the average DWF quality and quantity.
The DWF quantity and quality computations are discussed further in
Sections 6 and 12, respectively, of this report.
DWLOAD is called by TRANS to compute the initial conditions of sedimentation
within the sewer based upon the number of dry weather days prior to
the storm.
INITAL is called by TRANS to initialize flows, areas, and pollutant
concentrations to values corresponding to DWF plus infiltration.
ROUTE is called by TRANS to route the flow through the sewer elements.
QUAL is called by TRANS to route the pollutants through the sewer elements.
PRINT is called by TRANS to print the total hydrographs and pollutographs
for the desired elements.
TSTORG is called by ROUTE to compute flow storage within the sewer
system. TSTORG is discussed further in Section 9.
THEORETICAL DEVELOPMENT
.Overall Model
Jnput Data. To categorize sewer systems conveniently prior to flow
touting, each component of a system is classified as a certain type of
Sewer "element." All elements in combination form a conceptual represen-
tation of a system in a manner similar to that of links and nodes.
117
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Elements may be classified as conduits, manholes, lift stations, storage
units, or other appurtenances by specifying element types, e.g., manhole
(type 16), circular conduit (type 1), and storage unit (type 19).
Conduits themselves may be of different types depending upon their
geometrical cross-section (e.g., circular, rectangular, horseshoe, etc.).
Data input has been structured so as to allow element description on a
"one element per data card" basis.
During preliminary development of the Transport Model, it was noted that
the number of elements used to represent any given sewer system would
necessarily have to be limited to less than 150 to conserve computer
core space; approximately half of the elements would necessarily be
devoted to non-conduits, leaving only 75 to conduits. To overcome this
limitation, it was decided to defer consideration of the numerous and
smaller lateral conduits and to aggregate remaining trunk conduits, if
necessary. So as not to neglect the effect of lateral sewers upon flow
routing, it was agreed that they would be considered as special gutters
and, therefore, incorporated into surface runoff routing. Any necessary
aggregation of remaining trunk conduits will be left essentially to
judgment on the part of the user. However, an upper limit of approxi-
mately 3,000 feet will avoid inaccuracy in flow routing due to extremely
large conduit length. Conduit elements of less than this length would
be defined whenever significant changes in cross-section, slope, rough-
ness, or incoming branches occur at shorter distances. Although criteria
ultimately relate to changes in conduit flow-area relationships, it
remains for the user to determine which changes are significant enough
118
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to warrant defining a new conduit element. Reference to Figure 8-1
should assist in describing sewer elements by showing an example sewer
element schematic.
Non-conduit elements serve as convenient boundaries in the finite dif-
ference scheme used in conduit flow routing by providing for flow input,
diversion, and storage. The most useful type of non-conduits are man-
holes, providing input locations for surface runoff, wastewater, infil-
tration, and upstream conduit flows and storage of temporary surcharging
from downstream conduits. Thus, manholes would logically be placed as
the most upstream element on each branch of the trunk system to allow
flow input. All conduits should be linked by non-conduits, either to
represent real manholes in the system, or to delineate conveniently
changes in slope, roughness, etc., of adjoining conduit sections.
Element Sequencing. An extremely flexible sequencing routine was devel-
oped to order elements for routing. As a result, sewer elements defined
on a sewer system schematic, such as shown in Figure 8-1, may be numbered
in any order desired. By requiring that each element data card include
that element's number and the numbers of elements directly connected
upstream, elements can then be ordered within the computer by progres-
sively searching for elements for which all upstream elements have been
sequenced for routing. This progressive searching sequences elements
regardless of the order in which element data are input. Thus, flexi-
bility has been introduced by allowing both random numbering and random
ordering of inputting elements.
119
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POTOMAC RIVER
Figure 8-1. SEWER SCHEMATIC FOR THE KINGMAN LAKE
(WASHINGTON, D.C.) STUDY AREA
120
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Inflows. Non-conduit element numbers nearest to the desired input point
for wastewater and surface runoff are used to coordinate inflow. Waste-
water flows estimated for subareas within the study area are assumed to
enter at non-conduits located near the center of each subarea. Surface
runoff estimated for each subarea within the study area are assumed to
enter at non-conduits located at the downstream point of each subarea.
For convenience, infiltration flows estimated for each conduit are
allowed to enter at the upstream end of each respective conduit.
Flow Routing by the Transport Model
The Transport Model Routing Technique. The continuity relationship,
Eq. 2, is put into finite difference form, with reference to Figure 8-2.
The subscript j denotes upstream conditions of flow, Q, and area, A,
and the subscript j + 1 denotes downstream conditions. The subscript
n denotes conditions at the previous time-step, and the subscript n + 1
denotes conditions at the new time-step. The time derivative will be
weighted w at point j + 1 and 1 - w at point j. The spatial
derivative is weighted w-' at time-step n + 1 and 1 - w at time-
X X
step n. The continuity equation is then
(1 - w, ) (A. - A. ) + w. (A. _ _ - A. _ )
_ t J,n+l j,n t j+l,n+l 3+l,n
At
(3)
• ** = 0
Ax
The equations will ultimately be solved by starting at the upstream end
and working downstream. Thus, at each time-step, the only unknowns will
be the flow and area at the downstream end of the conduit length. Eq. 3
121
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Qj.n
A X
CONDITIONS AT
Element M
Ax = Dist(M)
CONDITIONS AT t*
TIME
M-l
t
At
__1
ELEMENTS
M
J,n
— AX —
Figure 8-2. FINITE DIFFERENCE DEFINITION SKETCH
FOR ELEMENT M, ROUTING THROUGH ALL
ELEMENTS AT EACH TIME-STEP
122
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can be rearranged to isolate the downstream flow and area.
w
Ax t Ax
Qj+l,n+l + At w~ Aj+l,n+l + AtTir I(1"wt) (Aj,n+l " AJ,n}
1-w (4)
Wt - - =
Eq. 4 is now normalized vising values of flow and area for conditions of
the conduit flowing full, denoted by the subscript f. The dimensionless
area is denoted by a,
A
a = — (5)
Af
and the dimensionless flow rate by \l>,
(6)
Eq. 4 can then be written
C2
where
Ax w A-
and
Ax
C« =
2 = At W
JL £
(9)
1-w
123
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Since the parameters C., and C2 will be known at each time-step,-
Eq. 7 can be solved if a second relationship between the flow rate and
area is known. Such a relationship can be found from Eq. 1 after first
defining the friction slope, S , in the usual manner, using Manning's
equation .
2 2
Sf = - T~47J = - 2 2 4/3 (10)
i-49 * 1.49 A R4/3
2 2
n n
The variable R denotes the hydraulic radius, and n is Manning's
roughness. The simplest result available from Eq. 1 is then obtained
when all the terms on the left hand side are neglected. The resulting
uniform flow relationship is
Q . j
If Eq. 11 is normalized by the full-flow values of Q, A, and R,
there results
*-f A R
f Af Rf
The normalized flow rate will be a function only of the normalized area
since the hydraulic radius is a known function of the flow area for a
given geometry. The relationship of Eq. 12 is illustrated in Figure 8-3
for three conduit shapes; it may be similarly derived for any conduit
cross-sectional geometry.
In the development of the Transport Model, the first technique tried
was simply to use Eq. 11 (leading to Eq. 12) , as the required second
124
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o-
•
1.0-
0.9
08
0.7
0.6
0.5
0.4
0.3
0.2-
0.1
00
CIRCULAR
SEMI-ELLIPTICAL
EGG SHAPED
0.0 .10 .20 .30 .40 .50 .60 .70 .80 .90 1.0
A/Af
Figure 8-3. NORMALIZED FLOW-AREA RELATIONSHIP FOR UNIFORM FLOW
125
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relationship between flow and area. When Eq. 12 is substituted into
Eq. 7, the resulting non-linear algebraic equation is readily solvable
by the Newton-Raphson method or other techniques. Hydrographs produced
by this method were good for conduits on relatively steep slopes, but
not as good at low slopes, (on the order of 0.001 or less). This is to
be expected, since all dynamic terms are neglected, and at low slopes,
backwater effects become appreciable.
In order to improve the predicted hydrographs, yet retain the basic
simplicity of the method, it was decided to include additional terms
from Eq. 1 in the calculation of the slope for use in Eq. 11. When
Eq. 11 is normalized, the slope parameter disappears. Hence, the primary
difference is that the full flow rate, Q_, must be calculated anew for
each conduit length at each time-step when terms from the left hand side
of Eq. 1 are used. In particular, it was decided to include the water
^
surface slope, 3y/3x, and velocity head slope, — T—, since they
g ox
can be calculated from the velocities and areas at the upstream and
downstream ends of each conduit, known from the previous time-step.
Then the full flow rate is calculated thus:
Q . idi A R2/3 (s _|v__v|vl/2 (13)
f n f f o 3x g ox
The derivatives are evaluated in finite difference form at time-step n.
22
3v _ __3 v\ _ yj,n " y V " V
;
__
3x ~ g 3x ~ ~ 3x 2g Ax 2gAx
(14)
126
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When this method was used, agreement between predicted hydrogrphs on low
slopes and a standard of comparison (to be described later) was consider-
ably improved. However, undesirable oscillations appeared in the pre-
dicted results. In an effort to eliminate the oscillations, an iterative
procedure was developed in which, at each time-step, Q_ was calculated
two or more times for each conduit, using the values of velocity and
depth calculated on the preceding iteration. The small remaining
oscillations were removed by using a value of Q. taken as the average
of the value from the previous iteration, and that just calculated. If
the subscript i represents the number of the iteration, then at iter-
ation i,
2 2 (15)
* j.j-1 - vVl.j-1 1/2
2g Ax '
Four iterations were found to produce satisfactory results. When con-
duits have steep slopes, no iterations are required, and the invert slope,
S , can be used alone. In order to avoid the possibility of a square
root of a negative number, the sum of the slope terms is not allowed to
be less than S . Since the only change is in the calculation of Q,. ,
o z
it is still necessary only to substitute Eq. 12 into Eq. 7 and solve for
a and ty . The values of A and Q are subsequently obtained from
Eqs. 5 and 6.
Stability of the Finite Difference Scheme. The stability of the method
can be investigated using the techniques of Ref. 9,- when the equations
127
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are linearized. It is found that the scheme is unconditionally stable"
(i.e., for any choice of Ax and At ), for w and w both greater
t X
than 0.5, neutrally stable for w and w equal to 0.5, and unstable
t. a
(i.e., errors grow with time) for w and w less than 0.5. After
t X
numerous trials, a value of 0.55 was chosen for w and w since it
t X
resulted in the best attentuation of the hydrograph peaks, as well as
insured stability.
Surcharging and Flow Routing in Manholes. Flow routing is accomplished
in manholes by specifying that the outflow equals the sum of the inflows.
Head losses at manholes are not considered a factor in trunk sewer flow
routing, but could be accounted for simply by increasing the roughness
coefficient of adjacent conduits. Unless diverted to an internal (in-
system) storage element, surcharge volume from a downstream conduit is
stored at the upstream manhole. Surcharged flows offer an additional
flow input whenever excess flow capacity develops in the downstream conduit.
Flow Routing at Lift Stations. Lift stations are assumed to operate
when wet well volume reaches a designated value which actuates a single,
constant-discharge pump. Pumping continues until the wet well is emptied.
Flooding caused when wet well capacity is exceeded is not considered.
Use of Flow Dividers. Flow dividers are programmed to perform in either
of two ways. The first and simplest type assumes that diverted flow
equals zero until an overflow setting is exceeded, after which all flow
in excess of the setting is diverted. Junctions for relief sewers,
bypasses, and other overflow structures occasionally perform in this
manner.
128
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Flow may also be diverted over a weir, in which case overflow is propor-
tional to head above the weir taken to the 1.5 power. To determine head
above the weir, flow depth through divider elements is assumed proportional
to the flow rate. This head is calculated by multiplying the distance
between the weir height and the top of the structure with the ratio of the
incoming flow to the maximum possible flow. Side weirs as well as end
weirs may be modeled by inputting the appropriate weir constant as data.
Flow Routing at Internal Storage Units. Flow through storage units located
elsewhere than at the downstream point of a sewer system is routed by speci-
fying a type 19 element. Storage units may be natural or man-made with
weir and/or orifice outlets. Three routing options exist, namely, routing
flow without quality, routing flow and quality assuming plug flow, and
routing flow quality assuming complete mixing during each time-step.
The internal version of the Storage Model differs in structure from
external storage (see Section 9) so as to allow more than one storage
unit to serve on a time-step basis as a transport element. Also, as
storage units at upstream locations will probably be smaller, no quality
improvements, such as by settling, are modeled within internal storage.
Refer to the Storage Model discussion (Section 9) for further description
of storage routing.
Modeling of Backwater Conditions. An accurate simulation of transient
backwater conditions is not possible without an exact solution of the St.
Venant equations simultaneously throughout the sewer system. The Transport
Model does, in fact, include backwater effects for flow routing in a given
129
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conduit length by means of the iterative scheme described previously.
However, since upstream conduits are routed independently of those down-
stream and no transfer of water depths is made, a continuous backwater
profile is not simulated. The results (shown in Figures 8-5, 8-6, and 8-8)
have shown the Transport Model to be very adequate in spite of this limitation.
However, backwater effects due to ponding as a result of a flow control
structure can be simulated by a combination of conduit routing and in-
system storage. The primary effect of such ponding is for upstream
flows to be "felt" at the flow control structure earlier than if they
were to flow normally through the intermediate conduits. The Transport
Model simulates this effect by first assigning an extent of backwater
by projecting the water surface horizontally upstream from the flow
control structure at maximum depth until intersecting the invert slope.
It is recognized that the actual extent of backwater as determined from
an exact calculation would most probably be further upstream than
indicated above. However, the intention is to model the "reservoir" or
"ponding" effect only, and the assumption of a horizontal water surface
slope considerably simplifies this task. A "backwater element," which
is actually a special type of flow divider, is then placed at the
location of the extent of backwater, and a storage element is placed at
the location of the flow control structure. The concept is illustrated
in Figure 8-4.
The backwater element is programmed to pass flow directly to the storage
element or to the intermediate conduits, depending upon the amount of
flow currently stored in the backwater region. In this way the upstream
130
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Sewer
Inflow, QI
Extent of
Backwater
/ /
Orifice Flows
Into Intercepting
Sewer
SEWER PROFILE
Intercepted
Flow
Downstream
Weir
.
Conduit
Conceptual Flow Path
to Storac
Backwater
Element
Type 22
Conduit
Conduit
Manhole
Element
Type 16
Conduit
Storage Conduit
Element
Type 19
SCHEMATIC REPRESENTATION OF STORAGE IN THE TRANSPORT MODEL
Figure 8-4. TYPICAL IMPLEMENTATION OF A BACKWATER ELEMENT
-------
flows are "felt" at the flow control structure (as simulated in the
operation of the storage element) earlier than if they were routed
totally through the intermediate conduits. By assuming constant width
for upstream conduits, backwater length can be shown to be proportional
to the square root of current storage within the same upstream elements.
Then at each time-step, the backwater element computes the ratio, r,
of current to maximum storage volume in the downstream storage element.
Then
Q01 = QI -\ (16)
and
QO2 = QI - QO1 (17)
where Q01 = Flow directly into storage unit
Q02 = Flow into intermediate conduits
QI = Inflow to backwater element
TEST APPLICATION (Conduit Routing Method)
Ideally, the Transport Model should be tested against measured hydrographs
in a real sewer system, but such data were unattainable during the
testing phases. Hence, an attempt was made to compare predicted flow
hydrographs with depth hydrographs measured in a long circular pipe
(Ref . 3) . However, comparison of the flows and depths was difficult to
do quantitatively. Thus, it was decided to develop an exact solution
of Eqs. 1 and 2, and to compare the Transport Model with this solution.
Consequently, a solution was attained numerically using the method of
132
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characteristics in a manner similar to that described in Refs. 4 and 10.
This was tested against the measured depth hydro-graphs of Ref. 3 and
found to be in very good agreement. The characteristics solution was
subsequently used as a basis of comparison of the Transport Model.
Comparisons of hydrographs predicted using the Transport Model and the
characteristics solution can be seen in Figures 8-5 and 8-6 for the
different time-steps and distance increments shown in Figure 8-7. The
results are good even for the long total length of conduit used in the
tests. Use of a long test section with no intermediate inflows was
chosen to simulate the most unfavorable simulation conditions since
results would be expected to improve when there were numerous inflows of
known hydrographs along the test section. A further comparison was
made with the published analytical results of Ackers and Harrison
(Ref. 11) for a 1-foot diameter pipe on a slope of 0.001. The results
are equally good, as shown in Figure 8-8.
These tests indicate the Transport Model to be an accurate and reliable
tool for flow routing in sewers.
A comparison of actual and predicted hydrographs of a real sewer system
can be found in Volume II of this report. A further description of the
solution technique and computer program can be found in the "User's
Manual."
133
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ll
-
:
100-
Characteristics Solution, x
Characteristics Solution, x
Characteristics Solution, x
Transport Model, DT = 5 min
Transport Model, DT = 2 min
5,000 ft
18,000 ft
30,000 ft
40
80
\zo
FLOW (MIN)
Figure 8-5. COMPARISON OF TRANSPORT MODEL AND EXACT SOLUTIONS FOR
PIPELINE CONSISTING OF 8 CONDUIT LENGTHS
-------
IOO-I
80-
-
Characteristics Solution, x
Characteristics Solution, x
Characteristics Solution, x
Transport Model, DT = 5 min
Transport Model, DT = 2 min
5,000 ft
18,000 ft
30,000 ft
-vo
TIME (MIN)
Figure 8-6. COMPARISON OF TRANSPORT MODEL AND EXACT SOLUTIONS FOR
PIPELINE CONSISTING OF 15 CONDUIT LENGTHS
-------
8 CONDUIT LENGTHS (ft)
4,000 4,000
1,000
6,000
1,000
4,000
4,000
6,000
15 CONDUIT LENGTHS (ft)
1,000 2,000 1,500 1,000 3,000 1,500
4,000
500 3,500 500 4,000 1,000 500 3,000
3,000
DIAM = 6.0 ft
0.001
N = 0.012
A = 28.27 ft Q_ = 145.48 cfs Q = 157.12 cfs
£ £ IftclX
108-
Cn
28'
Input
Hydrograph
40 80 ' 300
TIME (KIN)
Figure 8-7. HYPOTHETICAL INPUT FOR ROUTING COMPARISONS
136
-------
Transport Model
Exact Solution
V / ^
Input Hydrograph
x = 28.4 ft
x = 255.7 ft
x = 483.0 ft
x = 710.2 ft
S = 0.001
D = 1 ft
n = 0.0117
.10
100
2OO
3OO 40O
TIME (SEC)
500
600
Figure 8-8 . COMPARISON OF TRANSPORT MODEL WITH EXACT SOLUTION
OF ACKERS AND HARRISON
-------
SECTION 9
STORAGE MODEL
Page
OBJECTIVES 141
BACKGROUND 141
THE MODEL SUBROUTINE 144
Internal Storage 144
External Storage j_4c
THEORETICAL DEVELOPMENT 145
Type of Storage 145
Type of Outlet 146
Routing 147
Through-Flow 148
TEST APPLICATION 14g
139
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SECTION 9
STORAGE MODEL
OBJECTIVES
The objectives of the Storage Model are to:
1. Determine the modifying effects (attenuating or withholding)
of various types (intentional or unintentional) of the storage
element upon flows through sewer systems.
2. Simulate the movement of storm water within a storage unit.
3. Provide data required for the estimation of the costs of the
specified storage installation.
BACKGROUND
The functions and benefits of storage may be described as:
1. Reduction of the peak flow rate, thus
a. Reducing the size needed for a proposed storm drain.
b. Eliminating the need for a relief storm drain.
c. Enabling the handling of a, more intense (lesser frequency)
storm.
2. Reduction of pollutants in overflows by:
a. Capturing the solids contained in the first flush.
b. Providing continuous sedimentation and detention on a
flow-through basis after storage volume has been filled.
These two uses of storage may not be compatible. For example, to
reduce the peak it might be desirable to hold the storage in reserve
until the design capacity of the conduit is almost reached and then to
141
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divert the excess flow to off-line storage. On the other hand, to trap
the first flush of solids, the storage must be put in operation early,
and it may be full by the time the peak flow arrives.
To capture the first flush in large drainage basins in flat country
may require a considerable number of small storage tanks located on the
principal branches upstream from the outlet. Just such a solution was
proposed for large combined sewers in Buffalo by Riis-Carstensen in
1962 (Ref. 1).
In the past, most storage basins were designed as settling tanks and
thus, in addition to storage, provided some degree of treatment through
sedimentation. Although the design of new storage basins may not be
optimal in terms of sedimentation theory, it is anticipated that some
degree of treatment will be provided. Recognizing this limitation,
the external version (see below) of the Storage Model assumes, however,
that a storage basin will function efficiently as a settling tank.
Treatment of pollutants by sedimentation is discussed in Section 15.
Two alternative versions of storage, requiring different modifica-
tions to a basic program, were considered for this study. The first,
known as "internal" storage, was as one or more small storage tanks
located on major upstream branches of the transport (sewer) system.
Quality improvement (settling) within these smaller units was neglected;
the units were modeled as elements of the transport system (see
Section 8).
142
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The second version, known as "external" storage, was as a major
installation at the sewer system outfall. Many other methods of
sewage treatment besides sedimentation might be provided in addition to
this storage (see Section 15).
With either version, the first running of the Storage Model in a
particular study project was visualized to include only existing storage
reservoirs. After reviewing the results, and available locations for
new storage reservoirs, the engineer would select the location and
characteristics of proposed storage units. The data would then be
read into the computer and the model re-run.
After reviewing these re-run results, additional runs could be made
using reservoirs of different sizes and possibly adding or subtracting
reservoirs at some locations until an acceptable solution is obtained.
The development of the Storage Model was based on the basic storage
equation (outflow = inflow +_ change in storage) with provisions for
alternate facilities, such as holding/routing; artificial/natural;
alternate inlet and outlet controls (weir, orifice, pumping); and
alternate locations of installation. While the theory required to
simply model the above features is quite fundamental and well under-
stood, the nature of the flow through the storage unit may be a far
more involved process. Types of through-flow considered include: plug
flow, complete mixing, and short-circuiting.
143
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THE MODEL SUBROUTINE
The Storage Model processes inflow hydrograph and pollutograph data
on a step-by-step basis. These data would usually have been generated
by the Transport Model; it would also be possible to separately
process data based on observed values. The time-step method of execu-
tion was adopted to simplify incorporation of the program into the
Transport Model (internal storage).
Options of fixed (pumped) or variable (weir or orifice) outflows are
provided, together with alternative types of flow through the reservoir,
such as plug flow and complete mixing.
Internal Storage
With the internal version of storage, one or two small storage tanks
may be located on major upstream branches of the transport system.
Quality improvements, such as sedimentation in the tanks, cannot be
modeled with this version. The characteristics of the unit(s) to be
modeled are specified via the Transport Model for internal storage.
The simulation proceeds on a time-step basis within the Transport
Model, thus enabling the flows in all transport elements, including
storage units, to be solved at each time-step, as the inflows become
known.
If the water depth in any storage element exceeds at any time a pre-
viously specified maximum value, the unit is deemed to have flooded and
the modeling is discontinued.
144
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External Storage
With the external version of storage, only a single, and usually major,
installation may be modeled at the sewer system outfall.
The characteristics of the unit are specified, and the execution of
the simulation is governed, by the Storage Block (see "User's Manual")
in this case. Within the Storage Block many other methods of sewage
treatment may be specified (see Section 15) in addition to the sedi-
mentation that must occur within the storage unit.
The model accepts as input the output hydrograph and pollutographs
from the Transport Model which have been stored on a disk or tape.
The Storage Block is driven by the Executive Model quite independently
of other models (blocks); flow through storage and associated treat-
ment proceeds on a time-step basis.
If the water depth in the storage unit at any time reaches a previously
specified maximum value, an inlet control structure is assumed to by-
pass any additional flows that would otherwise further increase the
depth.
Output from the Storage Block (hydrograph and pollutographs) is again
stored on a disk or tape, for possible later use as input to the
Receiving Water Model (both quantity and quality).
THEORETICAL DEVELOPMENT
Type of Storage
Two basically different types of storage are included. The first is
that of an irregular (natural) reservoir. In this case 11 pairs of
145
-------
depth versus surface area data must be provided by the user. The
second type of storage is that of a regular (artificial, man-made)
unit. Here the user must provide information on the base area, cir-
cumference, and side slopes, from which the depth/surface area relation
may be computed.
From the depth increments and areas, the depth versus storage relation
is easily obtained in either of the above cases.
Type of Outlet
Orifice and weir outlets are included for gravity (variable rate)
outflows, both separately and in combination.
For an orifice with known effective area C^A (coefficient of discharge
times orifice area), the outflow (cfs) is computed from:
Qout
where D = Water depth (ft) above the orifice centerline
For a weir of known height (above the storage = 0 level) and
length L (ft), the outflow (cfs) is computed from:
Q . = 3.33 LH1'5
*
where H = Head (ft) over the weir crest
Fixed-rate outflows are also included, under the pumped outflow option.
In this case, the buffer volume in storage between pump start and stop
depths is computed and compared with the volume capable of being pump-
146
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ed out per time-step. If the buffer volume is too small, a message is
printed recommending remedial measures and warning that subsequent
computations are possibly unreliable.
Routing
With gravity outflows, the program requires that the basic routing
equation is satisfied, i.e., that
0.5(1.,^ + I2)Dt = 0.5(0.,^ + 02)Dt + (S2 - S.^ (3)
where I = Inflow rate (cfs)
0 = Outflow rate (cfs)
S = Stored volume (cf)
Dt = Hydrograph time-step size (sec)
and where subscript
1 represents conditions existing at the start of Dt
2 represents conditions existing at the end of Dt
Rearranging to place the unknowns at time 2 on the left hand side of
the equation,
(0.5)0 Dt + S, » 0.5 (I. + I_)Dt - ((0.5)0 Dt - S ) (4)
*• ~ J. Z 1 1
The quantity on the left hand side, given the FORTRAN name ATERM in
the program, may thus be evaluated for a new time-step. Knowing the
storage and outlet characteristics of the reservoir (discussed above),
the relation between ATERM and (0.5)0 Dt may be obtained. This relation
is stored in the computer in the form of 11 pairs of routing parameters;
intermediate points are obtainable by simple linear interpolation.
147
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Prom this selection the value of (0.5)C>2Dt corresponding to the known
ATERM is obtained; the required values of 82 and 02 for this
reservoir and time are then easily found from these known quantities.
The hydrograph is routed through the reservoir by repeating this pro-
cedure for each time-step.
The initial conditions within the reservoir must be specified. For
outlet controls such as the weir, with the initial storage below the
weir crest, the program will simulate the filling period before outflow
begins.
While routing the flows, the program accumulates the total volume of
storage inflow and outflow during the storm. These volumes are after-
wards compared with the initial and final volumes in storage, to provide
a continuity check.
Through-Flow
Having solved for the outflow rates from the storage reservoir or tank,
the nature of the flow inside the unit is of concern insofar as it
governs the movements, detention times, and thus the releases of the
accompanying pollutants.
The types of through-flow considered were: complete mixing, plug flow,
and short-circuiting. Which, if any, of these would actually occur is
a complex question, probably depending upon the shape of the storage
unit, arrangement of the inlet and outlet(s), the flow rate, the pollu-
tants load, and other factors.
148
-------
With the option of complete mixing, the inflow is thoroughly mixed with
the existing contents in storage, resulting in "averaged" qualities
the outflow.
With the plug flow option, the inflow during each time-step, here called
a plug, is labeled and queued through the storage volume. Transfer of
pollutants between plugs is not permitted, but contributions of several
plus are averaged in the outflow time-step. The program identifies the
inflow plugs, or fractions thereof, which comprise each outflow plug; thus
the pollutant load and detention time for each outflow fraction is easily
found.
Short-circuiting could occur to considerably varied extents, depending
even more upon the above-mentioned factors of shape and load, etc.
For these reasons, the simulation of short-circuiting has not been in-
cluded in this model.
Neither sedimentation nor scour are simulated within the Storage Model.
The pollutant loads are only traced and redistributed as indicated
above. With the external version of the storage program, sedimentation
in storage is computed by the Treatment Model (Section 15).
TEST APPLICATION
The Selby Street outfall in San Francisco, chosen to test the use of
this model, serves a tributary area of some 3,800 acres. An interceptor
normally carries dry weather flow to a treatment plant. The combined
sewer outfall was built as three rectangular compartments, as shown in
Figure 9-1. During storms these compartments may fill up and overflow
a 100-foot long weir into San Francisco Bay (Ref. 2).
149
-------
tfl
X
*
Ul
COMBINED SEWER CONDUIT
2.8 OO FT
VOLUME IN STORAGE
BEFORE OVERFLOW
2^50 FT
543
DISTANCE (THOUSANDS OF FT)
ASSUMED WEIR
ELEVATION,7.50FTX
30
20
I0_
POINT OF OVERFLOW
TO ISLAIS CREEK
(INTERCEPTER CLOSED)
1350 FT
-10
-20
Figure 9-1. OUTFALL STORAGE, SELBY STREET, SAN FRANCISCO
-------
The Storage Model as developed was used to calculate the effects of
this external outfall storage on the combined outflow hydrograph.
Because of the more complex shape of this storage unit, the irregular
type of storage was specified. The required data pairs of depth versus
surface area were taken from Figure 9-1 and are presented in Table 9-1.
More data points were taken above the weir crest (at 7,50-feet depth),
where more sensitivity is preferred.
Table 9-1. STORAGE MODEL INPUT DATA,
SEWER STORAGE BASIN, SELBY STREET,
SAN FRANCISCO
Data Pair
Number
1
2
3
4
5
6
7
8
9
10
11
Depth ,
ft
0.00
2.00
5.00
7.50
8.00
8.50
9.00
9.50
10.00
10.50
11.00
Surface Area,
sq ft
0
49,900
102,200
136,200
129,700
121,100
112,600
114,500
116,000
109,200
102,000
Due to the elongated shape of this storage unit, plug flow is probably
more appropriate than complete mixing for the simulation of pollutant
movements in this case.
The inflow hydrographs and pollutographs used were output from a
simulation with the Transport Model of the storm of November 6, 1966
151
-------
(Ref. 2) in the contributing sewer system. A 10-minute time-step was
used.
The hydrologic results of the test application are presented in
Figure 9-2. Hydrograph (1) is the input to the Storage Model, being
the output from the Transport Model without storage. Hydrograph (2) is
the output from the Storage Model, i.e., the result of routing hydro-
graph (1) through the sewer storage basin. Hydrograph (3) is the
reported hydrograph (Ref. 2), which must include the storage effect.
Differences between hydrographs (2) and (3), the total volume of flow
under the curves in particular, clearly result from assumptions made in
the previous modeling and generation of hydrograph (1). However, the
effects of storage as indicated by the differences between hydrographs
(1) and (2) are as might be expected. In particular, the delay in the
start of the rising limb while the reservoir was filling agrees well
with the reported time that overflow started.
The continuity error was negligible, being less than one millionth of
the total inflow.
The quality results of the test application are given in two further
figures. Variations with time of BOD and suspended solids concentrations
are presented in Figures 9-3 and 9-4 respectively. The observed concen-
trations (Ref. 2) are compared in both figures with the output from the
Storage Model using both the complete mixing and plug flow options
described earlier. Results are also given for a third through-flow model
152
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-
9:00
Note:
SELBY ST., SAN FRANCISCO
NOV. 6, 1966
3,800 ACRES
WITHOUT STORAGE
35% IMPERVIOUS
TIME OF ENTRY = 10 WIN
lO'OO
:00
12:00 13=00
CLOCK TIME (HR)
I4'00
and(3)refer to hydrograph numbers.
Figure 9-2. HYDROGRAPH MODIFICATION PRODUCED BY OUTFALL STORAGE,
SELBY STREET, SAN FRANCISCO
15:00
-------
400
SAN FRANCISCO-SELBY ST
COMBINED SEWER
NOV. 6. 1966 STORM
SHORT- CIRCUITING
MODEL (REJECTED)
PLUG FLOW MODEL
COMPLETE MIXING MODEL
11=00 I2'00
CLOCK TIME (HR)
13:00
14^00
Figure 9-3. MODIFICATIONS TO BOD CONCENTRATION
PRODUCED BY OUTFALL STORAGE,
SELBY STREET, SAN FRANCISCO
154
-------
1200
SAN FRANCISCO-SELBY ST
COMBINED SEWER
NOV. 6, 1966
SHORT-CIRCUITING MODEL
(REJECTED)
COMPLETE MIXING MODEL
PLUG FLOW MODEL
10 = 00
11=00 12=00 13=00
CLOCK TIME (HR)
14:00
Figure 9-4. MODIFICATIONS TO SUSPENDED SOLIDS CONCENTRATION PRODUCED
BY OUTFALL STORAGE, SELBY STREET, SAN FRANCISCO
155
-------
option, which was a version of short-circuiting based on APWA catchbasin
data (see the Surface Quality model).
Predicted suspended solids concentrations are seen to agree with the
observed data rather better than do the BOD concentrations. However,
some of the differences may be attributed to the differences between
the observed and predicted hydrographs (Figure 9-2). The short-circuiting
through-flow model was clearly less acceptable, particularly for suspended
solids modeling, and was therefore excluded from the Storage Model.
156
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SECTION 10
RECEIVING WATER QUANTITY MODEL
Page
OBJECTIVE 159
RELATION TO STORM WATER PROGRAM 159
THE MODEL SUBROUTINE 160
THEORETICAL DEVELOPMENT 161
Geometric Representation 162
Solution Procedure 166
Transient Hydrodynamics 169
Alternate Boundary conditions 170
TEST APPLICATION 170
157
-------
SECTION 10
RECEIVING WATER QUANTITY MODEL
OBJECTIVE
The objective of the Receiving Water Quantity model is to provide the
hydraulic basis for the determination of the receiving water quality
responses resulting from storm water pollution. The receiving water
body may be an estuary, a stream, or a lake. The model simulates the
movement of water for each type of water system.
The receiving water bodies may have different geometric configurations
with various boundary conditions. To be of wide applicability, the
model must use a system that can readily be adapted to any prototype
condition by simply changing the input data.
For this purpose, the model represents the water body by a network of
nodal points connected by channels. The nodal points and channels are
idealized hydraulic elements which are characterized by parameters, such
as surface area, cross-sectional area, length, and friction coefficient.
Equations of motion and continuity can thus be applied to each element
and solved simultaneously to produce a time-history of stage, velocity,
and flow at the various points of the water system.
RELATION TO STORM WATER PROGRAM
The receiving water body is the end point where the pollutional effects
of storm water are to be evaluated. At this point, the runoff hydrograph
at each outfall and associated pollutographs for various chemical
159
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constituents have already been computed by a sequential operation of the
Runoff, Transport/ and Storage Blocks of the Storm Water Management
Model.
The nodal point of the receiving water system adjacent to an outfall will
accept a runoff hydrograph input. The confuted stage and flow conditions
of the receiving water are then passed on to the Receiving Water Quality
model for quality routing. The transfer of information between the
programs is normally handled by interfacing storage devices such as mag-
netic tape written in compatible format.
THE MODEL SUBROUTINE
Liaison between the Storm Water Management Model and the Receiving Water
Quantity model is provided by subroutine RECEIV which accepts the hydro-
graph and pollutograph at the outfalls from the Transport Model. The
model consists of six major subroutines, i.e., SWFLOW, INDATA, TIDCF,
TRIAN, PRTOUT, and OUTPUT. Hydrograph information is used in the
hydraulic computation and pollutograph information is passed on to the
Receiving Water Quality model discussed in Section 14.
RECEIV calls SWFLOW which then takes over the control to perform hydro-
dynamic computations with the assistance of other subroutines* For
example, INDATA is called to read input data pertaining to geometric
information of channels and junctions and control parameters specifying
the days of simulation, time interval of computation, and so forth. If
the water body is a lake, coefficients for the weir formula at the down-
stream outlet will be read by SWFLOW. Otherwise, SWFLOW will call
160
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TIDCF to determine the tidal coefficients describing the boundary con-
straint at the mouth of the estuary.
On the basis of the data received through INDATA, TRIAN uses the laws of
trigonometry to interpolate geometric information for hydraulic elements
of the water systems which otherwise would have to be deduced from a map
manually.
Upon completion, SWFLOW calls PRTOUT to print hydraulic stage and flow
behavior at selected points in the water system. It also calls OUTPUT
to prepare computational results for graphical display by a printer plot
routine. SWFLOW itself then writes detailed hydrodynamic information for
subsequent use by the Receiving Water Quality model.
THEORETICAL DEVELOPMENT
The hydrodynamic behavior of a water body influenced by external forces
is governed by two fundamental equations, i.e., the equation of motion
and the equation of continuity. A complete description of the movement
of water requires a simultaneous solution of the two equations.
While the differential equations of motion and continuity have been des-
cribed for various coordinate systems since the eighteenth century, the
solutions have been developed only for limited cases with simple boundary
conditions. For example, the flow problems and their analytical solution
for the one-dimensional channel have been studied quite extensively for
constant boundary conditions, such as a steady inflow and/or a downstream
head control. When the inflow is variable, the problems become too
complicated to be solved by conventional analytical methods. The degree
161
-------
of difficulty compounds further as the water body becomes so. big that
flow can occur in a two-dimensional plan or in a three-dimensional volume.
Yet, these are the kinds of problems that need to be solved in the
Storm Water Management Model.
Recently, these complex hydrodynamic problems have been approached by
numerical methods assisted by advanced computer technology. One such
approach, developed by WRE, has attempted to develop an iterative solution
technique for the hydrodynamic equations to be performed by a computer.
While this hydrodynamic model has proven to be very versatile in dealing
with various geometric and boundary conditions, it has never been used
to accept a hydrograph input. The modification of the model to treat
the transient hydrodynamic behavior and the associated problems caused
by storm water inflow was considered the next logical step in its
development.
Geometric Representation
The computer model requires a nodal point and grid system for the repre-
sentation of the prototype receiving water body. For a simple stream,
one can conceptually represent the body of water by sectioning the river
into reaches. A reach is defined as a channel where water flows from
one end to the other. The end of the reach is further defined as a
junction where two reaches meet.
If the head at the junction at any given time is known, the hydraulic
gradient along the channel and thus the flow rate may be calculated.
162
-------
By transferring water from one end to the other according to the com-
puted flow, the head at the junction will subsequently be altered.
Therefore, a stepwise hydraulic computation can be performed on a dis-
cretized system representing the water body.
To facilitate the hydraulic computation, it is necessary to supply the
surface width, length, average depth, and friction coefficient for the
channels and the surface area, head, and floor elevation for the junctions,
The junction surface area is defined as one-half_of_thje_surface areas of
.the preceding and succeeding reaches; the floor elevation is defined as
the depth of the bottom ground surfa^ce^,froBL.a given ^datum plane such as
mean low low water. All of these geometric parameters are readily
measurable from a navigation map. It must be noted that the floor
elevations are referenced to the same datum for all junctions.
For a lake or estuary, the water body may not be represented reasonably
well by a single channel. In this case, the channel and junction system
is used to form a grid covering the water body. Several channels can now
meet at a junction, enabling the depiction of two-dimensional flow
characteristics in a horizontal plan. Since the channel is the hydraulic
element where water flows^the layout of the principal channel must con-
form with the direction of current as closely as possible^ Figure 10-1
shows the geometric representation of a receiving water with some of the
possible hydrologic inputs.
The shape of the grid system is flexible in that_it can bei orthogonal,
triangular, or irregular. If the condition warrants, the use of a
163
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LEGEND
Outfalls
Node 13
Node 14
Rivers
Node 10
Node 16
Node 18
[Sj Node (typical)
Channel (typical)
Scale: 1 in. = 10,000 ft
DWF (cfs)
20
.
50
500
2,000
TYPICAL INPUT
HYOROGRAPH
Figure 10-1. GEOMETRIC REPRESENTATION OF A RECEIVING WATER
164
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triangular shape is recommended. Many of the data for a triangular
system can be deduced from the laws of trigonometry and thus the data
preparation is greatly simplified.
The channel width in a grid system is not as well defined as that for a
simple stream. The present,
the distance between two lines parallei to thechannelimdpassi
the centroids of two triangles sharing the channel^ if it is not a
triangular grid, the centroid of whatever shape is used will still be
used foj^jmas^ring tihe^channel width.
The length of the channel is governed by a stability criterion of the
numerical integration technique. This criterion was described by
Garrison et al. as follows (Ref. 1) :
A± < i gn2 |v| At (1)
Ax ~ 2.21 R4/3
where V = Mean velocity
A = Cross-sectional area
B = Surface width
g = Gravitational acceleration
n = Manning's resistance coefficient
R = Hydraulic radius
At = Time interval
Ax = Channel length
165
-------
For channels, A/B is equal to depth h. The relationship can then be
simplified to
At < a Ax (2)
where a = Proportionality constant
"\/gh = Celerity of wave
Since the computational time interval is normally constant throughout
the system, the deeper channel should have a longer length according to
the expression. A channel length longer than necessary favors the
— ---------------- — '
stability, but it reduces the accuracy of hydraulic and quality compu-
^——~m*^f*—— ___________ __-,>-SVS*S£l«
a- value ranging^from 0.7 to 0.8.
\^jglggfjfjpjjQ£lftfjyjfjfjjtUiitli6tituHHlii^
Solution Procedure
Basically, the hydraulic computations for each time interval proceeds as
follows :
1. Compute the flow rate in each channel according to the
hydraulic gradient and other hydraulic conditions existing
at the beginning of a time interval.
2. Compute the rise or fall of the water surface (head) at
each junction based on the channel flow and the importation
or withdrawal of water at the junction.
3. Update the geometric and hydraulic conditions for the
computation of the next time interval.
166
-------
Thus, the iterative procedure uses the equation of motion to calculate
the channel flow and then uses the equation of continuity to determine
the junction head. Since the computations proceed step-by-step, the
boundary conditions, such as the tide and the hydrologic input, can be
varied from one time interval to the next.
Mathematically, the equation of motion for a one-dimensional. channel
can be written as follows:
where V = Velocity
t = Time
x = Distance
H = Water surface elevation measured from the datum plane
g = Gravitational acceleration
S_ = Energy gradient
S - Wind stress
w
The energy gradient S of turbulent flow is proportioned to the square
of the mean velocity according to Manning's equation,
sf—:
2.2
where n = Friction coefficient
R = Hydraulic radius of the channel
The wind stress can be approximated by the following expression:
K oa 2 ,
= — • -J-— u cos ty
167
-------
where K = Dimensionless coefficient with a value of 0.0026 (Refs. 2,3)
d = Depth of flow
pa = Air density \-Jk*tjj4 SJUv^
pw = Water density
U = Wind velocity
4» = Angle between the wind direction and the axis of the channel
The second equation necessary to complete the mathematical formulation
of the problem is furnished by the continuity requirement at the junctions.
This requirement states that the net effect of water flowing into the
junction through channels or importation is to raise the water surface
elevation at the junction, i.e.,
3H. k
As J iJ - .f x Qi + Bj (6)
where A . = Surface area associated with the junction j
Q. = Flow of a connecting channel
Q . = Water importation rate to the junction
The equation still applies for cases where the water surface elevation
is lowered resulting from outflow.
Numerical solution of Eqs. 3 and 6 entails a rewriting of both equations
in finite difference form. The initial value of various parameters at
time t is used to determine the rate changes of flow and water head
during a short period of time (integration interval At) . Based on the
rate change, the next value is computed and the whole procedure is
repeated.
168
-------
Various numerical methods have been developed to solve this type of
initial value problem. The present model uses a modified Runge-Kutta
technique where the interval of integration is divided into four. The
intermediate time-step computations improve the stability and accuracy
of the model.
Transient Hydrodynamics
As stated previously, the model requires initial values at time t to
compute values of the next time interval, t + At. With the detailed
finite element representation of the receiving water body, however, there
is difficulty in obtaining the starting conditions for each channel and
junction.
This difficulty was resolved by starting the program from a standstill
condition with the mean tide elevation at each junction as the initial
head. The specifiable boundary conditions, such as the tide or head
relationship at the governing downstream point, are then imposed on the
model to proceed with the computation. In the first two days of compu-
tation, the system is in a transient state toward a dynamic steady state
in which the stage and current throughout the system are synchronized
to the given tidal condition.
The program, equipped with all necessary hydraulic information to start
the actual simulation, will then accept the storm water inflow for the
calculation of hydrodynamic responses in the receiving water. The
system will again be in the transient state until the storm is ended and
its residual effect diminished.
169
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Alternate Boundary Conditions
The distinction between estuaries and streams or lakes in the present
model is strictly a problem of downstream boundary conditions. In
estuaries, the boundary condition is usually a specified tide at the
mouth, such as the Golden Gate of San-Francisco Bay. A lake is constrained
by a head-flow relationship, (i.e., weir equation) of the outlet.
Rivers can be a special case of either estuaries or lakes depending again
on the downstream condition, i.e., a constant head or a stage-flow
relationship of the channel.
For the lake, thermal stratification may occur at certain times of the
year, influencing the hydraulic response. Prediction of thermal behav-
ior in conjunction with the storm water inflow is beyond the scope of
this study. However, the location of a thermocline can be expected to be
known for a particular simulation through field measurement. For storm
water purposes, one can then neglect the presence of water below the
thermocline in estimating depths for the hydraulic computation.
TEST APPLICATION
Actual data were not available for testing the hydrodynamic response of
the receiving water under the storm water effect. Present model testing
is therefore based on the engineering evaluation of the reasonableness
of the answers. The general method of procedure, however, has been
proven valid, for several prototype conditions accepting the constant
inflow (Refs. 4,5,6).
170
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Several tests were made using the geometric system of Figure 10-1. As
shown, each channel was 10,000 feet long, with a depth ranging from 15
feet at channel 28 to 20 feet throughout the open water body.
Figure 10-2 shows the input hydrographs applied to the system. Not
shown in the figure are the hydrograph inflows to junctions 13 and 10
which are identical in shape and time to those of junctions 14 and 16,
respectively, except that the flow coordinate is ten times smaller.
These input hydrographs are superimposed on the dry weather flow of
2,000 cfs at junction 18, 500 cfs at junction 16, 50 cfs at junctions
10 and 14, and 20 cfs at junction 13.
For the test of an estuary case, a tidal wave was imposed on junction 1.
A typical dynamic response of flow in channel 24 is plotted in Figure
10-2. The transient effect of storm water inflow is noted to push the
flow pattern toward outflow (seaward) direction. The case shown herein
is a shallow estuary with a strong tide at the mouth. Tidal influence,
therefore, dominates the system behavior and yet the transient hydro-
dynamic effect caused by storm water inflow is discernible after the
fifth day of simulation.
This response appears reasonable as do others when the system is con-
sidered a lake and a stage-flow relationship is specified for junction
1. Verification runs for the Receiving Water Model were made at three
demonstration sites and are described in Volume II of the final report.
171
-------
3 r
a
o
o
U_
u_
o
2 -
I -
INPUT HYDROGRAPHS
o
o
Q.
o
LL.
20
CHANNEL 24
FLOW
i 3 4 ~5
TIDAL CYCLES (DAY)
Figure 10-2. TEST SYSTEM FLOWS SHOWING HYDROGPAPH EFFECTS
ff""WITHOUT HYOROGRAPH
It INPUT
/ WITH HYDROCRAPH
INPUT
-------
PART 3
QUALITY SUBROUTINES
-------
SECTION 11
SURFACE RUNOFF QUALITY MODEL
Page
OBJECTIVES 175
BACKGROUND 175
IDENTIFICATION OF POLLUTANTS 175
THE MODEL SUBROUTINE 176
THEORETICAL DEVELOPMENT 177
Initial Theory 177
The Cincinnati Study 179
Estimation of Pollutants on the Ground, P 180
Tests Indicate Modifications Necessary 184
Availability Factor, A 184
BOD Modification 191
BOD From Catchbasins 192
Displacement and First Flush Effects 194
Coliforms in Surface Runoff 194
TEST APPLICATION . 195
173
-------
SECTION 11
SURFACE RUNOFF QUALITY MODEL
OBJECTIVES
The objectives of the Surface Runoff Quality model are to:
1. Identify the quality constituents or pollutants.
2. Determine the quantities of pollutants on each subcatchment
prior to the storm event.
3. Determine the rate of removal of pollutants during a storm
event.
BACKGROUND
The literature contains many studies on the determination of the volume
of surface runoff from both natural watersheds and urban sewered areas,
and some notable compilations of the quality of overflows from combined
sewers and the discharge of separate storm drains. These studies have
amply demonstrated that storm water overflows contribute significantly
to the overall water pollution problem and should be investigated. Only
a very few studies, however, have included data on both runoff quantity
and quality in sufficient detail so that the quality of direct surface
runoff could be computed as a function of the runoff intensity. Con-
sequently, in the development of the Surface Runoff Quality model it
was necessary to rely on a theoretical approach, with the values of the
coefficients determined by and checked against the available data. The
development and preliminary verification of the theory is described in
this section.
175
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IDENTIFICATION OF POLLUTANTS
Many different determinations are made in the analysis of wastewater to
determine its pollution load. Pollutants may be classified as con-
servative or nonconservative. Examples of conservative pollutants are:
total and volatile suspended solids, ammonia and organic nitrogen,
phosphate, and oil and grease. Examples of nonconservative pollutants
are BOD, COD, and coliform content. The modeling of the surface runoff
quality from a drainage area assumes that all pollutants are conservative
because of the short transport times involved. Pollutants may also be
classified as soluble or nonsoluble. The modeling method will handle
any pollutant for which data are available. To date, the data have
permitted the modeling of BOD, suspended solids, and coliforms.
THE MODEL SUBROUTINE
The model (subroutine SFQUAL) accepts as input the hydrograph of surface
runoff developed for the subarea and produces three pollutographs, one
of BOD and one of suspended solids, both in pounds of pollutants per
time-step, and the other of coliforms in MPN per time-step. At the head
end of the system, the hydrograph of surface runoff and the three
pollutographs are delivered to the Transport Block which combines the
hydrograph with the volumes of infiltration and dry weather flow, and the
three pollutographs with the BOD, suspended solids, and coliforms con-
tributed by the dry weather flow. The pollution contribution of the
infiltration is assumed to be zero. The Transport Block routes the
resultant hydrograph and three pollutographs down the sewer to the next
inlet point, taking account of the volume of wastewater and pounds of
176
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pollutants—or in the case of coliforms, MPN—in the sewer at the start
of the rain, as well as the changing volume of wastewater and the amount
of pollutants stored in the sewer during each time-step. At the next
inlet point, the contributions from the next subarea are added to the
hydrograph and three pollutographs modified by passage through the
Transport Block. Then, the combined hydrograph and three pollutographs
are routed down the next stretch of sewer by the Transport Block.
This process is continued at successive inlet points. A multi-branched
sewer system is assumed.
The process is facilitated by initially expressing the pollutants in
pounds or MPN per time-step. To obtain the concentration in mg/L or
MPN/100 ml, it is only necessary to divide the total pounds in any time-
step by the total volume of flow during the same time-sttjp using the
correct conversion factor. Both the pollutograph (which gives the pounds
or MPN) and the hydrograph (which gives the volume of flow) must be for
the same point in the sewer system. At the end of the subroutine SFQUAL,
the pollutants are converted to Ib/min or MPN/min for coliforms before
being transferred to the Transport Block via output file.
THEORETICAL DEVELOPMENT
Initial Theory
At the start of the rain, the amount of a particular pollutant on surfaces
which produce runoff (both impervious and pervious) will be P , pounds
per subarea. Assuming that the pounds of pollutant washed off in any
time interval, dt , are proportional to the pounds remaining on the
177
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ground, P , the first order differential equation is:
which integrates to
P - P = P (l-e~kt) (2)
o o
in which P - P equals the pounds washed away in the time, t .
o
In order to determine k , it was assumed that k would vary in direct
proportion to the rate of runoff, r , or k = br . To determine b it
was assumed that a uniform runoff of 1/2 inch per hour would wash away
90 percent of the pollutant in one hour. This leads to the equation:
P - P = P (l-e"4'6rt) (3)
o o
where r = Runoff rate (in./hr)
t = Time interval (hr)
(Other assumptions for determining b could be made but this original
assumption has proven satisfactory in all test applications to date for
urban areas.)
In using this equation, a uniform time-step t is selected; values of
r are determined from the inlet hydrograph; and the equation is applied
successively, the value of P determined at the end of the nth interval
becoming the value of P at the beginning of the (n+l)th interval.
The value of r = 0.5(r +r ). (4)
n n+1
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The concentration in each interval may be determined by dividing P - P
by the runoff in cfs and multiplying by a constant which depends on the
time interval. This constant equals 268 divided by the time interval
in minutes. Since r in inches per hour - cfs per acre, the runoff in
cfs = r times area in acres. The concentration may be expressed in the
form of an equation as follows:
(P - P) in Ib
., 268 o ...
Cone, in mg/L = time_step in min * r in in./hr x area in acres (5)
Note: in./hr times acres is equal to runoff in cfs.
Catchbasins as a source of pollution are considered later in this section.
The Cincinnati Study
A paper (Ref. 1) describing the results of a study by the U.S. Public
Health Service (USPHS) of a 27-acre area in Cincinnati served by separate
sewers contains data which were used as a preliminary check on the fore-
going theory. The preliminary trial runs indicated that the theory would
produce figures of the right order of magnitude for a storm similar to
'the first 4 hours of the reported storm of March 16, 1963, if appropriate
values of P were assumed. Further, the concentration of suspended
solids and BOD were shown, as in Table IV of the paper, to decrease with
the length of the storm, although not as rapidly. Since Table IV gives
mean values which would not apply precisely to a particular storm, the
agreement with the general trend was considered a satisfactory check.
The comparative figures are not reproduced herein because refinements
in the estimation of the values of P and in the application of the
method to suspended solids make the original figures of historical interest
179
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only. The Cincinnati paper proved invaluable in the further development
of the method as described hereinafter.
Estimation of Pollutants on the Ground, P
o
The Cincinnati study gives estimates of the pounds of pollutants in the
storm water runoff "based on essentially complete measurement of rainfall
and consequent runoff and quality at the study site during September
through November 1962, and March through September 1963, projected to
average annual rainfall at Cincinnati" as shown in Table 11-1.
Table 11-1. ESTIMATED ANNUAL RUNOFF OF POLLUTANTS
FROM CINCINNATI AREA
Constituent
SS
vss
COD
BOD
PC-
4
Total N
Lb/acre/yr
730
160
240
33
2.5
8.9
Source: S. R. Weibel et al., "Urban Land Runoff as
a Factor in Stream Pollution," July 1964
(Ref. 1, excerpt from Table V).
Dividing the figures in Table 11-1 by 365 provides average figures for
the proportion of the daily accumulation that appears in the surface
runoff. These may be considered reasonable averages for urban conditions
in the Midwest and East, i.e., for urban areas having similar annual
weather and rainfall patterns. They do not, however, provide the amount
of pollutants on the ground at the start of a rain as affected by ante-
cedent conditions, street cleaning practices, and neighborhood character-
istics.
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These necessary data were found in the American Public Works Association
(APWA) study (Ref. 2) and are incorporated in the model. The study gives
the daily accumulation of dust and dirt, D/D, per 100 feet of curb and
its soluble BOD content for various types of neighborhoods in Chicago.
These are reproduced in Table 11-2. In this section and in the model
terminology the terms curb and gutter are used interchangeably.
Table 11-2. DAILY DUST AND DIRT ACCUMULATION
IN CHICAGO AREA
Dust and Dirt, D/D, BOD of D/D,
Land Use lb/day/100 ft of curb mg/gram
Single family
Multiple family
Commercial
Industrial
Average of above,
weighted
0.7
2.3
3.3
4.6
1.5
5.0
3.6
7.7
3.0
5.0
Source: APWA, "Water Pollution Aspects of Urban Runoff,"
January 1969, WP-20-15 (Ref. 2, p. 56).
The figures in Table 11-2 represent the accumulation on the streets and
in the gutters of the dust and dirt fraction of the litter deposted in
18 test areas in Chicago and were incorporated into the model with the
average accumulation of D/D and BOD used for parks directly and undeveloped
land.
In using these data it is first necessary to estimate the number of feet
of gutter per acre. This is best done from a map, but if none is
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available, a reasonable estimate may be made based on the size of the
blocks. For example, blocks 330 feet square, or 220 feet by 500 feet,
would have approximately 465 feet of gutter per acre. Although this
size is small for Chicago, it may be a fairly good average, except where
lot sizes are larger than 1/4 acre and blocks are unusually long.
The amount of this material on the ground at the start of the rain will
depend on the frequency and efficiency of street sweeping methods as well
as on the number of dry days since the last rain. At present the
following procedures are being used to allow for these effects: if the
number of dry days since the last rain is less than or equal to the
frequency of cleaning, the D/D accumulation per day from the table is
multiplied by the number of dry days to find the accumulation on the
ground at the start of the rain. This procedure would appear to err on
the high side, since it tacitly assumes that the streets are not swept in
the interval, but it is probably on the low side during weeks when it
rains every day or every other day, since the APWA study found very little
effect on the accumulation of D/D due to rainfall between street cleanings
(Ref. 2, p. 42). For a series of computer runs covering several months'
or a year's rainfall the high and low estimates will probably average out.
In attempting to check the results in a particular storm preceded by
only one or two dry days it may be necessary to determine, if possible,
when the streets were cleaned, or to assume a minimum number of days'
accumulations, or to make allowance for the D/D not washed off by the
preceding rains. A case in point is the storm of November 15, 1967,
on the Laguna Street area in San Francisco (Ref. 3), which will be
discussed later in this section.
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If the number of dry days since the last rain exceeds the cleaning
frequency, the equivalent number of days of accumulation is computed
by the following formulas:
NCLEAN = DRDA¥
CLFREQ
(6)
TOTDD = CLFREQ x DD x [l + (1 - REFF) + ... + (1 - BEFF)NCLEAN]
where DRDAY = Number of dry days before storm event
CLFREQ = Number of days between street cleanings
TOTDD = Pounds of dust and dirt on the ground before the
start of storm
DD = Dust and dirt accumulation rate per subarea
REFF = Efficiency of street cleanings (see Table 11-3)
For example, in the case of the March 10, 1967, storm on the Laguna
Street area in San Francisco, the number of dry days preceding the storm
was 40, the cleaning frequency was 7 days, and the efficiency of cleaning
was assumed to be 75 percent, resulting in an equivalent accumulation of
9.33 days.
The cleaning efficiency, REFF, is assumed to depend on both the number
of passes of the sweeper and the frequency of cleaning in accordance with
Table 11-3, which is based on a table in the APWA study and has been
incorporated in the model.
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Table 11-3. EFFICIENCY OF STREET SWEEPING
IN CHICAGO AREA
Cleaning
Frequency
15 days or more
8 to 15 days
7 days or less
Efficiency
1 Pass
.60
.70
.75
as a Decimal
2 Passes
.88
.92
.95
Fraction
3 Passes
.98
.98
.98
Source: APWA, "Water Pollution Aspects of Urban Runoff,"
January 1969, WP-20-15 (Ref. 2, p. 147).
Tests Indicate Mbdifications Necessary
When P was estimated directly from the APWA results and applied to the
o
Cincinnati area without modification of the theory, it became evident
immediately that the suspended solids were 5 to 10 times too high and
the BOD was much less than reported. Preliminary trials using San
Francisco data from Ref. 3 gave similar results.
This was temporarily disconcerting but eventually beneficial because it
led to a more detailed study and deeper understanding 6f the APWA report.
The effort resulted in modifications of the theory which have been
checked satisfactorily against data available for the Laguna Street
combined sewer in San Francisco (Ref. 3). In arriving at the necessary
modifications, data in the Cincinnati study were used to great advantage.
Availability Factor, A
Attention was directed primarily to suspended solids because of the very
large differences encountered, and the conclusion was reached that not
all the dust and dirt was normally available for the production of sus-
pended solids.
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That portion of the street litter passing a 1/8-inch hardware cloth was
defined as the dust and dirt portion in the APWA study. Sieve analyses
were made of dust and dirt removed by hand sweeping and by various
machine methods and are reported in Appendix E of Ref. 2. Screen sizes
were 10, 16, 20, and 30-mesh, so all that was measured was the grit
component. The amount passing the 30-mesh sieve varied from 0.62 percent
to 13.6 percent in 4 samples (one additional sample gave 42.06 percent)
removed by machine sweeping; from 58.8 percent to 82.5 percent in 4 samples
removed by hand sweeping; and from 65.48 percent to 93.18 percent in 4
samples removed by vacuum cleaning following machine sweeping.
Assuming a 70 percent efficiency for machine sweeping, it can be inferred
from these data that approximately one-quarter to three-quarters of the
dust and dirt is finer than 30-mesh, and that machine sweepers remove
about 85 percent of the coarser material but a very much smaller proportion
of the finer material. It is the finer material that contributes to the
suspended solids load. The coarser material, if it gets into the sewers,
constitutes grit, and, while its removal is essential in sewage treatment
plants, it amounts to less than 2.5 percent of the suspended solids
(Ref. 2, p. Ill). These facts, plus the fact that the occurrence of
rainfall between cleanings had little effect on the amount of dust and
dirt removed (Ref. 2, p. 42), confirm the foregoing conclusion that only
a portion of the dust and dirt is normally available for the production
of suspended solids.
There is considerable information on dust fallout in the APWA study.
Dust fallout on the Cincinnati area was also reported. It is stated
185
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(Ref. 2, p. 105) that dustfall particulates vary in size from 1 to over
100 microns, but from another statement (p. 23) it can be concluded that
the bulk of dustfall particulates range in size from 20 to 40 microns
(.02 to .04 mm). Note that a 400-mesh screen has an opening size of
37 microns, and that 100 microns lies between 100- and 200-mesh. Grit
chambers are usually designed to remove material coarser than 65-mesh,
and in extreme cases coarser than 100-mesh. Dustfall that is washed
into the sewers appears as suspended solids.
The following significant figures on dust fallout are contained in the
APWA study (Ref. 2, pp. 23-25):
Yearly Average Tons/sq mi/nro
1954-65 54.9
1965 41.0
1966 36.9
The range in measurements at 20 stations in Chicago in 1966 was from
20.6 to 61.4 tons/sq mi/ino. The dustfall on the Cincinnati area was
reported as 506 Ib/acre/yr, which is equivalent to 13.5 tons/sq mi/mo,
or less than the lowest Chicago reading. Figure 2 (Ref. 2, p. 25) shows
the dustfall on a 10-acre unit area varying throughout the year from
0.30 ton/mo to 0.79 ton/mo. The average of the seven summer months is
0.50 ton/mo or 3.3 Ib/acre/day compared with a yearly average of 0.58
ton/mo. The corresponding figures at the minimum and maximum Chicago
stations are 1.84 and 5.5 Ib/acre/day. The Cincinnati figure, unadjusted
for monthly variations, equals 1.38 Ib/acre/day.
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The weighted average D/D from Table 11-2, assuming 364 feet of curb per
acre based on normal Chicago residential blocks 330 feet by 660 feet with
no curb allowance for alleys, equals 1.5 x 3.64 or 5.46 Ib/acre/day. The
average summer dustfall of 3.30 Ib/acre/day amounts to 60 percent of this
figure. However, since the average imperviousness of the typical 10-acre
unit area is 36 percent, of which 46 percent is roof area and 54 percent
streets and alleys, the amount of dustfall in the D/D samples is 60 x
.36 x .54 or 11.7 percent. It would be somewhat more if the wind blows
dust off the roofs and trees into the street. An additional 10 percent
settles on roof areas originally and may remain there until flushed off
by rain or blown onto streets or grassed areas.
A theoretical study of overland flow from pavements combined with
Shields' equation for sediment transport (Ref. 4) indicates that the
closer a particle is to the gutter, the smaller the runoff rate necessary
to transport it there, and the larger the particle, the greater the runoff
rate required. This study indicated that a rainfall rate of .14 inch
per hour would begin to move 20-micron material, and a rate of .65 inch
per hour would begin to move 40-micron material. The action of traffic
has a tendency to concentrate the dirt and dust as well as the street
litter in or close to the gutter. Once in the gutter the finer material
is readily transported. Using the equations for flow in gutters in Tholin
and Kiefer's paper (Ref. 5), it was found that a runoff rate of .01 inch
per hour would transport 20-micron material, and a rate of .03 inch per
hour would transport 40-micron material. The overland flow equations
indicate that very large rates of runoff would be required to remove
187
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dust and dirt from grass plots, and that unless erosion takes place from
ungrassed areas, the contribution of pervious surfaces to suspended
solids content is minor. However, the runoff from pervious surfaces
may contain significant amounts of soluble pollutants.
The above analysis indicates that at the beginning of a rain a small
proportion of the dust and dirt is immediately available, and that as
the rain increases, more and more dust and dirt, represented by larger
particles and particles farther from the water channels, becomes available.
Figure 9 of Ref . 1 shows the suspended solids concentration plotted
against the mean flow of increasing flow ranges to fall on a straight
line which can be represented by the following equation:
j3s a-e-4-6 rt>
188
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Using a time-step of 10 minutes, or t = 1/6 hr , values of suspended
solids were determined by both equations for each of the plotted points
of Figure 9 in Ref. 1 and equated to determine values of AP . A figure
of 2,510 pounds was estimated for P , equivalent to 93 pounds per acre,
based on the figures in Table 11-2, assuming the land use to be 50 percent
commercial and 50 percent single-family residential, 465 feet of curb per
acre, and 10 antecedent dry days without street sweeping in the interim,
i.e., 10 days accumulation of dust and dirt.
Using this value of P allowed the computation of values of A which
were plotted against r . The following equation of several tested
fitted the data best and was adopted initially:
A = .057 + 1.4 r1'1 (10)
The maximum computed value of A was .44 for r = .31 . Based on the
foregoing qualitative discussion of the amount and availability of the
finer portions of the D/D, a maximum value of .75 is suggested for A
except where soil erosion is a factor, and is incorporated in the model.
The equation was first applied to the Cincinnati area for the storm of
March 16, 1963, using P = 2,510 pounds. In the first application of the
availability factor, a new value of A for each time increment was multi-
plied by 2,510 pounds, and the sum of the suspended solids removed in all
previous time increments was deducted from this product to obtain the
amount available at the beginning of each time-step. The concentration
of suspended solids in each time-step, as well as the plain and weighted
averages, were plotted against the runoff in cfs. Only the initial points
189
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of low runoff lay on the curve of Figure 9 in Ref. 1, and both averages
lay below it, indicating that the available solids were decreasing too
rapidly as the computation proceeded.
A second computation was made in which the pounds removed in each time
increment were deducted from D/D on the ground at the beginning of the
time increment before multiplying by A , to obtain a new amount available,
or REMDD, the D/D remaining on the ground. The computed results were
much closer to the curve of Figure 9 in Ref. 1, and the plain and weighted
averages straddled the curve. This method of computation was therefore
adopted for further testing and is incorporated in the model.
A third method of computation similar to the first method was tried using
a revised equation for A which was modified so as to make the computed
points fit the curve of Figure 9 in Ref. 1 better, but instead of
deducting iDD/dt from A times initial P , the amount removed up to
the beginning of the time-step was recomputed as 2 DD/dt, or what it
would have been if the runoff had not exceeded the runoff in the time-step
being computed. This procedure was based on the assumption that each
increase in r and A involved larger or more remote particles tnat
became available progressively as r increased, but that any portion
available incrementally and removed for values of r in previous time-
steps greater than r in the time-step under consideration, should not
be deducted from A times initial P since it is not contained in
o
the new value of A . This procedure appeals theoretically, but the
results were not significantly different from those of the second method
and the computation procedure was a great deal more complicated. There-
fore this method was not adopted.
190
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All three methods of computation produced suspended solids concentrations
of approximately the right order of magnitude, but none of them exhibited
the pattern of decreasing concentration with length of storms as shown
in Table IV of the Cincinnati study (Ref. 1). Since this table gives
average results for a wide variety of storms, lack of agreement for a
particular storm is not especially significant.
BOD Modification
In tests of the method using the storm of March 16, 1963, on the Cincinnati
area, the amount of BOD removed was approximately half of the annual
average BOD in the storm runoff on a Ib/acre/day basis, computed from
Table 11-1, and the concentrations in mg/L were approximately half of
those given in Table IV of Ref. 1. Initial attempts to correct this
discrepancy in checking against Laguna Street data required adding the
equivalent of 5 percent of the suspended solids removed to the BOD
removed on the assumption that this was nonsoluble BOD not included in
the analysis for BOD in the APWA study (Ref. 2) . The addition of 10
percent was required in checking Selby Street, San Francisco. A closer
look, however, at the method of anlaysis used in that study does not
indicate that the BOD tests were run on filtered samples; therefore the
figures given in Table 11-2 should include both soluble and nonsoluble
BOD. The APWA figures would not include BOD due to leaves, grass, or
organic material not passing the 1/8-inch hardware cloth used to sareen
out the coarse solids, it is also evident that the BOD figures in the
table cannot include BOD in the drainage from roofs, areaways, parking
lots, grassed areas, and garden plots. The latter areas produce soluble
191
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BOD from decaying vegetation, fertilizer applications, and animal excreta.
In Table 11-1, taken from the Cincinnati study, the BOD in the surface
runoff amounts to 4-1/2 percent of the suspended solids load, as against
an average of 5 mg per gram of dust and dirt on the streets from the APWA
study. Until further data become available during field checking of the
program, it is proposed that a percentage equivalent of the suspended
solids removed in each time-step be added to the BOD obtained by applica-
tion of the procedures outlined herein. It is anticipated that the
percentage may range from 3 to 10 percent. The current model includes a
figure of 5 percent.
BOD from Catchbasins
Catchbasins traditionally have been built on inlets to combined sewers
and storm drains for the purpose of removing heavy grit and detritus
which might otherwise settle out in the piping system. The construction
provides a trapped pocket of liquid and solids in which the organic
component undergoes decomposition between rains. The APWA study (Ref. 2,
p. 85) listed the BOD content of 7 Catchbasins, sampled after several
days without rain. The BOD varied from 35 to 225 mg/L at 5 commercial
locations and from 50 to 85 mg/L at 2 residental locations. Limited
sampling of 11 Catchbasins in Washington, D.C., during storms was carried
out over a period of one year (Ref. 6). The BOD ranged from 6 to 625
mg/L and averaged 126 mg/L. Palmer (Ref. 7) sampled Catchbasins in
Detroit in 1949, reporting an initial BOD of 234 mg/L in the business
district decreasing to 96 mg/L after 2-1/2 hours. These data show that
catchbasins constitute an important source of pollution. The data quoted
192
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above for Washington and Detroit include the BOD of the surface wash
flowing through the basins and do not correlate concentration with runoff
rate.
In order to determine how the pollution load in catchbasins at the start
of a storm is flushed into the sewers, the APWA study added 15 to 45
pounds of salt dissolved in water to a catchbasin containing 353 gallons.
Water from a hydrant was discharged through a hose and water meter to
the gutter adjacent to the catchbasin. Samples were taken when various
total quantities up to 1,685 gallons had been added to and passed through
the basin. A stirring device ensured thorough mixing of the samples,
which were analyzed for chloride content. From the results the cumulative
percent of salt discharged and by inference the percent of pollution dis-
charged was plotted against gallons of liquid added (Ref. 2, Figure 9,
p. 88).
The following empirical equation has been developed to fit the curve of
this figure:
-x
R = 100(1.0 - e1<6v) (11)
where R = Percent of catchbasin source pollution removed
x = Cumulative inflow to catchbasin (gal.)
v = Trapped volume of liquid in basin before storm (gal.)
The number of catchbasins per acre, the assumed BOD concentration in
mg/L, and the average volume of liquid in the basins below the overflow
level are read into the program as data, and the pounds of BOD removed
193
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in each time-step are computed in accordance with the above equation and
added to the BOD washed off the surface during each time-step. No
adjustments are made as long as the antecedent dry period is at least a
day, but if the period between storms is less than a day the model
multiplies the initial pollution load by the square root of the length
of the dry period expressed as a fraction of a day. Thus fat the effect
of catchbasins on pollutant concentration has been confined to BOD.
Displacement and First Flush Effects
The effect of the displacement or crowdiny of the dry weather pollution
load in combined sewers towards the outlet due to the increase in velocity
in the sewers with increasing storm flow was satisfactorily modeled by
the Transport Model. It also takes account of deposition and scour in
the sewers where it is a factor.
Coliforms in Surface Runoff
The method used to model coliforms in surface runoff is again based on
APWA (Ref. 2, p. 55) data related to studies conducted in Chicago. The
APWA study reported that the confirmed total coliforms per gram of dust
and dirt swept from the streets were of the following magnitudes:
Single-family residential areas 1.3x10
Multi-family residential areas 2.7x10
Commercial areas 1.7x10
Using these values, with appropriate unit conversion, provided a simple
estimate of total coliforms available in each subcatchment and, by direct
194
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relationship with the suspended solids, the amount washed into storm
water inlets during each time-step of a storm event.
TEST APPLICATION
As a test of the method it was applied to the Laguna Street sewer in
San Francisco. This is a combined system draining a steeply sloping
area of 370 acres, mostly apartment houses, with a population density of
68 persons per acre. The drainage area rises to an elevation of about
300 feet above the outlet, and the trunk sewer, which is 8,600 feet long,
contains some relatively steep grades. Ref. 3 contains measurements of
flow and quality, including suspended solids and BOD, for the storms of
March 10 and March 15, 1967.
The storm of March 10 was preceded by an antecedent dry period of 40
days, except for .01 inch of rain on 4 days and .04 inch on one day in
this period which were considered small enough to ignore. As mentioned
earlier, using a street sweeping frequency of 7 days and an efficiency
of 75 percent, the accumulation of D/D on the ground at the start of the
rain was equal to 9.33 days.
Since the sewer system is of the combined type it was necessary to allow
for the suspended solids and BOD of the dry weather flow. The BOD con-
tributed by the catchbasins was also included. Furthermore, due to the
status of program development at the time these checks were made, it was
necessary to consider the area as a whole, instead of being made up 6f
a number of subareas which are routed through the Transport Model and
combined with other areas as the routing proceeds downstream. To allow
195
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for the possible effect of this difference a displacement effect was
temporarily included in the checking program to substitute for the effect
of the Transport Model. All these allowances had very little effect on
the suspended solids but a considerable effect on the BOD. Figure 11-1
shows the comparison with the reported results. In view of the differences
between the cities of Chicago and Cincinnati, which furnished the basic
data for the method, and San Francisco, the agreement is remarkable.
The agreement at peak flows is better than at the low flows, which means
that the total pounds of pollution (the product of flow and concentration)
are being modeled satisfactorily. A similar comparison between the
reported and computed total coliforms is shown in Figure 11-2.
The storm of March 15 was also used as a check, considering suspended
solids only, and neglecting any contributions or effects of the dry
weather flow. The antecedent dry period was assumed to be 5 days. This
storm began about 8:20 p.m. with a light rain which increased the overflow
rate from 7 to 12.5 cfs at 8:30 p.m. The flow then steadily decreased
to 2.0 cfs at 9:30 p.m., followed by a large increase to 108 cfs at
10:30 p.m. It dropped to 11.4 cfs at 11 p.m. and then rose to a secondary
peak of 76 cfs at 11:15 p.m., which decreased to 44 cfs by midnight.
The method successfully modeled the suspended solids level at the first
high peak at 10:30 p.m. and at the preceding and following low flows.
It was low on the first minor rise at 8:30 p.m. and hijh on the second
high peak at 11:15 p.m. It was later discovered that significant rain
occurred on four of the preceding five days, as the records from the
Federal Building show in the list which follows.
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SAN FRANCISCO-LAGUNA ST.
COMBINED SEWER
MAR. 10, 1967 STORM
'(483)
570 ACRES
MULTI-FAMILY RESIDENTIAL
68 PERSONS/ACRE
— 0.00
;-
I
li
0.10
0.20
25O
200
400
350
300
35O
20O
150
IOO
£l
;t
.
Figure 11-1.
TIME
^~
BOD AND SS TEST RESULTS FOR COMBINED SEWERS,
LAGUNA STREET, SAN FRANCISCO
-------
8xlO
DRY WEATHER AVERAGE
COMPUTED TOTAL
COLIFORMS
REPORTED
TOTAL
COLIFORMS
4x10
50 100 150 200
TIME AFTER BEGINNING OF OVERFLOW (MIN)
250
San Francisco-Laguna St.
Combined Sewer March 10, 1967 Storm
Figure 11-2. TOTAL COLIFORM TEST RESULTS FOR COMBINED SEWERS
198
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Date Pain (in.)
March 10 .49
March 11 .45
March 12 .58
March 13 .50
March 14 .03
March 15 .43
The rain on these days was all of the same order of magnitude as the rain
on March 10 during which storm 16 percent of the D/D initially on. the
ground was removed. If it is assumed that the streets were swept on
March 11, and that each day's rain except the sprinkle on March 14
removed 16 percent of the D/D on the streets after allowing for the
addition of that day's contribution, there would have been an accumulation
of 4.84 days on the street at the beginning of the rain on March 15.
This analysis may justify the above described check based on 5 days. It
also indicates that in such cases it may be desirable to assume a mini-
mum number of antecedent dry days, say 3 to 5 days, regardless of the
weather pattern.
199
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SECTION 12
DRY WEATHER FLOW QUALITY MODEL
Page
OBJECTIVES 203
INITIAL CONCEPTS 203
THE MODEL SUBROUTINE 204
THEORETICAL DEVELOPMENT 204
Domestic Flow 205
Commercial Flow 205
Industrial Flow 207
Infiltration 208
Computations 208
Case 1 208
Case 2 209
Hourly Variation 209
Default Values 210
TEST APPLICATIONS 211
CONCLUSION 211
201
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SECTION 12
DRY WEATHER FLOW QUALITY MODEL
OBJECTIVES
The objectives of the DWF Quality Model are to:
1. Provide reasonable estimates of the modeled quality constituent
concentrations based on non-storm influences.
2. Function compatibly with other modeling subroutines with
emphasis on time and spatial variations.
3. Require minimal input data consistent with desired results.
INITIAL CONCEPTS
One way to establish a valid estimate of DWF quality is to sample and
analyze it. For larger systems such sampling may be accomplished on a
routine basis at the municipal sewage treatment facility. Since these
data would normally, or most economically, be available at only one or
a few points in the prototype system, a means to extrapolate or apportion
results over the entire system is required.
A second approach for estimating DWF quality is to assume average per
capita values and to compute results on the basis of population distri-
bution.
These concepts, coupled with variations according to flow source (resi-
dential, industrial and/or commercial), family income, and other record-
ed parameters, form the basis for the model development.
203
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THE MODEL SUBROUTINE
The DWF Quality model is embedded within subroutine FILTH in the
Transport Block. Subroutine FILTH also computes the DWF quantity
estimate and provides a vehicle for adding infiltration (INFIL) so that
both concentrations and mass values may be determined.
Since the Transport Model operates on a true simulation theory—i.e.,
pipe configurations and flow source locations are critical—DWF computa-
tions are designed to yield representative flows at several geographically
distributed entry points.
The sum of all entry point values is, of course, the total DWF of the
system.
Furthermore, if the entry point values are summed in sequence starting
with the most upstream elements, valid subtotals may be printed out at
intervals along the main trunk sewer for intermediate checks.
Once picked up by the Transport Model the DWF is mixed and routed in a
manner identical to the storm water routing, discussed elsewhere.
THEORETICAL DEVELOPMENT
Dry weather flow (that flow measured in combined sewer systems between
storm events) is assumed to be divisible into the following four
categories:
Domestic flow
commercial flow
Industrial flow
Infiltration.
204
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Domestic Flow
The domestic flow represents the flow from the homes of all residents
of an area whether they be barracks, apartments, multi-family, or single-
family dwellings.
The first concern in computing domestic flow quality is a population
estimate, which for most urban areas is readily available in Census
Tract data tabulations. First approximations as to the quality makeup
may use average values in Ib/capita/day or similar units taken from
standard sanitary engineering textbooks, such as Fair and Geyer
(Ref. 1).
Next in importance is an estimate of the percentage of households
equipped with garbage grinders, as these units appreciably increase the
waste concentrations in the flow. A sample comparison of ground garbage
with sewage is shown in Table 12-1 as taken from Haseltine (Ref. 2).
Finally the strength of the wastewater flows, as well as volume, may
vary with family income as shown in Table 12-2 taken from Watson (Ref. 3)
Commercial Flow
Flows from areas zoned for commercial use may be expected to include
domestic flow from the overlapping resident population plus flows from
stores, offices, and other business units (laundromats, movies, hotels,
etc.). Hubbell (Ref. 4) found these flows generally similar to resi-
dential area flows. In the same work, Hubbell also reported hospital,
resident, school, and institutional flows to be generally stronger (lb/
capita/day) than "normal" domestic flow. Because hospitals, schools,
205
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Table 12-1. COMPARISON OF QUALITY CONSTITUENTS
OF GROUND GARBAGE WITH SEWAGE
Ground
Garbage, Sewage,
Ib/capita/day Ib/capita/day
Total solids
Total volatile solids
Suspended matter
5 Day BOD
Fats and greases
Nitrogen
Moisture
0.15
0.13
0.10
0.08
0.03
0.002
0.45
0.55
0.32
0.20
0.17
0.05
0.04
Source: T. R. Haseltine, "Addition of Garbage to Sewage,"
1950 (Ref. 2).
Table 12-2. COMPARISON OF QUALITY CONSTITUENTS
WITH FAMILY INCOME
Item Home 1 Home 2 Home 3
Approximate market value
Total number of people
Water consumption,
gal . /capita/day
Suspended solids,
Ib/capi ta/day
COD, Ib/capi ta/day
BOD5, Ib/capita/day
Grease, Ib/capita/day
$45,000
5
78
0.23
0.45
0.35
0.06
$25,000
5
66
0.16
0.30
0.16
0.18
$18,000
5
24
0.10
0.18
0.10
0.13
Source: K. S. Watson et al., "The Contribution from the Individual
Home to the Sewer System," 1967 (Ref. 3).
206
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and institutions are better represented as point rather than area sources
of waste, they are most easily modeled as special cases of industrial
flow discussed below. Selected findings by Hubbell are reported in
Table 12-3.
Table 12-3. ESTIMATED TYPICAL WASTEWATER
FLOW AND CHARACTERISTICS
Source
Suburban residential
Hospitals
Factories
Motels
Shopping centers
Schools, non-resident
Schools, resident
Institutions
Flow ,
gal . /capita/day
75
175
20
50
60*
10
75
120
BOD,
Ib/capita/day
0.17
0.25
0.10
0.17
0.18*
0.03
>0.17
0.31
ss,
Ib/capita/day
0.20
—
0.10
0.20
0.18*
—
>0.20
0.31
*Per employee.
Source: J. W. Hubbell, "Commercial and Industrial Wastewater Holdings,"
1962 (Ref. 4).
Industrial Flow
Flows from areas zoned for industrial use, like commercial areas, may
be expected to include domestic flow from overlapping resident population
and domestic-type wastes from employees. Most important, however, are
the process flows (wastes generated by wet industrial processes), which
vary with the type of product produced and rate of production less
removals accomplished prior to discharge (pretreatment). Measured
characteristics are used to the extent available in model applications
and are supplemented, when necessary, by generalized data, such as may
be found in Rudolph (Ref. 5). In modeling, one data card is required
207
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for each significant industrial process flow source describing its
average daily flow and constituent quality coroentrations.
Infiltration
Infiltration is assumed to be pure (free of contaminants) unless known
to be contaminated by passage through soils having significant soluble
impurities of the type being modeled.
Computations
Computations proceed along one of two paths depending upon whether
measured characteristics are available (Case 1), or whether average per
capita values must be assumed (Case 2). In each case the quality con-
stituents modeled are BOD, total suspended solids, and total coliforms.
Case 1. In this situation the total quantity and characteristics of the
average DWF are known, either from direct sampling and analyses or
available treatment facility data, and the quantities and distribution
of DWF and infiltration are known from previous modeling routines. The
proper distribution of the known waste characteristics is accomplished
by first deducting the non-domestic flows and characteristics from the
total values, following the equation:
/ total flow and \
I characteristics) ~ (infiltration)
7 (1)
/process flows and\ _ /domestic flows and\
) I characteristics J
\ characteristics
Further refinement in the estimate of domestic flow and characteristics
is made by weighting the values according to the fraction of commercial
208
-------
flow, high income residential flow, average income residential flow, low
income residential flow, and the percent usage of garbage grinders.
For BOD and suspended solids the base average quality characteristics
are then determined from the weighted estimates in terms of Ib/day/cfs
of flow. The base average for coliforms is simply the measured value,
MPN/day, divided by the total population.
These base averages are then coupled with the appropriate modifiers
(income, commercial use, garbage grinders, or population) and flow to
reconstruct the DWF and characteristics for each subarea within the
system. Process flows, characteristics, and infiltration are likewise
added at the appropriate geographical location.
Case 2. In this case the procedure is similar to Case 1 except that the
base average quality constituents are computed directly, based on average
textbook values or figures from earlier model runs.
Hourly Variation
The results of the foregoing computations yield average daily values.
Since both flow volumes and quality characteristics change throughout
the day (Refs. 6,7), hourly variation factors are incorporated to adjust
these averages to real time conditions corresponding to the start and
duration of the storm event.
Further discussion and explanation of the procedures are given in the
"User's Manual."
209
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Default Vrlues
Default values used in programming the model are built in as follows:
MODIFIERS
Item Value
Commercial flows 0.9
Low family income, less than
$7,000 per yr 0.8
Average family income,
$7,000-15,000 per yr 1.0
High family income, greater
than $15,000 per yr 1.2
Garbage grinders in use
(in addition to income modifier) 1.3
AVERAGE QUALITY CONSTITUENTS (Case 2 only)
Item Value
BOD, average family income 0.20 Ib/capita/day
SS, average family income 0.22 Ib/capita/day
Total coliforms (Ref. 1) 200 billion/capita/day
Flow without infiltration 85 gal./capita/day
Flow with infiltration 100 gal./capita/day
Family incomes are based on reported 1960 census data. The table values
were selected as being somewhat credible and can readily be changed for
specific applications. Hourly variation factors for flow and quality
are considered too important to be locked into the program and thus must
be fed in as basic data for each new system.
210
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TEST APPLICATIONS
The lack of data reporting DWF characteristics measured simultaneously
at several points in a conveyance system precluded any comprehensive
test applications. Good DWF quality monitoring results for single
points in two San Francisco systems (Ref. 6), however, provided a limited
base for model analysis.
The most significant outcome of these tests was the realization of the
significance of the compounded factors for hourly variation. Measured
values of both flow and quality variations showed the extreme variation
of pounds of BOD released per 10-minute interval exceeded a ratio of
50 to 1 (largest 10-minute release divided by the smallest) in one day.
CONCLUSION
A simple modeling technique has been devised to distribute quality
constituents known at a single downstream point to their approximate
source locations within a catchment area. This distribution is based
on land use, population, family income, use of garbage grinders, and
known or estimated process flows.
This breakdown is necessary to account properly for routing in the
conveyance system during storm events and to support the Decay (sediment-
scour) model discussed in Section 13.
Where quality constituents are not known, average values are provided
for initial approximations.
211
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Hourly variations in DWF quality constituents may exceed a range of
50 to 1 between extreme values in one day; thus the magnitude of DWF
quality contribution to combined sewer overflows is heavily dependent
on the real time occurrence of the storm event.
212
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SECTION 13
DECAY MODEL
Page
OBJECTIVE 215
THE MODEL SUBROUTINE 215
THEORETICAL DEVELOPMENT 216
Literature Survey 216
Methodology 217
TEST APPLICATION 22°
Selby Street, San Francisco 221
FMC Project 224
CONCLUSION 229
213
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SECTION 13
DECAY MODEL
OBJECTIVE
The Decay model was developed to route pollutants and to account for the
decay of pollutants during transit in a sewer system.
THE MODEL SUBROUTINE
The computer model consists of two parts, a quality section (subroutine
QUAL) and a dry weather load section (subroutine DWLOAD); both are in-
corporated into the Transport Model. The basic method61ogy developed
for the Decay model is found in QUAL. An extension of this concept is
the DWLOAD section.
In QUAL, mass balance and first order decay of pollutants provide a
basis for the model. The general assumptions are that mixing within each
sewer element in the system is instantaneous and complete, and that the
nonconservative pollutants decay according to the first order reaction.
An unidirectional transportation concept was used to describe the move-
ment of pollutants through any specified sewer system, given sewer data
and concurrent flows and velocities. The four quality parameters con-
sidered in the model are BOD, DO, suspended solids, and a conservative
pollutant (P). Quality constituents such as coliforms are handled
as a conservative pollutant. A sediment uptake and deposition phenomenon
is conroproated into the model for the case of suspended solids.
Relative to the sediment uptake and deposition concept developed for
QUAL, DWLOAD was developed to establish the initial sediment load within
215
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the sewer system. An iterative method is used to estimate daily sediment
accumulation in each section of the sewer under DWF conditions. Also,
using the assumption that the daily sediment build-up is constant over
consecutive dry weather days, initial sediment load estimates for each
conduit are made possible.
THEORETICAL DEVELOPMENT
An investigation into the area of the decay of pollutants and sediment
transport in sewers did not reveal any practical applications of extant
theoretical developments and experiments. Thus, model development was
geared toward a methodology that would encompass the major facttors and
information obtained from the literature search combined with present
knowledge of river systems.
Literature Survey
Further research is needed in the theory related to the decay of pollu-
tants and sediment transport in sewer systems. Some doubt exists as to
the significance of quality change, other than mixing, during rainfall-
runoff periods. It has been suggested (Ref. 1) that the time of transit
through the sewer system is too short to consider bacterial decay or
reduction of BOD with time.
Decay of pollutants and sediment transport, as with infiltration, has a
basis for theoretical analysis (Ref. 2). Raths and McCauley studied
sediment transport in sewers (Ref. 3). The FMC Corporation also has
conducted a study on periodic flushing and sediment transport (Ref. 4).
Through these analyses, it is evident that particle size and specific
216
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gravity, depth of flow, and the slope of the conduit are important
factors affecting deposition. Hill et al. (Ref. 5) in a recent study, in-
vestigated the flat bed phenomenon in alluvial channels. Also useful in
developing a methodology for sediment uptake and deposition were the
velocity relationships in Fair and Geyer (Ref. 6) and in Carstens1 work
on heterogeneous flow of solids in conduits (Ref. 7). Data needs relative
to particle size were obtained from an APWA report (Ref. 8). Oxygen
balance in sewers is described by Gustafsson and Westberg (Ref. 1).
These authors applied the classic Streeter-Phelps equation (Ref. 9} to
flowing sewage and solved for the oxygen uptake as a function of time,
temperature, slope, and flow conditions in sewers.
Methodology
The general equation of the model representing continuity of mass is as
follows:
Pounds in Pounds in
element at = element at + Pounds - Pounds +
new time-step old time-step entering leaving -
(1)
Pounds Pounds entering or
decayed or +_ leaving from
generated source or sink
The mathematical rigor related to the development of the Decay model,
using the concept of Eq. 1 and expanding it into its mathematical form,
is given in Appendix B. Assuming complete mixing along with the use of
217
-------
a finite difference scheme, the final computer model for routing pollu-
tants is in the form:
"n+1
D2}) -
(C. Q. ) , + D,,
in*in n+1 2
(2)
where C = Cone, of pollutant in element (Ib/cf)
V = Volume in element (cf)
n = Time-step number
Q = Flow rate (cfs)
D = Decay rate or oxygen utilization rate (I/day)
D = Growth rate or reaeration rate (I/day)
S = Maximum growth or oxygen saturation value (mg/L)
At = Time increment (sec)
As mentioned earlier for the case of suspended solids, a sediment uptake
and deposition model was incorporated into the Decay Model. When inves-
tigating deposition in sanitary sewers, Raths and McCauley (Ref. 3)
claimed that consideration must be given to the importance of: type,
size, and specific gravity of potential deposition material; quantity of
flow; depth of flow; velocity of flow; pipe slope; pipe alignment; pipe
size, pipe joints; pipe age; pipe roughness coefficients; and sewer
construction practices. Thus, in developing the sediment model, the
objectives were to relate the variables as closely as possible to the
218
-------
factors affecting deposition and to use the information available from
existing models, such as the Transport Model.
The sediment model consists of two subroutines which follow similar
mathematical procedures. First, DWLOAD determines the amount of sedi-
ment accumulated in each conduit since the last cleansing of the sewers.
DWLOAD calculations are performed prior to flow routing, thus establish-
ing initial sediment conditions in the conduits before actual routing.
The next subroutine (ROUTE) determines the amount of sediment uptake and
deposition during storm conditions. This subroutine is used continually
during flow routing to determine (cin)n+1- E
-------
Using Eq. 3 as a basis for the model, the final equations resulting from
the mathematical development of a sediment algorithm are
Sc = Sc + P x (T + T + T ) x At (4)
. ,
I (1 - P) x (T± + T2 + T3)J
Sc = P x Sc (6)
where Css = Concentration of suspended solids (Ib/cf)
P = Fraction of sediment in suspension with diameter greater
than or equal to the critical particle diameter
Sc = Amount of settled sediment in element (Ib)
The process is that for each time-step the amount of sediment at the
bottom of each conduit is determined by Eq. 4. Then, using Eq. 5, the
amount of sediment to be routed is determined. This information is then
used in Eq. 2. Finally, Eq. 6 updates the amount of sediment at the
bottom of the sewer element for the next time-step. The detailed devel-
opment of the model is presented in Appendix B.
TEST APPLICATION
Sensitivity analyses were performed with the Decay model using data from
the Selby Street, San Francisco, combined sewer system (Ref. 10) and the
FMC Corporation study (Ref. 4). Results from the FMC sewer flushing
project were used for a detailed investigation of the sediment uptake
and deposition model.
220
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Selby Street/ San Francisco
The main test areas used for these analyses are shown in Figure 13-1.
Test Area 1 includes the first ten elements and Test Area 2 includes
these ten elements plus the main trunk sewers in the system. In the
simulation of conservative pollutants/ the initial conditions for the
sewer system were assumed at zero concentration. For nonconservative
pollutants, i.e., BOD and suspended solids, initial conditions were set
at DWF concentrations, but for DO, initial conditions were assumed at
zero concentration.
Analyses were first performed for a mathematical breakdown of Eq. 2.
These tests confirmed the existence of consistency in the continuity of
mass and the complete mixing assumption. Conservative pollutants were
then studied using Test Areas 1 and 2. The procedure was to check the
system randomly at the elements to see if the total pollutant quantity
input was equal to total output. These runs were successful using
different pollutograph concentrations.
The next step was to study the model's reaction to different values of
Dl and D2 in Eq. 2. The rate constant Dl was analyzed according to
information obtained on the range of the rate constant for deoxygenation
in raw sewage at 20°C (Ref. 1). Values used for the decay rate are in
the range 0 £ Dl <_ 3.0. Results of the runs are shown in Figure 13-2.
As anticipated, the analyses revealed that there is a dependency only on
the duration and intensity of the storm and not on the pollutograph used.
System response to the DO quality parameter also was tested for various
hypothetical situations. Using Dl, D2, and S, these results showed that
221
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NJ
NJ
NJ
Test Area 2
A Inputs (manhole) from runoff
• Manholes (no input)
Notes: (1) 73 elements total.
(2) 1 in. = approximately
2,000 ft
23
Figure 13-1. SCHEMATIC DRAWING OF TEST AREAS, COMBINED SEWER
(NUMBERED), SELBY STREET, SAN FRANCISCO
-------
3.0i
to
to
U)
cu
g
01
O
2.0-
November 14 Storm
November 6 Storm
1.0
2.0
4iO 5.0
% DEPLETION OF BOD
6.0
TiO
8.O
Figure 13-2. RESULTS OF SENSITIVITY RUNS FOR RATE CONSTANT FOR DECAY (Dl),
STORMS OF NOVEMBER 6 AND 14
-------
reaeration of DO occurred and that the model was functioning as expected.
Prom the results of these tests, the rate constants for deoxygenation
and reaeration were set as 0.2 per day and 0.3 per day, respectively.
Preliminary tests also were performed on the sediment model using the
Selby Street drainage area shown in Figure 13-1. Storm runoff hydro-
graphs and hypothetical pollutographs at element one were used to study
the sediment build-up in the conduits for Test Areas 1 and 2. Compari-
sons were made of flow versus sediment build-up in the conduit for re-
corded storms (Ref. 10) in the area. Results of the November 6 and
November 14 storms are shown in Figures 13-3 to 13-5. Note that in
Figure 13-3 the initial sediment build-up, or bed load, is for one dry
weather day, and in Figure 13-4 the bed load is for 47 dry weather days.
Results were as expected which confirmed that the model is a stable
system.
FMC Project
Analyses using experimental data from the FMC sewer flushing project
proved very rewarding in evaluating the performance of the sediment model.
Computer simulations were made using data from the physical model
developed by FMC. Results from these simulations were then compared
with the experimental results of the physical model. A percentage of
deviation was calculated for the suspended solids deposited and the out-
flow of suspended solids. Results from some of these tests are shown in
Table 13-1. An 18-inch pipe with a length of 795 feet was used in this
comparison.
224
-------
ro
to
Ul
Q
W
w
Outflow Hydrograph from
Manhole 71
1,000
-800
-600
-400
-BOO
1,800 3j500 5,400
7^200 9,OOO 10,800 I2J60O 14400 16,200 18,000
TIME (SEC)
w
ft
i
Figure 13-3. BED LOAD IN CONDUIT 72, STORM OF NOVEMBER 6, DWDAY=1
-------
DWLOAD Bed Load
10
a\
Outflow Hydrograph from
Manhole 71
1,000
-000
-600
-400
U
§
200
1,800 3,600 5,400
7,200 9,000 IOJ900 I2JBOO 14,400 16,200 (8.000
TIME (SEC)
Figure 13-4. BED LOAD IN CONDUIT 72, STORM OF NOVEMBER 6, DWDAY=47
-------
to
K>
H
Q
W
to
Outflow Hydrograph from
Manhole 71
poo apoo
54OO 7,2OO %QOO 10,800 12/BOO 14400
TIME v(SEC)
Figure 13-5. BED LOAD IN CONDUIT 72,
STORM OF NOVEMBER 14, DWDAY=1.0
•300
-ZOO
too
I8POO
-------
Table 13-1. TEST RESULTS USING FMC PROJECT DATA,
BED LOAD ANALYSIS FOR 18-INCH SEWER WITH A LENGTH OF 795 FEET*
to
to
00
(1)
Flow,
gpm
50
10
30
30
30
(2)
ss
Input ,
mg/L
230
686
201
201
201
(3)
Assumed
Specific
Gravity
2.70
2.70
2.70
2.49
2.51
(4)
SS
(5)
Deposited
Measured, Simulated,
Ib
5.133
15.744
14.369
14.369
14.369
Ib
8.573
23.233
17.165
12.923
13.319
(6)
Deviation,
percent
40.13%
32.23
19.45
10.06
7.30
(7)
SS
Measured,
Ib
57.167
35.656
61.131
61.131
61.131
(8)
Outflow
Simulated,
Ib
51.977
28.356
58.415
62.659
62.263
(9)
Deviation,
percent
9.98%
25.74
4.44
2.50
1.82
*Pipe slope =0.1 ft/100 ft; roughness coefficients = 0.0099.
-------
Without further information on the characteristics of the suspended
solids at the input, it is felt that practical assumptions are made con-
cerning Shield's criterion, specific gravity, and the sewer sieve analysis
relationship, as presented in Appendix B. Columns 4 and 5 in Table 13-1
illustrate a reduction in the percentage of deviation after a logical
weighted average adjustment on specific gravity was made with the FMC
data supplied on volatile solids.
CONCLUSION
A general model has been developed which describes the movement of pollu-
tants during transit in a prespecified sewer system. It has the capabil-
ities of accounting for decay of nonconservative pollutants and allowing
for sediment uptake and deposition when dealing with suspended solids.
The analyses performed verified the concepts used for complete mixing,
continuity of mass, deoxygenation and reaeration, and sediment transport.
229
-------
SECTION 14
RECEIVING WATER QUALITY MODEL
Page
OBJECTIVES . 233
RELATION TO STORM WATER PROGRAM 234
THEORETICAL DEVELOPMENT 234
Quality Routing 234
Solution Procedure 237
Simulation Time Interval 238
Linear Property 239
THE MODEL SUBROUTINES 239
TEST APPLICATION 240
231
-------
SECTION 14
RECEIVING WATER QUALITY MODEL
OBJECTIVES
The ultimate goal of the Storm Water Management program is to assess
and evaluate the cost effectiveness of various pollution control mea-
sures. The objective of the Receiving Water Quality model is to pro-
vide a means for measuring the effect.
Runoff resulting from storm water carries with it various kinds of
pollutants. Discharged into the receiving water, these pollutants are
transported and dispersed into the aquatic environment. The job of the
Receiving Water Quality model is to trace or route the pollutants,
determining their temporal and spatial variation in the system.
Since the quality routing requires the receiving water quantity infor-
mation, the model was developed to operate only in conjunction with the
Receiving Water Quantity model described in Section 10. Both models
use the same geometric representation which is capable of depicting the
temporal and spatial distribution of pollutants as well as the hydro-
dynamics. To facilitate a rapid evaluation of the required removal by
various treatment processes, however, the model is flexible in that it
can perform several water quality simulations for a given quantity
solution. This is desirable especially when many treatment processes
modify the removal rate of pollutants rather than the change in hydrau-
lic characteristics.
233
-------
RELATION TO STORM WATER PROGRAM
storm Agate r hvdrngraph and
pollutograph inputs^^r^m^i^r.^
water Qu^t^y mQdei • Ifc also
accepts from RECEIV the quantity solution of the Receiving Water Quantity
model .
Upon completion of the computations, the model prints and plots the
concentration of various water quality constituents versus time for a
selected number of junctions. The execution of the program will then
be terminated.
THEORETICAL DEVELOPMENT
Pollutants received from storm water and other inflows can basically be
classified into three types, i.e., a conservative _substance such as
chlorideipn; a nonconservative substance such as BOD; and a conserva-
'iMWiaWMM'l"a*>|MB* - ...... -TII-— n»— •* -"— ^ ' ~"— **"'•'"'''*— ---r in ri ijj-iiir """^'miHiUMi mi in ....... ~"
oxygen, that can jje consumed by a noncon-
servative substance BOD. A conservative substance is defined as the
one that does not decay itself, whereas a nonconservative substance is
the one that will decay in proportion to the amount of material present,
i.e., a first order reaction. There are other types of substances, but
these three classes are of concern in the present model development.
Quality Routing
Physical dispersion of a quality constituent in a receiving water is
caused by transport phenomena, including advective transport and diffu-
sion. If the quality constituent is nonconservative, it will be
234
-------
subjected to a continuous chemical reaction of decay. In addition,
physical importation of water to the junction and/or extraction of water
from the junction may carry with it the quality constituent. The alge-
braic sum of import and export may be termed a source or sink. The
source and/or sink may include that of tidal exchange at the mouth of
the estuary.
These mechanisms are operated simultaneously to modify the water quality
constituent in all parts of the receiving water system, described by
junctions. The basic equation describing these processes is the con-
tinuity equation. It can be written in finite difference form as
follows:
Ac. Ac.
-A-- = - v ?—*- - kc. + s, (1)
At Ax j 3 v
where c = Constituent concentration
t = Time
v = Velocity averaged over the cross-section of the reach or
channel
x = Distance
k = Decay constant
s = Source and/or sink
j = Junction number
The first term on the right hand side of Eq. 1 is an advective transport
which, in the case of a non-branch system, is illustrated by Figure 14-la.
According to the expression, the advective transport simply translates
235
-------
o
-------
the linear concentration gradient along the flow path during the short
period of time interval. During that period, the concentration at the
downstream junction increases or decreases depending on the sign of
concentration gradient.
It is noted that Eq. 1 does not include a term for diffusion transport.
Experience
used, the major_transgort mechanism is by advection and thus the
diffusion term can be safely neglected.
iMM^«M
-------
time-step are furnished by the Receiving Water Quantity model. The
initial value of parameters is substituted into the equation to determine
the changing rate of concentration. The concentration is continuously
updated from one time-step to the next.
Sequential computation proceeds as follows:
1. Compute the rate change of concentration due to the advective
transport.
2. Determine the amount of decay, if any.
3. Calculate the import and export amount.
4. Compute the new concentration of the quality constituent at
the end of the period based on the above calculations.
These procedures are repeated for all the junctions before the compu-
tation is advanced to the next period. Six constituents can be solved
simultaneously. When the solution for BOD is made, its exertion on
DO and the resulting DO levels are determined simultaneously.
This is again the solution procedure for the familiar initial value
problem. To increase the accuracy of computation, a modified Euler's
method was used by instigating a half-time-step computation.
Simulation Time Interval
Water quality routing does not have the severe stability problem found
in the Receiving Water Quantity model solution, gxpe^ignce has shown
that an hourly__intgrval_of computation provides good results for both
lake and estuary systems.
238
-------
As a rule, the time-step for quality computation is much longer than
that for quantity computation. The intermediate hydraulic results
computed in each quality time-step (an hour) are therefore averaged for
quality simulation.
Linear Property
Because the continuity equation governing the water quality response
as posed is linear, the pollutional effect of each point source can be
computed separately. The overall effect is additive of each individual
discharge provided that all the flow quantities of discharge have
entered the quantity computation. This property simplifies the eval-
uation of the cost-effectiveness of the treatment by any given storm
water polluter.
THE MODEL SUBROUTINES
The program consists of four core subroutines, i.e., SWQUAL, INQUAL,
LOOPQL, and QPRINT. SWQUAL is the subroutine called by RECEIV to take
over control of the quality subroutine with the assistance of other
subroutines.
INQUAL is the subroutine for reading input data. Depending on the
number of days to be simulated, SWQUAL will call LOOPQL once per day to
perform the quality routing described previously. QPRINT prints quality
response for various constituents at a selected number of time-steps
and junctions for engineering interpretation of results.
239
-------
TEST APPLICATION
The general method of quality routing described herein has been proven
valid for several prototype systems and conditions receiving waste load
inputs other than the impulse type pollutograph (Refs. 1,2,3). Actual
data, however, were not available for the verification of the receiving
water quality dynamic response to the storm water pollution.
Hypothetical cases were therefore used to test for the functionality of
the model. This was done by imposing a wide variety of input conditions
on an assumed receiving water system. The system response was then
evaluated and compared with the system behavior that can reasonably be
expected to occur.
The hydraulic system used for the quality routing is the same as the
one used for the Receiving Water Quantity Model (see Figure 10-1).
Briefly, each channel was 10,000 feet long, with a depth ranging from
15 feet at channel 28 to 20 feet throughout the open water body. Dry
weather flow was 2,000 cfs at junction 18, 500 cfs at junction 16,
50 cfs at junctions 10 and 14, and 20 cfs at junction 13. Input hydro-
graphs were superimposed on the dry weather flow and a prescribed sinus-
oidal tide was imposed on junction 1.
In addition to hydraulic inputs, the Receiving Water Quality model
accepted a waste input to junction 14 as shown in Figure 14-2. A
similar waste input with a peak value of 250,000 pounds per day was
imposed on junction 13. The model was asked to evaluate the quality
impact of waste discharge from these particular point sources. Note
240
-------
1200 1500-1
5-
1000
I
V)
o
1
I
3
4-
800
i
3-
2
- 400-
o
Q.
I-
200-
HYDROGRAPH
BOO POLLUTOGRAPH
INFLOW BOO CONCENTRATION
I
TIDAL CYCLES
Figure 14-2. INPUT TO NODE 14 OF TEST SYSTEM
241
-------
that the irflow BOD concentration decreased with time as it is typically
observed in the field. The product of the hydrograph and the inflow
concentration constituted the BOD pollutograph in the units of mass
emission rate. The shape of the pollutograph resembled that of the
hydrograph.
The receiving water body was started with zero BOD concentration through-
out the system and the saturation for DO was assumed as 8.0 mg/L. The
responses of BOD and DO at junction 14 are plotted in Figure 14-3b and
3c. Figure 14-3a shows the flow characteristics in channels 24 and 25
which meet at junction 14.
As expected, the receiving water BOD at junction 14 peaked at about the
same time as the BOD pollutograph. This is because junction 14 was the
immediate node receiving the waste input.
The high concentration of BOD was then transported and dispersed seaward
until the next flood tide which brought it back at reduced concentration.
This is the reason for the secondary peak of BOD concentration after one
tidal cycle, even though the pollutograph became essentially zero at
that time.
The DO concentration was noted to be high when BOD was low and vice
versa. During the first tidal cycle, the DO level remained above 6.6
mg/L. This is understandable because the water volume flowing through
junction 14 was relatively high and thus it provided a large resource
of DO for BOD exertion. During the second tidal cycle, the DO level
242
-------
o
Q
10
O
Q
O
OJ
60
40
20
CHANNEL 24 FLOW
TIDAL CYCLES (DAY)
Figure 14-3. RECEIVING WATER QUALITY MODEL RESULTS
FOR NODE 14 OF TEST SYSTEM
243
-------
was lowered to 5.3 mg/L, resulting from the accumulative effect of the
BOD and DO relationship in the estuary.
These results and others that were tested for the lake system pointed
out the reasonableness of the answers. Real verification, however,
awaited testing which is described in Volume II of this report.
244
-------
SECTION 15
TREATMENT MODEL
Page
OBJECTIVES 247
BACKGROUND 247
THE MODEL SUBROUTINE 248
PUMPING STATIONS 251
THEORETICAL DEVELOPMENT (Treatment Processes) 252
Bar Racks (Treatment Option 12) 252
Fine Screens (Treatment Options 33 and 34) 254
Sedimentation (Treatment Option 35) 255
Dissolved Air Flotation (Treatment Option 32) 259
Dissolved Air Flotation Preceded by Fine
Screens (Treatment Option 33) 262
Microstrainers (Treatment Option 42) 264
High Rate Filters (Treatment Option 43) 277
Effluent Screens (Treatment Option 52) 283
Chlorination (Treatment Option 72) 284
SIZE OF DESIGN EVENT AND QUALITY OF TOTAL OVERFLOW
RELEASED TO RECEIVING WATERS 286
245
-------
SECTION 15
TREATMENT MODEL
OBJECTIVES
The objectives of the Treatment model are to:
1. Provide the capability of modeling a considerable number
of alternative sewage treatment processes to be located at
or near a sewer outfall, and to restrict certain process
combinations which are deemed inadmissible.
2. Simulate improvements in overflow quality produced by each
component of the selected combination of treatment processes.
3. Summarize data required for the estimation of treatment
costs for the specified installation.
BACKGROUND
Processes applicable to the treatment of overflows from combined sewers
and storm sewer discharges should meet the following criteria:
1. They should operate efficiently when called upon after varying
and extended periods of inactivity.
2. They should have large throughput capacity.
3. They should be simple and compact, requiring as little land
area as possible.
4. They should not produce odors, either during or between storms.
5. The benefit to the community should be worth the cost.
To meet these criteria, there are available the existing primary treat-
ment processes, supplemented by chlorination, which are familiar to all
247
-------
sanitary engineers, plus a variety of ultrafine straining and filtration
processes now undergoing intensive investigation under FWQA sponsorship.
Data incorporated in the model relative to these latter processes are
based on currently available information and may require revision when
results of the completed investigations are published.
Storage, either alone or combined with sedimentation, may be used to
reduce the hydraulic capacity of the treatment units and is incorporated
in the model.
The first criterion eliminates the use of biological processes, except
in specially favorable situations, because of the difficulty and cost of
maintaining a large supply of active biological media during dry weather
to have available in sufficient quantity during storms. For this reason
biological processes are not included in the model.
THE MODEL SUBROUTINE
The Transport Model will provide a hydrograph of flow and pollutographs
of BOD, suspended solids, and coliforms at the point of discharge. These
either will pass directly to the Treatment model or will be routed through
the Storage Model first. In either case the input to the Treatment model
will consist of a hydrograph of flow and pollutographs of BOD, suspended
solids, and total coliforms (most probable number) for each storm event
analyzed. Additional pollutographs for other polluting constituents may
be added in the future when data become available.
248
-------
The Treatment model is shown in Figure 15-1. The input to the model will
be from storage (02) or directly from the sewer without storage (01).
(The numbers refer to treatment options in Figure 15-1.) Immediately
following the start of the Treatment model an overflow is shown for flows
in excess of design capacity. This overflow is combined with the treated
effluent, and the model computes both the quantity and quality of the
effluent discharged to the receiving waters.
The model includes all of the alternative processes considered applicable
at this time, and the engineer will have to select, for each particular
location, the process to be modeled. For example, treatment by fine
screens followed by high rate filters and disinfection of the effluent
with bar racks and pumping ahead of treatment would be obtained by the
selection of route 12-22-34-43-51-61-72 through the model.
Chlorine would be added ahead of the contact tank. The quantity and
quality of inflow to and outflow leaving each level of treatment, as well
as the quantity and quality of the flow released to the receiving waters,
are computed for each time-step. The Baker Street combined sewer overflow
facility in San Francisco (EPA Project No. 11023 DXC), which is one of
the catchment areas used for verification, would be modeled by selection
of route 12-21-32-41-51-61-71 with or without chemicals and/
or chlorine added ahead of the dissolved air flotation tank.
It will also be necessary for the engineer to select a design storm
event so that the model can select the number and size of units of each
type required by the process selected.
249
-------
NO STORAGE
PRECEDING
(BYPASS)
OVERFLOW
NONE
(BYPASS)
NONE
(BYPASS)
(
(BYPASS) (31)
DIS
Fl
INFLOW
1
T
STORAGE
(01) MODEL
PRECEDING
f
*
C START )
1
*
(H) BAR RACKS
i
,,n INLET
t21' PUMPING
*
|-» — CHEM
*
32) (FINE SCREENS)
(33)
i
SOLVED AIR (34) t
.OTATION "" ISEDIM
I
J* — CHEM
(BYPASS) (41)
1
MICRO- U2, HIG
STRAINERS v ' FIL'
T
*
NONE
(BYRftSS)
NONE
(BYPASS)
T
/.,» EFFLUENT
l5" SCREENS
+
,T .
(61) OUTLET
PUMPING
*
«• — CHEM
NONE
(BYPASS)
,, f ,.
m, CONTACT
171 ' TANK
t
J
1
(02)
(12) LEVEL 1
(22) LEVEL 2
(35)
ENTATION [ LEVEL 3
T^
1(43)
H RATE LEV£L 4
FERS
""T
(52) LEVEL 5
(62) LEVEL 6
[72) LEVEL 7
RECOMBINED OUTFLOW
NOTE: Numbers in parentheses label treatment options.
Figure 15-1. TREATMENT MODEL
250
-------
The design of the plant is based on combinations of modules of specific
sizes, resulting in plants having the following maximum hydraulic
capacities in mgd: 5, 10, 15, 20, 25, 30, 35, 50, 75, 100, 125, 150,
200, 250, 300, 350, 400, 450, and 500. The engineer will select the
percentage of the peak flow of the design event for which he wishes to
size the units (80 percent is suggested), and the model will automatically
size the plant for the next larger modular flow from the above list.
Alternatively, the engineer may select a design flow irrespective of the
storm to be handled, and the model will design the plant for the modular
flow equal to or (next) greater than the selected flow. After the model
has computed the number and size of units, it can be used to compute the
operating performance for any storm or succession of storms in a given
study period.
The model will sum up the flow treated, the BOD, suspended solids, and
coliforms in the influent and effluent of the complete combination of
treatment processes, and the removals in each level of treatment. It
will compute the treatment efficiency with and without allowance for
overflow quantities bypassing the treatment units. It will also compute
the construction cost, including the cost or value of the land required
and the annual cost of operation and maintenance.
PUMPING STATIONS
The need for pumping stations will depend on the topography and the
available head. It is assumed that sufficient variable speed pumps are
included in each pumping station so that the rate of pumping will exactly
equal the inflow rate. The inclusion or omission of a pumping station
251
-------
will therefore have no effect on the hydrograph and pollutographs of the
flows to be treated. The size of the pumping station necessary to handle
the design event, the head, and the quantity pumped must be computed so
that the costs can be determined.
THEORETICAL DEVELOPMENT (Treatment Processes)
The following discussion of the various treatment processes will include
the criteria adopted for selecting the number and size of units, and the
operating efficiency adopted for each process, together with the basis
therefore. (For the actual working of each model subroutine see the
"User's Manual." For the cost figures incorporated in the model, see
Section 16. )
Bar Racks (Treatment Option 12)
It was assumed that bar racks would be required in all treatment systems,
except where sedimentation occurring in storage units is the only or
primary treatment. The Treatment model handles the latter process by
selection of route 02 - 11 - 21 - 35 which may be followed by filtration
or microstraining and disinfection.
It was assumed that bars would be spaced from 1-inch clear opening to
2-inches on centers, and that the racks would be mechanically cleaned
with operation initiated by a float switch. There will be at least two
units in each installation, so that if one unit is undergoing maintenance!
at least half of the flow capacity and probably somewhat more will be
available at all times. Units will be sized for a 3.0-fps velocity in
the approach channel at peak design flow and will be installed at a
252
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slope of 1 horizontal on 2 vertical. Channels will be designed for
2-feet freeboard. It was assumed that the maximum size of units would
be 8 feet submerged depth by 10 feet wide, or a vertically projected
submerged area of 80 square feet. This results in a maximum capacity per
bar rack of 240 cfs.
The quantity of screenings removed is based on screenings removal at
municipal sewage treatment plants. Screenings removal varies from 0.1 to
5 cubic feet per million gallons (Ref. 1), but very few cities report
more than 2.5 cubic feet per million gallons. For purposes of this
study, 2.0 cubic feet per million gallons has been taken as a liberal
average. These are annual average results, and it is a well known fact
that the quantity of screenings increases greatly during storms,
especially for combined sewer systems. It is not known whether the
proportion of screenings in the overflows will be as great as in the
intercepted flows, but to be on the safe side it has been assumed that
they will. A factor of 3 has been used to allow for the greater quantity
of screenings in storm flows, or 6 cubic feet per million gallons.
If it is assumed that screenings weigh 50 pounds per cubic foot and con-
tain 85 percent moisture, the dry solids removal amounts to 5.4 mg/L.
Solids of this type are generally excluded from samples subjected to
suspended solids analysis. Nevertheless, in order to indicate some
treatment effectiveness, 5.4 mg/L has been used for suspended solids
removal and 5 percent of that figure has been used for BOD removal.
253
-------
Fine Screens (Treatment Options 33 and 34)
Fine screens, popular as an alternate to sedimentation tanks 50 years
ago and still in use in some locations such as Milwaukee, have slotted
holes varying from 3/64-inch to 1/8-inch wide by 2 inches long. A num-
ber of manufacturers have been making rotary drum screens for industrial
processing, including the screening of industrial waste waters before
discharge. These screens are similar to the well publicized microstrainer
but with a coarser wire mesh. The screen wire normally available varies
from 6-mesh to 60-mesh. The openings in the 60-mesh wire are .009 inch,
equivalent to 230 microns. It is anticipated that fine screens of this
type could provide economical treatment of storm water overflows. A
pilot plant (EPA Project No. 11023 FDC) containing such a screen with
50-mesh wire (openings equal to 297 microns) has been operated on storm
overflows in Milwaukee in combination with a dissolved air flotation unit
(Ref. 2) and has provided significant data for both processes, individ-
ually and in combination. The modeling of the fine screens is based
almost entirely on the data in Ref. 2.
The pilot plant (Ref. 2) was operated at a hydraulic loading rate of
50 gpm per square foot and this rate has been adopted for sizing tne
units. At least two units would be installed, with the total capacity
of all units equalling the design flow for the modular plant.
The removal of suspended solids by the screen in Ref. 2 varied from
24.9 +_ 9.8 percent during the summer and fall to 28.8 +_ 10.5 percent
in the spring. The removal of BOD varied from 20.3 + 6.5 percent in the
254
-------
summer and fall to 23.4 +_9.3 percent in the spring. Sufficient data
are not available to correlate removal efficiency with storm water
quality. Removal efficiency will undoubtedly vary with the size distri-
bution of solids, and hence possibly with the time of flow in the sewers.
For the present, the Treatment model assumes an average removal of 27
percent of the suspended solids and 22 percent of the BOD. The backwash
rate has been assumed to be 0.75 percent of the flow. This flow will be
pumped or will flow by gravity to a sanitary sewer or interceptor for
transportation to the sewage treatment plant.
Sedimentation (Treatment Option 35)
Sedimentation in sedimentation tanks or storage units is an obvious way
to improve the quality of sewer overflows. The sizing of sedimentation
tanks and their treatment efficiency depends primarily on the overflow
rate. Similarly, the treatment efficiency due to sedimentation in storage
units will depend primarily on the overflow rate, but the overflow rate
in this case will be based on the design of the basin as a storage unit
and not as a sedimentation tank. Types of flow and pollutant increments
through larger storage units are discussed in Section 9.
Primary sedimentation tanks in municipal sewage treatment plants were
formerly designed for detention periods of one to two hours, but if the
depth is fixed, the overflow rate is also fixed. Regulatory agencies
now limit overflow rates to 600 gpsf per day for small plants (less than
1.0 mgd), but permit up to 1,000 gpsf per day for larger plants where
the tanks are followed by secondary treatment units. Since the maximum
flow at sewage treatment plants normally varies from 1.5 to 2.0 times the
255
-------
average design flow and may be as high as 2.5 to 3.0 times the average
design flow, especially at small plants, it is logical to increase the
overflow rate for tanks designed on a peak flow basis. The Treatment
model provides for selection of the overflow rate by the engineer. An
overflow rate of 800 times 2, or 1,600 gpsf per day is suggested. An
average tank water depth of 8 feet is assumed.
The removal of suspended solids decreases as overflow rates increase
(Ref. 1, p. 93) and as detention periods decrease (Ref. 3, p. 338, and
Ref. 4, p. 610). It is also evident from Ref. 3 that the removal
efficiency increases as the strength of the sewage increases.
The data in Tables 9, 10, and 11 of Ref. 1 were plotted with percent
removal of suspended solids as ordinates versus overflow rates as
abscissas. Figure 15-2 is a plot of only those tanks with influent
suspended solids concentration between 100 and 200 ppm. The average
removal is given by the following equation:
>,«/ -300.
Removal = .70 - .40( ^
where OVFRA = Overflow rate in gpm/sq ft/day
If the percentage removals for more concentrated sewages are plotted on
similar diagrams, the average removal curves are displaced upward
parallel to the line on Figure 15-2. The additional removal amounts to:
(S5 cone. - 140} x ^ Qr S3 conc.^x .06 _ ^ (2)
256
-------
.90
.80
.70
.60
CO
CO
U. .50
UJ
cc
.40
.30
.20
.10
\
Ui
"1
0
I-
§
Ul
0.
o
°z
2
o
°0
\
o
CO
^-ASSUMED MAX REMOVAL
/ 0
O
\ ^-R
\
O
O
o
o
:MOVAL= .7<
(KM
INI
V
\^
N.
O^v
O
o
)-.40(OVFF
2,0
>-200 PPW
rLUENT )
\
tA- 300)
DO
SS IN
^SUGGESTED
^ OVERFLOW RATE
FOR DESIGN
FLOW (MAX)
\
\
O
\
\
^ASSUMED
MIN 1
REMOVAL
0 500 1,000 1,500 ^000 2,500
OVERFLOW RATE (GPM/SQ FT/DAY)
Figure 15-2. TREATMENT OF OVERFLOWS BY SEDIMEN-
TATION TANKS
257
-------
When Eq. 2 is combined with Eq. 1 the formula for removal of suspended
solids becomes:
SS cone. X .06 ^,QVFRA - 3QOt ...
Removal = 0.656 + - — -- .40( - 2~0(}0 -
Eq. 3 has been incorporated into the model for the determination of sus-
pended solids with the following limitations: the overflow rate will be
assumed to be at least 300, and the removal efficiency will be not less
than 0.30 nor more than 0.76. It is assumed that scour of already
deposited solids will not be a problem.
The percentage of BOD removed is assumed to be 0.55 times the removal of
suspended solids. Inspection of the BOD removal data in Tables 9, 10,
and 11 of Reft 1 and on p. 610 of Ref. 4 substantiates this assumption.
If chlorine is applied ahead of the sedimentation tanks, the removal of
BOD will be increased. It has been assumed that the increase will amount
to 20 percent, resulting in a BOD removal of 0.66 times the suspended
solids removal .
The sludge volume removed has been based on a solids content of 5 percent,
and also on a minimum sludge pumping rate of 45 gpm (0.1 cfs) . The
sludge is assumed to be pumped continuously to a sanitary sewer or inter-
ceptor for transport to the sewage treatment plant.
The efficiency of the sedimentation tanks has been based on the efficiency
of similar tanks in municipal sewage treatment practice. Somewhat differ-
ent results may be obtained from sedimentation tanks installed at the
outlet of storm drains, especially where soil erosion is a factor.
258
-------
For combined sewers where soil erosion is not a factor, the data used
appear to be applicable without further adjustment.
Dissolved Air Flotation (Treatment Option 32)
A dissolved air flotation plant is under construction on the Baker Street
outfall into San Francisco Bay. When operating data from this facility
become available, the following determination of the treatment efficiency
of dissolved air flotation units should be reviewed and revised if neces-
sary. The plans and specifications as well as the engineers' preliminary
reports for this project were made available for this study. The facility
is designed to handle 15 percent of the peak flow from a five-year storm,
or a runoff rate of 0.20 inches per hour at an overflow rate, not
including a recycle flow of 4,050 gpsf per day. The flotation tanks
will be preceded by mechanically cleaned bar racks, and excess flows
will be bypassed. Facilities will be installed for the addition of
chemical coagulants and chlorine.
The data in Ref. 2 for the combined operation of fine screens and dissol-
ved air flotation has also been useful. Based on Ref. 2, the fine screens
removed 27 percent of the suspended solids and the dissolved air flotation
process removed 33 percent of what was left, for an overall removal of
51 percent. Since the dissolved air flotation tank would contain sludge
removal equipment as well as scum removal equipment, it was assumed that
the same percentage of removal would be obtained without the fine screens
at the cost of somewhat more air and possibly a slightly greater recycle
rate. This efficiency was attained in the pilot plant at an overflow
rate of 3 gpm per square foot (4,320 gpsf per day) with no recycle.
259
-------
(A portion of the effluent from the fine screens was pressurized instead
of recycled flotation tank effluent. Recycling may be more practical in
a full size plant.) No tests were made at other overflow rates but
additional tests at higher rates of flow are contemplated.
The model allows the engineer to select the overflow rate based on design
flow plus recirculation, the percent of recycle flow, and the tank depth.
An overflow rate of 5,000 gpsf per day, 15 percent recycle, and a tank
depth of 10 feet are suggested for normal design.
It was assumed that the removal efficiency would be comparable to the
removal efficiency of plain sedimentation tanks, but that this efficiency
would be obtained at higher overflow rates due to the rapid rise of the
air bubbles. Since the 51 percent removal reported for the pilot plant
of Ref. 2 at an overflow rate of 4,320 gpsf per day is obtained (in
plain sedimentation tanks treating 100-200 ppm suspended solids at an
overflow rate of 1,250 gpsf per day), we have used the percentage
removals for plain sedimentation, but for overflow rates equal to
4,320/1,250, or 3.5 times the rates for plain sedimentation. This leads
to the following equation for the removal of suspended solids:
Removal = 0.656 + SS <*** '°6 - .40( ') (4)
In using Eq. 4 and the following modifications a minimum overflow rate
of 1,000 gpsf per day is assumed by the model.
The addition of chemicals increased the overall removal of suspended
solids from 51 percent to 68.3 percent (Ref. 2). The actual removal
260
-------
can be expected to decrease as the overflow rate increases, To allow
for this factor, the increased removal due to chemicals was assumed to be
n 20 - OVFRA x *
°'20
10,000
or 15 percent at an overflow rate of 5,000 gpsf per day. This can be
simplified to
20,000 - OVFRA .,.
( 100,000 ;
and this term has been added to the removal equation when chemicals are
added. The complete equation becomes
__RPMV _ „-, .06 x SSINF OVFRA - 1,000 Trnr,1f 20,000 - OVFRA
SSREMV - .656 + ~ -- .40( - ^-^ - )+ ICHEM( 100/000 )
(7)
where SSREMV = Suspended solids removed
SSINF = Suspended solids in inflow
ICHEM = 0 if no chemicals are added
ICHEM = 1 if chemicals are added
The amount of chemicals added is computed at 12 mg/L, based on Ref . 2.
Regardless of the equations the model will restrict the removal of
suspended solids to not less than 0.20 and not more than 0.82.
The reported results in Ref. 2 indicate a BOD removal without the
addition of chemicals of approximately 90 percent of the suspended solids
removal. If chemicals are added the increase is only 2 percent. The
chemicals would have little effect on the soluble BOD. If chlorine is
added about 2 ppm of BOD is eliminated per 1 ppm of chlorine used up.
261
-------
It is assumed that this will amount to an average increase in BOD removal
of 15 percent. Adopting the above as the basis for BOD removal; the
following equation is obtained:
BODREM = .59 4- '°5 ' - . 36 (') + ICHEM x .02
ICL2 x .15 (8)
where ICHEM and ICL2 equal 1 or 0, depending on whether or not
chemicals and/or chlorine are added. In order to keep the percentage
removals of BOD within practical limits for all contingencies, the
model restricts the BOD removal (BODREM) to not less than 0.18 and not
more than 0.60.
The amount of chlorine used is taken at 10 mg/L if the BOD of the influent
is 130 or less, and at 15 mg/L if it is more.
The volume of sludge and scum is taken equal to 1.5 percent of the flow
(Ref . 2) . This will be pumped to a sanitary sewer or interceptor for
transport to the sewage treatment plant.
The detention time in the flotation tank will be computed and if it is
less than 15 minutes it will be used in subroutine KILL to compute the
removal of coliforms. (See Chlorination discussion.)
Dissolved Air Flotation Preceded by Fine Screens (Treatment Option 33)
For the combination of fine screens followed by dissolved air flotation
it has been assumed that the fine screens would perform exactly as des-
cribed earlier, i.e., they would remove 27 percent of the suspended
262
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solids and 22 percent of the BOD, regardless of the flow rate or concen-
tration of pollutants.
Since tests of this combination of processes in Ref. 2 were used to es-
tablish the performance of dissolved air flotation alone at an overflow
rate of 4,320 gpsf per day, it follows that the overall efficiency of
removal predicted by the model should be the same in treatment option 33
with fine screens as in treatment option 32 without fine screens at an
overflow rate of 4,320 gpsf per day. However, since part of the suspen-
ded solids and BOD has been removed by the fine screens, a different
removal efficiency must be applied to the fine screen effluent. No test
results of the combination at other overflow rates are available, but it
is reasonable to assume that the overall results of the combination would
vary with the overflow rate in about the same manner as for dissolved air
flotation alone. Accordingly, the equations for suspended solids and
BOD removal for dissolved air flotation alone were adjusted to give
approximately the same overall removals at overflow rates of 1,000 and
4,320 gpsf per day, when combined with the removals by the fine screens.
To obtain comparable removal efficiencies it was also necessary to limit
the minimum overflow rate to 1,000 gpsf per day as before, and to impose
reasonable limits on the maximum and minimum values of suspended solids
and BOD removal whether or not chemicals and/or chlorine are added.
263
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The resulting equations, to be applied to the effluent from the fine
screens, are as follows:
SSPEMV = 0.528 + SS ""^ '°6 - 0.486 (OWR^'000) +
(9)
. 0.475 + . cone.
(10)
ICHEM x 1.30 x 0.02 + ICL2 x 1.30 x 0.15
where ICHEM = 1 if chemicals are applied and 0 if chemicals are not
applied
ICL2 = 1 if chlorine is applied and 0 if chlorine is not
applied
Regardless of the above equations, the model will limit the suspended
solids removal to not more than 75 percent and not less than 15 percent,
and the BOD removal to not more than 48 percent and not less than 15
percent.
In comparing the performance of dissolved air flotation tanks with and
without fine screens ahead of them, different overflow rates and recir-
culation rates may be assumed for the two cases.
Micros trainers (Treatment Option 42)
A micros trained consists of a rotating drum covered with screen cloth
operating partly submerged in a concrete tank. The water enters one
end of the drum and flows outward through the screen cloth. As the drum
264
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revolves the solids caught on the inside of the cloth are carried to the
top of the drum where they are washed into a trough by high pressure jets
of strained effluent and discharged to waste. Microstrainer screen cloth
comes in three mesh sizes, designated Mark 0, I, and II with effective
aperture sizes of 23, 35, and 60 microns. Developed originally in
England for straining algae out of water supplies, microstrainers have
been used in England for polishing sewage treatment plant effluents
since 1950 (Ref. 5), and have recently been undergoing tests in this
country to determine their suitability as tertiary treatment units on
activated sludge effluents at Lebanon, Ohio (Ref. 6), and Chicago
(Ref. 7).
Under a contract with the EPA a microstrainer with a diameter of 5
feet and a length of 3 feet was installed on the overflow of a combined
sewer serving the 11.2-acre Callowhill residential area in Philadelphia.
Preliminary data are contained in Ref. 8. This filter had a submerged
area of about 30 square feet, and the individual capacities of the pumps
supplying the filter were 5,000 and 12,000 gph for a combined capacity
of 17,000 gph or 284 gpm, roughly equivalent to 9.5 gpm per square foot
of submerged area. Initial tests were made with Mark I cloth, but
Mark 0 cloth was substituted after six months resulting in greatly
improved efficiencies. No difficulties due to plugging of the screen
were experienced with either cloth.
At Lebanon, a microstrainer with a diameter of 5 feet and a length of
1 foot was operated on activated sludge effluent for a period of five
months. Capacity at a 6-inch head loss was 3.8 gpm per square foot of
265
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total area for the Mark 0 cloth and 4.5 gpm per square foot for the
Mark I. These are based on a filterability index, I = 17.0, for
both cloths corresponding to a suspended solids concentration of 25 mg/L
in the influent for the Mark 0 cloth and 35 mg/L for the Mark I. The
peripheral speed of the drum was 50 fpm.
At the Hanover plant of the Metropolitan Sanitary District of Greater
Chicago (Ref. 7), a full size microstrainer with a diameter of 10 feet
and a length of 10 feet was installed with Mark 0 cloth. This unit was
built for a maximum head loss of 6 inches and a hydraulic loading of
6.6 gpm per square foot of total screen area equivalent to about 10 gpm
per square foot of submerged area. The maximum solids loading of secon-
dary effluent handled by the microstrainer was 0.88 psf per day equivalent
to 11.1 ppm at the maximum flow of 6.6 gpm per square foot. On the
other hand, the unit was able to handle a synthetic mixture of effluent,
fortified with activated sludge at a rate of 3.8 psf per day, which is
6.8 gpm per square foot at 50 ppm solids concentration. This type of solids
will filter much more readily than the pinpoint type of floe typical of
secondary effluents. This fact must be kept in mind in applying the
Callowhill results generally to the treatment of storm water overflows.
There are at least four manufacturers of this type of equipment using
screen cloth with apertures of about 25 microns. The term "Microstrainer"
is the copyrighted trade name of the Glenfield and Kennedy Division of
the Crane Company. A scanning of the hydraulic capacities quoted in the
trade literature yields figures varying from 4.6 to 28 gpm per square
foot of total area, equivalent to 8 to 45 gpm per square foot of
266
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submerged area. Head losses range up to 30 inches, with 6 to 12 inches
recommended. All literature contains statements to the effect that the
capacity of the unit depends on the type of media (screen cloth) used,
and the concentration and characteristics of the solids to be removed.
In sharp contrast to the Chicago and Lebanon data, the Callowhill results
indicate that the microstrainer with Mark 0 cloth successfully handled
suspended solids concentrations varying from 21 to 498 ppm and averaging
169 ppm. The peak flows and high concentrations were of short duration
and the flows were not given. However, it was found possible to increase
the flow per square foot fivefold by blanking off 80 percent of the area,
thus increasing the differential head up to 30 inches. The actual flow
rates for this condition were not given, but if both pumps were used, a
flow rate of 47.5 gpm would have been possible. The explanation for the
great difference in these results and those in Chicago and Lebanon would
appear to be in the character of the suspended solids. For an area as
small as 11 acres, the sewage would undoubtedly be fresh and would con-
sist of discrete particles that had not had time to disintegrate. This
would not be the case with large areas for which an adjustment factor is
included in the model.
The above contrasts have made the sizing and performance estimates for
the microstrainers difficult. The Callowhill data have been relied
upon primarily but theoretical computations based on Chicago and Lebanon
and other data have been used as a check. From Ref. 7 it was learned
that the suspended solids removed would plot as a straight line versus
the suspended solids in the influent. These data for Mark 0 cloth from
267
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Table 1 of Ref. 8 have been plotted on Figure 15-3. The straight line,
drawn -by eye, has the equation
y = x - 35 (11)
where y = Suspended solids removed .(ppm)
x = Suspended solids in influent (ppm)
Since this equation would yield zero removal for influent suspended
solids less than 35 ppm, it was restricted to suspended solids equal to
or greater than 70 ppm. A parabolic curve having the equation
was inserted between the origin and x = 70. Eqs. 11 and 12 are incor-
porated in the Treatment model for determining the suspended solids
removal of the flow through the screen cloth. They give no hint as to
the capacity of the unit.
For determining capacity, other considerations were necessary. First,
for economical reasons, as large a capacity as possible was desired,
say 40 gpm per square foot of submerged area. This is about half the
capacity of the 50 gpm per square foot of total area used for sizing the
fine screens. It is four times the capacity of the Chicago unit and six
times the capacity of the Lebanon unit, and approaches the maximum
pumping rate possible at the Callowhill unit with the screen area reduced
80 percent. It was realized that this unit would have to be designed
for a 30-inch differential head. It was also anticipated that the
capacity might be reduced at high solids concentration with part of the
268
-------
Q
LLJ
LJ
o:
CO
CO
*J\J\J
Af\f\
*HJw
"v^n
\j\j\j
200
inn
i \j\j
Q
CM O
x ^-
*•
"
o
UJ
m
1
O
m
<
oa
x/»
V y^~
^7
~*^r /
O
°X
/
y
/
x. /* o
/°
y
./ 0
^r
/
/
/
/
/
X =70
/
"/
-STRAIGHT
>
' LINE,
SLOPE = 1.0
EQ: Y=X-35
1 JCT OF 2 EQUATIONS'- Y = 35
SLOPE = 1.0
0 IOO 2OO 300 4OO 5OO 6C
SS IN INFLUENT (MG/L)
LEGEND
6-15-69 TO 7-23-69
O CONTROL CHANGE - MAX DIFFERENTIAL INCREASED
7-28-69 TO 8-4-69
X FILTER AREA REDUCED 80% 9-3-69
Figure 15-3.
MICROSTRAINER AT CALLOWHILL (PHILADELPHIA),
J!4ARK O SCREEN CLOTH
269
-------
flow bypassing the unit. The throughput of the unit should therefore be
made dependent on the solids concentration and also a factor denoting
the composition and condition of the solids.
The head loss through the microstrainer is given by the following equation:
H -- - - (13)
where H = Head loss (in.)
Q = Constant total flow rate (gpm)
C_ = Initial (clean) strainer resistence (ft as measured
in filterability test)
A = Effective submerged area (sq ft)
S = Speed of strainer in effective fabric area entering
water (sq ft/min)
I = Filterability index
m and n = Constants with values dependent on the units used
(for the above units, m = 0.0267 and n = 0.1337)
It will be seen from Eq. 13 that the head loss is not a simple function
of Q, that it increases as the filterability index increases, and that
it decreases as the speed of rotation increases (S increasing) .
Based on the Lebanon data (Ref. 6) and its filterability index, I = 17.0,
the flow was computed at various heads as a ratio to the flow Q at a
head loss of 6 inches. Then the index was reduced successively to 10,
5, 3, and 1 and the flow was computed at various head losses. The results
are shown on Figure 15-4. The filterability is the reciprocal of the
270
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BASIS: SEWAGE TREATMENT PLANT EFFLUENT
LEBANON, OHIO, 5 FT DIAM x I FT LONG TEST UNIT
Q, = 58 GPM —•• 58/9 = 6.45 GPM/SQ FT OF SUBMERGED AREA
PERIPHERAL SPEED = SO FPM
S =44.5 SQ FT/MIN
to
PROPOSED MICROSTRAINER RATING
40 GPM AT 30 IN. HEAD LOSS
EQUIV. I = 2.43
LEBANON, OHIO
RATING POINT
I = FILTERABILITY INDEX
HANOVER PARK
RATING POINT
Z 4 6 8 10
Q2/Q| (Q|=6.45 GPM/SQ FT OF SUBMERGED AREA)
Figure 15-4. MICROSTRAINER CAPACITY, MARK 0 SCREEN CLOTH
-------
filterability index, and it will be noted that as I decreases, the
advantage of operation at greater heads increases. The proposed oper-
ating point for the Treatment model and for Chicago and Lebanon plants
is shown.
Figure 15-5 shows the capacity at a 30-inch head versus the filterability
index I and versus the filterability I/I. The following equation has
been fitted to these curves:
169 (14)
y + 1.8
where x = Capacity (gpm/sq ft submerged area)
y = Filterability index, I
Eq. 14 gives I = 2.43 for the proposed rating point. Since there were
no known measurements of I on storm overflows there was no direct method
of checking this figure. It is included for comparison with test results
which undoubtedly will become available in the future.
A millipore filter with a pore size of 8.0 microns has a capacity to
filter 37 gpm per square foot of clean water at 25°C and at 30-inch head
loss, which is almost double the capacity of the next smaller pore size
filter (5.0 microns). This would appear to indicate that 40 gpm per
square foot is attainable as a reasonable maximum.
The maximum solids concentration compatible with a capacity of 40 gpm
per square foot was estimated in the following manner. At Hanover Park
in Chicago the maximum solids loading of the applied effluent was 0.88
psf of total area per day, of which 65 percent was removed on the average.
272
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FILTERABILITY =1/1
FILTERABILITY INDEX T_
FITTED EQUATION:
169
Y -»- 1.8
WHERE
X s CAPACITY
Y s I
Figure 15-5. MICROSTRAINER CAPACITY AT 30-INCH HEAD LOSS,
MARK 0 SCREEN CLOTH
273
-------
This amount-s to 0.000092 psf per revolution. However, as noted earlier,
the microstrainer handled a synthetic mixture of effluent fortified with
activated sludge at a rate of 3.8 psf per day. Using this figure as
more representative of the solids in storm water overflows and assuming
65 percent removal as above, the solids accumulation becomes 0.0004 psf
per revolution. Assuming 1 percent solids in the sludge film, the
thickness of the mat equals 0.0077 inch. Now, if it is assumed that
the solids in storm overflows consist of 10 percent organics and 90 per-
cent silt, and that the 10 percent organics constitute a sludge with
96 percent moisture content filling the pores of the silt, the mixture
has a specific gravity of 1.15 of which 29.4 percent is dry solids. The
same thickness of mat, 0.0077 inch, of this material would contain
0.0135 pounds of suspended solids per square foot per revolution.
Microstrainers are assumed to have a capacity of either 5.0 mgd each for
the smaller plants or 12.5 mgd each for the larger modular plants. At
40 gpm per square foot of submerged area, (12.5 x 695)/40 or 217
square feet are required, equal to 69 percent of the total area of a
microstrainer with a diameter of 10 feet and a length of 10 feet. At
4.3 rpm, 40 gpm per square foot of submerged area, and 69 percent sub-
mergence, 0.0135 pound of solids per square foot per revolution is
equivalent to a removal of 252 mg/L. Multiplying this by 40 gpm per
square foot gives 10,100, or say 10,000, as the product of gpm per
square foot and suspended solids removal in mg/L. From this, the follow-
ing equation for the capacity of the unit in terms of the removal of
274
-------
suspended solids in mg/L is obtained:
10,000 x F
gpm/sq ft submerged area = ss removal in mg/L
When the inflow suspended solids equals 287 ppm, Eq. 15, combined with
the removal efficiency, gives a capacity of 40 gpm per square foot for
F = 1.0. The model restricts the flow rate to not over 40 gpm per square
foot of submerged area regardless of the solids concentration. If the
solids concentration is so great that all the flow cannot be strained,
part is bypassed and the overall performance is computed by the model.
F is introduced into Eq. 15 to allow for the effect of comminution and
disintegration of the solids due to time of flow in the sewers. It has
a maximum value of 1.0. The following is suggested for the value of F,
subject to future pilot plant verification on large drainage basins,
and is incorporated in the model:
V
400 (16)
area in acres
The value of F is suggested on the basis that no reduction" would be
necessary until the drainage basin exceeded 400 acres, and that then the
reduction would be in proportion to the time of flow assumed proportional
to the square root of the area.
The rate of backwash at Lebanon and at Chicago was 2.5 to 3.0 percent of
the smaller flows treated, or approximately 50 gpm for a full size unit.
It has been assumed that no greater quantity of wash water would be
required, since this amounts to 5 gpm per linear foot of filter.
275
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The backwash water rate has been rounded off to a constant flow of 0.1
cfs per microstrainer which will be pumped or will flow by gravity to
a sanitary sewer or interceptor for transport to the sewage treatment
plant.
With the operating performance determined on the basis of suspended
solids, the remaining task was to compute the BOD removals. At Hanover
Park, BOD removals were as good or even better than suspended solids
removals, and at Lebanon they were about 90 percent of the suspended
solids removal. On the other hand, the removals at Callowhill were
erratic; many negative values were obtained. This may have been due to
disintegration of the solids during pumping. The BOD removals at Callow-
hill cannot be used as a basis for the model.
On the other hand, excellent data were obtained at Callowhill on the
removal of volatile suspended solids. BOD versus volatile suspended
solids were plotted in the storm flows of the Laguna Street sewer in
San Francisco for the storms of March 10 and March 15, 1967, reported
by Engineering-Science (Ref. 9). The BOD was found to equal 80 percent
of the volatile suspended solids. The removals of volatile suspended
solids versus the volatile suspended solids in the influent were plotted
as given in Table 3 of Ref. 8. The straight line equations obtained
were multiplied by 0.8 to convert to BOD. The following equations were
obtained and incorporated in the model:
BOD removed (ppm) = BOD in influent (ppm) - 10.0, if the BOD in the
(17)
influent is equal to or greater than 27 ppm
276
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BOD removed (ppm) = 17.0 x BOD in influent (ppm)/27.0, if the BOD
(18)
in the influent is less than 27 ppm
Due to the form of Eqs. 11, 12, 17, and 18, there would be no improve-
ment in the suspended solids and BOD concentrations in the effluent from
the microstrainers if the flow is given primary treatment in Level 3
unless the suspended solids and BOD concentrations in the influent to
the microstrainers were reduced below 70 and 27 mg/L, respectively.
However, in the case of heavy concentrations of suspended solids or large
drainage basins, primary treatment in Level 3 could eliminate or greatly
reduce the amount of flow bypassing the units, thus resulting in consid-
erable overall improvement of the effluent.
High Rate Filters (Treatment Option 43)
Various types of rapid filters are being investigated for tertiary
treatment of sewage plant effluents and for the treatment of overflows
from storm and combined sewers. At Hanover Park in Chicago (Ref. 7) two
Hardinge automatic backwash filters were installed to test their appli-
cability for treating activated sludge plant effluent. They were oper-
ated in parallel with the microstrainer. Each filter contained 11 inches
of sand, with an effective size of 0.58 millimeters and a uniformity
coefficient of 1.62, supported on porous plates. These filters were
operated with and without chemicals at a capacity of 2.5 gpm per square
foot for a low head of 4.4 inches and at a capacity of 6 gpm per square
foot for a high head of 11.5 inches. Suspended solids removals varied
from 65 to 78 percent. The maximum solids removal at the higher rate
277
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was 0.65 psf per day equivalent to 9 ppm. The backwashing cycle takes
30 minutes to clean the whole bed, a narrow strip at a time.
For economical treatment of sewer overflows, considerably higher flow
rates are desirable. Higher rates will require higher operating heads
and coarser media. To obtain good efficiencies and large solids holding
capacity, multiple media filters with a greater overall depth will
probably be required. If the automatic backwash filter can be modified
along the above lines to triple its capacity while maintaining good
efficiency, it would be an ideal unit for this service.
In Washington, D.C., (Ref. 10) a synthetic storm overflow wastewater,
developed by diluting domestic sewage and adding clays and silts to
provide a waste comparable to combined sewer overflows analyzed at the
time, was filtered through three laboratory filters. Each filter con-
sisted of a 9-foot jointed glass pipe with an inside diameter of 4 inches.
One filter contained fiber glass. A second filter contained 36 inches of
anthracite, 24 inches of a garnet sand mixture, and 3 inches of coarse
garnet supported on 9 inches of gravel. The third filter consisted of
48 inches of medium garnet and 9 inches of coarse garnet supported on
9 inches of gravel. It was designed and operated as an upflow filter,
and performed reasonably well at flow rates between 5 and 15 gpm per
square foot with suspended solids removals of 60 percent and BOD removals
of 45 percent. At filtration rates exceeding 15 gpm per square foot the
efficiency dropped sharply, as would be expected for this type of
filter.
278
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The second tri-media filter was operated as a downflow filter at a rate
of 10 gpm per square foot. Runs lasted two hours with suspended solids
removals of 80 to 95 percent and BOD removals of 50 to 80 percent. The
higher rates were obtained with chemical additions, 150 mg/L of alum
and 4 mg/L of flocculant aid. The same efficiencies were maintained at
rates up to 20 gpm per square foot, but filter runs were shortened to
one-half hour.
The fiber glass filter performed remarkably well at rates between 15 and
50 gpm per square foot with suspended solids removals in the range of 87
to 95 percent and BOD removals ranging from 60 to 75 percent; however,
severe backwash problems were encountered. Runs lasted from one-half to
one hour with 750 to 1,000 mg/L of suspended solids in the influent.
Further tests of this filter should be made in a pilot plant of adequate
size to determine design criteria and plant scale operating performance.
Until such data are available, design estimates should be based on more
conventional units, similar to the tri-media filter.
Pending further tests of the applicability of high rate filters to the
treatment of storm and combined sewer overflows, a flexible program has
been developed which will permit the engineer to select the following
filter parameters:
1. Maximum flow rate, gpm per square foot
2. Maximum head loss
3. Holding capacity, pounds of dry solids per square foot at
maximum rate and maximum head loss.
279
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Initial values of these parameters are suggested in the following dis-
cussion and have been incorporated in the model.
Based on the tri-media filter described above, a design capacity of not
more than 20 gpm per square foot and preferably less should be selected
for sizing the units at the design flow. Each installation will contain
an even number of units, not less than four. This will permit taking
a unit out of service for backwashing. Maximum size of filter units
will be 1,400 square feet, each with a maximum capacity of 40 mgd or
62 cfs.
A maximum head loss not greater than 10 feet is suggested.
Assuming that the water applied to the tri-media filter contained 750
mg/L of suspended solids of which 80 percent were removed and that a
half-hour run at 20 gpm per square foot was feasible before backwashing,
the solids removed by the filter amounted to:
20 JffiS- x 30 min x 750 =3. x 0.80 x ^ ***' = 3.0 psf (19)
sq ft L . .6 mg/L
It is suggested that this value or a lesser figure be taken as the
holding capacity of the filter.
The suspended solids removal of the ripened filters has been taken at 80
percent without chemicals and 95 percent if coagulating chemicals are
used. The BOD removal has been taken at 50 percent without chemicals
and 80 percent with chemical additions. These removals are based on Ref. 10.
280
-------
To allow for reduced efficiencies of clean filters, both efficiencies
have been reduced by one-half when filters are first placed in service,
and are allowed to increase uniformly with the pounds of suspended solids
removed until 5 percent of the filter holding capacity has been accumu-
lated, at which point the full efficiencies stated above are attained.
Chemicals, if used, are computed at the rate of 150 mg/L of alum and
4 mg/L of flocculant aid based on Ref . 10.
Head losses will undoubtedly be high when operating at high rates such
as these. For 24 inches of granular media with an effective size of
1.0 millimeters, the head losses at 68°P computed by Rose's method as
given by Fair and Geyer (Ref. 4) are as follows:
Gpm/sq ft Head Loss, ft
5 0.89
10 1.97
20 4.58
These losses do not include losses in the underdrain system which could
be substantial. The head loss above varies approximately as the 1.18
power of the flow, and, on the basis of the above figures, it has been
assumed that the head loss through a clean filter would be 40 percent of
the maximum head at the design rate. At other rates of flow the head
loss through a clean -filter is given by the following equation :
"clean" ^/V * '4° Hm <20>
281
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The head loss due to filter clogging is assumed to vary directly with
the rate of flow and the solids accumulation:
Head loss due to clogging = -^— x - — x (.60 H ) (21)
gm Sqm m
where S = Integrated sum of the solids removed in each time-step (psf)
Sqm = Solids holding capacity of the filter
The total head loss is equal to the sum of the head loss clean and the
head loss due to clogging. When the total head with one unit out of
service reaches 90 percent of the maximum head, the backwashing cycle
is initiated and the filters are washed in rotation. This will allow
for some head build-up on the last filters to be washed.
The backwashing of each filter, including taking out of service and
placing back in service, is assumed to last one 10-minute time-step and
to require an average backwash flow of 15 gpm per square foot over the
10 minutes. The backwash water will be discharged by gravity or pumped
to a sanitary sewer or interceptor for transport to the sewage treatment
plant.
When the first filter washed is placed back in service, integration of
the solids accumulated on the filter begins anew. Efficiency of the
clean filter is assumed to be reduced 50 percent for the first time-step;
full efficiency is assumed for subsequent time-steps. The head loss on
the first filter washed is allowed to reach maximum head, HM, the second
time around before the washing cycle is again initiated, because each
of the other filters will have been in operation a shorter length of
time since they were cleaned.
282
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WARNING; Later information in regard to the laboratory tests in Ref. 10,
on which the program is based, indicates that the head loss was allowed
to build up to 15 psi in roost runs under which conditions the solids
removed from the wastes were so compacted into the filter media that
backwashing was time-consuming and difficult. It cannot be too strongly
emphasized that the filter performance contained in the model has not
been substantiated and remains purely speculative. There is no assurance
that the filters will not plug up and overflow at design rates if solids
concentrations are high. The model does not warn of or allow for this
situation. High rate filters should not be proposed without pretreatment
in Level 3. To do so is contrary to all experience with granular filters
in the waterworks field.
Effluent Screens (Treatment Option 52)
Effluent screens are included for aesthetic improvement of overflows
discharged at the shoreline or for treatment processes not including
fine screening or filtering processes. No significant improvement in
suspended solids or BOD can be computed for such installations.
Effluent screens were installed at the Rockaway high rate activated
sludge plant of New York City to eliminate all traces of visible sewage
solids which might pass through the plant and be discharged at the seawall.
In many cases the aesthetic and psychological benefits, admittedly dif-
ficult to estimate, could be well worth the cost, especially if the
installation of effluent screens made unnecessary the installation of
more costly equipment. They are included in the Treatment model so that
their cost can be estimated.
283
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It is assumed that screens would be of the waterworks travelling basket
type with 6-mesh wire. Two or more screens would be installed. They
would have a capacity of 450 gpm per square foot based on the design
flow. Assuming a maximum submerged area for each screen of 100 square
feet, the maximum capacity per unit would be 100 cfs.
The volume of screenings removed is estimated at 0.05 cubic feet per
million gallons. These would be removed by truck and disposed of in a
sanitary landfill or at the municipal incinerator.
Chlorination (Treatment Option 72)
Disinfection of storm and combined sewer overflows can be justified as
a public health measure to protect downstream water supplies, bathing
beaches, and other water uses. Chlorination is the most widely used
method of disinfection and is the only method included in the Treatment
model. While the decision whether or not to chlorinate will be based
entirely on the need for disinfection, the addition of chlorine will
result in an incidental reduction of BOD. Hence the Treatment model
computes the reduction in both BOD and.coliform organisms due to chlori-
nation. Chlorination has no effect on suspended solids removals. The
engineer must select the point of chlorine injection. Injection may be
ahead of the sedimentation tanks or the dissolved air flotation tanks,
which will serve as the chlorine contact tank if either sedimentation
or dissolved air flotation is used. Otherwise it will be necessary to
construct a chlorine contact tank. The volume of the tank is selected
to provide a 15-minute detention period at the design flow.
284
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It is assumed that the wastewater will be chlorinated to a residual.
This requires estimation of the chlorine demand. The chlorine demand
is estimated at 10 percent of the BOD content measured just ahead of
the point of application (this figure is available in the Treatment
model)/ but regardless of the value thus obtained/ the chlorine demand
is taken at not less than 6 ppm and not more than 25 ppm. The lower
figure is based on Symons1 work at Buffalo (Ref. 11) as reported by
Camp (Ref. 12). The upper figure is based on the standards of the New
York State Health Department for chlorination of primary effluents
(fief. 13). The number of chlorinators is equal to the chlorine demand
in pounds per day, divided by 2,000 if the total demand is less than
8,000. if the total demand is greater than 8,000, it is assumed that
chlorinators with a capacity of 8,000 pounds per day will be used, and
the number is estimated by dividing the total demand by 8,000. If a
chlorine contact tank is used the reduction of BOD is computed at 2.0
times the chlorine demand, in accordance with Ref. 14, but not more than
50 percent, if chlorine is applied ahead of sedimentation or dissolved
air flotation the reduction in BOD has already been computed in a slightly
different manner, but in a way that should yield comparable results.
Up to this point in the Treatment model there has been no discussion of
the coliform content of the wastewater. With the application of chlorine
for disinfection, however, the coliform content becomes of primary
importance.
The coliform content of the wastewater is supplied by the Transport
Model. . The coliform content at the point of application of the chlorine
285
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is assumed to be reduced by the removal of suspended solids by previous
treatment processes in accordance with the following formula:
SS at point of
Coliforms at _ col i forms in application
point of application influent SS at influent
to treatment units
The efficiency of chlorination is conservatively estimated to be 99.9
percent effective (Ref. 15). Coliform reductions are computed in sub-
routine KILL. If the detention period for chlorine contact in any time-
step is less than 15 minutes, the efficiency is multiplied by
detention period
15 minutes
SIZE OF DESIGN EVENT AND QUALITY OF TOTAL OVERFLOW
RELEASED .TO RECEIVING WATERS
At this time it is not possible to state what the size of the design event
should be. It will be less than the maximum possible storm runoff
because even the storm sewers are not designed for the maximum storm.
For the sake of economy, except where public health is a consideration,
it will probably be less than the runoff from a one-year storm. It may
be different for drainage basins of different size and different locality.
The ease with which the computer can compute results for events of
different size will make it possible to compute the economic costs and
benefits of varying design criteria. Experience with the program
eventually will develop a better idea of the optimum size of the design
event.
286
-------
In any case, if the storms in any typical year are run through the model
successively, the smaller storms will receive complete treatment,
whereas the larger storms will produce some bypassing of the treatment
units. In these cases the Treatment model will compute the content of
suspended solids, BOD, and coliform organisms in the combined discharge
to the receiving waters.
287
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PART 4
ECONOMIC DATA
-------
SECTION 16
COST-EFFECTIVENESS MODEL
Page
OBJECTIVE 291
BACKGROUND 291
THE MODEL SUBROUTINES 292
Subroutine TSTCST 292
Subroutine TRCOST 292
THEORETICAL DEVELOPMENT 293
Capital Costs 294
Operation and Maintenance Costs 295
Land Costs 295
BASIS FOR INDIVIDUAL TREATMENT COSTS 295
Capital Costs 295
Irreducible Costs 30!
Storm Event Costs 301
DEFAULT VALUES 302
DATA LIMITATION 302
TEST APPLICATIONS 304
289
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SECTION 16
COST-EFFECTIVENESS MODEL
OBJECTIVE
The objective of the Cost-Effectiveness model is to illustrate the
desirable size and type of treatment to be selected by providing:
1. Realistic costs of storage treatment for each storage option.
2. Realistic costs of treatment for each unit process.
The model is intended to provide guidance in the selection of the least
costly combination of treatment processes and storage treatment sizes
for varied storm patterns and locations.
BACKGROUND
The effectiveness of treatment is computed in terms of removal efficiencies
in the Treatment model and by the trace and the concentration histories
of the waste field in the Receiving Water Quality model.
The cost model will enable the user to obtain associated costs with:
1. Each level of efficiency selected.
2. The efficiencies required to satisfy water quality standards.
The associated costs can be minimized by variation of the treatment and
storage options selected. Automatic cost minimization, a desirable
feature, was not within the scope of this study.
291
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THE MODEL SUBROUTINES
The internal storage costs are calculated by subroutine TSTCST within
the internal storage model. Treatment costs and external storage costs
are calculated by subroutine TRCOST within the Treatment model.
The operation of TSTCST and the internal storage model is governed by
the Transport Block. The operation of TRCOST and the Treatment model
is governed by the Storage Block.
Subroutine TSTCST
Capital costs of hypothetical storage capacities are based on the maxi-
mum storage requirements.
The total cost is obtained from the fixed installation cost, and from
the variable cost of reservoir capacity and the required land. Unit
processes (see default values subsection) are used to compute storage
and land costs.
Subroutine TRCOST
Given a design flow (hence unit capacities), subroutine TRCOST determines
the capital cost for the selected options (shown in Table 16-1) in the
Treatment model. The cumulative operating costs are computed after
simulation on each unit.
The sequence of operations in -subroutine TRCOST is:
1. Read and summarize all unit costs and factors>utilized in
the computations.
2. Compute land and capital costs for each unit process selected
and convert to annual costs.
292
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Table 16-1. TREATMENT PROCESSES
Storage
Bar racks
Pumping stations (influent and effluent)
Sedimentation tanks
Fine screens
Microstrainers
Dissolved air flotation
High rate filters
Effluent screens
Chlorine contact tanks
3. Compute variable costs due to occurrence of storm events.
4. Present summary of all treatment costs.
Regional adjustments for the derived costs can be made by using the
ratio of the individual city ENR (Engineering News-Record) index to the
national average index. Also adjustments to future years may be made
using projected values of the appropriate index. A set of suggested
values for the years 1970 to 1980 is supplied (Volume III, Section 5).
These future indexes were derived from the postwar ENR construction in-
dexes .
THEORETICAL DEVELOPMENT
When feasible the computed costs are based on generalized .cost functions:
covering the range of treatment capacities (5 to 500 mgd).
293
-------
The cost functions derived from one of the following forms, depending
on the unit process selected:
Unit cost = aQb (1)
Unit cost = cQ (2)
log unit cost = a + b\og Q (3)
where Q = Design flow
a, b, c = Parameters to be derived
The preceding functions closely agree with the latest study on treatment
process costs (Ref. 1).
The cost data utilized were adjusted for both variation in time and geo-
graphical location of the construction by using the ENR cost indexes.
Where data were not sufficient to derive a function, the unit costs
were based on recent actual bid prices allowing for reduction in unit
costs of larger installations. Further details on the basis of the
individual treatment costs will follow.
The total treatment cost is based upon capital costs, operation and
maintenance costs, and the cost of land.
Capital Costs
The capital costs for each treatment process are calculated on the
basis of maximum installed capacity determined by the "design flow."
294
-------
The costs are converted to equivalent uniform annual costs using the
supplied interest rate and the effective life of the installation.
Operation and Maintenance Costs
In subroutine TRCOST operation and maintenance costs are divided into
two parts: (1) the costs resulting from the existence of the plant,
called irreducible costs, which are independent of the plant operation;
and (2) the costs associated with storms, called storm event costs,
which depend upon the quantity and quality of the influents.
Land Costs
The user of the program may have more accurate data in terms of availa-
bility and cost of local land. However, in the absence of such infor-
mation, a typical unit price is provided (see default values subsection)
Land costs are computed on the basis of the area required for each unit
process. These costs have also been converted to equivalent annual
costs using:
Annual cost = (L x i)/100 (4)
where L = Total land costs
i = Percentage interest rate
BASIS FOR INDIVIDUAL TREATMENT COSTS
Capital Costs
The basis for the cost of individual treatment processes are briefly
described below, followed by a presentation of the equations used
295
-------
(Table 16-2). Examples of the computed costs appear in the test
application subsection.
1. Storage
The storage cost is based on a unit cost for reservoir
construction allowing for the reduction of this cost for
larger installations.
2. Bar Racks
This cost is based on actual adjusted prices for screen units.
Installation costs modified from Smith (Ref. 2) include the
cost of screen chamber, overflow, bypass chamber, and Parshall
flume.
3. Pumping Stations
Capital costs of both influent and effluent pumping stations are
based on cost files (Metcalf & Eddy cost files developed for
internal use) which were obtained from actual construction costs.
4. Sedimentation Tanks
The computed cost of sedimentation tanks is based on similar
cost file data. The costs are derived for rectangular tanks
and can be adjusted to variable surface loading.
5. Fine Screens
The use of fine screens for sewage treatment in the United
States is at the experimental stage. For example, the
Stephan and Schaffer. paper (Ref. 3) does not include any plant
using fine screening.
296
-------
Table 16-2. TREATMENT COST SUMMARY
Option
Derived Capital Cost
Equation, Dollars
Applicable
Capacity
Range, mgd
Bar Racks
Supply:
1000(11
where n » Nvnnber of screens
S » screen capacity (cfs) -120,
with a minimum of zero
ENR « ENR index for prescribed year
(see Volume III)
F " Site factor (see Volume III)
All
Installs
i« MM -0.625 .ENR ._
10,000 Q (5557) P
1,780
where Q - Capacity (mgd)
£ 100
> 100
Inlet Pumping
50,000
32,000
32,000 Q (100)"& 100
Dissolved Air
Flotation
•t « n .«. r 2.3026 I/±±HL_)P
i.35 B exp L0.2075+0.0114 LogQJI1098 100
Fine Screens
12.000
All
Sedimentation
In new tanks
In storage
430
where R • Overflow rate (gpd/sq ft )
where U - Construction cost ($/cy)
V " Maximum storage during storm (cy)
< 100
>, 100
All
Micros trainers
30,000
20,000 Q(fgj)P
< 25
> 25
297
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Table 16-2. TREATMENT COST SUMMARY (Continued)
Option
Derived Capital Cost
Equation, Dollars
Applicable
Capacity
Range, mgd
High Rate Filters
54,000
All
Effluent Screens
Supply and
install:
Channel works:
5,000
200 g F
7,000 Q
1,246 Q
0.625.ENR
*1034'
< 100
£100
< 100
> 100
Outlet Pumping
(Same as Inlet Pumping)
Chlorine Contact
Tank & Equipment
18,350
16,000 Q
-------
Two types of designs are envisioned. The first is based on a
pilot plant installation at Seattle, Washington. The alternative
design would use an installation identical to the microstraining
process but with coarser screens. The capital costs derived
are based on the latter alternative because of the wider use of
such processes in Europe and the United States (two installations
at Chicago, one at Lebanon, Ohio, and one at Denver). The capital
cost of fine screens is directly comparable to microstrainers
after allowance is made for increased capacities due to consider-
ably larger open screen areas. A cost factor 6f 1/2 was used in
this study.
6. Dissolved Air Flotation
Dissolved air flotation is also a relatively new process, hence
it was felt that the most accurate basis for the derivation of
capital costs would be the actual bid prices for a 25-mgd facility
presently being constructed in San Francisco. The prices
were modified to allow for:
a. Reduction in capital costs due to inclusion of units which
were not an integral part of the process.
b. A 15 percent allowance for engineering and contingencies.
c. A 30 percent reduction in costs because of the difficult
urban location of the site and possible conservative design
capacity due to the untried nature of the treatment process.
d. Allowance was made for the variation in costs due to the
size of the installation.
299
-------
7. Microstrainers
Cost estimates for microstraining equipment were obtained
from several manufacturers. However, when these costs
(expressed per mgd of installed capacity) were compared to the
actual bid prices for the few existing treatment plants, sharp
variations in unit prices were obtained. Although available
equipment costs can be considered reliable, installation costs
per unit basis cannot. The primary reason for the inconsistency
can be attributed to the large variations in installed capacities
and uncertainty relative to the ultimate capacity of the
microstraining units. Hence the unit prices that were used allow
for larger design loading than is presently used and do not
represent the price for any single installation.
8. High Rate Filters
These costs are based on cost file data and cost functions
derived by Smith (Ref. 2). The costs are adjusted to allow
for high surface loading of the filters.
9. Effluent Screens
These costs are based on several manufacturers' bid prices plus
an allowance made for installation costs similar to bar rack
installations.
10. Contact Tanks
The costs of contact tanks are based on function derived by
Smith (Ref. 2). Separate costs of chlorinators are derived on
the basis of cost file data.
300
-------
Irreducible Costs
For all unit processes the irreducible costs are assumed to be a fixed
percentage of the initial capital investment. The amounts vary between
1 percent and 2 percent and depend upon the mechanical complexity of
the equipment. Irreducible costs are presented in Table 16-3.
Table 16-3. IRREDUCIBLE MAINTENANCE COSTS
Assumed Percentage of
Treatment Process Total Capital Investment Per Year
Bar screens 1%
Pumping station, influent 2
Dissolved air flotation 2
Fine screens 2
Sedimentation tanks 1
Microstrainers 2
High rate filters 2
Effluent screens 1.5
Pumping station, effluent 2
Chlorine contact tanks 2
Storm Event Costs
The storm event costs are derived based on a fixed cost assumed to be
associated with clean-up or check-up activity and a variable cost
depending on the volume of the influent processed. These costs are
summarized in Table 16-4.
301
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Table 16-4. STORM EVENT COSTS
Treatment Process
Assumed Variable
Cost
Assumed Fixed
Cost, $/storms
Bar racks
Pumping station
Dissolved air
flotation
Fine screens
Sedimentation tanks
Microstrainers
High rate filters
Effluent screens
Pumping station
Chlorine contact
tanks including
chlorinators
Based on the volume
of solids to be
disposed.
Based on 2
-------
Table 16- 5. DEFAULT VALUES FOR COST SUBROUTINES
Item Value Programmed
Interest rate 7%
Amortization period 25 years
Site factor 1-00
Unit cost land $20,000/acre
Unit cost power 2$/kwh
Unit cost chlorine 20
-------
TEST APPLICATIONS
Several runs selecting design flow, location, and actual storm patterns
were made. The results are summarized in Table 16-6. Costs per acre
of the tributary drainage basin, as well as total costs, are reported
for ease of comparison of alternate solutions.
304
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Table 16-6. SAMPLE TEST RUNS
Location Smithville, U.S.A.
Tributary area 500 acres
Design flow 25 mgd
Total volume of
influents processed 12 million gal.
CAPITAL COSTS ANNUAL COSTS
TREATMENT "LEVEL" "iNiTAL LAND" "TSSTAL LAND KlN'MATST
8AR RACKS ""I •.MISIK" ""im" "Hi7«7 55 " ""lW§ "
NO INLET PUMPING 2 0. 0. 0. 0 0
DISS AIR FLOAT -N 3 ISWiZ. 3581. 132976. 251 30993
BYPASS LEVEL " "ffiSTAL MSB Mlii'WlNf
BAR RACKS 1 9«7>7" "" J5CI7" "Tllj «T 915T"
NO INLET PUMIMNU 2 0. 0. 0 0. 0.
SfDIKENTATION 3 310310. 8815. 26C.I8 C17. 3103.
MICRGSIKAIUKKS d HSifcO. 11017. 29
-------
PART 5
ACKNOWLEDGMENTS, REFERENCES, PUBLICATIONS,
GLOSSARY AND ABBREVIATIONS, AND APPENDICES
-------
SECTION 17
ACKNOWLEDGMENTS
307
-------
SECTION 17
ACKNOWLEDGMENTS
The consortium is deeply indebted to the following persons and their
organizations for the services they rendered to the project group in the
development, demonstration, and verification of the EPA Storm Water
Management Model:
1. Mr. William A. Rosenkranz, Chief, and Mr. Darwin R. Wright,
Project Officer, of the Storm and Combined Sewer Pollution
Control Branch of the Environmental Protection Agency,
Washington, D.C., for their generous assistance and guidance.
2. Mr. Alan 0. Friedland, Chief, Mr. Harold C. Coffee, Jr., and
Mr. Robert T. Cockburn of the Division of Sanitary Engineering,
City of San Francisco, and Mr. T. G. Shea of Engineering-
Science , Inc., for furnishing data on the Baker and Selby
Street systems.
3. Dr. Louis M. Laushey and Dr. Herbert C. Preul of the Civil
Engineering Department of the University of Cincinnati and the
graduate student project group coordinated by Abdul S. Rashidi
for providing necessary data on the Bloody Run drainage basin,
Cincinnati, Ohio.
4. Mr. George A. Moorehead, Chief of Systems and Planning,
Department of Sanitary Engineering, District of Columbia, and
Mr. Michael S. Neijna of Roy F. Weston, Inc., for furnishing
data on the Kingman Lake study area.
5. Mr. Joseph V. Radziul, Chief, and Mr. William L. Greene of the
Research and Development Unit of the City of Philadelphia Water
309
-------
Department for furnishing data on the Wingohocking and Callowhill
study areas.
The consortium management and the project work of Metcalf & Eddy, inc.,
were under the direction of Mr. Dean F. Coburn, Senior Vice President,
and Mr. John A. Lager, Project Manager and Principal Investigator.
Other key personnel of Metcalf & Eddy, Inc., were Drs. Byrne Perry,
George Tchobanoglous, and E. John Finnemore, and Messrs. William G.
Smith, Dennis A. Sandretto, Charles D. Tonkin, and Ferdinand K. Chen.
Particular acknowledgment is given to Mr. Allen J. Burdoin, staff con-
sultant, for his worthy contributions to the theoretical development of
the surface quality and treatment models.
The project work of the Department of Environmental Engineering of the
University of Florida was directed by Dr. Edwin E. Pyatt, Chairman and
Principal Investigator, and Mr. Larry W. Russell, Senior Research
Assistant. Other key personnel for the University of Florida were
Drs. Wayne C. Huber and James F. Heaney, and Messrs. Ralph A. Aleman
and B. James Carter. Dr. John C. Schaake, Jr., consultant, provided
valuable assistance in the development of the Transport Model.
The project work of Water Resources Engineers, Inc., was directed by
Drs. Gerald T. Orlob, President, and Robert P. Shubinski, Principal
Engineer and Project Leader. Other key personnel for Water Resources
Engineers were Mr. Marvin R. Lindorf, Vice President, Drs. Ian King and
Carl W. Chen, and Mr. John R. Monser.
310
-------
SECTION 18
REFERENCES
311
-------
SECTION 18
REFERENCES
Model Overview (Section 3)
1. American Public Works Association, "Water Pollution Aspects of
Urban Runoff," January 1969, Federal Water Pollution Control
Administration Contract WP-20-15.
2. Sullivan, Richard H., "Assessment of Combined Sewer Problems,"
presented at the Seminar on Storm and Combined Sewer Overflows,
November 1969, Federal Water Quality Administration Laboratory,
Edison, New Jersey.
Surface Runoff Quantity Model (Section 5)
1. Rogers, R. A., "Rational - Rational Method of Storm Drainage Design,"
Journal of the Irrigation and Drainage, American Society of civil
Engineers, Vol. 94, No. IR4, December 1968, pp. 465-480.
2. Watkins, L. H. and Young, C. P.,"Developments in Urban Hydrology in
Great Britain," August 1964, Paper presented at the Conference on
Urban Hydrology Research, at Proctor Academy, New Hampshire.
3. Izzard, C. F., "Hydraulics of Runoff from Developed Surfaces,"
1946, Proc. Highway Research Board, Vol. 26, pp. 129-150.
4. Linsley, Jr., R. K., Kohler, M. A., and Paulhus, J. L. H., Applied
Hydrology, McGraw-Hill Book Company, Inc., New York, 1949.
5. Tholin, A. L. and Keifer, C. J., "Hydrology of Urban Runoff,"
Transactions, American Society of Civil Engineers, Paper No. 3061,
Vol. 125, 1960.
6. Crawford, N. H. and Linsley, R. K., "Digital Simulation in Hydrology,
Stanford Watershed Model IV," Technical Report No. 39, July 1966,
Department of Civil Engineering, Stanford University.
7. McCracken, D. D. and Dorn, W. S., Numerical Method and FORTRAN
Programming, John Wiley and Sons, Inc., New York, 1964.
8. American Society of Civil Engineers, Manual of Engineering Practice
No. 37, "Design and Construction of Sanitary and Storm Sewers,"
tWater Pollution Control Federation, Manual of Practice No. 9),
1960.
313
-------
9. Tucker, L. S., "Oakdale Gaging Installation, Chicago - Instrumenta-
tion and Data," Technical Memorandum No. 2, August 15, 1968,
American Society of Civil Engineers, Urban Water Resources Research
Program.
10. Tucker, L. S., "Northwood Gaging Installation, Baltimore - Instru-
mentation and Data," Technical Memorandum No. 1, August 1968,
American Society of Civil Engineers, Urban Water Resources Research
Program.
Dry Weather Flow Quantity Model (Section 6)
1. American Public Works Association, "Water Pollution Aspects of Urban
Runoff," January 1969, Federal Water Pollution Control Administration
Contract WP-20-15.
2. Linaweaver, F. P., "Final and Summary Report on the Residential
Water Use Research Project," July 1966, Johns Hopkins University,
Baltimore, Maryland.
3. Hittman Associates, Inc., "Main I, A System of Computerized Models
for Calculating and Evaluating Municipal Water Requirements -
Volume I," June 1968, OWRR Contract 14-01-001.
4. U. S. Department of Commerce, Bureau of the Census, Washington, D. C.,
"Water Use in Manufacturing, 1963 Census of Manufacturers," Prelim-
inary Report, Subject Series MC63(1)-10.
5. Linaweaver, F. P. and Geyer, J. C., "Commercial Water Use Project,"
Johns Hopkins University, Baltimore, Maryland.
6. Howe, C. W. and Linaweaver, F. P., "The Impact of Price on Residential
Water Demand and Its Relation to System Design and Price Structure,"
Water Resources Research, Vol. 3, No. 1, 1967.
Infiltration Model (Section 7)
1. Lentz, J. J., Estimation of Design Maximum Domestic Sewage Flow
Rates, Johns Hopkins University, Department of Sanitary Engineering
and Water Resources, Baltimore, Maryland, May 1963.
2. Brooks, R. H. and Corey, A. T., "Properties of Porous Media Affecting
Fluid Flow," Journal of the Irrigation and Drainage Division,
Proceedings of the American Society of Civil Engineers, Vol. 92,
No. 1R2, June 1966, pp. 61-88.
314
-------
3. Metcalf s Eddy, inc., "storm Water Problems and Control," Federal
Water Quality Administration, Program No. 11022EQG, May 1970.
4. U. S. Department of Commerce, Environmental Data Service, National
Weather Records Center, Asheville, North Carolina 28801, "Local
Climatological Data."
5. Santry, Jr., I. W. , "Infiltration in Sanitary Sewers," Journal of
the Water Pollution Control Federation, Vol. 36, No. 10, October
1964.
6. Geyer, J. C. and Lentz, J. J., "An Evaluation of the Problems of
Sanitary Sewer System Design, " Johns Hopkins University, Department
of Sanitary Engineering and Water Resources, Baltimore, Maryland,
1963.
7. American Society of Heating and Air Conditioning Engineers, "Heating,
Ventilating, Air Conditioning Guide," Annual Publication, 1956.
8. Linsley, Jr., R. K., Kohler, M. A., and Paulhus, J. L. H., Applied
Hydrology, McGraw-Hill Book Company, Inc.,. New York, 1949, p. 414.
Transport Model (Section 8)
1. Chow, V. T., Open-Channel Hydraulics, McGraw-Hill Book Company,
1959.
2. Henderson, F. M., Open Channel Flow, MacMillan, 1966.
3. Yevjevich, v., "Computed and Observed Unsteady Water-Surface
Profiles in a Circular Cross-Section," Paper presented at the
American Society of Civil Engineers Hydraulics Division, 16th
Annual Specialty Conference, August 1968.
4. Harris, G., "Development of a Computer Program to Route Runoff
in the Minneapolis-St. Paul Interceptor Sewers," University of
Minnesota, St. Anthony Falls Hydraulic Laboratory, Memorandum
No. M-121, December 1968.
5. American Society of Civil Engineers, Manual of Engineering
Practice No. 37, "Design and Construction of Sanitary and Storm
Sewers>" (Water Pollution Control Federation, Manual of Practice
No. 9), 1960.
6. Eagleson, P. S., "Unit Hydrograph Characteristics for Sewered
Areas," Proceedings of the American Society pf Civil Engineers,
Vol. 88, No. HY2, March 1962, pp. 1-25.
315
-------
7. Watkins, L. H. and Young, C. P., "Developments in Urban Hydrology
in Great Britain," August 1964, Paper presented at the Conference
on Urban Hydrology Research at Proctor Academy, New Hampshire.
8. Terstriep, M. L. and Stall, J. B., "Urban Runoff by Road Research
Laboratory Method," Proceedings of the American Society of Civil
Engineers, Vol. 95, No. HY6, November 1969, pp. 1809-1834.
9. O'Brien, G. G., Hyman, M. A., and Kaplan, S., "A Study of the
Numerical Solution of Partial Differential Equations," Journal
Math, and Physics, No. 29, 1951, pp. 223-251.
10. Streeter, V. L. and Wiley, E. B., Hydraulic Transients, McGraw-
Hill Book Company, 1967.
11. Ackers, P. and Harrison, A. J. M., "Attenuation of Flood Waves
in Part-Pull Pipes," Proceedings of the Institution of Civil
Engineers, Vol. 28, 6777, July 1964, pp. 361-381.
Storage Model (Section 9)
1. Riis-Carstensen, Erik, "Sewage Works, Improving the Efficiency of
Existing Interceptors," Sewage and Industrial Wastes, Vol. 27,
No. 10, October 1955.
2. Engineering-Science, Inc., "Characterization and Treatment of
Combined Sewer Overflows," City and County of San Francisco,
Department of Public Works, November 1967, Federal Water
Pollution Control Administration Grant WPC-112-01-66.
Receiving Water Quantity Model (Section 10)
1. Garrison, J. M., Granju, J. P., and Price, J. T., "Unsteady Flow
Simulation in Rivers and Reservoirs," Journal of the Hydraulics
Division, American Society of Civil Engineers, Vol. 95, No. HY5,
September 1969.
2. Neumann, G. and Pierson, Jr., W., Principles of Physical Oceanography,
Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1966.
3. Sverdrup, H. U., Johnson, M. W., and Fleming, R. H., The Oceans,
Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1942.
4. Water Resources Engineers, Inc., "A Water Quality Model of the
Sacramento-San Joaquin Delta," June 1965, report to the United
States Public Health Service, Division of Water Supply and
Pollution Control, Region Nine.
316
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5. Water Resources Engineers, Inc., "A Mathematical Model of Port
Phillip," 1968, report to Melbourne and Metropolitan Board of
Works, Melbourne, Australia.
6. Callaway, R. J., Byram, K. V., and Ditsworth, G. R., "Mathematical
Model of the Columbia River from Pacific Ocean to Bonneville Dam,
Part I," November 1969, Federal Water Pollution Control Administra-
tion, Northwest Region, Pacific Northwest Water Laboratory.
Surface Runoff Quality Model (Section 11)
1. Wiebel, S.R., Anderson, R. J., and Woodward, R. L., "Urban Land
Runoff as a Factor in Stream Pollution," Journal of the Water Pol-
lution Control Federation, Vol. 36, No. 7, July 1964.
2. American Public Works Association, "Water Pollution Aspects of Urban
Runoff," January 1969, Federal Water Pollution Control Administration
Contract WP-20-15.
3. Engineering-Science, Inc., "Characterization and Treatment of Com-
bined Sewer Overflows," City and County of San Francisco, Depart-
ment of Public Works, November 1967, Federal Water Pollution Control
Administration Grant WPC-112-01-66.
4. Fair, G. M. and Geyer, J. C., Water Supply and Wastewater Disposal,
John Wiley and Sons, Inc., New York, 1954, p. 398.
5. Tholin, A. L. and Kiefer, C. J., "Hydrology of Urban Runoff,"
Transactions, American Society of Civil Engineers, Paper No. 3061,
Vol. 125, 1960.
6. U. S. Department of Health, Education, and Welfare, U» S. Public
Health. Service, "Pollutional Effects of Stormwater and Overflows
from Combined Sewer Systems - A Preliminary Appraisal," November
1964.
7. Palmer, C. L., "The Pollutional Effects of Stormwater Overflows
from Combined Sewers," Sewage and Industrial Wastes, February 1950.
Dry Weather Flow Duality Model (Section 12)
1. Fair, G. M. and Geyer, J. C., Water Supply and Wastewater Disposal,
John Wiley and Sons, Inc., New York, 1954.
2. Haseltine, T. R., "Addition of Garbage to Sewage," Water and Sewage
Works, 1950.
317
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3. Watson, K. S., et al.,"The Contribution from the Individual Home
to the Sewer System," Journal of the Water Pollution Control
Federation, Vol. 39, No. 12, 1967, p. 2039.
4. Hubbell, J. W., "Commercial and Institutional Wastewater Loadings,"
Journal of the Water Pollution Control Federation, Vol. 34, No. 9,
1962, p. 962.
5. Rudolph, W., "Principles of Sewage Treatment," National Lime
Association, Washington, D.C., 1955.
6. Engineering-Science, Inc., "Characterization and Treatment of
Combined Sewer Overflows," City and County of San Francisco,
Department of Public Works, November 1967, Federal Water Pollution
Control Administration Grant WPC-112-01-66.
7. Gameson, A. L. H. and Davidson, R. N., "Storm-Water Investigations
at Northampton," Journal of the Institute of Sewage Purification,
1963, pp. 117-119.
Decay Model (Section 13)
1. Gustafsson, B. and Westberg, W., "Oxygen Consumption and Reaeration
in Sewers," Advances in Water Pollution Research, Proceedings from
the Second International Conference of Water Pollution Research,
Tokyo, Vol. 1, August 1964.
2. Velzy, C. R. and Sprague, J. M., "Infiltration Specifications and
Tests," Sewage and Industrial Wastes, Vol. 27, No. 3, March 1955.
3. Raths, C. H. and McCauley, R. F., "Deposition in a Sanitary Sewer,"
Water and Sewage Works, May 1962.
4. FMC Corporation, Central Engineering Laboratories, "Feasibility of
a Periodic Flushing System for Combined Sewer Cleansing," August
1967, Federal Water Pollution Control Administration Contract No.
14-12-19.
5. Hill, H. M., Srnvasan, V. S., and Unny, T. E., "Instability of Flat
Bed in Alluvial Channels," Journal of the Hydraulics Division,
American Society of Civil Engineers, September 1969.
6. Fair, G. M. and Geyer, J. C., Water Supply and Wastewater Disposal,
John Wiley and Sons, Inc., New York, 1954, p. 398.
7. Carstens, M. R., "A Theory for Heterogeneous Flow of Solids in
Pipes," Journal of the Hydraulics Division, American Society of
Civil Engineers, September 1969.
318
-------
8. American Public Works Association, "Water Pollution Aspects of
Urban Runoff," January 1969, Federal Water Pollution Control
Administration Contract WP-20-15.
9. Streeter, W. H. and Phelps, E. B., "A Study of the Pollution and
Natural Purification of the Ohio River," February 1925, Public
Health Bulletin No. 146.
10. Engineering-Science, Inc., "Characterization and Treatment of
Combined Sewer Overflows," City and County of San Francisco,
Department of Public Works, November 1967, Federal Water Pollution
Control Administration Grant WPC-112-01-66.
Receiving Water Quality Model (Section 14)
1. Water Resources Engineers, Inc., "A Water Quality Model of the
Sacramento-San Joaquin Delta," June 1965, report to the United
States Public Health Service, Division of Water Supply and
Pollution Control, Region Nine.
2. Water Resources Engineers, Inc., "A Mathematical Model of Port
Phillip," 1968, report to Melbourne and Metropolitan Board of
Works, Melbourne, Australia.
3. Callaway, R. J., Byram, K. V., and Ditsworth, G. R., "Mathematical
Model of the Columbia River from Pacific Ocean to Bonneville Dam,
Part I," November 1969, Federal Water Pollution Control Adminis-
tration, Northwest Region, Pacific Northwest Water Laboratory.
Treatment Model (Section 15)
1. American Society of Civil Engineers, Manual of Engineering Practice
No. 36, "Sewage Treatment Plant Design," (Water Pollution Control
Federation, Manual of Practice No. 8), 1959.
2. Mason, Donald G., "The Use of Screening/Dissolved Air Flotation for
Treating Combined Sewer Overflow," presented at the Seminar on
Storm and Combined Sewer Pollution Overflows, November 1969, Federal
Water Quality Administration Laboratory, Edison, New Jersey.
3. Metcalf & Eddy, Inc., American Sewerage Practice, 3rd ed., Vol. Ill,
McGraw-Hill Book Company, Inc., 1935.
4. Fair, G. M. and Geyer, J. C., Water Supply and Wastewater Disposal,
John Wiley and Sons, Inc., New York, 1954.
5. Klein, River Pollution, Vol. Ill, Butterworth, Inc., pp. 155-6.
319
-------
6. Bodien and Stenburg, "Microstraining Effectively Polishes Activated
Sludge Plant Effluent," Water and Wastes Engineering, September
1966.
7. Lynam, Ettelt, and McAloon, "Tertiary Treatment at Metro Chicago
by Means of Rapid Sand Filters and Microstrainers," Journal of the
Water Pollution Control Federation, February 1969.
8. Keilbaugh, Clover, and Yatsuk, "Microstraining - with Ozonation or
Chlorination - of Combined Sewer Overflows," presented at the
Seminar on Storm and Combined Sewer Pollution Overflows, November
1969, Federal Water Quality Administration Laboratory, Edison,
New Jersey.
9. Engineering-Science, Inc., "Characterization and Treatment of
Combined Sewer Overflows," City and County of San Francisco,
Department of Public Works, November 1967, Federal Water Pollution
Control Administration Grant WPC-112-01-66.
10. DeFilippi, John A., "Assessment of Alternative Methods for Control/
Treatment of Combined Sewer Overflows," presented at the Seminar
on Storm and Combined Sewer Overflows, November 1969, Federal
Water Quality Administration Laboratory, Edison, New Jersey.
11. Symons, Simpson, and Kin, "Variation in the Chlorine Demand of
Buffalo Sewage," Sewage Works Journal, March 1941.
12. Camp, Thomas R., "Chlorination of Mixed Sewage and Stormwater,"
and discussion, Journal Sanitary Engineering Division, American
Society of Civil Engineers, January 1961.
13. New York State, Department of Health, "Standards for Waste
Treatment Works," May 1965, Bulletin 1, Part I.
14. American Public Health Association, "Chlorination in Sewage
Treatment," 1933, report of Committee on Sewage Disposal.
15. Camp, Thomas R., Water and Its Impurities, Reinhold, 1963.
Cost-Effectiveness Model (Section 16)
1. Shah, Kanti L. and Reid, George W., "Techniques for Estimating
Construction Costs of Waste Treatment Plants," Journal of the
Water Pollution Control Federation, May 1970.
320
-------
2. Smith, Robert, "Cost of Conventional and Advanced Treatment of
Wastewater," Journal of the Water Pollution Control Federation,
September 1968.
3. Stephen, David G. and Schaffer, Robert B., "Wastewater Treatment
and Renovation Status of Process Development," Journal of the Water
Pollution Control Federation, March 1970.
321
-------
SECTION 19
PUBLICATIONS
323
-------
SECTION 19
PUBLICATIONS
Chen, C. W. and Shubinski, R. P., "Computer Simulation of Urban Storm
Water Runoff," Journal of Hydraulics Division, Proceedings of the
American Society of Civil Engineers, Vol. 97, No. HY2, February 1971,
pp. 289-301.
Lager, J. A., "A Simulation Technique for Assessing Storm and Combined
Sewer Systems," Combined Sewer Overflow Seminar Papers, Federal Water
Pollution Control Administration, DAST-37, November 1969, pp. 150-170.
Lager, J. A., Shubinski, R. P., and Russell, L. W., "Triumvirate Model
for Storm Water Management," presented at 43rd Annual Conference of the
Water Pollution Control Federation, October 1970, and has been accepted
for publication in the Journal of the Water Pollution Control Federation,
1971.
325
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SECTION 20
GLOSSARY AND ABBREVIATIONS
327
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SECTION 20
GLOSSARY
WATERSHED - The area which is drained by a river system.
DRAINAGE BASIN (STUDY AREA) - The area which contributes runoff to a
stream at a given point (an individual section of a watershed).
SUBCATCHMENT - A subdivision of a drainage basin (generally determined
by topography and pipe network configuration).
SUBAREA - A subdivision of a subcatchment (generally based upon a single
land use but may be identical to a subcatchment).
ABBREVIATIONS
APWA - American Public Works Association
ASCE - American Society of Civil Engineers
EPA - Environmental Protection Agency
MSB - Metcalf & Eddy, Inc.
UF - University of Florida
USPH - U.S. Public Health Service
WRE - Water Resources Engineers, Inc.
BOD - biochemical oxygen demand (5-day)
cf - cubic feet
cfs - cubic feet per second
COD - chemical oxygen demand
DO - dissolved oxygen
DWF - dry weather flow
fpm - feet per minute
329
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fps
ft
gal.
gal./capita/day
gpd
gph
gpm
gpm/sq ft
gpsf
hr
in.
in./hr
JCL
Ib
Ib/acre/day
Ib/acre/yr
Ib/capi ta/day
Ib/cf
Ib/day/cfs
Ib/ft
Ib/sec
mgd
mg/gram
mg/L
min
mm
feet per second
feet
gallons
gallons per capita per day
gallons per day
gallons per hour
gallons per minute
gallons per minute per square foot
gallons per square foot
hour
inches
inches per hour
job control language
pounds
pounds per acre per day
pounds per acre per year
pounds per capita per day
pounds per cubic foot
pounds per day per cubic feet per second
pounds per foot
pounds per second
million gallons per day
milligrams per gram
milligrams per liter
minutes
millimeters
330
-------
MPN
ppm
psf
psi
rpm
sec
sq ft
sq ft/min
SS
tons/mo
tons/sq mi/mo
VSS
yr
A
a
E
n
0
- most probable number
- parts per million
- pounds per square foot
- pounds per square inch
- revolutions per minute
- second
- square feet
- square feet per minute
- suspended solids
- tons per month
- tons per square mile per month
- volatile suspended solids
- year
SYMBOLS
delta
alpha
sigma
less than
greater than
partial differentiation
rho
psi
Pi
theta
331
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SECTION 21
APPENDICES
A. PRELIMINARY INFILTRATION ANALYSIS
B. DETAILED THEORETICAL DEVELOPMENT FOR DECAY MODEL
SEWER QUALITY ROUTING
General Equation for Continuity of Mass
Assumptions and Properties of the Various
Hydraulic Elements in the Transport Model
SEDIMENT UPTAKE AND DEPOSITION MODEL
Procedure for Suspended Solids
Definition of Variables
Hydraulic Radius (Function RADH)
333
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APPENDIX A
PRELIMINARY INFILTRATION ANALYSIS
It was originally thought that a generalized predictive equation for
infiltration could be developed. By incorporating both spatially and
time dependent variables, the generalized equation could then be applied
to predicting sewer infiltration in any urban area in the country for
any time of the year. The following summarizes the development of such
an equation and the reasons for reverting to the analysis described in
Section 7. (References cited are all in. Section 7 of References).
One reason that so little is known of the importance and effect of infil-
tration on sewer flow is the lack of actual flow measurements of infil-
tration. This lack of flow data posed a severe constraint on justifying,
developing, and verifying any theoretical or empirical Infiltration
Model. To overcome this constraint, minimum daily sewage flow data
recorded over a two-year period on the Johns Hopkins Residential Sewerage
Research Project (Ref. 1)* for seven areas throughout the country were
obtained. Because of the inclusion of foundation drains in at least
one of the seven areas and the possibility of some sewage flow, the data
give a slightly inflated estimate of infiltration.
Additional data were sought to supplement the above data since it has
been noted that infiltration has been shown (Refs. 6,5) to vary with
conditions of the sewer, level of groundwater, amount of precipitation,
and soil conditions. By obtaining appropriate sewer, soil, and
335
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precipitation information, a sufficient data base was established.
Categories and sources of information gathered are as follows:
1. Climatological data - U. S. Weather Bureau
2. Groundwater data - U. S. Geological Survey
3. Sewer system data - individual cities.
In addition, the following manufacturers of sewer pipe were contacted:
1. National Clay Pipe Institute
2. Cast Iron Research Association
3. Dickey Clay Mfg. Company
4. Portland Cement Association
5. American Concrete Pipe Association
6. Hamilton Kent Mfg. Company
7. K. T. Snyder Company, Inc.
8. American Pipe Services.
Multiple regression techniques were then applied to the data to describe
daily variation in the recorded minimum flows. Flow variance was initially
divided into that due to either location-dependent or time-dependent
variables with a separate analysis performed for each. Location-
dependent variables describing the seven study areas were correlated
with three-month average minimum flows using the following procedure:
1. Determination of the existence of regression using three-month
averages for the following study area data:
a. Number of service connections
b. Area
c. Distance between manholes
336
-------
d. Pipe diameter
e. Total pipe length
f. Pipe grade
g. Jointing material
h. Age
i. Pipe material
j. Water table head.
2. Elimination of variables accounting for the least amount of
variance.
3. Elimination of redundant variables.
4. Transformation of the remaining variables to obtain better
correlation and regression.
From the above data manipulations, total pipe length/ pipe diameter,
jointing compound, and water table height above the sewer accounted for
95 percent of the variance in minimum sewage flows. Water table height
was taken as an average and squared to increase correlation. Jointing
compounds were qualified by noting their relative susceptibility to root
penetration. Prom the amount of sewer clogging due to root penetration
in the seven study areas, relative factors for joints were established:
1. Cement mortar, 11.0
2. Lime mortar, 9.0
3. Bituminous hot pour, 3.5
4. Rubber gasket, 1.0.
337
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After receiving necessary climatological and geological information for
each of the seven study areas, analysis of variance was done on time-
dependent variables and minimum flows. Data manipulation over time was
as follows:
1. Determination of the existence of regression using the
following recorded data:
a. Rainfall
b. Groundwater level
c. Temperature
d. Relative humidity.
2. Elimination of variables accounting for the least amount of
variance.
3. Transformation of remaining variables to obtain better
correlation and regression as follows:
a. Use of time delays ranging from one to six days on rainfall
and water table data.
b. Use of power transformation on water table data.
c. Use of a precipitation index to indicate soil moisture
conditions.
From the above data manipulations, only rainfall significantly accounted
for minimum flow variation in each study area. Transformations on rain-
fall data using both a time delay depending on soil type and an antece-
dent precipitation index (Ref.8 ) were proposed and tested successfully.
Time delays were found by regressing rainfall from each of six previous
days on daily minimum sewage flows. From data from four of the seven
338
-------
study areas, rain falling on the indicated soil type and the indicated
number of days prior to minimum flow measurement correlated best as
follows:
1. Day 3 for sandy soil
2. Day 4 for rocky soil
3. Day 5 for clay soil.
Soil moisture was accounted for with the antecedent precipitation index
found by applying Eq. Al to prior daily rainfall.
API = b.P. + ... + b P + ... + b P (Al)
11 t t n n
where P = Amount of precipitation (in.) which occurred t days prior
to flow measurement
bt = Kfc with
K = 0.86 to 0.89 for eastern and central portions of country
0.76 for high precipitation portions of country
0.94 for low precipitation portions of country
Remaining variables from the above analyses were finally combined in an
overall regression analysis to form a predictive equation for infiltra-
tion that depends upon subarea characteristics and time. Eq. A2
accounted for 83 percent of the variation in the Johns Hopkins data and
exhibited significant regression at the 95 percent confidence level.
QINFIL = -20.64 + 15.41(API_) + 2.79 (DIAM) - 31.71(RNY) +
(A2)
0.64(CJOIT) + 0.25(LEN)
339
-------
where API = Antecedent precipitation index
DIAM = Diameter of largest subarea pipe (in.)
RNY = Rainfall Y days prior to infiltration estimate (in.),
Y = 3 for sandy soil, Y = 4 for rocky soil, and Y = 5
for clay soil
CJOIT = Joint factor
LEN = Total sewer length in each subarea (miles)
By showing significant regression, Eq. A2 satisfied the initial assump-
tion that infiltration could be modeled using information on the avail-
ability, movement, and entry of moisture into sewers. Availability of
moisture is included in the two-time dependent variables, API and RNY.
In addition, RNY introduces a time delay due to soil conditions affecting
movement of soil moisture. Although important in preliminary analyses,
water table height above the sewer was eliminated in the final regression
analysis for Eq. A2 because of very low correlation. The variables LEN,
CJOIT, and DIAM control moisture's ability to enter sewer pipe. Results
of testing the preliminary infiltration equation on three subareas
studied by M&E were extremely helpful in testing the equation. Specific
results from the comparison (see, for example, Figure A-l of the Glen
Street subarea, Berkeley, California) were that the preliminary predic-
tions consistently exceeded corresponding measurements on an average of
80 gpm (0.18 cfs) and failed to account for abrupt flow changes. To
account for these discrepancies, additional developments led to the
approach described in Section 7.
340
-------
1*0 r-
:
-40 *—
Predicted
Source: Metcalf & Eddy, Inc., "Storm Water Problems and Control," (Ref.
Figure A-l. COMPARISON OF PREDICTED AND MEASURED INFILTRATION FLOWS M&E STUDY,
GLEN STREET (BERKELEY, CALIFORNIA) SUBAREA
-------
APPENDIX B
DETAILED THEORETICAL DEVELOPMENT FOR DECAY MODEL
SEWER QUALITY ROUTING
General Equation for Continuity of Mass
Pounds in
element at
new time-step
Pounds in
element at
old time-step
Pounds
entering
Pounds
leaving —
Pounds Pounds entering or
decayed or +_ leaving from
generated source or sink
Notation for Eq. Bl
C = Cone, in element (Ib/cf) D
V = Volume in element (cf) D ••
n = Time-step S ••
A = Cross-sectional area (sq ft) At =
L = Length of conduit (ft) WELL =
SURGE = Volume stored during
surcharging (cf)
Expanding Eq. Bl with the above notation yields:
(Bl)
Decay rate
Growth rate
Maximum growth
Time increment
Volume stored in lift
station wet well
(CV)
-------
By assuming complete mixing
(C ) . = C . and (C . ) = C (B3)
out n+1 n+1 out n n
and substituting Eq. B3 into Eq. B2 and collecting terms,
n+1 n+1 2 12 22
] •
E(V ) V V 1
/ 2HL.D. _ At D -£ - At D -2- +
n 2 12 221
(C. V. ) + (C. V. ) .. V + V ..
in in n in in n+1 . n n+1
-+ At D S
Since
t out+1 At
Multiplying by 2/At Eq. B4 then becomes:
Cn+lVl (2/At + Dl + V
Solving for C yields:
n+J.
Cn+l ' Cn VAt- (D1+ D2» - «Wn+ (Cin«in>n
D2 S(Vn + VlH/IV^Sl + (°1 + V
344
(B4)
(V ) (V )
out n+1 . , , out n _ . . . _.
(B5)
[5
L r
|Vn (2/At - Dx - D2) - (Qout)nJ + (B6)
-------
Eq. B7 becomes Eq. B8 by the following notation:
n = Old time-step, 1
n+1 = New time-step, 2
j = Upstream point, 1, of element M
j+1 = Downstream point, 2, of element M
VOLl = Mixing volume, Vfi
VOL2 = Mixing volume, ^n+^
DT = At
CPOLL = C
CPOLL(M,2,1) = Concentration of a given pollutant in element M,
downstream and at the old time-step
CPOLL(M,2,2) = |cPOLL(M, 2,1)
D (S) (VOLl + VOL2) + CPOLL (M,1,1)Q(M, 1,1) +
CPOLL(M,l,2)Q(M,l,2)J/rVOL2(jJ-+ ^
,2,2)1
(B8)
+ D ) +
Q(M
Assumptions and Properties of the Various Hydraulic Elements in the
Transport Model
1. Conduits: L = length, A = area
(A. _ + A.!,, _)
VOLl = L
345
-------
2. Manholes and Flow Dividers
VOL1 = SURGEIW
VOL2 = SURGE2 (M)
3. Lift Stations
VOL1 = WELLl(M)
VOL2 = WELL2 (M)
4. Storage Units
Quality routing is accomplished according to the procedure given
in the Storage Model.
SEDIMENT UPTAKE AND DEPOSITION MODEL
The objective is to determine for each conduit in a general sewer system
the quantity of sediment uptake and deposition under DWF and/or storm
conditions. Given input pollutographs for suspended solids and DWF/ for
each time increment DT, let the average velocity of flow, V, needed
to transport particles of diameter d in a sewer element, M, be
defined as:
V - Rd (B9)
where N = Manning's N for roughness
R = Hydraulic radius
d = Particle diameter
k = Shields' magnitude of sediment characteristic
ss ~ Specific gravity of particle
346
-------
Using Manning's formula for V we have
R2/3 (S-) (BIO)
in which N = Manning's N for roughness
R = Hydraulic radius
S1 = Slope of invert of pipe (hydraulic energy line)
Setting Eqs. B9 and BIO equal and solving for d, then
RS1
k (Ss - 1)
(BID
The above procedure is used to solve for the particle diameter, d,
corresponding to the velocity in the sewer conduit. For example/ given
the velocity (V) at any element in the sewer system for a specific time
increment (DT), there is a critical particle diameter (CRITD) related to
sediment uptake and a CRITD for deposition.
For sediment uptake, Case 1, that portion of sewer bed load that has a
particle diameter (PD) equal to or greater than the critical particle
diameter (PD >^ CRITD) will remain at the bottom of the sewer. All
particles with PD < CRITD will be transported. When dealing with
deposition, Case 2, particles with PD >^ CRITD will settle to the bottom
of the sewer element while particles with PD < CRITD will be transported
down the element.
A sieve analysis curve is used to describe sediment characteristics with-
in a sewer. This curve was developed from data obtained in the APWA
347
-------
report (Ref. 8, Section 13). The data were averaged to represent a
typical sieve analysis curve for sewer sediment. The curve now being
used in QUAL is shown in Figure B-l. Three straight lines are used to
approximate the plot. However, if actual sieve analyses of sewer sedi-
ment are taken, this information should be used to replace the present
curve. Also, an updating of the curve for Case 1 and Case 2 should be
considered along with a more detailed breakdown on suspended solids.
Eq. Bll is used to determine CRITD. From the information available on
sewer sediment, an average S of 2.7 is assumed. Shields' value for
k is taken to equal .056 and the values for S are obtained from the
Transport Model. The procedure used in calculating R is presented in
function RADH, the last section in this appendix.
Procedure for Suspended Solids
Step 1. Calculate average velocity in each conduit. This is general
information since V is not used in Eq. Bll.
Step 2. Calculate hydraulic radius as shown in function RADH.
Step 3. Determine CRITD for Case 1 and CRITD for Case 2 using Eq. Bll.
Step 4. Determine PCT1 and PCT2 using the equations representing
Figure B-l.
Step 5. Use the following equations to determine sediment uptake and
deposition:
SCOUR(M) = SCOUR(M) + PCT2(TOTAL1 + TOTAL2 + TOTAL3) (DT) (B12)
348
-------
H
U
0.80-
0.60-
A PCT(1,2) = -1.2471(CRITD)
+ 1.00 0 <_ CRITD £ .59
B PCT(1,2) = -0.1501 (CRITD
+ 0.3527 .59 < CRITD '_
2.0
C PCT(1,2) = -0.00656(CRITD)
+ 0.0656 2.0 < CD < 10.0
0.40-
0.20-
0.00
0.0
10.0
PARTICLE DIAMETER (MM), CRITD
Figure B-l. SIEVE ANALYSIS PLOT FOR SEWER SEDIMENT
CPOLL(M,1,2,2)
[(1 - PCT2) (TOTAL1 + TOTAL2 +
TOTALS)[/QI(M) + (1-PCTl) SCOUR(M)/VOL2
SCOUR(M)
(PCT1) SCOUR(M)
(B13)
(B14)
Step 6. Use Eq. B2 for routing pollutant.
Definition of Variables
SCOUR (M)
CPOLL(M,N,O,IP)
PCT1, PCT2
DT
TOTAL1
f settled sediment in sewer element M (Ib)
= Concentration of pollutant IP at sewer element M
(lb/cf)
= Fraction of sediment with diameter greater than or
equal to CRITD
= Time increment
= Sum of all pollutant flow rates from sewer elements
immediately upstream (Ib/sec)
349
-------
TOTAL2,TOT"\L3 = Pollutant flow rate of incoming DWF and runoff,
respectively (Ib/sec)
QI(M) = Input flow rate at element M (cfs)
VOL2 = Current volume of wastewater within each element
(cf).
M = Sewer element number
N = For inlet end of sewer element (=1), for outlet end
(=2)
0 = Previous time-step (=1) or this time-step (=2)
IP = Pollutants: BOD(=1), SS(=2), COLIFORM(=3) and DO(=4)
Hydraulic Radius (Function RADH)
The objective is to compute the hydraulic radius of a given area of flow
in a conduit. Let the hydraulic radius of a conduit be defined as:
i • j- Area of flow ,„,,-,
Hydraulic radius = ———; :—-— (B15)
J wetted perimeter
Examples of the procedure used in calculating the hydraulic radius of a
circular conduit and a rectangular conduit are given in Figures B-2 and
B-3. Similar procedures are used for a modified basket handle, rectang-
ular conduit with triangular bottom and rectangular conduit with round
bottom. All other conduit shapes are found by calculating an equivalent
circular diameter and using the procedure given in Figure B-2.
350
-------
where AA
D
r
d
1
s
RADH
AA
= Area of flow
= Conduit diameter
= D/2
= Depth of flow
= Wetted perimeter
= Hydraulic radius
1) For conduit flows less than half full:
= r - d.
a)
b) ^
c) 0/2 = tan
d) s = r0
- d.
-1
2) For conduit flowing over half full:
a) d2 = d1 - r
b),c) Same as in 1
d) s = 2llr - r0
= r(2ll - 0)
3) For conduit flowing half full:
s = Ilr
4) After wetted perimeter has been calculated, RADH = AA/s, Eq. B15.
Figure B-2. CIRCULAR CHANNEL SECTION
351
-------
-AA
where AA
d
L,
1)
2)
s
s
RADH
Area of flow
Conduit height
Conduit width
Depth of flow
Wetted perimeter
' Ll+2dl
= AA/S, Eq. B15.
Figure B-3. RECTANGULAR CHANNEL SECTION
. GOVERNMENT PRINTING OFFICE: 1972 484-485/207 1-3
352
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1
5
Accession Number
2
s
Organization
Metcalf & Eddy
ibjet-l Fir
013B
, Inc.,
Id & Group
Palo
SELECTED WATER RESOURCES ABSTRACTS
INPUT TRANSACTION FORM
Alto, California
Water Resources Engineers, Inc., Walnut Creek, California
Title
STORM WATER MANAGEMENT MODEL
10
Authors)
Lager, John A.,
Pyatt, Edwin E., and
Shubinski, Robert P.
16
21
Project Designation
EPA Contract Nos. 14-12-501, 502, 503
Note
Set of four volumes: Volume I - Final Report,
Volume II - Verification and Testing, Volume III
User's Manual, Volume IV - Program Listing
Citation
23
Descriptors (Starred First)
Water Quality Control*, Computer Model*, Storm Water*, Simulation Analysis, Rainfall-
Runoff Relationships, Sewerage, Storage, Waste Water Treatment, Cost Benefit Analysis
25
Identifiers (Starred First)
Combined Sewer Overflows*, Urban Runoff
27
Abstract
A comprehensive mathematical model, capable of representing urban storm water runoff,
has been developed to assist administrators and engineers in the planning, evaluation,
and management of overflow abatement alternatives. Hydrographs and pollutographs
(time varying quality concentrations or mass values) were generated for real storm
events and systems from points of origin in real time sequence to points of disposal
(including travel in receiving waters) with user options for intermediate storage
and/or treatment facilities. Both combined and separate sewerage systems may be
evaluated. Internal cost routines and receiving water quality output assisted in
direct cost-benefit analysis of alternate programs of water quality enhancement.
Demonstration and verification runs on selected catchments, varying in size from
180 to 5,400 acres, in four U.S. cities (approximately 20 storm events, total) were
used to test and debug the model. The amount of pollutants released varied
significantly with the real time occurrence, runoff intensity duration, pre-storm
history, land use, and maintenance. Storage-treatment combinations offered best
cost-effectiveness ratios. A user's manual and complete program listing were prepared.
"Abstractor
John A. Laqer
Institution
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Continued from inside front cover.,
11022 -
11023 -
11020 -
11023 -
- 08/67
- 09/67
-- 12/67
- 05/68
11031 08/68
11030 DNS 01/69
11020 DIH 06/69
11020 DES 06/69
H020 06/69
11020 EXV 07/69
11020 DIG 08/69
11023 DPI 08/69
11020 DGZ 10/69
11020 EKO 10/69
11020 10/69
11024 FKN 11/69
11020 DWF 12/69
11000 01/70
11020 FKI 01/70
11024 DOK 02/70
11023 FDD 03/70
11024 DMS 05/70
11023 EVO 06/70
11024 06/70
11034 FKL 07/70
11022 DMU 07/70
11024 EJC 07/70
11020 08/70
11022 DMU 08/70
11023 08/70
11023 FIX 08/70
11024 EXF 08/70
Phase I - Feasibility of a Periodic Flushing System for
Combined Sewer Cleaning
Demonstrate Feasibility of the Use of Ultrasonic Filtration
in Treating the Overflows from Combined and/or Storm Sewers
Problems of Combined Sewer Facilities and Overflows, 1967
(WP-20-11)
Feasibility of a Stabilization-Retention Basin in Lake Erie
at Cleveland, Ohio
The Beneficial Use of Storm Water
Water Pollution Aspects of Urban Runoff, (WP-20-15)
Improved Sealants for Infiltration Control, (WP-20-18)
Selected Urban Storm Water Runoff Abstracts, (WP-20-21)
Sewer Infiltration Reduction by Zone Pumping, (DAST-9)
Strainer/Filter Treatment of Combined Sewer Overflows,
(WP-20-16)
Polymers for Sewer Flow Control, (WP-20-22)
Rapid-Flow Filter for Sewer Overflows
Design of a Combined Sewer Fluidic Regulator, (DAST-13)
Combined Sewer Separation Using Pressure Sewers, (ORD-4)
Crazed Resin Filtration of Combined Sewer Overflows, (DAST-4)
Stream Pollution and Abatement from Combined Sewer Overflows •
Bucyrus, Ohio, (DAST-32)
Control of Pollution by Underwater Storage
Storm and Combined Sewer Demonstration Projects -
January 1970
Dissolved Air Flotation Treatment of Combined Sewer
Overflows, (WP-20-17)
Proposed Combined Sewer Control by Electrode Potential
Rotary Vibratory Fine Screening of Combined Sewer Overflows,
(DAST-5)
Engineering Investigation of Sewer Overflow Problem -
Roanoke, Virginia
Micros training and Disinfection of Combined Sewer Overflows
Combined Sewer Overflow Abatement Technology
Storm Water Pollution from Urban Land Activity
Combined Sewer Regulator Overflow Facilities
Selected Urban Storm Water Abstracts, July 1968 -
June 1970
Combined Sewer Overflow Seminar Papers
Combined Sewer Regulation and Management - A Manual of
Practice
Retention Basin Control of Combined Sewer Overflows
Conceptual Engineering Report - Kingman Lake Project
Combined Sewer Overflow Abatement Alternatives -
Washington, B.C.
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