United States
Environmental Protection
Agency
Municipal Environmental Research
Laboratory
Cincinnati OH 45268
Research and Development
EPA-600/S2-84-020 Mar. 1984
<>ERA Project Summary
Procedures for Estimating
Dry Weather Sewage In-Line
Pollutant Deposition
Phase II
William C. Pisano and Celso S. Queiroz
.\»
Planners, engineers, and municipal
managers are given generalized
procedures/equations to estimate the
amount of pollutants deposited in
combined sewer systems during dry
weather so they can make intelligent
decisions about sewer flushing
programs and other combined sewer
management controls.
The predictive equations relate the
total daily mass of accumulated
pollutants deposited within a collection
system to the physical characteristics
of collection systems such as per capita
waste rate, service area, total pipe
length, average pipe slope, average
diameter, and other more complicated
parameters that derive from analysis of
pipe slope characteristics. Several
other predictive equations that can be
used with different available data and
user resources are given. Pollutant
parameters include suspended solids,
volatile suspended solids, biochemical
oxygen demand, chemical oxygen
demand, total organic nitrogen, and
total phosphorous.
The equations were developed from
data assembled from three major
sewage systems in eastern Massachu-
setts and from a portion of the
combined sewer system in the eastern
district of Cleveland. This study was an
extension of earlier work; broader data
was used here to prepare the predictive
relationships.
This Project Summary was developed
by EPA's Municipal Environmental
Research Laboratory, Cincinnati, OH,
to announce key findings of the
research project that is fully
documented in a separate report of the
same title (see Project Report ordering
information at back).
Summary of Results
Results using the augmented data base
are summarized. Various predictive
models are described, relating total
suspended solids deposition within a
collection system with independent
variables under the assumption of clean
pipe conditions. These relationships
therefore apply to situations in which the
sewer piping system is properly
maintained.
Statistical Summary of
Regression Data
In Table 1 are found the means and
standard deviations of the independent
variables used in this regression analysis.
L, A, and D measurements for the
augmented data base increased over
those of the prior data base. By including
data from the relatively flat Cleveland
collection systems, the average slope
parameters (§, SPD, and SPD/4) all
decreased.
The average collection-system
deposition rate computed over all four per
capita waste discharge levels (260, 190,
110, 40 gpcd, respectively) is 1.94
Ib/day/acre of service area. The average
and standard deviation of the rates
computed for a per capita waste rate of
260 gpcd are 1.07 and 1.64 Ib/day/acre
of service area, respectively. The average
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Table 1. Means and Standard Deviations of the Independent Variables Used in the Regression
A* fit
Variable}.
L(ft)
A (acre)
S(ft/ft)
5 (in.)
SPD (ft/ft)
SpD,4 (ft/ ft)
Mean
13702.
76.
0.0210
11.5
0.0101
0.0037
Standard
Deviation
22867.
102.
00126
2.0
0.0093
0.0033
Mean
14720.
106.9
0.0166
16.9
0.0067
0.0034
Standard
Deviation
20044.
110.8
0.0130
6.1
0.0072
0.0029
*A = the prior data base, i.e., 75 collection systems from the three major sewerage systems in
eastern Massachusetts;
ffi = all data, the augmented data base, i.e., the previous 75 plus 28 collection systems located
within the eastern district of Cleveland combined sewer system;
Ji = total length of all pipe in the sewer shed, in ft;
A = the collection system area, in acres;
B - average diameter of pipe in the collection system, in in.,
S = the average collection-system pipe slope, in ft/ft;
S PD = t he slope corresponding toPLD, in ft/ft (PL D= the percentage of pipe length corresponding to
where 80 percent of the solids deposit in the collection system);
Spo/4 = the slope corresponding to PL 0/4 .in ft/ft (PL D,t = one-fourth of the percentage of pipe length
where 80 percent of the solids deposit).
deposition rates for per capita waste rates
of 190, 110, and 40 gpcd are 1.35, 1.91,
and 3.42 Ib/day/acre of service area,
respectively.
Alternative Equation Selections
Two regression equations are present-
ed and recommended for user applica-
tion; the alternative forms reflect the
availability of data, or user resources, or
both. The simple form requires few data
and has the least predictive reliability;
whereas the more elaborate equation,
requiring greater user resources and data
availability, provides estimates with
extremely high reliability.
The Elaborate Equation
The highest multiple correlation coeffi-
cient, R = 0.970 (variance explained, R2 =
0.940) was obtained using this equation:
TS = 0.00108
<; -0.148 n-0
SPD/4 1
PD
where:
TS = deposited solids loading in Ib/day
q = per capita waste rate, in gpcd
The value PLD (the percentage of pipe
length corresponding to 80% of the loads
depositing in the collection system) is
derived from the extensive computer
analyses. A discussion involving
estimation of SPD and SPD/4are contained
in USEPA report numbers EPA-600/2-
77-120 (NTIS No. PB 270 695) and EPA-
600/2-79-133 (NTIS No. PB 80-118-
524), respectively. The probability of the
pipe slopes can either be derived from
histograms computed from local pipe
slope data, or it can be defined with
reasonable approximation from the mean
pipe slope, S only. If the pipe slopes are
not available, a regression relationship of
mean ground slope and mean pipe slope
can be used to estimate mean pipe slope.
The Simple Equation
The highest R2 value that can be
obtained with the least number of
independent variables is given by the
relatively simple regression equation:
TS = 0.0088 L1-066 (S)-°-433 q-o.539 (R2
=0.880)
The exponents of the independent
variables and the multiplicative constant
of the equation changed only slightly in
comparison with the equation derived
from eastern Massachusetts collection
system data. The degree of fit is high
(R2=0.0880) and superior to that of the
prior fit for eastern Massachusetts data
(R2=0.845).
Estimation of Total Pipe Length
The total pipe length of the system, L,
and its corresponding collection area. A,
are generally assumed to be known. In
cases where this information is not
known and where crude estimates will
suffice, the total pipe length can be
estimated from the total basin area, using
the expressions: A
L = 220.9 A"-84? (R2=0.804) - low popula- \
tion density (10-20 people/acre)
L = 238.0 A°-8*7 (R2=0.804) - moderate-
high population density (30-60 people/
acre)
These equations were developed from a
least squares analysis of the augmented
data base.
Estimation of Pipe Slope
If data on pipe slope are not available,
an approximate estimate of average
collection-system pipe slope can be
obtained by computing a mean value for
the ground slope and then using this
equation:
§ = 0.320 (§G)0-79° (R2=0.850,
where:
SG = mean ground slope, in ft/ft.
The above equation resulted from a
regression of mean ground and mean
pipe slope for all 103 collection systems.
The procedure used in estimating ground
slope data for the Cleveland collection
systems was similar to the method used *
in the earlier study of eastern Massachu- \
setts collection systems and is included in
the project report.
Discussion of Prior and
New Results
Table 2 presents an overview of the
predictive equations prepared from the
original and the new combined data set
appended to the original data. The R2 for
the two elaborate equations are very
similar. All three collection-system slope
parameters (S, S PD and SPD/4) entered the
regression equation at a high
significance level (Student's t values
exceeding 4.0) for the combined data set;
whereas, only S PD and SPD/4 entered the
elaborate equation for the original set.
This ifference is due, in part, to the limited
range qf_average collection-system pipe
slopes, S, for the three sewerage systems
comprising the original data set. The
range of the average pipe slopes
computed for the collection systems
within each of the three sewerage
systems in eastern Massachusetts was
from 0.0175 to 0.0254 and for the 28
systems in Cleveland, 0.0028 to 0.0178.
The inclusion of flatter pipe slope data
from the Cleveland sewerage system
increased the overall range of average^
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collection system variable, S, by an order
of magnitude. The_ average collection-
system pipe slope, S, for the combined set
of data assumed a more dominant role as
an explanatory variable in describing the
variance of estimated deposition solids
loadings per collection system. A visual
scanning of the average collection-
system pipe slope for the entire data set,
revealed a fairly reasonable spread of
observations along the entire range,
thereby minimizing the concern of
spurious correlation created by data
clustering at opposite ends of the range.
The results for the simple equations
shown in Table 2 are similar and confirm
the above discussion in that the R2 is 4.5
percent higher for the combined data set.
As a side note, the original equations
(derived from eastern Massachusetts
data) were used to estimate daily deposits
for the 28 Cleveland collection systems.
The resulting R2 values for the Cleveland
data, using the equations generated from
eastern Massachusetts data, are 0.717
and 0.811 for the elaborate and simple
equations, respectively. The modified
equations (derived for the combined data
set) were then used to estimate daily
deposits for the 75 eastern Massachu-
setts collection systems. The R2 values for
the eastern Massachusetts data, using
the equations generated from the
combined data base, are 0.821 and 0.867
for elaborate and simple equations,
respectively. In these numerical
sensitivity experiments, note that the
degree of fits was superior, in a predictive
sense, for the simple equations in
comparison with those of the elaborate.
The more favorable R2 results for the
simple equations suggest that the
elaborate equations are too specific and
sensitive to changes in data input. In
addition, the simple equations require
comparatively little input data compared
with that needed for the elaborate. The
user needs only prepare estimates of the
total collection-system pipe length, L; the
average collection-system pipe slope, S;
and an estimate of the per capita waste
rate, q, to use the simple equations.
The simple equations are therefore
preferred. Since the exponents of the
independent variables and the
multiplicative constant of the simple
equation for eastern Massachusetts
differ only slightly from those of the
combined (eastern Massachusetts and
Cleveland) data, the equation derived
from the combined data, based on a
broader base, is recommended.
The full report was submitted in partial
fulfillment of Grant No. R-804578 by
Table 2.
Equation
Elaborate
Elaborate
Simple
Simple
Comparison of Deposition Predictive Equations
Data Source ft2 Explanatory Variables
E. Mass.
Combined
E. Mass.
Combined
.949
.940
.845
.880
L, Spg, SpD/4,
L, SPQ. SpD/4,
L. S, q
L'S.q
q
S.q
Northeastern University and Environ-
mental Design and Planning, Inc., under
the sponsorship of the U.S. Environment-
al Protection Agency.
William C. Pisano and Celso S. Queiroz are with Environmental Design &
Planning, Inc., Boston, MA 02134.
Richard Field is the EPA Project Officer (see below).
The complete report, entitled "Procedures for Estimating Dry Weather Sewage
In-Line Pollutant Deposition: Phase II," (Order No. PB 84-141 480; Cost:
$8.50, subject to change) will be available only from:
National Technical Information Service
5285 Port Royal Road
Springfield, VA 22161
Telephone: 703-487-4650
The EPA Project Officer can be contacted at:
Municipal Environmental Research Laboratory
U.S. Environmental Protection Agency
Cincinnati, OH 45268
«US GOVERNMENT PRINTING OFFICE 1984-759-015/7320
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